THERMODYNAMICS 
 
 OF THE 
 
 STEAM-ENGINE 
 
 AND 
 
 OTHER HEAT-ENGINES 
 
 BY 
 
 CECIL H. PEABODY 
 
 PROFESSOR OF NAVAL ARCHITECTURE AND MARINE ENGINEERING, 
 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 
 
 FIFTH EDITION, REWRITTEN 
 
 FIRST THOUSAND 
 
 NEW YORK 
 
 JOHN WILEY & SONS 
 
 London : CHAPMAN & HALL, Limited 
 1907 
 
< 
 
 < 
 
 -S"' 
 
 I UiSHhHY of CONGRESS 
 Two Cooles Received 
 
 OCT 18 »9or 
 
 Copyngh! Entry 
 
 CUsIa XXc.,N6. 
 
 COPY B 
 
 Copyright 1889, 1898, 1907 
 
 BY 
 
 CECIL H. PEABODY 
 
 y^^Jf// 
 
PREFACE TO FIFTH EDITION. 
 
 When this work was first in preparation the author had before 
 liim the problem of teaching thermodynamics so that students in 
 engineering could use the results immediately in connection with 
 experiments in the Engineering Laboratories of the Massachu- 
 setts Institute of Technology. The acceptance of the book by 
 teachers of engineering appears to justify its general plan, which 
 will be adhered to now that the development of engineering calls 
 for a complete revision. 
 
 The author is still of the opinion that the general mathematical 
 presentation due to Clausius and Kelvin is most satisfactory and 
 carries with it the ability to read current thermodynamic inves- 
 tigations by engineers and physicists. At the same time it is 
 recognized that recent investigations of superheated steam are 
 presented in such a way as to narrow the applications of the 
 general method so that there is justification for those who prefer 
 special methods for those appHcations. To provide for both 
 views of this subject, the general mathematical discussion is 
 presented in a separate chapter, which may be omitted at the 
 first reading (or altogether), provided that the special methods, 
 which also are given in the proper places, are taken to be sufficient. 
 
 The first edition presented fundamental data not generally 
 accepted at that time, so that it was considered necessary to 
 justify the data by giving the derivation at length; much of this 
 matter, which is no longer new, is removed to an appendix, to 
 relieve the student of discussions that must appear unnecessary 
 and tedious. 
 
 The introduction of the steam-turbine has changed adiabatic 
 calculations for steam, from an apparent academic abstraction, to 
 a common necessity. To meet this changed condition, the Tables of 
 
 iii 
 
IV PREFACE 
 
 Properties of Saturated Steam have had added to them columns 
 of entropies of vaporization; and further there has been 
 computed a table of the quahty (or dryness factor) the heat 
 contents and volume at constant entropy, for each degree 
 Fahrenheit. This table will enable the computer to deter- 
 mine directly the efifect of adiabatic expansion to any pres- 
 sure or volume, and to calculate with ease the external work 
 in a cylinder or the velocity of flow through an orifice or nozzle 
 including the effect of friction; and also to tietermine the distri- 
 bution of work and pressure for a steam-turbine. For the 
 greater part of practical work this table may be used without 
 interpolation, or by interpolation greater refinement may be had. 
 
 Advantage is taken of recent experiments on the properties of 
 superheated steam and of the application to tests on engines to 
 place that subject in a more satisfactory condition. Attention 
 is also given to the development of internal combustion engines 
 and to the use of fuel and blast-furnace gas. A chapter is given 
 on the thermodynamics of the steam-turbine with current method 
 of computation, and results of tests. 
 
 So far as possible the various chapters are made independent, 
 so that individual subjects, such as the steam-engine, steam-tur- 
 bine, compressed-air and refrigerating machines, may be read 
 separately in the order that may commend itself. 
 
 PREFACE TO FIRST EDITION. 
 
 This work is designed to give instruction to students in 
 technical schools in the methods and results of the application 
 of thermodynamics to engineering. While it has been considered 
 desirable to follow commonly accepted methods, some parts 
 differ from other text-books, either in substance or in manner of 
 presentation, and may require a few words of explanation. 
 
 The general theory or formal presentation of thermodynamics 
 
PREFACE V 
 
 is that employed by the majority of writers, and was prepared 
 with the view of presenting clearly the difficulties inherent in the 
 subject, and of giving famiHarity with the processes employed. 
 
 In the discussion of the properties of gases and vapors the 
 original experimental data on which the working equations, 
 whether logical or empirical, must be based are given quite 
 fully, to afford an idea of the degree of accuracy attainable in 
 calculations made with their aid. Rowland's determination of 
 the mechanical equivalent of heat has been adopted, and with it 
 his determination of the specific heat of water at low tempera- 
 tures. The author's "Tables of the Properties of Saturated 
 Steam and Other Vapors" were ^calculated to accompany this 
 work, and may be considered to be an integral part of it. 
 
 The chapters on the flow of gases and vapors and on the 
 injector are beheved to present some novel features, especially 
 in the comparisons with experiments. 
 
 The feature in which this book differs most from similar 
 works is in the treatment of the steam-engine. It has been 
 deemed advisable to avoid all approximate theories based on 
 the assumption of adiabatic changes of steam in an engine 
 cyUnder, and instead to make a systematic study of steam- 
 engine tests, with the view of finding what is actually known on 
 the subject, and how future investigations and improvements 
 may be made. For this purpose a large number of tests have 
 been collected, arranged, and compared. Special attention is 
 given to the investigations of the action of steam in the cylinder 
 of an engine, considerable space being given to Hirn's researches 
 and to experiments that provide the basis for them. Directions 
 are given for testing engines, and for designing simple and com- 
 pound engines. 
 
 Chapters have been added on compressed-air and refrigerating 
 machines, to provide for the study of these important subjects 
 in connection with the theory of thermodynamics. 
 
 Wherever direct quotations have been made, references have 
 been given in foot-notes, to aid in more extended investigations. 
 It does not appear necessary to add other acknowledgment of 
 
VI PREFACE 
 
 assistance from well-known authors, further than to say that 
 their writings have been diUgently searched in the preparation 
 of this book, since any text-book must be largely an adaptation of 
 their work to the needs of instruction. 
 
 C. H. P. 
 
 Massachusetts Institute of Technology, 
 May, 1889. 
 
 PREFACE TO FOURTH EDITION. 
 
 A THOROUGH revision of this work has been made to bring 
 it into accord with more recent practice and to include later 
 experimental work. Advantage is taken of this opportunity to 
 make changes in matter or in arrangement which it is beHeved 
 will make it more useful as a text- book. 
 
 C. H. P. 
 Massachusetts Institute of Technology 
 July, 1898. 
 
TABLE OF CONTENTS. 
 
 CHAPTER PAGK 
 
 I. Thermal Capacities ...,.- i 
 
 II. First Law of Thermodynamics ............. 13 
 
 III. Second Law of ThermTodynamics 22 
 
 IV. General Thermodynamic Method 43 
 
 V. Perfect Gases . . . 54 
 
 VI. Saturated Vapor ' „ 76 
 
 VII. Superheated Vapors , 100 
 
 VIII. The Steam-engine 128 
 
 IX. Compound Engines , . . . . 156 
 
 X. Testing Steam-engines 183 
 
 XI. Influence of the Cylinder Walls jgg 
 
 XII. Economy of Steam-engines 237 
 
 XIII. Friction of Engines 285 
 
 XIV. Internal-Combustion Engines ............... 298 
 
 XV. Compressed Air 3^8 
 
 XVI. Refrigerating Machines , » . . . . 396 
 
 XVII. Flow of Fluids .. ..... , 423 
 
 XVIII. Injectors .... , . » 447 
 
 XIX. Steam-turbines •.,...,.,..,... 472 
 
THERMODYNAMICS OF THE STEAM-ENGINE, 
 
 CHAPTER I. 
 
 THERMAL CAPACITIES. 
 
 The object of thermodynamics, or the mechanical theory of 
 heat, is the solution of problems involving the action of heat, 
 and, for the engineer, more especially those problems presented 
 by the steam-engine and other thermal motors. The substances 
 in which the engineer has the most interest are gases and vapors, 
 more especially air and steam. Fortunately an adequate treat- 
 ment can be given of these substances for engineering purposes. 
 
 First General Principle. — In the development of the theor)^ 
 of thermodynamics it is assumed that if any two characteristics 
 or properties of a substance are known these two, treated as 
 independent variables, will enable us to calculate any third 
 property. 
 
 As an example, we have from the combination of the laws of 
 Boyle and Gay-Lussac the general equation for gases, 
 
 pv = RT, 
 
 in which p is the pressure, v is the volume, T is the absolute 
 temperature by the air-thermometer, and i? is a constant which 
 for air has the value 53.22 when English units are used. It is 
 probable that this equation led to the general assumption just 
 quoted. That assumption is purely arbitrary, and is to be justi- 
 fied by its results. It may properly be considered to be the first 
 general principle of the theory of thermodynamics; the other 
 two general principles are the so-called first and second laws of 
 thermodynamics, which will be stated and discussed later. 
 
2 THERMAL CAPACITIES 
 
 Characteristic Equation. — An equation which gives the 
 relations of the properties of any substance is called the charac- 
 teristic equation for that substance. The properties appearing 
 in a characteristic equation are commonly pressure, volume, 
 and temperature, but other properties may be used if convenient. 
 The form of the equation must be determined from experiments, 
 either directly or indirectly. 
 
 The characteristic equation for a gas is, as already quoted, 
 
 pv = RT. 
 
 The characteristic equation for an imperfect gas, like super- 
 heated steam, is likely to be more complex; for example, the 
 equation given by Knoblauch, Linde, and Klebe is 
 
 pv=BT-p{i+ ap) [c {^-d\- 
 
 On the other hand, the properties of saturated steam, especially 
 if mixed with water, cannot be represented by a single equation. 
 
 Specific Pressure. — The pressure is assumed to be a hydro- 
 static pressure, such as a fluid exerts on the sides of the con- 
 taining vessel or on an immersed body. The pressure is 
 consequently the pressure exerted hy the substance under con- 
 sideration rather than the pressure on that substance. For 
 example, in the cylinder of a steam-engine the pressure of the 
 steam is exerted on the piston during the forward stroke and 
 does work on the piston; during the return stroke, when the 
 steam is expelled from the cylinder, it still exerts pressure on 
 the piston and abstracts work from it. 
 
 For the purposes of the general theory pressures are 
 expressed in terms of pounds on the square foot for the English 
 system of units. In the metric system the pressure is expressed 
 in terms of kilograms on the square metre. A pressure thus 
 expressed is called the specific pressure. In engineering practice 
 other terms are used, such as pounds on the square inch, inches 
 of mercury, millimetres of mercury, atmospheres, or kilograms 
 on the square centimetre. 
 
TEMPERATURE 3 
 
 Specific Volume. — It is convenient to deal with one unit of 
 weight of the substance under discussion, and to coAsider the 
 volume occupied by one pound or one kilogram of the substance; 
 this is called the specific volume, and is expressed in cubic feet or 
 in cubic metres. The specific volume of air at freezing-point 
 and imder the normal atmospheric pressure is 12.39 cubic feet; 
 the specific volume of saturated steam at 2i2°F. is 26.6 cubic 
 
 feet ; and the specific volume of water is about - — ■ , or nearly 
 
 62.4 
 
 0.016 of a cubic foot. 
 
 Temperature is commonly measured by aid of a mercurial 
 thermometer which has for its reference-points the freezing- 
 point and boiling-point of water. A centigrade thermometer 
 has the volume of the stem between the reference- points divided 
 into one hundred equal parts called degrees. The Fahrenheit 
 thermometer differs from the centigrade in having one hundred 
 and eighty degrees between the freezing-point and the boiling- 
 point, and in having its zero thirty-two degrees below freezing. 
 
 The scale of a mercurial thermometer is entirely arbitrary, 
 and its indications depend on the relative expansion of glass and 
 mercury. Indications of such thermometers, however carefully 
 made, differ appreciably, mainly on account of the varying 
 nature of the glass. For refined investigations thermometric 
 readings are reduced to the air- thermometer, which has the 
 advantage that the expansion of air is so large compared with 
 the expansion of glass that the latter has little or no effect. 
 
 It is convenient in making calculations of the properties of 
 air to refer temperatures to the absolute zero of the scale of the 
 air-thermometer. To get a conception of what is meant by this 
 expression we may imagine the air-thermometer to be made of 
 a uniform glass tube with a proper index to show the volume 
 of the air. The position of the index may be marked at boiling- 
 point and at freezing-point as on the mercurial thermometer, 
 and the space between may be divided into one hundred parts 
 or degrees. If the graduations are continued to the closed end 
 of the tube there will be found to be 273 of them. It will be 
 
4 THERMAL CAPACITIES 
 
 shown later that there is reason to suppose that the absolute 
 zero of temperature is 273° centigrade below the freezing-point 
 of water. Speculations as to the meaning of absolute zero and 
 discussions concerning the nature of substances at that temper- 
 ature are not now profitable. It is sufficient to know that 
 equations are simplified and calculations are facilitated by this 
 device.. For example, if temperature is reckoned from the 
 arbitrary zero of the centigrade thermometer, then the charac- 
 teristic equation for a perfect gas becomes 
 
 -£+') 
 
 R, 
 
 in which a is the coefficient of dilatation and — = 273 nearly. 
 
 a 
 
 In order to distinguish the absolute temperature from the 
 temperature by the thermometer we shall designate the former 
 by T and the latter by t, bearing in mind that 
 
 T = t -\- 273° centigrade, 
 T = t + 459.5 Fahrenheit. 
 
 Physicists give great weight to the discussion of a scale of 
 temperature that can be connected with the fundamental units 
 of length and weight like the foot and the pound. Such a scale, 
 since it does not depend on the properties of any substance 
 (glass, mercury, or air), is considered to be the absolute scale of 
 temperature. The differences between such a scale and the 
 scale of the air-thermometer are very small, and are difficult to 
 determine, and for the engineer are of little moment. At the 
 proper place the conception of the absolute scale can be easily 
 stated. 
 
 Graphical Representation of the Characteristic Equation. — 
 Any equation with three variables may be represented by a 
 geometrical surface referred to co-ordinate axes, of which surface 
 the variables are the co-ordinates. In the case of a perfect gas 
 which conforms to the equation 
 
 pv = RT, 
 
STANDARD TEMPERATURE 5 
 
 the surface is such that each section perpendicular to the axis 
 of r is a rectangular hyperbola (Fig. i). 
 
 Returning now to the general case, 
 it is apparent that the characteristic /, 
 
 equation of any substance may be repre- /'Tw 
 sented by a geometrical surface referred \ oA \ 
 to co-ordinate axes, since the equation is j \ 
 assumed to contain only three variables; j /V/""^"'^'^'^ 
 but the surface will in general be less ij/^ ! /- 
 
 simple in form than that representing the ' ^~~ 
 
 combined laws of Boyle and Gay-Lussac. 
 
 If one of the variables, as T, is given a special constant value, 
 it is equivalent to taking a section perpendicular to the axis of 
 T\ and a plane curve will be cut from the surface, which may 
 be conveniently projected on the (^, v) plane. The reason for 
 choosing the (^, v) plane is that the curves correspond with 
 those drawn by the steam-engine indicator. 
 
 Considerable use is made of such thermal curves in explaining 
 thermodynamic conceptions. As a rule, a graphical process 
 or representation is merely another way of presenting an idea 
 that has been, or may be, presented analytically; there is, how- 
 ever, an advantage in representing a condition or a change to 
 the eye by a diagram, especially in a discussion which appears 
 to be abstract. A number of thermal curves are explained on 
 page 16. 
 
 Standard Temperature. — For many purposes it is convenient 
 to take the freezing-point of water for the standard temperature, 
 since it is one of the reference-points on the thermometric scale; 
 this is especially true for air. But the properties of water change 
 rapidly at and near freezing-point and are very imperfectly 
 known. It has consequently become customary to take 62° F. 
 for the staildard temperature for the English system of units; 
 there is a convenience in this, inasmuch as the pound and yard 
 are standards at that temperature. For the metric system 15° C. 
 is used, though the kilogram and metre are standards at freezing- 
 point. 
 
O THERMAL CAPACITIES 
 
 Thermal Unit. — Heat is measured in calories or in British 
 thermal units (b. t. u.). A British thermal unit is the heat 
 required to raise one pound of water from 62° F. to 63° F.; in 
 like manner a calorie is the heat required to raise one kilogram 
 of water from 15° C. to 16° C. 
 
 Specific Heat is the number of thermal units required to raise 
 a unit of weight of a given substance one degree of temperature. 
 The specific heat of water at the standard temperature is, of 
 course, unity. 
 
 If the specific heat of a given substance is constant, then the 
 heat required to raise one pound through a given range of tem- 
 perature is the product of the specific heat by the increase of 
 temperature. Thus if c is the specific heat and ^ — /j is the range 
 of temperature the heat required is 
 
 Q = c (t — /i), and c = — ^— • 
 
 If the specific heat varies the amount of heat must be obtained 
 by integration — that is," 
 
 Q = J cdt, 
 
 and conversely 
 
 dQ 
 
 dt 
 
 It is customary to distinguish two specific heats for perfect 
 gases; specific heat at constant pressure and specific heat at 
 constant volume, which may be represented by 
 
 = ©/"'^^" = (?)/ 
 
 the subscript attached to the parenthesis indicates the property 
 which is constant during the change. It is evident that the 
 specific heats just expressed are partial differential coefficients. 
 
 Latent Heat of Expansion is the amount of heat required to 
 increase the volume of a unit of weight of the substance by one 
 
EFFECTS PRODUCED BY HEAT 7 
 
 cubic foot, or one cubic metre, at constant temperature. It 
 may be represented by 
 
 \Bv/t 
 
 I 
 
 Thermal Capacities. — The two specific heats and the latent 
 heat of expansion are known as thermal capacities. It is cus- 
 tomary to use three other properties suggested by those just 
 named which are represented as follows: 
 
 The first represents the amount of heat that must be applied 
 to one pound of a substance (such as air) to increase the pressure 
 by the amount of one pound per square foot at constant tem- 
 perature; this property is usually negative and represents the 
 heat that must be abstracted to prevent the temperature from 
 rising. The other two can be defined in like manner if desired, 
 but it is not very important to state the definitions nor to try to 
 gain a conception as to what they mean, as it is easy to express 
 them in terms of the first three, for which the conceptions are 
 not difficult. They have no names assigned to them, which is, 
 on the whole, fortunate, as, of the first three, two have names that 
 have no real significance, and the third is a misnomer. 
 
 General Equations of the Effects Produced by Heat. — In 
 order to be able to compute the amount of heat required to 
 produce a change in a substance by aid of the characteristic 
 equation, it is necessary to admit that there is a functional rela- 
 tion between the heat applied and some two of the properties 
 that enter into the characteristic equation. It will appear later 
 in connection with the discussion of the first law of thermody- 
 namics that an integral equation cannot in general be written 
 directly, but we may write a differential equation in one of the 
 three following forms: 
 
 «-(l)/-(i),*. 
 
THERMAL CAPACITIES 
 
 
 or substituting for the partial differential coefficients the letters 
 which have been selected to represent them, 
 
 dQ = c^dt + Idv (i) 
 
 dQ = Cpdt + mdp (2) 
 
 dQ = ndp + odv (3) 
 
 This matter may perhaps be 
 clearer if it is presented graph- 
 ically as in Fig. 2, where ah is 
 intended to represent the path 
 of a point on the characteristic 
 surface in consequence of the 
 addition of the heat dQ. There 
 will in general be a change of 
 temperature volume and pres- 
 sure as indicated on the figure. 
 Now the path ah, which 
 for a small change may 
 be considered to be a straight 
 line, will be projected on 
 the three planes at a'V , a"h" and a'^'h'" . The projection on the 
 iy^T) plane may be resolved into the components ^v and ^T\ 
 the first represents a change of volume at constant temperature 
 requiring the heat Idv, and the second represents a change of tem- 
 perature at constant volume requiring the heat c^dt. Conse- 
 quently the heat required for the change in terms of the volume 
 and temperature is 
 
 dQ = c^dt + Idv. 
 
RELATIONS OF THE THERMAL CAPACITIES 9 
 
 Relations of the Thermal Capacities. — The three equations 
 (5), (6), and (7), show the changes produced by the addition of 
 an amount of heat dQ to a unit of weight of a substance, the 
 difference coming from the methods of analyzing the changes. 
 We may conveniently find the relations of the several thermal 
 capacities by the method of undetermined coefficients. Thus 
 equating the right-hand members of equations (5) and (6), 
 
 c^dt + Idv = Cpdt + mdp (4) 
 
 From the characteristic equation we shall have in general 
 
 v = F(p, T), 
 
 as, for example, for air we have 
 
 RT 
 
 p 
 
 and consequently we may write 
 
 which substituted in equation (4) gives, 
 
 -j-dt + -^dp\' 
 c, + Ij-) di + I ^dp . . (5) 
 
 It will be noted that, as T differs from t only by the addition 
 of a constant, the differential dt may be used in all cases, whether 
 we are dealing with absolute temperatures, or temperatures on 
 the ordinary thermometer. 
 
 In equation (5) p and T are independent variables, and each 
 may have all possible values; consequently we may equate Hke 
 coefficients. 
 
lO THERMAL CAPACITIES 
 
 Also, equating the remaining coefficients, 
 
 ^8^ = ^" (7) 
 
 If the characteristic equation is solved for the pressure we 
 shall have 
 
 p = F, (T, v\ 
 
 so that 
 
 '^^=&-* + &'^^ w 
 
 which substituted in equation (4) gives 
 
 Cpdt + m l-~ dt + ~-dv] = c^dt + Idv, 
 
 /. icp + m -~] dt -\- m~dv = c^dt + Idv, 
 
 Equating like coefficients, 
 
 Cp + m-^^ == c, (9) 
 
 - ^~§^= Cp — c„ . . . . (10) 
 
 From equations (2) and (3) 
 
 Cpdt + mdp = ndp + odv , . . . (11) 
 
 and from an equation 
 
 T = F, (V, p) 
 
 ht , 3/ , 
 
 which latter substituted in equation (11) gives 
 
 ^t , U ^ . . n 
 
 Cp~ dv + Cp ^- dp + mdp = ndp + odv. 
 
 Equating coefficients of dv, 
 
 = Cp-^ . , , . . . (12) 
 
RELATIONS OF THE THERMAL CAPACITIES ii 
 
 Finally, from equations (i) and (3), 
 
 c^dt + Idv = ndp -{- odv (13) 
 
 Substituting for dt as above, 
 
 CvT~~ dv + c„-r— dp -{- Idv = ndp + odv, 
 ov op 
 
 Equating coefficients of dp, 
 
 ^ = ^«S^ • • (14) 
 
 For convenience the several relations of the thermal capacities 
 may be assembled as follows : 
 
 Zv Sp 
 
 "*" '"Sp' " ' '" s, 
 
 "^^^^ 
 
 They are the necessary algebraic relations of the literal func- 
 tions growing out of the first general principle, and are inde- 
 pendent of the scale of temperature, or of any other theoretical 
 or experimental principle of thermodynamics other than the one 
 already stated — namely, that any two properties of a given 
 substance, treated as independent variables, are sufficient to 
 allow us to calculate any third property. 
 
 Of the six thermal capacities the specific heat at constant 
 pressure is the only one that is commonly known by direct 
 experiment. For perfect gases this thermal capacity is a con- 
 stant, and, further, the ratio of the specific heats 
 
 is a constant, so that c^ is readily calculated. The relations of 
 the thermal capacities allow us to calculate values for the. 
 
12 THERMAL CAPACITIES 
 
 Other thermal capacities, /, m, n, and o, provided that we can 
 first determine the several partial differential coefficients which 
 appear in the proper equations. But for a perfect gas the 
 characteristic equation is 
 
 pv = RT, 
 from which we have 
 
 ^_ R, ^ __ R. 
 
 Si " p' St " V ' 
 
 Bp ~ R' 8v " r' 
 
 Substituting these values in the equations for the thermal 
 capacities, we have 
 
 ^ = I fe — ^r) ; — w = ^ (^p- Cv) ; 
 V p 
 
 by aid of which the several thermal capacities may be calculated 
 numerically, or, what is the usual procedure, may be represented 
 in terms of the specific heats. 
 
CHAPTER II. 
 
 FIRST LAW OF THERMODYNAMICS. 
 
 The formal statement of the first law of thermodynamics is: 
 
 Heat and mechanical energy are mutually convertible^ and 
 heat requires for its production and produces by its disappearance 
 a definite number of units of work for each thermal unit. 
 
 This law, which may be considered to be the second general 
 principle of thermodynamics, is the statement of a well-deter- 
 mined physical fact. It is a special statement of the general 
 law of the conservation of energy, i.e., that energy may be trans- 
 formed from one form to another, but can neither be created 
 nor destroyed. It should be stated, however, that the general 
 law of conservation of energy, though universally accepted, has 
 not been proved by direct experiment in all cases; there may be 
 cases that are not susceptible of so direct a proof as we have for 
 the transformation of heat into work. 
 
 The best determinations of the mechanical equivalent of heat 
 were made by Rowland, whose work will be considered in detail 
 in connection with the properties of steam and water. From 
 his work it appears that 778 foot-pounds of work are required to 
 raise one pound of water from 62° to 63° Fahrenheit; this value 
 of the mechanical equivalent of heat is now commonly accepted 
 by engineers, and is verified by the latest determinations by 
 Joule and other experimenters. 
 
 The values of the mechanical equivalent of heat for the Eng- 
 lish system and for the metric system are: 
 
 I B. T. u. = 778 foot-pounds. 
 
 I calorie = 426.9 metre-kilograms. 
 
 This physical constant is commonly represented by the letter 
 J] the reciprocal is represented by A, 
 
 13 
 
14 FIRST LAW OF THERMODYNAMICS 
 
 In older works on thermodynamics the values of J are com- 
 monly quoted as 772 for the English system and 424 for the 
 metric system. The error of these values is about one per cent. 
 
 Effects of the Transfer of Heat. — Let a quantity of any sub- 
 stance of which the weight is one unit — i.e., one pound or one 
 kilogram — receive a quantity of heat dQ. It will, in general, 
 experience three changes, each requiring an expenditure of 
 energy. They are: (i) The temperature will be raised, and, 
 according to the theory that sensible heat is due to the vibra- 
 tions of the particles of the body, the kinetic energy will be 
 increased. Let dS represent this change of sensible heat or 
 vibration work expressed in units of work. (2) The mean 
 positions of the particles will be changed; in general the body 
 will expand. Let dl represent the units of work required for 
 this change of internal potential energy, or work of disgregation. 
 (3) The expansion indicated in (2) is generally against an exter- 
 nal pressure, and to overcome the same — that is, for the change 
 in external potential energy — there will be required the work 
 
 If during the transmission no heat is lost, and if no heat is 
 transformed into other forms of energy, such as sound, electricity, 
 etc., then the first law of thermodynamics gives 
 
 dQ = A{dS ^- dl -^ dW) (15) 
 
 It is to be understood that any or all of the terms of the equa- 
 tion may become zero or may be negative. If all the terms 
 become negative heat is withdrawn instead of added, and dQ is 
 negative. It is not easy to distinguish between the vibration 
 work and the disgregation work, and for many purposes it is 
 unnecessary; consequently they are treated together under the 
 name of intrinsic energy, and we have 
 
 dQ = A (dS + dl + dW) = A(dE + dW) . . (16) 
 
 The inner work, or intrinsic energy, depends on the state of 
 the body, and not at all on the manner by which it arrived at 
 
EFFECTS OF THE TRANSFER OF HEAT 15 
 
 that state; just as the total energy of a falhng body, with refer- 
 ence to a given plane consisting of kinetic energy and potential 
 energy, depends on the velocity of the body and the height 
 above the plane, and not on the previous history of the body. 
 
 The external work is assumed to be done by a fluid-pres- 
 sure; consequently 
 
 dW = pdv (17) 
 
 W 
 
 , pdv (18) 
 
 where v^ and v^ are the final and initial volumes. 
 
 In order to find the value of the integral v in equation (18) it 
 is necessary to know the manner in which the pressure varies 
 with the volume. Since the pressure may vary in different ways, 
 the external work cannot be determined from the initial and 
 final states of the body; consequently the heat required to effect 
 a change from one state to another depends on the manner in 
 which the change is effected. 
 
 Assuming the law of the variation of the pressure and volume 
 to be known, we may integrate thus: 
 
 Q = A (e, -E,+ £' pdv) .... (19) 
 
 In order to determine E for any state of a body it would be 
 necessary to deprive it entirely of vibration and disgregation 
 energy, which would of course involve reducing it to a state of 
 absolute cold; consequently the direct determination is impossi- 
 ble. However, in all our work the substances operated on are 
 changed from one state to another, and in each state the intrinsic 
 energy depends on the state only; consequently the change of 
 intrinsic energy may be determined from the initial and final 
 states only, without knowing the manner of change from one to 
 the other. 
 
 In general, equations will be arranged to involve differences 
 
i6 
 
 FIRST LAW OF THERMODYNAMICS 
 
 of energy only, and the hypothesis involved in a separation into 
 vibration and disgregation v^^ork avoided. 
 
 Thermal Lines. — The external work can be determined only 
 when the relations of p and v are known, or, in general, when 
 the characteristic equation is known. It has already been 
 shown that in such case the equation may be represented by a 
 geometrical surface, on which so-called thermal lines can be 
 drawn representing the properties of the substance under con- 
 sideration. These lines are commonly projected on the (/>, v) 
 plane. It is convenient in many cases to find the relation of p 
 and V under a given condition and represent it by a curve drawn 
 directly on the (^, v) plane. 
 
 Lines of Equal Pressure. — The change of 
 condition takes place at constant pressure, and 
 consists of a change of volume, as represented in 
 Fig, 3. The tracing- point moves from a^ to a^, 
 and the volume changes from v^ to v^. The 
 work done is represented by the rectangular area 
 under a^a^, or by 
 
 Fig. 3. 
 
 w 
 
 r 
 
 dv = p(v^ — v^) 
 
 (20) 
 
 During the change the temperature may or may not change; 
 the diagram shoWs nothing concerning it. 
 
 Lines of Equal Volume. — The pressure in- 
 creases at constant volume, and the tracing-point 
 moves from a^ to a^. The temperature usually 
 increases meanwhile. Since dv is zero. 
 
 W 
 
 ,^ Pdv = o 
 
 (21) 
 
 Fig. 4. 
 
 Isothermal Lines, or Lines of Equal Temperature. — The 
 
 temperature remains constant, and a line is drawn, usually 
 convex, toward the axis OV. The pressure of a mixture of a 
 
ADIABATIC LINES 
 
 17 
 
 p 
 
 ttl 
 
 
 
 \<a2 
 
 
 
 
 V' 
 
 liquid and its vapor is constant for a given temperature; con- 
 sequently the isothermal for such a mixture is a line of equal 
 pressure, represented by Fig. 3. The iso- 
 thermal of a perfect gas, on the other hand, is 
 an equilateral hyperbola, as appears from the 
 law of Boyle, which may be written 
 
 pV = C. Fig. 5. 
 
 Isodynamic or Isoenergic Lines are lines representing changes 
 during which the intrinsic energy remains constant. Conse- 
 quently all the heat received is transformed into external work. 
 It will be seen later that the isodynamic and isothermal lines 
 for a gas are the same. 
 
 Adiabatic Lines. — A very important problem in thermo- 
 dynamics is to determine the behavior of a substance when a 
 change of condition takes place in a non-conducting vessel. 
 During the change — for example, an increase of volume or 
 expansion — some of the heat in the substance may be changed 
 into work; but no heat is transferred to or from the substance 
 through the walls of the containing vessel. Such changes are 
 called adiabatic changes. 
 
 Very rapid changes of dry air in the cylinder of an air-com- 
 pressor or a compressed-air engine are very nearly adiabatic. 
 Adiabatic changes never occur in the cylinder of a steam-engine 
 on account of the rapidity with which steam is condensed on or 
 vaporized from the cast-iron walls of the cylinder. 
 
 Since there is no transmission of heat to (or from) the working 
 substance, equation (19) becomes 
 
 pdv) .... (22) 
 
 E,-E,=£jpdv (23) 
 
 that is, the external work is done wholly at the expense of the 
 intrinsic energy of the working substance, as must be the case 
 in conformity with the assumption of an adiabatic change. 
 
i8 
 
 FIRST LAW OF THERMODYNAMICS 
 
 Fig. 6. 
 
 Relation of Adiabatic and Isothermal Lines. ^- An important 
 
 property of adiabatic lines can be shown to advantage at this 
 
 place, namely, that such a line 
 is steeper than an isothermal 
 line on the {p, v) plane where 
 they cross, as represented in 
 Fig. 6. The essential feature of 
 adiabatic expansion is that no 
 heat is supplied and that conse- 
 quently the external work of 
 expansion is done at the expense 
 of the intrinsic energy which 
 consequently decreases. The 
 intrinsic energy is the sum of 
 the vibration energy and the 
 disgregation energy, both of 
 which in general decrease during an adiabatic expansion; in partic- 
 ular the decrease of vibration energy means a loss of temperature. 
 Conversely an adiabatic compression is accompanied by an in- 
 crease of temperature. If an isothermal compression is repre- 
 sented by ch, then an adiabatic compression will be represented 
 by a steeper hne like ca, crossing the constant pressure line ha to 
 the right of h, and thus indicating that at that pressure there is 
 a greater volume, as must be the case for a body which expands 
 during a rise of temperature at constant pressure. 
 
 It is very instructive to note the relation of these lines on the 
 surface which represents the characteristic equation for a perfect 
 gas. In Fig. 6, which is an isometric projection, the general 
 form of the surface can be recognized from the following condi- 
 tions : — a horizontal section representing constant pressure 
 cuts the surface in a straight line which indicates that the volume 
 increases proportionally to the absolute temperature, and this 
 line is projected as a horizontal line on the {p, v) plane; a vertical 
 section parallel to the {p, t) plane shows that the pressure in 
 this case increases as the absolute temperature, and the line of 
 intersection with the surface is projected as a vertical line on the 
 
THERMAL LINES AND THEIR PROJECTIONS 
 
 19 
 
 {pi '^) plane; finally vertical sections parallel to the {p, v) plane 
 are rectangular hyperbolae which are projected in their true 
 form on the {p, v) plane. If AC is an adiabatic curve on the 
 characteristic surface, its loss of temperature is properly repre- 
 sented by the fact that it crosses a series of isothermals in passing 
 from A to C; ^^ is a line of constant pressure showing a decrease 
 of temperature between the isothermals through A and through 
 C; finally the projection of ABC on to the {p, v) plane shows that 
 the adiabatic line ac is steeper than the isothermal line he. 
 Attention should be called to the fact that the first statement 
 of this relation is the more general as it holds for all substances 
 that expand with rise of temperature at constant pressure what- 
 ever may be the form of the characteristic equation. 
 
 Thermal Lines and their Projections. — The treatment given 
 of thermal lines is believed to be the simplest and to present 
 the features that are most useful in practice. There is, how- 
 ever, both interest and instruction in Considering their relation 
 in space and their projections on the three thermal planes. It 
 is well to look attentively at Fig. 6, which is a correct isometric 
 projection of the characteristic surface of a gas following the 
 law of Boyle and Gay-Lussac, noting that every section by a 
 plane parallel to the {p, v) plane is 
 a rectangular hyperbola which has 
 the same form in space and when 
 projected on the {p, v) plane. The 
 sections by a plane parallel to the 
 {p, t) plane are straight fines and are 
 of course projected as straight lines 
 on that plane and on the (_/>, v) plane; 
 in like manner the sections by planes 
 parallel to the (/, v) plane are straight 
 lines. The adiabatic fine in space 
 and as projected on the {p, v) plane is probably drawn a little 
 too steep, but the divergence from truth is not evident to the eye. 
 
 In Fig. 7 the same method of projection is used, but other 
 fines are added together with their projections on the several 
 
20 
 
 FIRST LAW OF THERMODYNAMICS 
 
 planes. Beginning at the point a in space the line ah is an 
 isothermal which is projected as a rectangular hyperbola a'h^ 
 on the (p, v) plane, and as straight lines a^'b^^ and a'"h"' on 
 the (/>, /) and (/, v) plane. The adiabatic hne ac is steeper 
 than the isothermal, both in space and on the (^, v) plane, as 
 already explained; it is projected as a curve {a"c" or a"'c'") on 
 the other planes. The section showing constant pressure is 
 represented in space by the straight line ae which projected on 
 the (^, t) plane is parallel to the axis <?/, and on the (^, v) 
 plane is parallel to the line itself in space; on the (^, v) plane it is 
 horizontal, as shown in Fig. 3. In much the same way ad is the 
 section by a plane parallel to the (/, v) plane, and a'd\ a"d'' 
 and a"'d'" are its projections. 
 
 Graphical Representations of Change of Intrinsic Energy. — 
 Professor Rankine first used a graphical method of representing 
 a change of intrinsic energy, employing adiabatic lines only, as 
 follows: 
 
 Suppose that a substance is originally in the state A (Fig. 8), 
 and that it expands adiabatically; then the external work is done 
 at the expense of the intrinsic energy; hence if the expansion 
 has proceeded to A^ the area AA^a^a, which represents the 
 external work, also represents the change of intrinsic energy. 
 Suppose that the expansion were to continue indefinitely; then 
 the adiabatic will approach the axis OV 
 indefinitely, and the area representing the 
 work will be included between the curve Aa 
 3 produced indefinitely, the ordinate Aa, and 
 ^ the axis OV; this area will represent all the 
 work that can be obtained by the expansion 
 of the substance; and if it be admitted that 
 during the expansion all the intrinsic energy is transformed 
 into work, so that at the end the intrinsic energy is zero, it rep- 
 resents also the intrinsic energy. In cases for which the equa- 
 tion of the adiabatic can be found it is easy to show that 
 
 £1 
 
 pdv 
 
 (24) 
 
CHANGE OF INTRINSIC ENERGY 
 
 21 
 
 is. a finite quantity; and in any case, if we admit an absolute zero 
 of temperature, it is evident that the intrinsic energy cannot 
 be infinite. On the other hand, if an isothermal curve were 
 treated in the same way the area would be infinite, since heat 
 would be continually added during the expansion. 
 
 Now suppose the body to pass from the condition represented 
 by A to that represented by B, by any path whatever — that is, 
 by any succession of changes whatever — for example, that 
 represented by the irregular curve AB. The intrinsic energy 
 in the state B is represented by the area VhB^. The change of 
 intrinsic energy is represented by the area ^BbaAa, and this 
 area does not depend on the form of the curve AB. This graph- 
 ical process is only another way of saying that the intrinsic 
 energy depends on the state of the substance only, and that 
 change of intrinsic energy depends on the final and initial states 
 only. 
 
 Another way of representing change of intrinsic energy by 
 aid of isodynamic lines avoids an infinite diagram. Suppose 
 the change of state to be represented by the 
 curve ^^ (Fig. 9). Draw an isodynamic 
 line AC through the point A, and an adia- 
 batic line BC through B, intersecting at C; 
 in general the isoenergic fine is distinct 
 from the isothermal line; for example, the 
 isothermal line for a saturated vapor is a F1G.9. 
 
 straight line parallel to the OV axis, and 
 the isoenergic line is represented approximately by the equation 
 
 pv 
 
 const. 
 
 Then the area ABba represents the external work, and the area 
 bBCc represents the change of intrinsic energy; for if the body be 
 allowed to expand adiabatically till the intrinsic energy is reduced 
 to its original amount at the condition represented by A the 
 external work bBCc will be done at the expense of the intrinsic 
 energy. 
 
CHAPTER III. 
 
 SECOND LAW OF THERMODYNAMICS. 
 
 Heat-engines are engines by which heat is transformed into 
 work. All actual engines used as motors go through continuous 
 cycles of operations, which periodically return things to the 
 original conditions. All heat-engines are similar in that they 
 receive heat from some source, transform part of it into work, 
 and deliver the remainder (minus certain losses) to a refrigerator. 
 The source and refrigerator of a condensing steam-engine are 
 the furnace and the condenser. The boiler is properly con- 
 sidered as a part of the engine, and receives heat from the source. 
 Garnet's Engine. — It is convenient to discuss a simple ideal 
 engine, first described by Carnot. 
 
 Let P of Fig. lo represent a cyhnder with non-conducting 
 walls, in which is fitted a piston, also of non-conducting material, 
 
 and moving without friction; on the 
 other hand, the bottom of the cyhnder 
 is supposed to be of a material that is 
 a perfect conductor. There is a non- 
 ^ I conducting stand C on which the 
 P^^ ^^ cyhnder can be placed while adiabatic 
 
 changes take place. The source of 
 heat ^ at a temperature / is supposed to be so maintained 
 that in operations during which the cylinder is placed on it, 
 and draws heat from it, the temperature is unchanged. The 
 refrigerator B at the temperature t^ in like manner can with- 
 draw heat from the cylinder, when it is placed on it, at a 
 constant temperature. 
 
 Let there be a unit of weight (for example, one pound) of a 
 certain substance in the cylinder at the temperature t of the 
 source of heat. Place the cylinder on the source of heat A 
 
CARNOT'S ENGINE 
 
 23 
 
 (Fig. 10), and let the substance expand at the constant tem- 
 perature ty receiving heat from the source A. 
 If the first condition of the substance be 
 represented by A (Fig. 11), then the second 
 will be represented by B, and AB will be an 
 isothermal. If Ea and Ej, are the intrinsic 
 energies at A and B, and if Wab, represented 
 by the area aABby be the external work, the 
 heat received from A will be 
 
 Fig. 
 
 Q = A {E,-Ea + Wab) (25) 
 
 Now place the cylinder on the stand C (Fig. 10), and let 
 the substance expand adiabatically until the temperature is 
 reduced to ^1, that of the refrigerator, the change being rep- 
 resented by the adiabatic BC (Fig. 11). If E^ is the intrinsic 
 energy at C, then, since no heat passes into or out of the 
 cylinder', 
 
 = A (E,-E,+ W,,) (26) 
 
 where Wbc is the external work represented by the area bBCc. 
 Place the cylinder on the refrigerator B, and compress the sub- 
 stance till it passes through the change represented by CD, 
 yielding heat to the refrigerator so that the temperature remains 
 constant. If Ed is the intrinsic energy at D, then 
 
 -Q^^A(Ea-E,- W,d) 
 
 (27) 
 
 is the heat yielded to the refrigerator, and Wed, represented by 
 the area cCDd, is the external work, which has a minus sign, 
 since it is done on the substance. 
 
 The point D is determined by drawing an adiabatic from A 
 to intersect an isothermal through C. The process is completed 
 by compressing the substance while the cylinder is on the stand 
 C (Fig. 10) till the temperature rises to /, the change being 
 represented by the adiabatic DA. Since there is no transfer 
 of heat, 
 
 = A {Ea- Ed- Wda) (28) 
 
24 SECOND LAW OF THERMODYNAMICS 
 
 Adding together the several equations, member to member, 
 Q -Q^^ A (Wa, + W,, - W,a - W,,) . . (29) 
 
 or, if W be the resulting work represented by the area A BCD, 
 then 
 
 Q-Q, = AW (30) 
 
 that is, the difference between the heat received and the heat 
 delivered to the refrigerator is the heat transformed into work. 
 
 A Reversible Engine is one that may run either in the usual 
 manner, transforming heat into work, or reversed, describing 
 the same cycle in the opposite direction, and transforming work 
 into heat. 
 
 A Reversible Cycle is the cycle of a reversible engine. 
 
 Carnot's engine is reversible, the reversed cycle being 
 ADCBA (Fig. 11), during which work is done by the engine 
 on the working substance. The engine then draws from the 
 refrigerator a certain quantity of heat, it transforms a certain 
 quantity of work into heat, and delivers the sum of both to the 
 source of heat. 
 
 No actual heat-engine is reversible in the sense just stated, 
 for when the order of operations can be reversed, changing the 
 engine from a motor into a pump or compressor, the reversed 
 cycle differs from the direct cycle. For example, the valve- 
 gear of a locomotive may be reversed while the train is running, 
 and then the cylinders will draw gases from the smoke-box, 
 compress them, and force them into the boiler. The locomotive 
 as ordinarily built is seldom reversed in this way, as the hot 
 gases from the smoke- box injure the surfaces of the valves and 
 cylinders. Some locomotives have been arranged so that the 
 exhaust- nozzles can be shut off and steam and water supplied 
 to the exhaust-pipe, thus avoiding the damage from hot gases 
 when the engine is reversed in this way. Such an engine may 
 then have a reversed cycle, drawing steam into the cylinders, 
 compressing and forcing it into the boiler; but in any case the 
 
EFFICIENCY 
 
 25 
 
 reversed cycle differs from the direct cycle, and the engine is 
 not properly a reversible engine. 
 
 A Closed Cycle is any cycle in v^hich the final state is the same 
 as the initial state. Fig. 12 represents such a 
 cycle made up of four curves of any nature 
 whatever. If the four curves are of two species 
 only, as in the diagram representing the cycle 
 of Carnot 's engine, the cycle is said to be simple. 
 In general we shall have for a cycle like that of Fig. 12, 
 
 Fig. 12. 
 
 Qa6 + Qbc - Q< 
 
 = A {W\ + W,, 
 
 W 
 
 cd 
 
 W^). 
 
 p 
 
 A 
 
 B 
 
 
 
 
 c 
 
 ^ 
 
 -i 
 
 D - 
 
 
 V 
 
 Fig. 13. 
 
 A closed curve of any form may be consid- 
 ered to be the general form of a closed cycle, 
 as that in Fig. 13. For such a cycle we have 
 
 j dQ = A I dW, which is one more way of 
 
 stating the first law of thermodynamics. 
 
 It may make this last clearer to consider the cycle of Fig. 14 
 composed of the isothermals AB, CD, and EG, and the 
 adiabatics BC, DE, and GA. The cycle 
 may be divided by drawing the curve 
 through from C to F. It is indifferent 
 whether the path followed be A BCD EG A 
 or ABCFCDEGA, or, again, ABCFGA + 
 CDEFC. 
 
 Again, an irregular figure may be 
 imagined to be cut into elementary areas by isothermals and 
 adiabatic lines, as in Fig. 15. The summation of the areas will 
 give the entire area, and the summation of the works represented 
 by these will give the entire work represented by the entire area. 
 
 The Efficiency of an engine is the ratio of the heat changed 
 into work to the entire heat applied; so that if it be represented 
 by e, 
 
 _AW_ -Q' 
 "~ Q ' Q 
 
 Fig. 
 
 (31) 
 
26 SECOND LAW OF THERMODYNAMICS 
 
 for the heat Q' rejected to the refrigerator is what is left after 
 AW thermal units have been changed into work. 
 
 Camot's Principle. — It was first pointed 
 out by Carnot that the efficiency of a 
 reversible engine does not depend on the 
 nature of the working substance, but that 
 it depends on the temperatures of the 
 ^ source of heat and the refrigerator. 
 
 Fig. 15. Let us sce what would be the conse- 
 
 quence if this principle were not true. 
 Suppose there are two reversible engines R and A^ each taking 
 Q thermal units per second from the source of heat, of which 
 A is the more efficient, so that 
 
 Q Q -^"^^ 
 
 is larger than 
 
 AW^ _ Q- Q/ 
 Q Q ^^^^ 
 
 this can happen only because Qa is less than Q/, for Q is assumed 
 to be the same for each engine. Let the engine R be reversed 
 and coupled to A, which can run it and still have left the useful 
 work Wa — Wr- This useful work cannot come from the 
 source of heat, for the engine R when reversed gives to the source 
 Q thermal units per second, and A takes the same amount in the 
 same time. It must be assumed to come from the refrigerator, 
 which receives Qa thermal units per second, and gives up Q/ 
 thermal units per second, so that it loses 
 
 (2/ -Qa' = A {Wa - Wr) 
 
 thermal units per second. This equation may be derived from 
 equations (32) and (33) by subtraction. 
 
 Now it cannot be proved by direct experiment that such an 
 action as that just described is impossible. Again, the first law 
 of thermodynamics is scrupulously regarded, and there is no 
 
SECOND LAW OF THERMODYNAMICS 27 
 
 contradiction or formal absurdity of statement. And yet when 
 the consequences of the negation of Carnot's principles are 
 clearly set forth they are naturally rejected as improbable, if not 
 impossible. The justification of the principle is found in the 
 fact that theoretical deductions from it are confirmed by 
 experiments. 
 
 Second Law of Thermodynamics. — The formal statement 
 of Carnot's principle is known as the second law of thermody- 
 namics. Various forms are given by different investigators, 
 none of which are entirely satisfactory, for the conception is not 
 simple, as is that of the first law. 
 
 The following are some of the statements of the second law: 
 (i) All reversible engines working between the same source of 
 heat and refrigerator have the same efficiency. 
 
 (2) The efficiency of a reversible engine is independent of the 
 working substance. 
 
 (3) ^ self-acting machine cannot convey heat from one body 
 to another at a higher temperature. 
 
 The second law is the third general principle of thermody- 
 namics; it differs from each of the others and is independent 
 of them. Summing up briefly, the first general principle is a 
 pure assumption that thermodynamic equations may contain 
 only two independent variables; the second is the statement of 
 an experimental fact; the third is a choice of one of two 
 propositions of a dilemrha. The first and third are justified 
 by the results of the applications of the theory of thermo- 
 dynamics. 
 
 So far as efficiency is concerned, the second law of thermo- 
 dynamics shows that it wotild be a matter of indifference what 
 working substance should be chosen; we might use air or steam 
 in the same engine and get the same efficiency from either; 
 there would, however, be a great difference in the power that 
 would be obtained. In order to obtain a diagram of convenient 
 size and distinctness, the adiabatics are made much steeper than 
 the isothermals in Fig. 11 ; as a matter of fact the diagram drawn 
 correctly is so long and attenuated that it would be practically 
 
a 
 
 V 
 
 b 
 
 
 
 28 SECOND LAW OF THERMODYNAMICS 
 
 worthless even if it could be obtained with reasonable approxi- 
 mation in practice, as the work of the cycle would hardly over- 
 come the friction of the engine. The isothermals for a mixture 
 of water and steam are horizontal, and the diagram takes the 
 form shown by Fig. 16. In practice a dia- 
 gram closely resembhng Carnot's cycle is 
 chosen as the ideal, differing mainly in that 
 steam is assumed to be supphed and ex- 
 hausted. In a particular case an engiiie 
 working between the temperatures 362°. 2 F. 
 and 158° F. had an actual thermal efficiency of 0.18; the 
 ideal cycle had an efficiency of 0.23, and Carnot's cycle had 
 an efficiency of 0.25. The ratio of 0.18 to 0.23 is about 0.81, 
 which compares favorably with the efficiency of turbine water- 
 wheels. 
 
 Carnot's Function. — Carnot 's principle asserts that the 
 efficiency of a reversible engine is independent of the nature of 
 the working substance; consequently the expression for the 
 efficiency will not include such properties of the working sub- 
 stance as specific volume and specific pressure. But the prin- 
 ciple asserts also that the efficiency depends on the temperatures 
 of the source of heat and the refrigerator, which indeed are the 
 only properties of the source and refrigerator that can affect 
 the working of the engine. 
 
 We may then represent the efficiency as a function of the tem- 
 peratures of the source of heat- and the refrigerator, or, what 
 amounts to the same thing, as a function of the superior tem- 
 perature and the difference of the temperatures, and may write 
 
 AW _ Q -Q' 
 e= -Q-- Q = F (t,t-n 
 
 where Q is the heat received, Q^ the heat rejected, and / and /' 
 are the temperatures of the source of heat and of the refrigerator 
 on any scale whatsoever, absolute or relative. 
 
 If the temperature of the refrigerator approaches near that of 
 
KELVIN'S GRAPHICAL METHOD 
 
 29 
 
 the source of heat Q — Q' and t — tf become A(3 and A/, and at 
 the Hmit dQ and dt, so that 
 
 'f=Fit, dt) 
 
 (34) 
 
 It is convenient to assume that the equation can be expressed 
 in the form 
 
 dQ 
 
 Q 
 
 f (t) dt. 
 
 The function/ (/) is known as Carnot's function, and physi- 
 cists consider that the isolation of this function and the relation 
 of the function to temperature are of great theoretical importance. 
 
 Absolute Scale of Temperature. — It is convenient and cus- 
 
 tomary to assign to Carnot's function the form — 
 
 where T is 
 
 the temperature by the absolute scale referred to on page 3, 
 measured from the absolute zero of temperature. This assump- 
 tion is justified by the facts that the theory of thermodynamics 
 is much simplified thereby, and that the difference between 
 such a scale of temperature and the scale of the air-thermometer 
 is very small. ^ 
 
 Kelvin's Graphical Method. — This treatment of Carnot 's 
 function was first proposed by Lord Kelvin, who illustrated the 
 general conception by the following graphical construction: 
 
 In Fig. 17 let ak and bi be two adiabatic lines, and let the 
 substance have its condition 
 represented by the point a. 
 Through a and d draw iso- 
 thermal hnes ; then the diagram 
 ahcd represents the cycle of a 
 simple reversible engine. Draw 
 the isothermal line /e, so that 
 the area dcef shall be equal to 
 abed] then the diagram dcef 
 represents the cycle of a reversible engine, doing the same 
 amount of work per stroke as that engine whose cycle is repre- 
 
 FiG. 17. 
 
30 
 
 SECOND LAW OF THERMODYNAMICS 
 
 sented by ahcd; and the difference between the heat drawn 
 from the source and deUvered to the refrigerator — i.e., the heat 
 transformed into work — is the same. The refrigerator of the 
 first engine might serve for the source of heat for the second. 
 
 Suppose that a series of equal areas are cut off by isothermal 
 lines, di?>fegh, hgik, etc., and suppose there are a series of reversible 
 engines corresponding; then there will be a series of sources of 
 heat of determinate temperatures, which may be chosen to 
 establish a thermometric scale. In order to have the scale cor- 
 respond with those of ordinary thermometers, one of the sources 
 of heat must be at the temperature of boiling water, and one at 
 that of melting ice; and for the centigrade scale there will be one 
 hundred, and for the Fahrenheit scale one hundred and eighty, 
 such cycles, with the appropriate sources of heat, between boiling- 
 point and freezing-point. To establish the absolute zero of the 
 scale the series must be imagined to be continued till the area 
 included between an isothermal and the two adiabatics, continued 
 indefinitely, shall not be greater than one of the equal areas. 
 
 This conception of the absolute zero 
 may be made clearer by taking wide 
 intervals of temperature, as on Fig. 
 1 8, where the cycle abed is assumed 
 to extend between the isothermals of 
 o° and ioo° C; that is, fr,om freez- 
 ing-point to boiling-point. The 
 next cycle, cdef, extends to — ioo° C, 
 and the third cycle, efgh, extends 
 to — 200° C. The rernaining area, 
 which is of infinite_Jength and ex- 
 tremely attenuated, is bounded by the 
 isothermal gh and the two adiabatics 
 ha and g^. The diagram of course 
 cannot be completed, and conse- 
 quently the area cannot be measured; 
 but when the equations to the isothermal and the adiabatics 
 are known it can be computed. So computed, the area is found 
 
 Fig. 18. 
 
SPACING OF ADIABATICS 
 
 31 
 
 to be -^^ of one of the three equal areas ahcd, cdfe, and efhg. 
 100 
 
 The absolute zero is consequently 273° C. below freezing-point. 
 
 Further discussion of the absolute scale will be deferred till 
 
 a comparison is made with the air-thermometer. 
 
 Spacing of Adiabatics. — Kelvin 's graphical scale of temper- 
 ature is clearly a method of spacing isothermals which depends 
 only on our conceptions of thermodynamics and on the funda- 
 mental units of weight and length. Evidently the same method 
 may be applied to spacing adiabatics, and thereby a new concep- 
 tion of great importance may be introduced into the theory of 
 thermodynamics. On this conception is based the method for 
 solving problems involving adiabatic expansion of steam, as 
 will be explained in the discussion of that subject. 
 
 In Fig. 19 let an and do 
 be two isothermals, and let 
 adj he, Im and no be a series 
 of adiabatics, so drawn that 
 the areas of the figures ahcd, 
 blmc, and Inom are equal; 
 then we have a series of 
 adiabatics that are spaced in 
 the same manner as are the 
 isothermals in Figs. 17 and 
 18, and, as with those iso- 
 thermals, the spacing depends only on our conceptions of ther- 
 modynamics and the fundamental units of weight and length. 
 
 In the discussion of Figs. 17 and 18 it was shown that the area 
 of the strip between the initial isothermal ab and the two adiabatic 
 lines must be treated as finite, and that in consequence the 
 graphical process leads to an absolute zero of temperature. On 
 the contrary, the area between the adiabatic ad and the two 
 isothermals an and do if extended infinitely will bejnfinite, and 
 it will be found that there is no lim it to the number of adia- 
 batics that can be drawn with the spacing indicated. A like 
 result will follow if the isothermals arc extended to the right and 
 
 Fig. 
 
32 SECOND LAW OF THERMODYNAMICS 
 
 Upward, and if adiabatics are spaced off in the same manner. 
 This conclusion comes from the fact pointed out on page 21, 
 that the area under an isothermal curve which is extended with- 
 out limit is infinite, because heat is continuously supplied, some 
 part of which can be changed into work. 
 
 It is convenient to introduce a new function at this 
 place which shall express the spacing of adiabatics as 
 represented in Fig. 19, and which will be called entropy. 
 From what precedes it is evident that entropy has the 
 same relations to the adiabatics of Fig. 19 that temperature 
 has to the isothermals of Figs. 17 and 18, but that there is this 
 radical difference, that while there is a natural absolute zero of 
 temperature, there is no zero of entropy. Consequently in prob- 
 lems we shall always deal with differences of entropy, and if we 
 find it convenient to treat the entropy of a certain condition of a 
 given substance as a zero point it is only that we may count up 
 and down from that point. 
 
 If the adiabatic line ad in Fig. 19 should be extended to the 
 right, it would clearly lie beneath the adiabatic no, which agrees 
 with the tacit convention of that figure, i.e., that as spaced the 
 adiabatics are to be numbered toward the right and that the 
 entropy increases from a toward n. 
 
 The simplest and the most natural definition of entropy from 
 the present considerations, is that entropy is that function which 
 remains constant for any thange represented by a reversible 
 adiabatic expansion (or compression). With this definition in 
 view, the adiabatic lines might be called isoentropic lines. It 
 should be borne in mind that our present discussion is purposely 
 limited to expansion in a non-conducting cylinder closed by a 
 piston, or to like operations. More complex operations than 
 that just mentioned may require an extension of the conception 
 of entropy and lead to fuller definitions. Such extensions of the 
 conception of entropy have been found very fruitful in certain 
 physical investigations, and many writers on thermodynamics 
 for engineers consider that they get like advantages from them. 
 There is, however, an advantage in limiting the conception of a 
 
GRAPHICAL REPRESENTATION OF EFFICIENCY 
 
 33 
 
 new function, however simple that conception may be ; and there 
 is an added advantage in being able to return to a simple con- 
 ception at will. 
 
 Efficiency of Reversible Engines. — Returning to equation 
 
 (34) and replacing Carnot's function/ (t) by — j as agreed, we 
 
 have for the differential equation of the efficiency of a reversible 
 engine 
 
 Q 
 
 or, integrating between limits, 
 
 " Q 
 
 r 
 
 
 
 and the efficiency ior the cycle becomes 
 Q - 0' T - T 
 
 (35) 
 
 This result might have been obtained before (or without) the 
 discussion of Kelvin 's graphical method, and leads to the same 
 conclusion, that the absolute temperature can be made to depend 
 on the efficiency of Carnot's cycle, and may, therefore, be inde- 
 pendent of any thermometric substance. 
 As has already been said, this conception 
 is more important on the physical side 
 than on the engineering side, and its reit- 
 eration need not be considered to call for 
 any speculation by the student at this time. 
 
 Graphical Representation of Efficiency. 
 — Let Fig. 20 represent the cycle of 
 a reversible heat-engine. For convenience 
 it is supposed there are four degrees of temperature from the 
 isothermal AB \o the isothermal DC^ and that there are three 
 intervals or units of entropy between the adiabatics AD and 
 
 Fig. 20. 
 
34 SECOND LAW OF THERMODYNAMICS 
 
 BC. First it will be shown that all the small areas into which 
 the cycle is divided by drawing the intervening adiabatics and 
 isothermals are equal. Thus we have to begin with a = b and 
 a = c by construction. But engines w^orking on the cycles a 
 and b have the same efficiency and reject the same amounts 
 of heat. These heats rejected are equal to the heats supplied 
 to engines w^orking on the cycles c and d, which consequently 
 take in the same amounts of heat. But these engines work 
 between the same limits of temperature and have the same 
 efficiency, and consequently change the same amount of heat 
 into work. Therefore the areas c and d are equal. In like 
 manner all the small areas are equal, and each represents one 
 thermal unit, or 778 foot-pounds of work. 
 
 It is evident that the heat changed into work is represented by 
 
 {T - T') {4.' - <j>), 
 
 and, further, that the same expression would be obtained for a 
 
 similar diagram, whatever number of degrees there might be 
 
 between the isothermals, or intervals of entropy between the 
 
 adiabatics, and that it is not invalidated by using fractions of 
 
 degrees and fractions of units of entropy. It is consequently 
 
 the general expression for the heat changed into work by an 
 
 engine having a reversible cycle. 
 
 It is clear that the work done on such a cycle-ilici-eases as the 
 
 lower temperature T' decreases, and that it is a maximum when 
 
 T^ becomes zero, for which condition all of the heat applied is 
 
 changed into work. Therefore the heat applied is represented 
 
 by 
 
 Q=T (4>'~ <!>), 
 
 and the efficiency of the engine working on the cycle represented 
 by Fig. 20 is 
 
 AW _ Q - Q' _ (T -r)(<j>' - cj>) _ T - T 
 
 Q ~ Q ~ T {4>^ -ct>) r ' 
 
 as found by equation (35). The deduction of this equation by 
 integration is more simple and direct, but the graphical method 
 
EXPRESSION FOR ENTROPY 
 
 35 
 
 A 
 
 
 T 
 
 
 R 
 
 
 D 
 
 
 
 
 4>' 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 T' 
 
 
 
 Fig. 21 
 
 is interesting and may give the student additional light on this 
 subject. 
 
 Temperature-Entropy Diagram. — Thermal diagrams are com- 
 monly drawn with pressure and volume for the co-ordinates, 
 but for some purposes it is convenient to use other properties 
 as co-ordinates, in particular temperature and entropy. For 
 exarnple, Fig. 21 represents Carnot's cycle 
 drawn with entropies for abscissae and tem- 
 peratures for ordinates, with the advantage 
 that indefinite extensions „ of the lines are 
 avoided, and the areas under consideration 
 are' evidently finite and nieasurable. With 
 the exception that there appears now to be no 
 necessity to show that the areas obtained by subdivision are all 
 equal, the discussion for Fig. 20 drawn with pressures and vol- 
 umes may be repeated with temperatures and entropies. 
 
 Expression for Entropy. — One advantage of using the tem- 
 perature-entropy diagram is that it leads at once to a method 
 for computing changes of entropy. Thus in Fig. 22 let AB 
 represent an isothermal change, and let Aa 
 and Bh be adiabatics drawn to the axis of 0; 
 then the diagram ABha may be considered to 
 be the cycle for a Carnot's engine working 
 between the temperature T and the -absolute 
 — zero, and consequently having the efficiency 
 unity. The heat changed into work may there- 
 fore be represented by 
 
 Q = T {4>' -4>) (36) 
 
 If we are deahng with a change under any other condition 
 than constant temperature, we may for an infinitesimal change, 
 write the expression 
 
 # = f . . . . . . . . (37) 
 
 and for the entire change may express the change of entropy by 
 
 Fig. 22. 
 
36 SECOND LAW OF 'THERMODYNAMICS 
 
 which should for any particular case either be integrated 
 between limits or else a constant of integration should be 
 determined. 
 
 Attention should be called to the fact that the conception of 
 the spacing of isothermals and adiabatics is based fundamen- 
 tally on Carnot's cycle and the second law of thermodynamics, 
 which has been applied only to reversible operations. The 
 method of calculating changes of entropy applies in like manner 
 to reversible operations; and when entropy is employed for 
 calculations of operations that are not reversible, discretion 
 must be used to avoid inconsistency and error. 
 
 On the other hand, the entropy of a unit weight of a given 
 substance under certain conditions is a perfectly definite quan- 
 tity and is independent of the previous history of the substance. 
 This may be made evident by the consideration that any point 
 on the line no, Fig. 19, page 31, has a certain number of units of 
 entropy (for example, three) more than that of any point on 
 the adiabatic ad. 
 
 Example. — There may be an advantage in giving a calcu- 
 lation of a change of entropy to emphasize the point that it can 
 be represented by a number. Let it be required to find the 
 change of entropy during an isothermal expansion of one pound 
 air from four cubic feet to eight cubic. 
 
 The heat applied may be obtained by integrating the expression 
 
 , , .dO Idv , . p dv 
 
 the value of the latent heat having been taken from page 12. 
 From the characteristic equation 
 
 pv = RT 
 the above expression may be reduced to 
 d<p = [Cp — c„) — " 
 
APPLICATION TO A REVERSIBLE CYCLE 
 
 37 
 
 or 
 
 (0-2375 — 0.1690) loge - 
 4 
 
 0.0475. 
 
 Fig. 23. 
 
 A problem for air is chosen because it can be readily worked 
 out at this place; as a matter of fact, there are few occasions in 
 practice where there is reason to refer to entropy of air. 
 
 Application to a Reversible Cycle. — A very important result 
 is obtained by the application of equation (37) to the calcula- 
 tion of entropy during a reversible cycle. In the first place, 
 it is clear that the entropy of a substance having its condition 
 represented by the point a (Fig. 23), depends on the adiabatic 
 line drawn through it; in other words, the entropy depends only 
 on the condition of the substance. 
 In this regard entropy is like intrin- 
 sic energy and differs from external 
 work. Suppose now that the sub- 
 stance is made to pass through a 
 cycle of operations represented by 
 the point a tracing the diagram on 
 Fig. 23; it is clear that the entropy will be the same at the end 
 of the cycle as at the beginning, for the tracing-point will then 
 be on the original adiabatic line. As the tracing- point moves 
 toward the right from adiabatic to adiabatic the entropy 
 increases, and as it moves to the left the entropy decreases, the 
 algebraic sum of changes of entropy being zero for the entire 
 cycle. This conclusion holds whether the cycle is reversible 
 or non-reversible. The cycle represented by Fig. 23 is purposely 
 drawn like a steam-engine indicator diagram (which is not 
 reversible) to emphasize the fact that the change of entropy is 
 zero in any case. 
 
 If the cycle is reversible, then equation (37) may be used for 
 calculating the several changes of entropy, and for calculating 
 the change for the entire cycle, giving for the cycle 
 
 T 
 
 n 
 
 (38) 
 
38 SECOND LAW OF THERMODYNAMICS 
 
 This is a very important conclusion from the second law of 
 thermodynamics, and is considered to represent that law. The 
 second law is frequently applied by using this equation in con- 
 nection with a general equation or a characteristic equation, in 
 a manner to be explained later. 
 
 Though the discussion just given is simple and complete, 
 there is some advantage in showing that equation (38) holds 
 for certain simple and complex reversible cycles. 
 
 Thus for Carnot's cycle, represented by Fig. 20, the increase 
 of entropy during isothermal expansion is 
 
 ^■~*-ff-iP^-4 
 
 T . 
 
 because the temperature is constant. In like manner the 
 decrease during isothermal compression is 
 
 so that the change of entropy for the cycle is 
 
 2 _ 2: 
 
 T T 
 
 But from the efficiency of the cycle we have 
 
 Q~ Q' _ T— T . 2! _ Z! • 2 _ 2! _ 
 
 Q " ^ T ' " Q~ T ' " T 7' ~ °' 
 
 A complex cycle like that represented by Fig. 24 may be 
 broken up into two simple cycles ABFG 
 and CDFE, for each of which individually 
 tjie same result will be obtained — that is, 
 the increase of entropy from ^ to ^ is 
 equal to the decrease from F to G, and 
 the increase from C to D is equal to the 
 
 Fig. 24. 
 
 decrease from E to F, so that the sum- 
 mation of changes for the entire cycle gives zero. 
 
MAXIMUM EFFICIENCY 
 
 39 
 
 Fig. 25 represents the simplified ideal diagram of a hot-air 
 engine, in which by the aid of a regenerator the adiabatic lines 
 of Carnot's cycle are replaced by 
 vertical lines without affecting the 
 reversibility or the efficiency of the 
 cycle. We may replace the actual 
 diagram by a series of simple cycles 
 made up of isothermals and adia- 
 batics, so drawn that the perimeter 
 of the complex cycle includes the 
 same area and corresponds ap- 
 proximately with that of the 
 actual diagram. The summation 
 for the complex cycle is clearly 
 drawing the adiabatic lines near 
 make 
 
 Fig. 25. 
 
 of the change of entropy 
 zero, as before. But by 
 enough together we may 
 the perimeter approach that of the actual diagram as 
 nearly as we please, and we may therefore conclude that the 
 integration for the changes of entropy for that cycle is also zero. 
 Maximum Efficiency. — In order that heat may be trans- 
 formed into work with the greatest efficiency, all the heat should 
 be applied at the highest practicable temperature, and the heat 
 rejected should be given up at the lowest practicable tempera- 
 ture; this condition is found for Carnot's cycle, which serves 
 as the ideal type to which we approach as nearly as practical 
 conditions allow. Deviations from the ideal type are of two 
 sorts, (i) commonly a different and inferior cycle is chosen as 
 being practically more convenient, and (2) the material of 
 which the working cylinder is made absorbs heat at high tem- 
 perature and gives out heat at low temperature, thus interfering 
 with the attainment of the cycle selected. 
 
 The principle just stated must be accepted as immediately 
 evident; but there may be an advantage in giving an illustration. 
 The complex cycle of Fig. 24 is made up of two simple Carnot 
 cycles ABFG and CDEF\ if two thirds of the heat is appHed 
 during the isothermal expansion AB Sit 500° C, and one third 
 during the expansion CD, at 250° C, and if all the heat is re- 
 
40 SECOND LAW OF THERMODYNAMICS 
 
 jected at 20° C, the combined efficiency of the diagram may be 
 computed to be 
 
 2 ^ 500 - 20 ^ !__ X ^-^^-^^ =0.56; 
 
 3 500 + 273 3 250 + 273 
 
 had the heat been all applied at 500° C, the efficiency would 
 have been 
 
 SCO — 20 
 
 0.62. 
 
 500 + 273 
 
 The loss in this case from applying part of the heat at lower 
 temperature is, therefore, 
 
 0.62 — o.c;6 
 
 — — = 0.097. 
 
 0.62 
 
 Non-reversible Cycles. — If a process or a cycle is non-rever- 
 sible, then the change of entropy cannot be calculated by equa- 
 tion (37), and equation (38) will not hold. The entropy will, 
 indeed, be the same at the end as at the beginning of the cycle, 
 
 but the integration of -~ for the cycle will not give zero. On 
 
 the contrary, it can be shown that the integration of -~ for the 
 
 entire cycle will give a negative quantity. Thus let the non- 
 reversible engine A take the same amount of heat per stroke as 
 the reversible engine R which works on Carnot 's cycle, but let 
 it have a less efficiency, so that 
 
 P-<^' < a^^ (3,) 
 
 where Q/ represents the heat rejected by the engine A. Then 
 
 Q -Q/ <Q-Q'= {T-T') (^' - <A) . . (40) 
 
 Suppose now that T^ approaches zero and that </>' approaches ^, 
 then at the limit we shall have* 
 
 dQi < dQ = Tdcf), 
 or 
 
 f^ < #. 
 
NON-REVERSIBLE CYCLES 41 
 
 Integrating for the entire cycle, we shall have 
 
 where — N represents a negative quantity. The absolute 
 value of N will, of course, depend on the efficiency of the non- 
 reversible engine. If the efficiency is small compared with that 
 of a reversible engine, then the value of N will be large. If 
 the efficiency approaches that of a reversible engine, then N 
 approaches zero. It is scarcely necessary to point out that N 
 cannot be positive, for that would infer that the non-reversible 
 engine had a greater efficiency than a reversible engine working 
 between the same temperatures. 
 
 Some non-reversible operations, like the flow of gas through 
 an orifice, result in the development of kinetic energy of motion. 
 In such case the equation representing the distribution of energy 
 contains a fourth term K to represent the kinetic energy, and 
 equation (15) becomes 
 
 dQ = A (dS + dT + dW + dK) . . .(42) 
 
 As before S represents vibration work, / represents disgregation 
 work, and W represents external work. If the vibration and 
 disgregation work cannot be separated, then we may write 
 
 dQ = A {dE + dW + dK) (43) 
 
 If a non-reversible process like that just discussed takes place 
 in apparatus or appliances that are made of non-conducting 
 material, or if the action of the walls on the substance contained 
 can be neglected, the operation may properly be called adiabatic ; 
 such a use is clearly an extension of the idea stated on page 32, 
 and conclusions drawn from adiabatic expansion in a closed 
 cylinder cannot be directly extended to this new application. 
 Such a non -reversible operation is not likely to be isoen tropic, 
 and there is some advantage in drawing a distinction between 
 operations which are isoentropic and those which are adiabatic. 
 
42 SECOND LAW OF THERMODYNAMICS 
 
 A non-reversible operation in non-conducting receptacles may be 
 isothermal, or may be with constant intrinsic energy, as will 
 appear in the discussion of flow of air in pipes on page 380, and 
 the discussion of the steam calorimeter, page 191. Any non- 
 reversible process is likely to be accompanied by an increase of 
 entropy; this will appear in special cases discussed in the 
 chapter on flow of fluids. 
 
 Since the entropy of a pound of a given substance under 
 given conditions, reckoned from an arbitrary zero, is a perfectly 
 definite numerical quantity, it is possible to determine its entropy 
 for any series of conditions, without regard to the method of 
 passing from one condition to another. It is, therefore, always 
 possible to represent any changes of a fixed weight of a sub- 
 stance, by a diagram drawn with temperatures and entropies 
 for co-ordinates. If the diagram can be properly interpreted, 
 conclusions from it will be valid. It is, however, to be borne in 
 mind that thermodynamics is essentially an analytical mathemat- 
 ical treatment ; the treatment, so far as it applies to engineering, 
 is neither extensive nor difficult. But the student is cautioned 
 not to consider that because he has drawn a diagram represent- 
 ing a given operation to the eye, he necessarily has a better 
 conception of the operation. If any operation involves an 
 increase (or decrease) of weight of the substance operated on, 
 thermal diagrams are likely to be difficult to devise and liable 
 to misinterpretation. 
 
CHAPTER IV. 
 
 GENERAL THERMODYNAMIC METHOD. 
 
 In the three preceding chapters a discussion has been given 
 of the three fundamental principles of thermodynamics, namely, 
 (i) the assumption that the properties of any substance can 
 be represented by an equation involving three variables; (2) the 
 acceptance of the conservation of energy; and (3) the idea of 
 Carnot's principle. In the ideal case each of these principles 
 should be represented by an equation, and by the combination 
 of the three several equations all the relations of the properties 
 of a substance should be brought out so that unknown proper- 
 ties may be computed from known properties, and in particular 
 advantage may be taken of opportunities to calculate such prop- 
 erties as cannot be readily determined by direct experiment from 
 those which may be determined experimentally with precision. 
 
 Recent experiments have so far changed the condition of 
 affairs that there is less occasion than formerly for such a general 
 treatment. Of the three classes of substances that are interest- 
 ing to engineers, namely, gases, saturated vapors, and super- 
 heated vapors, the conditions appear to be as follows. For 
 gases there are sufficient experimental data to solve all problems 
 without referring to the general method, though the ratio of the 
 specific heats is probably best determined by that method. For 
 saturated steam there is one property, namely, the specific vol- 
 ume, which is computed by aid of the general method, but there 
 are experimental determinations of volume which are reliable 
 though less extensive. The characteristic equation of super- 
 heated steam is now well determined, and the specific heat is 
 determined with sufficient precision for engineering purposes, 
 so that there is no difficulty in making the customary 
 calculations. 
 
 43 
 
44 GENERAL THERMODYNAMIC METHOD 
 
 The one class of substances for which the necessary properties 
 must be computed by aid of the general method, are those vola- 
 tile fluids like ammonia and sulphur dioxide, which are used 
 for refrigerating machines. 
 
 On the whole, even with conditions as stated, it is desirable 
 that the student should master the general thermodynamic 
 method, given in this chapter. That method is neither long 
 nor hard, and is so commonly accepted that students who have 
 mastered it will have no difhculty in reading standard works 
 and current literature involving thermodynamic discussions. 
 Those cases remaining where the general method or its equiva- 
 lent must be used, are best treated by that method, and in the 
 case of volatile fluids can be treated only by that method. 
 
 The case having been presented as fairly as possible, dis- 
 cretion may be left with the student or his instructor whether 
 he shall read the remainder of this chapter before proceeding, 
 or whether the chapter shall be altogether omitted. 
 
 The following method of combining the three general prin- 
 ciples of thermodynamics, which is due to Lord Kelvin, depends 
 on the use of the expression 
 
 BySz BzS V 
 
 as the basis of an operation. This expression is generally used 
 as a criterion to determine whether a certain differential is an 
 exact differential that can be integrated directly, or whether 
 some additional relation must be sought by aid of which the 
 expression may be transformed so that it can be integrated. 
 
 Conversely, if we know, from the nature of a given property 
 like intrinsic energy, that it can be always calculated for a given 
 condition as represented by two variables like temperature and 
 volume, then we are justified in concluding that the expression 
 
 8v8t ~ 8t8v ^^^^ 
 
 must be true and that we can use it as the basis of an operation. 
 
APPLICATION OF THE FIRST LAW 
 
 45 
 
 Now in laying out a general method it is impossible to select 
 any particular characteristic equation, and for that reason, if 
 no other, the form of the integral equation connecting E with 
 / and V cannot be assigned. But the fact remains that the possi- 
 bility of working out any method depends on the assumption of 
 the ultimate possibility of writing such an equation, and that 
 assumption carries with it the assumption that dE is an exact 
 differential. 
 
 Application of the First Law. — The first general principle 
 may be taken to be represented by equation (i), 
 
 dQ ^ Cydt + Idv, 
 
 and the first law of thermodynamics by equation (i6), 
 dQ = A (dE + dW) = A (dE-h pdv). 
 
 Combining these equations gives 
 
 and comparing with the general form, 
 
 dE =-^ dt -]- -r- dv, 
 ot ov 
 
 it is evident that 
 
 ^E c, ,Be I ■ 
 
 Now equation (44) is an abbreviated way of writing the 
 expression for continued differentiation which may be expanded 
 to 
 
 . se . se 
 
 Sv Bt 
 
46 GENERAL THERMODYNAMIC METHOD 
 
 or replacing the first partial differential coefficients by their 
 equivalents, 
 
 ■■■-M-mht <«) 
 
 the subscripts being written to avoid possible confusion with 
 other partial differential coefficients to be deduced later. 
 
 From the first law of thermodynamics and equation (2) we 
 have in like manner 
 
 dQ = A (dE + pdv) = Cpdt + mdp. 
 
 Since the differential dv is inconvenient, we may replace it by 
 
 ov ov 
 
 so that 
 
 dE + p ~ dp + p -~- dtj = Cpdt + mdp. 
 
 Making 
 
 use of the equation 
 
 
 
 
 
 
 
 ^87 
 
 'bp 
 
 
 
 Sp - 
 
 ~ Bi 
 
 
 gives 
 
 
 8 
 
 Bp 
 
 &- 
 
 
 S (m 
 ' St \a 
 
 -^sp)- 
 
 
 I /8c; 
 
 \ - 
 
 Bv 
 
 ^8V 
 
 I (Bm\ 
 
 
 .Sp/t St ^ BpSt A\St/p ^ SiSp 
 
APPLICATION OF THE SECOND LAW 47 
 
 But the assumption of a characteristic equation connecting 
 py V, and t carries with it the assumption that 
 
 so that 
 
 3 [©,-(!'),]= I <^') 
 
 Again, from equation (3) we may have 
 
 dQ = A (dE + pdv) = ndp + odv. 
 
 :.dE='^dp+{^j-p)dv (47) 
 
 or, making use of 
 
 Bv^p SpSv 
 A\Bv)p~ A \8p)v~~ '• 
 
 ■■i[©,-(£)j= '« 
 
 Application of the Second Law. — The second law of thermo- 
 dynamics can be expressed by equation (^S), page 37, 
 
 /^=». 
 
 T 
 
 which makes ■— or d<j) an exact differential, so that we may write 
 To prepare equation (i) for this transformation, we may write 
 
48 GENERAL THERMODYNAMIC METHOD 
 
 SO that the preceding equation gives 
 Bv 
 
 ' T\Bvl 
 
 \t) Bt \t) 
 
 y^2 
 
 or 
 
 Performing a like operation on equation (2) we have 
 
 f-^-^/ + f#, 
 
 
 Bp \t) Bt \tJ 
 
 
 '• T\Bp)t T' 
 
 
 " \Bp)t \Bt)p~ f ' 
 
 
 juation (3) we have 
 
 
 f =1^^ + ^^.. 
 
 
 B /n\ B /o\ 
 " By [t/~ Bp \t)' 
 
 
 -IBr't '•©.- 
 
 
 r 
 
 (50) 
 
 First and Second Laws Combined. — The result of applying 
 both the first and the second laws of thermodynamics to the 
 
ALTERNATIVE METHOD 49 
 
 equations (i), (2), and (3) may be obtained by combining the 
 equations resulting from the appHcation of the laws separately. 
 Thus equations (45) and (49) give 
 
 h_ _ I I 
 
 h~ AT 
 Equations (46) and (50) give 
 
 jS i^ £ w 
 
 h. " AT 
 
 (52) 
 
 (53) 
 
 And equations (48) and (51) give 
 
 ^ = ^("|-'*^) (54) 
 
 It is convenient to transform this last equation by taking 
 values of n and from page 12, yielding 
 
 c,-c.=^ATj^ ....... (55) 
 
 The equations deduced in this chapter show the necessary 
 relations among the thermal capacities if the laws of thermo- 
 dynamics are accepted. Some of them, or equations deduced 
 from them, have been used by writers on thermodynamics to 
 establish relations or compute properties that cannot be readily 
 obtained by direct experiments. 
 
 For the student familiarity with the processes is of more 
 importance than any of the results. 
 
 Alternative Method. — Some writers on thermodynamics re- 
 serve the discussion of temperature until they are ready to 
 define or assume an absolute scale independent of any substance 
 and depending only on the fundamental units of length and 
 weight. Of the three general equations (i), (2), and (3) they 
 use at first only the latter: 
 
 dQ = ndp + odv. 
 
50 
 
 GENERAL THERMODYNAMIC METHOD 
 
 Now from equation (i6), representing the first law of thermo- 
 dynamics, 
 
 dQ = A (dE + pdv), 
 
 it is evident that dQ is not an exact differential, since the equa- 
 tion cannot be integrated directly. The fact that in certain 
 cases p may be expressed as a function of Vy and the integral 
 for external work can be deduced, does not affect this general 
 statement. Suppose that there is some integrating factor, 
 
 which may be represented by — , so that 
 
 IQ^ldp + ^dv 
 s s ^ s 
 
 may be integrated directly; we may then consider that we have 
 a series of thermal lines represented by making 
 
 •- = const., — = const., — = const., etc. 
 
 o o o 
 
 These lines with a series of adiabatic lines represented by 
 (j) = const., (j>^ = const., ^'' = const., etc., 
 
 allow us to draw a simple cycle of operations represented by Fig. 
 25a, in which AB and CD are represented by the equations 
 
 I = C, and ^ = C, 
 
 Is while AD and BC are adiabatics. The effi- 
 b le V ciency of a reversible engine receiving the 
 Fig. 2sa. Yieat Q during the operation AB, and reject- 
 
 ing the heat Q' during the operation CD, will be 
 
 Q-Q' AW 
 
 But -^ is an exact differential, and depends on the state of 
 
ZEUNER'S EQUATIONS 51 
 
 the substance only, and consequently is the same at the end as 
 at the beginning of the cycle, so that for the entire cycle 
 
 V(3 
 
 /f 
 
 Now during the operations represented by the adiabatics AD 
 and BC no heat is transmitted, and during the operations rep- 
 resented by the lines AB and CDj --is constant; consequently 
 the integration of the above equation for the cycle gives 
 
 Q G' 
 
 — — -^^ = o. 
 
 S S' 
 
 . Q -Q' _ s - s\ 
 
 " Q S ' 
 
 that is, the efficiency of an engine v^orking on such a cycle depends 
 on 5 and 5', and on nothing else. 
 
 Zeuner's Equations. — A special form of thermodynamic 
 equations has been developed by Zeuner and through his influ- 
 ence has been impressed to a large extent on German writings. 
 These equations can be deduced from those already given in 
 the following manner. 
 
 From the application of the first law of thermodynamics to 
 equation (3) we have equation (47), page 47, 
 
 
 dE -- 
 
 =>- 
 
 Ki- 
 
 -.) 
 
 dv. 
 
 Now 
 
 dE - 
 
 ■1^' 
 
 ^g 
 
 dv. 
 
 
 so that 
 
 
 
 
 
 
 
 n 
 A ~ 
 
 - Bp' 
 
 
 
 A ~ 
 
 SE 
 
 ' Sv 
 
 + P 
 
 These properti 
 
 as Zeuner writes 
 
 
 
 
 X = 
 
 
 Y = 
 
 P + 
 
 SE 
 Sv- 
 
52 GENERAL THERMODYNAMIC METHOD 
 
 Solving equation (54) 
 
 first for and then for 
 
 n. 
 
 
 AT + 
 
 
 
 
 AT-, 
 
 - « = ;- 
 
 Bt 
 
 
 ^^, 
 
 In equation (3) 
 
 dQ = ndp + odVj 
 
 we may substitute the above ^values successively giving 
 dQ = ^ In ^ dp -}- n J- dv + A Tdv] • 
 
 /. dQ ^ ^ indt + ATdvj 
 
 hp 
 
 hi h , 
 
 because dt = ^— dp + r— a^' • 
 
 op ov 
 
 And also 
 
 dQ='^{o^^dp^olLdv--ATdp). 
 
 ',dQ = ^(odt ~ ATdp]' 
 
 hv 
 
 Replacing and n by their values in terms of X and F, 
 dQ =A (Xdp + Ydv), 
 
 dQ=jJ^Xdl+ (^4-/) ^4 
 
 Tp 
 
 dQ = f^[Ydt + {l + t)dp]. 
 
ZEUNER'S EQUATIONS 53 
 
 In these equations a is tlie coefficient of dilatation, or — h / is 
 equal to T, and 
 
 If this derivation of Zeuner's equations is borne in mind, the 
 treatment of thermodynamics by many German writers may be 
 readily recognized to be only a variant on that developed by 
 Clausius and Kelvin. 
 
CHAPTER V. 
 
 PERFECT GASES. 
 
 The characteristic equation for a perfect gas is derived from 
 a combination of the laws of Boyle and Gay-Lussac, which 
 may be stated as follows: 
 
 Boyle's Law. — When a given weight of a perfect gas is com- 
 pressed (or expanded) at a constant temperature the product 
 of the pressure and the volume is a constant. This law is nearly 
 true at ordinary temperatures and pressures for such gases as 
 oxygen, hydrogen, and nitrogen. Gases which are readily 
 liquefied by pressure at ordinary temperatures, such as ammonia 
 and carbonic acid, show a notable deviation from this law. The 
 law may be expressed by the equation 
 
 pv = p,v, . . • (56) 
 
 in which p^ and v^ are the initial pressure and volume; p is any 
 pressure and v is the corresponding volume. 
 
 Gay-Lussac's Law. — It was found by Gay-Lussac that any 
 volume of gas at freezing-point increases about 0.003665 of its 
 volume for each degree rise of temperature. Gases which are 
 easily liquefied deviate from this law as well as from Boyle's 
 law. In the deduction of this law temperatures were measured 
 on or referred to the air-thermometer, and the law therefore 
 asserts that the expansibility or the coefficient of dilatation of 
 perfect gases is the same as that of air. Gay-Lussac 's law may 
 be expressed by the equation 
 
 V = v^{i + at) . (57) 
 
 in which t^o is the original volume at freezing-point, a is the 
 coefficient of dilatation or the increase of volume for one degree 
 rise of temperature, and v is the volume corresponding to the 
 temperature t measured from freezing-point. 
 
 54 
 
CHARACTERISTIC EQUATION 55 
 
 Characteristic Equation. — From equation (57) we may 
 calculate any special volume, such as v^, getting 
 
 ^'l = Vq (1 + at). 
 
 Assuming that p^ in equation (56) is the normal pressure of 
 the atmosphere pQ, and substituting the value just found for Vj^, 
 we have for the combination of the laws of Boyle and Gay- 
 Lussac 
 
 pv =poVo (i + at) =poVoa (^ + ^ j • • • • (5^) 
 
 If it be assumed that a gas contracts a part of its volume at 
 freezing-point for each degree of temperature below freezing 
 
 then the absolute zero of the air-thermometer will be — degrees 
 below freezing, and 
 
 a 
 
 may be replaced by T, the absolute temperature by the air- 
 thermometer. 
 
 The usual form of the characteristic equation for perfect 
 gases may be derived from equation (58) by substituting Tq, 
 
 the absolute temperature of freezing-point, for - , giving 
 
 p = ^T=RT (59) 
 
 ^ 
 
 where i? is a constant representing the quantity 
 
 0^0 
 
 T 
 ^ 
 
 For solution of examples it is more convenient to write equa- 
 tion (59) in the form 
 
 ^=^ (60) 
 
56 PERFECT GASES 
 
 Absolute Temperature. — Recent investigations of the prop- 
 erties of hydrogen by Professor Callender * indicate that the 
 absolute zero is 273°.! C. below freezing-point. This does 
 not differ much from taking a = 0.003665 as given by Regnault, 
 for v^^hich the reciprocal is 272.8. In this w^ork we shall take 
 for the absolute temperature 
 
 r = / + 273° centigrade scale. 
 r = ^ + 459°.5 Fahrenheit scale. 
 
 These figures are convenient and sufficiently exact. 
 
 Relation of French and English Units. — For the purpose of 
 conversion of units from the metric system (or vice versa) the 
 following values may be used: 
 
 one metre = 39.37 inches, 
 one kilogram = 2.2046 pounds. 
 
 Specific Pressure. — The normal pressure of the atmosphere . 
 is assumed to be equivalent to that of a column of mercury, 
 760 mm. high at freezing-point. Now Regnault t gives for 
 the weight of a litre, or one cubic decimetre, of mercury 13.5959 
 kilograms; consequently the specific, pressure of the atmosphere 
 under normal conditions is 
 
 p^ = 10,333 kilograms per square metre. 
 
 Using the conversion units given above for reducing this 
 specific pressure to the English system of units gives 
 
 po = 2116.32 pounds per square foot, 
 
 which corresponds to 
 
 14.697 pounds per square inch, 
 or to 
 
 29.921 inches of mercury. 
 
 It is customary and sufficient to use for the pressure of the 
 atmosphere 14.7 pounds to the square inch. 
 
 * Phil. Mag., Jan., 1903. 
 
 t Memoir es de PInstitni.de France, vol. xxi. 
 
SPECIFIC VOLUMES 
 
 57 
 
 Specific Volumes of Gases. — From recent determinations of 
 densities of gases by Leduc, Morley, and Raleigh it appears that 
 the most probable values of the specific volume of the commoner 
 gases are 
 
 VOLUMES IN CUBIC METRES OF ONE KILOGRAM. 
 
 Atmospheric air ...,.„..,.,.. 0.7733 
 
 Nitrogen 0.7955 
 
 Oxygen ....,..,..,...,. 0.6996 
 
 Hydrogen .-..'.,.„. 11.123 
 
 The corresponding quantities for English units are given in 
 the next table: 
 
 VOLUMES IN CUBIC FEET OF ONE POUND. 
 
 Atmospheric air . . » . „ 12.39 
 
 Nitrogen , , , . , . . 12.74 
 
 Oxygen 12.21 
 
 Hydrogen 178.2 
 
 To these may be added the value for carbon dioxide, 0.506 
 cubic metre per kilogram or 8.10 cubic feet per pound; but 
 as the critical temperature for this substance is about 31° C, or 
 88° F., calculations by the equations for gases are liable to be 
 affected by large errors. 
 
 Value of R. — The constant R which appears in the usual 
 form of the characteristic equation for a gas represents the 
 expression 
 
 To ' 
 The values for R corresponding to the French and the English 
 system of units may be calculated as follows: 
 
 French units, R = ^^^^-^ ^ ^'^^^^ = 29.27 . . (61) 
 
 273 
 
 T- T 1. •. 7-» 2116.^ X 12.^0 ,. X 
 
 English units, R = ^ ^ = 53.35 . . (62) 
 
 491-5 
 
 \^alue of R for other gases may be calculated in a like manner. 
 
58 PERFECT GASES 
 
 Solution of Problems. — Many problems involving the proper- 
 ties of air or other gases may be solved by the characteristic 
 equation 
 
 pv = RT, ' 
 
 or by the equivalent equation 
 
 T To 
 
 which for general use is the more convenient. 
 
 In the first of these two equations the specific pressure and 
 volume to be used for EngHsh measures are pounds per square 
 foot, and the volume in- cubic feet of one pound. 
 
 For example, let it be required to find the volume of 3 pounds 
 of air at 60 pounds gauge-pressure and at 100° F. Assuming a 
 barometric pressure of 14.7 pounds per square inch, 
 
 V = ^^ ^^ ^^^^ ^ = 2.774 cubic feet 
 
 (14.7 +,60)144 
 
 is the volume of i pound of air under the given conditions, and 
 3 pounds will have a volume of 
 
 3 X 2.774 = 8.322 cubic feet. 
 
 The second equation has the advantage that any units may 
 be used, and that it need not be restricted to one unit of weight. 
 
 For example, let the volume of a given weight of gas, at 100° C. 
 and at atmospheric pressure, be 2 cubic yards; required the 
 volume at 200° C. and at 10 atmospheres. Here 
 
 10 V _ 1X2 
 
 473 373 ' • 
 
 V = -^-^ = 0.2 1; ^6 cubic yards. 
 
 10 X 373 ^^ ^ 
 
 Specific Heat at Constant Pressure. — The specific heat for 
 true gases is very nearly constant, and may be considered to be 
 
APPLICATION OF LAWS OF THERMODYNAMICS 59 
 
 SO for thermodynamic equations. Regnault gives for the mean 
 values for specific heat at constant pressure the following results : 
 
 Atmospheric air ............. 0.2375 
 
 Nitrogen 0.2438 
 
 Oxygen 0.2175 
 
 Hydrogen 3 . 409 
 
 Ratio of the Specific Heats. — By a special experiment oh 
 the adiabatic expansion of air, Rontgen* determined for the 
 ratio of the specific heats of air, at constant pressure and at 
 constant volume, 
 
 tc = ■£■= 1.405. 
 
 This value agrees well with a computation to follow, which 
 depends on the application of the laws of thermodynamics to a 
 perfect gas, and also with a determination from the theory of 
 gases by Lovef that the ratio for air should be 1.403. If the 
 given value for this ratio be accepted the remainder of the work 
 in this chapter follows without any reference to the laws of 
 thermodynamics . 
 
 Application of the Laws of Thermodynamics. — The preced- 
 ing statements concerning the specific heats of perfect gases 
 and their ratio would be satisfactory were it definitely determined 
 by experiment that the specific heat at constant volume is as 
 nearly constant as is the specific heat at constant pressure. 
 None of the experimental determinations (not even that by Joly %) 
 can be considered as satisfactory as those for the specific heat 
 at constant pressure; consequently there is considerable impor- 
 tance to be attached to the application of the laws of thermo- 
 dynamics to the characteristic equation for a perfect ga;s, and, 
 moreover, this application furnishes one of the most satisfactory 
 determinations of the ratio of the specific heats. 
 
 * Poggendorff's Annalen, vol. cxlviii, p. 580. 
 
 t Phil. Mag., July, 1899. 
 
 t Proc. Royal Soc, vol. xli, p. 352, 1886. 
 
6o PERFECT GASES 
 
 It is convenient at this place to make the appHcation of the 
 laws of thermodynamics by aid of equation (55), page 49. 
 
 From the equation 
 we have 
 
 Cp- c. 
 
 = AT 
 
 , I 
 8tBt° 
 
 
 
 8v Sp 
 
 pv = 
 
 RT, 
 
 
 3/ 
 
 p St 
 R'Sp 
 
 V 
 
 ^ r' 
 
 .-. Cp 
 
 — c, = 
 
 = AR 
 
 (63) 
 
 (64) 
 
 This equation shows conclusively that if the characteristic 
 equation is accepted the differences of the specific heats must be 
 considered to be constant, and if one is treated as constant so 
 also must the other. Conversely, the assumption of constant 
 specific heats for any substance is in effect the assumption of 
 the characteristic equation for a perfect gas. 
 
 The solution of equation (64) for the ratio of the specific 
 heats gives 
 
 f. AR 
 
 ic= = 1.406. 
 
 J _ 10333 X 0'7733 
 426.9 X 273 X 0.2375 
 
 For those who have not read Chapter IV, the following deriva- 
 tion of equation (64) may be interesting. In Fig. 26 let ah repre- 
 sent the change of volume at constant pressure due 
 to the addition of heat c^A/ where A/ is the increase 
 of temperature ; and let cb represent the change of 
 V pressure due to the addition of heat c^A/; if ac is 
 
 Fig. 26. ^n isothermal, the latter change of temperature will 
 be equal to the former, but the heat applied will be less on account 
 of the external work pi^v (approximtely). Consequently, 
 
 Cp — c,^ Ap ^ = AR, 
 
ISOTHERMAL LINE 6l 
 
 the last transformation making use of the partial derivative 
 
 S/ " p 
 
 Thermal Capacities. — The values of the several thermal 
 capacities for a perfect gas were derived on page 12 and may be 
 written 
 
 I = ^ (Cp - c,,) = - (Cp — c^) . . e . (66) 
 
 K V 
 
 -(c,-c„)=-- 
 
 ^^ — l^{(^P~^v) =— - (Cp — C^) . . (67) 
 
 w = - Cr = 7 c« . (68) 
 
 K p 
 
 =^Cp= ■- Cp ........ (69) 
 
 K v 
 
 the transformations in equations (66) and (67) being made by 
 aid of the characteristic equation. 
 
 General Equations. — To deduce the general equations for 
 gases from equations (i), (2), and (3), it is only necessary to 
 replace the letters /, m, n, and by their values just obtained, 
 giving 
 
 T 
 dQ =- cjt + (Cp — c^) - dv (70) 
 
 "^ 
 
 T 
 
 dQ = Cpdt -r (c^ — Cp)-- dp . . : . . (71) 
 
 P 
 
 T T 
 dQ == c^ - dp + Cp - dv (72) 
 
 p V 
 
 Isothermal Line. — The equation to the isothermal Hne for 
 a gas is obtained by making T a constant in the characteristic 
 equation, so that 
 
 pv =^ RT^ = p,v„ 
 or 
 
 pv = p,v^ ...... (73) 
 
 This equation will be recognized as the expression of Boyle's 
 law. It is, of course, the equation to an equilateral hyperbola*. 
 
62" PERFECT GASES 
 
 To obtain the external work during an isothermal expansion 
 we may substitute for p in the expression 
 
 W 
 
 Jpd^. 
 
 from the equation to the isothermal line just stated, using for 
 limits the final and initial volumes, V2 and z\j 
 
 W 
 
 ^ ^1^^ A "^7 = ^1^1 ^^^' ~ • • ' • (74) 
 
 If the problem in any case calls for the external work of one 
 unit of weight of a gas, then v^ and V2 must be the initial and 
 final specific volumes; but in many cases the initial and final 
 volumes are given without any reference to a weight, and it is 
 then sufficient to find the external work for the given expansion 
 from the initial to the final volume without considering whether 
 or not they are specific volumes. 
 
 The pressures must always be specific pressures ; in the English 
 system the pressures must be expressed in pounds on the square 
 foot before using them in the equation for external work, or, for 
 that matter, in any thermodynamic equation. 
 
 For example, the specific volume of air at freezing-point and 
 at 14.7 pounds pressure per square inch is about 12.4 cubic feet; 
 at the same temperature and at 29.4 pounds per square inch the 
 specific volume is 6.2 cubic feet. The external work during 
 an isothermal expansion of one pound of air from 6.2 to 12.4 
 cubic feet is 
 
 PI - p^v, I — = p,v, log, - 
 
 124 
 = 29.4 X 144 X 6.2 loge -~ =18,190 foot-pounds. 
 
 6.2 
 
 For example, the external work of isothermal expansion from 
 3 cubic feet and 60 pounds pressure by the gauge to a volume 
 of 7 cubic feet is 
 
 W =■■ (60 + 14.7) 144 X 3 logg^ = 27,340 foot-pounds. 
 
 3 
 
ISOENERGIC LINE 63 
 
 In both problems the pressure per square inch is multipHed 
 by 144 to reduce it to the square foot. In the first problem the 
 pressures are absolute, that is, they are measured from zero 
 pressure; in the second problem the pressure by the gauge is 
 60 pounds above the pressure of the atmosphere, which is here 
 assumed to be 14.7 pounds per square inch, and is added to 
 give the absolute pressure. In careful experimental work the 
 pressure of the atmosphere is measured by a barometer and is 
 added to the gauge-pressure. 
 
 Isoenergic Line. — The isothermal line for a perfect gas is 
 also the isoenergic line, a fact that may be proved as follows : 
 The heat applied during an isothermal expansion may be cal- 
 culated by making T a constant in equation (70) and then 
 integrating; thus: 
 
 ^1 V v., 
 
 or, substituting for c^ — c„ from equation (64), 
 
 Q = ART, log,^ = Ap,v, log, J . . . (75) 
 
 A comparison of equation (75) with equation (74) shows 
 that the heat applied during an isothermal expansion is equiv- 
 alent to the external work, or we may say that all the heat applied 
 is changed into external work, so that the intrinsic energy is not 
 changed. This conclusion is based on the assumption that 
 the properties are accurately represented by the characteristic 
 equation and that the specific heats are constant. As both 
 assumptions are approximate so also is the conclusion, as will 
 appear in the discussion of flow through a porous plug. 
 
 An interesting corollary of the discussion just given is that 
 an infinite isotherftial expansion gives an infinite amount of 
 work. Thus the area contained between the 
 axis OV (Fig. 27), the ordinate ah, and the 
 isothermal line aa extended without limit is 
 
 W = p,v^ log, — - ^^ . 
 
 \ 
 
 
 Fig. 27. 
 
64 PERFECT GASES 
 
 This may also be seen from the consideration that if heat be 
 continually applied, and all changed into work, there will be a 
 hmitless supply of work. 
 
 Adiabatic Lin«s. — During an adiabatic change — for exam- 
 ple, the expansion of a gas in a non-conducting cylinder — heat 
 is not communicated to, nor abstracted from, the gas; conse- 
 quently dQ in equations (70), (71), and (72) becomes zero. 
 
 From equation (72) 
 
 T T 
 
 o = dQ = c„ — dp + Cp — dv; 
 
 p V 
 
 ^dv __ _ dp 
 
 *' c^ V p ' 
 
 '-(#-'*(?)■ 
 
 The ratio — of the specific heats may be represented by ^c, and 
 the above equation may be written 
 
 (76) 
 
 v^p = v^^pi = const (77) 
 
 
 This is the adiabatic equation for a perfect gas which is most 
 frequently used. If adiabatic equations involving other varia- 
 bles, such as^i and Tj, are desired, they may be derived from 
 equation (76) by aid of the characteristic equation, which for 
 this purpose may be written 
 
 pv _ pjV^ 
 
 T ~ t/ 
 
 so that £1 _ vT^ 
 
 p" v,t' 
 
 Q'-^i--. ..... :.m 
 
 /. Tv^-^ = T.vr'' (79) 
 
ADIABATIC LINES 
 
 65 
 
 Or equations (78) and (79) may be deduced directly from 
 equation (70) as equations (76) and (77) were from equation 
 
 (72). 
 
 In like manner we may deduce from equation (71) 
 
 l-K l-K 
 
 Tp ' = T,p, ^ (80) 
 
 or we may derive it from equation (76). 
 To find the external work the equation 
 
 W = 
 
 / pdv 
 
 may be used after substituting for p from equation (77) 
 
 W 
 
 
 In Fig. 28 the area between the axis OV, p 
 the ordinate ba, and the adiabatic line aa ex- 
 tended without limit, becomes 
 
 W, 
 
 AC — I 
 
 \, 
 
 Fig. 28. 
 
 and not infinity, as is the case with the isothermal line. 
 
 Here, as with the calculation of external work during iso- 
 thermal expansion, specific volumes should be used when the 
 problem involves a unit of weight; but work may be calculated 
 for any given initial and final volumes without considering 
 whether they are specific volumes or not. The pressures are 
 always pounds on the square foot for the English system. 
 
 For example, the external work of adiabatic expansion from 
 3 cubic feet and 60 pounds pressure by the gauge to the volume 
 of 7 cubic feet is 
 
 W 
 
 ^ 74-7 X^i44 X 3 I ^ _ ^ly-- j ^ ^3^^^^ foot-pounds, 
 
66 PERFECT GASES 
 
 which is considerably less than the work for the corresponding 
 isothermal expansion. 
 
 Attention should be called to the fact that calculations by this 
 method are subject to a considerable error from the fact that 
 the denominator of the coefficient contains the term /c — i equal 
 to 0.405 ; if it be admitted that the last figure is uncertain to the 
 extent of two units, the error of calculation becomes half a per 
 cent. 
 
 Intrinsic Energy. — Since external work during an adiabatic 
 expansion is done at the expense of the intrinsic energy, the work 
 obtainable by an infinite expansion cannot be greater than the 
 intrinsic energy. If it be admitted that such an expansion 
 changes all of the intrinsic energy into external work we shall 
 have 
 
 E,^W, = -^^ (82) 
 
 fc — 1 
 
 which gives a ready way of calculating intrinsic energy. In 
 practice we always deal with differences of intrinsic energy, so 
 that even if there be a residual intrinsic energy after an infinite 
 adiabatic expansion the error of our method will be eliminated 
 from an equation having the form 
 
 E,-E,= 1^--^ ..... (83) 
 
 Exponential Equation. — The expansions and compressions 
 of air and other gases in practice are seldom exactly isothermal or 
 adiabatic; more commonly an actual operation is intermediate 
 between the two. It is convenient and usually sufficient to 
 represent such expansions by an exponential equation, 
 
 pv"" = p,v,- (84) 
 
 in which n has a value between unity and 1.405. The form of 
 integration, for external work is the same as for that of adiabatic 
 expansion, and the amount of external work is intermediate 
 between that for adiabatic and that for isothermal expansion. 
 
ENTROPY 
 
 67 
 
 Change of temperature during such an expansion may be 
 calculated by the equations 
 
 T,v--' ....... (85) 
 
 Tp ^ 
 
 l-n 
 
 (86) 
 
 which may be deduced from equation (84) by aid of the char- 
 acteristic equation ^ „„ 
 ^ pv = RT 
 
 as equation (79) is deduced from equation (76). 
 
 If it is desired to find the exponent of an equation representing 
 a curve passing through two points, as a^ and 6^2 
 (Fig. 29), we may proceed by taking logarithms 
 of both sides of the equation 
 
 giving 
 
 o 7. 
 
 so that 
 
 n log v^ +log p^ = n log v^ + log p^, 
 los: p^ — log p^ 
 
 Fig. 29. 
 
 n = :-— r— (87) 
 
 log V, - log V, 
 
 For example, the exponent of an equation to a curve passing 
 through the points 
 
 Pi = 74-7. "^1 = 3y and p^ = 30, v^ = 7, 
 
 is log 74.7 — log so 
 
 n = 7 ^^ ^ , ^ ^ = 1. 104. 
 
 log 7 — log 3 
 
 It should be noted that as n approaches unity the probable 
 
 error of calculation of external work is liable to be very large. 
 
 Entropy. — For anv reversible process 
 
 - ' # = f; 
 
 consequently from equations (70), (71), and (72) we have 
 d(t> 
 
 dt , . 
 
 . dv 
 
 Cv) > 
 
 V 
 
 d(t> 
 
 dt 
 
 (^p-i^ + {^v — Cp) -f ' 
 
 T p 
 
 d<p = c^ -j- + Cp — ; 
 p V 
 
68 PERFECT GASES 
 
 and, integrating between limits, 
 
 </>,-(/>, = c, log,^ + {c^ - c,) log, -^ . . (88) 
 
 *2 - *i = Cp loge =r- + (S - (^v) log, ^' . . (89) 
 
 J- 1 ^2 
 
 j) V 
 
 ^■l — ^l- Cv loge r + ^P log« -"•••• (90) 
 
 Pi -- - V 
 
 which give ready means of calculating changes of entropy. 
 These equations give the entropy changes per pound, and are to 
 be multiplied by the weight in pounds to give the change for 
 the actual conditions. 
 
 For example^ the change of entropy in passing from the pres- 
 sure of 74.7 pounds absolute per square inch and the volume 
 of 3 cubic feet to the pressure of 30 pounds absolute and the 
 volume of 7 cubic feet is 
 
 <f>2 — <Pi = — ^^ loge -"^— + 0.2375 loge - = 0.0454. 
 1.405 74.7 3 
 
 Since the pressures form the numerator and denominator of 
 a fraction, there is no necessity to reduce them to the square 
 foot. In this problem the pressures and volumes are taken at 
 random; they correspond to a temperature of 146° F., at the 
 initial condition. As has already been said, there is seldom 
 occasion in practice for using the entropy of a gas. 
 
 Comparison of the Air-Thermometer with the Absolute Scale. 
 — In connection with the isodynamic line it was shown that the 
 intrinsic energy is a function of the temperature only. This 
 conclusion is deduced from the characteristic equation on the 
 assumption that the scale of the air-thermometer coincides with 
 the thermodynamic scale, and it affords a delicate method of 
 testing the truth of the characteristic equation, and of comparing 
 the two scales. 
 
COMPARISON OF THE AIR THERMOMETER 69 
 
 The most complete experiments for this purpose were made 
 by Joule and Lord Kelvin, who forced air slowly through a porous 
 plug in a tube in such a manner that no heat was transmitted 
 to or from the air during the process. Also the velocity both 
 before and beyond the plug was so small that the work due to 
 the change of velocity could be disregarded. All the work that 
 would be developed in free expansion from the higher to the 
 lower pressure was used in overcoming the resistance of friction 
 in the plug, and so converted into heat, and as none of this heat 
 escaped it was retained by the air itself, the plug remaining at a 
 constant temperature. It therefore appears that the intrinsic 
 energy remained the same, and that a change of temperature 
 indicated a de^dation from the assumptions of the theory of 
 perfect gases. 
 
 In the discussion of results given by Joule and Lord Kelvin* 
 in 1854 they gave for the absolute temperature of freezing-point 
 273°. 7 C. As the result of later experiments t they stated that 
 the cooling for a difference of pressure of 100 inches of mercury 
 was represented on the centigrade scale by 
 
 o.°93 {^) 
 
 ' From these experiments and from other considerations con- 
 cerning the constant-volume hydrogen thermometer. Professor 
 Callendar has determined that the most probable value for the 
 absolute temperature of freezing-point is 273°.! C, as already 
 given, and gives a table of corrections to the hydrogen ther- 
 mometer to obtain temperatures on the absolute scale. As 
 the correction at any temperature between — 200° and + 450° 
 C. is not more than t^tf of a degree this is interesting mainly 
 to physicists. The corrections for the air-thermometer at con- 
 stant pressure are somewhat larger, but approach tV of a degree 
 only at 300° C. 
 
 * Phil. Trans, vol. cxliv, p. 349, 
 t Ihid. vol. clii, p. 579. 
 
70 
 
 PERFECT GASES 
 
 Deviation from Boyle's Law. — Early experiments on the 
 permanent gases (as they were then known) indicated that 
 there were small deviations evident to a physicist, but not of 
 importance to engineers; but now that air is compressed to 
 pressures as high as 2500 pounds per square inch, it becomes 
 necessary to take account of such deviations in engineering 
 practice. 
 
 Perhaps the best conception of this subject, and of the four 
 recognized states of fluids, can be had from a consideration of 
 Andrews' * experiments, which for the present purpose are con- 
 veniently represented by his isothermal curves, which are repro- 
 duced in Fig. 29a, together with the curves for air. The latter 
 are approximate hyperbolae referred to the proper axes, that 
 for zero pressure being nearly the whole height of the diagram 
 below the figure as it is drawn. At 48°.! C, the isothermal for 
 carbonic acid shows a marked deviation from the hyperbola, as 
 may be seen by comparison with the curves for air, or better 
 from the fact that a rectangular hyperbola through P will pass 
 through Q. On the other hand, the isothermal for 13°.! resem- 
 bles that for steam, which is commonly known as a saturated 
 vapor whose pressure is constant at constant 
 temperature; the horizontal part of this line 
 represents a mixture of liquid and vapor 
 which at the left runs into the liquid curve, 
 and as liquid carbonic acid has considerable 
 compressibility, this curve becomes a straight 
 line with an appreciable inclination to the 
 axis of zero volume. At the right, the iso- 
 thermal shows a decided break and slopes 
 away as the volume becomes larger than 
 that of the saturated vapor. The isothermal 
 for 21°. 5 shows similar characteristics, but 
 the passages from one condition to another are more gradual. 
 The dotted curve is drawn through the points of saturation and 
 liquefaction, and its crest corresponds to the critical temperature. 
 
 * Phil. Trans., 1869, part ii, p. 575, and 1876, part ii, p. 421. 
 
 LOO- 
 95- 
 
 90- 
 85- 
 80 
 ffS- 
 70' 
 6S 
 60 
 '55- 
 
 Fig. 29a. 
 
DENSITY AT HIGH PRESSURE 71 
 
 The isothermal for 31.°! is clearly above the critical tempera- 
 ture and does not indicate a liquefaction. 
 
 The several states of a fluid may be enumerated as 
 
 1 . Liquid. 
 
 2. Saturated vapor, including mixtures of liquid and vapor. 
 
 3. Superheated vapor characterized by a larger volume than 
 
 saturated vapor for a given temperature and pressure. 
 
 4. Gas; near the critical temperature the deviations from 
 
 Boyle's law are very large, at higher temperature the 
 deviations diminish and become unimportant. 
 Critical Temperatures. — The foUov^ing table of critical 
 temperatures and of boiling-points at atmospheric pressure is 
 taken in part from Preston's " Theory of Heat," 1904. 
 
 Boiling-Point. Critical Temperature. 
 
 Hydrogen . -252.^7 C. -234.°5 C. 
 
 Nitrogen —194.4 —146 
 
 Oxygen —182.2 — 118.8 
 
 Air —1 91. 4 —140 
 
 Carbon monoxide ....... — 190 —139.5 
 
 Carbon dioxide —78.3 +31 -35 
 
 Sulphur dioxide —10 -hi 57.0 
 
 Ether 34.5 175 
 
 Alcohol 78.4 248 
 
 Carbon bisulphide 43.3 254 
 
 Water 100 362 
 
 Density at High Pressure. — If the usual methods (given on 
 page 58) for the solution of problems involving the properties 
 of gases, are applied v^ith very high pressure, errors amounting 
 to two or three per cent are liable to be incurred, owing to the 
 deviation from Boyle's law. In some cases, this error may be 
 ignored in engineering practice; in some cases the error may be 
 included in a practical factor, as will be indicated in the design of 
 air compressors; and in other cases allowances must be made 
 from the experimental information furnished by Armagat, and 
 which may be found in Landolt and Bornstein's Tables. 
 
72 
 
 PERFECT GASES 
 
 Rontgen's Experiments. — Direct experiments to determine 
 K may be made as follows. Suppose that a vessel is filled with 
 air at a pressure p^, while the pressure of the atmosphere is pa. 
 Let a communication be opened with the atmosphere sufficient 
 to suddenly equalize the pressure; then let it be closed, and let 
 the pressure p^ be observed after the air has again attained the 
 temperature of the atmosphere. If the first operation is suffi- 
 ciently rapid it may be assumed to be adiabatic, and we may 
 use equation (77), from which 
 
 ^^ \ogp,-\ogPa 
 
 log Va - log V^ 
 
 The second operation is at constant volume; consequently 
 the specific volume is the same at the final state as after the 
 adiabatic expansion of the first operation. But the initial and 
 final temperatures are the same; consequently 
 
 .-. log v^ — log V, = log Pi — log />2, 
 which substituted in equation (91) gives 
 
 ^ ^ log^^-logi, 
 
 log p, - log p, ^^ ^ 
 
 The same experiment may be made by rarefying the air in 
 the vessel, in which case the sign of the second term changes. 
 
 Rbntgen* employed this method, using a vessel containing 
 70 htres, and measuring the pressure with a gauge made on 
 the same principle as the aneroid barometer. Instead of assum- 
 ing the pressure pa at the instant of closing the stop- cock to be 
 that of the atmosphere, he measured it with the same instrument. 
 A mean of ten experiments on air gave 
 
 /c = 1.4053. 
 
 * Poggendorff's Annalin, vol. cxlviii, p. 580. 
 
EXAMPLES 73 
 
 EXAMPLES. 
 
 1. Find the weight of 4 cubic metres of hydrogen at 30° C, 
 and under the pressure of 800 mm. of mercury. Ans. 0.341 kg. 
 
 2. Find the volume of 3 pounds of nitrogen at a pressure of 
 45 pounds to the square inch by the gauge and at 80° F. Ans. 
 11.05. 
 
 3. Find the temperature at which one kilogram of air will 
 occupy one cubic metre when at a pressure of 20,000 kilograms 
 per square metre. Ans. 410° C. 
 
 4. Oxygen and hydrogen are. to be stored in tanks 10 inches 
 in diameter and 35 inches long. At a maximum temperature 
 of 110° F., the pressure must not exceed 250 pounds gauge. 
 What weight of oxygen can be stored in one tank? What of 
 hydrogen? Ans. Oxygen 2.21 pounds. Hydrogen 0.138 pound. 
 
 5. A balloon of 12,000 cubic feet capacity, weighing with car, 
 occupant, etc., 665 pounds, is inflated with 9500 cubic feet 
 hydrogen at 60° F., the barometer reading 30 inches. Find 
 the weight of the hydrogen and the pull on the anchor rope; 
 find also the amount that the balloon must be lightened to reach 
 a height where the barometer reads 20 inches, and the tempera- 
 ture is 10° below zero Fahrenheit. Ans. Weight hydrogen 
 50.4 pounds; pull on rope 12 pounds; balloon lightened 7.5 
 pounds. 
 
 6. A gas-receiver holds 14 ounces of nitrogen at 20° C, and 
 under a pressure of 29.6 inches of mercury. How many will it 
 hold at 32° F., and at the normal pressure of 760 mm.? Ans. 
 15.18 ounces. 
 
 7. A gas- receiver having the volume of 3 cubic feet contains 
 half a pound of oxygen at 70° F. What is the pressure ? Ans. 
 29.6 pounds per square inch. 
 
 8. Two cubic feet of air expand at 50° F. from a pressure 
 of 80 pounds to a pressure of 60 pounds by the gauge. What 
 is the external work? Ans. 6464 foot-pounds. 
 
 9. What would have been the external work had the air 
 expanded adiabatically ? Ans. 4450 foot-pounds. 
 
74 PERFECT GASES 
 
 10. Find the external work of 2 pounds of air which expand 
 adiabatically until the volume is doubled, the initial pressure 
 being 100 pounds absolute and the initial temperature 100° F. 
 Ans. 36,100 foot-pounds. 
 
 11. Find the external work of one kilogram of hydrogen, 
 which, starting with the pressure of 4 atmospheres and with the 
 temperature of 500° C, expands adiabatically till the tempera- 
 ture becomes 30° C. Ans. 489,000 m.-kg. 
 
 12. Find the exponent for an exponential curve passing 
 through the points ^ = 30, v = 1.9, and ^1 = 15, Vi = 9.6. 
 Ans. 0.4279. 
 
 13. Find the exponent for a curve to pass through the points 
 p = 40, V = 2y and pi = 12, Vi = 6. Ans. 1.0959. 
 
 14. In examples 12 and 13 let ^ be the pressure in pounds on 
 the square inch smdv the volume in cubic feet. Find the external 
 work of expansion in each case. Ans. 21,900 and 12,010 foot- 
 pounds. 
 
 15. Find the intrinsic energy of one pound of nitrogen under 
 the standard pressure of one atmosphere and at freezing-point 
 of water. Ans. 66,500 foot-pounds. 
 
 16. A cubic foot of air at 492.7° F. exerts 14.7 pounds gauge 
 pressure per square inch. How much do its internal energy and 
 its entropy exceed those of the same air under standard condi- 
 tions? Ans. 5052 foot-pounds; .00912 units of entropy. 
 
 17. Find the increase in entropy of 2 pounds of a perfect gas 
 during isothermal expansion at 100° F. from an initial pressure 
 of 84.3 pounds gauge and a volume of 20 cubic feet to a final 
 volume of 40 cubic feet. Ans. 0.453. 
 
 18. A kilogram of oxygen at the pressure of 6 atmospheres 
 and at 100° C. expands isothermally till it doubles its volume. 
 Find the change of entropy. Ans. 0.0434. 
 
 19. Twenty pounds of air are heated at a constant pressure 
 of 200 pounds absolute per square inch until the volume increases 
 from 20 cubic feet to 40 cubic feet. Find the initial and final 
 temperatures, the change in internal energy and the increase in 
 entropy. How much heat is added? Ans. 80° and 620°; 
 
EXAMPLES 
 
 75 
 
 increase of intrinsic energy 1,420,000 foot-pounds; increase in 
 entropy 3.29; heat 2570 b.t.u. 
 
 20. Suppose a hot-air engine, in which the maximum pressure 
 is 100 pounds absolute, and the maximum temperature is 600° F., 
 to work on a Carnot cycle. Let the initial volume be 2 cubic 
 feet, let the volume after isothermal expansion be 5 cubic feet, 
 and the volume after adiabatic expansion be 8 cubic feet. Find 
 the horse-power if the engine is double-acting and makes 30 
 revolutions per minute. Ans. 8.3 horse-power. 
 
CHAPTER VI. 
 
 SATURATED VAPOR. 
 
 For engineering purposes steam is generated in a boiler which 
 is partially filled with water, and arranged to receive heat from 
 the fire in the furnace. The ebullition is usually energetic, and 
 more or less water is mingled with the steam; but if there is a 
 fair allowance of steam space over the water, and if proper 
 arrangements are provided for with drawing the steam, it will 
 be found when tested to contain a small amount of water, usu- 
 ally between half a per cent and a per cent and a half. Steam 
 which contains a considerable percentage of water is passed 
 through a separator which removes almost all the water. Such 
 steam is considered to be approximately dry. 
 
 If the steam is quite free from water it is said to be dry and 
 saturated; steam from a boiler with a large steam space and 
 which is making steam very slowly is nearly if not quite dry. 
 
 Steam which is withdrawn from the boiler may be heated to a 
 higher temperature than that found in the boiler, and is then said 
 to be superheated. 
 
 Our knowledge of the properties of saturated steam and other 
 vapors is due mainly to the experiments of Regnault,* who 
 determined the relations of the temperature and pressure, the 
 total heat of vaporization, and the heat of the Uquid for many 
 volatile liquids. Since his time, Rowland's determination of 
 the mechanical equivalent of heat, gave a more exact determi- 
 nation of the specific heat of water at low temperatures, and 
 recently Dr. Barnes has given a very precise determination of 
 that property for water. Again, certain work by Knoblauch, 
 Linde, and Klebe, has given us a good knowledge of the properties 
 
 * Memoires de VlnstitiU de France, etc., tome xxvi. 
 76 
 
PRESSURE OF SATURATED VAPORS 77 
 
 of superheated steam which can be extended to give the specific 
 volume of saturated steam over a considerable range of temper- 
 ature. At the time when the first edition of this work was pre- 
 pared it appeared desirable to compute tables of the properties 
 of saturated vapor, taking advantage of Rowland's work, 
 and eliminating some uncertainties due to the way in which 
 Regnault used his empirical equations in computating tables. 
 As all this involved changes of sufficient magnitude to influence 
 engineering computations, it seemed necessary to quote the 
 original data at length and to give computations in detail. This 
 introduction to the chapter on saturated vapors was found to be 
 somewhat confusing to students reading it for the first time, and 
 since the main points are now commonly accepted, this work is 
 given only in the introduction to the " Tables of the Properties of 
 Saturated Steam," the reason for printing it being that it is not 
 given elsewhere, as the earlier editions have passed out of print. 
 
 Recent correction of the absolute temperature of the freezing- 
 point of water by Callendar and the determination of the specific 
 heat of water by Barnes make it necessary to recompute the 
 " Tables of the Properties of Saturated Steam " which are 
 intended to accompany this book, and opportunity is taken to 
 introduce further data in those tables, and in addition a table 
 has been prepared which will be found to greatly facilitate calcu- 
 lations of adiabatic changes of steam and water. 
 
 Pressure of Saturated Vapors. — Regnault expressed the 
 results of his experiments on the temperature and pressure of 
 saturated vapors in the form of the following empirical equation, 
 
 \ogp= a + 6a:" + c/r (94) 
 
 where p is the pressure, n is the temperature minus the temper- 
 ature to of the lowest Hmit of the range of temperature to which 
 the equation appHes, i.e., 
 
 n = t — Iq. 
 
 The constants for the above equation as apphed to saturated 
 steam have been recomputed and reduced to the latitude of 45°, 
 and are as follow: 
 
78 SATURATED VAPOR 
 
 B. For steam from o° to ioo° C. expressing the pressure in 
 mm. of mercury, 
 
 log ^ = a — Ja" + c/?" 
 
 « = 4-7395022 
 log b = 0.6117400 
 log c — 8.13204 — 10 
 log a = 9.996725828 — 10 
 log ^ = 0.0068641 
 
 C. For steam from 100° to 220° C. expressing the pressure in 
 mm, of mercury, 
 
 «= 5-4575701 
 
 log h = 0.41 2002 1 
 log c = 7.7416789 — 10 
 log a = 9. 99741 1 296 — 10 
 
 log ^ = 0.007641 801 ' 
 
 n ^ t ~ 100 
 
 B^. For steam from 32° to 212° F. in pounds per square inch, 
 
 a = 3.025906 
 log h = 0.61 1 7400 
 log c = 8.13204 — 10 
 logo: = 9.998181015 — 10 
 log/? = 0.0038134 
 
 w = i — 32 
 
 Cj. For steam from 212° to 428° F. in pounds per square 
 inch, 
 
 « = 3-743976 
 
 log h = 0.4120021 
 log c = 7.74168 — 10 
 log a = 9.998561831 — 10 
 log/? = 0.0042454 
 n = t — 212 
 
 Pressure of Other Vapors. — Regnault determined also the 
 pressure of a large number of saturated vapors at various tem- 
 peratures, and deduced equations for each in the form of equa- 
 tion (94). The equations and the constants as determined by 
 him for the commoner vapors are given in the following table: 
 
DIFFERENTIAL COEFFICIENT 
 
 79 
 
 
 log/ 
 
 a 
 
 h 
 
 c 
 
 Alcohol ....... 
 
 Ether . 
 
 Chloroform ...... 
 
 Carbon bisulphide . . 
 Carbon tetrachloride 
 
 a + &a~ - c/^^ 
 a - fttt" - c^" 
 a - ha"" - c^l 
 
 a — ban — c^8 
 
 5.4562028 
 5.0286298 
 5.2253893 
 5. 401 I 662 
 12.0962331 
 
 4.9809960 
 0.0002284 
 2.9531281 
 3.4405663 
 9.1375180 
 
 0.0485397 
 3.1906390 
 0.0668673 
 0.2857386 
 1.9674890 
 
 Alcohol 
 
 Ether 
 
 Chloroform. » . . , 
 Carbon bisulphide . 
 Carbon tetrachloride 
 
 log, 
 
 1-99708557 
 
 H"°i45775 
 1.9974144 
 T. 9977628 
 T. 9997120 
 
 log/3 
 
 1.9409485 
 1.996877 
 1.9868176 
 T. 991 1997 
 1.9949780 
 
 fl 
 
 
 t + 
 
 20 
 
 ^ + 
 
 20 
 
 t - 
 
 20 
 
 t + 
 
 20 
 
 t + 
 
 20 
 
 - 20°, + 150° c. 
 
 - 20°, + 120° c. 
 + 20°, + 164° c. 
 
 - 20°, + 140° c. 
 
 - 20°, + 188° c. 
 
 Zeuner * states that there is a sHght error in Regnault 's cal- 
 culation of the constants for aceton, and gives instead 
 
 log p = a ~ ba^ + c/?"; 
 
 « = 5-3085419; 
 log &«** = +0.5312766—0.0026148^; 
 logc/?''^ —0.9645222 — 0.0215592 i. 
 
 dp 
 Differential Coefficient —-. — From the general form of 
 
 equation (94) we have 
 
 M M M 
 
 (95) 
 
 M being the modulus of the common system of logarithms. 
 Differentiating, 
 
 ^^ = ^Mog.a.«»+i-clog.^./r; 
 or, reducing to common logarithms, 
 
 ^?=i^'''"8"-«'' + ^^i°s^-^= 
 
 l_dp_ 
 p dt 
 
 i_dp 
 p dt 
 
 M' 
 
 = Aa"" + 5/?^ 
 
 * Mechanische Warmetheorie. 
 
So SATURATED VAPOR 
 
 The constants to be used with equation (95) are: 
 
 French Units. 
 
 B. For o^ to 100° C, mm. of mercury, 
 
 log^ = 8.8512729 — 10; 
 logB = 6,69305 - 10; 
 log a, = 9.996725828 - 10; 
 
 log /?! = 0.0068641. 
 
 C. For 100° to 220° C, mm. of mercury, 
 
 log^ = 8.5495158 - 10; 
 log B = 6.34931 - 10; 
 log a, = 9. 99741 1296 — 10; 
 log P 1= 0.0076418. 
 
 English Units. 
 
 B,. For 32° to 212° F., pounds on the square inch, 
 log .4 = 8.5960005 — 10; 
 log B = 6,43778 — 10; 
 log ttg = 9.998181015 — 10; 
 log ^2 = 0.0038134, 
 
 Cj. For 212° to 428° F., pounds on the square inch, 
 
 log^ = 8.2942434 — 10; 
 log B = 0,09403 — 10; 
 log a^ = 9. 99856183 1 — 10; 
 log ^2 = 0.0042454. 
 
 It is to be remarked that -~ may be found approximately 
 
 at 
 
 by dividing a small difference of pressure by the corresponding 
 
 difference of temperature; that is, by calculating --. With a 
 
 table for even degrees of temperature we may calculate the 
 value approximately for a given temperature by dividing the 
 difference of the pressures corresponding to the next higher and 
 the next lower degrees by two. 
 
 The following table of constants for the several vapors named 
 were calculated by Zeuner from the preceding equations for 
 temperature and pressure of the same vapors: 
 
MECHANICAL EQUIVALENT OF HEAT 
 
 8l 
 
 DIFFERENTIAL COEFFICIENT 
 
 p dt 
 
 
 Sign. 
 
 log (^a") 
 
 log {B^"^) 
 
 
 yla" 
 
 5^" 
 
 
 Alcohol 
 
 Ether 
 
 + 
 + 
 4- 
 + 
 + 
 + 
 
 + 
 
 + 
 
 + 
 
 — 1. 1720041 — 0.0029143/ 
 
 — 1.3396624 — 0.0031223/ 
 
 — 1.3410130—0.0025856/ 
 
 - 1.4339778-0.0022372/ 
 
 - 1.8611078-0.0002880/ 
 
 - 1.3268535-0.0026148/ 
 
 — 2.9992701 — 0590515 t 
 
 — 4.4616396+0.0145775 / 
 
 Chloroform 
 
 Carbon bisulphide . . . 
 Carbon tetrachloride . . 
 Aceton ....... 
 
 — 2.0667124—0.0131824/ 
 
 — 2.0511078—0.0088003/ 
 
 — 1.3812195—0.0050220/ 
 
 — 1.9064582— 0.0215592 / 
 
 Standard Temperature. — It is customary to refer all calcu- 
 lations for gases to the standard conditions of the pressure of 
 the atmosphere (760 mm. of mercury) and to the freezing-point 
 of water. Formerly the freezing-point was taken as the standard 
 temperature for water and steam as even now it is the initial point 
 for tables of the properties of saturated vapors. But the investi- 
 gation of the mechanical equivalent of heat by Rowland resulted 
 in a determination of the specific heat of water with much greater 
 delicacy than is possible by Regnault ^s method of mixtures, and 
 showed that freezing-point is not well adapted for the standard 
 temperature for water. It has been the habit of physicists 
 for many years to take 15° C. as the standard temperature, 
 and this corresponds substantially with 62° F., at which the 
 English units of measure are standard. Professor Callendar 
 recommends 20° C. as the standard temperature which would 
 make a variation of about toVo in the value of the mechanical 
 equivalent of heat and in the specific heat of water. 
 
 Mechanical Equivalent of Heat. — The most authoritative 
 determination of the mechanical equivalent of heat appears to be 
 that by Rowland,* from which the work required to raise the 
 temperature of one pound of water from 62° to 63° F. is 
 
 778 foot-pounds. 
 
 This is equivalent to 
 
 427 metre kilograms 
 
 in the metric system. Since his experiments were made this 
 important physical constant has been investigated by several 
 
 * Proc. Am. Acad., vol. xv (N. S. vii), 1879. 
 
82 SATURATED VAPOR 
 
 experimenters, and also a recomputation of his results has been 
 made after a recomparison of his thermometers. The conclu- 
 sion appears to be that his results may be a little small, but the 
 differences are not important, and it is not certain that the con- 
 clusion is valid. There seems, therefore, no sufficient reason for 
 changing the accepted values given above. 
 
 Heat of the Liquid. — The most reliable determination of the 
 specific heat of water is that by Dr. Barnes,* v^ho used an electrical 
 method devised by Professor Callendar and himself, and who 
 extended the method to and below freezing-point by carefully 
 coohng water without the formation of ice, to — 5° C. This 
 method gives relative results with great refinement, and gives also 
 a good confirmation of Rowland 's determination of the mechan- 
 ical equivalent of heat. Dr. Barnes reports values of the specific 
 heat of water up to 95° C. In the following table his results are 
 quoted from 0° to 55° C.; from 55° to 95° his results have been 
 slightly increased to join with results determined by recomput- 
 ing Regnault's experiments on the heat of the liquid for water 
 (which experiments range from 110° C. to 180° C.) by allowing 
 for the true specific heat at low temperature from Dr. Barnes's 
 experiments. The maximum effect of modifying Dr. Barnes's 
 results is to increase the heat of the liquid at 95° by one- tenth of 
 one per cent» 
 
 SPECIFIC HEAT OF [WATER. 
 
 Temperature. 
 
 
 Temperature. 
 
 
 Temperature. 
 
 
 
 
 Specific 
 Heat. 
 
 
 
 Specific 
 Heat. 
 
 
 
 Specific 
 Heat. 
 
 
 
 
 
 
 
 C. 
 
 F. 
 
 
 C. 
 
 F. 
 
 
 C. 
 
 F. 
 
 
 
 
 32 
 
 I . 0094 
 
 45 
 
 113 
 
 0.99760 
 
 90 
 
 194 
 
 I . 00705 
 
 5 
 
 41 
 
 1.00530 
 
 50 
 
 122 
 
 . 99800 
 
 95 
 
 203 
 
 1.00855 
 
 10 
 
 50 
 
 1.00230 
 
 55 
 
 131 
 
 0.99850 
 
 100 
 
 212 
 
 I.OIOIO 
 
 15 
 
 59 
 
 I . 00030 
 
 60 
 
 140 
 
 0.99940 
 
 120 
 
 248 
 
 I. 01620 
 
 20 
 
 68 
 
 0.99895 
 
 ^5 
 
 149 
 
 I . 00040 
 
 140 
 
 284 
 
 1.02230 
 
 25 
 
 77 
 
 0.99806 
 
 70 
 
 i5« 
 
 I. 001 50 
 
 160 
 
 320 
 
 1.02850 
 
 30 
 
 86 
 
 0-99759 
 
 l^ 
 
 167 
 
 1.00275 
 
 180 
 
 35b 
 
 1.03475 
 
 35 
 
 95 
 
 o- 99735 
 
 80 
 
 176 
 
 I. 00415 
 
 200 
 
 392 
 
 I. 04100 
 
 40 
 
 104 
 
 o- 99735 
 
 «5 
 
 185 
 
 I « 0055 7 
 
 220 
 
 428 
 
 1.04760 
 
 * Physical Review, vol. xv, p. 71, 1902. 
 
HEAT OF THE LIQUID 83 
 
 Heat of the Liquid. — The heat required to raise one unit of 
 
 weight of any Hquid from freezing-point to a given temperature 
 
 is called the heat of the liquid at that temperature; and also at the 
 
 corresponding pressure. Since the specific heat for water varies 
 
 we may obtain the heat of the liquid by integration as indicated 
 
 by the equation n 
 
 q = \ cdt (96) 
 
 In order to use this equation it would be necessary to obtain 
 an empirical equation connecting the specific heat with the 
 temperature; such an equation has not been proposed and would 
 probably be complex. -Another method is to draw a curve with 
 temperatures as abscissae and specific heats as ordinates and inte- 
 grate graphically. The fact that the specific heat is nearly 
 equal to unity at all temperatures and that consequently the heat 
 of the liquid for the Centigrade thermometer is not very different 
 from the temperature suggests the following method : 
 
 Let c = 1 -{- k 
 
 when k is the difference between the specific heat and unity at 
 any temperature, k being positive or negative as the case may be. 
 
 ^^^^ q = t +Jkdt (97) 
 
 which may be obtained by plotting values of k as ordinates and 
 integrating graphically, which will have the advantage that the 
 required curve may be drawn to a large scale and give correspond- 
 ingly accurate results. The values for the heat of the liquid for 
 water in the " Tables of the Properties of Saturated Steam " were 
 obtained in this way. 
 
 The following table gives equations for the heats of the liquids 
 of other substances than water, determined by Regnault. 
 
 HEAT OF THE LIQUID. 
 
 Alcohol ,.,... o , q= 0.54754^-1- 0.0011218/2 
 
 -|- 0.000002206/^ 
 Ether .. = ,,....,...., ^ = 0.52901 /-(- 0.0002959/^ 
 
 Chloroform q= 0.23235/-}- 0.0000507/^ 
 
 Carbon bisulphide .,.,.„..,$= 0.23523 /-f 0.0000815/^ 
 
 Carbon tetrachloride ^ = o. 19798 / 4- 0.0000906 /^ 
 
 Aceton c q = 0.50643/4- 0.0003965/^ 
 
84 SATURATED VAPOR 
 
 The specific heat for any of these Hquids may be obtained by 
 differentiation; for example, the specific heat for alcohol is 
 
 c = 0.54754 + 0.0022436 / + 0.000006618 f^ 
 
 Total Heat. — This term is defined as the heat required to 
 raise a unit of weight of water from freezing-point to a given 
 temperature, and to entirely evaporate it at that temperature. 
 The experiments made by Regnault were in the reverse order; 
 that is, steam was led from a boiler into the calorimeter and 
 there condensed. Knowing the initial and final weights of 
 the calorimeter, the temperature of the steam, and the initial 
 and final temperatures of the water in the calorimeter, he was 
 able, after applying the necessary corrections, to calculate the 
 total heats for the several experiments. 
 
 The results from these experiments are represented by the 
 following equations: 
 
 For the metric system, 
 
 H = 606.5 + 0.305 t (98) 
 
 For the English system, 
 
 H = 1091.7 + 0.305 (/ — 32) : . . (99) 
 
 An investigation of the original experimental results, 
 allowing for the true specific heat of the water in the calorimeter, 
 showed that the probable errors of the method of determining 
 the total heat were larger than the deviations of the true specific 
 heats from unity, the value assumed by Regnault; and, further, 
 it appeared that his equation represents our best knowledge of 
 the total heat of steam. There appears to be no reason for 
 changing this equation till new experimental values shall be 
 supplied. The deviation of individual experimental results 
 from corresponding computations by the equation is Kkely to be 
 one in five hundred. There is further some uncertainty whether 
 the method of drawing steam from the boiler did not involve 
 some error due to entrained moisture. The best check upon 
 Regnault 's results is a comparison with Knoblauch's work on 
 superheated steam. 
 
SPECIFIC VOLUME OF LIQUIDS 85 
 
 Regnault gives the equations following for other liquids; 
 
 Ether H = 94 +0.45/ - 0.00055556 f^ 
 
 Chloroform il = 67 + 0.1375^ 
 
 Carbon bisulphide H= 90 + o. 14601 «— 0.0004123 /^ 
 
 Carbon tetrachloride H = 52 + 0.14625 f — 0.000172 ^^ 
 
 Aceton il = 140.5 + 0.36644 ^ — 0.000516 /^ 
 
 Heat of Vaporization. — If the heat of the liquid be sub- 
 tracted from the total heat, the remainder is called the heat of 
 vaporization, and is represented by r, so that 
 
 r = H — q . (100) 
 
 Specific Volume of Liquids. — The coefficient of expansion of 
 most liquids is large as compared with that of solids, but it is 
 small as compared with that of gases or vapors. Again, the 
 specific volume of a vapor is large compared with that of the 
 liquid from which it is formed. Consequently the error of neg- 
 lecting the increase of volume of a liquid with the rise of temper- 
 ature is small in equations relating to the thermodynamics of a 
 saturated vapor, or of a mixture of a liquid and its vapor when 
 a considerable part by weight of the mixture is vapor. It is 
 therefore customary to consider the specific volume of a liquid 
 cr to be constant. 
 
 The following table gives the specific gravities and specific 
 volumes of liquids: 
 
 SPECIFIC GRAVITIES AND SPECIFIC VOLUMES OF LIQUIDS. 
 
 Alcohol 
 
 Ether . 
 
 Chloroform ... 
 Carbon bisulphide . 
 Carbon tetrachloride 
 
 Aceton 
 
 Sulphur dioxide . 
 
 Ammonia 
 
 Water 
 
 Specific 
 Gravity 
 compared 
 with Water 
 at 4° C. 
 
 0.80625 
 0.736 
 
 1-527 
 I . 2922 
 1.6320 
 0.81 
 
 T.4336 
 0.6364 
 I 
 
 Specific Volume. 
 
 Cubic Metres. Cubic Feet 
 
 o 001240 
 o 001350 
 0.000655 
 o 000774 
 0.00613 
 0.00123 
 0.0006981 
 O.OOI57I 
 
 O.OOI 
 
 O.OII2 
 0.0252 
 0.01602 
 
86 
 
 SATURATED VAPOR 
 
 Experiments were made by Hirn* to determine the volumes 
 of liquid at high temperatures compared with the volume at 
 freezing-point, by a method which was essentially to use them 
 for the expansive substance of a thermometer. The results are 
 given in the following equations: 
 
 SPECIFIC VOLUMES OF HOT LIQUIDS. 
 
 Water, 
 
 ioo° C. to 200° C. 
 
 (Vol. at 4° = unity.) 
 
 Alcohol, 
 
 30° C. to 160° C. 
 
 (Vol. at 0° = unity.) 
 
 Ether, 
 
 30° C. to 130° C. 
 
 (Vol. at 0° = unity.) 
 
 Carbon Bisulphide, 
 
 30° C. to 160° C. 
 
 (Vol. at 0° = unity.) 
 
 Carbon Tetrachloride, 
 
 30° C. to 160° C. 
 (Vol. at 0° = unity.) 
 
 V = I -{- 0.00010867875 t 
 
 + 0.0000030073653 f^ 
 + 0.000000028730422 t^ 
 
 — 0.0000000000066457031 t' 
 
 V — 1 -\- 0.00073892265 t 
 
 + 0.00001055235 1^ 
 
 — 0.000000092480842 t^ 
 
 + 0.00000000040413567 f* 
 
 V = I + 0,0013489059 t 
 
 + 0.0000065537/^ 
 
 — 0.000000034490756 <^ 
 + 0.00000000033772062 t* 
 
 •y = I + 0.0011680559/ 
 
 + 0.0000016489598/' 
 
 — 0.0000000008 1 1 19062 t^ 
 + 0.000000000060946589/* 
 
 V = I + 0.0010671883 / 
 
 + 0.0000035651378/' 
 
 — 0.00000001494928 1 /^ 
 
 + o . 000000000085 182318/* 
 
 Logarithms. 
 
 6.0361445 - 10 
 4.4781862 — 10 
 
 1. 4583419 - 10 
 8.8225409 — 20 
 
 6.8685991 — 10 
 3.0233492 - 10 
 2.9660517 — 10 
 0.6065278 — 10 
 
 7.1299817 — 10 
 4.8164866 — 10 
 2.5377028 - 10 
 0-5285571 - 10 
 
 7.0674636 — 10 
 4.2172103 — 10 
 0.9091229 — 10 
 9.7849494 - 20 
 
 7.0282409 — 10 
 4-5520763 - 10 
 2. 174620^ — 10 
 9-9303494 - 20 
 
 Quality or Dryness Factor. — All the properties of saturated 
 steam, such as pressure, volume and heat of vaporization, depend 
 on the temperature only, and are determinable either by direct 
 experiment or by computation, and are commonly taken from 
 tables calculated for the purpose. 
 
 Many of the problems met in engineering deal with mixtures of 
 liquid and vapor, such as water and steam. In such problems 
 it is convenient to represent the proportions of water and steam 
 by a variable known as the quality or the dryness factor; this 
 
 * Annales de Chimie et de Physique, 1867. 
 
GENERAL EQUATION 87 
 
 factor, Xj is defined as that portion of a pound of the mixture 
 which is steam; the remnant, 1 — x, is consequently water. 
 
 Specific Volume of Wet Steam. — Let the specific volume of 
 the saturated vapor be 5 and that of the liquid be <r; then the 
 change of volume is s — a- = u on passing from the liquid to 
 the vaporous state. If a pound of a homogeneous mixture of 
 water and steam is x part steam, then the specific volume may 
 be represented by 
 
 V = xs -\- {1 ~ x) a- = xu + or . . ... (lOl) 
 
 where u is the increase of volume due to vaporization. 
 
 Internal and External Latent Heat. — The heat of vaporiza- 
 tion overcomes external pressure, and changes the state from 
 liquid to vapor at constant temperature and pressure. The 
 external work is 
 
 p {s ~ a) = pu, 
 
 and the corresponding amount of heat, or the external latent 
 heat, is 
 
 Ap (s — a-) = Apu. 
 
 The heat required to do the disgregation work, or the internal 
 latent heat, is 
 
 p = r — Apu ....'... (102) 
 
 General Equation. — In order to apply the general thermo- 
 dynamic method to a mixture of a liquid and its vapor, it is 
 customary to write a differential equation involving the tem- 
 perature t, the quality x, . the specific heats of water and steam c 
 and h, and the heat of vaporization r; these three last properties 
 are assumed to be functions of the temperature only. 
 
 The principal result of the application of the general method 
 to such an equation is a formula for calculating the specific 
 volume J, as will appear later. Following the general method, a 
 special derivation of the formula for s will be given which may 
 be preferred by some readers. 
 
 When a mixture of liquid and its vapor receives heat there is 
 
88 SATURATED VAPOR 
 
 in general an increase in the temperature of the portion x of 
 vapor and in the portion i — x oi Kquid, and there is a vaporiza- 
 tion of part of the liquid. Taking c for the specific heat of the 
 liquid and h for the specific heat of the vapor, while r is the heat 
 of vaporization, we shall have for an infinitesimal change, 
 
 dQ = hxdt + c (i — x) dt -\- rdx .(103) 
 
 Application of the First Law. — The first law of thermo- 
 dynamics is applied to equation (103) by combining it with 
 equation (16), so that 
 
 dQ = A (dE -I- pdv) = hxdt -\- c (i — x) dt + rdx; 
 
 I T 
 
 dE = — [hx 4- c (i — x)] dt -\- -: dx — pdv. 
 
 Jx Jx 
 
 Now 1' is a function of both t and x, as is evident from equation 
 (loi), in which w is a function of /; consequently, 
 
 dv = -TT dt -\- -^r- dx. 
 bt ox 
 
 But E being expressed in terms of t and x gives 
 
 B^ E _ S^£ 
 Bt 8x Bx Bt 
 
 so 
 
 B ii,, , ,-, Bv i B fr Bv\ 
 
 that _J-[/.. + .(._.)]-^-J=_(--^-). 
 
 Bearing in mind that all the functions but x and v are functions 
 of / only, the differentiation gives 
 
 i_ , V 3^ u 1 dr dp_^ 3^ i; 
 
 A^ ^""^"^ BtBx~ A dt dt Bx ^ Bx Bt ' 
 
FIRST AND SECOND LAWS COMBINED 89 
 
 Equation (loi) gives 
 
 
 
 dv 
 dx 
 
 w, 
 
 and 
 
 
 hH 
 
 B'v 
 
 V 
 
 
 BtBx 
 
 SxSt' 
 
 so that the above 
 
 equation 
 
 reduces to 
 
 | + .-.^.,f .... .(.04) 
 
 Application of the Second Law. — The second law of thermo- 
 dynamics makes 
 
 T ^ 
 
 for a reversible process, so that the general equation (103) may 
 be reduced to 
 
 T T T 
 
 Bx Bt Bt Bx 
 
 B hx — c (1 — x) B r 
 ''' B^ T ^ Bt f' 
 
 h — c at 
 
 But 
 
 dr , J r / \ 
 
 dt T . ^ ^^ 
 
 First and Second Laws Combined. — The combination of 
 equations (104) and (105) gives 
 
 r = AuT ^ (106) 
 
p 
 
 
 
 a 
 
 T 
 
 • \ 
 
 \ 
 
 
 \ 
 
 d 
 
 T-AT 
 
 c 
 
 
 
 
 V 
 
 go SATURATED VAPOR 
 
 Special Method. — The preceding equation may be obtained^ 
 by a special method making use of the 
 diagram abed in Fig. 30 which repre- 
 sents Camot 's cycle for a mixture of a 
 liquid and its vapor, the change of 
 temperature A T being very small. Let 
 a represent the volume of one pound of 
 water at the temperature T, and b the 
 Fig. 30. volume of one pound of steam at the same 
 
 temperature and pressure. The line ab 
 therefore represents the vaporization of one pound of water at 
 constant temperature, involving the application of the heat of 
 vaporization r, and the increase of volume 
 
 where s and cr are the specific volumes of steam and water. By 
 
 the second law of thermodynamics the efficiency of this cycle will 
 
 be 
 
 T — (T — AT) _ AT 
 
 T ~ T ' 
 
 so that the heat changed into work will be 
 
 rAT 
 
 But by the first law of thermodynamics this heat is equivalent 
 to the external work, which in this case is approximately equal 
 to the increase of volume u multiplied by the change of pressure 
 Ap; consequently, 
 
 ^^^ A^ 
 
 J^ = uAp, 
 
 or, at the limit as AT approaches zero, 
 
 dt 
 
SPECIFIC VOLUME AND DENSITY 91 
 
 Specific Volume and Density. — The most important result of 
 the application of the methods of thermodynamics to the prop- 
 erties of saturated vapor is expressed by equation (106), which 
 gives a method of calculating the specific volume; thus, 
 
 ^ = ^ + -=^^ + - (107) 
 
 dt 
 
 The numerical value of o" for water for French units is 0.00 1, 
 and for English units is -^ = 0.016, nearly. The density, or 
 weight of a unit of volume, is of course the reciprocal of the 
 specific volume. 
 
 It is of interest to consider the degree of accuracy that may be 
 expected from this method of calculating the density of saturated 
 vapor. The value of r depends on H and q, the total heat and the 
 heat of the liquid ; the latter is now well known, but the total heat 
 is probably in doubt to the extent of ^^^o and may be more. The 
 absolute temperature T appears to be better known and may be 
 subject to an error of no more than toVo or Woo ; and the mechan- 
 ical equivalent of heat — is perhaps as well determined as the 
 
 absolute temperature. The least satisfactory factor in the 
 
 dj) 
 expression is the differential coefficient -j- , which is derived by 
 
 differentiating one of the empirical equations on pages 78 and 79. 
 It is true that the resulting equations on pages 79 and 80 afford a 
 ready means of computing values of the coefficient with great 
 apparent accuracy, but some idea of the essential vagueness of 
 the method may be obtained by comparing computations of the 
 specific volume of saturated steam at 212° C, a point for which 
 either equation B^ or equation C^ will give the pressure as 14.6967 
 pounds per square inch. The specific volume by aid of equation 
 (107 ), using equation B^ for determining the differential coefficient, 
 is 26.62, while the differential coefficient from equation C^ gives 
 26.71; the discrepancy is about ^^^; or if the mean 26.66 betaken 
 as the probable value, either computed value is subject to an 
 error of ^^0. 
 
92 
 
 SATURATED VAPOR 
 
 Experimental Determinations of Specific Volume. — By far the 
 
 best direct determinations of the specific volumes of saturated 
 steam are those reported by Knoblauch, Linde, and Klebe, as 
 expressed by their characteristic equation for superheated steam 
 given on page no. These experiments determined the pres- 
 sures for various temperatures at constant volume, and the 
 results were so treated as to give the volume at saturation by 
 exterpolation with great certainty. The following is a com- 
 parison of specific volume determined by them and volumes com- 
 puted by equation (107). 
 
 SPECIFIC VOLUMES OF SATURATED STEAM. 
 By Knoblauch, Linde, and Klebe. 
 
 
 Volume Cu. M. 
 
 
 Volume Cu. M. 
 
 
 Volume Cu. M. 
 
 Temper- 
 
 
 Temper- 
 
 
 Temper- 
 
 
 
 
 
 
 
 
 ature. 
 
 Experi- 
 
 Com- 
 
 ature. 
 
 Experi- 
 
 Com- 
 
 ature. 
 
 Experi- 
 
 Com- 
 
 
 mental. 
 
 puted. 
 
 
 mental. 
 
 puted. 
 
 
 mental. 
 
 puted. 
 
 100 
 
 1.674 
 
 1.665 
 
 130 
 
 0.6690 
 
 . 6604 
 
 160 
 
 0.3073 
 
 0.3039 
 
 105 
 
 1.420 
 
 I. 412 
 
 135 
 
 0.5822 
 
 0-5747 
 
 165 
 
 0.2729 
 
 0.2703 
 
 IIO 
 
 I. 211 
 
 I. 212 
 
 140 
 
 0.5091 
 
 0.5021 
 
 170 
 
 0.2430 
 
 O.2411 
 
 "5 
 
 1-037 
 
 1.027 
 
 145 
 
 0.4466 
 
 0.4405 
 
 H^ 
 
 0.2170 
 
 0.2157 
 
 120 
 
 0.8922 
 
 0.8826 
 
 150 
 
 0.3921 
 
 0.3880 
 
 180 
 
 0.1943 
 
 0.1934 
 
 125 
 
 0.7707 
 
 0.7617 
 
 155 
 
 0.3470 
 
 0.3428 
 
 
 
 
 Nature of the Specific Heats. — In the appHcation of the gen- 
 eral thermodynamic method on page SS the term h is intro- 
 duced to represent the specific heat of saturated steam, and there 
 is sonie interest in the determination of the true nature of this 
 property, which clearly cannot be a specific heat at constant 
 pressure, nor a specific heat at constant volume, since both pressure 
 and volume change with the temperature. The specific heat of 
 the liquid c properly is affected by the same consideration, but 
 as the increase of volume is small and is neglected in thermo- 
 dynamic discussions, the importance of the consideration is much 
 less. The specific heat h of saturated vapor is the amount of 
 heat necessary to raise the temperature of one pound of the 
 vapor one degree, under the condition that the pressure shall 
 
NATURES OF SPECIFIC HEATS 93 
 
 increase with the temperature, according to the law for saturated 
 vapor. 
 
 Equation (105) gives a ready way of calculating the specific 
 heat for a vapor, for from it 
 
 , dr r 
 
 Now r may be readily expressed as a function of /, and then 
 
 d/Y 
 by differentiation — may be determined. For steam 
 
 Culr 
 
 r = H - q= 606.5 + 0-305 i-[qx + c {t- /J], 
 
 in which t^ is the temperature at the beginning of the range, as 
 given by the table on page 80, within which / may fall. There- 
 fore 
 
 dr 
 
 dt 
 
 and 
 
 h = 0.305 — — 
 
 For other vapors the equations, deduced from the empirical 
 equations for q and H on pages d>2i and 85, are somewhat more 
 complicated, but they involve no especial difficulty. 
 
 The following table gives the values of h for steam at several 
 absolute pressures: 
 
 SPECIFIC HEAT OF STEAM. 
 
 Pressures, lbs. per sq. in., p S 50 100 200 300 
 
 Temperatures, ^° F. . . . 162.3 280.9 327.6 381.7 4i7-4 
 
 Specific heat, /t —1.30 ~o-93 —0.82 —0.70 —0.63 
 
 The negative si^n shows that heat must be abstracted from 
 saturated steam when the temperature and pressure are increased, 
 otherwise it will become superheated. On the other hand, 
 steam, when it suddenly expands with a loss of temperature and 
 pressure, suffers condensation, and the heat thus liberated sup- 
 plies that required by the uncondensed portion. 
 
94 SATURATED VAPOR 
 
 Hirn * verified this conclusion by suddenly expanding steam in 
 a cylinder with glass sides, whereupon the clear saturated steam 
 suffered partial condensation, as indicated by the formation of a 
 cloud of mist. The reverse of this experiment showed that steam 
 does not condense with sudden compression, as shown by Cazin. 
 
 Ether has a positive value for h. As the theory indicates, a 
 cloud is formed during sudden compression, but not during sud- 
 den expansion. 
 
 The table of values of h for steam shows a notable decrease 
 for higher temperatures, which indicates a point of inversion at 
 which h is zero and above which h is positive, but the tempera- 
 ture of that point cannot be determined from our experimental 
 knowledge. For chloroform the point of inversion was calcu- 
 lated by Cazin f to be 123^.48, and determined experimentally by 
 him to be between 125° and 129°. The discrepancy is mostly 
 due to the imperfection of the apparatus used, which substituted 
 finite changes of considerable magnitude for the indefinitely 
 small changes required by the theory. 
 
 Isothermal Lines. — Since the pressure of saturated vapor is a 
 function of the temperature only, the isothermal line of a mixture 
 of a liquid and its vapor is a line of constant pressure, parallel to 
 the axis of volumes. Steam expanding from the boiler into the 
 cylinder of an engine follows such a line; that is, the steam- line 
 of an automatic cut-off engine with ample ports is nearly parallel 
 to the atmospheric line. 
 
 The heat required for an increase of volume at constant press- 
 ure is 
 
 Q = r {x^ — x^) (108) 
 
 in which r is the heat required to vaporize one pound of liquid, 
 and x^ and x^ are the initial and final qualities, so that x.^ — x^ 
 is the weight of Uquid vaporized. 
 
 The external work done during an isothermal expansion is 
 
 W = p (v^ — vj = pu (x^ — x^) . . . , (109) 
 
 * Bulletin de la Societe Ind. de Mulhouse, cxxxiii. 
 t Comptes rendus de VAcademie des Sciences, Ixii. 
 
ISOENERGIC OR ISODYNAMIC LINES 
 
 95 
 
 Intrinsic Energy. — Of the heat required to raise a pound of 
 any Hquid from freezing-point to a given temperature and to 
 completely vaporize it at that temperature, a part q is required 
 to increase the temperature, another part p is required to change 
 the state or do disgregation work, and a third part Apu is required 
 to do the external work of vaporization. Consequently for com- 
 plete vaporization we may have, 
 
 Q = A{S + I-^W) = q + p + Apu = H, 
 
 For partial vaporization the heat required to do the disgrega- 
 tion work will be x/3, and the heat required to do the external 
 work will be Apxu. Therefore the heat required to raise a pound 
 of a liquid from freezing-point to a given temperature and to 
 vaporize x part of it will be 
 
 Q = q + xp + Apxu = A{E + W) 
 
 where E is the increase of intrinsic energy from freezing-point. 
 It is customary to consider that 
 
 E = ~^{xp + q) (no) 
 
 represents the intrinsic energy of one unit of weight of a mixture 
 of a liquid and its vapor. 
 
 Isoenergic or Isodynamic Lines. — If a change of a mixture 
 of a liquid and its vapor takes place at constant intrinsic energy, 
 the value of E will be the same at the initial and final conditions, 
 and 
 
 ?2 — ?i + ^292 — ^iPi = o .... (in) 
 
 which equation, with the formulae 
 
 v^ = x^u^ + o"; 1^1 = x^u^ + o" . . . . (112) 
 
 enable us to compute the initial and final volumes. If desired, 
 intermediate volume corresponding to intermediate temperature 
 can be computed in the same way, and a curve can be drawn 
 in the usual way with pressures and volumes for the coordinates. 
 Eor example, if a mixture of -^0 steam and tV water expands 
 
96 SATURATED VAPOR 
 
 isoenergically from loo pounds absolute to 15 pounds absolute, 
 the final condition will be 
 
 _ ^1 - ^2 + ^iPi _ 297.9 - 181.8 + o.Q X 802.8 _ 
 ""'- p, ~ 892.6 -0-9395- 
 
 The initial and final specific volumes are 
 v^ = x^u^ + «r = 0.9 (4.403 — 0.016) + 0.016 = 3.964; 
 v^ = x^u^ -\- a = 0.9395 (26.15 "~ o-oi6) + 0.016 = 24.54. 
 
 The converse problem requiring the pressure corresponding to 
 a given volume cannot be solved directly. The only method 
 of solving such a problem is to assume a probable final pressure 
 and find the corresponding volume; then, if necessary, assume 
 a new final pressure larger or smaller as may be required, and 
 solve for the volume again; and so on until the desired degree 
 of accuracy is obtained. 
 
 This method does not give an explicit equation connecting the 
 pressures and volumes, but it will be found on trial that a curve, 
 drawn by the process given above can be represented fairly well 
 by an exponential equation, for which the exponent can be 
 determined by the method on page 66. 
 
 Having given or determined the initial and final volumes, the 
 exponential equation may be determined, and then the external 
 work may be calculated by the equation 
 
 For example^ the exponent for the equation representing the 
 expansion of the above problem is 
 
 ^ _ log p, - log p , _ log 100 - log 15 _ ^^^^^^ 
 log v^ — log v^ log 24.54 — log 3.964 
 
 and the external work of expansion is 
 
 „r 100 X 144 X ^.064 ( I'x.q6a\°-°'^^) -^ ,, 
 
 W = ^^ o_v_if 1 J _ ( v^ V ^ J f ^ 100,000 ft.-lbs. 
 
 1.041 — I ( \24.54/ ) 
 
ENTROPY OF THE LIQUID gy 
 
 Since there is no change in the intrinsic energy during an 
 isoenergic expansion, the external work is equivalent to the heat 
 applied. Thus in the example just solved the heat applied is 
 equal to 
 
 100,000 ^ 778 = 129B.T.U. 
 
 There is little occasion for the use of the method just given, 
 v^hich is fortunate, as it is not convenient. 
 
 Entropy of the Liquid. — Suppose that a unit of weight of a 
 liquid is intimately mingled with its vapor, so that its tempera- 
 ture is always the same as that of the vapor; then if the pressure 
 of the vapor is increased the liquid will be heated, and if the 
 vapor expands the liquid will be cooled. So far as the unit of 
 weight of the liquid under consideration is concerned, the pro- 
 cesses are reversible, for it will always be at the temperature of 
 the substance from which it receives or to which it imparts heat, 
 i.e., it is always at the temperature of its vapor. 
 
 The change of entropy of the liquid can therefore be calculated 
 by equation (37), 
 
 which may here be written 
 
 ^=/f=/f (-3) 
 
 On page 83 it is suggested that the specific heat of water for 
 temperature Centigrade may be expressed as follows: 
 
 c =^ 1 + k 
 
 where ^ is a small corrective term that may be positive or negative 
 as the case may be. Using this correction, equation (113) may 
 be written 
 
 . rdt , rkdt . ^ 
 
gS SATURATED VAPOR 
 
 The first term can readily be integrated and computed, and the 
 second term, which is small, can be determined graphically, so 
 that the expression for entropy, of water becomes 
 
 = \og.^+ fk^. . . . . .(115) 
 
 The columns of entropy of water in the tables were determined 
 in this manner. 
 
 In ithe discussion of entropy on page 31 it was pointed out 
 that there is no natural zero of entropy corresponding to the abso- 
 lute zero of temperature. It is customary to treat the freezing- 
 point of water as the zero of entropy both for that liquid and 
 for other volatile liquids; some liquids therefore have negative 
 entropies at temperatures below freezingr point of water in the 
 appropriate tables of their properties. 
 
 For a liquid like ether which has the heat of the liquid repre- 
 sented by an empirical equation, 
 
 q = 0.52901 / + 0.0002959 t^, 
 
 the specific heat is first obtained by differentiation, giving 
 
 c = 0.52901 + 0.0005918 /. 
 
 Then the increase of entropy above that for the freezing-point of 
 water may be obtained by aid of equation (113), which gives for 
 ether with the French system of units, 
 
 ^^Jm )°-5290i + 0.0005918 (T- 273) |y; 
 
 •*• ^^J273 (0-3670 Y + 0-0005918 c^^j; 
 
 I. 
 
 T 
 
 /. 0= 0.0005918 (T — 273) -f 0.3670 loge 
 
 273 
 
 T 
 
 ^= 0.0005918 / + 0.3670 loge^ (116) 
 
 273 
 
ENTROPY OF A MIXTURE OF A LIQUID 99 
 
 For temperatures below the freezing-point of water, equation 
 (116) gives negative numerical results. 
 
 Other liquids for which equations for the heat of the liquid 
 are given on page 83, may be treated in a similar method. 
 
 Entropy due to Vaporization. — When a unit of weight of a 
 liquid is vaporized r thermal units, equal to the heat of vaporiza- 
 tion, must be applied at constant temperature. Treating such 
 a vaporization as a reversible process, the change of entropy may 
 be calculated by the equation 
 
 > — <^o ^ ^ 
 
 This property is given in the " Tables for Saturated Steam," 
 but not in general for other liquids. 
 
 Entropy of a Mixture of a Liquid and its Vapor. — The increase 
 in entropy due to heating a unit of weight of a liquid from freez- 
 ing-point to the temperature t and then vaporizing x portion of 
 it is 
 
 where 6 is the entropy of the liquid, r is the heat of vaporization, 
 
 r 
 
 and T is the absolute temperature. For steam — may be taken 
 
 from the tables; for other vapors it must usually be calculated. 
 
 For any other state determined by x^ and t^ we shall have, for 
 the increase of entropy above that of liquid at freezing-point. 
 
 The change of entropy in passing from one state to another 
 is ^ 
 
 <\>-<\>. = ^ + e-^-e, . . . („7) 
 
 Whlen the condition of the mixture of a liquid and its vapor 
 is given by the pressure and value of x, then a table giving the 
 properties at each pound may be conveniently used for this work. 
 
lOO SATURATED VAPOR 
 
 Adiabatic Equation for a Liquid and its Vapor. — During an 
 
 adiabatic change the entropy is constant, so that equation (117) 
 gives 
 
 I + 0^^ :^+e, ..... (118) 
 
 When the initial state, determined by x^ and t^ or p^^ is known 
 and the final temperature t^, or the final pressure p2, the final 
 value x^ may be found by equation (118). The initial and final 
 volumes may be calculated by the equations 
 
 v^ = x^u^ + a- and v^ = x^u.^ + o" . . . (119) 
 
 Tables of the properties of saturated vapor commonly give the 
 
 specific volume s^ but 
 
 5 = W + cr. 
 
 The value of cr for water is 0.016, and for other liquids will be 
 found on page 85. 
 
 For example, one pound of dry steam at 100 pounds absolute 
 pressure will have the values 
 
 h = 327°-6 F., ri = 884.0, e^ = 0.4733, ^1 = I- 
 If the final pressure is 15 pounds absolute, we have 
 /2 = 213°. o F., r^ = 965.1, ^2 = 0.3143; 
 
 whence 
 
 884.0 , Q6t;.i:x;2 , 
 
 788.3 ^^^^ 673.7 ^ ^^' 
 
 .*. x^ = 0.894. 
 
 The initial and final volumes are 
 
 ^1 = s^ = 4.40 
 
 V2 = ^2^2 + ^ = 23.4. 
 
 Problems in which the initial condition and the final tem- 
 perature or pressure are given may be solved directly by aid of 
 the preceding equations. Those giving the final volume instead 
 
ADIABATIC EQUATION FOR A LIQUID lOI 
 
 of the temperature or pressure can be solved only by approxi- 
 mations. An equation to an adiabatic curve in terms of p and v 
 cannot be given, but such a curve for any particular case may 
 be constructed point by point. 
 
 Clausius and Rankine independently and at about the same 
 time deduced equations identical with equations (117) and 
 (118), but by methods each of which differed from that given 
 here. 
 
 Rankine called the function 
 
 T 
 
 the thermodynamic function ; Clausius called it entropy. 
 
 In the discussion of the specific heat h oi a saturated vapor, it 
 appeared that the expansion of dry saturated steam in a non- 
 conducting cyhnder would be accompanied by partial conden- 
 sation. The same fact may be brought out more clearly by the 
 above problem. 
 
 On the other hand, h is positive for ether, and partial conden- 
 sation takes place during compression in a non-conducting 
 cylinder. 
 
 For example^ let the initial condition for ether be 
 
 ti = 10° C ., r^ = 93.12, B = 0.0191, JCj = I, 
 
 and let the final conditions be 
 
 /j = 120° C, ^2 = 72.26, ^2 = 0-2045; 
 
 , QS-I2 , 72.26X2 , 
 
 then -^ h 0.0191 = + 0.2045, 
 
 283 393 
 
 and X2 = 0.724. 
 
 Equation (118) apphes to all possible mixtures of a liquid and 
 its vapor, including the case oi x^ = o or the case of liquid with- 
 out vapor, but at the pressure corresponding to the temperature 
 according to the law of saturated vapor. When applied to hot 
 water, this equation shows that an expansion in a non-conduct- 
 ing cylinder is accompanied by a partial vaporization. 
 
I02 SATURATED VAPOR 
 
 There is some initial state of the mixture such that the value 
 of X shall be the same at the beginning and at the end, though it 
 may vary at intermediate states. To find that value make X2 = 
 x^ in equation (118) and solve for x^, which gives 
 
 X = AizA_. 
 
 '2 _ '1 
 
 The value of x^ for steam to fulfil the conditions given varies 
 with the initial and final temperatures chosen, but in any case it 
 will not be much different from one half. It may therefore be 
 generally stated that a mixture of steam and water, when 
 expanded in a non-conducting cylinder, will show partial con 
 densation if more than half is steam, and partial evaporation if 
 more than half water. If the mixture is nearly half water and 
 half steam, the change must be investigated to determine whether 
 evaporation or condensation will occur; but in any case the 
 action will be small. 
 
 External Work during Adiabatic Expansion. — Since no heat 
 is transmitted during an adiabatic expansion, all of the intrinsic 
 energy lost is changed into external work, so that, by equation 
 (no), 
 
 1^ = ^1 - ^2 = J (?1 - ?2 + ^£x — ^2P2) ' ' (120) 
 
 For example, the external work of one pound of dry steam in 
 expanding adiabatically from 100 pounds to 15 pounds absolute 
 is 
 
 W = 778 (297.9 — 181.8 + I X 802.8 — 0.894 X 892.6) 
 
 IF = 120.2 X 778 = 93,500 foot-pounds. 
 
 Attention should be called to the unavoidable defect of this 
 method of calculation of external work during adiabatic expan- 
 sion, in that it depends on taking the difference of quantities 
 which are of the same order of magnitude. For example, the 
 above calculation appears to give four places of significant figures, 
 
EXTERNAL WORK DURING ADIABATIC EXPANSION 
 
 103 
 
 while, as a matter of fact, the total heat H from which p is derived 
 
 is affected by a probable error of or perhaps more. Both 
 
 the quantities 
 
 q^ + x^p^ and q^ + x^p^ 
 
 have a numerical value somewhere near 1000, and an error of 
 
 is nearly equivalent to two thermal units, so that the probable 
 
 error of the above calculation is nearly two per cent. For a 
 wider range of temperature the error is less, and for a narrower 
 range it is of course larger. This matter should be borne in 
 mind in considering the use of approximate methods of calcula- 
 tions; for example, the temperature- entropy diagram to be dis- 
 cussed later. 
 
 The adiabatic curve cannot be well represented by an expo- 
 nential equation; for if an exponent be determined for such a 
 curve passing through points representing the initial and final 
 states, it will be found that the exponent will vary widely with 
 different ranges of pressure, and still more with different initial 
 values of x\ and that, further, the intermediate points will not be 
 well represented by such an exponential curve even though it 
 passes through the initial and final points. 
 
 This fact was first pointed out by Zeuner, who found that the 
 most important element in determining n was x^, the initial con- 
 dition of the mixture. He gives the following empirical formula 
 for determining w, which gives a fair approximation for ordinary 
 ranges of temperature : 
 
 n = 1.035 + cioorVj. 
 
 There does not appear to be any good reason for using an 
 exponential equation in this connection, for all problems can be 
 solved by the method given, and the action of a lagged steam- 
 engine cylinder is far from being adiabatic. An adiabatic line 
 drawn on an indicator-diagram is instructive, since it shows 
 to the eye the difference between the expansion in an actual 
 engine and that of an ideal non-conducting cylinder; but it can 
 
I04 
 
 SATURATED VAPOR 
 
 be intelligently drawn only after an elaborate engine test. For 
 general purposes the hyperbola is the best curve for comparison 
 with the expansion curve of an indicator-diagram, for the reason 
 that it is the conventional curve, and is near enough to the curve 
 of the diagrams from good engines to allow a practical engineer 
 to guess at the probable behavior of an engine, from the diagram 
 alone. It cannot in any sense be considered as the theoretical 
 curve. 
 
 Temperature-Entropy Diagram. — If the entropies of the 
 liquid and the entropies of vaporization for steam are plotted with 
 temperature for ordinates we get a diagram like 30a; very com- 
 monly absolute temperatures 
 are taken in drawing the dia- 
 gram in order to emphasize 
 the role played by absolute 
 temperatures in the deter- 
 mination of the efficiency of 
 Carnot 's cycle. It would seem 
 better to take the temperature 
 by the centigrade or the Fah- 
 renheit thermometer, as they 
 are the basis of steam-tables, 
 and the temperature- entropy diagram is the equivalent of such a 
 table. 
 
 Now the entropy of a mixture containing x part steam is 
 
 Fig. 30a. 
 
 -}- X 
 
 r 
 
 so that the entropy of a mixture containing x part of steam can 
 be determined by dividing the line such as de (which represents 
 the entropy of vaporization) in the proper ratio. 
 
 dc 
 de 
 
 = X. 
 
 It is convenient to divide the several lines like ah and de into 
 tenths and hundredths, and then, if an adiabatic expansion is 
 
TEMPERATURE-ENTROPY DIAGRAM 105 
 
 represented by a vertical line like be, the entropy at c may be 
 determined by inspection of the diagram. Conversely, by noting 
 the temperature at which a given line of constant entropy crosses 
 a line of given quality we may determine the temperature to 
 which it is necessary to expand to attain that quality, a determina- 
 tion which cannot be made directly by the equation. 
 
 When a temperature- entropy diagram is used as a substitute 
 for a "Table of the Properties of Saturated Steam," it is custom- 
 ary to draw the lines of constant quality or dryness factor, and 
 other lines like constant volume lines and lines of constant heat 
 contents or values of the expression 
 
 xr + q, 
 
 the use of which will appear in the discussion of steam-engines 
 and steam-turbines. 
 
 To get a series of constant volume lines we may compute the 
 volume for each quality x^ = .i^, x^ = .2, x = .3, etc., by the 
 equation 
 
 V = XU + (T, 
 
 and since the volume increases proportionally to the increase in 
 X, we may readily determine the points on that line for which 
 the volume shall be whole units, such as 2 cubic feet, 3 cubic feet, 
 etc. Points for which the volumes are equal may now be con- 
 nected by fair curves, so that for any temperature and entropy the 
 volume may readily be estimated. 
 
 Curves of equal heat contents can be constructed in a similar 
 way. 
 
 If desired, a curve of temperatures and pressures can be drawn 
 so that many problems can be solved approximately by aid of the 
 compound diagram. 
 
 At the back of this book a temperature- entropy diagram will 
 be found which gives the properties of saturated and superheated 
 steam. It is provided with a scale of temperatures at either 
 side, and a scale of entropies at the bottom, while there is a scale 
 of pressure at the top. 
 
Io6 SATURATED VAPOR 
 
 To solve a problem like that on page loo, i.e., to find the quality 
 after an adiabatic expansion from loo pounds absolute to 15 
 pounds absolute, and the specific volume at the initial and final 
 states, proceed as follows: 
 
 From the curve of temperatures and pressures, select the tem- 
 perature line which corresponds to 100 pounds and note where it 
 cuts the saturation curve, because it is assumed that the steam is 
 initially dry. The diagram gives the entropy as approximately 
 1.6 1. Note the temperature line which cuts the temperature- 
 pressure curve at 15 pounds, and estimate the value of x from its 
 intersection with the entropy line 1.6 1; by this method the value 
 of X is found to be about 0.89. In hke manner the volume may 
 be estimated to be about 23.4 cubic feet. 
 
 Temperature-Entropy Table. — Now that the computation of 
 isoentropic changes has ceased to be the diversion of students 
 of theoretical investigations and has become the necessity of 
 engineers who are engaged in such matters as the design of 
 steam-turbines, the somewhat inconvenient methods which were 
 incapable of inverse solutions, have become somewhat burdei^- 
 some. A remedy has been sought in the use of temperature- 
 entropy diagrams just described. Such a diagram to be really 
 useful in practice must be drawn on so large a scale as to be very 
 inconvenient, and even then is liable to lack accuracy. To meet 
 this condition of affairs a temperature- entropy table has been com- 
 puted and added to the " Tables of the Properties of Saturated 
 Steam." In this table each degree Fahrenheit from 180° to 430^ 
 is entered together with the corresponding pressure. There 
 have been computed and entered in the proper columns the 
 following quantities, namely, quality x, heat contents xr + q, and 
 specific volume v, for each hundredth of a unit of entropy. 
 
 In the use of this table it is recommended to take the nearest 
 degree of temperature corresponding to the absolute pressure 
 if pressures are given. Following the line across the table select 
 that column of entropy which corresponds most nearly with the 
 initial condition; the corresponding initial volume may be read 
 direc|ly. Follow down the entropy column to the lower temper- 
 
TEMPERATURE-ENTROPY TABLE 
 
 107 
 
 ature and then find the value of x and the specific volume. The 
 external work for adiabatic expansion may now readily be found 
 by aid of equation (120), page 102. As will appear later, the 
 problems that arise in practice usually require the heat contents 
 and not the intrinsic energy, so that property has been chosen 
 in making up the table. 
 
 For example, the nearest temperature to 100 pounds per square 
 inch is 328° F.; the entropy column 1.59 gives for x, 0.995, which 
 indicates half of one per cent of moisture in the steam. The corre- 
 sponding volume is 4.39 cubic feet. The nearest temperature to 
 15 pounds absolute is 213° F., and at 1.59 entropy the quality 
 is 0.888 and the specific volume corresponding is 23.2 cubic 
 feet. 
 
 If greater accuracy is desired we must resort to interpolation. 
 Usually it will be sufficient to interpolate between the lines for 
 temperature in a given column of entropy, because the quantity 
 that must be determined accurately is usually the dijjerence 
 
 ^/i + ?i — (^2^2 + ^2) 
 
 and this difference for two given temperatures t^ and /g is very 
 nearly the same if taken out of two adjacent entropy columns. 
 A similar result will be found for the difference 
 
 ^iPl + ?1 — (^2P2 + ^2); 
 
 if computed for values of x found in adjacent columns. 
 
 Another way of looking at this matter is that one hundredth 
 of a unit of entropy at 330 pounds corresponds to one per cent 
 of moisture. 
 
 Evidently this table can be used to solve problems in which 
 the final volumes are given, or, as will appear later, to determine 
 intermediate pressures for steam-turbines. 
 
Io8 SATURATED VAPOR 
 
 EXAMPLES. 
 
 1. Water at ioo° F. is fed to a boiler in which the pressure is 
 1 20 pounds absolute per square inch. How much heat must 
 be supplied to evaporate each pound? Ans. 11 18 b.t.u. 
 
 2. One pound wet steam at 150 pounds absolute occupies 2.5 
 cubic feet. What per cent of moisture is present ? What is the 
 "quality" of the steam? Ans. 17.1 per cent of moisture x = 
 .829. 
 
 3. A pound of steam and water at 150 pounds pressure is 
 0.6 steam. What is the increase of entropy above that of water at 
 32° F. ? Ans. 1. 144. 
 
 4. A kilogram of chloroform at 100° C. is 0.8 vapor. What is 
 the increase of entropy above that of the liquid at 0° C. ? Ans. 
 0.1959. 
 
 5. The initial condition of a mixture of water and steam is 
 / = 320° ¥., X = 0.8. What is the final condition after adiabatic 
 expansion to 212° F. ? Ans. 0.74. 
 
 6. The initial condition of a mixture of steam and water is ^ = 
 3000 mm., X = 0.9. Find the condition after an adiabatic expan- 
 sion to 600 mm. Ans. 0.828. 
 
 7. A cubic foot of a mixture of water and steam, x = 0.8, is 
 under the pressure of 60 pounds by the gauge. Find its volume 
 after it expands adiabatically till the pressure is reduced to 10 
 pounds by the gauge; also the external work of expansion. Ans. 
 2.68 cubic feet and 9980 foot-pounds. 
 
 8. Three pounds of a mixture of steam and water at 120 
 pounds absolute pressure occupy 4.5 cubic feet. How much 
 heat must be added to double the volume at the same pressure, 
 and what is the change of intrinsic energy? Ans. 1065 b.t.u.; 
 750,400 foot-pounds. 
 
 9. Find the intrinsic energy, heat contents and volume of 
 5 pounds of a mixture of water and steam which is 80 per cent 
 steam, the pressure being 150 pounds absolute. Ans. Intrinsic 
 energy, 3,710,000; heat contents, 5095 b.t.u.; volume, 12. i cubic 
 feet. 
 
TEMPERATURE-ENTROPY TABLE 
 
 109 
 
 10. Three pounds of water are heated from 60° F, and evapor- 
 ated under 135.3 pounds gauge pressure. Find the heat added, 
 and the changes in volume, and intrinsic energy. Ans. Heat 
 added, 3490 b.t.u.; increase in volume, 8.99 cubic feet; intrinsic 
 energy, 2,520,000. 
 
 11. A pound of steam at 337^.7 F. and 100 pounds gauge 
 pressure occupies 3 cubic feet. Find its intrinsic energy and its 
 entropy above 32° F. Ans. Intrinsic energy, 718,000; entropy, 
 
 1-336. 
 
 12. Two pipes deliver water into a third. One supplies 300 
 gallons per minute at 70° F. ; the other, 90 gallons per minute at 
 200° F. What is the temperature of the water after the two 
 streams unite? Ans. 100° F. 
 
 13. Ten gallons of water per minute are to be heated from 
 65° to 212° F. by passing through a coil surrounded by steam at 
 120 pounds gauge pressure. How much steam is required per 
 minute? Ans. 12 pounds. 
 
 14. A test of an engine with the cut-off at 0.106 of the stroke, 
 and the release at 0.98 of the stroke, and with 4.5 per cent clear- 
 ance, gave for the pressure at cut-off 62.2 pounds by the indicator, 
 and at release 6.2 pounds; the mixture in the cylinder at cut-off 
 was 0.465 steam, and at release 0.921 steam. Find (i) condition 
 of the mixture in the cylinder at release on the assumption of 
 adiabatic expansion to release; (2) condition of mixture on the 
 assumption of hyperbolic expansion, or that pv = piV^] (3) the 
 exponent of an exponential curve passing through points of cut- 
 off and release; (4) exponent of a curve passing through the initial 
 and final points on the assumption of adiabatic expansion; (5) 
 the piston displacement was 0.7 cubic feet, find the external work 
 under exponential curve passing through the points of cut-off and 
 release; also under the adiabatic curve. Ans. (i) 0.472; (2) 
 0.524; (3) n = 0.6802; (4) n = 1.0589; (5) 3093 and 2120 foot- 
 pounds. 
 
CHAPTER VII. 
 
 SUPERHEATED VAPORS. 
 
 A DRY and saturated vapor, not in contact with the liquid 
 from which it is formed, may be heated to a temperature greater 
 than that corresponding to the given pressure for the same 
 vapor when saturated; such a vapor is said to be superheated. 
 When far removed from the temperature of saturation, such a 
 vapor follows the laws of perfect gases very nearly, but near the 
 temperature of saturation the departure from those laws is too 
 great to allow of calculations by them for engineering purposes. 
 
 All the characteristic equations that have been proposed, 
 have been derived from the equation 
 
 pv = RT, 
 
 which is very nearly true for the so-called perfect gases at mod- 
 erate temperatures and pressures; it is, however, well known 
 that the equation does not give satisfactory results at very high 
 pressures or very low temperatures. To adapt this equation to 
 represent superheated steam, a corrective term is added to the 
 right-hand side, which may most conveniently be assumed to 
 be a function of the temperature and pressure, so that calcula- 
 tions by it may be made to join on to those for saturated steam. 
 
 The most satisfactory characteristic equation of this sort is 
 that given by Knoblauch,* Linde, and Klebe, 
 
 pv = BT- p{i+ap)\c{^)'-D]^ . . (i2i) 
 
 in it the pressure is in kilograms per square metre, v is in 
 cubic metres, and T is the absolute temperature by the 
 
 * MiUeilungen uher Forschungsarheiten, etc., Heft 21, S. TiZ^ 1905- 
 
SUPERHEATED VAPORS III 
 
 centigrade thermometer. The constants have the following 
 values : 
 
 B = 47.10, a = 0.000002, C = 0.031, D = 0.0052. 
 
 In the English system of units, the pressures being in pounds 
 per square foot, the volumes in cubic feet per pound, and the 
 temperatures on the Fahrenheit scale, we have 
 
 pv=^.^s r-^(i +0.00000976^) ('-^^^^^°- 0.0833) (122) 
 
 The following equation may be used with the pressure in 
 pounds per square inch : 
 
 pv=o.sg62 T~p (i +0.0014 P) r^°'^3^'^^^ -Q>o833J • (123) 
 
 The labor of calculation is principally in reducing the cor- 
 rective term, and especially in the computation of the factor 
 containing the temperature. A table on page 112 gives values 
 of this factor for each five degrees from 100° to 600° F.; the 
 maximum error in the calculation of volume by aid of the table 
 is about 0.4 of one per cent at 336 pounds pressure and 428° F.; 
 that is at the upper limit of our table for saturated steam. At 
 150 pounds and 358° F., which is about the middle range 
 of our table for saturated steam, the error is not more than 0.2 
 of one per cent, which is not greater than the probable error of 
 the equation itself under those conditions. At lower pressures 
 and at higher temperatures the error tends to diminish. 
 
 The following simple equation is proposed by TumHrz * based 
 on experiments by Battelli. 
 
 pv = BT — Cp (124) 
 
 where p is the pressure in kilograms per square metre, v the 
 specific volume in cubic metres, and T the absolute temperature 
 centigrade. The constants have the values 
 
 B = 47.10 C = 0.016. 
 
 * Math. Naturw. Kl. Wien,, 1899, Ha S. 1058. 
 
112 
 
 SUPERHEATED VAPORS 
 
 In the English system with the pressure in pounds per square 
 foot and the volumes in cubic feet, for absolute temperatures 
 Fahrenheit, 
 
 pv = 85.85 T-0.2S6P (125) 
 
 This equation has a maximum error of 0.8 of one per cent as 
 compared with equation (121). 
 
 TABLE I. 
 
 -.T 1 r 1 f ii;o,^oo,ooo _ 
 
 Values of the factor ' 0.0833. 
 
 Temperature. 
 
 Value 
 
 Temperature. 
 
 Value 
 
 Temp 
 
 >erature . 
 
 Value 
 
 Temperature. 
 
 Value . 
 
 
 
 of 
 
 
 
 /-if 
 
 
 
 /->f 
 
 
 
 nf 
 
 
 
 01 
 
 Factor. 
 
 
 
 01 
 Factor. 
 
 
 
 01 
 Factor. 
 
 
 
 01 
 
 Factor. 
 
 Fahr. 
 
 Abs. 
 
 
 Fahr. 
 
 Abs. 
 
 
 Fahr. 
 
 Abs. 
 
 
 Fahr. 
 
 Abs. 
 
 
 200 
 
 659-5 
 
 0.441 
 
 300 
 
 759-5 
 
 0.260 
 
 400 
 
 859-5 
 
 0.153 
 
 500 
 
 959-5 
 
 0.087 
 
 205 
 
 664 
 
 5 
 
 0.429 
 
 305 
 
 764-5 
 
 0.253 
 
 405 
 
 864 
 
 5 
 
 0.149 
 
 505 
 
 964.5 
 
 0.084 
 
 210 
 
 669 
 
 5 
 
 0.417 
 
 310 
 
 769-5 
 
 0.247 
 
 410 
 
 869 
 
 5 
 
 0.145 
 
 510 
 
 969-5 
 
 0.083 
 
 215 
 
 674 
 
 5 
 
 0.405 
 
 315 
 
 774-5 
 
 0. 240 
 
 415 
 
 874 
 
 5 
 
 0. 141 
 
 515 
 
 974-5 
 
 0.079 
 
 220 
 
 679 
 
 5 
 
 0-395 
 
 320 
 
 779-5 
 
 0.234 
 
 420 
 
 879 
 
 5 
 
 0.138 
 
 520 
 
 979-5 
 
 0.077 
 
 225 
 
 684 
 
 5 
 
 0-385 
 
 325 
 
 784.5 
 
 0.228 
 
 425 
 
 884 
 
 5 
 
 0.134 
 
 525 
 
 984.5 
 
 0.074 
 
 230 
 
 689 
 
 5 
 
 0-375 
 
 330 
 
 789-5 
 
 0.222 
 
 430 
 
 889 
 
 5 
 
 O.131 
 
 530 
 
 989-5 
 
 0.072 
 
 235 
 
 694 
 
 5 
 
 0-365 
 
 335 
 
 794-5 
 
 0.216 
 
 ■435 
 
 894 
 
 5 
 
 0.127 
 
 535 
 
 994-5 
 
 0.070 
 
 240 
 
 699 
 
 5 
 
 0-356 
 
 340 
 
 799.5 
 
 0.2II 
 
 440 
 
 899 
 
 5 
 
 0.123 
 
 540 
 
 999-5 
 
 0.067 
 
 245 
 
 704 
 
 5 
 
 0.347 
 
 345 
 
 804.5 
 
 0.205 
 
 445 
 
 904 
 
 5 
 
 0. 120 
 
 545 
 
 T004.5 
 
 0.065 
 
 250 
 
 709 
 
 5 
 
 0-338 
 
 350 
 
 809.5 
 
 0. 200 
 
 450 
 
 909 
 
 5 
 
 0. 117 
 
 550 
 
 1009.5 
 
 0.063 
 
 255 
 
 714 
 
 5 
 
 0.329 
 
 355 
 
 814.5 
 
 0.195 
 
 455 
 
 914 
 
 5 
 
 O.I13 
 
 555 
 
 1014.5 
 
 o.o6t 
 
 260 
 
 719 
 
 5 
 
 0.320 
 
 360 
 
 819.5 
 
 0. 190 
 
 460 
 
 919 
 
 5 
 
 0. ITO 
 
 560 
 
 10T9.5 
 
 0.059 
 
 265 
 
 724 
 
 5 
 
 0.312 
 
 365 
 
 824.5 
 
 0.185 
 
 465 
 
 924 
 
 5 
 
 0. 107 
 
 565 
 
 1024.5 
 
 0.057 
 
 270 
 
 729 
 
 5 
 
 0.304 
 
 370 
 
 829.5 
 
 0. 180 
 
 470 
 
 929 
 
 5 
 
 0. 104 
 
 570 
 
 1029.5 
 
 0.055 
 
 275 
 
 734 
 
 5 
 
 0.296 
 
 375 
 
 834.5 
 
 0.175 
 
 475 
 
 934 
 
 5 
 
 0. lOI 
 
 575 
 
 1034.5 
 
 0-053 
 
 280 
 
 739 
 
 5 
 
 0.288 
 
 380 
 
 839-5 
 
 0. 171 
 
 480 
 
 939 
 
 5 
 
 0.098 
 
 580 
 
 1039-5 
 
 0.051 
 
 585 
 
 744 
 
 5 
 
 0.281 
 
 385 
 
 844-5 
 
 0.166 
 
 485 
 
 944 
 
 5 
 
 0.095 
 
 585 
 
 1044.5 
 
 0.049 
 
 290 
 
 749 
 
 5 
 
 0.274 
 
 390 
 
 849.5 
 
 0. 162 
 
 490 
 
 949 
 
 5 
 
 0.092 
 
 590 
 
 1049.5 
 
 0.047 
 
 295 
 
 754-5 
 
 0.267 
 
 395 
 
 854.5 
 
 0.158 
 
 495 
 
 954-5 
 
 0.090 
 
 595 
 
 1054.5 
 
 0.045 
 
 Specific Heat. — Two investigations have been made of the 
 specific heat of superheated steam at constant pressure, one by 
 Professor Knoblauch* and Dr. Jakob and the other by Pro- 
 fessor Thomas and Mr. Short; f the results of the latter 's inves- 
 tigation have been communicated for use in this book in 
 anticipation of the publication of the completed report. 
 
 * Mitteilungen uher Forschungsarheiten, Heft 36, p. 109. 
 t Thesis by Mr. Short, Cornell University 
 
SPECIFIC HEAT 
 
 113 
 
 Professor Knoblauch's report gives the results of the inves- 
 tigations made under his direction in the form of a table giving 
 specific heats at various temperatures and pressures and in a 
 diagram, which can be found in the original memoir, and he 
 also gives a table of mean specific heats from the temperature of 
 saturation to various temperatures at several pressures. This 
 latter table is given here in both the metric system and in the 
 English system of units. 
 
 SPECIFIC HEAT OF SUPERHEATED STEAM. 
 
 Knoblauch and Jakob 
 
 /KgperSqCm 
 p Lbs per Sq In. 
 
 t» Cent. 
 
 i$ Fahr. 
 
 1 
 
 14.2 
 
 99° 
 210° 
 
 2 
 
 28.4 
 120° 
 248° 
 
 4 
 
 56-9 
 143° 
 289° 
 
 6 
 
 85-3 
 158° 
 
 316^ 
 
 8 
 
 113. 8 
 169° 
 336° 
 
 10 
 
 142.2 
 
 179° 
 350° 
 
 12 
 
 170.6 
 187° 
 368° 
 
 14 
 
 199. 1 
 
 194° 
 381° 
 
 16 
 
 227.5 
 200° 
 392° 
 
 18 
 
 156.0 
 206° 
 403° 
 
 20 
 
 284.4 
 211° 
 412° 
 
 Fahr. 
 212° 
 302° 
 392° 
 482° 
 
 572° 
 662° 
 
 752° 
 
 Cent. 
 
 100° 
 150° 
 200° 
 250° 
 300° 
 350° 
 400° 
 
 0.463 
 0.462 
 0.462 
 0.463 
 0.464 
 0.468 
 0-473 
 
 o.'478 
 
 0-475 
 0.474 
 
 0-475 
 0.477 
 0.481 
 
 0-515 
 0. 502 
 
 0-495 
 0.492 
 0.492 
 0.494 
 
 0-530 
 0.514 
 
 0-505 
 0.503 
 0.504 
 
 0.560 
 0.532 
 0.517 
 0.512 
 0.512 
 
 
 
 
 
 
 597 
 552 
 530 
 522 
 520 
 
 0.635 
 0.570 
 0.541 
 
 0.529 
 0. 526 
 
 0.677 
 0.588 
 0.550 
 0.536 
 0-531 
 
 
 
 
 
 
 609 
 561 
 
 543 
 537 
 
 
 
 
 
 
 635 
 572 
 
 550 
 542 
 
 
 
 
 
 
 664 
 
 585 
 
 557 
 547 
 
 The construction of this table is readily understood from the 
 following example: — Required the heat needed to superheat a 
 kilogram of steam at 4 kilograms per square centimetre from 
 saturation to 300° C. The saturation temperature (to the nearest 
 degree) is 143° C; so that the steam at 300° is superheated 157°, 
 and for this is required the heat 
 
 157 X 0.492 = 77.2 calories. 
 
 The experiments of Professor Knoblauch were made at 2, 4, 
 6, and 8 kilograms per square centimetre; the remainder of the 
 table was obtained from the diagram which was extended by aid 
 of cross- curves to the extent indicated. Within the limits of 
 the experimental work the table may be used with confidence. 
 Exterpolated results are probably less reliable than those 
 obtained directly by Professor Thomas. 
 
114 
 
 SUPERHEATED VAPORS 
 
 The following table gives the mean specific heat of super- 
 heated steam as measured on a facsimile of Professor Thomas's 
 original diagram without exterpolation. 
 
 SPECIFIC HEAT OF SUPERHEATED STEAM 
 
 Thomas and Short. 
 
 
 
 Pressure Lbs 
 
 . per Sq. In 
 
 (Absolute.) 
 
 
 Degrees of 
 Superheat Fahr. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6 
 
 15 
 
 30 
 
 50 
 
 100 
 
 200 
 
 400 
 
 20° 
 
 0-536 
 
 0-547 
 
 0.558 
 
 0.571 
 
 0.593 
 
 0.621 
 
 0.649 
 
 50° 
 
 0.522 
 
 
 
 532 
 
 0.542 
 
 0.555 
 
 0.575* 
 
 0.600 
 
 0.621 
 
 100° 
 
 o-S^Z 
 
 
 
 512 
 
 0.524 
 
 0.537 
 
 0.557 
 
 0.581 
 
 0.599 
 
 150° 
 
 0.486 
 
 
 
 496 
 
 0.508 
 
 0.522 
 
 0.544 
 
 0.567 
 
 0.585 
 
 200° 
 
 0.471 
 
 
 
 480 
 
 0.494 
 
 0.509 
 
 0.533 
 
 0.556 
 
 0.574 
 
 250° 
 
 0.456 
 
 
 
 466 
 
 0.481 
 
 0.496 
 
 0.522 
 
 0.546 
 
 0.564 
 
 300° 
 
 0.442 
 
 0-453 
 
 0.468 
 
 0.484 
 
 0.511 
 
 0.537 
 
 0.554 
 
 Here again the arrangement of the table can be made evident 
 by an example : — Required the heat needed to superheat steam 
 100 degrees at 200 pounds per square inch absolute. The mean 
 specific heat from saturation is 0.581, so that the heat required 
 is 58.1 thermal units. 
 
 Total Heat. — In the solution of problems that arise in engi- 
 neering it is convenient to use the total amount of heat required 
 to raise one pound of water from freezing-point to the tempera- 
 ture of saturated steam at the given pressure and to vaporize 
 it and to superheat it at that pressure to the given temperature. 
 This total heat may be represented by the expression 
 
 H 
 
 Sup. 
 
 r + c^ {t— ts) 
 
 where / is the superheated temperature of the superheated 
 steam, 4 is the temperature of saturated steam at the given 
 pressure p, and q and r are the corresponding heat of the liquid 
 and heat of vaporization. The mean specific heat Cp may 
 usually be selected from one of the given tables without inter- 
 
ENTROPY 
 
 115 
 
 polation, as a .small variation does not have a very large 
 effect. 
 
 The total heat or heat contents of superheated steam in the 
 temperature- entropy table were obtained by the following 
 method. From Professor Thomas's diagram giving mean 
 specific heats, curves of specific heats at various temperatures 
 and at a given pressure were obtained, and the curves thus 
 obtained were faired after a comparison with curves constructed 
 with Professor Knoblauch 's specific heats at those temperatures. 
 These curves were then integrated graphically and the results 
 checked by comparison with his mean specific heats. 
 
 Entropy. — By the entropy of superheated steam is meant 
 the increase of entropy due to heating water from freezing-point 
 to the temperature of saturated steam at the given pressure, to 
 the vaporization and to the superheating at that pressure. This 
 operation may be represented as follows: 
 
 
 ^ cpdt 
 
 in which T is the absolute temperature of the superheated steam, 
 and Ts is the temperature of the saturated steam at the given 
 
 pressure; and— maybe taken from the '^ Tables of Saturated 
 
 Steam." The last term was obtained for the temperature- 
 entropy table by graphical integration of curves plotted 
 
 with values of -£^ derived from the curves of specific heats at 
 
 various temperatures just described under the previous section. 
 
 If the temperature- entropy table is not at hand, the last term 
 of the above expression may be obtained approximately by divid- 
 ing the heat of superheating, by the mean absolute temperature 
 of superheating. 
 
 This may be expressed as follows: 
 
 h (t- t,) + 459-5 
 
Il6 SUPERHEATED VAPORS 
 
 where / is the temperature of the superheated steam, 4 is the 
 temperature of saturated steam at the given pressure, and Cp is 
 the mean specific heat of superheated steam. 
 
 If this method is considered to be too crude, the computation 
 can be broken into two or more parts. Thus if t^ is an inter- 
 mediate temperature, the increase of entropy due to superheat- 
 ing may be computed as follows: 
 
 ^ {h - is) + 459-5 2 {t - h) + 459-5 
 
 where cj is the mean specific heat between 4 and /^ and c/' is 
 the specific heat between 4 and /. This method may evidently 
 be extended to take in two intermediate temperatures and give 
 three terms. 
 
 Adiabatic Expansion. — The treatment of superheated steam 
 in this chapter resembles that for saturated steam in that it does 
 not yield an explicit equation for the adiabatic line. If the 
 steam were strongly superheated during the whole operation it 
 is probable that the adiabatic line would be well represented 
 by an exponential equation, and for such case a mean value of 
 the exponent could be determined that would suffice for engi- 
 neering work. But even with strongly superheated steam at 
 the initial condition the final condition is likely to show moisture 
 in the steam after adiabatic expansion, or, for that matter, after 
 expansion of the steam in the cylinder of an engine or in a steam- 
 turbine. 
 
 Problems involving adiabatic expansion of steam which is 
 initially superheated can be solved by an extension of the method 
 for saturated steam, and this method applies with equal facility 
 to problems in which the steam becomes moist during the expan- 
 sion. The most ready method of solution is by aid of the tempera- 
 ture-entropy table, which may be entered at the proper pressure 
 (or the corresponding temperature of saturated steam) and the 
 proper superheated temperature, it being in practice sufficient to 
 take the line for the nearest tabular pressure and the column 
 
PROPERTIES OF SULPHUR DIOXIDE I17 
 
 showing the nearest degree of superheating. Following down 
 the column for entropy to the final pressure, the properties for 
 the final condition will be found; these will be the heat con- 
 tents, specific volume, and either the temperature of superheated 
 steam or the quality x, depending on whether the steam remains 
 superheated during the expansion or becomes moist. 
 
 If the external work of adiabatic expansion of steam initially 
 superheated is desired, it can be had by taking the difference of 
 the intrinsic energies. The heat equivalent of intrinsic energy 
 of moist steam is 
 
 xp -\- q = X (r — Apu) -{- q = xr -{- q — Apxu^ 
 
 and of this expression the quantity xr + q may be taken from 
 the temperature- entropy table, and the quantity Apxu can 
 be determined by aid of the steam table. In like manner the 
 heat contents of superheated steam 
 
 / 
 
 cjt 
 
 which is computed and set down in the temperature- entropy 
 table may be made to yield the heat equivalent of the intrinsic 
 energy by subtracting the heat equivalent of the external work 
 of vaporizing and superheating the steam 
 
 Ap {v- 0-), 
 
 where v is the specific volume of the superheated steam. This 
 method is subject to some criticism, especially when the steam 
 is not highly superheated, because some heat will be required 
 to do the disgregation work of superheating. Fortunately the 
 greater part of problems arising in engineering involve the heat 
 contents, so that this question is avoided. 
 
 Properties of Sulphur Dioxide. — One of the most interesting 
 and important applications of the theory of superheated vapors 
 is found in the approximate calculation of properties of certain 
 volatile liquids which are used in refrigerating- machines, and for 
 which we have not sufficient experimental data to construct tables 
 in the manner explained in the chapter on saturated vapors. 
 
Il8 SUPERHEATED VAPORS 
 
 For example, Regnaulf made experiments on the pressures 
 of saturated sulphur dioxide and ammonia, but did not de- 
 termine the heat of the Kquid nor the total heat. He did, 
 however, determine some of the properties of these substances 
 in the gaseous or superheated condition, from which it is pos- 
 sible to] construct the characteristic equations for the super- 
 heated vapors. These equations can then be used to make 
 approximate calculations of the saturated vapors, for such equa- 
 tions are assumed to be appHcable down to the saturated con- 
 dition. Of course such calculations are subject to a considerable 
 unknown error, since the experimental data are barely sufficient 
 to establish the equations for the superheated vapors. 
 
 The specific heat of gaseous sulphur dioxide is given by 
 Regnault * as 0.15438, and the coefficient of dilatation as 
 0.0039028. The theoretical specific gravity compared with air, 
 calculated from the chemical composition, is given by Landolt 
 and Bornstein f as 2.21295. Gmelin J gives the following 
 experimental determinations: by Thomson, 2.222; by Berzelius, 
 2.247. The figure 2.23 will be assumed in this work, which 
 gives for the specific volume at freezing-point and at atmospheric 
 pressure 
 
 y = '' ''^'^ = 0.347 cubic metres. 
 2.23 
 
 The corresponding pressure and temperature are 10,333 ^^^ 
 273° c. 
 
 At this stage it is necessary to assign a probable form for the 
 characteristic equation, and for that purpose the form 
 
 pv = BT - Cp"" (125) 
 
 proposed by Zeuner has commonly been used, and it is con- 
 venient to admit that it may take the form 
 
 pv = -^aT- Cp^ (126) 
 
 * Memoir es de VInstitut de France, tome xxi, xxvi. 
 t Physikalische-chemische Tabellen. 
 % Watt's translation, p. 280. 
 
PROPERTIES OF SULPHUR DIOXIDE II9 
 
 The value of the arbitrary constant a may be determined 
 from the coefficient of dilatation as follows. The coefficient 
 of dilatation is the ratio of the increase of volume at constant 
 pressure, for one degree increase of temperature, to the original 
 volume; so that the preceding equation applied at 0° C. and at 
 1° C. gives f 
 
 p,v, = ^aT,- Cpo^; 
 
 The value of a obtained by substituting known values in the 
 above equation is 0.212. Now as a appears in both the first and 
 the last terms of the right-hand side of equation (126), a con- 
 siderable change in a has but little effect on the computations 
 by aid of that equation. As will appear later an assumption 
 of a value 0.22 for a will make equation (126) agree well with 
 certain experiments on the compressibility of sulphur dioxide, 
 and it will consequently be chosen. If now we reverse the process 
 by which a was calculated from the coefficient of dilatation, 
 the latter constant will appear to have a computed value of 
 0.004, which is but little different from the experimental value. 
 
 To compute C we have 
 
 0.15438 X 426.9 X 0.22 = 14.5, 
 and the coefficient of p"" is 
 
 14.5 X 273 - 10333 X 0.347 ^ ^8 ^,^,ly. 
 
 10333 
 
 so that the equation becomes 
 
 pv= 14.5^-48/-^^ ..... (127) 
 Regnault found for the pressures 
 
 p^ = 697.83 mm. of mercury, 
 p2 = 1341.58 mm. of mercury, 
 and at 7°. 7 C. the ratio 
 
 ^=1.02088. 
 
I20 SUPERHEATED VAPORS 
 
 Reducing the given pressures to kilograms on the square 
 metre, and the temperature to the absolute scale, and applying 
 to equation (127), we obtain 1.016 instead of the experimental 
 value for the above ratio. 
 
 Regnault gives for the pressure of saturated sulphur dioxide, 
 in mm. of mercury, the equation 
 
 logp = a — ha"" — c/T; 
 
 a = 5.6663790; 
 logb = 0.4792425; 
 logc = 9.1659562 — 10; 
 log a = 9.9972989 — 10; 
 log /? = 9.98729002 — 10; 
 
 w = / + 28° c. 
 Applying equation (95), page 76, to this case, 
 
 ijA^Aa' + BlT; 
 p at 
 
 log a = 9.9972989; 
 
 log /? =^ 9.98729002; 
 
 log^ -= 8.6352146; 
 
 log^ = 7.9945332; 
 
 n = t + 28° C. 
 
 The specific volume of saturated sulphur dioxide may be 
 calculated by inserting in equation (127) for the superheated 
 vapor the pressures calculated by aid of the above equation. 
 The results at several temperatures are as follows: 
 
 / — 30° C. o + 30° C. 
 
 5 0.8292 0.2256 0.0825 
 
 Andreeff * gives for the specific gravity of fluid sulphur dioxide 
 1.4336; consequently the specific volume of the liquid is 
 
 o" = 0.0007. 
 
 * Ann. Chem. Pharm., 1859. 
 
PROPERTIES OF SULPHUR DIOXIDE 121 
 
 The value of r, the heat of vaporization, may now be calcu- 
 lated at the given temperatures by equation (106), page 89, 
 
 dt 
 in which it = s — o". 
 
 The results are 
 
 / - 30° C. o + 30° C. 
 
 r 106.9 97.60 90.54 
 
 Within the limits of error of our method of calculation, the 
 value of r may be found by the equation 
 
 r = 98 — 0.27 t (128) 
 
 The specific heat of the liquid is derived by the following 
 device. First assume that the entropy of the superheated vapor 
 may be calculated by the equation 
 
 T p 
 
 given on page 67 for perfect gases. This may be transformed 
 
 dcl> = c,[^---^-dp) .... (129) 
 
 But if we introduce into the equation for a perfect gas 
 
 pv = RT, 
 the value of R from the equation 
 
 Cp — c^ = AR, 
 
 the characteristic equation may take the form 
 
 Cpic — I 
 
 pv = ^ T- 
 
 ^ A It 
 
 Comparison of this equation with equation (126) suggests 
 
 ic — I 
 replacing the term in equation (129) by the arbitrary 
 
 factor a, so that it may read 
 
 d4> - Cj,[-^ - a-dp^ . . . . . (130) 
 
122 SUPERHEATED VAPORS 
 
 The expression for the entropy of a Uquid and its vapor is 
 
 XT Y I 
 
 -=- + ^ or -- + I cdt 
 T T J 
 
 if the vapor is dry. When differentiated this yields 
 
 d^ ^ ~ ^cdt -h dr - j^dt^ . . . .(131) 
 
 If it be assumed that equations (130) and (131) may both be 
 appHed at saturation v^^e have 
 
 / Tdp\ ^ dr r , . 
 
 '^['~''-p-dt)=='^-di~T ' • ■ ^'^'^ 
 
 If it be admitted further that the differential coefhcient -7- can 
 
 dt 
 
 be computed by the equation on page 120, the above equation 
 affords a means of estimating the specific heat of the liquid. At 
 0° C, this method gives for the specific heat 
 
 c = 0.4. 
 In English units v^e have for superheated sulphur dioxide 
 
 pv=^ 26.4T-1S4P'-'' (133) 
 
 the pressures being in pounds on the square foot, the volumes 
 in cubic feet, and the temperatures in Fahrenheit degrees 
 absolute. 
 
 For pressures in pounds on the square inch at temperatures 
 on the Fahrenheit scale, 
 
 logp = a— ha'' — c/?"; 
 
 ^ = 3-9527847; 
 log h = 0.4792425; 
 log c = 9.1659562 — 10; 
 log a = 9.9984994 — 10; 
 log /? = 9.99293890 — 10; 
 
 n = t + i8°.4 F. 
 
PROPERTIES OF AMMONIA 
 
 123 
 
 For the heat of vaporization 
 
 r = 176 — 0.27 (/ — 32) (134) 
 
 and for the specific heat of the Hquid 
 
 c = 0.4. 
 
 . In applying these equations to the calculation of a table of 
 the properties of saturated sulphur dioxide the pressures corre- 
 sponding to the temperatures are calculated as usual. Then 
 the heat of the liquid is calculated by aid of the constant specific 
 heat. The heat of vaporization is calculated by aid of equation 
 (134). Next the specific volume is calculated by inserting the 
 given temperature and the corresponding pressure for the sat- 
 urated vapor in the characteristic equation (133). Having 
 the specific volume of the vapor and that of the liquid, the heat 
 equivalent (Apu) of the external work is readily found. Finally, 
 the entropy of the liquid is calculated by the equation 
 
 rp 
 
 . 0= doge— (135) 
 
 ^ 
 
 If the reader should object that this method is tortuous and 
 full of doubtful approximations and assumptions, he must bear 
 in mind that any method that can give approximations is better 
 than none, and that all the computations for refrigerating- 
 machines, that use volatile fluids, depend on results so obtained. 
 And further, much of the waste and disappointment of earlier 
 refrigerating- machines could have been avoided if tables as good 
 as those computed by this method were then available. 
 
 Properties of Ammonia. — The specific heat of gaseous 
 ammonia, determined by Regnault, is 0.50836. The theoretical 
 specific gravity compared with air, calculated from the chemical 
 composition, is given by Landolt and Bornstein as 0.58890. 
 Gmelin gives the following experimental determinations: by 
 Thomson, 0.5931; by Biot and Arago, 0.5967. For this work 
 the figure 0.597 will be assumed, which gives for the specific 
 volume at freezing-point and at atmospheric pressure 
 
 ^ ^ '1166 = J c?o cubic metres. 
 0-597 
 
124 SUPERHEATED VAPORS 
 
 The coefficient of dilatation has not been determined, and con- 
 sequently cannot be used to determine the value of a in equation 
 (126). It, however, appears that consistent results are obtained 
 if a is assumed to be \. The coefficient of T then becomes 
 
 0.50836 X 426.9 X i = 54-3^ 
 
 and the coefficient of p^ is 
 
 54.3 X 273 - 10333 X 1.30 . 
 
 . J-4^> 
 
 10333 
 
 SO that the equation becomes 
 
 P'^ = 54-3 T —\\2 p^ (136) 
 
 The coefficient of dilatation, calculated by the same process 
 as was used in determining a for sulphur dioxide, is 0.00404, 
 which may be compared with that for sulphur dioxide. 
 
 Regnault found for the pressures 
 
 P\ = 703.50 mm. of mercury, 
 ^2 = 1435-3 rnin- of mercury, 
 
 and at 8°.i'C. the ratio 
 
 ^^^1.0188, 
 
 while equation (136) gives under the same conditions 1.0200. 
 For saturated ammonia Regnault gives the equation 
 
 log^ = a — haJ" — c/T; 
 
 a = 11.5043330; 
 log h = 0.8721769; 
 log c = 9.9777087 — 10; 
 log a = 9.9996014 — 10; 
 log /? = 9.9939729 — 10; 
 
 ^ - / + 22° C; 
 
PROPERTIES OF AMMONIA 
 
 125 
 
 by aid of which the pressures in mm. of mercury may be calculated 
 for temperatures on the centigrade scale. The differential 
 coefficient may be calculated by aid of the equation 
 
 p at 
 log A = 8.1635170 — 10; 
 log 5 = 8.4822485 — 10; 
 log a = 9.9996014 — 10; 
 log /? = 9.9939729 - 10; 
 n = / + 22° C. 
 
 The specific volume of saturated ammonia calculated by 
 equation (136) at several temperatures are 
 
 / — 30° C. o + 30° C 
 
 s 0.9982 0.2961 0.1167 
 
 Andreeff gives for*1ftie specific gravity of liquid ammonia at 
 0° C. 0.6364, so that the specific volume of the Hquid is 
 
 (T = 0.0016. 
 
 The values of r at the several given temperatures, calculated 
 by equation (128), are 
 
 / - 30° C. o + 3o°C. 
 
 ^ 325-7 300-15 277.5 
 
 which may be represented by the equation 
 r = 300 — 0.8 /. 
 
 The specific heat of the liquid, calculated by aid of equation 
 
 (132), is 
 
 C = I.I. 
 
 In Enghsh units the properties of superheated or gaseous 
 ammonia may be represented by the equation 
 
 pv = gg T — 710 p^, 
 
 in which the pressures are taken in pounds on the square foot 
 and volumes in cubic feet, while T represents the absolute 
 temperature in Fahrenheit degrees. 
 
126 SUPERHEATED VAPORS 
 
 I'he pressure in pounds on the square inch may be calculated 
 by the equation 
 
 log^ = a'— ba" — c^"", 
 
 a = 9.7907380; 
 log b = 0.8721769 — 10; 
 log c - 9.9777087 — 10; 
 log a = 9.9997786 — 10; 
 log /? = 9.9966516 — 10; 
 n = t + 7° 6 F. 
 
 The heat of vaporization may be calculated by the equation 
 r = 540 - 0.8 (/- 32), 
 and the specific heat of the hquid is 
 
 C = I.I. 
 
 m 
 
 EXAMPLES. 
 
 1. What is the weight of one cubic foot of superheated steam 
 at 500° F. and at 60 pounds pressure absolute? Knoblauch's 
 equation. Ans. 0.106 pounds. 
 
 2. Superheated steam at 50 pounds absolute has half the 
 density of saturated steam at the same pressure. What is the 
 temperature? Tumlirz's equation. Ans. 930° F. 
 
 3. What is the volume of 5 pounds of steam at 129.3 pounds 
 gauge pressure and at 359^.5 F. ? Ans. 15.8. 
 
 4. At 129.3 pounds gauge pressure 2 pounds of steam occupy 
 7 cubic feet. Find its temperature. Assume value of T for 
 entering Table I, page 112, and solve by trial. Ans. 424° F. 
 
 5. A cubic foot of steam at 140 pounds absolute weighs 0.30 
 pounds. What is its temperature? Ans. 374*^ F. 
 
 6. Two pounds of steam and water at 129.3 pounds pressure 
 above the atmosphere occupy 6 cubic feet. Heat is added and 
 the pressure kept constant till the volume is 8.5 cubic feet. Find 
 the final condition, and the external work done in expanding. 
 Ans. Temperature 681° F.; work 51800. 
 
EXAMPLES 
 
 127 
 
 7. Saturated steam at 150 pounds gauge, containing 2 per cent 
 of water, passes through a superheater on its way to an engine. 
 Its final temperature is 400° F. Find the increase in volume 
 and the heat added per pound. 
 
 8. Let the initial temperature of superheated steam be 380° F. 
 at the pressure of 150 pounds absolute. Find the condition 
 after an adiabatic expansion to 20 pounds absolute. Determine 
 also the initial and final volumes. Ans. (i) 0.895; (2) 3.09 
 cubic feet; (3) 17.8 cubic feet. 
 
 9. In example 9, page 109, suppose that the steam at cut-ofi" 
 were superheated 10° F. above the temperature of saturated 
 steam at the given pressure, and solve the example. Ans. 
 (i) 0.887; (2) 87° superheating; (3) same as before; (4) n = 
 i-i37> (5) 1972 and 1950 foot-pounds. 
 
CHAPTER VIII. 
 
 THE STEAM-ENGINE. 
 
 The steam-engine is still the most important heat-engine, 
 though its supremacy is threatened on one hand by the steam- 
 turbine and on the other by the gas-engine. When of large size 
 and properly designed and managed its economy is excellent and 
 can be excelled only by the largest and best gas-engines, 
 and in many cases these engines (even with the advantage of 
 a more favorable range of temperature) depend for their com- 
 mercial success on the utilization of by-products. 
 
 It can be controlled, regulated, and reversed easily and posi- 
 tively — properties which are not possessed in like degree by 
 other heat-engines. It is interesting to know that the theory 
 of thermodynamics was developed mainly to account for the 
 action and to provide methods of designing steam-engines; 
 though neither object is entirely accomplished, on account of 
 the fact that the engine-cylinder must be made of some metal to 
 be hard and strong enough to endure service, for all metals are 
 good conductors of heat, and seriously affect the action of a con- 
 densable fluid like steam. 
 
 Carnot^s Cycle for a steam-engine is repre- 
 sented by Fig. 31, in which ah and cd are 
 isothermal lines, representing the application 
 and rejection of heat at constant temperature 
 and at constant pressure, he and da are 
 adiabatic lines, representing change of tem- 
 perature and pressure, without transmission 
 
 ^^'^^' of heat through the walls of the cyhnder. 
 
 The diagram representing Carnot 's cycle has an external resem- 
 blance to the indicator-diagram from some actual engines, 
 but it differs in essential particulars. 
 
 128 
 
CARNOT'S CYCLE 
 
 129 
 
 In the condition represented by the point a the cylinder con- 
 tains a mixture of water and steam at the temperature /^ and 
 the pressure p^. If connection is made with a source of heat 
 at the temperature t^, and heat is added, some of the water will 
 be vaporized and the volume will increase at constant pressure 
 as represented by ab. If thermal communication is now inter- 
 rupted, adiabatic expansion may take place as represented by be 
 till the temperature is reduced to t2, the temperature of the 
 refrigerator, with which thermal communication may now be 
 established.. If the piston is forced toward the closed end of 
 the cylinder some of the steam in it will be condensed, and the 
 volume will be reduced at constant pressure as represented by 
 cd. The cycle is completed by an adiabatic compression rep- 
 resented by da. 
 
 If the absolute temperature of the source of heat is T^, and 
 if that of the refrigerator is T^, then the efficiency is 
 
 , - r. - r. 
 
 whatever may be the working fluid. 
 
 For example, if the pressure of the steam during isothermal 
 expansion is 100 pounds above the atmosphere, and if the pressure 
 during isothermal compression is equal to that of the atmos- 
 phere, then the temperatures of the source of heat and of the 
 refrigerator are 337°.6 F. and 212° F., or 797.1 and 671.5 abso- 
 lute, so that the efficiencv is 
 
 707.1 — 671. c; 
 
 ^^ —^^= 0.157. 
 
 797-1 
 
 The following table gives the efficiencies worked out in , a 
 similar way, for various steam- pressures, — both for t^ equal to 
 212° F., corresponding to atmospheric pressure, and for t^, 
 equal to 116° F., corresponding to an absolute pressure of 1.5 
 pounds to the square inch: 
 
I30 
 
 THE STEAM-ENGINE 
 
 EFFICIENCY OF CARNOT'S CYCLE FOR STEAM-ENGINES. 
 
 Initial Pressure 
 by the Gauge, 
 
 above the 
 Atmosphere. 
 
 Atmospheric 
 Pressure. 
 
 i.S Pounds 
 Absolute. 
 
 15 
 30 
 
 0-053 
 0.084 
 
 0.189 
 0.215 
 
 60 
 
 0. 124 
 
 0.249 
 
 100 
 
 o»i57 
 
 0.278 
 
 150 
 
 0.186 
 
 0.302 
 
 200 
 
 0,207 
 
 0.320 
 
 300 
 
 0.238 
 
 0-347 
 
 The column for atmospheric pressure may be used as a 
 standard of comparison for non-condensing engines, and the 
 column for 1.5 pounds absolute may be used for condensing 
 engines. 
 
 It is interesting to consider the condition of the fluid in the 
 cylinder at the different points of the diagram for Carnot's 
 cycle. Thus if the fluid at the condition represented by b in 
 Fig. 31 is made up of x^ part steam and i—Xf, part water, then 
 from equation (118) the condition at the point c is given by 
 
 ^. = ^(^% + ^.-^.) • • • • (137) 
 
 In like manner the condition of the mixture at the point d is 
 
 ^d 
 
 (|^ x„ + e,- e,j .... (138) 
 
 It is interesting to note that if Xf, is larger than one-half, that 
 is, if there is more steam than water in the cylinder at ft, then 
 the adiabatic expansion is accompanied by condensation. Again, 
 if Xa is less than one-half, then the adiabatic compression is also 
 accompanied by condensation. Very commonly it is assumed 
 that Xb is unity, so that there is dry saturated steam in the cylin- 
 der at b\ and that Xa is zero, so that there is water only in the 
 
EFFICIENCY OF CARNOT'S CYCLE 
 
 131 
 
 P60 
 
 cylinder at a; but there is no necessity for such assumptions, 
 and they in no way affect the efficiency. 
 
 The temperature-entropy diagram for Carnot's cycle for a 
 steam-engine is shown by Fig. 32, on which are drawn also the 
 lines for entropy of the liquid 
 mdj and the entropy of satur- 
 ated vapor bCy as well as the 
 lines which represent the value 
 of Xy the dryness factor. This 
 diagram represents to the eye 
 the vaporization during the 
 isothermal expansion ab, the 
 partial condensation during 
 the adiabatic expansion be, 
 the isothermal condensation 
 
 0.1 0.2 0.3 
 
 ¥ 
 
 Fig. 32. 
 
 along cdj and the condensation 
 during the adiabatic compression da. In the diagram the work- 
 ing substance is shown as water at a and as dry steam at b; 
 the efficiency would clearly be the same for a cycle a' y c' d' , 
 which contains a varying mixture of water and steam under all 
 conditions. 
 
 If the cylinder contains M pounds of steam and water, the 
 heat absorbed by the working substance during isothermal 
 expansion is 
 
 Q^ = Mr^ {^x^ - x„) , (139) 
 
 and the heat rejected during isothermal compression is 
 
 so that the heat changed into work during the cycle is 
 Qi - Q^ = M\r^ {Xf, - Xa) - r^ (x^ - Xa)l 
 
 But from equations (137) and (138) 
 
 -^ 1 
 
132 
 
 THE STEAM-ENGINE 
 
 and the expression for the heat changed into work becomes 
 
 Q^-Q2- Mr, (x, - xj ^1 ~ ^' . . . (140) 
 
 ^ 1 
 
 This equation is deduced because it is convenient for making 
 comparisons of various other volatile liquids and their vapors, 
 with steam, for use in heat-engines. It is of course apparent 
 
 from equations (139) and (140), a conclusion which is known 
 independently, and indeed is necessary in the development of 
 the theory of the adiabatic expansion of steam. 
 
 In the discussion thus far it has been assumed that the work- 
 ing fluid is steam, or a mixture of steam and water. But a 
 mixture of any volatile liquid and its vapor will give similar 
 results, and the equations deduced can be applied directly. The 
 principal difference will be due to the properties of the vapor 
 considered, especially its specific pressures and specific volumes 
 for the temperatures of the source of heat and the refrigerator. 
 
 For example, the efficiency of Carnot's cycle for a fluid 
 working between the temperatures 160° C. and 40° C. is 
 
 160 — 40 
 
 — =^— = 0.277. 
 
 160 + 273 
 
 The properties of steam and of chloroform at these tempera- 
 tures are 
 
 Pressure, mm. mercury 
 Volume, cubic metres . 
 Heat of vaporization, r 
 Entropy of liquid, . . 
 
 For simplicity, we may assume that one kilogram of the fluid 
 is used in the cylinder for Carnot's cycle, and that Xi, is unity 
 while Xa is zero, so that from equation (140) 
 
 T - T 
 
 Steam 
 
 
 Chloroform. 
 
 40° c. 
 
 160° c. 
 
 4o°C. 160° C. 
 
 54.91 
 
 4651.4 
 
 369.26 8734.2 
 
 19.74 
 
 0-3035 
 
 0.4449 0.0243 
 
 78.7 
 
 494.2 
 
 63-13 50.53 
 
 0.1364 
 
 0.4633 
 
 0.03196 O.IIO41 
 
 r. 
 
EFFICIENCY OF CARNOT'S CYCLE 133 
 
 and for steam 
 
 Qi - Q2 == 494-2 X 0.277 = 137 calories, 
 while for chloroform 
 
 Qi - Q2= 50-53 X 0.277 = 14 calories. 
 
 After adiabatic expansion the qualities of the fluid will be, 
 from equation (137), for steam 
 
 and for chloroform 
 
 Xr = — ^ I 5_Oj _|. 0.IIO4I — 0.0^106) = 0.060. 
 
 63.13 U60 + 273 4 5 y / y y 
 
 The specific volumes after adiabatic expansion are, conse- 
 quently, for steam 
 
 v^ = XcU^ + o" = 0.795 (19.74 — o.ooi) + o.ooi = 15.7, 
 
 and for chloroform 
 
 Vc = x^u^ + o" = 0.969 (0.4449 — 0.000655) + 0.000655 = 0.431. 
 
 These values for v^ just calculated are the volumes in the 
 cylinder at the extreme displacement of the piston, on the 
 assumption that one kilogram of the working fluid is vaporized 
 during isothermal expansion. A better idea of the relative 
 advantages of the two fluids will be obtained by finding the 
 heat changed into work for each cubic metre of maximum piston- 
 displacement, or for a cylinder having the volume of one cubic 
 metre. This is obtained by dividing Q^ — Q^, the heat changed 
 into work for each kilogram by v^. For steam the result is 
 
 (Qi - Q2) -^ ^c = 137 - 15-7 == 8.73, 
 
 and for chloroform it is 
 
 (Qi - Q2) - ^^c =- 14 -^ 0.413 = 34; 
 from which it appears that for the same volume chloroform 
 can produce more than three and a half times as much power. 
 
134 
 
 THE STEAM-ENGINE 
 
 Even if we consider that the difference of pressure for chloro- 
 form, 
 
 8734.2 - 369.3 = 8364.9 mm., 
 
 is nearly twice that for steam, which has only 
 4651:4 - 54.9 = 4596.5 mm. 
 
 difference of pressure, the advantage appears to be in ; favor of 
 chloroform. If, however, the difference of pressures given for 
 chloroform is allowable also for steam, giving 
 
 8364.9 + 54.9 = 8419.8 mm. 
 
 for the superior pressure, then the initial temperature for steam 
 becomes 184^.9 C-> ^^^ ^^^ efficiency becomes 
 
 184.9 "-40 o 
 
 — ^ =0.^18, 
 
 184.9 +273 
 
 instead of 0.277. On the whole, steam is the more desirable 
 fluid, even if we do not consider the inflammable and poisonous 
 nature of chloroform. Similar calculations will show that on 
 the whole steam is at least as well adapted for use in heat-engines 
 as any other saturated fluid; in practice, the cheapness and 
 incombustibility of steam indicate that it is the preferable fluid 
 for such uses. 
 
 Non-conducting Engine. Rankine Cycle. — The conditions 
 required for alternate isothermal expansion and adiabatic expan- 
 sion cannot be fulfilled for Carnot's cycle with steam any more 
 than they could be for air. The diagram for the cycle with 
 steam, however, is well adapted to production of power; the 
 contrary is the case with air, as has already been shown. 
 
 In practice steam from a boiler is admitted to the cylinder of 
 the steam-engine during that part of the cycle which corre- 
 sponds to the isothermal expansion of Carnot 's cycle, thus, trans- 
 ferring the isothermal expansion to the boiler, where steam is 
 formed under constant pressure. In like manner the isothermal 
 compression is replaced by an exhaust at constant pressure, 
 during which steam may be condensed in a separate condenser, 
 
a 
 
 V 
 
 
 
 
 NON-CONDUCTING ENGINE 135 
 
 cooled by cold water. The cylinder is commonly made of cast 
 iron, and is always some kind of metal; there is consequently 
 considerable interference due to the conductivity of, the walls of 
 the cylinder, and the expansion and compression are never 
 adiabatic. There is an advantage, however, in discussing first 
 an engine with a cylinder made of some non-conducting material, 
 although no such material proper for making cylinders is now 
 known. 
 
 The diagram representing the operations in a non-conducting 
 cylinder for a steam-engine (sometinies called the Rankine cycle) 
 can be represented by Fig. 33. ab represents 
 the admission of dry saturated steam from 
 the boiler; be is an adiabatic expansion to the 
 exhaust pressure; cd represents the exhaust; 
 and da is an adiabatic compression to the ''"' fig. 33. 
 initial pressure. It is assumed that the small 
 volume, represented by a, between the piston and the head of 
 the cylinder is filled with dry steam, and that the steam remains 
 homogeneous during exhaust so that the quality is the same at 
 d as at c. These conditions are consistent and necessary, 
 since the change of condition due to adiabatic expansion (or 
 compression) depends only on the initial condition and the 
 initial and final pressures; so that an adiabatic expansion from 
 a to d would give the same quality at ^ as that found at c after 
 adiabatic expansion from b, and conversely adiabatic compres- 
 sion from d to a gives dry steam at a as required. 
 
 The cycle represented by Fig. 33 differs most notably from 
 Carnot's cycle (Fig. 32) in that ab represents admission of steam 
 and cd represents exhaust of steam, as has already been pointed 
 out. It also differs in that the compression da gives dry steam 
 instead of wet steam. The compression line da is therefore 
 steeper than for Carnot's cycle, and the area of the figure is 
 slightly larger on this account. This curious fact does not 
 indicate that the cycle has a higher efficiency; on the contrary, 
 the efficiency is less, and the cycle is irreversible. 
 
 If the pressure during admission (equal to the pressure in 
 
136 THE STEAM-ENGINE 
 
 the boiler) is p^, and if the pressure during exhaust is p^j then 
 the heat required to raise the water resuhing from the conden- 
 sation of the exhaust-steam is 
 
 where q^ is the heat of the Uquid at the pressure p^y and q^ is the 
 heat of the Uquid at the pressure p^. The heat of vaporization 
 at the pressure p^ is r^, so that the heat required to raise the feed- 
 water from the temperature of the exhaust to the temperature 
 in the boiler and evaporate it into dry steam is 
 
 Oi = ^ +?i - ?2 (141) 
 
 and this is the quantity of heat supplied to the cylinder per 
 pound of steam. 
 
 The steam exhausted from the cylinder has the quality x^y 
 calculated by aid of the equation 
 
 and the heat that must be withdrawn when it is condensed is 
 
 Q2 = ^2^ (142) 
 
 this is the heat rejected from the engine. The heat changed 
 into work per pound of steam is 
 
 <3i - 62 = ^1 + ?i - ?2 - ^2^2 . . . • (143) 
 
 The efficiency of the cycle is 
 
 If values are assigned to p^ and p^ and the proper numerical 
 calculations are made, it will appear that the efficiency for a 
 non-conducting engine is always less than the efficiency for 
 Carnot's cycle between the corresponding temperatures. 
 
 It should be remarked that the efficiency is not affected by 
 the clearance or space between the piston and the head of the 
 cylinder and the space in the steam-passages of the cylinder, 
 provided that the clearance is filled with dry saturated steam as 
 
USE OF THE TEMPERATURE-ENTROPY DIAGRAM 
 
 137 
 
 indicated in Fig. t,2>' This is evident from the fact that no term 
 representing the clearance, or volume at a, Fig. 33, appears in 
 equation (144). Or, again, we may consider that the steam in 
 the cylinder at the beginning of the stroke, occupying the vol- 
 ume represented by a, expands during the adiabatic expansion 
 and is compressed again during compression, so that one 
 operation is equivalent to and counterbalances the other, and 
 so does not affect the efficiency of the cycle. 
 
 Use of the Temperature-Entropy Diagram. — The Rankine 
 cycle is drawn with a varying quantity of steam in the cylinder, 
 beginning at a, Fig. 33, with the steam caught in the clearance 
 and finishing at b, with that weight plus the weight drawn from 
 the boiler; consequently a proper temperature-entropy diagram, 
 which represents the changes of one pound of the working sub- 
 stance, cannot be drawn. 
 
 We may, however, use the temperature-entropy diagram 
 (like Fig. 30, page 104, or the plate at the end of the book) for 
 solving problems connected with that cycle instead of equations 
 (143) and (144)- 
 
 In the first place we have by equa- 
 tion (96), page S3, 
 
 I 
 
 cdl, 
 
 and by equation (113), page 97, 
 
 -/ 
 
 cdt 
 T 
 
 for a volatile liquid. From the latter 
 we have 
 
 cdt = TdO; 
 
 therefore 
 
 / 
 
 = / TdO. 
 
 Fig. 34- 
 
 From this last equation it is evident that the heat of the liquid qi 
 for water represented by the point a in Fig. 34, is measured by 
 
138 THE STEAM-ENGINE 
 
 the area Omao. In like manner the heat of the liquid q^ cor- 
 responding to the point d, is represented by the area Omdn. 
 Again, the heat added during the vaporization represented by 
 
 ah, is ^j, while the increase of entropy is — ^ . Therefore the heat 
 
 of vaporization can be represented by the area oahp. In like 
 manner the partial vaporization x^r^ can be represented by the 
 area ndcp. Therefore the heat changed into work for the cycle 
 in Fig. 33, which has been represented by 
 
 ^1 + ?i - (^2^2 + ?2)> 
 can equally well be represented by the area 
 
 abed = area Omao + area oahp 
 — (area Omdn + area ndcp). 
 
 It will consequently be sufficient to measure the area abed 
 by any means, for example, by aid of a planimeter, in order to 
 determine the heat changed into work during the operation of the 
 non-conducting engine working on the Rankine cycle. If the plan- 
 imeter determines the area in square inches, the scale of the draw- 
 ing for Fig. 34 should be one inch per degree, and one inch per 
 unit of entropy, or, if other and more convenient scales are to be 
 used, proper reductions must be made to allow for those scales. 
 
 It must be firmly fixed in mind that the use of a diagram like 
 Fig. 34 is justified because it has been proved that the area 
 abed (drawn to the proper scale) is numerically equal to the 
 heat changed into work as computed by equation (143), and 
 that the diagram does not represent the operations of the cycle. 
 This is entirely different from the case of the diagram. Fig. 32, 
 which icorrectly represents the operations of Carnot 's cycle. 
 
 The illustration of the use of the temperature-entropy diagram 
 for this purpose is chosen for convenience with dry saturated 
 steam at b, Fig. 34. It is evident that it could (with equal 
 propriety) be applied to an engine supplied with moist steam if 
 r^ is replaced by x^r^ in equation (143) and if b is located at the 
 proper place between a and b. 
 
 The actual measurement of areas by a planimeter is seldom 
 
INCOMPLETE CYCLE 1 39 
 
 if ever applied, but the diagram is used effectively in the dis- 
 cussion of certain problems of non-reversible flow of steam in 
 nozzles and turbines, with allowance for friction. 
 
 It further suggests an approximation that may sometimes be 
 useful, especially if the change of pressure (and temperature) is 
 small. Thus the area ahcd may be approximately represented 
 by the expression 
 
 i (ah + dc) be = \{^ + ^) (.h - h), 
 
 SO that in place of equation (143) we may have 
 
 for the heat changed into work by Rankine's cycle. 
 
 This approximation depends on treating ah as a straight line, 
 and this assumption is more correct as the difference of temper- 
 ature is less; that is for those cases in which equation (143) 
 deals with the difference of quantities of about the same magni- 
 tude, and may consequently be affected by a large relative error. 
 
 Temperature-Entropy Table. — The temperature- entropy table 
 which has been described on page 106 was computed for solu- 
 tion of problems of this nature, more especially in turbine 
 design, and enables us to determine the heat changed into work 
 directly with sufficient accuracy for engineering work, without 
 interpolation ; it also gives the quality x and the specific volume. 
 
 Incomplete Cycle. — The cycle for a non-conducting engine 
 may be incomplete because the expansion is not carried far 
 enough to reduce the pressure to that 
 of the back-pressure line, as is shown 
 in Fig. 35. Such an incomplete cycle 
 has less efficiency than a complete cycle, 
 but in practice the advantage of using 
 a smaller cylinder and of reducing fric- 
 tion is sufficient compensation for the 
 small loss of efficiency due to a moderate drop at the end of 
 the stroke, as shown in Fig. 35. 
 
 p 
 a 
 
 h 
 
 ^' 
 
 
 e 
 
 
 
 
 
 
 
 V 
 
 Fig. 35- 
 
I40 THE STEAM-ENGINE 
 
 The discussion of the incomplete cycle is simplified by assum- 
 ing that there is no clearance and no compression as is indicated 
 by Fig. 35. It will be shown later that the efficiency will be the 
 same with a clearance, provided the compression is complete. 
 
 The most ready way of finding the efficiency for this cycle is 
 to determine the work of the cycle. Thus the work during 
 admission is 
 
 where u^ is the increase of volume due to vaporization of a pound 
 of steam, and cr is the specific volume of water. The work during 
 expansion is 
 
 ^b - E, =j (/?, + q, - x,p, - q,), 
 
 where q^ and p^ are the heat of the liquid and the heat- equivalent 
 of the internal work during vaporization at the pressure p^, 
 while qc and pc are corresponding quantities for the pressure at c. 
 x^ is to be calculated by the equation 
 
 - = ^&^^-'')- 
 
 The work done by the piston on the steam during exhaust is 
 
 The total work of the cycle is obtained by adding the work 
 during admission and expansion and subtracting the work 
 during exhaust, giving 
 
 J (p^ + Ap^u, - x,p, - Ap.j)c,u, + 9i - q,) + (/>, - p^) 0-. (146) 
 
 The last term is small, and may be neglected. Adding and 
 subtracting Ap^x^u^ and multiplying by ^, we get for the heat- 
 equivalent of the work of the cycle 
 
 Qi- Q2 = ^1- ^crc + ^(/ - P2) ^'^c +qt- qc (147) 
 
STEAM-CONSUMPTION OF NON-CONDUCTING ENGINE 141 
 
 which is equal to the difference between the heat suppHed and 
 the heat rejected as indicated. The heat supplied is 
 
 61 = ^ + ?i - (Iv 
 as was deduced for the complete cycle; the cost of making the 
 steam remains the same, whether or not it is used efficiently. 
 Finally, the efficiency of the cycle is 
 
 e = gi ~ Q2 _ r, + q, - ^crc - qc + A {p, - p,) x,u, 
 
 <2i ^ + ?i - q, 
 
 ^ + ?i - ?2 
 
 If pc is made equal to p\ in the preceding equation, it will be 
 reduced to the same form as equation (144), because the expan- 
 sion in such case becomes complete. 
 
 Steam-Consumption of Non-conducting Engine. — A horse- 
 power is 33000 foot-pounds per minute or 60 X 33000 foot-pounds 
 per hour. But the heat changed into work per pound of steam 
 by a non-conducting engine with complete expansion is, by 
 equation (143), 
 
 ''1 + ?1 - ?2 - ^2^V 
 
 SO that the steam required per horse-power per hour is 
 
 60 X 33000 
 
 778 K + ?i - ?2 - ^2^2) 
 
 Similarly, the steam per horse-power per hour for an engine 
 with incomplete expansion, by aid of expression (146), is 
 
 60 X 33000 
 
 778 {p^ + Ap^u^ - x,p, - Ap^x.u, + ?i - qc)' 
 
 The value of x^ or Xc is to be calculated by the general equation 
 
 The denominator in either of the above expressions for the 
 steam per horse-power per hour is of course the work done per 
 pound of steam, and the parenthesis without the mechanical 
 
(i49) 
 
 142 THE STEAM-ENGINE 
 
 equivalent 778 is equal to Q^ — Q^. If then we multiply and 
 divide by 
 
 Qi = ^1 + ?i - ?2. 
 
 that is, by the heat brought from the boiler by one pound of 
 steam, we shall have in either case for the steam consumption 
 in pounds per hour 
 
 60 X 33000 X Q, 60 X 33000 
 
 where 
 
 is the efficiency for the cycle. 
 
 Actual Steam-Engine. — The indicator-diagram from an actual 
 steam-engine differs from the cycle for a non-conducting engine 
 in two ways: there are losses of pressure between the boiler and 
 the cylinder and between the cylinder and the condenser, due 
 to the resistance to the flow of steam through pipes, valves, and 
 passages; and there is considerable interference of the metal of 
 the cylinder with the action of the steam in the cylinder. The 
 losses of pressure may be minimized for a slow-moving engine 
 by making the valves and passages direct and large. The 
 interference of the walls of the cylinder cannot be prevented, 
 but may be ameliorated by using superheated steam or by steam- 
 jacketing. 
 
 When steam enters the cylinder of an engine, some of it is 
 condensed on the walls which were cooled by contact %with 
 exhaust-steam, thereby heating them up nearly to the tempera- 
 ture of the steam. After cut-off the pressure of the steam is 
 reduced by expansion and some of the water on the walls of 
 the cylinder vaporizes. At release the pressure falls rapidly 
 to the back-pressure, and the water remaining on the walls is 
 nearly if not all vaporized. It is at once evident that so much 
 of the heat as remains in the walls until release and is thrown 
 out during exhaust is a direct loss; and again, the heat which 
 is restored during expansion does work with less efficiency^ 
 
ACTUAL STEAM-ENGINE 1 43 
 
 because it is reevaporated at less than the temperature in the 
 boiler or in the cylinder during admission. A complete state- 
 ment of the action of the walls of the cylinder of an engine, 
 with quantitative results from tests on engines, was first given 
 by Hirn. His analysis of engine tests, showing the interchanges 
 of heat between the walls of the cylinder and the steam, will be 
 given later. It is sufficient to know now that a failure to con- 
 sider the action of the walls of the cylinder leads to gross errors, 
 and that an attempt to base the design of an engine on the theory 
 of a steam-engine with a non-conducting cylinder can lead only 
 to confusion and disappointment. 
 
 The most apparent effect of the influence of the walls of the 
 cylinder on the indicator-diagram is to change the expansion 
 and the compression lines ; the former exhibits this change most 
 clearly. In the first place the fluid in the cylinder at cut-off 
 consists of from twenty to fifty per cent hot water, which is found 
 mainly adhering to the walls of the cylinder. Even if there 
 were no action of the .walls during expansion the curve would be 
 much less steep than the adiabatic line for dry saturated steam. 
 But the reevaporation during expansion still further changes the 
 curve, so that it is usually less steep than the rectangular 
 hyperbola. 
 
 It may be mentioned that the fluctuations of temperature 
 in the walls of a steam-engine cylinder caused by the conden- 
 sation and reevaporation of water do not extend far from the sur- 
 face, but that at a very moderate depth the temperature remains 
 constant so long as the engine runs under constant conditions. 
 
 The performance of a steam-engine is commonly stated in 
 pounds of steam per horse-power per hour. For example, a 
 small Corliss engine, developing 16.35 horse-power when 
 running at 61.5 revolutions per minute under 77.4 pounds 
 boiler-pressure, used 548 pounds of steam in an hour. The 
 steam consumption was 
 
 548 -^ 16.35 = 33-5 • 
 
 pounds per horse-power per hour. 
 
144 
 
 THE STEAM-ENGINE 
 
 This method was considered sufficient in the earlier history 
 of the steam-engine, and may now be used for comparing simple 
 condensing or non-condensing engines which use saturated 
 steam and do not have a steam-jacket, for the total heat of steam, 
 and consequently the cost of making steam from water at a given 
 temperature increases but slowly with the pressure. 
 
 The performance of steam-engines may be more exactly 
 stated in British thermal units per horse-power per minute. 
 This method, or some method equivalent to it, is essential in 
 making comparisons to discover the advantages of superheat- 
 ing, steam-jacketing, and compounding. For example, the 
 engine just referred to used steam containing two per cent of 
 moisture, so that x^ at the steam-pressure of 77.4 pounds was 
 0.98. The barometer showed the pressure of the atmosphere 
 to be 14.7 pounds, and this was also the back-pressure during 
 exhaust. If it be assumed that the feed-water was or could 
 be heated to the corresponding temperature of 212° F., the 
 heat required to evaporate it against 77.4 pounds above the 
 atmosphere or 92.1 pounds absolute was 
 
 ^/i + ?i ~ ?2 ^ o-9^ ^ 888.0 + 292.1 - 180.3 = 982.0 B.T.U. 
 The thermal units per horse-power per minute were 
 
 60 
 
 Efficiency of the Actual Engine. — When the thermal units 
 per horse-power per minute are known or can be readily cal- 
 culated, the efficiency of the actual steam-engine may be found by 
 the following method : A horse-power corresponds to the develop- 
 ment of 33000 foot-pounds per minute, which are equivalent to 
 33000 -^ 778 = 42.42 
 
 thermal units. This quantity is proportional to Q^ — Q^y and 
 the thermal units consumed per horse-power per minute are 
 proportional to Q^, so that the efficiency is 
 
 g _ QjL^Z^^ 42-42 ^ 
 
 Qj B.T.U. per H.P. per min. * 
 
EFFICIENCY OF THE ACTUAL ENGINE 
 
 145 
 
 For example, the Corliss engine mentioned above had an 
 efficiency of 
 
 42.42 -r 548 - 0.077. 
 
 This same method may evidently be applied to any heat- 
 engine for which the consumption in thermal units per horse- 
 power per hour can be apphed. 
 
 From the tests reported in Chapter XIII it appears that the 
 engine in the laboratory of the Massachusetts Institute of Tech- 
 nology on one occasion used 13.73 pounds of steam per horse- 
 power per hour, of which 10.86 pounds were supplied to the 
 cylinders and 2.87 pounds were condensed in steam-jackets on the 
 cylinders. The steam in the supply-pipe had the pressure of 
 1.57.7 pounds absolute, and contained 1.2 per cent of moisture. 
 The heat supplied to the cylinders per minute in the steam 
 admitted was 
 
 10.86 (x/j + q^- q^) - 60 
 
 = 10.86 (0.988 X 858.6 -f 333.9 - 120.0) -V- 60 
 
 = 191 B.T.U. ; 
 
 ^2 being the heat of the liquid at the temperature of the back- 
 pressure of 4.5 pounds absolute. 
 
 The steam condensed in the steam-jackets was witMrawn 
 at the temperature due to the pressure and could have been 
 returned to the boiler at that temperature; consequently the 
 heat required to vaporize it was r^, and the heat furnished by 
 the steam in the jackets was 
 
 2.87 X 0.98 X 858.6 -=- 60 = 40.6 B.T.U. 
 The heat consumed by the engine was 
 
 191 -f 40.6 = 232 B.T.U. 
 
 per horse-power per minute, and the efficiency was 
 e = 42.42 -^ 232 = 0.183. 
 
146 THE STEAM-ENGINE 
 
 The efficiency of Carnot 's cycle for the range of temperatures 
 corresponding to 157.7 and 4.5 pounds absolute, namely, 82i°.7 
 and 61 7°. 2 absolute, is 
 
 T. - r„ 821.7 — 617.2 
 
 e = -^ — 2 == '- '— = 0.248. 
 
 T^ 821.7 
 
 The efficiency for a non-conducting engine with complete 
 expansion, calculated by equation (144), is for this case 
 
 X r^ 0.821 X 1004.1 
 
 J — — = 0.227 
 
 ^ + ?i - ?2 S58.6 + 333-9 - 126.0 
 
 where x^ is calculated by the equation 
 
 617.2 / 858.6 , „ ■ \ _ 
 
 = — ' — • I -r V 0.^180 - 0.2282 = 0.821. 
 
 1004.1 \821.7 •" ^ I 
 
 During the test in question the terminal pressure at the end of 
 the expansion in the low-pressure cylinder was 6 pounds abso- 
 lute, which gives 
 
 629.6 /858.6 ,0 \ o 
 
 = ^(d7:7 + °-5'«9-°-475J= 0.832, 
 
 and the efficiency by equation (148) was 
 ^/// _ J __ ^c^c - Qc + q,. - A (p, - p.^) x,u, 
 
 ^1 + ?1 - ?2 
 _ _ 0.832X995.8- 138.0+ 126.0+^1(6-4.5)0.832 X62 
 
 858-6 + 333.9 - 126.0 
 
 = 0.222. 
 
 The real criterion of the perfection of the action of an engine 
 is the ratio of its actual efficiency to that of a perfect engine. 
 If for the perfect engine we choose Carnot 's cycle the ratio is 
 
 e 0.18^ ^ 
 
 -; = ;f- = 0.7^6. 
 
 e' 0.2485 ^^ 
 
EFFICIENCY OF THE ACTUAL ENGINE 147 
 
 But if we take for our standard an engine with a cylinder of non- 
 conducting material the ratio for complete expansion is 
 
 e o.i8s o 
 
 - = f- = 0.807. 
 
 e" 0.227 
 
 For incomplete expansion the ratio is 
 
 e 0.183 o 
 
 — = ^ =0.824. 
 
 e'" 0.222 
 
 To complete the comparison it is interesting to calculate 
 the steam-consumption for a non-conducting steam-engine by 
 equation (149), both for complete and for incomplete expan- 
 sion. For complete expansion we have 
 
 60 X 3SOOO J 
 ^- =10.5 pounds, 
 
 778 X 0.227 (858.6 + 333.9 - 126.0) 
 
 and for incomplete expansion 
 
 60 X 33000 ■ 
 
 778 X 0.222 (858.6 -f 333.9 - 126.0) 
 
 = 10.7 pounds 
 
 per horse-power per hour. 
 
 But if these steam-consumptions are compared with the 
 actual steam-consumption of 13.73 pounds per horse-power 
 per hour, the ratios are 
 
 IO-5 -^ 1373 = 0-766 and 10.7 -^ 13.73 = 0.783, 
 
 which are very different from the ratios of the efficiencies. The 
 discrepancy is due to the fact that more than a fourth of the 
 steam used by the actual engine is condensed in the jackets 
 and returned at full steam temperature to the boiler, while the 
 non-conducting engine has no jacket, but is assumed to use all 
 the steam in the cylinder. 
 
 From this discussion it appears that there is not a wide margin 
 for improvement of a well-designed engine running under favor- 
 able conditions. Improved economy must be sought either by 
 increasing the range of temperatures (raising the steam- pressure 
 
148 
 
 THE STEAM-ENGINE 
 
 or improving the vacuum), or by choosing some other form of 
 heat-motor, such as the gas-engine. 
 
 Attention should be called to the fact that the real criterion of 
 the economy of a heat-engine is the cost of producing power by 
 that engine. The cost may be expressed in thermal units per 
 horse-power per minute, in pounds of steam per horse-power 
 per hour, in coal per horse-power per hour, or directly in money. 
 The expression in thermal units is the most exact, and the best 
 for comparing engines of the same class, such as steam-engines. 
 If the same fuel can be used for different engines, such as steam- 
 and gas-engines, then the cost in pounds of fuel per horse-power 
 per hour may be most instructive. But in any case the money 
 cost must be the final criterion. The reason why it is not more 
 frequently stated in reports of tests is that it is in many cases 
 somewhat difficult to determine, and because it is affected by 
 market prices which are subject to change. 
 
 At the present time a pressure as high as 150 pounds above 
 the atmosphere is used where good economy is expected. It 
 appears from the table on page 132, showing the efficiency of 
 Carnot's cycle for various pressures, that the gain in econom}- 
 by increasing steam-pressure above 150 pounds is slow. The 
 same thing is shown even more clearly by the following table: 
 
 EFFECT OF RAISING STEAM-PRESSURE. 
 
 Boiler- 
 
 Efficiency, 
 Carnot's Cycle. 
 
 Non-conducting Engine. 
 
 Probable Performance, 
 Actual Engine. 
 
 pressure by 
 Gauge. 
 
 Efficiency. 
 
 B.T.U. per 
 H.P. per 
 Minute. 
 
 B.T.U. per 
 H.P. per 
 Minute. 
 
 Steam per 
 
 H.P. per 
 
 Hour. 
 
 150 
 200 
 300 
 
 0.302 
 0.320 
 0.347 
 
 0.272 
 0.288 
 0.306 
 
 156 
 147 
 
 195 
 184 
 169 
 
 IO-5 
 9.6 
 
 In the calculations for this table the steam is supposed to be 
 dry as it enters the cylinder of the engine, and the back-pressure 
 is supposed to be 1.5 pounds absolute, while th6 expansion for 
 the non-conducting engine is assumed to be complete. The 
 
CONDENSERS 
 
 149 
 
 heat-consumption of the non-conducting engine is obtained by 
 dividing 42.42 by the efficiency; thus for 150 pounds 
 42.42 ^ 0.272 = 156. 
 
 The heat-consumption of the actual engine is assumed to be 
 one-fourth greater than that of the non-conducting engine. The 
 steam-consumption is calculated by the reversal of the method 
 of calculating the thermal units per horse-power per minute 
 from the steam per horse-power per hour, and for simplicity 
 all of the steam is assumed to be supplied to the cylinder. But 
 an engine which shall show such an economy for a given pressure 
 as that set down in the table must be a triple or a quadruple 
 engine and must be thoroughly steam-jacketed. The actual 
 steam-consumption is certain to be a little larger than that given 
 in the table, as steam condensed in a steam-jacket yields less 
 heat than that passed through the cylinder. 
 
 It is very doubtful if the gain in fluid efficiency due to increasing 
 steam- pressure above 1 50 or 200 pounds is not offset by the greater 
 friction and the difficulty of maintaining the engine. Higher 
 pressures than 200 pounds are used only where great power must 
 be developed with small weight and space, as in torpedo-boats. 
 
 Condensers. — Two forms of condensers are used to condense 
 the steam from a steam-engine, known as jet-condensers and 
 surface-condensers. The former are commonly used for land 
 engines; they consist of a receptacle having a volume equal to 
 one-fourth or one-third of that of the cylinder or cylinders that 
 exhaust into it, into which the steam passes from the exhaust-pipe 
 and where it meets and is condensed by a spray of cold water. 
 
 If it be assumed that the steam in the exhaust-pipe is dry 
 and saturated and that it is condensed from the pressure p and 
 cooled to the temperature /^^j then the heat yielded per pound 
 of steam is ^ _ ^^^ 
 
 where H is the total heat of steam at the pressure p^ and q^ is the 
 heat of the liquid at the temperature t]c. The heat acquired by 
 each pound of condensing or injection water is 
 
 qk - Qh 
 
150 THE STEAM-ENGINE 
 
 where q^ is the heat of the liquid at the temperature /, of the 
 injection- water as it enters the condenser. Each pound of steam 
 will require 
 
 G = ^.±±^^ (^ ^) 
 
 qic -qi ^ ^ 
 
 pounds of injection-water. 
 
 For example, steam at 4 pounds absolute has for the total 
 heat 1 1 28.6. If the injection- water enters with a temperature 
 of 60° F., and leaves with a temperature of 120° F., then each 
 pound of steam will require 
 
 r + q — q^ _ 11 28.6 — 88.0 _ 
 
 qk - qi ~ 88.0 - 28.12 ~ ^^'^ 
 
 pounds of injection-water. This calculation is used only to 
 aid in determining the size of the pipes and passages leading 
 water to and from the condenser, and the dimensions of the air- 
 pump. Anything like refinement is useless and impossible, 
 as conditions are seldom well known and are liable to vary. 
 From 20 to 30 times the weight of steam used by the engine is 
 commonly taken for this purpose. 
 
 The jet-condensers cannot be used at sea when the boiler- 
 pressure exceeds 40 pounds by the gauge; all modern steamers 
 are consequently supplied with surface-condensers which consist 
 of receptacles, which are commonly rectangular in shape, into 
 which steam is exhausted, and where it is condensed on horizontal 
 brass tubes through which cold sea-water is circulated. The 
 condensed water is drained out through the air-pump and is 
 returned to the boiler. Thus the feed-water is kept free from 
 salt and other mineral matter that would be pumped into the 
 boiler if a jet-condenser were used, and if the feed-water were 
 drawn from the mingled water and condensed steam from 
 such a condenser. Much trouble is, however, experienced 
 from oil used to lubricate the cylinders of the engine, as it is 
 likely to be pumped into the boilers with the feed-water, even 
 though attempts are made to strain or filter it from the water. 
 
 The water withdrawn from a surface-condenser is likely to 
 
AIR-PUMP 
 
 151 
 
 have a different temperature from the cooHng water when it 
 leaves the condenser. If its temperature is /^ then we have 
 instead of equation (150) 
 
 G = '-±^^ (151) 
 
 qk - qi 
 
 for the coohng water per pound of steam. The difference is 
 really immaterial, as it makes little difference in the actual value 
 of G for any case. 
 
 Cooling Surface. — Experiments on the quantity of cooling 
 surface required by a surface-condenser are few and unsatis- 
 factory, and a comparison of condensers of marine engines 
 shows a wide diversity of practice. Seaton says that with an 
 initial temperature of 60°, and with 120° for the feed- water, a 
 condensation of 13 pounds of steam per square foot per hour 
 is considered fair work. A new condenser in good condition 
 may condense much more steam per square foot per hour than 
 this, but allowance must be made for fouling and clogging, 
 especially for vessels that make long voyages. 
 
 Seaton also gives the following table of square feet of cooling 
 surface per indicated horse-power: 
 
 Absolute Terminal Pressure, 
 Pounds per Square Inch. 
 
 20 
 
 15 
 
 Squ 
 per 
 
 are Feet 
 I. H.P. 
 
 
 •17 
 
 
 57 
 
 
 50 
 
 
 43 
 
 
 37 
 
 
 30 
 
 I2i 
 
 10 
 
 8 
 
 6 
 
 For ships stationed in the tropics, allow 20 per cent more; 
 for ships which occasionally visit the tropics, allow 10 per cent 
 more; for ships constantly in a cold climate, 10 per cent less 
 may be allowed. 
 
 Air-Pump. — The vacuum in the condenser is maintained 
 by the air-pump, which pumps out the air which finds its way 
 there by leakage or otherwise; the condensing water carries 
 
152 THE STEAM-ENGINE 
 
 a considerable volume of air into the condenser, and the size 
 of the air-pump can be based roughly on the average percentage 
 of air held in solution in water; the air which finds its way into 
 a surface-condenser enters mainly by leakage around the low- 
 pressure piston-rod and elsewhere. 
 
 It is customary to base the size of the air-pump on the dis- 
 placement of the low-pressure piston (or pistons); for example, 
 the capacity of a single-acting vertical air-pump for a merchant 
 steamer, with triple- expansion engines, may be about 2V of the 
 capacity of the low-pressure cylinder. 
 
 With the introduction of steam-turbines, the importance of 
 a good vacuum becomes more marked, and the duty of the air- 
 pump, which commonly removes air and also the water of con- 
 densation from the condenser, is divided between a dry-air 
 pump, which removes air from the condenser, and a water- 
 pump, which removes the water of condensation. Air-pumps 
 are treated more at length on page 374, in connection with the 
 discussion of compressed air. 
 
 Designing Engines. — The only question that is properly 
 discussed here is the probable form of the indicator-diagram, 
 which gives immediately the method of finding the mean effective 
 pressure, and, consequently, the size of the cylinder of the engine. 
 
 The most reliable way of finding the expected mean effective 
 pressure in the design of a new engine is to measure an indicator- 
 diagram from an engine of the same or similar type and size, 
 and working under the same conditions. 
 
 If a new engine varies so 
 
 PBoilerpressnre ^^^^1 ilOm the typC OU which 
 
 the design is based that the 
 
 diagram from the latter cannot 
 
 be used directly, the following 
 
 method may be used to allow 
 
 Fig. 3sa. for modcratc changes of boiler 
 
 pressure or expansion. The 
 
 type diagram either on the original card or redrawn to a larger 
 
 scale, may have added to it the axis of zero pressure and vol- 
 
DESIGNING ENGINES 1 53 
 
 ume OV and OP (Fig. 35a). The former is laid off parallel to 
 the atmospheric line and at a distance to represent the pressure 
 of the atmosphere, using the scale for measuring pressure on the 
 diagram. The latter is drawn vertical and at a distance from af 
 which shall bear the same ratio to the length of the diagram as 
 the clearance space of the cylinder has to the piston-displace- 
 ment. The boiler-pressure line may be drawn as shown. The 
 absolute pressure may now be measured from O V with the proper 
 scale and volume from OP with any convenient scale. 
 
 Choosing points a and b at the beginning and end of expan- 
 sion determine the exponent for an exponential equation by the 
 method on page 66; do the same for the compression curve cf. 
 
 Draw a diagram like Fig. 35 for the new engine, making the 
 proper allowance for change of boiler- pressure or point of cut- 
 off, using the probable clearance for determining the position 
 of the line af. Allowing for loss of pressure from the boiler to 
 the cylinder, and for wire-drawing or loss of pressure in the 
 valves and passages, locate the points a and b. The back- 
 pressure line de can be drawn from an estimate of the probable 
 vacuum. The volumes at c and e are determined by the action 
 of the valve gear. By aid of the proper exponential equations 
 locate a few points on be and ef and sketch in those curves. 
 Finish the diagram by hand by comparison with the type dia- 
 gram. If necessary draw two such diagrams for the head and 
 crank ends of the cylinder. The mean effective pressure can 
 now be determined by aid of the planimeter and used in the 
 design of the new engine. 
 
 Usually the refinements of the method just detailed are 
 avoided, and an allowance is made for them in the lump by a 
 practical factor. The following approximations are made: 
 (i) the pressure in the cylinder during admission is assumed 
 to be the boiler pressure, and during the exhaust the vacuum 
 in the condenser; (2) the release is taken to be at the end of 
 the stroke; (3) both expansion and compression lines are treated 
 as hyperbolae. The mean effective pressure is then readily 
 computed as indicated in the following example. 
 
154 
 
 THE STEAM-ENGINE 
 
 Problem. — Required the dimensions of the cylinder of an 
 engine to give 200 horse- power; revolutions 100; gauge pressure 
 80 pounds; vacuum 28 inches; cut-off at \ stroke; release at end 
 of stroke; compression at jV stroke; clearance 5 per cent. 
 
 The absolute boiler-pressure is 94.7 pounds, and the absolute 
 pressure corresponding to 28 inches of mercury is nearly one 
 pound. It is convenient to take the piston displacement as 
 one cubic foot and the stroke as one foot for the purpose of 
 determining the mean effective pressure. The volume of cut- 
 off is consequently i cubic foot due to the motion of the piston 
 plus To cubic foot due to the clearance or 0.35 cubic foot; the 
 volume at release is 1.05 cubic foot, and at compression is 0.15 
 cubic foot. 
 
 The work during admission (corresponding to a6, Fig. 35a) is 
 
 94.7 X 144 X 0.35 foot-pound, 
 and during expansion is 
 
 p^v^ log,^ = 94.7 X 144 X 0.35 loge ^• 
 
 The work during exhaust done by the piston in expelling the 
 steam is 
 
 I X 144 X (i - 0.15)^ 
 
 and the work during compression is 
 
 , CIS 
 
 I X 144 X 0.1 S ioge ^• 
 
 0.05 
 
 The mean effective pressure in pounds per square inch is 
 obtained by adding the first two works and subtracting the last 
 two and then dividing by 144, so that 
 
 M.E.P. = 94.7 X 0.25 -V 94.7 X 0.35 log, ^. 
 
 0-35 
 
 - I X 0.85 - I X 0.15 loge ^^ = 59.1. 
 
 0.05 
 
 The probable mean effective pressure may be taken as t% 
 of this computed pressure, or 53.2 pounds per square inch. 
 
DESIGNING ENGINES 
 
 155 
 
 Given the diameter and stroke of an engine together with the 
 mean effective pressure, and revolutions, we may find the horse- 
 power by the formula 
 
 I.H.P. = ^ ^^^^ 
 33000 
 
 where j^ is the mean effective pressure, / is the stroke in feet, a is 
 the area of the circle for the given diameter in square inches, and 
 n is the number of revolutions per minute. For our case we 
 may assume that the stroke is twice the diameter, whence 
 
 
 
 
 
 
 
 
 ?.d 
 
 
 ird' 
 
 
 
 
 
 2 
 
 X 
 
 s,s« 
 
 ,2 
 
 X 
 
 
 X 
 
 
 X 
 
 100 
 
 200 
 
 __ 
 
 
 
 
 
 
 
 
 12 
 
 
 ^ 
 
 
 
 33000 
 
 /. d = 16.8 inches, 5 = 33.6 inches. 
 
 In practice the diameter would probably be made i6| inches 
 and the stroke ^^i inches. 
 
CHAPTER IX. 
 
 COMPOUND ENGINES. 
 
 A COMPOUND engine has commonly two cylinders, one of 
 which is three or four times as large as the other. Steam from 
 a boiler is admitted to the small cylinder, and after doing work in 
 that cylinder it is transferred to the large cylinder, from which 
 it is exhausted, after doing work again, into a condenser or 
 against the pressure of the atmosphere. If we assume that the 
 steam from the small cylinder is exhausted into a large receiver, 
 the back-pressure in that cylinder and the pressure during the 
 admission to the large cylinder will be uniform. If, further, we 
 assume that there is no clearance in either cyHnder, that the 
 back-pressure in the small cylinder and the forward pressure in 
 the large cylinder are the same, and that the expansion in the 
 small cyUnder reduces the pressure down to the back-pressure in 
 that cylinder, the diagram for the small cylinder will be A BCD, 
 
 F V 
 
 Fig. 36. 
 
 Fig. 37- 
 
 Fig. 36, and for the large cylinder DCFG. The volume in the 
 large cylinder at cut-off is equal to the total volume of the small 
 cylinder, since the large cylinder takes from the receiver the same 
 weight of steam that is exhausted by the small cylinder, and, in 
 this case, at the same pressure. 
 
 The case just discussed is one extreme. The other extreme 
 occurs when the small cylinder exhausts directly into the large 
 
 156 
 
COMPOUND ENGINES 1 57 
 
 cylinder without an intermediate receiver. In such engines the 
 pistons must begin and end their strokes together. They may 
 both act on the beam of a beam engine, or they may act on one 
 crank or on two cranks opposite each other. 
 
 For such an engine, A BCD, Fig. 37, is the diagram for the 
 small cylinder. The steam line and expansion line AB and BC 
 are like those of a simple engine. When the piston of the small 
 cylinder begins the return stroke, communication is opened with 
 the large cylinder, and the steam passes from one to the other, 
 and expands to the amount of the difference of the volume, it 
 being assumed that the communication remains open to the end 
 of the stroke. The back-pressure line CD for the small cylinder, 
 and the admission line HI for the large cylinder, gradually fall 
 on account of this expansion. The diagram for the large cylin- 
 der is HIKG, which is turned toward the left for convenience. 
 
 To combine the two diagrams, draw the line abed, parallel to 
 V'OV, and from h lay off hd equal to ca; then d is one point of the 
 expansion curve of the combined diagram. The point C corre- 
 sponds with H, and E, corresponding with /, is as far to the right 
 as / is to the left. 
 
 For a non-conducting cylinder, the combined diagram for a 
 compound engine, whether with or without a receiver, is the same 
 as that for a simple engine which has a cylinder the same size 
 as the large cylinder of the compound engine, and which takes 
 at each stroke the same volume of steam as the small cylinder, 
 and at the same pressure. The only advantage gained by the 
 addition of the small cylinder to such an engine is a more even 
 distribution of work during the stroke, and a smaller initial stress 
 on the crank-pin. 
 
 Compound engines may be divided into two classes — those 
 with a receiver and those without a receiver; the latter are called 
 " Woolf engines " on the continent of Europe. Engines without 
 a receiver must have the pistons begin and end their strokes at 
 the same time; they may act on the same crank or on cranks 180° 
 apart. The pistons of a receiver- compound engine may make 
 strokes in any order. A form of receiver compound engine with 
 
158 COMPOUND ENGINES 
 
 two cylinders, commonly used in marine work, has the cranks at 
 go° to give handiness and certainty of action. Large marine 
 engines have been made with one small cylinder and two large 
 or low-pressure cylinders, both of which draw steam from the 
 receiver and exhaust to the condenser. Such engines usually 
 have the cranks at 120°, though other arrangements have been 
 made. 
 
 Nearly all compound engines have a receiver, or a space 
 between the cylinders corresponding to one, and in no case is 
 the receiver of sufficient size to entirely prevent fluctuations of 
 pressure. In the later marine work the receiver has been made 
 small, and frequently the steam-chests and connecting pipes have 
 been allowed to fulfil that function. This contraction of size 
 involves greater fluctuations of pressure, but for other reasons it 
 appears to be favorable to economy. 
 
 Under proper conditions there is a gain from using a com- 
 pound engine instead of a simple engine, which may amount to 
 ten per cent or more. This gain is to be attributed to the division 
 of the change of temperature from that of the steam at admission 
 to that of exhaust into two stages, so that there is less fluctua- 
 tion of temperature in a cylinder and consequently less inter- 
 change of heat between the steam and the walls of the cylinder. 
 Compound Engine without Receiver. — The indicator-dia- 
 grams from a compound engine without a receiver are repre- 
 sented by Fig. 38. The steam line and expan- 
 sion line of the small cylinder, AB and BC, do 
 not differ from those of a simple engine. At C 
 the exhaust opens, and the steam suddenly 
 expands into the space between the cylinders 
 and the clearance of the large cylinder, and the 
 pressure falls from C to D. During the return 
 stroke the volume in the large cylinder increases more rapidly 
 than that of the small cylinder decreases, so that the back-press- 
 ure line DE gradually falls, as docs also the admission line HI 
 of the large cylinder, the difference between these two lines being 
 due to the resistance to the flow of steam from one to the other. 
 
COMPOUND ENGINE WITH RECEIVER 
 
 159 
 
 At E the communication between the two cylinders is closed by 
 the cut-off of the large cylinder; the steam is then compressed 
 in the small cylinder and the space between the two cylinders 
 to F, at which the exhaust of the small cylinder closes; and the 
 remainder of the diagram FGA is like that of a simple engine. 
 From 7, the point of cut-off of the large cylinder, the remainder 
 of the diagram IKLMNH is like the same part of the diagram 
 of a simple engine. 
 
 The difference between the lines ED and HI and the '' drop " 
 CD at the end of the stroke of the small piston indicate waste 
 or losses of efficiency. The compression EFG and the accom- 
 panying independent expansion IK in the large cylinder show a 
 loss of power when compared with a diagram like Fig. 37 for an 
 engine which has no clearance or intermediate space; but com- 
 pression is required to fill waste spaces with steam. The com- 
 pression EF is required to reduce the drop CZ>, and the compres- 
 sion FG fills the clearance in anticipation of the next supply from 
 the boiler. Neither compression 
 is complete in Fig. 2^^. 
 
 Diagrams from a pumping en- 
 gine at Lawrence, Massachusetts, 
 are shown by Fig. 39. The 
 rounding of corners due to the 
 indicator makes it difficult to de- 
 termine the location of points like 
 D, E, F, and / on Fig. 38. The 
 low-pressure diagram is taken 
 with a weak spring, and so has an 
 exaggerated height. 
 
 Compound Engine with Receiver. — It has already been 
 pointed out that some receiver space is required if the cranks 
 of a compound engine are to be placed at right angles. When 
 the receiver space is small, as on most marine engines, the fluc- 
 tuations of pressure in the receiver are very notable. This is 
 exhibited by the diagrams in Fig. 40, which were taken from a 
 yacht engine. An intelligent conception of the causes and meaning 
 
 Fig. 39. 
 
l6o COMPOUND ENGINES 
 
 of such fluctuations can be best obtained by constructing ideal 
 diagrams for special cases, as explained on page 164. 
 
 Triple and Quadruple Expansion - 
 Engines. — The same influences which 
 introduced the compound engines, when 
 the common steam-pressure changed 
 from forty to eighty pounds to the 
 square inch, have brought in the succes- 
 sive expansion through three cylinders 
 ^'°" '*°" (the high-pressure, intermediate, and 
 
 low-pressure cylinders) now that 150 to 200 pounds pressure are 
 employed. Just as three or more cylinders are combined in 
 various ways for compound engines, so four, five, or six cylinders 
 have been arranged in various manners for triple-expansion 
 engines; the customary arrangement has three cylinders with the 
 cranks at 180°. 
 
 Quadruple engines with four successive expansions have been 
 employed with high-pressure steam, but with the advisable 
 pressures for present use the extra complication and friction 
 make it a doubtful expedient. 
 
 Total Expansion. — In Figs. 36 and 37, representing the dia- 
 grams for compound engines without clearance and without 
 drop between the cylinders, the total expansion is the ratio of 
 the volumes at E and at B ; that is, of the low-pressure piston dis- 
 placement to the displacement developed by the high-pressure 
 piston at cut-off. The same ratio is called the total or equiva- 
 lent expansion for any compound engine, though it may have 
 both clearance and drop. Such a conventional total expansion 
 is commonly given for compound and multiple-expansion engines, 
 and is a convenience because it is roughly equal to the ratio of 
 the initial and terminal pressures; that is, of the pressure at 
 cut-off in the high-pressure cyHnder and at release in the low- 
 pressure cylinder. It has no real significance, and is not equiva- 
 lent to the expansion in the cylinder of a simple engine, by which 
 we mean the ratio of the volume at release to that at cut-off, tak- 
 ing account of clearance. And further, since the clearance of 
 
LOW-PRESSURE CUT-OFF l6i 
 
 the high- and the low-pressure cylinders are different there can 
 be no real equivalent expansion. 
 
 If the ratio of the cylinders is R and the cut-off of the high- 
 pressure cylinder is at - of the stroke, then the total expansion 
 is represented by 
 
 E =^ eR 
 
 ^^^ - = R -^ E 
 
 This last equation is useful in determining approximately the 
 cut-off of the high-pressure cylinder. 
 
 For example, if the initial pressure is loo pounds absolute and 
 the terminal pressure is to be lo pounds absolute, then the total 
 expansions will be about lo. If the ratio of the cylinders is 
 3I, then the high-pressure cut-off will be about 
 
 - = 3I ^ 10 = 0.35 
 of the stroke. 
 
 Low-pressure Cut-off. — The cut-off of the low-pressure 
 cylinders in Figs. 36 and 37 is controlled by the ratio of the 
 cylinders, since the volumes in the low-pressure cylinder at cut- 
 olBf is in each case made equal to the high-pressure piston dis- 
 placement; this is done to avoid a drop. If the cut-off were 
 lengthened there would be a loss of pressure or drop at the end 
 of the stroke of the high-pressure 
 piston, as is shown by Fig. 41, 
 for an engine with a large receiver 
 and no clearance. Such a drop will 
 have some effect on the character of 
 the expansion line C"F of the low- 
 pressure cylinder, both for a non-con- 
 ducting and for the actual engine 
 with or without a clearance. Its 
 principal effect will, however, be on '^* *'* 
 
 the distribution of work between the cylinders; for it is evident 
 that if the cut-off of the low-pressure cylinder is shortened the 
 
l62 COMPOUND ENGINES 
 
 pressure at C" will be increased because the same weight of steam 
 is taken in a smaller volume. The back-pressure DO of the 
 high-pressure cylinder will be raised and the work will be 
 diminished; while the forward pressure DC'^ of the low- 
 pressure cylinder will be raised, increasing the work in that 
 cylinder. 
 
 Ratio of Cylinders. — In designing compound engines, more 
 especially for marine work, it is deemed important for the smooth 
 action of the engine that the total work shall be evenly distributed 
 upon the several cranks of the engines, and that the maximum 
 pressure on each of the cranks shall be the same, and shall not 
 be excessive. In case two or more pistons act on one crank, 
 the total work and the resultant pressure on those pistons are 
 to be considered; but more commonly each piston acts on a 
 separate crank, and then the work and pressure on the several 
 pistons are to be considered. 
 
 In practice both the ratio of the cylinders and the total expan- 
 sions are assumed, and then the distribution of work and the 
 maximum loads on the crank-pins are calculated, allowing for 
 clearance and compression. Designers of engines usually have 
 a sufficient number of good examples at hand to enable them 
 to assume these data. In default of such data it may be neces- 
 sary to assume proportions, to make preliminary calculations, 
 and to revise the proportions till satisfactory results are obtained. 
 For compound engines using 80 pounds steam-pressure the ratio 
 is 1 : 3 or 1 : 4. For triple-expansion engines the cylinders may 
 be made to increase in the ratio i : 2 or i : 2^. 
 
 Approximate Indicator- Diagrams. — The indicator-diagrams 
 from some compound and multiple-expansion engines are irreg- 
 ular and apparently erratic, depending on the sequence of the 
 cranks, the action of the valves, and the relative volumes of the 
 cylinders and the receiver spaces. A good idea of the effects and 
 relations of these several influences can be obtained by making 
 approximate calculations of pressures at the proper parts of the 
 diagrams by a method which will now be illustrated. 
 
 For such a calculation it will be assumed that all expansion 
 
DIRECT-EXPANSION ENGINE 163 
 
 lines are rectangular hyperbolae, and in general that any change 
 of volume will cause the pressure to change inversely as the 
 volume, further, it will be assumed that when communication 
 is opened between two volumes where the pressures are different, 
 the resultant pressure may be calculated by adding together the 
 products of each volume by its pressure, and dividing by the sum 
 of the volumes. Thus if the pressure in a cylinder having the 
 volume z'c is pc, and if the pressure is pr in a receiver where 
 the volume is Vr, then after the valve opens communication from 
 the cylinder to the receiver the pressure will be 
 
 p,V, + pr'Vy 
 P = . 
 
 The same method will be used when three volumes are put into 
 communication. 
 
 It will be assumed that there are no losses of pressure due to 
 throttling or wire-drawing; thus the steam line for the high- 
 pressure cylinder will be drawn at the full boiler-pressure, and 
 the back-pressure line in the low-pressure cylinder will be drawn 
 to correspond with the vacuum in the condenser. iVgain, cylin- 
 ders and receiver spaces in communication will be assumed to 
 have the same pressure. 
 
 For sake of simplicity the motions of pistons will be assumed 
 to be harmonic. 
 
 Diagrams constructed in this way will never be realized in 
 any engine; the degree of discrepancy will depend on the type 
 of engine and the speed of rotation. For slow-speed pumping- 
 engines the discrepancy is small and all irregularities are easily 
 accounted for. On the other hand the discrepancies are large 
 for high-speed marine-engines, and for compound locomotives 
 they almost prevent the recognition of the events of the stroke. . 
 
 Direct- expansion Engine. — If the two pistons of a compound 
 engine move together or in opposite directions the diagrams 
 are like those shown by Fig. 42. Steam is admitted to the high- 
 pressure cylinder from a to b; cut-off occurs at b, and be repre- 
 sents expansion to the end of the stroke; be being a rectangular 
 
164 
 
 COMPOUND ENGINES 
 
 hyperbola referred to the axes O V and OP, from which a, b, and 
 c are laid off to represent absolute pressures and volumes, includ- 
 ing clearance. 
 
 p p 
 
 Fig. 42. 
 
 At the end of the stroke release from the high-pressure 
 cylinder and admission to the low-pressure cylinder are assumed 
 to take place, so that communication is opened from the. high- 
 pressure cylinder through the receiver space into the low-press- 
 ure cylinder. As a consequence the pressure falls from c to d, 
 and rises from n to h in the low-pressure cylinder. The line 
 O^P^ is drawn at a distance from OP, which corresponds to the 
 volume of the receiver space, and the low-pressure diagram is 
 referred to O^P^ and O^V as axes. 
 
 The communication between the cylinders is maintained until 
 cut-off occurs at i for the low-pressure cylinder. The lines de 
 and hi represent the transfer of steam from the high-pressure 
 to the low-pressure cylinder, together with the expansion due to 
 the increased size of the large cylinder. After the cut-off at i, 
 the large cylinder is shut off from the receiver, and the steam in 
 it expands to the end of the stroke. The back-pressure and 
 compression lines for that cylinder are not affected by compound- 
 ing, and are like those of a simple engine. Meanwhile the small 
 piston compresses steam into the receiver, as represented by 
 ef, till compression occurs, after which compression into the 
 clearance space is represented hy fg. The expansion and com- 
 pression lines ik and mn are drawn as hyperbolae referred to the 
 axes O'P' and O' V\ The compression line ef is drawn as an hyper- 
 bola referred to O' V and O^P^j while fg is referred to OF and OP. 
 
direct-exTpansion engine 165 
 
 In Fig. 42 the two diagrams are drawn with the same scale 
 for volume and pressure, and are placed so as to show to the 
 eye the relations of the diagrams to each other. Diagrams 
 taken from such an engine resemble those of Fig. 39, which 
 have the same length, and different vertical scales depending 
 on the springs used in the indicators. 
 
 Some engines have only one valve to give release and com- 
 pression for the high-pressure cylinder and admission and cut- 
 off for the low-pressure cylinder. In such case there is no 
 receiver space, and the points e and /coincide. 
 
 When the receiver is closed by the compression of the high- 
 pressure cylinder it is filled with steam with the pressure repre- 
 sented by /. It is assumed that the pressure in the receiver 
 remains unchanged till the receiver is opened at the end of the 
 stroke. It is evident that the drop cd may be reduced by short- 
 ening the cut-off of the low-pressure cylinder so as to give more 
 compression from e io f and consequently a higher pressure at 
 / when the receiver is closed. 
 
 Representing the pressure and volume at the several points 
 by p and v with appropriate subscript letters, and represent- 
 ing the volume of the receiver by v^, we have the following 
 equations : 
 
 pa =" pb = initial pressure; 
 Pi = P>n^ back- pressure; 
 pc = Pb-Vb -^ 'Vc', 
 
 Pn = Pm'^m ^ '^n', ^ 
 
 Pd = Ph= {pc'Vc + Pn'Vn + PfVr) "^ K + ^^» + ^r); 
 
 Pe = pi = pd (Vc +'Un + "Vr) ^ (^e + '^i + Vr)\ 
 
 Pf = Pe i'Ve + Vr) - (^^ + '^r)', 
 
 Po = Pf^f ^ '^o'y 
 
 Pk = Pi-Vi ^ Vk. 
 
 The pressures p,. and pn can be calculated directly. Then the 
 equations for p,i, p^, and p/ form a set of three simultaneous 
 equations with three unknown quantities, which can be easily 
 solved. Finally, p,j and pjt may be calculated directly. 
 
l66 COMPOUND ENGINES 
 
 For example, let us find the approximate diagram for a direct- 
 expansion engine which has the low-pressure piston displacement 
 equal to three times the high-pressure piston displacement. 
 Assume that the receiver space is half the smaller piston dis- 
 placement, and that the clearance for each cylinder is one-tenth 
 of the corresponding piston displacement. Let the cut-off for 
 each cylinder be at half-stroke, and the compression at nine- 
 tenths of the stroke; let the admission and release be at the end 
 of the stroke. Let the initial pressure be 65.3 pounds by the 
 gauge or 80 pounds absolute, and let the back-pressure be two 
 pounds absolute. 
 
 If the volume of the high- pressure piston displacement be 
 taken as unity, then the several required volumes are: 
 
 'Vh = 'Vn = 3 X o-i = 0-3 
 ,1 Vi = 3 (0.5 +0.1) = 1.8 
 
 'Vk = ^^ = 3 (i-o +0.1) = T,.2> 
 V,, = 3 (o.i +0.1) = 0.6 
 
 ^r = 0.5 
 
 The pressures may be calculated as follows: 
 
 pa = Pb = ^o; pi = p^ = 2; 
 
 pc = Pb'^b ^ i^c = 80 X 0.6 -^ I.I = 43.6; 
 
 Pn = Pm'i^m - ^„ == 2 X 0.6 ^ O.3 = 4; 
 
 Pe = Pd {'Vc +'Vn + 'Vr) "^ {'^e + ^i + ^^r) = pd (l-I + O.3 + O.5) 
 
 -- (0.6 + 1.8 -f 0.5) = 0.655 pd] 
 
 Pf = pe K + -i^r) - iyf + ^,) = Pe (0.6 + O.5) ^ (o.2 -f O.5) 
 
 = 1.57 p, = 1.57 X 0.655 pd = 1.03 Pd\ 
 
 pd = (Me + Pn-l^n + Pfl^r) ^ iyc + ^„ + ^r) 
 
 = (80 X 0.6 + 4 X 0.3 + 0.5 pf) -^ (0.6 + 0.3 -f 0.5) 
 
 = 25.89 + 0.26 pf] 
 
 pa = 25.89 + 0.26 X 1.03 pa; pd = 35-36; 
 p, = Pi = 0.655 pd = 0.655 X 35.36 = 23.2; 
 pf = 1-03 P<i = 1.03 X 35.36 = 36.5; 
 Pd = PPf - *^p = 36.5 X 0.2 - 0.1 = 73; 
 Pk = M- ^ 'Vk = 23.2 X 1.8 -^ 3.3 = 12.6. 
 
 Vb 
 
 = 
 
 0-5 
 
 4- 
 
 0.1 
 
 = 
 
 ■ 0.6 
 
 •Vc 
 
 = 
 
 -Va -- 
 
 = ] 
 
 .0 
 
 + 
 
 0.1 = 
 
 -Ve 
 
 = 
 
 0-5 
 
 + 
 
 0.1 
 
 = 
 
 0.6 
 
 ^/ 
 
 = 
 
 0.1 
 
 + 
 
 0.1 
 
 = 
 
 0.2 
 
 Va 
 
 = 
 
 0.1 
 
 
 
 
 
DIRECT-EXPANSION ENGINE 167 
 
 As the pressures and volumes are now known the diagrams 
 of Fig. 42 may be drawn to scale. Or, if preferred, diagrams 
 like Fig. 39 may be drawn, making them of the same length and 
 using convenient vertical scales of pressure. If the engine runs 
 slowly and has abundant valves and passages the diagrams 
 thus obtained will be very nearly like those taken from the engine 
 by indicators. If losses of pressure in valves and passages are 
 allowed for, a closer approximation can be made. 
 
 The mean effective pressures of the diagrams may be readily 
 obtained by the aid of a planimeter, and may be used for esti- 
 mating the power of the engine. For this purpose we should 
 either use the modified diagrams allowing for losses of pressure, 
 or we should affect the mean effective pressures by a multiplier 
 obtained by comparison of the approximate with the actual dia- 
 grams from engines of the same type. For a slow-speed pump- 
 ing-engine the multiplier may be as large as 0.9 or even more; 
 for high-speed engines it may be as small as 0.6. 
 
 The mean effective pressures of the diagrams may be calcu- 
 lated from the volumes and pressures if desired, assuming, of 
 course, that the several expansion and compression curves are 
 hyperbolae. The process can be best explained by applying it 
 to the example already considered. Begin by finding the mean 
 pressure during the transfer of steam from the high-pressure 
 cylinder to the low-pressure cylinder as represented by de and hi. 
 The net effective work during the transfer is 
 
 / 
 
 pdv = p^ v^ log, ^ = 144 pa {Va +Vn -\- Vr) log /' ^^" ^^ 
 
 'V^ Va + Vh + '^r 
 
 / . . \ 1 0.6 4- 1.8 -f 0.5 
 = 144 X 35.4(1.1 +0.3 -}-o.5)loge ; ; 
 
 I.I +0.3 + 0.5 
 
 = 4120 foot-pounds 
 
 for each cubic foot of displacement of the high-pressure piston. 
 This corresponds with our previous assumption of unity for the 
 displacement of that piston. The increase of volume is 
 
 v^-i-Vi-^v^ - (va+Vf,+Vr) =o.6-f-i.8-fo.5- (i.i +0.3 -fo.5) = i; 
 
l68 COMPOUND ENGINES 
 
 SO that the mean pressure during the transfer is 
 4120 -^ I X 144 = 28.6 = pjc 
 
 pounds per square inch, which acts on both the high- and the 
 low-pressure pistons. 
 
 The effective work for the small cylinder is obtained by add- 
 ing the works under ah and he and subtracting the works under 
 de, ef, and fg. So that 
 
 Wu 
 
 144 \pa (V — Va) + pbVb loge ~ - px (v d - Vc) 
 
 - pe {Ve + Vr) loge J' , '''' - pfVf loge J7 
 
 = 144 j8o (0.6 - o.i) + 80 X 0.6 loge ^- 28.6 (i.i - 0.6) 
 r ^ , N , 0-6 -1- o.:; , , 0.2 ) 
 
 - 23.2 (0.6 + 0.5) loge o^^^fT^ - 36.5 X 0.2 logo — j 
 
 = 144 X 33.26 = 4789 foot-pounds. 
 
 This is the work for each cubic foot of the high- pressure piston 
 displacement, and the mean effective pressure on the small piston 
 is evidently 33.26 pounds per square inch. 
 
 In a like manner the work of the large piston is 
 
 WL =144 \px iVi — Vh) + pi Vi loge — — pi (Vi —Vn^) — pmVn log» " " [ 
 
 = 144 28.6(1.8-0.3)+ 23.2 X 1.8 log. ^ 
 
 — 2 {^.T, — 0.6) — 2 X 0.6 loge ~^— I = 144 X 61.92 = 8916 foot-pounds. 
 
 Since the ratio of the piston displacements is 3, the work for 
 each cubic foot of the low-pressure piston displacement is one-third 
 of the work just calculated; and the mean effective pressure on 
 the large piston is 
 
 61.92 -^- 3 = 20.64 
 
 pounds per square inch. 
 
 The proportions given in the example lead to a very uneven 
 distribution of work; that of the large cylinder being nearly 
 twice as much as is developed in the small cylinder. The dis- 
 
CROSS-COMPOUND ENGINE 
 
 169 
 
 tribution can be improved by lengthening the cut-off of the 
 large cylinder, or by changing the proportions of the engine. 
 
 As has already been pointed out, the works just calculated 
 and the corresponding mean effective pressures are in excess 
 of those that will be actually developed, and must be affected 
 by multipliers which may vary from 0.6 to 0.9, depending on 
 the type and speed of the engine. 
 
 Cross- compound Engine. — A two-cylinder compound engine 
 with pistons connected to cranks at right angles with each other 
 is frequently called a cross-compound engine. Unless a large 
 receiver is placed between the cylinders the pressure in the space 
 between the cylinders will vary widely. 
 
 Two cases arise in the discussion of this engine according as 
 
 
 6 a 
 
 P 
 
 p' 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 <-Vr-> 
 
 
 
 
 
 
 d 
 
 
 k 
 
 I 
 
 n 
 
 
 
 - p 
 
 V !! j 1 : 
 
 
 
 n> Ls 
 
 1 
 
 1— : 
 
 
 1 
 1 
 
 q V' 
 
 Fig. 43. 
 
 the cut-off of the large cylinder is earlier or later than half-stroke; 
 in the latter case there is a species of double admission to the 
 low-pressure cylinder, as is shown in Fig. 43. For sake of 
 simplicity the release, and also the admission for each cylinder, 
 is assumed to be at the end of the stroke. If the release is early 
 the double admission occurs before half-stroke. 
 
 The admission and expansion of steam for the high-pressure 
 cylinder are represented by ab and he. At c release occurs, 
 putting the small cylinder in communication with the inter- 
 mediate receiver, which is then open to the large cylinder. There 
 is a drop at cd and a corresponding rise of pressure mn on the 
 large piston, which is then at half-stroke; it will be assumed 
 that the pressures at d and at n are identical. From d io e the 
 
170 COMPOUND ENGINES 
 
 Steam is transferred from the small to the large cylinder, and 
 the pressure falls because the volume increases; no is the corre- 
 sponding line on the low-pressure diagram. The cut-off at 
 for the large cylinder interrupts this transfer, and steam is then 
 compressed by the small piston into the intermediate receiver 
 with a rise of pressure as represented by ef. The admission to 
 the large cylinder, tk, occurs when the small piston is at the 
 middle of its stroke, and causes a drop, /^, in the small cylinder. 
 From g to h steam is transferred through the receiver from the 
 small to the large cylinder. The pressure rises at first because 
 the small piston moves rapidly while the large one moves slowly 
 until its crank gets away from the dead-point; afterwards the 
 pressure falls. The line kl represents this action on the low- 
 pressure diagram. At h compression occurs for the small 
 cylinder, and hi shows the rise of pressure due to compression. 
 For the large cylinder the line Im re-presents the supply of steam 
 from the receiver, with falling pressure which lasts till the double 
 admission at mn occurs. 
 
 The expansion, release, exhaust, and compression in the large 
 cylinder are not affected by compounding. 
 
 Strictly, the two parts of the diagram for the low-pressure 
 cylinder, mnopq and stklm, belong to opposite ends of the cylin- 
 der, one belonging to the head end and one to the crank end. 
 With harmonic motion the diagrams from the two ends are 
 identical, and no confusion need arise from our neglect to deter- 
 mine which end of the large cylinder we are dealing with at any 
 time. Such an analysis for the two ends of the cylinder, taking 
 account of the irregularity due to the action of the connecting- 
 rod, would lead to a complexity that would be unprofitable. 
 
 A ready way of finding corresponding positions of two pistons 
 connected to cranks at right angles with each other is by aid 
 of the diagram of Fig. 44. Let O be the centre of the crank- 
 shaft and pRyRxq be the path of the crank-pin. When one piston 
 has the displacement py and its crank is at ORy, the other crank 
 may be 90° ahead at OR^ and the corresponding piston displace- 
 ment will be px. The same construction may be used if the 
 
Cl^OSS-COMPOUND ENGINE 
 
 171 
 
 crank is 90° behind or if the angle RyORj; is other than a right 
 angle. The actual piston position and crank angles when 
 affected by the irregularity due to the 
 connecting-rod will differ from those found 
 by this method, but the positions found 
 by such a diagram will represent the aver- 
 age positions very nearly. 
 
 The several pressures may be found as 
 
 follows : Fig. 44. 
 
 pb = pa = initial pressure; 
 ps = pq = back-pressure; 
 
 Pc = Pb'Vb -^ '^cl 
 Pt = Ps'^s -^ ^o 
 
 Pd = Pn= IPc'Vc + pmi'Vm + ^r) \ -^ {v, -{- V„ + Vr)\ 
 Pe = Po = Pd ('Uc + Vn^ + V,.) -^ (v, + V, + Vr)', 
 P/= Pe i'Ve +^r) - (^> + Vr) ', 
 Pg = Pk = \Pf (Vf + 'Vr) + MS - (1^/+ V, + V,); 
 
 Ph = pi = pg (^/ +Vt ^ V,.) - {vn + vj + ^',.); 
 
 Pm= Pl {I'l + 1'r) ^ i^n + "Vr) ', 
 
 pi = phVh ^ "Vt; 
 pp = Mo -^ *^7.- 
 
 The pressures pc and pn can be found directly from the initial 
 pressure and the back-pressure, and finally the last two equa- 
 tions give direct calculations for pi and pp so soon as pn and po 
 are found. There remain six equations containing six unknown 
 quantities, which can be readily solved after numerical values 
 are assigned to the known pressures and to all the volumes. 
 
 The expansion and compression lines, be and hi, for the high- 
 pressure diagrams are hyperbolae referred to the axes OF and 
 OP; and in like manner the expansion and compression lines op 
 and si, for the low-pressure diagram, are hyperbolae referred to 
 O' F' and 0'P\ The curve efis an hyperbola referred to O' F and 
 O'P^, and the curve Im is an hyperbola referred to OV^ and 
 OP. The transfer lines de and no, gh and kl, are not hyper- 
 bolae. They may be plotted point by point by finding corre- 
 
172 COMPOUND ENGINES 
 
 spending intermediate piston positions, p^^ ^-nd py, by aid of Fig. 
 44, and then calculating the pressure for these positions by the 
 equation 
 
 PT= Py - Pd {Vd + 'Vm + -^r) -4- {V^ -\-Vy + V^). 
 
 The work and mean effective pressure may be calculated in a 
 manner similar to that given for the direct-expansion engine; 
 but the calculation is tedious,' and involves two transfers, de and 
 nOj and gh and kl. The first involves only an expansion, and 
 presents no special difficulty; the second consists of a compres- 
 sion and an expansion, which can be dealt with most conveniently 
 by a graphical construction. All things considered, it is better 
 to plot the diagrams to scale and determine the areas and mean 
 effective pressures by aid of a planimeter. 
 
 If the cut-off of the low-pressure is earlier than half-stroke so 
 as to precede the release of the high-pressure cylinder the transfer 
 represented by de and no, Fig. 43, does not occur. Instead there 
 is a compression from d to /and an expansion from / to m. The 
 number of unknown quantities and the number of equations are 
 reduced. On the other hand, a release before the end of the 
 stroke of the high- pressure piston requires an additional unknown 
 quantity and one more equation. 
 
 Triple Engines. — The diagrams from triple and other mul- 
 tiple-expansion engines are likely to show much irregularity, the 
 form depending on the number and arrange- 
 ment of the cylinders and the sequence of the 
 cranks. A common arrangement for a triple 
 engine is to have three pistons acting on 
 cranks set equidistant around the circle, as 
 shown by Fig. 45. Two cases arise depending 
 on the sequence of the cranks, which may be 
 in the order, from one end of the engine, of 
 high-pressure, low-pressure, and intermediate, as shown by Fig. 
 45; or in the order of high-pressure, intermediate, and low- 
 pressure. 
 
 With the cranks in the order, high-pressure, low-pressure, and 
 
TRIPLE ENGINES 
 
 173 
 
 intermediate, as shown by Fig. 45, the diagrams are Hke those 
 given by Fig. 46. The admission and expansion for the high- 
 pressure cyKnder are represented by ahc. When the high- 
 pressure piston is at release, its crank is at H, Fig. 45, and the 
 intermediate crank is at /, so that the intermediate piston is 
 near half-stroke. If the cut-off for that cylinder is later than 
 
 i \ Scale 160 \ 
 
 
 1 1 Atmospheric line ^ | 
 
 
 
 Fig. 46. 
 
 half-Stroke, it is in communication with the first receiver when 
 its crank is at /, and steam may pass through the first receiver 
 from the high-pressure to the intermediate cylinder, and there is 
 a drop cd, and a corresponding rise of pressure no in the inter- 
 mediate cyHnder. The transfer continues till cut-off for the 
 
174 COMPOUND ENGINES 
 
 intermediate cylinder occurs at p, corresponding to the piston 
 position e for the high-pressure cylinder. From the position e 
 the high- pressure piston moves to the end of the stroke at /, 
 causing an expansion, and then starts to return, causing the 
 compression fg. When the high-pressure piston is at g the 
 intermediate cylinder takes steam at the other end, causing the 
 drop gh and the rise of pressure xl. Then follows a transfer of 
 steam from the high-pressure to the intermediate cylinder repre- 
 sented by hi and Im. At i the high-pressure compression ik 
 begins, and is carried so far as to produce a loop at k. After 
 compression for the high-pressure cylinder shuts it from the 
 lirst receiver, the steam in that receiver and in the intermediate 
 cylinder expands as shown by mn. The expansion in the inter- 
 mediate cylinder is represented by pq and the release by qr, 
 corresponding to a rise of pressure a/? in the low-pressure cylin- 
 der, rs and /?7 represent a transfer of steam from the inter- 
 mediate cylinder to the low-pressure cylinder. The remainder 
 of the back-pressure line of the intermediate cylinder and the 
 upper part of the low-pressure diagram for the low-pressure 
 cylinder correspond to the same parts of the high-pressure and 
 the intermediate cylinders, so that a statement of the actions in 
 detail does not appear necessary. 
 
 The equations for calculating the pressure are numerous, but 
 they are not difficult to state, and the solution for a given exam- 
 ple presents no special difficulty. Thus we have 
 
 II. 
 
 pa 
 
 = Pb = 
 
 initial pressure; 
 
 Vp = vol. 
 
 first receiver; 
 
 pc 
 
 = pbVb 
 
 ^Vc ; 
 
 
 Vj2= vol. 
 
 second 
 
 receiver; 
 
 Pa 
 
 - po=^ 
 
 [PcVc+P 
 
 n {Vo+Vp)\ - 
 
 4- (Va+Vo +Vr); 
 
 
 
 Pe 
 
 = Pp = 
 
 pd (Vd + V 
 
 'o+'yp) ^ {v. 
 
 + Vp -i- Vp); 
 
 
 
 Pf 
 
 = Pe (V 
 
 •e+Vp) -. 
 
 - {vf+ Vp); 
 
 
 
 
 Pa 
 
 = pf{Vf+ Vp) -^ 
 
 iva+ Vp); 
 
 
 
 
 P'^ 
 
 = pl = 
 
 \py{Vg+Vp) + P^V^l 
 
 -^ (vn+vi + Vp); 
 
 
 
 pi 
 
 = Pn.= 
 
 ph {Vh + 
 
 Vi + Vp) ^ {Vi +Vm+ Vp); 
 
 
 
 p. 
 
 = piVi ■ 
 
 ■4- Vk ; 
 
 
 
 
 
 Pn 
 
 = pm {Vm, + Vp) - 
 
 ^ {vn + Vp); 
 
 • 
 
 
 
 A 
 
 = Pp'^l 
 
 ^-v^', 
 
 
 
 
 
TRIPLE ENGINES 175 
 
 pe= py = pr (Vr + Va V^) H- (v^ + Vy-\- Vj^); 
 pi = p,iv, + Vji) -f- (Vt+ Vf,); 
 P* = Pt {Vt + Vr) ^ {Vu + Vj^y, 
 
 IV. pp= {pu (x;u + Vj^) + priVri\ -^ (v„ + Vri + V^); 
 
 pw= pv (v, + vr, + Vj^) -7- (v„ + V, + v^); 
 
 pm= pwV„ ^ Vx; 
 
 P» = {V, + Vj^) H- {Va + Vj^Yy 
 
 ps = pyVy -T- vs; 
 
 pe = p^ = back-pressure; 
 
 Pv = Pcv^~^ '^'J- 
 
 The pressures at c and at v can be calculated immediately 
 from the initial pressure and from the back-pressure. Then it 
 will be recognized that there are four individual equations for 
 finding pf, p^, pt, and p^. The fourteen remaining equations, 
 solved as simultaneous equations, give the corresponding four- 
 teen required pressures, some of v^hich are used in calculating 
 the four pressures which are determined by the four individual 
 equations. The most ready solution may be made by contin- 
 uous substitution in the four equations which are numbered at the 
 left hand. Thus for pg in equation II, we may substitute, 
 
 p = y, ^/ + ^p _ p ^^ +^P "^z + ^P,_ p 'Vd^rJloj^_y^'iie±v^ ^ 
 
 ^ ^Vg +VR 'Vf -\-v^ Vg ^Vp '^v^ + Vp + Vp Vg +Vp 
 
 In the actual computation the several volumes and the proper 
 sums of volumes are to be first determined; consequently the 
 factors following pa will be numerical factors which may be con- 
 veniently reduced to the lowest terms before introduction in the 
 equation. This system of substitution will give almost immedi- 
 ately four equations with four unknown quantities which may 
 readily be solved; after which the determination of individual 
 pressures will be easy. In handhng these equations the letters 
 representing smaller pressures should be eliminated first, thus 
 giving values of higher pressure like pa to tenths of a pound; 
 afterward the lower pressure can be determined to a like degree 
 
176 COMPOUND ENGINES 
 
 of accuracy. A skilled computer may make a complete solu- 
 tion of such a problem in two or three hours, which is not exces- 
 sive for an engineering method. 
 
 If the cut-off for the intermediate cyhnder occurs before the 
 release of the high- pressure cylinder, then the transfer represented 
 by de and op does not occur. In like manner, if the cut-off for 
 the low-pressure cylinder occurs before the release for the inter- 
 mediate cylinder, the transfer represented by rs and /?7 does 
 not occur. The omission of a transfer of course simplifies the 
 work of deducing and of solving equations. 
 
 In much the same way, equations may be deduced for cal- 
 culating pressures when the cranks have the sequence high- 
 pressure, intermediate, and low-pressure. The diagrams take 
 forms which are distinctly unlike those for the other sequence of 
 cranks. In general, the case solved, i.e., high-pressure, low- 
 pressure, and intermediate, gives a smoother action for the 
 engine. 
 
 For example, the engines of the U. S. S. Machias have the 
 following dimensions and proportions: 
 
 High- Inter- Low- 
 
 pressure, mediate, pressure. 
 
 Diameter of piston, inches 15! 22^ 35 
 
 Piston displacement, cubic feet 2.71 5.53 13 -39 
 
 Clearance, per cent 13 14 7 
 
 Cut-off, per cent stroke 66 66 66 
 
 Release, per cent stroke 93 93 93 
 
 Compression, per cent stroke 18 18 18 
 
 Ratio of piston displacements i 2.04 4.94 
 
 Volume first receiver, cubic feet 2.22 
 
 Volume second receiver, cubic feet 6.26 
 
 Ratio of receiver volumes to high-pressure piston dis- 
 placement 0.82 2.31 
 
 Stroke, inches 24 
 
 Boiler-pressure, absolute, pounds per sq. in 180 
 
 Pressure in condenser, pounds per sq. in 2 
 
 If the volume of the high-pressure piston displacement is 
 taken to be unity, then the volumes required in the equations for 
 
TRIPLE ENGINES 
 
 177 
 
 Fig- 47. 
 
 calculating pressures, when the cranks have the order high- 
 pressure, low-pressure, and intermediate, are as follows: 
 
 V, = 0.79 
 
 v^ ^v^ = 0.29 
 
 Vy=-V^ = 0.35 
 
 ^'c = 'Z-'d = 1.06 
 
 v^ = 0.98 
 
 ^'^ = 2.02 
 
 Vg = 1. 10 
 
 Vn = Vo = 1-26 
 
 Va = Vp = 2.72 
 
 ly = 1. 13 
 
 ^P = 1-63 
 
 T^y = 3.60 
 
 Vg -= Vh = 0.88 
 
 v,^ = V, = 2.18 
 
 vs = V, = 4.94 
 
 z\ = 0.31 
 
 z', = 2.28 
 
 ^f = 1.23 
 
 ■^^V = I'a = 0.13 
 
 ^-'/ = 2.33 
 
 v^ = v^= 1.85 
 t;«, = 0.63 
 
 
I 78 COMPOUND ENGINES 
 
 The required pressures are: 
 
 Pa = Pb= 150 Pk = 165 Pw = Pz = 25.6 
 
 Pc = 112 pn = 60.0 ' p^ = 52.3 
 
 Pd = Po= 76-5 PQ = 50-5 Po^ = 22.1 
 
 Pe = Pp = 67.5 ^, = ^ = 28.3 Ps = 18.5 
 
 ^ = 67.5 p, = py= 25.3 p^=. p^ = ^ 
 
 Pg = 76.9 ^ = 25.1 p^ = 17.6 
 
 Ph= pi= 73-5 ^« = 29.0 
 
 pi = Pm= 69.3 Pv === Py = 28.2 
 
 Diagrams with the volumes and pressures corresponding to 
 this example are plotted in Fig. 46 with convenient vertical 
 scales. Actual indicator-diagrams taken from the engine are 
 given by Fig. 47. The events of the stroke come at slightly 
 different piston positions on account of the irregularity due to 
 the connecting-rod, and the drops and other fluctuations of 
 pressure are gradual instead of sudden; moreover, there is con- 
 siderable loss of pressure from the boiler to the engine, from one 
 cylinder to another, and from the low-pressure cylinder to the 
 condenser. Nevertheless the general forms of the diagrams are 
 easily recognized, and all apparent erratic variations are 
 accounted for. 
 
 Designing Compound Engines. — The designer of compound 
 and multiple-expansion engines should have at hand a well- 
 systematized fund of information concerning the sizes, pro- 
 portions, and powers of such engines, together with actual 
 indicator-diagrams. He may then, by a more or less direct 
 method of interpolation or exterpolation, assign the dimensions 
 and proportions to a new design, and can, if deemed advisable, 
 draw or determine a set of probable indicator-diagrams for the 
 new engines. If the new design differs much from the engines 
 for which he has information, he may determin'e approximate 
 diagrams both for an actual engine from which indicator-dia- 
 grams are at hand, and for the new design. He may then 
 sketch diagrams for the new engine, using the approximate 
 
DESIGNING COMPOUND ENGINES 
 
 179 
 
 diagrams as a basis and taking a comparison of the approximate 
 and actual diagrams from the engine already built, as a guide. 
 It is convenient to prepare and use a table showing the ratios of 
 actual mean effective pressures and approximate mean effective 
 pressures. Such a table enables the designer to assign mean 
 effective pressures to a cylinder of the new engine and to infer 
 very closely what its horse-power will be. It is also very useful 
 as a check in sketching probable diagrams for a new engine, 
 which diagrams are not only useful in estimating the power of the 
 new engine, but in calculating stresses on the members of that 
 engine. 
 
 A rough approximation of the power of an engine may be 
 made by calculating the power as though the total or equivalent 
 expansion took place in the low-pressure cylinder, neglecting/ 
 clearance and compression. The power thus found is to be 
 affected by a factor which according to the size and type of the 
 engine may vary from 0.6 to 0.9 for compound engines and from 
 0.5 to 0.8 for triple engines. Seaton and Rounthwaite * give the 
 following table of multipHers for compound marine engines: 
 
 MULTIPLIERS FOR FINDING PROBABLE M.E.P. COMPOTOTD 
 .\ND TRIPLE MARINE ENGINES. 
 
 Description of Engine. 
 
 Receiver-compound, screw-engines 
 
 Receiver-compound, paddle-engines 
 
 Direct expansion 
 
 Three-cylinder triple, merchant ships 
 
 Three-cylinder triple, naval vessels 
 
 Three-cylinder triple, gunboats and torpedo-boats 
 
 Jacketed. 
 
 0.67 to o. 73 
 
 o . 64 to o. 68 
 0.55 to 0.65 
 
 Un jacketed. 
 
 0.58 to Q.68 
 0.55 to 0.65 
 0.71 to 0.75 
 0.60 to 0.66 
 
 o . 60 to o. 67 
 
 For example, let the boiler- pressure be 80 pounds by the gauge, 
 or 94.7 pounds absolute; let the back-pressure be 4 pounds 
 absolute; and let the total number of expansions be six, so that 
 the volume of steam exhausted to the condenser is six times the 
 
 * Pocket Book of Marine Engineering. 
 
l8o COMPOUND ENGINES 
 
 volume admitted from the boiler. Neglecting the effect of clear- 
 ance and compression, the mean effective pressure is 
 
 94.7 X h + 94.7 X i log, f - 4 X I = 40.06 = M.E.P. 
 
 If the large cylinder is 30 inches in diameter, and the stroke 
 is 4 feet, the horse-power at 60 revolutions per minute is 
 
 — ^ X 40.06 X 2 X 4 X 60 -^ 33000 = 412 H.P. 
 4 
 
 If the factor to be used in this case is 0.75, then the actual 
 horse-power will be about 
 
 0.75 X 400 = 300 H.P. 
 
 Binary Engines. — Another form of compound engines using 
 two fluids like steam and ether, was proposed by du Trembly * in 
 1850, to extend the lower range of temperature of vapor-engines. 
 At that time the common steam-pressure was not far from thirty 
 pounds by the gauge, corresponding to a temperature of 250° F. 
 If the back-pressure of the engine be assumed to be 1.5 pounds 
 absolute (115° F.), the efficiency for Carnot's cycle would be 
 approximately 
 
 2t^O — 115 
 
 250 + 460 
 
 0.19. 
 
 If, however, by the use of a more volatile fluid the result at 
 lower temperature could be reduced to 65° F., the efficiency 
 could be increased to 
 
 250 - 65 , 
 
 -^ ^ = 0.26. 
 
 250 -f 460 
 
 At the present time when higher steam-pressures are common, 
 the comparison is less favorable. Thus the temperature of 
 steam at 150 pounds by the gauge is 365° F., so that with 1.5 
 
 * Manuel du Conducteur des Machines a Vaporous comhinees au Machines 
 Binaires, also Rankine Steam Engine, p. 444. 
 
BINARY ENGINES l8l 
 
 pounds absolute (or 1 1 5° F. ) for the back-pressure the efficiency 
 for Carnot 's cycle is 
 
 ^6s — lis 
 
 365 + 460 
 
 and for a resultant temperature of 65° F., the efficiency would be 
 
 -^-^ ^ = 0.36. 
 
 365 + 460 
 
 If a like gain of economy could be obtained in practice, it 
 would represent a saving of 17 per cent, which would be well 
 worth while. Further discussion of this matter of economy will 
 be given in Chapter XI, in connection with experiments on 
 binary engines using steam and sulphur-dioxide. 
 
 The practical arrangement of a binary engine substitutes for, 
 the condenser an appliance having somewhat the same form as 
 a tubular surface-condenser, the steam being condensed on the 
 outside of the tubes and withdrawn in the form of water of con- 
 densation at the bottom. Through the tubes is forced the 
 more volatile fluid, which is vaporized much as it would be in a 
 "water-tube" boiler. The vapor is then used in a cylinder 
 differing in no essential from that for a steam-engine, and in turn 
 is condensed in a surface-condenser which is cooled with water 
 at the lowest possible temperature. 
 
 An ideal arrangement for a binary engine avoiding the use of 
 air-pumps would appear to be the combination of a compound 
 non-condensing steam-engine with a third cylinder on the binary 
 system which should have for its working substance a fluid that 
 would give a convenient pressure at 212° F., and a pressure 
 somewhat above the atmosphere at 60° F. There is no known 
 fluid that gives both these conditions; thus ether at 212° F. gives 
 a pressure of about 96 pounds absolute, but its boiling-point at 
 atmospheric pressure is 94° F., consequently it would from 
 necessity require a vacuum and an air-pump unless the ether 
 could be entirely freed from air, and leakage into the vacuum 
 space entirely prevented. Sulphur-dioxide gives a pressure of 41 
 
l82 COMPOUND ENGINES 
 
 pounds absolute at 60° F., so that it can always be worked at a 
 pressure above the atmosphere; but 212° F. would give an incon- 
 venient pressure, and in practice it has been found convenient 
 to run the steam-engine with a vacuum of 22 inches of mercury 
 or about 4 pounds absolute, which gives a temperature of 155° F., 
 at which sulphur-dioxide has a pressure of 180 pounds per square 
 inch by the gauge. 
 
 The attempt of du Trembly to use ether for the second fluid 
 in a binary engine did not result favorably, as 'his fuel-con- 
 sumption was not less than that of good engines of that time, 
 which appears to indicate that he could not secure favorable 
 conditions. 
 
CHAPTER X. 
 
 TESTING STEAM-ENGINES. 
 
 The principal object of tests of steam-engines is to determine 
 the cost of power. Series of engine tests are made to 
 determine the effect of certain conditions, such as superheating 
 and steam-jackets, on the economy of the engine. Again, tests 
 may be made to investigate the interchanges of heat between the 
 steam and the walls of the cylinder by the aid of Hirn's analysis, 
 and thus find how certain conditions produce effects that are 
 favorable or unfavorable to economy. 
 
 The two main elements of an engine test are, then, the meas- 
 urement of the power developed and the determination of the 
 cost of the power in terms of thermal units, pounds of steam, or 
 pounds of coal. Power is most commonly measured by aid of 
 the steam-engine indicator, but the power delivered by the 
 engine is sometimes determined by a dynamometer or a friction 
 brake; sometimes, when an indicator cannot be used conven- 
 iently, the dynamic or brake power only is determined. When 
 the engine drives a dynamo-electric generator the power applied 
 to the generator may be determined electrically, and thus the 
 power delivered by the engine may be known. 
 
 When the cost of power is given in terms of coal per horse- 
 power per hour, it is sufficient to weigh the coal for a definite 
 period of time. In such case a combined boiler and engine test 
 is made, and all the methods and precautions for a careful boiler 
 test must be observed. The time required for such a test 
 depends on the depth of the fire on the grate and the rate of 
 combustion. For factory boilers the test should be twenty-four 
 hours long if exact results are desired. 
 
 When the cost of power is stated in terms of steam per horse- 
 power per hour, one of two methods may be followed. When 
 
 183 
 
l84 TESTING STEAM-ENGINES 
 
 the engine has a surface-condenser the steam exhausted from the 
 engine is condensed, collected, and weighed. One hour is 
 usually sufficient for tests under favorable conditions; shorter 
 intervals, ten or fifteen minutes, give fairly uniform results. 
 The chief objection to this method is that the condenser is liable 
 to leak water at the tube packings. Under favorable conditions 
 the results of tests by this method and by determining the feed- 
 water supplied to the boiler are substantially the same. In tests 
 on non-condensing and on jet-condensing engines the steam- 
 consumption is determined by weighing or measuring the feed- 
 water supplied to the boiler or boilers that furnish steam to the 
 engine. Steam used for any other purpose than running the 
 engine, for example, for pumping, heating, or making determi- 
 nations of the quality of the steam, must be determined and 
 allowed for. The most satisfactory way is to condense and 
 weigh such steam; but small quantities, as for determining 
 quality by a steam calorimeter, may be gauged by allowing it to 
 flow through an orifice. Tests which depend on measuring the 
 feed- water should be long enough to minimize the effect of the 
 uncertainty of the amount of water in a boiler corresponding to 
 an apparent height of water in a water-gauge; for the apparent 
 height of the water-level depends largely on the rate of vaporiza- 
 tion and the activity of convection currents. 
 
 When the cost of power is expressed in thermal units it is 
 necessary to measure the steam-pressure, the amount of moisture 
 in the steam supplied to the cylinder, and the temperature of the 
 condensed steam when it leaves the condenser. If steam is used 
 in jackets or reheaters it must be accounted for separately. 
 But it is customary in all engine tests to take pressures and 
 temperatures, so that the cost -may usually be calculated in 
 thermal units, even when the experimenter is content to state it 
 in pounds of steam. 
 
 For a Hirn's analysis it is necessary to weigh or measure the 
 condensing water, and to determine the temperatures at admis- 
 sion to and exit from the condenser. 
 
 Important engines, with their boilers and other appurtenances, 
 
TESTING STEAM-ENGINES 185 
 
 are commonly built under contract to give a certain economy, 
 and the fulfilment of the terms of a contract is determined by a 
 test of the engine or of the whole plant. The test of the entire 
 plant has the advantage that it gives, as one result, the cost of 
 power directly in coal ; but as the engine is often watched with more 
 care during a test than in regular service, and as auxiliary duties, 
 such as heating and banking fires, are frequently omitted from 
 such an economy test, the actual cost of power can be more 
 justly obtained from a record of the engine in regular service, 
 extending for weeks or months. The tests of engine and boilers, 
 though made at the same time, need not start and stop at the 
 same time, though there is a satisfaction in making them 
 strictly simultaneous. This requires that the tests shall be long 
 enough to avoid drawing the fires at beginning and end of the 
 boiler test. 
 
 In anticipation of a test on an engine it must be run for some 
 time under the conditions of the test, to eliminate the effects of 
 starting or of changes. Thus engines with steam-jackets are 
 commonly started with steam in the jackets, even if they are to 
 run with steam excluded from the jackets. An hour or more 
 must then be allowed before the effect of using steam in the 
 jackets will entirely pass away. An engine without steam- 
 jackets, or with steam in the jackets, may come to constant 
 conditions in a fraction of that time, but it is usually well to 
 allow at least an hour before starting the test. 
 
 It is of the first importance that all the conditions of a test 
 shall remain constant throughout the test. Changes of steam- 
 pressure are particularly bad, for when the steam-pressure rises 
 the temperature of the engine and 'all parts affected by the steam 
 must be increased, and the heat required for this purpose is 
 charged against the performance of the engine; if the steam- 
 pressure falls a contrary effect will be felt. In a series of tests 
 one clement at a time should be changed, so that the effect of 
 that element may not be confused by other changes, even though 
 such changes have a relatively small effect. It is, however, of 
 more importance that steam-pressure should remain constant 
 
1 86 TESTING STEAM-ENGINES 
 
 than that all tests at a given pressure should have identically the 
 same steam-pressure, because the total heat of steam varies more 
 slov^^Iy than the temperature. 
 
 All the instruments and apparatus used for an engine test 
 should be tested and standardized either just before or just 
 after the test; preferably before, to avoid annoyance when any 
 instrument fails during the test and is replaced by another. 
 
 Thermometers. — Temperatures are commonly measured by 
 aid of mercurial thermometers, of which three grades may be 
 distinguished. For work resembling that done by the physicist 
 the highest grade should be used, and these must ordinarily be 
 calibrated, and have their boiling- and freezing-points deter- 
 mined by the experimenter or some qualified person; since the 
 freezing-point is liable to change, it should be redetermined when 
 necessary. For important data good thermometers must be used, 
 such as are sold by reliable dealers, but it is preferable that they 
 should be calibrated or else compared with a thermometer that 
 is known to be reliable. For secondary data or for those requir- 
 ing little accuracy common thermometers with the graduation 
 on the stem may be used, but these also should have their errors 
 determined and allowed for. Thermometers with detachable 
 scales should be used only for crude work. 
 
 Gauges. — Pressures are commonly measured by Bourdon 
 gauges, and if recently compared with a correct mercury column 
 these are sufficient for engineering work. The columns used 
 by gauge-makers are sometimes subject to minor errors, and are 
 not usually corrected for temperature. It is important that 
 such gauges should be frequently retested. 
 
 Dynamometers. — The standard for measurement of power 
 is the friction-brake. For smooth continuous running it is 
 essential that the brake and its band shall be cooled by a stream 
 of water that does not come in contact with the rubbing sur- 
 faces. Sometimes the wheel is cooled by a stream of water cir- 
 culating through it, sometimes the band is so cooled, or both may 
 be. A rubbing surface which is not cooled should be of non- 
 conducting material. If both rubbing surfaces are metallic they 
 
INDICATORS 187 
 
 must be freely lubricated with oil. An iron wheel running in a 
 band furnished with blocks of wood requires little or no lubri- 
 cation. 
 
 To avoid the increase of friction on the brake- bearings due 
 to the load applied at a single brake-arm, two equal arms may 
 be used with two equal and opposite forces applied at the ends 
 to form a statical couple. 
 
 With care and good workmanship a friction- brake may be 
 made an instrument of precision sufficient for physical investi- 
 gations, but with ordinary care and workmanship it will give 
 results of sufficient accuracy for engineering work. 
 
 An engine which drives an electric-generator may readily have 
 the dynamic or brake- power determined from the electric out- 
 put, provided that the efficiency of the generator is properly 
 determined. 
 
 The only power that can be measured for a steam-turbine is 
 the dynamic or brake-power; when connected with an electric- 
 generator this involves no difficulty. For marine propulsion it 
 is customary to determine the power of steam-turbines by some 
 form of torsion-metre applied to the shaft that connects the 
 turbine to the propeller. This instrument measures the angle 
 of torsion of the shaft while running, and consequently, if the 
 modulus of elasticity has been determined, gives a positive 
 determination of the power delivered to the propeller. Under 
 favorable conditions a torsion-metre may have an error of not 
 more than one per cent. 
 
 Indicators. — The most important and at the same time the 
 least satisfactory instrument used in engine-testing is the indi- 
 cator. Even when well made and in good condition it is liable 
 to have an error which may amount to two per cent when used 
 at moderate speeds. At high speeds, three hundred revolutions 
 per minute and over, it is likely to have two or three times as 
 much error. As a rule, an indicator cannot be used at more 
 than four hundred revolutions per minute. 
 
 The mechanism for reducing the motion of the crosshead of 
 the engine and transferring it to the paper drum of an indicator 
 
l88 TESTING STEAM-ENGINES 
 
 should be correct in design and free from undue looseness. It 
 should require only a very short cord leading to the paper drum, 
 because all the errors due to the paper drum are proportional to 
 the length of the cord and may be practically eliminated by 
 making the cord short. 
 
 The weighing and recording of the steam-pressure by the indi- 
 cator-piston, pencil-motion, and pencil are affected by errors 
 which may be classified as follows : 
 
 1. Scale of the spring. 
 
 2. Design of the pencil-motion. 
 
 3. Inertia of moving parts. 
 
 4. Friction and backlash. 
 
 Good indicator-springs, when tested by direct loads out of 
 the indicator, usually have correct and uniform scales; that is, 
 they collapse under pressure the proper amount for each load 
 applied. When enclosed in the cylinder of an indicator the 
 spring is heated by conduction and radiation to the temperature 
 of the cylinder, and that temperature is sensibly equal to the 
 mean temperature in the engine-cylinder. But a spring is appre- 
 ciably weaker at high temperatures, so that when thus enclosed 
 in the indicator-cylinder, it gives results that are too large; the 
 error may be two per cent or more. 
 
 Outside spring-indicators avoid this difficulty and are to be 
 preferred for all important work. They have only one disad- 
 vantage, in that the moving parts are heavier, but this may be 
 overcome by increasing the area of the piston from half a square 
 inch to one square inch. 
 
 The motion of the piston of the indicator is multiplied five 
 or six times by the pencil-motion, which is usually an approx- 
 imate parallel motion. Within the proper range of motion 
 (about two inches) the pencil draws a line which is nearly 
 straight when the paper drum is at rest, and it gives a nearly 
 uniform scale provided that the spring is uniform. The errors 
 due to the geometric design of this part of the indicator are 
 always small. 
 
INDICATORS 189 
 
 When steam is suddenly let into the indicator, as at admission 
 to the engine-cylinder, the indicator-piston and attached parts 
 forming the pencil-motion are set into vibration, with a natural 
 time of vibration depending on the stiffness of the spring. A 
 weak spring used for indicating a high-speed engine may throw 
 the diagram into confusion, because the pencil will give a few 
 deep undulations which make it impossible to recognize the 
 events of the stroke of the engine, such as cut-off and release. 
 A stiffer spring will give more rapid and less extensive undu- 
 lations, which will be much less troublesome. As a rule, when 
 the undulations do not confuse the diagram the area of the dia- 
 gram is but little affected by the undulations due to the inertia 
 of the piston and pencil-motion. 
 
 The most troublesome errors of the indicator are due 
 to friction and backlash. The various joints at the piston 
 and in the pencil-motion are made as tight as can be without 
 undue friction, but there is always some looseness and some 
 friction at those joints. There is also some friction of the piston 
 in the cylinder and of the pencil on the paper. Errors from this 
 source may be one or two per cent, and are liable be excessive 
 unless the instrument is used with care and skill. A blunt 
 pencil pressed up hard on the paper will reduce the area of the 
 diagram five per cent or more; on the other hand, a medium 
 pencil drawing a faint but legible line will affect the area very 
 little. Any considerable friction of the piston of the indicator 
 will destroy the value of the diagram. 
 
 Errors of the scale of the spring can be readily determined and 
 investigated by loading the spring with known weights, when 
 properly supported, out of the indicator. This method is prob- 
 ably sufficient for outside spring indicators. Those that have 
 the spring inside the cylinder are tested under steam pressure, 
 measuring the pressure either by a gauge or a mercury column. 
 Considerable care and skill are required to get good results, 
 especially to avoid excessive friction of the piston as it remains 
 at rest or moves slowly in the cylinder. It must be borne in 
 mind that the indicator cylinder heats readily when subjected to 
 
I go TESTING STEAM-ENGINES 
 
 progressively higher steam pressures, but that it parts with heat 
 slowly, and that consequently tests made with falling steam 
 pressures are not valuable. 
 
 Scales. — ' Weighing should be done on scales adapted to the 
 load ; overloading leads to excessive friction at the knife-edges and 
 to lack of delicacy. Good commercial platform scales, when 
 tested with standard weights, are sufficient for engineering work. 
 
 Coal and ashes are readily weighed in barrows, for which the 
 tare is determined by weighing empty. Water is weighed in 
 barrels or tanks. The water can usually be pumped in or 
 allowed to run in under a head, so that the barrel or tank can be 
 filled promptly. Large quick-opening valves must be used to allow 
 the water to run out quickly. As the receptacle will seldom drain 
 properly, it is not well to wait for it to drain, but to close the 
 exit- valve and weigh empty with whatever small amount of water 
 may be caught in it. Neither is it well to try to fill the receptacle 
 to a given weight, as the jet of water running in may affect the 
 weighing. With large enough scales and tanks the largest 
 amounts of water used for engine tests may be readily handled. 
 
 Measuring Water. — When it is not convenient to weigh water 
 directly, it may be measured in tanks or other receptacles of 
 known volume. Commonly two are used, so that one may 
 fill while the other is emptied. The' volume of a receptacle may 
 be calculated from its dimensions, or may be determined by 
 weighing in water enough to fill it. When desired a receptacle 
 may be provided with a scale showing the depth of the water, 
 and so partial volumes can be determined. A closed recep- 
 tacle may be used to measure hot water or other fluids. 
 
 Water-Meters of good make may be used for measuring water 
 when other methods are not applicable, provided they are tested 
 and rated under the conditions for which they are used, taking 
 account of the amount and temperature of the water measured. 
 Metres are most convenient for testing marine engines because 
 water cannot be weighed at sea on account of the motion of the 
 ship, and arrangements for measuring water in tanks are expen- 
 sive and inconvenient. For such tests the metre may be placed 
 
THROTTLING-CALORIMETER 
 
 191 
 
 on a by-pass through which the feed-water from the surface- 
 condenser can be made to pass by closing a valve on the direct 
 line of feed-pipe. If necessary the metre can be quickly shut 
 ofif and the direct line can be opened. The chief uncertainty in 
 the use of a metre is due to air in the water; to avoid error from 
 this source, the metre should be frequently vented to allow air 
 to escape without being recorded by the metre. 
 
 Weirs and Orifices. — So far as possible the use of weirs and 
 orifices for water during engine tests should be avoided, for, in 
 addition to the uncertainties unavoidably connected with such 
 hydraulic measurements, difficulties are liable to arise from the 
 temperature of the water and from the oil in it. A very little oil 
 is enough to sensibly affect the coefficient for a weir or orifice. 
 The water flowing from the hot-well of a jet-condensing engine 
 is so large in amount that it is usually deemed advisable to 
 measure it on a w^eir; the effect of temperature and oil is less 
 than when the same method is used for measuring condensed 
 steam from a surface-condenser. 
 
 Priming-Gauges. — • When superheated steam is supplied to an 
 engine it is sufficient to take the temperature of the steam in the 
 steam-pipe near the engine. When moist steam is used the amount 
 of moisture must be determined by a separated test. Origi- 
 nally such tests were made by some form of calorimeter, and 
 that name is now commonly attached to certain devices which 
 are not properly heat-measurers. Three of these will be men- 
 tioned : (i ) the throttling-calorimeter, which can usually be applied 
 to all engine tests; (2) the separating-calorimeter, which can be 
 applied when the steam is wet; and (3) the Thomas electric calor- 
 imeter, intended for use with steam-turbines to determine the 
 moisture in steam at any stage of the turbine whatever may be 
 the pressure or quality of the steam. 
 
 Throttling-Calorimeter. — A simple form of calorimeter, 
 devised by the author, is shown by Fig. 48, where ^4 is a 
 reservoir about 4 inches in diameter and about 12 inches long 
 to which steam is admitted through a half-inch pipe b, with a 
 throttle- valve near the reservoir. Steam flows away through an 
 
ig: 
 
 TESTING STEAM-ENGINES 
 
 e ^==^ 
 
 inch pipe d. At / is a gauge for measuring the pressure, and at 
 e there is a deep cup for a thermometer to measure the temper- 
 ature. The boiler-pressure may be taken 
 from a gauge on the main steam-pipe 
 near the calorimeter. It should not be 
 taken from a pipe in which there is a 
 ^iltTl I rapid flow of steam as in the pipe ft, 
 
 since the velocity of the steam will affect 
 the gauge-reading, making it less than the 
 real pressure. The reservoir is wrapped 
 with hair-felt and lagged with wood to 
 reduce radiation of heat. 
 
 When a test is to be made, the valve on 
 the pipe d is opened wide (this valve is 
 frequently omitted), and the valve at h is 
 opened wide enough to give a pressure of 
 live to fifteen pounds in the reservoir. 
 Readings are then taken of the boiler- 
 gauge, of the gauge at /, and of the thermometer at e. It is well to 
 wait about ten minutes after the instrument is started before taking 
 readings so that it may be well heated. Let the boiler-pressure 
 be ^, and let r and q be the latent heat and heat of the liquid 
 corresponding. Let p^ be the pressure in the calorimeter, r^ the 
 heat of vaporization, q^ the heat of the liquid, and t^ the tempera- 
 ture of saturated steam at that pressure, while i^ is the tempera- 
 ture of the superheated steam in the calorimeter. Then 
 
 Fig. 48. 
 
 . ^ _ ^1 + ^, + c^ {is - t,) - q 
 
 (152) 
 
 Example. — The following are the data of a test made with 
 this calorimeter: 
 
 Pressure of the atmosphere .... 14.8 pounds; 
 Steam-pressure by gauge .... 69.8 " 
 Pressure in the calorimeter, gauge . 12.0 " 
 
 Temperature in the calorimeter . . 268°. 2 F. 
 
THROTTLING-CALORIMETER 
 
 193 
 
 Specific heat of superheated steam for the condition of the 
 test 0.48. 
 
 943.8 + 212.7 + Q-4^ (268.2 — 243.9) "~ 2^5-9 _ 
 892.3 
 
 Per cent of priming, 1.2. 
 
 X = 
 
 0.988; 
 
 A little consideration shows that this type of calorimeter 
 can be used only when the priming is not excessive; otherwise 
 the throttling will fail to superheat the steam, and in such case 
 nothing can be told about the condition of the steam either before 
 or after throttling. To find this limit for any pressure 4 may be 
 made equal to t^ in equation (152); that is, we may assume that 
 the steam is just dry and saturated at that limit in the calorimeter. 
 Ordinarily the lowest convenient pressure in the calorimeter is 
 the pressure of the atmosphere, or 14.7 pounds to the square inch. 
 The table following has been calculated for several pressures in 
 the manner indicated. It shows that the limit is higher for higher 
 pressures, but that the calorimeter can be applied only where 
 the priming is moderate. 
 
 When this calorimeter is used to test steam supplied to a 
 condensing-engine the limit may be extended by connecting the 
 exhaust to the condenser. For example, the limit at 100 pounds 
 absolute, with 3 pounds absolute in the calorimeter, is 0.064 
 instead of 0.040 with atmospheric pressure in the calorimeter. 
 
 LIMITS OF THE THROTTLING-CALORIMETER. 
 
 Pressure. 
 
 
 
 
 Priming. 
 
 Absolute. 
 
 Gauge. 
 
 300 
 
 285.3 
 
 0.077 
 
 250 
 
 235-3 
 
 0.070 
 
 200 
 
 185.3 
 
 0.061 
 
 175 
 
 160.3 
 
 0.058 
 
 150 
 
 135-3 
 
 0.052 
 
 125 
 
 no. 3 
 
 0.046 
 
 100 
 
 l^-^ 
 
 0.040 
 
 75 
 
 60.3 
 
 0.032 
 
 50 
 
 35-3 
 
 0.023 
 
194 TESTING STEAM-ENGINES 
 
 In case the calorimeter is used near its limit — that is, when 
 the superheating is a few degrees only — it is essential that the 
 thermometer should be entirely reliable; otherwise it might 
 happen that the thermometer should show superheating when 
 the steam in the calorimeter was saturated or moist. In any 
 other case a considerable error in the temperature will produce 
 an inconsiderable effect on the result. Thus at loo pounds 
 absolute with atmospheric pressure in the calorimeter, io° F. of 
 superheating indicates 0.035 priming, and 15° F. indicates 0.032 
 priming. So also a slight error in the gauge-reading has little 
 effect. Suppose the reading to be apparently 100.5 pounds 
 absolute instead of 100, then with 10° of superheating the prim- 
 ing appears to be 0.033 instead of 0.032. 
 
 It has been found by experiment that no allowance need be 
 made for radiation from this calorimeter if made as described, 
 provided that 200 pounds of steam are run through it per hour. 
 Now this quantity will flow through an orifice one-fourth of an 
 inch in diameter under the pressure of 70 pounds by the gauge, 
 so that if the throttle-valve be replaced by such an orifice the 
 question of radiation need not be considered. In such case a 
 stop- valve will be placed on the pipe to shut off the calorimeter 
 when not in use; it is opened wide when a test is made. If an 
 orifice is not provided the throttle- valve may be opened at first 
 a small amount, and the temperature in the calorimeter noted; 
 after a few minutes the valve may be opened a trifle more, where- 
 upon the temperature may rise, if too little steam was used at 
 first. If the valve is opened little by little till the temperature 
 stops rising, it will then be certain that enough steam is used to 
 reduce the error from radiation to a very small amount. 
 
 Separating-Calorimeter. — If steam contains more than 
 three per cent of moisture the priming may be determined by 
 a good separator which will remove nearly all the moisture. 
 It remains to measure the steam and water separately. The 
 water may be best measured in a calibrated vessel or receiver, 
 while the steam may be condensed and weighed, or may be 
 gauged by allowing it to flow through an orifice of known size. 
 
THE THOMAS ELECTRIC CALORIMETER 
 
 195 
 
 A form of separating-calorimeter devised by Professor Carpenter * 
 is shown by Fig. 49. 
 
 Steam enters a space at the top 
 which has sides of wire gauze and a 
 convex cup at the bottom. The water 
 is thrown against the cup and finds its 
 way through the gauze into an inside 
 chamber or receiver and rises in a 
 water-glass outside. The receiver is 
 caUbrated by trial, so that the amount of 
 water may be read directly from a gradu- 
 ated scale. The steam meanwhile passes 
 into the outer chamber which surrounds 
 the inner receiver and escapes from an 
 orifice at the bottom. The steam may 
 be determined by condensing, collecting, 
 and weighing it; or it may be calculated 
 from the pressure and the size of the 
 orifice. When the steam is weighed 
 there is no radiation error, since the 
 
 inner chamber is protected by the steam in the outer chamber. 
 This instrument may be guarded against radiation by wrapping 
 and lagging, and then if steam enough is used the radiation will 
 be insignificant, just as was found to be the case for the 
 throttling-calorimeter. 
 
 The Thomas Electric Calorimeter. — The essential feature of this 
 instrument (Fig. 50) is the drying and superheating of the steam 
 by a measured amount of electric energy. Steam is admitted 
 at B and passes through numerous holes in a block of soapstone 
 which occupies the middle of the instrument; these holes are 
 partially filled with coils of German silver wire which are heated 
 by an electric current that enters and leaves at the binding- 
 screws. The steam emerges dry or superheated at the upper 
 part of the chamber and passes down through wire gauze, which 
 surrounds the central escape pipe; this central pipe surrounds 
 
 * Trans. Am. Soc. Mech. Engs., vol. xvii, p. 608. 
 
 Fig. 49. 
 
196 
 
 TESTING STEAM-ENGINES 
 
 the thermometer cup, and leads to the exit at the top, which has 
 two orifices, either of which may be piped to a condenser or 
 
 elsewhere. 
 
 To use the instrument it is 
 properly connected by a sampling- 
 tube to the space from which 
 steam is drawn, and valves are 
 adjusted to supply a convenient 
 amount of steam which is assumed 
 to be uniform for steady pressure; 
 this last is a matter of some im- 
 portance. 
 
 The current of electricity is 
 then adjusted to dry the steam; 
 this may be determined by noting 
 the temperature by the thermom- 
 eter in the central thermometer 
 cup, because that thermometer 
 will show a slight rise corres- 
 ponding to a very small degree 
 of superheating which is sufficient 
 to indicate the disappearance of 
 moisture, but not enough to affect 
 the determination of quality by 
 the instrument. The wire gauze 
 surrounding the thermometer is an essential feature of this 
 operation, as it insures the homogeneity of the steam, which, 
 without the gauze, would be likely to be a mixture of super- 
 heated steam and moist steam. Readings are taken of the 
 proper electrical instruments from which the electrical energy 
 imparted can be determined in watts; let this energy required to 
 dry the steam be denoted by E^. Now let the electric current be 
 increased till the steam is superheated 30°, and let E^ be the 
 increase of electric input which is required to superheat the 
 steam. 
 
 If W is the weight of steam flowing per hour through the 
 
 Fig. 50. 
 
THE THOMAS ELECTRIC CALORIMETER 
 
 197 
 
 instrument under the first conditions, the weight when super- 
 heated will be CW, where C is a factor less than unity which 
 has been determined by exhaustive tests on the instrument. 
 The amount of electric energy required to superheat one pound 
 of steam 30° from saturation at various pressures has also been 
 determined and may be represented by 5; this constant has been 
 so determined as to include an allowance for radiation, and is 
 more convenient than the specific heat of superheated steam, in 
 this place. Making use of the factors C and S, we may write 
 
 E, = CSW, otW = ^, 
 
 which affords a means of eliminating the weight of steam used; 
 this is an important feature in the use of the instrument. 
 
 Returning now to the first condition of the instrument when 
 steam is dried by the application of E^ watts of electric energy, 
 we have for the equivalent heat 
 
 3.42 E^; 
 
 and dividing by the expression for the weight of steam flowing 
 per hour, we have for the heat required to dry one pound of 
 steam 
 
 where r is the heat of vaporization and i — jc is the amount of 
 water in one pound of moist steam. 
 
 Solving the above equation for x, we have 
 
 3.42 CS E, 
 X - I -^^ -^. 
 
 If desired, the constant factors may be united into one term, and 
 the equation may be written 
 
 _KE^ 
 r e/ 
 
 With each instrument is furnished a diagram giving values of 
 K for all pressures, so that the use of the instrument involves 
 
198 TESTING STEAM-ENGINES 
 
 only two readings of a wattmeter and the application of the above 
 simple equation. 
 
 For example, suppose that the use of the instrument in a 
 particular case gave the values E^ = 240, and E^ = 93.0 for 
 the absolute pressure 100 pounds per square inch. The value 
 of K from the diagram is 54.2, and r from the steam- tables is 884, 
 consequently 
 
 ^4.2 240 „ 
 
 884 93.0 
 
 Method of Sampling Steam. — It is customary to take a sample 
 of steam for a calorimeter or priming-gauge through a small 
 pipe leading from the main steam-pipe. The best method of 
 securing a sample is an open question; indeed, it is a question 
 whether we ever get a fair sample. There is no question but 
 that the composition of the sample is correctly shown by any of 
 the calorimeters described, when the observer makes tests with 
 proper care and skill. It is probable that the best way is to 
 take steam through a pipe which reaches at least halfway across 
 the main steam-pipe, and which is closed at the end and drilled 
 full of small holes. It is better to have the sampling- pipe at 
 the side or top of the main, and it is better to take a sample 
 from a pipe through which steam flows vertically upward. The 
 sampling-pipe should be short and well wrapped to avoid 
 radiation. 
 
CHAPTER XI. 
 
 INFLUENCE OF THE CYLINDER WALLS. 
 
 In this chapter a discussion will be given of the discrepancy 
 between the theory of the steam-engine as detailed in the previous 
 chapter, and the actual performance as determined by tests on 
 engines. It was early evident that this discrepancy was due 
 to the interference of the metal of the cylinder walls which 
 abstracted heat from the steam at high pressure and gave it out 
 at low pressure. In consequence there followed a long struggle 
 to determine precisely what action the walls exerted and how to 
 allow for that action in the design of new engines. The first 
 part has been accomplished; we can determine to a nicety the 
 influence of the cylinder walls for any engine already built and 
 tested; but as yet all attempts to systematize the information 
 derived from such tests in such a manner that it can be used 
 in the design of new engines has been utterly futile. Conse- 
 quently the discussion in this chapter is important mainly 
 in that it allows us to understand the real action of certain 
 devices that are intended to improve the economy of engines, 
 and to form a just opinion on the probability of future im- 
 provements. 
 
 As soon as the investigations by Clausius and Rankine 
 and the experiments by Regnault made a precise theory of 
 the steam engine possible, it became evident that engines used 
 from quarter to half again as much steam as the adiabatic 
 theory indicated, and in particular that expansion down to 
 the back-pressure was inadvisable. An early and a satis- 
 factory exposition of these points was made by Isherwood 
 after his tests on the U. S. S. Michigan^ which are given in 
 Table III. 
 
 199 
 
200 
 
 INFLUENCE OF THE CYLINDER WALLS 
 
 Table III. 
 
 TESTS ON THE ENGINE OF THE U. S. S. MICHIGAN. 
 
 CYLINDER DIAMETER, 36 INCHES; STROKE, 8 FEET. 
 
 By Chief-Engineer Isherwood, Researches in Experimental Steam 
 Engineering. 
 
 Duration, hours 
 
 Cut-off 
 
 Revolutions per minute 
 
 Boiler-pressure, pounds per sq in. above 
 
 atmosphere 
 
 Barometer, inches of mercury 
 
 Vacuum, inches of mercury 
 
 Steam per horse-power per hour, pounds 
 Per cent of water in cylinder at release 
 
 I. 
 
 II 
 
 
 III. 
 
 72 
 
 IV. 
 
 72 
 
 V. 
 
 72 
 
 VI. 
 
 72 
 
 72 
 
 72 
 
 II/I2 
 
 7/10 
 
 4/9 
 
 3/10 
 
 1/4 
 
 1/6 
 
 20.6 
 
 i5-t> 
 
 17-3 
 
 13-7 
 
 13-9 
 
 II. 2 
 
 21.0 
 
 19 -5 
 
 21.0 
 
 21.0 
 
 21.0 
 
 21.0 
 
 30.1 
 
 2Q 
 
 8 
 
 29.7 
 
 30.1 
 
 29-9 
 
 29-9 
 
 26.5 
 
 26 
 
 I 
 
 26.3 
 
 25.8 
 
 25.8 
 
 25.6 
 
 38.0 
 
 2>2> 
 
 8 
 
 32.7 
 
 34.7 
 
 34.5 
 
 36.8 
 
 10.7 
 
 15 
 
 3 
 
 27.2 
 
 41.7 
 
 39-^ 
 
 42.1 
 
 72 
 4/45 
 14. 1 
 
 22.0 
 
 29.9 
 24.1 
 41.4 
 
 45-1 
 
 U.S. g. MICHIGAN 
 
 Abscissae per cents of cut off 
 Ordinates pounds of steam 
 per horse power per hour. 
 
 In the first place the best economy for this engine w^as 32.7 
 pounds instead of 26.5 pounds as calculated by the expression 
 
 60 X 33000 
 
 778 (^1 + g, ~ oc^r.^ - g,) 
 
 deduced on page 141 for the steam-consumption for a non-con- 
 ducting engine with 
 complete expansion. 
 This result was ob- 
 tained with cut-off at 
 four-ninths of the 
 stroke which gave a 
 terminal pressure of 
 one pound above the 
 atmosphere. 
 
 The manner of the 
 variation of the steam 
 consumption with the 
 cut-off is clearly 
 shown by Fig. 51, in 
 
 which the fraction of stroke at cut-off is taken for abscissae and 
 
 the steam-consumptions as ordinates. 
 
 Fig. 
 
INFLUENCE OF THE CYLINDER WALLS 201 
 
 To make the diagram clear and compact, the axis of abscissae 
 is taken at 30 pounds of steam per horse-power per hour. An 
 inspection of this diagram and of the figures in the table shows 
 a regularity in the results which can be attained only when tests 
 are made with care and skill. The only condition purposely 
 varied is the cut-off; th^only condition showing important acci- 
 dental variation is the vacuum, and consequently the back- 
 pressure in the cylinder. To allow for the small variations in 
 the back-pressure Isherwood changed the mean effective pressure 
 for each test by adding or subtracting, as the case might require, 
 the difference between the actual back- pressure and the mean 
 back- pressure of 2.7 pounds per square inch, as deduced from 
 all the tests. 
 
 An inspection of any such a series of tests having a wide range 
 of expansions will show that the steam-consumption decreases 
 as the cut-off is shortened till a minimum is reached, usually at 
 ^ to B^ stroke ; any further shortening of the cut-off will be accom- 
 panied by an increased steam-consumption, which may become 
 excessive if the cut-off is made very short. Some insight into 
 the reason for this may be had from the per cent of water in the 
 cylinder, calculated from the dimensions of the cylinder and the 
 pressures in the cylinder taken from the indicator-diagram. 
 The method of the calculation will be given in detail a little later 
 in connection with Hirn's analysis. It will be sufficient now to 
 notice that the amount of water in the cylinder of the engine of 
 the Michigan at release increased from 10.7 per cent for a cut-off 
 at i^ of the stroke to 45.1 per cent for a cut-off at 4*3- of the 
 stroke. Now all the water in the cylinder at release is vaporized 
 during the exhaust, the heat for this purpose .being abstracted 
 from the cylinder walls, and the heat thus abstracted is wasted, 
 without any compensation. The walls may be warmed to some 
 extent in consequence of the rise of pressure and temperature 
 during compression, but by far the greater part of the heat 
 abstracted during exhaust must be supplied by the incoming 
 .steam at admission. There is, therefore, a large condensation 
 of steam during admission and up to cut-off, and the greater part 
 
202 INFLUENCE OF THE CYLINDER WALLS 
 
 of the Steam thus condensed remains in the form of water and 
 does little if anything toward producing work. This may be 
 seen by inspection of the table of results of Dixwell's tests on 
 page 270. With saturated steam and with cut-off at 0.217 of the 
 stroke, 52.2 per cent of the working substance in the cylinder 
 was water. Of this 19.8 per cent was reevaporated during ex- 
 pansion, and 32.4 per cent remained at release to be reevaporated 
 during exhaust. When the cut-off was lengthened to 0.689 of 
 the stroke, there was 27.9 per cent of water at cut-off and 23.9 
 per cent at release. The statement in percentages gives a 
 correct idea of the preponderating influence of the cylinder walls 
 when the cut-off is unduly shortened; it is, however, not true 
 that there is more condensation with a short than with a long 
 cut-off. On the contrary, there is more water condensed in 
 the cylinder when the cut-off is long, only the condensation 
 does not increase as fast as do the weight of steam supplied to 
 the cylinder and the work done, and consequently the conden- 
 sation has a less effect. 
 
 Graphical Representation. — The divergence of the actual 
 
 expansion line from the 
 adiabatic line can be 
 shown in a striking manner 
 by plotting the former on 
 the temperature-entropy 
 diagram as shown in 
 Fig. 53 which is con- 
 ^'°" ^^' structed from the indicator- 
 
 diagram in Fig. 52, shown with the axes of zero pressure and 
 zero volume drawn in the usual manner, allowing for clearance 
 and for the pressure of the atmosphere. 
 
 In order to undertake this construction the weight of steam 
 per stroke W as determined from the test of the engine during 
 which the diagrams were taken, must be determined, and the 
 weight of steam W^ caught in the clearance must be computed 
 from the pressure and volume/, the beginning of compression. 
 The dry steam line (Fig. 52) is drawn by the following process: 
 
 b 
 
 n 
 
 
 ,,^^^%&~— . 
 
GRAPHICAL REPRESENTATION 203 
 
 a line ae is drawn at a convenient pressure, and on it is laid off 
 the volume oi W -\- W ^ pounds of dry steam as determined 
 from the steam-table to the proper scale of the drawing. Thus 
 if Sg is the specific volume of the steam at the pressure p^ the 
 volume of steam present if dry and saturated would be 
 
 {W + W^) Se. 
 
 But the length of the diagram L, in inches is proportional to 
 the- piston displacement D in cubic feet. The latter is obtained 
 by multiplying the area of the piston in square feet by its stroke 
 in feet. For the crank end the net area of the piston is to be used, 
 allowing for the piston-rod. Consequently the proper abscissa, 
 
 representing the volume is obtained by multiplying by - , giving 
 
 (W + W,) L 
 D 
 and of this all except 5 is a constant for which a numerical result 
 can be found. 
 
 The diagram shown by Fig. 52 was taken from the head end 
 of the high-pressure cylinder of an experimental engine in the 
 laboratory of the Massachusetts Institute of Technology. The 
 value oiW+ W ^ was found to be 0.075 ^^ ^ pound; the piston 
 displacement was 1.102 cubic feet, and the length of the diagram 
 was 3.69 inches; consequently 
 
 ^---=0.251. 
 
 The line ae was drawn at 90 pounds absolute at which s = 4.86 
 cubic feet; the length of the line ae was consequently 
 
 0.251 X 4.86 = 1.22 inch. 
 Neglecting the volume of the water present, the volume of 
 steam actually present bore the same ratio to the volume of the 
 steam when saturated, that ac had to ae. This gave in the figure 
 at c 
 
 ac 0.04 
 x,= — = -^^ = 0.771. 
 ae I. 219 
 
204 
 
 INFLUENCE OF THE CYLINDER WALLS 
 
 To plot the point e on the temperature-entropy diagram, 
 ^ig- 53> we may find the temperature at 90 pounds absolute, 
 namely, 320° F., and on a line with that temperature as an ordi- 
 nate we may interpolate between the lines for constant values 
 
 of X. Other points can 
 be drawn in a like man- 
 ner, and the curve eg can 
 be sketched in; showing 
 that the steam continues 
 to yield heat to the cylin- 
 der walls from cut-off till c 
 is reached on Fig. 52, and 
 perhaps a trifle longer. 
 Beyond c the steam^ re- 
 ceives heat from the walls 
 until exhaust opens. 
 Fig. 52, by drawing the 
 The point d can be 
 
 Fig. 53. 
 
 The same feature is exhibited in 
 adiabatic line xdn from the point of cut-off. 
 located by multiplying the length ae, which represents the volume 
 of steam in the cylinder when dry by the value of x after adia- 
 batic expansion from the point of cut-off n. This point n is 
 readily included in the preceding investigation, so that x^ can be 
 determined. Locating n on the temperature-entropy diagram, 
 Fig. 53, we may draw through it a Vertical constant entropy line 
 and note where it cuts the lines corresponding to the pressure 
 lines like ae in Fig. 52, and interpolate for the values of x. 
 For example, the entropy at n in Fig. 53 appears to be 1.36, 
 and at 320° F., which corresponds to 90 pounds, this entropy 
 line gives by interpolation 0.78, so that the length of ad is 
 
 0.78 X 1.22 = 0.95. 
 
 In this discussion no attempt is made to distinguish the moisture 
 which may be in contact with the wall from the remainder of 
 steam and water in the cylinder. In reality that moisture has 
 furnished the heat which the cylinder walls acquire during 
 admission, and it abstracts heat from the walls during the expan- 
 
HIRN'S ANALYSIS 
 
 205 
 
 sion. The mixture, moreover, is not homogeneous, because the 
 moisture on the cylinder walls is likely to be colder than the 
 steam, though naturally it cannot be warmer. 
 
 Finally, the indicator-pencil is subject to a friction lag that 
 operates to produce the effect shown by Figs. 52 and 53 and is 
 liable to exaggerate them. That is to say, the pencil draws a 
 horizontal line and tends to remain at the same height after the 
 steam-pressure falls. It then lets go and falls sharply some 
 little time after the valve has closed at cut-off. Afterwards it 
 lags behind and shows a higher pressure than it should. 
 
 Him's Analysis. — Though the methods just illustrated 
 give a correct idea of the influence of the walls of the cylinder 
 of a steam-engine, our first clear insight into the action of the 
 walls is due to Hirn,* who accompanied his exposition by quan- 
 titative results from certain engine tests. The statement of his 
 method which will be given here is derived from a memoir by 
 Dwelshauvers-Dery.t 
 
 Let Fig. 54 represent the cylinder of a steam-engine and the 
 diagram of the actual cycle. For sake of simplicity the diagram 
 is represented without lead of admission 
 or release, but the equations to be deduced 
 apply to engines having either or both. 
 The points 1,2, 3, and o are the points of 
 cut-off, release, compression, and admission. 
 The part of the cycle from o to i, that is, 
 from admission to cut-off, is represented 
 by a\ in like manner, 6, c, and d represent ' yig. 54. 
 
 the parts of the cycle during expansion, 
 
 exhaust, and compression. The numbers will be used as sub- 
 scripts to designate the properties of the working fluid under 
 the conditions represented by the points indicated, and the 
 letters will be used in connection with the operations taking 
 place during the several parts of the cycle. Thus at cut-off the 
 
 * Bulletin de la Soc. Ind. de Mulhouse, 1873; Theorie Mechanique de la Chaleur, 
 vol. ii, 1876. 
 
 t Revue universelle des Mines, vol. viii, p, 362, 1880. 
 
 1 
 
 ^ 
 
2o6 INFLUENCE OF THE CYLINDER WALLS 
 
 pressure is p^, and the temperature, heat of the liquid, heat of 
 vaporization, quality, etc., are represented by /j, q^, r^, x^, etc. 
 The external work from cut-off to release is W^, and the heat 
 yielded by the walls of the cylinder due to reevaporation is Qi,. 
 
 Suppose that M pounds of steam are admitted to the cylinder 
 per stroke, having in the supply-pipe the pressure p and the 
 condition x; that is, each pound is x part steam mingled with 
 1 — X oi water. The heat brought into the cylinder per stroke, 
 reckoned from freezing-point, is 
 
 Q = M {q +xr) (153) 
 
 Should the steam be superheated in the supply-pipe to the 
 temperature 4, then 
 
 Q ^ M [r +q + J cdf] . . . . . . (154) 
 
 for which a numerical value can be found in the temperature- 
 entropy table. 
 
 Let the heat-equivalent of the intrinsic energy of the entire 
 weight of water and steam in the cylinder at any point of the 
 cycle be represented by /; then at admission, cut-off, release, 
 and compression we have 
 
 A = MA^o +^/o); (155) 
 
 I,= (M ^M,){q, +x,p,)- (156) 
 
 /,= (M +MJ {q, + x,p,)- (157) 
 
 A = M,{q + x^p,); (158) 
 
 in which p is the heat-equivalent of the internal work due to 
 vaporization of one pound of steam, and M^ is the weight of 
 water and steam caught in the cylinder at compression, calculated 
 in a manner to be described hereafter. 
 
 At admission the heat-equivalent of the fluid in the cylinder 
 is /q, and the heat supplied by the entering steam up to the point 
 of cut-off is Q. Of the sum of these quantities a part, AWa, is 
 used in doing external work, and a part remains as intrinsic 
 energy at cut-off. The remainder must have been absorbed by 
 
HIRN'S ANALYSIS 207 
 
 the walls of the cylinder, and will be represented by Qa- Hence 
 
 Qa = Q +1,-1,- AW,. 
 
 From cut-off to release the external work W^, is done, and at 
 release the heat-equivalent of the intrinsic energy is I^- Usually 
 the walls of the cylinder, during expansion, supply heat to the 
 steam and water in the cylinder. To be more explicit, some 
 of the water condensed on the cylinder walls during admission 
 and up to cut-off is evaporated during expansion. This action 
 is so energetic that I^is commonly larger than I,. Since heat 
 absorbed by the walls is given a positive sign, the contrary sign 
 should be given to heat yielded by them; it is, however, con- 
 venient to give a positive sign to all the interchanges of heat in 
 the equations, and then in numerical problems a negative sign 
 will indicate that heat is yielded during the operation under 
 consideration. For expansion, then, 
 
 Q, = A - /, -AW,. 
 
 During the exhaust the external work W^ is done by the engine 
 on the steam, the water resulting from the condensation of the 
 steam in the condenser carries away the heat Mq^, the cooling 
 water carries away the heat G (qj^ — qi), and there remains at 
 compression the heat-equivalent of intrinsic energy /j. So that 
 
 Q^ = I^-I^- Mq, - G (q, - q,) + AW,, 
 
 in which ^4 is the heat of the liquid of the condensed steam, and 
 G is the weight of cooling water per stroke which has on entering 
 the heat of the liquid q^, and on leaving the heat of the Hquid qjt. 
 
 During compression the external work W^ is done by the 
 engine on the fluid in the cylinder, and at the end of compression, 
 i.e., at admission, the heat-equivalent of the intrinsic energy is I^. 
 Hence 
 
 Q^ = I. -h +AWa. ■ 
 
 It should be noted (Fig. 54) that the work Wa is represented 
 
208 
 
 INFLUENCE OF THE CYLINDER WALLS 
 
 by the area which is bounded by the steam Hne, the ordinates 
 through o and i and by the base line. And in Hke manner the 
 works Wf,, Wc, and Wa are represented by areas which extend 
 to the base line. In working up the analysis from a test the 
 line of absolute zero of pressure may be 
 drawn under the atmospheric line as in 
 Fig. 55, or proper allowance may be 
 made after the calculation has been made 
 with reference to the atmospheric line. 
 For convenience these four equa- 
 FiG. 55. tions will be assembled as follows: 
 
 Qa = Q ^1,^-1,- AW,, (159) 
 
 Q, = I,- I,- AW (160) 
 
 Qc = I, - h - Mq, - G (q, - qd + AW, . (161) 
 Qa-I. -/o +AW, (162) 
 
 A' consideration of these equations shows that all the quanti- 
 ties of the right-hand members can be obtained directly from 
 the proper observations of an engine test except the several 
 values of I, the heat-equivalents of the intrinsic energies in the 
 cylinder. These quantities are represented by equations (155) 
 to (158), in which there are five unknown quantities, namely, 
 
 ^o» ^v ^v ^v and M,. 
 
 Let the volume of the clearance-space between the valve and 
 the piston when it is at the end of its stroke be F^; and let the 
 volumes developed by the piston up to cut-off and release be 
 Fj and Y ^\ finally, let V ^ represent the corresponding volume 
 at compression. The specific volume of one pound of mixed 
 water and steam is 
 
 xu 
 
 and the volume of M pounds is 
 
 F = Mv = M {xu + o-). 
 
HIRN'S ANALYSIS 209 
 
 At the points of admission, cut-off, release, and compression, 
 
 V,= M,(x„u, +0-) (163) 
 
 K„ + F, = (M + M„) {x,u, + <T) (164) 
 
 V, + \\ = {M + M„) {x,u, -,-0-) (165) 
 
 V\ + F, = M, (.T,«3 + "■) (166) 
 
 There is sufficient evidence that the steam in the cylinder 
 at compression is nearly if not quite dry, and as there is com- 
 paratively little steam present at that time, there cannot be 
 much error in assuming 
 
 x^ ^ 1. 
 
 This assumption gives, by equation (i66), 
 
 7 _i_ 7 V + V 
 
 ^o--^^xr = ■^-^'^ (^0 + ^)73 . .(167) 
 
 in which 73 is the density or v^eight of one cubic foot of dry 
 steam at compression. 
 
 Applying this result to equations (263) to (265) gives 
 
 
 X,= Tp^-— ....... (168) 
 
 _ F„ + F, f_ 
 
 *= - (M + M„) «, «.■"■■ ^'^°' 
 
 We are now in condition to find the values of I ^^ 7^, /g, and 
 73, and consequently can calculate all the interchanges of heat 
 by equations (159X to (162). 
 
 Should the value of x in any case appear to be greater than 
 unity it indicates that the steam is superheated; this may happen 
 for x^^ and then as the weight of steam M^ is relatively small, 
 and as the superheating is usually slight, it will be sufficient to 
 make x^ equal to unity. It is unlikely to be the case for x^ or x^^ 
 even though the steam is strongly superheated in the steam- pipe; 
 
2IO INFLUENCE OF THE CYLINDER WALLS 
 
 should the computation give a value slightly larger than unity 
 the steam may be assumed to be dry without appreciable error, 
 and the work may proceed as indicated. If in the use of very 
 strongly superheated steam a computed value of x^ is appre- 
 ciably larger than unity, we may replace the equation (i66) by 
 
 where v^ is the specific A^olume of superheated steam; conse- 
 quently 
 
 F 4- F 
 ' M ■\-M, 
 
 By aid of the temperature-entropy table we may find (by inter- 
 polation if necessary) the corresponding temperature t^ and the 
 value of the heat-contents or total heat. The heat-equivalent 
 of the intrinsic energy is then equal to this quantity minus Ap^v^. 
 
 In the diagram, Fig. 54, the external work during exhaust is 
 all work done by the piston on the fluid, since the release is 
 assumed to be at the end of the stroke. If the release occurs 
 before the end of the stroke, some of the work, namely, from 
 release to the end of the stroke, will be done by the steam on the 
 piston, and the remainder, from the end of the stroke back to 
 compression, will be done by the piston on the fluid. In such 
 case Wc will be the difference between the second and the first 
 quantities. If an engine has lead of admission, a similar method 
 may be employed; but at that part of the diagram the curves of 
 compression and admission can be distinguished with difficulty, 
 if at all, and little error can arise from neglecting the lead. 
 
 The several pressures at admission, cut-off, release, and 
 compression are determined by the aid of the indicator-diagram, 
 and the pressures in the steam-pipe and exhaust-pipe or con- 
 denser are determined by gauges. The weight M of steam 
 supplied to the cylinder per stroke is best determined by con- 
 densing the exhaust-steam in a surface-condenser and collecting 
 and weighing it in a tank. If the engine is non-condensing, or 
 if it has a jet-condenser, or if for any reason this method cannot 
 
HIRN'S ANALYSIS 211 
 
 be used, then the feed- water delivered to the boiler may be deter- 
 mined instead. The cooling or condensing water, either on 
 the way to the condenser or when flowing from it, may be weighed, 
 or for engines of large size may be measured by a metre or gauged 
 by causing it to flow over a weir or through an orifice. The 
 several temperatures t^, ti, and /^ must be taken by proper ther- 
 mometers. When a jet-condenser is used, and the condensing 
 water mingles with the steam, ^4 is identical with tj^. The quality 
 .V of the steam in the supply-pipe must be determined by a steam- 
 calorimeter. A boiler with sufficient steam-space will usually 
 deliver nearly dry steam; that is, x will be nearly unity. If 
 the steam is superheated, its temperature t^ may be taken by a 
 thermometer. 
 
 Let the heat lost by radiation, conduction, etc., be Q^; this 
 is commonly called the radiation. Let the heat supplied by 
 the jacket be Qj. Of the heat supplied to the cylinder per stroke, 
 a portion is changed into work, a part is carried away by the 
 condensed steam and the cooling or condensing water, and 
 the remainder is lost by radiation; therefore 
 
 Qe^Q + Qj--Mq,~G(q,-q,)-A(W,+W,-W,~W^) . (171) 
 
 The heat Qj supplied by a steam-jacket may be calculated 
 by the equation 
 
 Qj = m {x'r' ^(t - f) .... (172) 
 
 in which m is the weight of water collected per stroke from the 
 jacket; x', r', and ^' are the quality, the heat of vaporization, 
 and the heat of the liquid of the steam supplied; and ^" is the 
 heat of the liquid when the water is withdrawn. When the 
 jacket is supplied from the main steam-pipe, oc^ is the same as 
 the quality in that pipe. When suppUed direct from the boiler, 
 xf may be assumed to be unity. If the jacket is supplied 
 through a reducing-valve, the pressure and quality may be 
 determined either before or after passing the valve, since throt- 
 tling does not change the amount of heat in the steam. Should 
 
212 INFLUENCE OF THE CYLINDER WALLS 
 
 the steam applied to the jacket be superheated from any cause, 
 we may use the equation 
 
 Qj = m [r' -rq'+ c^ (/./ - /') - ^-] . . . (173) 
 
 in which / and 5' are the heat of vaporization and heat of 
 the Hquid of saturated steam at the temperature t\ and Cj is 
 the temperature of the superheated steam. 
 
 Equation (171) furnishes a method of calculating the heat 
 lost by radiation and conduction; but since Q^ is obtained by 
 subtraction and is small compared with the quantities on the 
 right-hand side of the equation, the error of this determination 
 may be large compared with Q^ itself. The usual way of deter- 
 mining (3e for an engine with a jacket is to collect the water 
 condensed in the jacket for a known time, an hour for example, 
 when the engine is at rest, and then the radiation of heat per 
 hour may be calculated. If it be assumed that the rate of radia- 
 tion at rest is the same as when the engine is running, the radia- 
 tion for any test may be inferred from the time of the test and the 
 determined rate. But the engine always loses heat more rapidly 
 when running than when at rest, so that this method of 
 determining radiation always gives a result which is too 
 small. 
 
 If a steam-engine has no jacket it is difficult or impossible 
 to determine the rate of radiation. The only available way 
 appears to infer the rate from that of some similar engine with 
 a jacket. Probably the best way is to get an average value of 
 Qe from the application of equation (171) to a series of care- 
 fully made tests. 
 
 It is well to apply equation (171) to any test before beginning 
 the calculation for Hirn's analysis, as any serious error is likely to 
 be revealed, and so time may be saved. 
 
 When the radiation Q^, is known from a direct determination 
 of the rate of radiation, we may apply Hirn's analysis to a test 
 on an engine even though the quantities depending on the con- 
 denser have not been obtained. For from equation (171) 
 
HIRN'S ANALYSIS 213 
 
 -Mq, -G{q,~ qi) = Q, -Q-Qj i- A(Wa + W," W ,- Wa), 
 and consequently 
 
 g. = /, - 7. - (? - Q:, + (2e + ^4 iyv,. -^W,-W,) . . (174) 
 
 Thus it is possible to apply the analysis to a non-con- 
 densing engine or to the high-pressure cylinder of a compound 
 engine. 
 
 It is apparent that the heat Qcj thrown out from the walls 
 of the cylinder during exhaust, passes without compensation 
 to the condenser, and is a direct loss. Frequently it is the 
 largest source of loss, and for this reason Hirn proposed to make 
 it a test of the performance and perfection of the engine; but 
 such a use of this quantity is not justifiable, and is likely to 
 lead to confusion. 
 
 The heat Q^ that is restored during expansion is supplied at 
 a varying and lower temperature than that of the source of heat, 
 namely, the boiler, and, though not absolutely wasted, is used 
 at a disadvantage. It has been suggested that an early com- 
 pression, as found in engines with high rotative speed, warms 
 up the cylinder and so checks initial condensation, thereby 
 reducing Qa and finally Q^ also. Such a storing of heat during 
 compression and restoring during expansion is considered to 
 act like the regenerator of a hot-air engine, and to make the 
 efficiency of the actual cycle approach the efficiency of the ideal 
 cycle more nearly than would be the case without compression. 
 It does not, however, appear that engines of that type have 
 exceeded, if they have equalled, the performance of slow-speed 
 engines with small clearance and little compression. 
 
 Application. — In order to show the details of the method of 
 applying Hirn's analysis the complete calculation for a test 
 made on a small Corliss engine in the laboratory of the Massa- 
 chusetts Institute of Technology will be given. Its usefulness is 
 mainly as a guide to any one who may wish to apply the method 
 for the first time. 
 
214 INFLUENCE OF THE CYLINDER WALLS 
 
 Diameter of the cylinder 8 inches. 
 
 Stroke of the piston 2 feet. 
 
 Piston displacement: crank end 0.6791 cu. ft. 
 
 head end 0.7016 " " 
 
 Clearance, per cent of piston displacement : 
 
 crank end •3-75 
 
 head end 5.42 
 
 Boiler-pressure by gauge 77.4 pounds. 
 
 Barometer 14.8 " 
 
 Condition of steam, two per cent of moisture. 
 Events of the stroke: 
 
 Cut-off: crank end 0.306 of stroke. 
 
 head end 0.320 " 
 
 Release at end of stroke. 
 
 Compression: crank end .... 0.013 o^ stroke. 
 
 head end 0.0391 " 
 
 Duration of the test, one hour. 
 
 Total number of revolutions 3692 
 
 Weight of steam used 548 pounds. 
 
 Weight of condensing water used . . . 14,568 " 
 
 Temperatures : 
 
 Condensed steam t^= 141°.! F. 
 
 Condensing water: cold U = $2°. 9 F. 
 
 warm 4 =- 88^.3 F. 
 
 * ABSOLUTE PRESSURES, FROM INDICATOR-DIAGRAMS, AND 
 CORRESPONDING PROPERTIES OF SATURATED STEAM. 
 
 
 Crank End. 
 
 Head End. 
 
 
 / 
 
 (7 
 
 p 
 
 u 
 
 / 
 
 1 
 
 p 
 
 M 
 
 Cut-off . . . 
 Release . . . 
 Compression . 
 Admission 
 
 83.6 
 29.2 
 14.8 
 21.8 
 
 284.6 
 217.8 
 181. 1 
 201.5 
 
 813.0 
 864.8 
 893.2 
 877.4 
 
 5.190 
 13.924 
 26.464 
 18.344 
 
 83-3 
 
 31-9 
 14.8 
 29.8 
 
 284.4 
 222.9 
 181. 1 
 219.0 
 
 813.2 
 860.8 
 893.2 
 863.9 
 
 5.207 
 I 2 . 804 
 26.464 
 13.664 
 
 * These values are taken from the first edition of the Tables of Properties of 
 Saturated Steam. 
 
APPLICATION 
 
 215 
 
 MEAN PRESSURES, -\ND HEAT-EQUIVALENTS OF EXTERNAL 
 
 WORKS. 
 
 
 Ckank End. 
 
 Head End. 
 
 
 Mean Pressures. 
 
 Equivalents of 
 Work. 
 
 Mean Pressures. 
 
 Equivalents of 
 Work. 
 
 Admission 
 Expansion .... 
 
 Exhaust 
 
 Compression . . . 
 
 87.7 
 
 44-5 
 14.8 
 
 18.3 
 
 3-369 
 3-877 
 1.836 
 
 0.0290 
 
 89-3 
 
 14.8 
 
 21.8 
 
 3-7II 
 
 4-159 
 1.847 
 
 0. I 104 
 
 VOLUMES, CUBIC FEET. 
 
 
 Crank End. 
 
 Head End. 
 
 At cut-oflF, ■^'o + ^'1 
 
 At release, Vq+ V^ 
 
 At compression, Vq+V^ 
 
 At admission, V^ 
 
 0.2333 
 0.7046 
 0.0343 
 0.02550 
 
 0.2626 
 0.7396 
 0.0655 
 0.03806 
 
 
 At the boiler-pressure, 92.1 pounds absolute, we have 
 
 r = 888.4, q = 291.7. 
 
 The steam used per stroke is 
 548 
 
 M 
 
 3692 
 
 = 0.0742 pound. 
 
 The steam caught in the clearance space at compression, on 
 the assumption that the steam is then dry and saturated, is 
 obtained by multiplying the mean volume at that point by the 
 weight of one cubic foot of steam at the pressure at compression, 
 which is 0.03781 of a pound. 
 
 ,, 0.0^43 + o.o6s^ „ - 
 
 .'. Mq = — "^-^ ^^ X 0.03781 = 0.0019 of ^ pound; 
 
 M -f- Mq = 0.0742 H- 0.0019 ^ 0.0761 pound. 
 The condensing water used per stroke is 
 
 G = 
 
 14568 
 2 X 3692 
 
 = I-973- 
 
2i6 INFLUENCE OF THE CYLINDER WALLS 
 
 Q = M (xr + q) = 0.0742(0.98 X 888.3 + 291.8) = 86.243; 
 i (0.02550 + 0.03806) 1 
 
 *'"" 0.0019X^(18.344+13.664) 62.4X^(18.344+13.664) 
 = 1.043. 
 
 This indicates that the steam is superheated at admission. 
 Such may be the case, or the appearance may be due to an 
 error in the assumption of dry steam at compression, or to errors 
 of observation. It is convenient to assume ^'0 = i. 
 
 ,. v. + v. 
 
 X 
 
 i (0-2333 + 0.2626) 
 
 ' 0.0761 X i (5.190 + 5.207) 62.4 X i(5-i9o + 5-207) 
 = 0.6236. 
 
 V -\- V 
 
 (M + MJ u^ u, ' 
 -I (0.7046 + 0.7396) 
 
 0.0761X^(13.924+12.804) 62.4x4(13.924+12.804) 
 = 0.7088. 
 
 .'. I(y= i X 0.0019 [201.5 + 219.0 + i.oo (877.4 + 863.9)] 
 = 2.054. 
 
 I,= (M +M,)iq,+x,p^); 
 
 •'- ^1 = 2 X 0.0761 [284.6 + 284.4 + 0.6236 (813.0 +813.2)] 
 = 60.238. 
 /, = {M +MJ {q, +x^,); 
 ,', I^ = i- X 0.0761 [217.8+222.0 + 0.7088 (864.8 + 861.8)] 
 = 63.311. 
 h = M,(q, +x^^); 
 .'. I3 = 0.0019 (181. 1 + 893.2) = 2.041. 
 
APPLICATION 217 
 
 Qa = Q +h- ^ -AW,; 
 .-. Qa = 86.243 + 2.054 - 60.238 - 1 (3.369+3-711) = 24.519. 
 
 .-. Q, = 60.238 - 63.311 - J (3.877 + 4.159) = - 7.091- 
 
 Qr = I,- Is- Mq, - G (q, - qd + AW,; 
 .-. Q, - 63.311 - 2.041 - 0.0742 X 109.3 
 
 - 1.973 (56.35 - 21.01) + i (1.836 + 1.847) 
 = - 14-721. 
 Q, = I,-h +AWa; 
 .-. Qd = 2.041 - 2.054 + J (0.0299 + 0.1104) = 0.157. 
 
 Qe = Qa +Qo +Qc +Q4- 2.764. 
 
 Also, equation (171) for this case gives 
 Qe-^Q- Mq, -G{q,- q,) - AW 
 
 = 86.243— 8. no — 69.723 — (3.540+4.018 — 1.841 — 0.070) 
 = 86.243—8.110 — 69.723 — 5.647 = 2.764. 
 
 It is to be remembered that the heat lost by radiation and 
 conduction per stroke, when estimated in this manner, is affected 
 by the accumulated errors of observation and computation, 
 which may be a large part of the total value of Q^. 
 
 Dropping superfluous significant figures, we have in b.t.u. 
 
 Q = 86.2, Qa = 24.5, Q.b= - 7-1, 
 
 Qc= - 14.7^ Qd = .06, Q, = 2.8. 
 
 Noting that 5.647 are the b.t.u. changed into work per stroke 
 and 3692 the total revolutions the horse-power of the engine is 
 
 778 X 5.6 4 7 X 3692 X 2 _ ^ jjp^, 
 
 60 X 33000 
 
 and the steam per horse-power per hour is 
 -^^— - 33-5 pounds. 
 
 16.35 
 For data and results of this test and others see Table IV. 
 
2l8 
 
 INFLUENCE OF THE CYLINDER WALLS 
 
 W 
 H 
 
 < 
 W 
 
 J?; 
 I— ( 
 
 o 
 w . 
 
 CO O 
 r ^ 
 
 >^ 
 
 
 1 
 
 s 
 
 < 
 
 1 
 
 ad 
 
 00 t^ aoooo 
 
 
 u 
 ^ 
 
 00 »^ O>00 00 
 
 4 « o fo >-< 
 
 N N S N P» 
 
 
 1^ 
 
 6 
 o 
 U 
 
 
 00 t^ OvOOOO 
 
 
 
 00 1^ OOOOO 
 
 4 4 4 4 4 
 
 
 1. 
 
 
 00 I^fOOO o 
 11 M N (N ro 
 
 
 
 vO r^oO w O 
 
 S 
 
 u 
 
 
 vd N r^ d f^ 
 
 1^00 1^00 00 
 
 C4 
 
 
 r^ fO 4 t^ <^ 
 j^oo t^r-oo 
 
 !;5 
 
 •spunod 'aSnHS 
 Xq 3jnss3jd-j9iiog "^ 
 
 r-O 'OOv ■* 
 
 CO 
 
 S 
 
 •qDUl aa^nbs aqj uo 
 spanod 'jajauioj^a 
 
 00 t^ coo 00 
 
 4 4 4 4 4 
 
 00 
 
 pi" 
 w 
 
 <: 
 p 
 
 II 
 
 -Suisn3puo3 '*' 
 
 00 
 r^ O O • fO 
 
 •pjOD i3JE,W 
 
 -3uisu9puo3 "^ 
 
 woo WVO O 
 
 dv 4 d. ro P» 
 rO>0 fOVO »^ 
 
 
 •uitajs 
 p3suapuo3 -^ 
 
 <0 >0 OOO w 
 1-4 n M ro 1- 
 
 
 •IUB3?S UI 
 
 Suiiuud JO JU3D jaj ' 
 
 m' pi P) n ft 
 
 
 •spunod 'ja}BM-3ui 
 -sugpuoD JO jqSiaAV 
 
 >0 t^ OOOvO 
 
 
 •spunod 'pasn 
 uiBajs JO »q3i3A\, 
 
 f*:! t^ O >ooo 
 Tj- P) r, a ■* 
 
 M fO M P) »0 
 
 
 'SuounioASJ 
 JO aaquihu lEjox 
 
 0> 0> Ov PI N 
 
 <^ O fO «^ Ov 
 
 
 •sajnuiui 'uopuinQ 
 
 fO>0 fO ■*vo 
 
 
 
 •iaquin^ 
 
 
 ^Meo^io 
 
 •spanod 1 
 'jnoq J3d j3Mod 
 -asjoq J3d lurajs 
 
 «^>o O P0«O 1 
 
 TT PO PO fO «»> 
 
 "o . 
 
 r 
 
 •j3MOd-3SJOq 
 
 pajraipui 
 
 pooo PI fo «^ ; 
 lo o r>- « po 1 
 
 vdcdod MVO 
 
 •JOJJ3 , 
 
 paE uopBipB^Oi 
 
 w fo Pi00<O 
 O »0 'T POt^ 
 
 PI M PI fO P» 
 
 •uoissajdiuoD ^ 
 
 Suijnp sipA\ O) 
 
 Xq paqjosqv 
 
 6 6 6 6 6 
 
 •lsnT?qx3 
 
 gUUnp SIJBM (5) 
 
 "Aq papBA 
 
 vd dv^^d>4 
 
 •aoiSHKdxa 
 
 SUUa'p SIIBA\ Q, 
 
 f^ o to t Ov 
 
 Pfvo MO o 
 
 j 
 
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 3uunp si[EM « 
 Aq paqjosqv 
 
 wvOOO Ov PI 
 
 Ov PI PI t^ lo 1 
 
 •lu^ajs jsioui 
 JO spunod Oi 
 
 2vS5_2? 
 
 to PI po 4vd 
 
 Tf ui lOOOO 
 
 1 
 
 o 
 
 "o 
 
 f 
 
 
 
 00- •t OvO o i 
 
 d d d d d 
 
 
 PI «0 PI Ov Ov 
 
 d d d d d 
 
 i^ 
 
 
 fo ooo Tj- 1^ 
 
 t~. PIO Tt 'i- 
 r^oOOOOOOO 
 
 M M M M M 
 
 
 r^ PI Tt OO 
 M p< lo ro CO 
 00 00 00 00 00 
 
 
 w 
 
 oJ^v^^s; 
 
 M r^ioOvM 
 ro K^ tOPTI 4 
 
 
 lo PI »^ r» 
 
 MOO O PI »>. 
 M PI c« loOO 
 
 f^ PO PO to PO 
 
 o 
 
 
 OvO PD r^ M 
 
 »^00 PO M M 
 
 Ov fOO PI t^ 
 
 d M M pi f^ 
 
 u 
 
 t^ IC MOO Ov 
 
 M M M PI fO 
 
 it 
 li 
 
 ■il 
 
 il 
 
 t4 
 
 r-O ■*© Ov 
 t^4ro4po 
 
 d 
 
 PI roOviOPO 
 
 PI M d M M 
 
 i 
 
 
 22222 
 
 c3 
 
 88888 
 
 to 
 
 o 
 
 u 
 
 p4 
 
 O PI O «oO 
 
 
 O PI O »o>0 
 
 
 •jaquinisi 
 
 
 1 ^««^« 
 
SUPERHEATED STEAM 219 
 
 Effect of Varying Cut-off. — An inspection of the interchanges 
 of heat shows that the values of Qa, the heat absorbed by the 
 walls during admission, increase regularly as the cut-off is 
 lengthened, and that the heat returned during expansion decreases 
 at the same time, so that there is a considerable increase in the 
 value of the heat Qc which is rejected during exhaust. Never- 
 theless there is a large gain in economy from restricting the 
 cut-off so that it shall not come earlier than one- third stroke. 
 Unfortunately tests on this engine with longer cut-off than one- 
 third stroke have not been made, and consequently the poorer 
 economy for long cut-off cannot be shown for this engine as for 
 the engine of the Michigan. 
 
 Hallauer*s Tests. — In Table V are given the results of a 
 number of tests made by Hallauer on two engines, one built by 
 Hirn having four flat gridiron valves, and the other a Corliss 
 engine having a steam-jacket. Two tests were made on the 
 former with saturated steam and six with superheated steam. 
 Three tests were made on the latter with saturated steam and 
 with steam supplied to the jackets. These tests have a historic 
 interest, for though not the first to which Hirn's analysis was 
 applied, they are the most widely known, and brought about the 
 acceptance of his method. They have also a great intrinsic 
 value, as they exhibit the action of two different methods of 
 ameliorating the effect of the action of the cylinder walls, namely, 
 by the use of superheated steam and of the steam-jacket. In all 
 these tests there was little compression, and Qa, the interchange 
 of heat during compression, is ignored. 
 
 Superheated Steam. — Steam from a boiler is usually slightly 
 moist, Xj the quality, being commonly 0.98 or 0.99. Some boilers, 
 such as vertical boilers with tubes through the steam space, give 
 steam which is somewhat superheated, that is, the steam has a 
 temperature higher than that of saturated steam at the boiler- 
 pressure. Strongly superheated steam is commonly obtained by 
 passing moist steam from a boiler through a coil of pipe, or a 
 system of piping, which is exposed to hot gases beyond the 
 boiler. 
 
220 
 
 INFLUENCE OF THE CYLINDER WALLS 
 
 < 
 
 W > 
 
 ^ 
 
 C -^ 
 
 
 pq 
 
 
 6 
 
 
 IT) O NO M r^ t^ 
 
 l-~ t^vO CO 00 1 
 
 -* Tt Tf 
 
 1- rj- Tt 
 
 1 
 
 !l 
 II 
 
 s-s 
 |l 
 
 6 
 
 
 
 M On •-« 
 LO rt Tj- 
 
 6 
 
 vo o 
 
 NO • (N r^NO • 
 
 NO' CO ^ 
 
 M M 
 
 
 W 1-1 M 
 
 6 
 
 
 lo t^oo xn <N • 
 
 <N On ^ 6 Tj- 1 
 
 cooo O 
 
 CN OnOC 
 
 « 
 o 
 
 O ro 
 
 rf • O • • • 
 
 u-j O *+ 
 
 m t-« 
 
 00 . (N . • • 
 
 t^ W5 O 
 
 d 
 
 ro On 
 00 CO 
 
 rt . O • • • 
 
 (N . M . • ■ 
 f>* . M . • • 
 
 rf w rf 
 e< w M 
 
 ■9)nuiui jsd 
 •JHJsd-a-X-a 
 
 lO On 
 
 NO U-) O t- O • 
 
 On ON W rtOO • 
 w W PO ro ro • 
 
 
 •spanod 'jnoq aad 
 
 On tT) 
 
 O t^ CS CN cs O 
 
 00 t^oo 
 
 O^ «^ 
 
 \0 »o t^OO O t^ 
 
 M M M M (N CN 
 
 t^ r^ t^ 
 
 •j3MOd-3saoH 
 
 
 NO O "* ionO CO 
 ►H '^ CN rf On t^ 
 
 ►-I CO -f CN CO t^ 
 
 NO M ON 
 
 CO On to 
 O CN U-5 
 
 •qoui 3iBnbs aad 
 spunbd '3»njosqB 
 'aanssaad-JiDEa 
 
 O <N 
 
 t^ r^ CN t^ lo . 
 
 M rfNO 
 
 <r> lo 
 
 M CN IT) CN CN • 
 
 C^ P< CN 
 
 'ipm aiBnbs jad 
 spun'od '3}niosq« 
 ♦sinssaad-jsiioa 
 
 
 w O NO rfNO (N 
 
 t^ t^NO NO I^NO 
 
 
 •saoisuEdxg 
 
 M ON 
 
 ■o to 
 
 M t^ On CS CN lO 
 NO -^ CO CN CN CO 
 
 CN 00 NO 
 
 ' 'ajnaiiu 
 jsd saoi)nioA3^ 
 
 rl-O 
 
 O O CN CO w O 
 
 ■+ M CO 
 
 o o 
 
 o o o o o o 
 
 CO CO CO CO CO CO 
 
 O M On 
 
 inxn "t 
 
 'IUE3JS pajBsqjadns 
 ' 9jn)CJ9daiaj, 
 
 
 CO OnOO coco 00 
 00 1-1 rj- CO P< ri 
 CO rj- -t Tt- Tf Tt 
 
 
 •uoijipuoo 
 
 
 p3jB9HJ3dns 
 
 pap^DBf 
 
 
 
 1-1 M 
 
 * 
 
 *s;3 
 
 N 
 
 M 
 
 o 
 
 ci) *^ 
 •S ^ 
 
 0) 
 
 C! 
 O 
 u 
 
 c 
 o 
 
 z 
 
SUPERHEATED STEAM 221 
 
 - Superheated steam may yield a considerable amount of heat 
 before it begins to condense; consequently where superheated 
 steam is used in an engine a portion of the heat absorbed by the 
 walls during admission is supplied by the superheat of the steam 
 and less condensation of steam occurs. This is very evident in 
 Dixwell's tests given by Table XXV, on page 271, where the 
 water in the cylinder at cut-off is reduced from 52.2 per cent to 
 27.4 per cent, when the cut-off is two-tenths of the stroke, by 
 the use of superheated steam; with longer cut-off the effect is 
 even greater. This reduction of condensation is accompanied 
 by a very marked gain in economy. 
 
 The way in which superheated steam diminishes the action 
 of the cylinder walls and improves the economy of the engine is 
 made clear by Hallauer's tests in Table V. A comparison of 
 tests I and 3, having six expansions, shows that the heat Q„ 
 absorbed during admission is reduced from 28.3 to 22.4 per cent 
 of the total heat supplied, and that the exhaust waste is corre- 
 spondingly reduced from 21.6 to 12.5 per cent. A similar 
 comparison of tests 2 and 5, having nearly four expansions, 
 shows even more reduction of the action of the cylinder walls. 
 The effect on the restoration of heat Qi, during expansion appears 
 to be contradictory: in one case there is more and in the other 
 case less. It does not appear profitable to speculate on the 
 meaning of this discrepancy, as it may be in part due to errors 
 and is certainly affected by the unequal degree of superheating 
 in tests 3 and 5. It may be noted that the actual value of Qc in 
 calories is nearly the same for tests i and 2, there being a small 
 apparent increase with the increase of cut-off, which is, however, 
 less than the probable error of the tests. The exhaust waste Q^ 
 is much more irregular for tests 3 to 7 for superheated steam. 
 The increase from 81 to 87 b.t.u. from test 6 to test 7 may 
 properly be attributed to a less degree of superheating; the 
 increase from 66 to 81 b.t.u. for tests 5 and 6 is due to longer 
 cut-off and less superheating; finally, the steady reduction from 
 75 to 66 B.T.U. for the three tests 3, 4, and 5 is probably due to 
 the rise of temperature of the superheated steam, which more 
 
222 INFLUENCE OF THE CYLINDER WALLS 
 
 than compensates for the effect of lengthening the cut-off. 
 Finally in test 8 the exhaust waste is practically reduced to 
 zero by the use of strongly superheated steam in a non-con- 
 densing engine; this shows clearly that the exhaust waste Qc by 
 itself is no criterion of the value of a certain method of using 
 steam. 
 
 Steam-jackets. — If the walls of the cylinder of a steam- 
 engine are made double, and if the space between the walls is 
 filled with steam, the cylinder is said to be steam- jacketed. 
 Both barrel and heads may be jacketed, or the barrel only may 
 have a jacket; less frequently the heads only are jacketed. The 
 principal effect of a steam-jacket is to supply heat during the 
 vaporization of any water which may be condensed on the 
 cylinder walls. The consequence is that more heat is returned 
 to the steam during expansion and the walls are hotter at the 
 end of exhaust than would be the case for an unjacketed engine. 
 This is evident from a comparison of tests i and ii in Table V. 
 In test I only a small part of the heat absorbed during admission 
 is returned during expansion, and by far the larger part is wasted 
 during exhaust. In test ii the heat returned during expansion 
 is equal to two-thirds that absorbed during admission, though a 
 part of this heat of course comes from the jacket. About half 
 as much is wasted during exhaust as is absorbed during admission. 
 The condensation of steam is thus reduced indirectly; that is, 
 the chilling of the cylinder during expansion, and especially 
 during exhaust, is in part prevented by the jacket, and conse- 
 quently there is less initial condensation and less exhaust waste, 
 and in general a gain in economy. The heat supplied during 
 expansion, though it does some work, is first subjected to a 
 loss of temperature in passing from the steam in the jacket to 
 the cooler water on the walls of the cylinder, and such a non- 
 reversible process is necessarily accompanied by a loss of effi- 
 ciency. On the other hand, the heat supplied by a jacket during 
 exhaust passes with the steam directly into the exhaust-pipe. 
 It appears, then, that the direct effect of a steam-jacket is to 
 waste heat; the indirect effect (drying and warming the cylinder) 
 
APPLICATION TO MULTIPLE-EXPANSION ENGINES 223 
 
 reduces the initial condensation and the exhaust waste and often 
 gives a notable gain in economy. 
 
 Application to Multiple-expansion Engines. — The application 
 of Hirn's analysis to the high- pressure cylinder of a compound* or 
 multiple-expansion engine may be made by using equations 
 (159), (160), and (162) for calculating Qa, Qb, and Qa, while 
 equation (174) may be used to find Qc. 
 
 A similar set of equations may be written for the next cylinder, 
 whether it be the low-pressure cylinder of a compound engine 
 or the intermediate cylinder of a triple engine, provided we can 
 determine the value of Q', the heat supplied to that cylinder. 
 But of the heat supplied to the high-pressure cylinder a part 
 is changed into work, a part is radiated, and a part is rejected 
 in the exhaust waste. The heat rejected is represented by 
 
 Q +Qj-AW -Q, (175) 
 
 where Q is the heat supplied by the steam entering the cylinder, 
 Qj is the heat supplied by the jacket, ^W is the heat-equivalent 
 of the work done in the cylinder, and Qe is the heat radiated. 
 Suppose the steam from the high-pressure cylinder passes to an 
 intermediate receiver, which by means of a tubular reheater or 
 by other means supplies the heat Q,., while there is an external 
 radiation Qre- The heat supplied to the next cylinder is con- 
 sequently 
 
 Q' = Q i^Qj- AW -Q,+ Qr -Qre • • (176) 
 
 In a like manner we may find the heat Q" supplied to the 
 next cylinder ; for example, to the low-pressure cylinder of a 
 triple engine. 
 
 It is clear that such an application of Hirn's analysis can be 
 made only when the several steam-jackets on the high- and the 
 low-pressure cylinders, and the reheater of the receiver, etc., 
 can be drained separately, so that the heat supplied to each 
 may be determined individually. 
 
 Table VI gives applications of Hirn's analysis to four tests 
 on the experimental triple-expansion engine in the laboratory 
 of the Massachusetts Institute of Technology. 
 
224 INFLUENCE OF THE CYLINDER WALLS 
 
 It will be noted that the steam in the cylinders becomes drier 
 in its course through the engine, under the influence of thorough 
 steam-jacketing with steam at boiler-pressure, and is practically 
 dry at release in the low-pressure cylinder. All of the tests 
 show superheating in the low-pressure cyhnder, which is of 
 course possible, for the steam in the jackets is at full boiler^ 
 pressure while the steam in the cylinder is below atmospheric 
 pressure. The superheating was small in all cases — not more 
 than would be accounted for by the errors of the tests. The 
 exhaust waste Q^' from the low-pressure cylinder in the triple- 
 expansion tests is very small in all cases — less than two per cent 
 of the heat supplied to the cylinders. The apparent absurdity of 
 a positive value for Q^' in two of the tests (indicating an absorp- 
 tion of heat by the cylinder walls during exhaust) may properly 
 be attributed to the unavoidable errors of the test. 
 
 In the fourth test, when the engine was developing 120.3 
 horse-power, there were 1305 pounds of steam supplied to the 
 cylinders in an hour, and 345 pounds to the steam-jackets; so 
 that the steam per horse-power per hour passing through the 
 cylinders was 
 
 1305 -^ 120.3 =^ 10.86 pounds, 
 
 while the condensation in the jackets was 
 
 345 ^ 120.3 "^ 2.87 pounds. 
 
 So that, as shown on page 145, the b.t.u. per horse-power per 
 minute supplied to the cylinders by the entering steam was 
 191. 1, while the jackets supplied 40.6 b.t.u., making in all 
 231.7 B.T.U. per horse-power per minute for the heat-consumption 
 of the engine. In the same connection it was shown that the 
 thermal efficiency of the engine for this test was 0.183, while 
 the efficiency for incomplete expansion in a non-conducting 
 cylinder corresponding to the conditions of the test was 0.222; 
 so that the engine was running with 0.824 of the possible efficiency. 
 In light of this satisfactory conclusion some facts with regard to 
 the test are interesting. 
 
APPLICATION OF HIRN'S ANALYSIS 
 
 225 
 
 Table VI. 
 
 APPLICATION OF HIRN'S ANALYSIS TO THE EXPERIMENTAL 
 ENGINE IN THE LABORATORY OF THE MASSACHUSETTS 
 INSTITUTE OF TECHNOLOGY. 
 
 TRIPLE-EXPANSIOX; CYLINDER DIAMETERS, 9, 1 6, AND 24 INCHES ; STROKE, 30 
 
 INCHES. 
 
 Trans. Am. Soc. Mech. Engrs., vol. xii, p. 740. 
 
 Duration of test, minutes 
 
 Total number of revolutions .... 
 
 Revolutions per minute 
 
 Steam-consumption during test, lbs. : 
 Passing through cylinders .... 
 Condensation in h.p. jacket , . . 
 
 in first receiver-jacket 
 
 in inter, jacket 
 
 in second receiver-jacket .... 
 
 in l.p. jacket 
 
 Total . 
 
 Condensing water for test, lbs. . . . 
 
 Priming, by calorimeter 
 
 Temperatures, Fahrenheit : 
 
 Condensed steam 
 
 Condensing-water, cold 
 
 Condensing-water, hot 
 
 Pressure of the atmosphere, by the 
 
 barometer, lbs. per sq. in 
 
 Boiler pressure, lbs. per sq. in. abso- 
 lute 
 
 Vacuum in condenser, inches of mer- 
 cury 
 
 Events of the stroke: 
 
 High-pressure cylinder — 
 
 Cut-off, crank end 
 
 head end 
 
 Release, both ends 
 
 Compression, crank end . . . 
 
 head end 
 
 Intermediate cylinder — 
 
 Cut-ofT, both ends ..... 
 
 Release, both ends 
 
 Compression, crank end . . . 
 
 head end 
 
 Low-pressure cylinder — 
 
 Cut-off, crank end 
 
 head end 
 
 Release, both ends 
 
 60 
 5299 
 
 1 193 
 
 57 
 61 
 
 85 
 53 
 
 1538 
 
 :2847 
 
 0.013 
 
 95-4 
 41.9 
 96. 1 
 
 14.8 
 
 155-3 
 25.0 
 
 o. 192 
 0.215 
 1 .00 
 
 0.05 
 0.0:; 
 
 60 
 
 5228 
 
 87- 
 
 1157 
 50 
 64 
 
 92 
 50 
 76 
 
 1489 
 
 22186 
 0.012 
 
 92. 1 
 42.1 
 96.6 
 
 14.8 
 
 155-5 
 25.1 
 
 0.194 
 0.205 
 1. 00 
 
 0.05 
 0.05 
 
 0.29 
 1. 00 
 0.03 
 0.04 
 
 0.38 
 
 0-39 
 1. 00 
 
 III. 
 
 IV 
 
 60 
 5173 
 
 86. 
 
 1234 
 29 
 69 
 
 97 
 
 52 
 90 
 
 ^571 
 
 20244 
 
 o.oii 
 
 102.4 
 
 43-0 
 106.3 
 
 14.7 
 
 156.9 
 
 24.1 
 
 0.245 
 0.271 
 1. 00 
 0.04 
 0.05 
 
 o. 29 
 1 .00 
 
 0.03 
 p. 04 
 
 0.38 
 0-39 
 
 1 .00 
 
 60 
 5148 
 85.8 
 
 1305 
 30 
 
 72 
 
 105 
 
 5^ 
 
 87 
 
 1650 
 
 20252 
 
 0.012 
 
 105-3 
 
 42.8 
 
 109.6 
 
 14.7 
 
 157-7 
 
 23-9 
 
 0.183 
 
 0-305 
 1 .00 
 0.04 
 0.05 
 
 0.29 
 1 .00 
 0.03 
 0.04 
 
 0.38 
 0.39 
 
2 26 
 
 INFLUENCE OF THE CYLINDER WALLS 
 
 Table VI — Continued. 
 
 Absolute pressures in the cylinder, 
 pounds per sq. in. : 
 High-pressure cylinder — 
 
 Cut-off, crank end 
 
 head end 
 
 Release, crank end 
 
 head end 
 
 Compression, crank end .... 
 
 head end 
 
 Admission, crank end 
 
 head end 
 
 Intermediate cylinder — 
 
 Cut-off, crank end 
 
 head end 
 
 Release, crank end 
 
 head end 
 
 Compression, crank end .... 
 
 head end 
 
 Admission, crank end 
 
 head end 
 
 Low-pressure cylinder — 
 
 Cut-off, crank end 
 
 head end 
 
 Release, crank end 
 
 head end 
 
 Compression and admission — 
 
 crank end , . 
 
 head end 
 
 Heat-equivalents of external work, 
 B.T.U., from a reason indicator- 
 diagram to line of absolute vacuum : 
 High-pressure cylinder — 
 During admission, 
 
 A Wd, crank end ...... 
 
 head end 
 
 During expansion, 
 
 .41^6, crank end 
 
 head end 
 
 During exhaust, 
 
 ylW^e, crank end 
 
 head end 
 
 T3uring compression, 
 
 ^l^d, crank end ...... 
 
 head end 
 
 Intermediate cylinder — 
 During admission, 
 
 A Wa, crank end 
 
 head end ... 
 
 During expansion, 
 
 A Wh , crank end 
 
 head end 
 
 145-9 
 143.2 
 
 41.3 
 41-5 
 43-7 
 48.7 
 
 64-5 
 75-3 
 
 5-71 
 6.6j 
 
 10.65 
 10.81 
 
 7-73 
 8.08 
 
 0.48 
 0.62 
 
 7-58 
 7-43 
 
 9-54 
 9. 22 
 
 145 
 
 143 
 
 41 
 
 40 
 
 45 
 47 
 68 
 
 74 
 
 37 
 35 
 
 T4 
 
 13 
 17 
 18 
 20 
 22 
 
 12 
 12 
 
 5 
 5 
 
 3 
 4 
 
 5-78 
 6-37 
 
 10.76 
 
 T I . 04 
 
 7.89 
 8.15 
 
 o. 60 
 
 0.64 
 
 9-54 
 9.3T 
 
 III. 
 
 138.8 
 
 140.3 
 
 44-7 
 
 45-7 
 48.5 
 54-5 
 72.2 
 
 38. 
 39- 
 14- 
 14. 
 18. 
 20. 
 22. 
 24. 
 
 12.4 
 
 13-1 
 
 5-1 
 
 5-9 
 
 4.1 
 4.6 
 
 7.00 
 8.42 
 
 10.40 
 11.22 
 
 8.44 
 9.04 
 
 0.49 
 0-73 
 
 7.98 
 8.46 
 
 9.91 
 10.37 
 
 IV. 
 
 138-3 
 140,6 
 
 48.4 
 49.8 
 53-2 
 62.0 
 81.2 
 97.8 
 
 40.9 
 42.6 
 16.0 
 16.0 
 19.0 
 22.4 
 23.1 
 26.7 
 
 13.2 
 
 14.0 
 
 5-7 
 
 6.4 
 
 4.2 
 
 4.7 
 
 8.19 
 9-5° 
 
 10.25 
 11.09 
 
 9.02 
 9.66 
 
 0.50 
 0.81 
 
 8.64 
 9. 10 
 
 10.64 
 
 TI . 14 
 
APPLICATION OF HIRN'S ANALYSIS 
 
 Table VI — Continued. 
 
 227 
 
 
 I. 
 
 II. 
 
 m. 
 
 IV. 
 
 Intermediate cylinder — 
 
 
 
 
 
 During exhaust, 
 
 
 
 
 
 ^P^/, crank end 
 
 9.27 
 
 9-47 
 
 9.64 
 
 10.54 
 
 head end 
 
 9.27 
 
 9-47 
 
 10.18 
 
 10.84 
 
 During' compression, 
 
 
 
 
 
 ^^/, crank end 
 
 0-39 
 
 0.43 
 
 0.57 
 
 0.46 
 
 head end 
 
 0.60 
 
 0. 70 
 
 0.78 
 
 0.84 
 
 Ix)w-pressure cylinder — 
 
 
 
 
 
 During admission, 
 
 
 
 
 
 ^HV, crank end 
 
 l-IS 
 
 7-95 
 
 8.33 
 
 8.97 
 
 head end 
 
 7 
 
 99 
 
 8.19 
 
 8.66 
 
 9-39 
 
 During expansion, 
 
 
 
 
 
 
 ^IPFft'', crank end 
 
 6 
 
 83 
 
 7.10 
 
 6.86 
 
 7-45 
 
 head end 
 
 6 
 
 87 
 
 7.12 
 
 7-34 
 
 .7.87 
 
 During exhaust, 
 
 
 
 
 
 
 ^Pi^/', crank end 
 
 5 
 
 08 
 
 5.08 
 
 4.62 
 
 5-09 
 
 head end 
 
 5 
 
 08 
 
 S-i6 
 
 4.81 
 
 5.00 
 
 During compression, 
 
 
 
 
 
 
 ^PF/', crank end 
 
 
 
 00 
 
 0.00 
 
 0,00 
 
 0.00 
 
 head end 
 
 
 
 00 
 
 0.00 
 
 0.00 
 
 0.00 
 
 < Quality of the steam in the cy Under. 
 
 
 
 
 
 At admission and at compression 
 
 
 
 
 
 the steam was assumed to be dry 
 
 
 
 
 
 and saturated: 
 
 
 
 
 
 High-pressure cylinder — 
 
 
 
 
 
 At cut-off x^ . 
 
 0.785 
 
 0.784 
 
 0.848 
 
 0-875 
 
 At release x^ . 
 
 0.899 
 
 0.903 
 
 0.920 
 
 0.931 
 
 Intermediate cyUnder — 
 
 
 
 
 
 At cut-off a;/ . 
 
 0.899 
 
 0.912 
 
 0.906 
 
 0.908 
 
 At release X2' . 
 
 0.994 
 
 * * * 
 
 ={= * * 
 
 * * * 
 
 Low-pressure cylinder — 
 
 
 
 
 
 At cut-off Xx" . 
 
 0.978 
 
 * * * 
 
 0.970 
 
 0.974 
 
 At release x/' . 
 
 :!< * * 
 
 * * * 
 
 * * * 
 
 * * * 
 
 Interchanges of heat between the 
 
 
 
 
 
 steam and the walls of the cylin- 
 
 
 
 
 
 ders, in B. T. u. Quantities 
 
 
 
 
 
 affected by the positive sign are 
 
 
 
 
 
 absorbed by the cylinder walls; 
 
 
 
 
 
 quantities affected by the negative 
 
 
 
 
 
 sign are yielded by the walls: . . 
 
 
 
 
 
 High-pressure cylinder — 
 
 
 
 
 
 Brought in by steam . Q . . . 
 
 132.93 
 
 130.77 
 
 141. II 
 
 149.84 
 
 During admission . . . Qd 
 
 23.54 
 
 23-43 
 
 17.49 
 
 14.93 
 
 During expansion . . . Qb . . 
 
 -18.69 
 
 -19.28 
 
 -15-33 
 
 — 14.03 
 
 During exhaust . . . . Qc . . 
 
 - 8.36 
 
 - 7.22 
 
 - 3-50 
 
 - 2.38 
 
 During compression . . Qd . . 
 
 0.45 
 
 0.51 
 
 0.49 
 
 0.52 
 
 Supplied by jacket ■ . Qj . . 
 
 4.56 
 
 4.08 
 
 2.39 
 
 2.50 
 
 Lost by radiation . . . Qc . . 
 
 T.5O 
 
 1.52 
 
 1.54 
 
 I -54 
 
 First intermediate receiver — 
 
 
 
 
 
 Supplied by jacket . . Qr ■ . 
 
 4.92 
 
 5.20 
 
 5-67 
 
 5-95 
 
 Lost by radiation . . . Qrc . . 
 
 0.58 
 
 0.58 
 
 0-59 
 
 0.59 
 
 Superheated. 
 
228 
 
 INFLUENCE OF THE CYLINDER WALLS 
 
 Table VI — Continued. 
 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 Intermediate cylinder — 
 
 
 
 
 
 Brought in by steam . Q' . . 
 
 131.89 
 
 129. 61 
 
 ^37-87 
 
 146.64 
 
 During admission . . . Qa' . . 
 
 13.62 
 
 11.74 
 
 11-33 
 
 ir-75 
 
 During expansion . . . Qb . . 
 
 -18.65 
 
 -18.84 
 
 -20.30 
 
 -21.88 
 
 During exhaust .... Q,/ . . 
 
 0.22 
 
 1-57 
 
 2.88 
 
 3-41 
 
 During compression . . Qd . ■ 
 
 0.44 
 
 0.51 
 
 0.62 
 
 0-59 
 
 SuppHed by jacket . . Q/ . . 
 
 6.82 
 
 7-50 
 
 7-97 
 
 8.64 
 
 Lost by radiation . . . Q/ ■ ■ 
 
 2.45 
 
 2.48 
 
 2.50 
 
 2.51 
 
 Second intermediate receiver - 
 
 
 
 
 
 Supplied by jacket . . Q/ . . 
 
 4.20 
 
 4.04 
 
 4.27 
 
 4.22 
 
 Lost by radiation . . . Qre' ■ ■ 
 
 1.20 
 
 1.22 
 
 1.23 
 
 1.24 
 
 Low-pressure cyHnder — 
 
 
 
 
 
 Brought in by steam . Q" . . 
 
 132.14 
 
 130-50 
 
 T38.61 
 
 147-33 
 
 During admission . . . Q/' ■ ■ 
 
 5.85 
 
 3-05 
 
 5-57 
 
 5-29 
 
 During expansion . . . Qb" ■ . 
 
 - 9-51 
 
 - 7-09 
 
 - 8.65 
 
 -10.13 
 
 During exhaust .... Q/' ■ ■ 
 
 2.53 
 
 2.23 
 
 - 1-44 
 
 — 0. II 
 
 During compression . . Qd" ■ . 
 
 0.00 
 
 0.00 
 
 0.00 
 
 0.00 
 
 Supplied by jacket . . Q/' . . 
 
 7-. 08 
 
 6. 20 
 
 7.41 
 
 7-14 
 
 Lost by radiation . . . Q/' . . 
 
 4.34 
 
 4.40 
 
 4.45 
 
 4-47 
 
 Total loss by radiation — 
 
 
 
 
 
 By preliminary tests . . ^Qe ■ . 
 
 10.07 
 
 10.20 
 
 10.31 
 
 10-35 
 
 By equation (171) 
 
 11.68 
 
 TO. IQ 
 
 8.75 
 
 8.07 
 
 Power and economy: 
 
 
 
 
 
 Heat-equivalents of works per 
 
 
 
 
 
 stroke — 
 
 
 
 
 
 H.P. cylinder , . . . AW . . 
 
 8.44 
 
 8.34 
 
 9.17 
 
 9.52 
 
 Interm. cyHnder. . . . AW . 
 
 7.12 
 
 6-95 
 
 7-77 
 
 8.42 
 
 L. P. cylinder . . . . AW" . 
 
 9.64 
 
 10.06 
 
 10.87 
 
 11.79 
 
 Totals 
 
 25.20 
 27.58 
 
 25-35 
 27.02 
 
 27.81 
 
 27.71 
 
 29-73 
 28.45 
 
 Total heat furnished by jackets . . 
 
 Distribution of work — 
 
 
 
 
 
 High-pressure cyHnder 
 
 1. 00 
 
 1. 00 
 
 1. 00 
 
 1. 00 
 
 Intermediate cylinder 
 
 0.84 
 
 0.83 
 
 0.85 
 
 0.88 
 
 Low-pressure cyHnder ..... 
 
 1. 14 
 
 1. 21 
 
 1. 19 
 
 1.24 
 
 Horse-power 
 
 104.9 
 14.65 
 
 104. 2 
 
 113. 1 
 13.90 
 
 120.3 
 13-73 
 
 Steam per H.P. per hour 
 
 14- 3' 
 
 B.T.U. per H.P. per minute . . . 
 
 247 
 
 241 
 
 236 
 
 232 
 
 It will be noted that for test IV 149.84 b.t.u. per stroke are 
 brought in by the steam suppHed to the high-pressure cylinder 
 and that 28.45 b.t.u. per stroke are supplied by the steam-jackets; 
 and that, further, 29.73 b.t.u. are changed into work while 10.35 
 are radiated. Thus it appears that the jackets furnished almost 
 as much heat as was required to do all the work developed. Of 
 the heat furnished by the jackets something more than a third 
 
QUALITY OF STEAM AT COMPRESSION 229 
 
 was radiated; the other two-thirds may fairly be considered 
 to have been changed into work, since the exhaust w^aste of the 
 low-pressure cylinder was practically zero. 
 
 Quality of Steam at Compression. — In all the work of this 
 chapter the steam in the cylinder at compression has been con- 
 sidered to be dry and saturated, and it has been asserted that 
 little if any error can arise from this assumption. It is clear 
 that some justification for such an assumption is needed, for a 
 relatively large weight of water in the cylinder would occupy 
 a small volume and might well be found adhering to the cylinder 
 walls in the form of a film or in drops; such a weight of water 
 would entirely change our calculations of the interchanges of 
 heat. The only valid objection to Hirn's analysis is directed 
 against the assumption of dry steam at compression. Indeed, 
 when the analysis w^as first presented some critics asserted that 
 the assumption of a proper amount of water in the cylinder is 
 all that is required to reduce the calculated interchanges of heat 
 to zero. It is not difficult to refute such an assertion from 
 almost any set of analyses, but unfortunately such a refutation 
 cannot be made to show conclusively that there is little or no 
 water in the cylinder at compression; in every case it will show 
 only that there must be a considerable interchange of heat. 
 
 For the several tests on the Hirn engine given in Table V, 
 Hallauer determined the amount of moisture in the steam in the 
 exhaust-pipe, and found it to vary from 3 to 10 per cent. Professor 
 Carpenter * says that the steam exhausted from the high-pressure 
 cylinder of a compound engine showed 12 to 14 per cent of 
 moisture. Numerous tests made in the laboratory of the 
 Massachusetts Institute of Technology show there is never a 
 large percentage of water in exhaust-steam. Finally, such a 
 conclusion is evident from ordinary observation. Starting from 
 this fact and assuming that the steam in the cylinder at com- 
 pression is at least as dry as the steam in the exhaust-pipe, we 
 are easily led to the conclusion that our assumption of dry steam 
 is proper. Professor Carpenter reports also that a calorimeter 
 
 ' * Trans. Am. Soc. Mech. Engrs., vol. xii, p. 811. 
 
230 INFLUENCE OF THE CYLINDER WALLS 
 
 test of steam drawn from the cylinder during compression 
 showed little or no moisture. Nevertheless, there would still 
 remain some doubt whether the assumption of dry steam at 
 compression is really justified, were we not so fortunate as to- 
 have direct experimental knowledge of the fluctuations of tem- 
 perature in the cylinder walls. 
 
 Dr. Hall's Investigations. — For the purpose of studying 
 the temperatures of the cylinder walls Dr. E. H. Hall used a 
 thermo-electric couple, represented by Fig. 56. / is a casi- 
 ^vwwsAi vi/ iron plug about three-quar- 
 
 HaJvwwnM/ 
 
 Fig. 56. 
 
 ters of an inch in diameter, 
 which could be screwed into 
 the hole provided for attach- 
 ing an indicator-cock to the 
 cylinder of a steam-engine. The inner end of the plug 
 carried a thin cast-iron disk, which was assumed to act as 
 a part of the cylinder wall when the plug was in place. To 
 study the temperature of the outside surface of the disk a nickel 
 rod N was soldered to it, making a thermo-electric couple. 
 Wires from / and N led to another couple made by soldering 
 together cast-iron and nickel, and this second couple was placed 
 in a bath of paraffine which could be maintained at any desired 
 temperature. In the electric circuit formed by the wires joining 
 the two thermo-electric couples there was placed a galvanometer 
 and a circuit-breaker. The circuit-breaker was closed by a 
 cam on the crank-shaft, which could be set to act at any point 
 of the revolution. If the temperature of the outside of the disk 
 5* differed from the temperature of the paraffine bath at the instant 
 when contact was made by the earn, a current passed through 
 the wires and was indicated by the galvanometer. By properly 
 regulating the temperature of the bath, the current could be 
 reduced and made to cease, and then a thermometer in the bath 
 gave the temperature at the surface of the disk for the instant 
 when the cam closed the electric circuit. Two points in the 
 steam-cycle were chosen for investigation, one immediately 
 after cut-off and the other immediately after compression, since 
 
CALLENDAR AND NICOLSON'S INVESTIGATIONS 231 
 
 they gave the means of investigating the heat absorbed during 
 compression and admission of steam, and the heat given up 
 during expansion and exhaust. 
 
 Three different disks were used : the first one half a miUimetre 
 thick, the second one miUimetre thick, and a third two miUi- 
 metres thick. From the fluctuations of temperature at these 
 distances from the inside surface of the w^all some idea could be 
 obtained concerning the variations of temperature at the inner 
 surface of the cylinder, and also how far the heating and cooling 
 of the walls extended. 
 
 The account given here is intended only to show^ the general 
 idea of the method, and does not adequately indicate the labor 
 difficulties of the investigation which involved many secondarv 
 investigations, such as the determination of the conductivity of 
 nickel. Having shown conclusively that there is an energetic 
 action of the walls of the cylinder. Dr. Hall was unable to continue 
 his investigations. 
 
 Callendar and Nicolson's Investigations. — A very refined 
 and complete investigation of the temperature of the cylinder 
 walls and also of the steam in the cylinder was made by 
 Callendar and Nicolson * in 1895 at the McGill University, 
 by the thermo-electric method. 
 
 The wall temperatures were determined by a thermo-electric 
 couple of which the cylinder itself was one element and a WTought- 
 iron wire was the other element. To make such a couple, the 
 cylinder wall was drilled nearly through, and the wire was 
 soldered to the bottom of the hole. Eight such couples were 
 established in the cylinder-head, the thickness of the unbroken 
 wall varying from o.oi of an inch to 0.64 of an inch. Four pairs 
 of couples were established along the cylinder-barrel, one near 
 the head, and the others at 4 inches, 6 inches, and 12 inches 
 from the head. One of each pair of wall couples was bored to 
 within 0.04 of an inch, and the other to 0.5 of an inch of the 
 inside surface of the cylinder. Other couples were established 
 along the side of the cylinder to study the flow of heat from the 
 
 * Proceedings of the Inst. Civ. Engrs., vol. cxxxii. 
 
232 
 
 INFLUENCE OF THE CYLINDER WALLS 
 
 head toward the crank end. The temperature of the steam 
 near the cyhnder-head was measured by a platinum thermometer 
 capable of indicating correctly rapid fluctuations of temperature. 
 
 The engine used for the investigations was a high-speed 
 engine, with a balanced slide-valve controlled by a fly-wheel 
 governor. During the investigations the cut-off was set at a 
 iixed point (about one-fifth stroke), and the speed was controlled 
 vxtcrnally. By the addition of a sufficient amount of lap to 
 prevent the valve from taking steam at the crank end the engine 
 was made single-acting. The normal speed of the engine was 
 250 revolutions per minute, but during the investigations the speed 
 was from 40 to 90 revolutions per minute. The diameter of the 
 cylinder was 10.5 inches and the stroke of the piston was 12 
 inches. The clearance was ten per cent of the piston displacement. 
 
 From the indicator-diagrams an analysis, nearly equivalent to 
 Hirn's analysis, showed the heat yielded to or taken from the 
 walls by the steam ; on the other hand the thermal measurements 
 gave an indication of the heat gained by or yielded by the walls. 
 The results are given in the following table; and considering the 
 difficulty of the investigation and the large allowance for leakage, 
 the concordance must be admitted to be very satisfactory. 
 
 Table VII. 
 
 INFLUENCE OF THE WALLS OF THE CYLINDER. 
 
 Callendar and Nicolson, Proc. Inst. Civ. Engrs., 1897. 
 
 Duration, minutes . . . 
 Revolutions per minute . 
 Mean gauge-pressure . . 
 Gross steam per revolution 
 Leakage correction . . . 
 Net steam per revolution 
 Steam caught at compression 
 Weight of mixture in cylinder 
 Indicated steam at quarter stroke 
 Indicated steam at release . 
 Increase of indicated weight 
 Adiabatic condensation 
 Indicated evaporation . 
 Calculated evaporation 
 Indicated condensation 
 Calculated condensation 
 Indicated horse-power 
 Steam per H.P. per hour, pounds 
 
 37 
 43-8 
 87.9 
 o. 1422 
 o. 1004 
 0.0418 
 0.0107 
 
 0.0525 
 
 0.0407 
 o . 0466 
 o . 0059 
 0.0019 
 0.0078 
 0.0076 
 0.0II8 
 0.0148 
 4.10 
 
 26.8 
 
 68 
 
 45-7 
 
 89.2 
 
 0.1437 
 
 0.0976 
 
 0.0461 
 
 0.0104 
 
 0.0565 
 
 0.0414 
 
 0.0456 
 
 0.0042 
 
 0.0020 
 
 0.0062 
 
 0.0073 
 
 0.0151 
 
 0.0142 
 
 4-34 
 
 29. 1 
 
 III. 
 
 55 
 47-7 
 94.4 
 0.1483 
 0.0990 
 o . 0493 
 0.0103 
 0.0596 
 0.0437 
 o . 0488 
 
 0.0051 
 0.0021 
 0.0072 
 0.0072 
 0.0159 
 0.0136 
 
 4.78 
 
 29-5 
 
 IV. 
 
 79 
 70.4 
 98.1 
 o. 1094 
 0.0697 
 0.0397 
 0.0099 
 0.0496 
 D.0418 
 o . 0460 
 0.0042 
 0.0020 
 0.0062 
 o . 0048 
 0.0078 
 0.0092 
 7.02 
 
 23.8 
 
 76 
 
 73-4 
 92.0 
 1036 
 0627 
 0409 
 0098 
 0507 
 0394 
 0436 
 0042 
 0019 
 0061 
 0046 
 0113 
 0089 
 6.67 
 27.1 
 
 VI. 
 
 35 
 
 81.7 
 
 94.2 
 
 o. 1000 
 
 0.0576 
 
 0.0424 
 
 O.OIOO 
 
 0.0524 
 o . 0408 
 
 0.0454 
 
 o . 0046 
 0.0020 
 o . 0066 
 0.0041 
 0.0116 
 o . 0080 
 
 7.71 
 
 26.9 
 
 VII. 
 
 25 
 
 97 o 
 
 96.0 
 0.0856 
 o . 0494 
 0.0362 
 0.0105 
 0.0467 
 0.0393 
 0.0426 
 0.0033 
 0.0019 
 0.0052 
 0.0035 
 0.0074 
 0.0067 
 
CALLENDAR AND NICOLSON'S INVESTIGATIONS 
 
 233 
 
 The platinum thermometer near the cy Under- head showed 
 superheating throughout compression, thus confirming our idea 
 that steam can be treated as dry and saturated at the beginning 
 of compression. This same thermometer fell rapidly during 
 admission and showed saturation practically up to cut-off, as 
 of course it should; after cut-off it began again to show a tem- 
 perature higher than that due to the indicated pressure, which 
 shows that the cylinder-head probably evaporated all the moisture 
 from its surface soon after cut-off. If this conclusion is correct, 
 there would appear to be little advantage from steam-jacketing 
 a cylinder-head, a conclusion which is borne out by tests on the 
 experimental engine at the Massachusetts Institute of Technology. 
 
 The following table gives the areas, temperatures, and the heat 
 absorbed during a given test by the various surfaces exposed to 
 steam at the end of the stroke, i.e., the clearance surface. 
 
 Table VIII. 
 
 CYCLICAL HEAT-ABSORPTION FOR CLEARANCE SURFACES. 
 
 Portions of surface considered. 
 
 Area 
 of surface, 
 square feet. 
 
 Mean 
 temperature, 
 
 Heat absorbed 
 
 B.T.U. 
 
 per minute. 
 
 Cover face, 10.5 inches diameter . . 
 
 Cover side, 3.0 inches 
 
 Piston face, 10.5 inches diameter. . . 
 
 Piston side, 0.5 inch 
 
 Barrel side, 3.0 inches 
 
 Counterbore, 0.5 inch 
 
 0,60 
 0. 70 
 0.60 
 
 O.ll 
 
 0.71 
 0.12 
 0.90 
 
 305 
 305 
 295 
 295 
 297 
 291 
 
 305 
 
 68 
 
 79 
 
 no 
 
 20 
 
 "I 
 
 
 
 Sums and means 
 
 3-74 
 
 301 
 
 530 
 
 The heat absorbed by the side of the cylinder wall uncovered 
 by the piston up to 0.25 of the stroke was estimated to be 55 
 B.T.U. per minute, which added to the above sum gives 585 b.t.u.; 
 from which it appears that 90 per cent of the condensation is 
 chargeable to the clearance surfaces, which were exceptionally 
 large for this type of engine. Further inspection shows that 
 the condensation on the piston and the barrel is much more 
 
234 INFLUENCE OF THE CYLINDER WALLS 
 
 energetic than on the cover or head. For example, the face of 
 the piston absorbs no b.t.u., while the face of the cover absorbs 
 only 68 b.t.u., and the sides of the cover and of the barrel, each 
 3 inches long, absorb 79 and 123 b.t.u. respectively. This 
 relatively small action of the surface of the head indicates in 
 another form that less gain is to be anticipated from the appli- 
 cation of a steam-jacket to the head than to the barrel of a 
 steam-engine. 
 
 The exposed surfaces at the side of the cylinder-head and 
 the corresponding side of the barrel are due to the use of a 
 deeply cored head which protrudes three inches into the counter- 
 bore of the cylinder, and which has the steam-tight joint at the 
 flange of the head. It would appear from this that a notable 
 reduction of condensation could be obtained by the 'simple expe- 
 dient of making a thin cylinder-head. 
 
 Leakage of Valves. — Preliminary tests when the engine was 
 at rest showed that the valve and piston were tight. The valve 
 was further tested by running it by an electric motor when the 
 piston was blocked, the stroke of the valve being regulated so 
 that it did not quite open the port, whereupon it appeared that 
 there was a perceptible but not an important leak past the valve 
 into the cylinder. There was also found to be a small leakage 
 past the piston from the head to the crank end. 
 
 But the most unexpected result was the large amount of leakage 
 past the valve from the steam-chest into the exhaust. This was 
 determined by blocking up the ports with lead and running the 
 valve in the normal manner by an electric motor. This leak- 
 age appeared to be proportional to the difference of pressure 
 causing the leak, and to be independent of the number of 
 reciprocations of the valve per minute. From the tests thus 
 made on the leakage to the exhaust, the leakage correction in 
 Table VII was estimated. Although the investigators concluded 
 that their experimental rate of leakage was quite definite, it 
 would appear that much of the discrepancy between the indicated 
 and calculated condensation and vaporization can be attributed 
 to this correction, which was two or three times as large as the 
 
LEAKAGE OF VALVES 235 
 
 weight of steam passing through the cyhnder. Under the most 
 favorable condition (for the seventh test) the leakage v^as 
 0.0494 of a pound per stroke, and since there were 97 strokes 
 per minute, it amounted to 
 
 0.0494 X 97 X 60 = 287.5 
 
 pounds per hour, or 32.6 pounds per horse-power per hour, so 
 that the steam supplied per horse-power per hour amounted to 
 56.4 pounds. If it be assumed that the horse-power is propor- 
 tional to the number of revolutions, then the engine running 
 double-acting will develop about 44 horse-power, and the leak- 
 age then would be reduced to 6.5 pounds per horse-power 
 per hour. Such a leakage would have the effect of increas- 
 ing the steam-consumption from 23.5 to 30 pounds of steam per 
 horse-power per hour. 
 
 To substantiate the conclusions just given concerning the 
 leakage to the exhaust, the investigators made similar tests on 
 the leakage of the valves of a quadruple-expansion engine, which 
 had plain unbalanced slide-valves. The valves chosen were the 
 largest and smallest; both were in good condition, the largest 
 being absolutely tight when at rest. Allowing for the size and 
 form of the valve and for the pressure, substantially identical 
 results were obtained. 
 
 The following provisional equation is proposed for calculat- 
 ing the leakage to the exhaust for slide-valves: 
 
 leakage = -y-, 
 
 where / is the lap and e is the perimeter of the valve, both in 
 inches, and p is the pressure in pounds in the steam-chest in 
 excess of the exhaust-pressure. The value of the constant 
 in the above equation is 0.021 for the high-speed engine used by 
 Callendar and Nicolson, and is 0.019 ^^^ ^^^ test each of the 
 valves for the quadruple engine, while another test on the large 
 valve gave 0.021. 
 
236 INFLUENCE OF THE CYLINDER WALLS 
 
 This matter of the leakage to the exhaust is worthy of further 
 investigation. Should it be found to apply in general to slide- 
 valve and piston- valve engines it would go far towards explaining 
 the superior economy of engines with separate admission- and 
 exhaust-valves, and especially of engines with automatic drop- 
 cut-off valves which are practically at rest when closed. It 
 may be remarked that the excessive leakage for the engine 
 tested appears to be due to the size and form of valves. The 
 valve was large so as to give a good port-opening when the cut-off 
 was shortened by the fly-wheel governor, and was faced off on 
 both sides so that it could slide between the valve-seat and a 
 massive cover-plate. The cover-plate was recessed opposite 
 the steam-ports, and the valve was constructed so as to admit 
 steam at both faces; from one the steam passed directly into the 
 cylinder, and from the other it passed into the cover-plate and 
 thence into the steam-port. This type of valve has long been 
 used on the Porter- Allen and the Straight-line engines ; the former, 
 however, has separate steam- and exhaust-valves. Such a valve 
 has a very long perimeter which accounts for the very large effect 
 of the leakage. 
 
 Callendar and Nicolson consider that the leakage is probably 
 in the form of water which is formed by condensation of steam 
 on the surface of the valve-seat uncovered by the valve, and say 
 further, that it is modified by the condition of lubrication of 
 the valve-seat, as oil hinders the leakage. 
 
CHAPTER XII. 
 
 ECONOMY OF STEAM-ENGINES. 
 
 In this chapter an attempt is made to give an idea of the 
 economy to be expected from various types of steam-engines 
 and the effects of the various means that are employed when 
 the best performance is desired. 
 
 Table X gives the economy of various types of engines, and 
 represents the present state of the art of steam-engine construc- 
 tion. It must be considered that in general the various engines 
 for which results are given in the table were carefully worked up 
 to their best performance when these tests were made. In 
 ordinary service these engines under favorable conditions may 
 consume five or ten per cent more steam or heat ; under unfavor- 
 able conditions the consumption may be half again or twice as 
 much. 
 
 All the examples in the table are taken from reliable tests; a 
 few of these tests are stated at length in the chapter on the influ- 
 ence of the cylinder walls; others are taken from various series 
 of tests which will be quoted in connection with the discussion 
 of the effects of such conditions as steam-jacketing and com- 
 pounding; the remaining tests will be given here, together with 
 some description of the engines on which the tests were made. 
 These tables of details are to be consulted in case fuller informa- 
 tion concerning particular tests is desired. 
 
 The first engine named in the table is at the Chestnut Hill 
 pumping-station for the city of Boston. Its performance is 
 the best known to the writer for engines using saturated steam. 
 Some engines using superheated steam have a notably less steam- 
 consumption; but the heat-consumption, which is a better criterion 
 of engine performance for such tests, is little if any better. The 
 first compound engine for which results are given, used 9.6 
 
 237 
 
238 
 
 ECONOMY OF STEAM-ENGINES 
 
 Table X. 
 
 EXAMPLES OF STEAM-ENGINE ECONOMY. 
 
 Type of Engine- 
 
 Triple-expansion engines : 
 
 Leavitt pumping-engine at Chestnut Hil 
 
 Sulzer mill-engine at Augsburg 
 
 Experimental engine at the Massachusetts 
 
 Institute of Technology 
 
 Marine engine Inna 
 
 Marine engine Meteor 
 
 Marine engine Brookline 
 
 Compound engines: 
 Horizontal mill-engine: 
 
 superheated 
 
 saturated 
 
 Leavitt pumping-engine at Louisville . . 
 
 Marine engine Rush 
 
 Marine engine Fusi Yama 
 
 Simple engines, condensing: 
 
 Corhss engine at Creusot 
 
 Corliss engine without jacket 
 
 Harris- Corliss engine at Cincinnati . . . 
 
 Marine engine Gallatin 
 
 Simple engines, non-condensing: 
 
 Corliss engine at Creusot 
 
 Corliss engine without jacket 
 
 Harris-Corliss engine at Cincinnati . . . 
 
 Harris-Corliss engine at the Massachusetts 
 Institute of Technology 
 
 Direct-acting steam-pumps: 
 
 Fire-pump at the Massachusetts Institute 
 
 of Technology 
 
 at reduced power 
 
 Steam- and feed-j)ump on the Minneapolis 
 at reduced power 
 
 « a, 
 
 50.6 
 56 
 
 92 
 61 
 
 72 
 94 
 
 128 
 T27 
 18.6 
 
 60 
 
 59 
 76 
 
 51 
 
 63 
 61 
 
 76 
 
 =QO 
 
 « CO-" 
 
 So 
 
 176 
 
 149 
 
 147 
 
 165 
 145 
 154 
 
 135 
 
 135 
 
 137 
 
 69 
 
 57 
 
 61 
 96 
 65 
 
 104 
 
 78 
 96 
 
 77 
 
 47 
 59 
 
 576 
 1823 
 
 125 
 
 645 
 
 1994 
 
 1136 
 
 115 
 127 
 
 643 
 266 
 
 371 
 
 176 
 150 
 145 
 260 
 
 237 
 209 
 120 
 
 16 
 
 41 
 6.8 
 8.8 
 1.6 
 
 £5 
 
 O O 
 
 SI 
 
 11.2 
 
 II-3 
 13-7 
 
 134 
 15.0 
 
 15-5 
 
 9.6 
 II. 8 
 12.2 
 18.4 
 21 .2 
 
 16.9 
 18. 1 
 19.4 
 22 
 
 21.5 
 24. 2 
 23-9 
 
 33-5 
 
 67 
 125 
 
 91 
 243 
 
 u s 
 
 u o • 
 
 Ho 1) 
 
 .-= a. 
 
 204 
 
 231 
 
 263 
 
 199 
 213 
 222 
 
 ;48 
 
 mo 
 
 2070 
 
 
 1.46 
 2.01 
 2 
 
 pounds of steam and 199 b.t.u. per minute, the gain being 
 hardly more than the variation that might be attributed to differ- 
 ence in apparatus, etc. The Chestnut Hill engine, which was de- 
 
 * Strokes per minute. 
 
TRIPLE-EXPANSION LEAVITT PUMPING-ENGINE 
 
 239 
 
 signed by Mr. E. D. Leavitt, has three vertical cylinders with their 
 pistons connected to cranks at 120°. Each cylinder has four 
 gridiron valves, each valve being actuated by its own cam on a 
 common cam-shaft; the cut-off for the high-pressure cylinder is 
 controlled by a governor. Steam-jackets are applied to the 
 heads and barrels of each cylinder, and tubular reheaters are 
 placed between the cylinders. Steam at boiler-pressure is sup- 
 plied to all the jackets and to the tubular reheaters. 
 
 Table XI. 
 
 TRIPLE-EXPANSION LEAVITT PUMPING-ENGINE AT THE 
 CHESTNUT HILL STATION, BOSTON, MASSACHUSETTS. 
 
 CYLINDER DIAMETERS 1 3. 7, 24.375, AND 39 INCHES; STROKE 6 FEET. 
 
 By Professor E. F. Mii,ler, Technology Quarterly, vol. ix; p. 72. 
 
 Duration, hours 24 
 
 Total expansion 21 
 
 Revolutions per minute 50 -6 
 
 Steam-pressure above atmosphere, pounds per square inch i75-7 
 
 Barometer, pounds per square inch 14.9 
 
 Vacuum in condenser, inches of mercury 27.25 
 
 Pressure in high and intermediate jacket and reheaters, pounds per 
 
 square inch 1 75 • 7 
 
 Pressure in low-pressure jacket, pounds per square inch 99-6 
 
 Horse-power , . . > 575-7 
 
 Steam per horse-power per hour, pounds 11. 2 
 
 Thermal units per honse-power per minute . . 204.3 
 
 Thermal efficiency of engine, per cent , 20.8 
 
 EflSciency for non-conducting engine, per cent . 28.0 
 
 Ratio of eflSciencies, per cent 74 
 
 Coal per horse-power per hour, pounds 1.146 
 
 Duty per 1,000,000 b.t.u 141,855,000 
 
 Efficiency of mechanism, per cent ..... 89 . 5 
 
 The Sulzer engine at Augsburg has four cylinders in all, a high- 
 pressure, an intermediate, and two low-pressure cylinders. The 
 high-pressure cylinder and one low-pressure cylinder are in line, 
 with their pistons on one continuous rod, and the intermediate 
 
240 
 
 ECONOMY OF STEAM-ENGINES 
 
 cylinder is arranged in a similar way with the other low-pressure 
 cylinder. The engine has two cranks at right angles, between 
 which is the fly-wheel, grooved for rope-driving. Each cylinder 
 has four double-acting poppet-valves, actuated by eccentrics, 
 links, and levers from a valve-shaft. The admission-valves 
 are controlled by the governors. Four tests were made on this 
 engine, as recorded in Table XII. 
 
 Table XII. 
 
 TRIPLE-EXPANSION HORIZONTAL MILL-ENGINE. 
 
 CYLINDER DIAMETERS 29.9, 44.5, AND TWO OF 5 1. 6 INCHES; STROKE 78.7 
 
 INCHES. 
 
 Built by SuLZER of Winterthur, Zeitschrift des Vereins Deutscher Ingenieure, 
 
 vol. xl, p. 534. 
 
 Duration, minutes 
 
 Revolutions per minute 
 
 Steam-pressure, pounds per square inch . 
 
 Vacuum, inches of mercury 
 
 Horse-povi^er 
 
 Steam per horse-power per hour, pounds 
 
 Mean for four tests . . . . 1 1 . 46 . . 
 Coal per horse-power per hour, pounds 
 
 Mean for four tests .... i . 30 . . 
 Steam per pound of coal 
 
 I 
 
 II 
 
 III 
 
 306 
 
 322 
 
 272 
 
 56.23 
 
 56.28 
 
 56.18 
 
 145-4 
 
 147-9 
 
 148.4 
 
 27.24 
 
 27.20 
 
 27.20 
 
 1872 
 
 1835 
 
 1850 
 
 11-53 
 
 11.49 
 
 11.49 
 
 1-37 
 
 1.36 
 
 1.29 
 
 8.78 
 
 8.49 
 
 8.97 
 
 IV 
 
 327 
 
 56.18 
 
 149.0 
 27.19 
 1823 
 
 1.19 
 9. 62 
 
 The test on the experimental engine at the Massachusetts 
 Institute of Technology is quoted here because its efficiency 
 and economy are chosen for discussion in Chapter VIII. Taking 
 its performance as a basis, it appears on page 148 that with 150 
 pounds boiler-pressure and 1.5 pounds absolute back-pressure 
 such an engine may be expected to give a horse-power for 11. 5 
 pounds of steam, from which it appears that under the same 
 conditions its performance compares favorably with the Sulzer 
 engine or even the Leavitt engine. 
 
MARINE-ENGINE TRIALS 
 
 241 
 
 Table XIII. 
 
 MARINE-ENGINE TRIALS. 
 
 By Professor Alexander B. W. Kennedy, Proc. Inst. Mech. Engrs., 1889-1892; 
 summary by Professor H. T. Beare, 1894, p. t,t^. 
 
 Triple or compound 
 
 Diameter high-pressure cylinder, inches 
 
 Diameter intermediate cylinder, inches = 
 
 Diameter low-pressure cylinder, inches ...... 
 
 Stroke, inches 
 
 Duration of trial, hours 
 
 Number of expansions 
 
 Revolutions per minute , 
 
 Steam-pressure above atmosphere, pounds per square 
 
 inch 
 
 Pressure in condenser, absolute, pounds per square 
 
 inch 
 
 Back-pressure, absolute, pounds per square inch . . . 
 
 Horse-power 
 
 Steam per horse-power per hour, pounds 
 
 Thermal units per horse-power per minute 
 
 Coal per horse-power per hour, pounds 
 
 Steam evaporated per pound of coal 
 
 Weight of machinery per horse-power, pounds . . . 
 
 C. 
 
 27.4 
 
 50-3 
 
 3,2> 
 
 14 
 .6.1 
 
 55-6 
 
 56.8 
 
 2.32 
 3-8 
 
 371 
 21. 2 
 
 380 
 2.66 
 7.96 
 
 603 
 
 C. 
 
 30 
 
 57 
 36 
 10.9 
 6.1 
 86 
 
 80. cr 
 
 2.51 
 
 3-4 
 1022 
 
 2T.7 
 398 
 2.9 
 
 7-49 
 448 
 
 > 
 
 C. 
 
 50.1 
 
 97.1 
 72 
 9 
 
 5-7 
 36 
 
 105.8 
 
 4.72 
 6.0 
 2977 
 20.8 
 367 
 2.3 
 8.97 
 272 
 
 T. 
 29.4 
 44 
 70. 1 
 48 
 
 17 
 
 10.6 
 
 71.8 
 
 145-2 
 
 2-73 
 3-3 
 1994 
 15.0 
 265 
 2.01 
 7.46 
 439 
 
 T. 
 21 .9 
 
 34 
 
 57 
 
 39 
 
 16 
 19.0 
 61. 1 
 
 165 
 
 o. 70 
 1.8 
 
 645 
 13-4 
 
 250 
 1 .46 
 
 9-15 
 701 
 
 The engines of the S. S. lona have an unusually large expansion 
 and give a correspondingly good economy. The engines of the 
 Meteor and of the Brookline give the usual economy to be 
 expected from medium-sized marine engines. Table XIII 
 gives details of tests on the engines of the first two ships 
 mentioned, together with tests on compound marine engines. 
 Table XIV gives tests on the engine of the Brookline. It 
 appears probable that the relatively poor economy of marine 
 engines compared with stationary engines is due to the 
 smaller degree of expansion, which is accepted to avoid using 
 large and heavy engines. 
 
242 
 
 ECONOMY OF STEAM-ENGINES 
 
 Table XIV. 
 
 TESTS ON THE ENGINE OF THE S. S. BROOKLINE. 
 
 CYLINDER DIAMETERS 23, 35, AND 57 INCHES; STROKE 36 INCHES. 
 
 By F. T. Miller and R. G. B. Sheridan, Thesis, 1895, M.I.T. 
 
 Duration, hours 
 
 Revohitions per minute 
 
 Steam-pressure, pounds per square inch above at- 
 mosphere 
 
 Vacuum, inches of mercury 
 
 Horse-power 
 
 Steam per horse-power per hour, pounds .... 
 
 Coal per horse-power per hour, pounds 
 
 B.T.U. per horse-power per minute 
 
 94.6 
 
 155 
 21.6 
 1242 
 17.2 
 
 2.22 
 292 
 
 2 
 93-6 
 
 155 
 21.0 
 1221 
 16.9 
 
 2. 17 
 288 
 
 III 
 
 IV 
 
 I 
 
 3i 
 
 93-^ 
 
 93 
 
 IS4 
 
 145 
 
 22.2 
 
 21.7 
 
 1136 
 
 1137 
 
 15-5 
 
 17.0 
 
 1.99 
 
 2.18 
 
 263 
 
 288 
 
 2h 
 
 93 
 
 148 
 
 20.9 
 
 1148 
 
 16.3 
 
 2.09 
 
 277 
 
 The horizontal mill-engine which heads the list of compound- 
 engines in Table X, is a tandem engine for which particulars 
 are given in Table XXVI on page 273. Its performance with 
 superheated steam is the best among the engines named, and 
 with saturated steam is a trifle superior to that of the Louisville 
 engine. 
 
 Table XV. 
 
 COMPOUND LEAVITT PUMPING-ENGINE AT LOUISVILLE, 
 KENTUCKY. 
 
 CYLINDER DIAMETERS 27.2 AND 54.I INCHES; STROKE lO FEET. 
 
 By F. W. Dean, Trans. Am. Soc. Mech. Engrs., vol. xvi, p. 169. 
 
 Duration, hours - 144 
 
 Revolutions per minute 18.6 
 
 Pressures, pounds per square inch: 
 
 Barometric 14.6 
 
 Boiler above atmosphere 140 
 
 At engine above atmosphere 137 
 
 Back-pressure, l.p. cyHnder 0.95 
 
 Total expansions 20 
 
 Moisture in steam, per cent 0.55 
 
 Horse-power 643.4 
 
 Steam per horse-power per hour, pounds 12.2 
 
 B.T.U. per horse-power per minute 222 
 
 Thermodynamic efficiency, per cent 19 
 
 Mechanical efficiency, per cent 93 
 
 This engine has two cylinders, each jacketed with steam at 
 boiler-pressure on barrels and heads, and steam at the same 
 pressure is used in a tubular reheater. Each cylinder has four 
 gridiron valves actuated by as many cams on a cam-shaft. 
 
AUTOMATIC CUT-OFF ENGINES 
 
 243 
 
 Table XVII. 
 
 ENGINES OF THE U. S. REVENUE STEAMERS RUSH AND 
 
 GALLATIN. 
 
 Diameters of cylinders, inches 
 
 Stroke, inches 
 
 Duration, hours 
 
 Revolutions per minute 
 
 Steam-pressure by gauge, pounds . . . . 
 
 Vacuum, inches of mercury 
 
 Total expansions 
 
 Horse-power 
 
 Steam per horse-power per hour, pounds 
 
 Rash. 
 
 
 Gallatin. 
 
 24 and 
 
 38 
 
 34.1 
 
 27 
 
 
 30 
 
 55 
 
 
 24 
 
 71 
 
 
 51 
 
 69.1 
 
 
 65.4 
 
 26.5 
 
 
 25.1 
 
 6.2 
 
 
 4.5 
 
 266.5 
 
 
 260.5 
 
 18.4 
 
 
 22 
 
 The details of the tests on the U. S. Revenue Steamers Rush 
 and Gallatin are given in Table XVII, as made about 1875 ^Y 
 a board of naval engineers to determine the advantages of com- 
 pounding and using steam-jackets. Three other engines were 
 tested at the same time, but they were of older types and are less 
 interesting. 
 
 A remarkably complete and important series of tests was made 
 in 1884 by M. F. Delafond. These tests are recorded in Tables 
 XXX and XXXI, from which there are quoted in Table X four 
 results with and without condensation and with and without 
 steam in the jackets. 
 
 Table XVIII. 
 
 AUTOMATIC CUT-OFF ENGINES. 
 
 CYLINDER DIAMETERS 1 8 INCHES; STROKE 4 FEET. 
 
 By J. W. Hill. 
 (First Millers' International Exhibition, Cincinnati, 1880.) 
 
 Duration 
 
 Cut-off 
 
 Revolutions per minute 
 
 Boiler-pressure alx>vc atmos.Jbs. per sq. in 
 
 Barometer, inches of mercury 
 
 Vacuum, inches of mercury 
 
 Back-pressure, absolute, lbs. per sq. in. . 
 
 Horse-power 
 
 Steam per horse-power per hour, pounds 
 B.T.U. per horse-power per hour . . . 
 
 
 Condensing. 
 
 Non-condensing. 
 
 R. 
 
 H. 
 
 W. 
 
 10 
 
 R. 
 
 H. 
 
 W. 
 
 10 
 
 10 
 
 9 
 
 10 
 
 10 
 
 0.124 
 
 0.119 
 
 0.131 
 
 0. 160 
 
 0.136 
 
 0.170 
 
 75.4 
 
 75-8 
 
 74.5 
 
 75-3 
 
 75-8 
 
 76.1 
 
 95-8 
 
 96.1 
 
 96.3 
 
 96.6 
 
 96.3 
 
 96.3 
 
 29.7 
 
 29.6 
 
 29.4 
 
 29.8 
 
 29.6 
 
 29-5 
 
 25-5 
 
 257 
 
 24.0 
 
 
 
 
 4.5 
 
 3-4 
 
 4-7 
 
 15-S 
 
 14-9 
 
 15-5 
 
 143-2 
 
 145. 1 
 
 143-9 
 
 121. 7 
 
 119-7 
 
 126.7 
 
 20.6 
 
 19.4 
 
 19-S 
 
 25-9 
 
 23-9 
 
 24.9 
 
 372 
 
 349 
 
 343 
 
 433 
 
 400 
 
 415 
 
244 
 
 ECONOMY OF STEAM-ENGINES 
 
 The details of the tests on the Harris- Corliss engine at Cin- 
 cinnati, together with tests on two similar engines, are given in 
 Table XVIII. 
 
 Table XIX. 
 
 DUPLEX DIRECT-ACTING FIRE-PUMP AT THE MASSACHUSETTS 
 INSTITUTE OF TECHNOLOGY. 
 
 TWO STEAM-CYLINDERS 1 6 INCHES DIAMETER, 12 INCHES STROKE. 
 
 Technology Quarterly, vol. viii, p. 19. 
 
 Single 
 strokes 
 
 Length 
 of stroke. 
 
 Length 
 of stroke. 
 
 Steam- 
 pressure 
 
 Horse- 
 power. 
 
 Horse- 
 power. 
 Water- 
 
 Steam 
 per horse- 
 
 B.T.U. 
 per horse- 
 
 Duty. (Foot- 
 pounds per 
 
 per 
 
 West. 
 
 £ast 
 
 by gauge. 
 
 Steam- 
 
 power per 
 
 power per 
 
 1 ,000, coo 
 
 minute. 
 
 
 cylinders. 
 
 cylinders. 
 
 hour. 
 
 minute. 
 
 B.T.U.) 
 
 99 
 
 11.40 
 
 10. 10 
 
 58.5 
 
 6.78 
 
 
 i25 
 
 2070 
 
 13,920,000 
 
 TT4 
 
 II. 70 
 
 11.07 
 
 55-6 
 
 12.48 
 
 
 lOI 
 
 1674 
 
 17,540,000 
 
 119 
 
 11.49 
 
 11.07 
 
 51-4 
 
 12.18 
 
 
 109 
 
 1809 
 
 16,980,000 
 
 135 
 
 11.60 
 
 II. 10 
 
 53-8 
 
 18.24 
 
 
 92 
 
 1530 
 
 19,850,000 
 
 156 
 
 10.90 
 
 10. 26 
 
 47-2 
 
 21.00 
 
 IQ.80 
 
 98 
 
 1619 
 
 18,280,000 
 
 193 
 
 10.09 
 
 10.31 
 
 45.6 
 
 32-9.5 
 
 
 78 
 
 1291 
 
 23.73o>ooo 
 
 'P 
 
 11-77 
 
 11.79 
 
 45.6 
 
 39-55 
 
 
 66 
 
 1083 
 
 27,980,000 
 
 180 
 
 11.74 
 
 11.66 
 
 46.5 
 
 41.20 
 
 
 67 
 
 IIIO 
 
 27,030,000 
 
 Table XX. 
 
 TESTS OF AUXILIARY STEAM MACHINERY OF THE U. S. 
 
 MINNEAPOLIS. 
 By P. A. Engineer W. W. White, U. S. N., Journal Am. Sac. Naval 
 Engrs., vol. x. 
 
 S. 
 
 Engine or pump tested. 
 
 Centre circulating-pump: 
 
 Full power 
 
 Reduced power* . . . 
 Starboard circulating-pump: 
 Reduced power .... 
 Starboard air-pump . . . 
 Centre air-pump f . . • . 
 Water-service pump . . . 
 Fire- and feed-pump . . . 
 
 Do 
 
 Do 
 
 Do 
 
 Fire-and bilge-pump . . . 
 
 Blower-engine 
 
 Dynamo-engine 
 
 Do 
 
 Ice-machine engine .... 
 
 O 13 
 . C 
 
 14 
 
 5 
 10.5 
 10.5 
 
 7 
 
 as '^ 
 
 0-0 
 
 - C 
 
 o.S 
 
 5 a 
 
 7-S 
 10.9 
 
 t2.0 
 
 10 
 
 10.8 
 
 11.2 
 
 4 
 5 
 5 
 
 ^ in 
 
 O C 
 
 <0 "*J 4J 
 
 ^ E 
 
 171. 6 
 90 
 
 82 
 16.6 
 
 IS-2 
 40.9 
 12.7 
 
 37-3 
 
 II. o 
 
 2.6 
 
 27.7 
 595 
 425 
 425 
 73-1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .s 
 
 g 
 
 '^ C 
 
 
 
 'S 
 
 ii% 
 
 2 
 
 3 
 
 ^a 
 
 « 
 
 c 
 
 3-7 
 
 18.9 
 
 2-50 
 
 4.1 
 
 3-28 
 
 2.0 
 
 2-58 
 
 6.5 
 
 3-2 
 
 25-2 
 
 2-59 
 
 1.04 
 
 3-31 
 
 0.78 
 
 1-46 
 
 6.4 
 
 2-23 
 
 8.8 
 
 3-27 
 
 1.6 
 
 2-2 
 
 2.5 
 
 1-24 
 
 16.3 
 
 l-IO 
 
 22.9 
 
 0-26 
 
 35-2 
 
 5-12 
 
 6.0 
 
 
 125 
 
 183 
 
 78 
 
 205 
 
 319 
 
 156 
 
 91 
 
 243 
 
 171 
 
 77 
 
 65 
 
 56 
 
 * One cylinder only supplied with steam. 
 
 t Pump loaded with three times the power developed during official trial, when main engine 
 indicated 7219 H.P. 
 
METHODS OF IMPROVING ECONOMY 
 
 245 
 
 The two tests on the direct-acting fire-pump at the 
 Massachusetts Institute of Technology are taken from Table 
 XIX, and the tests on the feed- and fire-pump on the Minneapolis 
 are given in Table XX. Both sets of tests show the extravagant 
 consumption of steam by such pumps when running at reduced 
 powers. The latter table is most interesting on account of the 
 light that it throws on the way that coal is consumed by a war- 
 vessel when cruising at slow speeds or lying in harbor. 
 
 Methods of Improving Economy. — The least expensive type 
 of engine to build is the simple non-condensing engine with slide- 
 valve gear; this type is now used only where economy is of little 
 importance, or where simplicity is thought to be imperative. 
 Starting with this as the most wasteful type of engine, improve- 
 ments in economy may be sought by one or more of the following 
 devices : 
 
 1. Increasing steam-pressure. 
 
 2. Condensing. 
 
 3. Increasing size. 
 
 4. Expansion. 
 
 5. Compounding. 
 
 6. Steam-jackets. 
 
 7. Superheating. 
 
 8. The binary engine. 
 
 An investigation of the conditions under which these various 
 devices can be used to advantage, of the gain to be expected, 
 and of their limitations, is one of the most interesting and impor- 
 tant problems for the engineer. For the student the process of 
 such an investigation is even of more importance than the 
 conclusions, because by it he may learn to form his own opinions 
 and may take account of other tests as they may be presented. 
 The order chosen is to some extent arbitrary, and cannot be 
 adhered to strictly, as the tests on which the investigation is 
 based were made for various purposes, and combine the several 
 devices in various manners. 
 
 Of these devices the first two and the last are clearly methods 
 of extending the temperature-range, and are indicated directly 
 
246 ECONOMY OF STEAM-ENGINES 
 
 by the ideas that have been presented in the general discussion 
 of thermodynamics, and in particular by the adiabatic theory of 
 the steam-engine; the fourth (expansion) may almost be included 
 in this category as a means of making the extension of temperature- 
 range effective. It has been seen that the necessity of making 
 the cylinder of metal which is a good conductor and has an 
 energetic action on the steam in the cylinder, interferes v^rith our 
 attempts to approach the efficiency that can . be computed for 
 non-condensing engines, and places limitations on the advantages 
 to be gained by increasing the temperature-range. The other 
 devices enumerated (increase of size, compounding, steam- 
 jackets, and superheating) are various methods v^hich have 
 been applied to diminish the influence of the cylinder v^^alls, 
 and allovv^ us to take advantage of a large temperature-range. It 
 appears at first sight that superheating should be included in 
 the first category, as it clearly does increase the temperature- 
 range betw^een the steam-pipe and the exhaust-pipe of the engine, 
 but the steam in the cylinder is seldom superheated at cut-off, 
 and it is better to consider this device as a means of reducing 
 cylinder condensation. 
 
 It is interesting to consider that condensation, expansion, and 
 steam-jackets v^ere used by Watt for his earliest engines, and that 
 he wsis limited in pressure by the condition of the art of engineer- 
 ing, so that there was no occasion for compounding; his cylinders 
 also had considerable size, though the powers of the engines 
 would not now appear to be large. In the course of his develop- 
 ment of the true steam-engine from the atmospheric engine, 
 which had the steam condensed in the cylinder by spraying in 
 water, Watt's attention was especially directed to the influence 
 of the cylinder walls ; he also made experiments on the properties 
 of saturated steam within the range of available pressures, and 
 had such an appreciation of the conditions of his problem that 
 little was left to his successors except to learn how to use the 
 higher steam-pressures which the developments of metallurgy 
 and machine-shop practice made possible. The fact that our 
 theory of the steam-engine was developed after his time, and 
 
EFFECT OF RAISING STEAM-PRESSURE 247 
 
 that the theory has sometimes been misappHed, has given an 
 erroneous opinion that the steam-engine has been developed 
 without or in spite of thermodynamics. And further, his use of 
 all the advantages then available has had a tendency to obscure 
 their importance, and makes it the more desirable to state the 
 several methods categorically as given above. 
 
 It is now commonly considered that the steam-engine has 
 been brought to full development, and that there is little if any 
 substantial improvement to be expected; in fact, this condition 
 was reached a decade or two ago, when the triple engine using 
 steam at 150 to 175 pounds by the gauge, was perfected. The 
 most recent change is the use of superheated steam at high 
 pressures, now that effective and durable superheaters have 
 been devised. Experiment and experience have settled fairly 
 well the limitations for the various methods of improving economy 
 and allow of a fair and conservative presentation to which there 
 will probably be few exceptions. We will, therefore, state the 
 general conclusions as briefly as may be, and give the tests on 
 which they may be based. 
 
 In order to bring out the advantage to be obtained by a certain 
 device, such as compounding, we will compare only the best 
 performance of the simple engine with the best performance of 
 the compound engine, each being given all the advantages that 
 it can use. The fact that marine compound engines have a 
 worse economy than stationary simple-engines, has no other 
 meaning for our present purpose, than that engines on ship- 
 board are subject to unfavorable limitations. 
 
 Effect of Raising Steam-Pressure. — A glance at the table on 
 page 148 which gives the efficiency for Carnot's cycle, will show 
 that if we begin with a low steam-pressure, there is a large advan- 
 tage from increasing the pressure and consequently the tem- 
 perature-range, but that this advantage becomes progressively 
 less marked. This conclusion is of course immediately evident 
 from the efficiency for Carnot's cycle, which may be written 
 
 T - T 
 
 e = -,= 
 
248 ECONOMY OF STEAM ENGINES 
 
 If /' is taken to be 100° F., and if / is made successively 200°, 
 300°, and 400°, the values of the efficiency are 0.15, 0.26, and 0.35. 
 But the influence of the cyUnder quickly puts a stop to this 
 improvement unless we resort to compounding, as will be seen by 
 "studying Delafond's tests in Table XXI, page 250, and by 
 Figs. 57 and 58 on pages 252 and 253, in which the steam-con- 
 sumption is plotted as ordinates on the fraction of the stroke at 
 cut-off, each curve being lettered with the steam-pressure which 
 was maintained while a series of tests was made. Fig. 57 rep- 
 resents tests without steam in the jackets, and Fig. 58, tests with 
 steam in the jackets. Those curves bearing the letter C were 
 with condensation, and those bearing the letter N were non- 
 condensing. Inspection of Fig. 57 shows a progressive reduc- 
 tion in steam-consumption, as the pressure is increased from 
 35 pounds by the gauge to 60 pounds for the condensing engine 
 without a steam-jacket, but raising the pressure from 60 pounds 
 to 80 and 100 pounds gives a marked increase in steam-con- 
 sumption. The same figure indicates that 100 pounds is probably 
 the limit for non-condensing, unjacketed engines. The curves 
 on Fig. 58 are not quite so conclusive; but we may from both 
 figures give the following as the best pressures to be used with 
 simple engines of good design and automatic valve-gear: 
 
 Desirable Pressures for Simple Engines. 
 
 Condensing, without steam-jackets, 60 pounds gauge. 
 
 Condensing, with steam-jackets, 80 pounds gauge. 
 
 Non-condensing, without steam-jackets, 100 pounds gauge. 
 
 Non-condensing, with steam-jackets, 125 pounds gauge. 
 
 Delafond's Tests. — In 1883 an extensive and important 
 investigation was made by Mons. F. Delafond on a horizontal 
 Corliss engine at Creusot to determine the conditions under 
 which the best economy can be obtained for such an engine. 
 The engine had a steam-jacket on the barrel, but was not jacketed 
 on the ends. Steam was supplied to the jacket by a branch 
 from the main steam-pipe, and the condensed water was drained 
 through a steam-trap into a can, so that the amount of steam 
 
DELAFOND'S TESTS 249 
 
 used in the jacket could be determined. The engine was tested 
 with and without steam in the jacket, both condensing and non- 
 condensing, and at various pressures from 35 to 100 pounds 
 above the pressure of the atmosphere. The effective power 
 and the friction of the engine were also obtained by aid of a 
 friction-brake on the engine-shaft. 
 
 The piping for the engine was so arranged that steam could be 
 drawn either from a general main steam-pipe or from a special 
 boiler used only during the test. Before making a test the 
 engine, which had been running for a sufficient time to come 
 to a condition of thermal equilibrium, was supplied with steam 
 from the general supply. At the instant for beginning the test 
 the general supply was shut off and steam was taken from the 
 special boiler during and until the end of the test, and then the 
 pipe from that boiler was closed. The advantage of this method 
 was that at the beginning and end of the test the water in the 
 boiler was quiescent and its level could be accurately determined. 
 At the end of a test the water-level was brought to the height 
 noted at the beginning. The water required for feeding the 
 special boiler during the test and for adjusting the water-level 
 at the end was measured in a calibrated tank. As the steam- 
 pressure in the general-supply main and in the special boiler 
 was the same, there was little danger of leakage through the 
 valves for controlling the steam-supply; the regularity and con- 
 sistency of results shown by the curves of Figs. 57 and 58 attest 
 to the skill and accuracy with which these tests were made. 
 
 Table XXI gives the results of tests made with condensation, 
 and Table XXII gives the results of tests without condensation. 
 All the tests both with and without condensation, but during 
 which no steam was used in the jackets, are represented by the 
 several curves of Fig. 57, while Fig. 58 represents tests made 
 with steam in the jackets. The curves are lettered to show the 
 mean steam-pressure for the series represented and the condition, 
 whether with or without condensation. Thus on Fig. 57 the 
 lowest curve 60C represents tests made without steam in the 
 jackets and with condensation, while the highest curve on Fig. 
 
250 
 
 ECONOMY OF STEAM-ENGINES 
 
 58 represents tests with steam in the jackets and without con- 
 densation, at 50 pounds boiler-pressure. The abscissae for the 
 curves are the per cents of cut-off, and the ordinates are the 
 steam-consumptions in pounds per horse-power per hour. The 
 
 Table XXI. 
 
 HORIZONTAL CORLISS ENGINE AT CREUSOT. 
 
 CYLINDER DIAMETER 21. 65 INCHES; STROKE 43-31 INCHES; JACKET ON 
 BARREL only; CONDENSING. 
 
 By F. Delafond, Annates du Mines, 1884. 
 
 Number 
 of test. 
 
 Duration, 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Cut-off in 
 
 per cent of 
 
 stroke. 
 
 Steam- 
 pressure, 
 pounds per 
 sq. in. 
 
 Vacuum, 
 inches of 
 mercury. 
 
 Steam 
 
 used in 
 
 jacket, 
 
 per cent. 
 
 Indicated 
 horse- 
 power. 
 
 Steam per 
 horse, 
 power 
 
 per hour, 
 pounds. 
 
 I 
 
 60 
 
 60.0 
 
 4 
 
 96.3 
 
 27.1 
 
 
 109 
 
 23.2 
 
 2 
 
 105 
 
 58.6 
 
 6 
 
 98.8 
 
 27.1 
 
 
 128.5 
 
 22.2 
 
 3 
 
 75 
 
 59-4 
 
 9 
 
 100 
 
 27.0 
 
 
 161 
 
 21.4 
 
 4 
 
 36 
 
 57-7 
 
 12.5 
 
 99.1 
 
 27.0 
 
 
 i86 
 
 22.0 
 
 5 
 
 73 
 
 58.8 
 
 5-5 
 
 104 
 
 27.4 
 
 '?' 
 
 141 
 
 17.1 
 
 6 
 
 55 
 
 61.5 
 
 6.7 
 
 102.4 
 
 27.1 
 
 ? 
 
 159- 5 
 
 16.7 
 
 7 
 
 80 
 
 59-9 
 
 6.7 
 
 103.8 
 
 27.4 
 
 2.9 
 
 155 
 
 16.5 
 
 8 
 
 39 
 
 S8.i 
 
 12.5 
 
 105.2 
 
 26.8 
 
 3.2 
 
 212 
 
 17.6 
 
 9 
 
 120 
 
 59.8 
 
 7.5 
 
 79.8 
 
 27.1 
 
 
 126 
 
 21.2 
 
 10 
 
 100 
 
 59-3 
 
 8.3 
 
 81.1 
 
 27.4 
 
 
 
 
 134 
 
 21. 1 
 
 n 
 
 90 
 
 59.8 
 
 10.5 
 
 80.1 
 
 27.1 
 
 
 
 
 150 
 
 20.8 
 
 12 
 
 55-5 
 
 58.0 
 
 14 
 
 85.5 
 
 27.1 
 
 
 
 
 17s 
 
 19.9 
 
 13 
 
 50 
 
 59- 1 
 
 18 
 
 84.8 
 
 26.5 
 
 
 
 
 194 
 
 20.4 
 
 14 
 
 94 
 
 59-6 
 
 5 
 
 8s. I 
 
 27.4 
 
 3.0 
 
 1X2 
 
 17.7 
 
 15 
 
 102 
 
 59-6 
 
 5-5 
 
 83.3 
 
 27.6 
 
 3.1 
 
 124 
 
 17.3 
 
 16 
 
 40 
 
 59.4 
 
 II-5 
 
 84.1 
 
 27.1 
 
 1.2 
 
 176 
 
 16.9 
 
 17 
 
 40 
 
 60 
 
 14 
 
 84.1 
 
 27.0 
 
 IS . 
 
 193 
 
 17-S 
 
 18 
 
 91 
 
 58.3 
 
 5-9 
 
 60.5 
 
 28.0 
 
 
 85.3 
 
 20.4 
 
 19 
 
 90 
 
 59-5 
 
 9 
 
 55.8 
 
 27.6 
 
 
 
 
 IIS 
 
 19.1 
 
 20 
 
 75 
 
 59.0 
 
 15-5 
 
 61.2 
 
 27.8 
 
 
 
 
 ISO 
 
 18. 1 
 
 21 
 
 75 
 
 58.3 
 
 22.7 
 
 58.3 
 
 27.6 
 
 
 
 
 172 
 
 18.4 
 
 22 
 
 31 
 
 59.2 
 
 25 
 
 61.2 
 
 27.1 
 
 
 
 
 i86 
 
 18.8 
 
 23 
 
 IIS 
 
 59-9 
 
 6 
 
 59-9 
 
 27.8 
 
 2.5 
 
 91.7 
 
 18.5 ■ 
 
 24 
 
 92 
 
 59-6 
 
 9 
 
 59-9 
 
 27.4 
 
 2.5 
 
 117 
 
 17.6 
 
 25 
 
 90 
 
 58.8 
 
 15-5 
 
 60.9 
 
 27.1. 
 
 1.8 
 
 ISO 
 
 173 
 
 26 
 
 71 
 
 59- 1 
 
 20 
 
 61.9 
 
 26.8 
 
 i-S 
 
 175 
 
 17.7 
 
 27 
 
 50 
 
 590 
 
 25 
 
 62.3 
 
 26.4 
 
 1.6 
 
 194 
 
 18.6 
 
 28 
 
 70 
 
 60.7 
 
 6 
 
 45 -o 
 
 28.0 
 
 
 75.6 
 
 20.7 
 
 ?9 
 
 80 
 
 58.8 
 
 9-5 
 
 48.9 
 
 28.1 
 
 
 
 
 94.3 
 
 19.4 
 
 30 
 
 III 
 
 60.4 
 
 15 
 
 47-9 
 
 27.6 
 
 
 
 
 120 
 
 18.8 
 
 31 
 
 54 
 
 58.8 
 
 21 
 
 47.8 
 
 27.6 
 
 
 
 
 140 
 
 19.0 
 
 32 
 
 55 
 
 59.4 
 
 29 
 
 47.6 
 
 27.1 
 
 
 
 
 i6s 
 
 19.8 
 
 33 
 
 98 
 
 60.3 
 
 5 
 
 45.8 
 
 28.0 
 
 2.6 
 
 68.8 
 
 19.3 
 
 34 
 
 63 
 
 57. '^ 
 
 10 
 
 51.6 
 
 27.6 
 
 2-3 
 
 95-5 
 
 18. 5 
 
 35 
 
 60 
 
 59.7 
 
 14-3 
 
 49.1 
 
 28.1 
 
 1.4 
 
 120 
 
 18.2 
 
 36 
 
 74 
 
 60.1 
 
 22 
 
 48.6 
 
 27.8 
 
 1.4 
 
 152 
 
 18.9 
 
 37 
 
 50 
 
 59- 5 
 
 29 
 
 50.2 
 
 26.8 
 
 1.2 
 
 179 
 
 19.7 
 
 38 
 
 85 
 
 60.3 
 
 18.2 
 
 33- 1 
 
 27.8 
 
 
 io6 
 
 20.5 
 
 39 
 
 68 
 
 61. 1 
 
 43 
 
 34-7 
 
 26.5 
 
 
 160 
 
 22.7 
 
 40 
 
 42.5 
 
 61.0 
 
 56.7 
 
 36.3 
 
 26.0 
 
 
 181 
 
 25-3 
 
 41 
 
 20 
 
 60.0 
 
 100 
 
 31.7 
 
 25.2 
 
 
 182 
 
 35. 9 
 
 42 
 
 73 
 
 60.7 
 
 19 
 
 32.0 
 
 27.6 
 
 V.6 
 
 III 
 
 19.8 
 
 43 
 
 80 
 
 61.9 
 
 42 
 
 33-0 
 
 26.5 
 
 I.I 
 
 162 
 
 22.1 
 
 44 
 
 40 
 
 61. 1 
 
 58 
 
 35.1 
 
 26.0 
 
 0.6 
 
 180 
 
 25.4 
 
 45 
 
 25 
 
 60.4 
 
 100 
 
 34.7 
 
 25.2 
 
 c 
 
 ).; 
 
 ' 
 
 199 
 
 33.0 
 
DELAFOND'S TESTS 
 
 251 
 
 results for individual tests are represented by dots, through 
 which or near which the curves are drawn. As there are only 
 a few tests in any series, a fair curve representing the series can 
 be drawn through all the points in most cases. The exceptions 
 
 Table XXII. 
 
 HORIZONTAL CORLISS ENGINE AT CREUSOT. 
 
 cylinder diameter 2 1. 65 inches; stroke 43. 3 1 inches; jacket on barrel 
 
 only: non-condensing. 
 
 
 B 
 
 y F, Delapond, Annates des Mities, 1884. 
 
 
 Number of 
 test. 
 
 Duration, 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Cut-off in 
 
 per cent of 
 
 stroke. 
 
 Steam- 
 pressure, 
 pounds per 
 square inch. 
 
 Steam used 
 in jacket, 
 per cent. 
 
 Indicated 
 horse- 
 power. 
 
 Steam per 
 
 horse-power 
 
 per hour, 
 
 pounds. 
 
 I 
 
 78 
 
 61.7 
 
 13 
 
 96.3 
 
 
 147-5 
 
 28.4 
 
 2 
 
 55 
 
 61.4 
 
 17 
 
 100.2 
 
 
 181. s 
 
 26.8 
 
 3 
 
 25 
 
 63.6 
 
 20 
 
 102.0 
 
 
 217 
 
 25.8 
 
 4 
 
 80 
 
 60.8 
 
 II 
 
 98.1, 
 
 2.5 
 
 143 
 
 22.8 
 
 5 
 
 60 
 
 62.0 
 
 13 
 
 103.8 
 
 3-4 
 
 177.5 
 
 22.1 
 
 6 
 
 36 
 
 62.0 
 
 16 
 
 103.0 
 
 3.1 
 
 194 
 
 22.4 
 
 7 
 
 30 
 
 62.7 
 
 20 
 
 103-5 
 
 2.0 
 
 237 
 
 21.5 
 
 8 
 
 66 
 
 62.0 
 
 15-5 
 
 73-7 
 
 
 121 
 
 27.6 
 
 9 
 
 60 
 
 60.9 
 
 18 
 
 77.0 
 
 
 136 
 
 26.7 
 
 10 
 
 60 
 
 60.0 
 
 24-5 
 
 76.7 
 
 
 178 
 
 24.6 
 
 II 
 
 30 
 
 60.6 
 
 32 
 
 77-5 
 
 
 209 
 
 24.2 
 
 12 
 
 70 
 
 61. 1 
 
 16.5 
 
 77.0 
 
 1-7 
 
 137 
 
 23-7 
 
 13 
 
 50 
 
 61.6 
 
 23-5 
 
 75-8 
 
 1.2 
 
 180 
 
 21.8 
 
 14 
 
 30 
 
 60.5 
 
 30 
 
 78.0 
 
 1-3 
 
 204 
 
 22.0 
 
 15 
 
 71 
 
 61.4 
 
 24.5 
 
 50.8 
 
 
 108 
 
 27-3 
 
 16 
 
 70 
 
 61. 1 
 
 37 
 
 51-2 
 
 
 147 
 
 27.2 
 
 17 
 
 50 
 
 60.9 
 
 58 
 
 50-5 
 
 
 173 
 
 30.2 
 
 18 
 
 25 
 
 60.6 
 
 100 
 
 34-9 
 
 
 145 
 
 46.8 
 
 19 
 
 70 
 
 60.5 
 
 23 
 
 52.6 
 
 1-5 
 
 108 
 
 25-3 
 
 20 
 
 60 
 
 60.5 
 
 34 
 
 51.8 
 
 I.I 
 
 141-5 
 
 25.2 
 
 21 
 
 50 
 
 60.3 
 
 58 
 
 46.2 
 
 0.7 
 
 168.5 
 
 28.7 
 
 22 
 
 30 
 
 61. I 
 
 100 
 
 33-7 
 
 0-3 
 
 147-5 
 
 46.3 
 
 are tests made with condensation for boiler-pressure of 80 and 
 100 pounds per square inch. The forms of the curves SoC 
 and looC, Fig. 57, were made to correspond in a general way 
 to the curves 50C and 60C. The discrepancies appear large 
 on account of the large scale for ordinates, but they are not 
 really of much importance; the largest deviation of a point from 
 the curve looC is half a pound out of about 22, which amounts 
 to little more than two per cent. On Fig. 58 the curve 80C is 
 drawn through the points, but though its form does not differ 
 
252 
 
 ECONOMY OF STEAM-ENGINES 
 
 radically from the curves 6oC and 50C, so marked a minimum 
 at so early a cut-off is at least doubtful. Considering that the 
 probable error of determining power from the indicator is about 
 
 30 
 28 
 26 
 24 
 22 
 20 
 18 
 
 
 
 
 
 
 y 
 
 
 \ 
 
 
 
 -py 
 
 / 
 
 
 \ 
 
 
 
 y 
 
 
 
 N 
 
 \ 
 
 ~j. 
 
 
 / 
 
 \ 
 
 
 
 
 ^ 
 
 
 < 
 
 
 
 
 
 
 \ 
 
 
 ::^ 
 
 
 
 
 
 bOC 
 
 
 
 
 
 10 
 
 20 
 
 30 
 
 Fig. 57. 
 
 40 
 
 50 
 
 two per cent, it would not be difficult to draw an acceptable 
 curve in place of 80C which should correspond to the forms of 
 60C and 50C. 
 
 The results of the four tests made with steam in the jacket 
 and with condensation, and which are numbered 5, 6, 7, and 8, 
 in Table XXII, are represented by dots inside of small circles 
 
CONDENSATION 253 
 
 on Fig. 58. It does not appear worth while to try to draw a 
 curve to represent these tests. 
 
 Condensation. — The complement of raising the steam-pressure 
 
 30 
 
 26 
 
 24 
 
 22 
 
 20 
 
 18 
 
 16 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 ^ 
 
 / 
 
 
 
 
 
 
 / 
 
 
 v^ 
 
 % 
 
 
 y" 
 
 
 
 'V 
 
 ^ 
 
 ^ 
 
 
 
 \ 
 
 ^ 
 
 ^G 
 
 V 
 
 
 
 
 
 ^^ 
 
 /^ 
 
 
 
 
 10 
 
 30 
 Fig. 58. 
 
 40 
 
 50 
 
 tiO 
 
 is the use of a condenser with a good vacuum. The advantage 
 to be obtained by this means can be determined from Delafond's 
 tests by aid of Figs. 57 and 58; taking the best conditions as 
 already recorded in Table X, the engine without a jacket and 
 without a vacuum used 24.2 pounds of steam per horse-power 
 per hour, and with a vacuum it used 18. i pounds; with steam in 
 the jackets the results were 21.5 and 16.9. A direct comparison 
 
254 ECONOMY OF STEAM-ENGINES 
 
 of either pair of results would appear to give a saving of about 
 25 per cent, which would be manifestly misleading. The results 
 of brake tests for this engine on page 273, show that the mechan- 
 ical efficiency when running non-condensing was 0.90, but that 
 it was only 0.82 when running condensing. The steam per 
 brake horse-power per hour can be obtained by dividing the 
 indicated steam by the mechanical efficiency, so that the above 
 pairs of results became for the engine without steam in the jacket, 
 non-condensing 26.9, and condensing 22.1, and for the engine 
 with steam in the jacket, 23.9 and 20.6; so that the real gain 
 from condensation was 
 
 26.0 — 22.1 „ 2^.0 — 20.6 
 
 — ^— = 0.18 or -^^-^ = 0.14. 
 
 26.9 23.9 
 
 The gain from condensation will vary with the type of engine 
 and the conditions of service, and may be estimated from ten 
 to twenty per cent. Clearly the gain is greater with a good 
 vacuum than with a poor vacuum. There is, however, another 
 feature which should be considered, namely, the mean effective 
 pressure; when the conditions of service are such that the mean 
 effective pressure is large, the gain from condensation and the 
 advantage of maintaining a good vacuum are not so great as 
 when the mean effective pressure is small. This feature can 
 be best illustrated with examples of triple-expansion engines, 
 which are able to work advantageously with a large total expan- 
 sion, and for them we may deal with the reduced mean effective 
 pressure, meaning by that expression the result obtained by the 
 following process: the mean effective pressure for the high- 
 pressure cylinder is to be multiplied by the area of that piston 
 and divided by the area of the low-pressure piston; the mean 
 effective pressure for the intermediate cylinder is to be treated 
 in a similar way; the two results are then to be added to the 
 mean effective pressure for the low-pressure cylinder; clearly 
 this sum, which is called the reduced mean effective pressure, 
 if it were applied to the low-pressure piston would develop the 
 actual power of the engine. Now the reduced mean effective 
 
INCREASE OF SIZE 
 
 255 
 
 pressure for a pumping-engine or mill-engine may be as low as 
 18 pounds per square inch, and a difference of one inch of 
 vacuum (or half a pound of back-pressure)- will be equivalent 
 to nearly three per cent in the power; on the other hand, a naval 
 engine is likely to have a reduced mean effective pressure of 
 forty pounds per square inch, and compared with it a difference 
 of one inch of vacuum is equivalent to a little more than one per 
 cent. In any case the gain in economy due to a small improve- 
 ment in vacuum is approximately equal to the reduction in the 
 absolute pressure in the condenser, divided by the reduced 
 mean effective pressure. 
 
 A very important matter is brought out in this discussion of 
 the gain from condensation, namely, that the real gain is deter- 
 mined by comparing the engine consumption for the net or 
 brake horse-powers. The only reason for using the indicated 
 power (as is most commonly done) is that the brake-power is 
 often difficult to determine and sometimes impossible. As 
 was pointed out on page 144, a true basis of comparison is the 
 heat-consumption of the engines compared in b.t.u. per horse- 
 power per hour. But that quantity was not determined for the 
 tests by Delafond, and since the comparisons are for two pairs 
 of tests, one pair with and the other without jackets there is no 
 objection to it in the cases discussed. 
 
 Increase of Size. — Since the failure to attain the economy 
 computed for the non-conducting engine is due mainly to the 
 action of the cylinder walls, and since the volume of the cylinder 
 are proportional to the cube of a linear dimension, while the sur- 
 face is only proportional to the square, a great advantage might 
 be expected by simply increasing the size of the engine. Such 
 an advantage is indicated by the comparison of the small Harris - 
 Corliss engine at the Massachusetts Institute of Technology with 
 the Corliss engine at Creusot, the steam-consumption without 
 condensation or steam-jackets being 33.5 pounds and 24.2 pounds 
 per horse-power per hour, and the gain from increase of 
 size being 
 
 -i-Z.K — 24.2 
 
 33-5 
 
256 ECONOMY OF STEAM-ENGINES 
 
 In this case the larger engine has about twelve times the cylinder 
 capacity of the smaller one. This feature appears to depend on 
 the absolute size of the engine, because, as will appear later, there 
 is little if any advantage in speed of rotation within the usual 
 limits of practice. 
 
 But the advantage from increase of size soon reaches a limit, 
 as will be apparent from the consideration that the best results 
 in Table X are for engines of moderate power, judged by modern 
 standards. These engines have the advantages of compounding, 
 and of the use of steam-jackets or superheated steam; the advan- 
 tages from jacketing or superheating decrease with the size, 
 and such devices are possibly of little advantage to massive 
 engines. 
 
 Expansion. — There are two limits to the amount of expansion 
 that can be advantageously used for a given engine: one limit 
 is imposed by the action of the cylinder walls, and the other is 
 imposed by the friction of the engine. Simple engines have the 
 most advantageous point of cut-off determined by the first limit, 
 which can be clearly determined by aid of Delafond's experi- 
 ments; compound and triple- expansion engines so divide up 
 the temperature-range that any desirable expansion can be 
 employed. The terminal pressure at the end of expansion for 
 a stationary, triple, or compound engine may be made as low as 
 five pounds absolute; and as the back- pressure is likely to be 
 a pound or a pound and a half, so that the terminal effective 
 pressure is three and a half or four pounds, and as it takes about 
 two pounds per square inch to drive the piston and connected 
 parts, there is evidently little to be gained in economy by further 
 expansion. 
 
 As for simple engines, an inspection of Figs. 57 and 58 on pages 
 252 and 253 shows that the best point of cut-off for non-conden- 
 sing engines is one-third stroke, and for condensing engines about 
 one sixth-stroke; if the engine has a steam-jacket, the cut-off 
 may be a little earlier than one-sixth stroke, but there probably 
 is little advantage from such an increase of expansion if we deal 
 with the net or brake horse-power. 
 
COMPOUNDING 
 
 257 
 
 The total expansion for a compound or triple engine can be 
 obtained in two ways: we may use a large ratio of the large 
 cylinder to the small cylinder, or we may use a short cut-off for 
 the high-pressure cylinder. The two methods may be illustrated 
 by the two Leavitt engines mentioned in Table X; the ratio of 
 .the large to the small cylinder of the compound engine at 
 Louisville, is a trifle less than four, and the cut-off for the high- 
 pressure cylinder is a little less than one- fifth stroke; on the 
 other hand, the triple engine at Chestnut Hill has a little more 
 than eight for the extreme ratio of the cylinders, and has the 
 cut-off for the high-pressure cylinder at a little more than four- 
 fifths. So large an extreme ratio as eight would not be con- 
 venient for a compound engine, but ratios of five or six have 
 been used, though not with the best results. 
 
 Marine engines usually have comparatively little total expan- 
 sion both for compound and for triple engines, and consequently 
 are unable to work with an economy equal to that for stationary 
 engines ; the type of valve-gear which the designers feel constrained 
 to use is also little adapted to give the best results. There is 
 some question whether there is not room for improvement in 
 both these directions. 
 
 Compounding. — The most efficacious method which has 
 been devised to increase the amount of expansion of steam in 
 an engine, and at the same time to avoid excessive cylinder- 
 condensation, is compounding; that is, passing the steam in 
 succession through two or more cylinders of increasing size. 
 An engine with two cyHnders, a small or high-pressure cylinder 
 and a large or low-pressure cylinder, is called a compound 
 engine. An engine with three cylinders, a high-pressure cylinder, 
 an intermediate cylinder, and a low-pressure cylinder, is called 
 a triple-expansion engine. A quadruple engine has a high- 
 pressure cylinder, a first and a second intermediate cylinder, 
 and a low-pressure cylinder. Any cylinder of a compound or 
 multiple-expansion engine may be duplicated, that is, may be 
 replaced by two cylinders which are usually of the same size. 
 Thus, at one time a compound engine with one high- pressure 
 
258 ECONOMY OF STEAM-ENGINES 
 
 and two low-pressure cylinders was much used for large steam- 
 ships. Many triple engines have two low-pressure cylinders, 
 which with the high-pressure and the intermediate cylinders 
 make four in all. Again, some triple engines have two high- 
 pressure cylinders and two low-pressure cylinders and one 
 intermediate cylinder, making five in all. 
 
 Two questions arise: (i) Under what conditions should the 
 several types of engines be used? and (2) What gain can be ex- 
 pected by using compound or triple expansion ? 
 
 Neither question can be answered explicitly. 
 
 From tests already discussed and for which the main results 
 are given in Table X, it appears that with saturated steam, the 
 best results were attained with the following pressures : for triple 
 engines about 175 pounds by the gauge, for compound engines 
 145 pounds, and for simple engines with about 80 pounds; all 
 for engines with condensation. Nearly as good results were 
 obtained for a compound engine with 135 pounds pressure, 
 and on the other hand the simple engine could use 100 pounds 
 with equal advantage. The information concerning the simple 
 engine is sufficient to serve as a reliable guide, but there is at 
 least room for discretion concerning the best pressures for com- 
 pound and triple engines. There will probably be little chance 
 of serious disappointment if the following table is used as a guide 
 in designing engines, all being with condensation and with 
 steam-jackets. 
 
 Best Gauge-Pressures for Steam- Engines. 
 
 Simple 80 
 
 Compound 140 
 
 Triple 175 
 
 If for any reason it is desired to use a higher or lower pressure 
 in any case, a variation of 20 pounds either way may be assumed 
 without much loss of efficiency; this, however, cannot be stated 
 quantitatively at the present time. 
 
 For non-condensing simple engines the pressure should 
 preferably be 100 pounds without a steam-jacket, and 125 
 
COMPOUNDING 
 
 259 
 
 pounds with a steam-jacket ; with an allowable variation of twenty 
 pounds. For a non-condensing compound engine we may take 
 as the preferred pressure about 175 pounds, but our tests do not 
 include this case, and the figure is open to question. There is 
 little, if any, occasion for using triple-expansion non-condensing 
 engines. 
 
 About ten years ago an attempt was made to introduce quad- 
 ruple-expansion engines, using steam at about 250 pounds for 
 marine purposes in conjunction with water-tube boilers, which 
 can readily be built for high-pressures ; but more recent practice 
 has been to adhere to triple engines even where the designer 
 has chosen a high-pressure for sake of developing a large power 
 per ton of machinery, or for any other purpose. 
 
 For convenience in trying to determine the gain from com- 
 pounding, the following supplementary table has been drawn off. 
 
 Data and Results. 
 
 Revolutions per minute 
 
 r-. above atmosphere, pounds 
 
 Steam-pressure 
 
 Total expansion 
 
 Ste^m per horse-power per hour, pounds 
 
 B.T.U. per horse-power per minute . , 
 
 Simple 
 
 Corliss at 
 
 Creusot. 
 
 Compound 
 Mill-Engine- 
 
 60 
 
 84 
 
 9 
 
 16. Q 
 
 127 
 148 
 
 20 
 
 II. 8 
 220 
 
 Triple 
 
 Leavitt at 
 
 Chestnut 
 
 Hill. 
 
 50.6 
 176 
 
 21 
 
 II. 2 
 204 
 
 Gain from compounding, 
 
 16.9 — 11.^ 
 
 16.9 
 
 0.30. 
 
 Gain from using triple engine in place of simple engine, 
 16.9 — II. 2 _ 
 
 16.9 
 
 0.34. 
 
 Gain from using triple engine in place of compound engine 
 II. 8 — II. 2 
 
 11.8 
 
 = 0.05. 
 
26o 
 
 ECONOMY OF STEAM-ENGINES 
 
 Compound and triple engines have been found well adapted 
 to marine work, where for various reasons a short cut-off cannot 
 well be used. Taking the engines of the three ships mentioned 
 in the following supplementary table to represent good practice, 
 we can determine the gain from compounding. 
 
 Data and Results. 
 
 Revolutions per minute ..... 
 
 Steam pressure by gauge 
 
 Total expansion 
 
 Steam per horse-power per hour, pounds 
 
 Simple 
 
 Compound 
 
 Galatin. 
 
 Rush. 
 
 5t 
 
 n 
 
 65 
 
 69 
 
 4.5 
 
 6.2 
 
 22 
 
 18.4 
 
 Triple 
 Meteor. 
 
 72 
 
 145 
 ro.6 
 
 IS 
 
 Gain from compounding, 
 
 22 
 
 18.4 
 
 = 0.16. 
 
 22 
 
 Gain from using triple engine instead of simple engine, 
 
 22 — iq 
 
 22 ^ 
 
 Gain from using triple engine instead of compound engine, 
 
 i8-4 - 15 
 18.4 
 
 = 0.18. 
 
 Two things are to be noted: first, that the total number of 
 expansions is very moderate even for the triple engine; and, 
 second, that the steam-consumption is correspondingly large 
 as compared with that for stationary engines. 
 
 A notable exception in marine practice is the engine of the 
 lona^ which was relatively much larger than can commonly be 
 placed in a steamer; it had the advantage of 165 pounds steam- 
 pressure and 19 total expansions, and had a steam-consumption 
 of only 13 pounds per horse- power per hour. 
 
EXPERIMENTAL ENGINE 261 
 
 Properly the comparison for finding the gain from compound- 
 ing should be based on thermal units per horse-power per minute, 
 but the data for such a comparison are not given for all the 
 engines, and as all the engines have steam-jackets, the comparison 
 of steam-consumptions is not much in error. 
 
 Steam-jackets. — As has already been pointed out in the 
 discussion of the influence of the cylinder walls, the beneficial 
 action of a steam-jacket is to dry out the cylinder during exhaust, 
 without unduly reducing the temperature of the cylinder walls, 
 and thus check the condensation during admission. The steam- 
 jacket does indeed supply some heat during expansion, but 
 that effect is of secondary importance, and the heat is applied 
 with a thermodynamic disadvantage. The principal effect is 
 thus to supply heat which is thrown out in the exhaust, which is 
 all lost in case of a simple engine; in case of a compound engine 
 the heat supplied by a jacket during exhaust from the high- 
 pressure cylinder is intercepted by the low-pressure cylinder, 
 and is not entirely lost. It would clearly be much more advan- 
 tageous to make the cylinders of non-conducting material, if 
 that were possible. A clear grasp of the true action of the 
 steam-jacket has a natural tendency to prejudice the mind 
 against that device, and this prejudice has in many cases been 
 strengthened by the confusion that has come from indiscriminate 
 comparison of many tests made to determine the advantage 
 from the use of steam-jackets. 
 
 There are two series of tests that appear to dispose of this 
 question, — those by Delafond on the Corliss engine at Creusot, 
 and those made at the Massachusetts Institute of Technology 
 on a triple-expansion experimental engine; the former has already 
 been given, and the latter will now be detailed; afterward the 
 gain from the use of the jacket will be discussed. 
 
 Experimental Engine at the Massachusetts Institute of 
 Technology. — This engine, which was added to the equipment 
 of the laboratory of steam-engineering of the Institute in 1890, 
 is specially arranged for giving instruction in making engine- tests. 
 It has three horizontal cylinders and two intermediate receivers. 
 
262 ECONOMY OF STEAM-ENGINES 
 
 the piping being so arranged that any cylinder may be used 
 
 340 
 
 aoo 
 
 240 
 
 220 
 
 200 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 ^V 
 
 
 
 
 
 
 
 
 
 
 s 
 
 N 
 
 ;/c 
 
 3mpou 
 
 id. 
 
 
 
 \ 
 
 
 
 
 y 
 
 W 
 
 ithout 
 
 jacket 
 
 J 
 
 
 ^ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 V 
 
 
 
 
 
 
 
 
 •s 
 
 \, 
 
 ^ 
 
 <, 
 
 
 
 
 
 
 
 ^ 
 
 v- 
 
 V, 
 
 ?^ 
 
 S 
 
 V 
 
 Trip 
 * with 
 
 le, 
 out ja 
 
 ikets 
 
 
 
 \ 
 
 / \ 
 
 ^^ 
 
 
 
 Tn 
 
 r^ on 
 
 ple,ja( 
 heads 
 
 kets 
 
 
 
 • 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 \ 
 
 \^ 
 
 N^ 
 
 
 Trii 
 - on ( 
 ^ and 
 
 le,jacl 
 ylinde 
 receiv 
 
 ets 
 
 
 
 
 
 • 
 
 
 < 
 
 ^on c 
 
 iple,ja 
 jrlinde 
 
 3kets 
 s only 
 
 
 
 
 
 
 n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 Fig. 59 
 
 singly or may be combined with one or both of the other cylinders 
 to form a compound or a triple engine. Each cylinder has 
 
EXPERIMENTAL ENGINE 263 
 
 Steam-jackets on the tarrel and the heads, and steam may be 
 supplied to any or all of these jackets at will. The steam con- 
 densed in the jackets of any one of the cylinders is collected under 
 pressure in a closed receptacle and measured. Originally the 
 receivers were also provided with steam-jackets; now they are 
 provided with tubular reheaters so divided that one-third, two- 
 thirds, or all the surface of the reheaters can be used. The 
 steam condensed in the reheaters is also collected and measured 
 in a closed receptacle. 
 
 The valve-gear is of the Corliss type with vacuum dash-pots 
 which give a very sharp cut-off. The high- pressure and inter- 
 mediate cylinders have only one eccentric and wrist-plate, and 
 consequently cannot have a longer cut-off than half stroke under 
 the control of the drop cut-off mechanism. The low-pressure 
 cylinder has two eccentrics and two wrist-plates, and the admission 
 valves can be set to give a cut-off beyond half stroke. The 
 governor is arranged to control the valves for any or all of the 
 cylinders. Each cylinder has also a hand-gear for controlling 
 its valves. For experimental purposes the governor is set to 
 control only the high-pressure valve-gear, when the engine is 
 running compound or triple-expansion. The hand-gear is 
 used for adjusting the cut-off for the other cylinder or cylinders; 
 usually the cut-off for such cylinder or cylinders is set to give a 
 very small drop between the cylinders. This arrangement 
 throws a very small duty on the governor, so that by the aid of 
 a large and heavy fly-wheel the engine can be made to give 
 nearly identical indicator-diagrams for an entire test during 
 which the load and the steam-pressure are kept constant. 
 
 The main dimensions of the engine are as follows: 
 
 Diameter of the high-pressure cylinder 9 inches. 
 
 intermediate " 16 '' 
 
 ** *' low-pressure '' 24 " 
 
 ' ' " piston-rods 2^^ " 
 
 Stroke 30 * ' 
 
264 ECONOMY OF STEAM-ENGINES 
 
 Clearance in per cent of the piston displacements: 
 
 High-pressure cylinder, head end, 8.83; crank end, 9.76 
 Intermediate " " '' 10.4 " '' 10.9 
 
 Low-pressure " '' "11.25 " " 8.84 
 
 Results of tests on the engine with the cylinders arranged in 
 order to form a triple-expansion engine are given in Table 
 XXIII, and are represented by the diagram Fig. 60 with the 
 cut-off of the high-pressure cylinder for abscissae and with the 
 consumptions of thermal units per horse-power per minute as 
 ordinates. 
 
 The most important investigation which has been made on 
 this engine is of the advantage to be obtained from the use of 
 steam in the jackets. Four series of tests were made for this 
 purpose: (i) with steam in all the jackets of the cylinders and 
 receivers, (2) with steam in the jackets of the cylinders, both 
 heads and barrels, (3) with steam in the jackets on the heads of 
 the cylinders only, and (4) without steam in any of the jackets. 
 
 The most economical method of running the engine was with 
 steam in all the jackets on the cylinders, but without steam in 
 the receiver-jackets, as shown by the lowest curve on Fig. 59. 
 There is a small but distinct disadvantage from using steam in 
 the receiver-jackets also. This fact could not be surely deter- 
 mined from any pair of tests, for the difference is not more than 
 two per cent, and is therefore not more than the probable error 
 for such a pair of tests, but a comparison of the two curves on 
 Fig. 59, representing tests under the two conditions, gives con- 
 clusive evidencfe with regard to this point. It may not be im- 
 proper in this connection to call attention to the three points 
 below the lowest curve and not connected with it ; they represent 
 tests which were made after the nine tests represented by points 
 joined to the curve, and when some additional non-conducting 
 covering had been applied to the piping and valves of the engine. 
 Here the slight gain from reduced radiation is made manifest, 
 though it is too small to be taken into account in making com- 
 parisons of the different conditions of running the engine. 
 
EXPERIMENTAL ENGINE 
 
 265 
 
 Table XXIII. 
 
 TRIPLE-EXPANSION EXPERIMENTAL ENGINE AT THE MASSA- 
 CHUSETTS INSTITUTE OF TECHNOLOGY. 
 
 Trans. Am. .Soc. Mech. Engs., 1892-1804; Technology Quarterly, 1896. 
 
 
 
 
 
 
 
 Steam used in jackets, 
 
 
 
 
 
 
 
 
 
 
 
 per cent. 
 
 
 
 
 
 
 
 i 
 ^ 
 
 ij 
 3^ 
 
 1 
 
 8s 
 
 1. 
 
 
 
 
 u 
 
 S3 
 
 k 
 
 ll 
 
 -S s 
 eg 
 
 Mo 
 
 
 a 
 
 ! 
 
 u 
 
 i 
 
 a 
 
 1 
 
 « 
 
 
 1 
 146.2 
 
 
 Is 
 
 1 
 
 
 i 
 
 is 
 1" 
 
 i 
 
 
 1 
 
 
 It 
 
 SB. 
 
 a 
 .0^ 
 
 1- oj 
 
 
 1 
 
 89-93 
 
 36.1 
 
 24.1 
 
 29.8 
 
 3-2 
 
 
 8.6 
 
 6.3 
 
 140.8 
 
 iv8 
 
 240 
 
 233 
 
 2 a . 
 
 90.60 
 
 35-0 
 
 147.0 
 
 24-7 
 
 30.3 
 
 2.5 
 
 
 8.8 
 
 
 5.4 
 
 138.0 
 
 13-9 
 
 241 
 
 237 
 
 3 5- 
 
 91-93 
 
 27-3 
 
 146.9 
 
 24-5 
 
 29-9 
 
 2-5 
 
 
 8.5 
 
 
 7.2 
 
 125.4 
 
 13.7 
 
 237 
 
 231 
 
 4 ^-S 
 
 91-55 
 
 27.0 
 
 146.7 
 
 25-4 
 
 30.1 
 
 3.2 
 
 
 9.8 
 
 
 8.1 
 
 123.9 
 
 13.7 
 
 239 
 
 236 
 
 
 92-37 
 
 25.0 
 
 146.6 
 
 24-5 
 
 30.7 
 
 3-4 
 
 
 10.4 
 
 
 10. 1 
 
 114-7 
 
 14.3 
 
 247 
 
 240 
 
 6 ^-^ 
 
 84-87 
 
 21.9 
 
 145.2 
 
 24-3 
 
 30.1 
 
 3-S 
 
 
 11-3 
 
 
 8.7 
 
 ioS-3 
 
 14.5 
 
 250 
 
 241 
 
 7 ^" 
 
 93-15 
 
 17.4 
 
 146.0 
 
 26.0 
 
 30.2 
 
 3.5 
 
 
 10.7 
 
 
 II. b 
 
 103-5 
 
 14.7 
 
 255 
 
 255 
 
 8 
 
 86.70 
 
 12.0 
 
 147.0 
 
 27.4 
 
 .30.5 
 
 6.1 
 
 
 15.2 
 
 
 12.2 
 
 78-3 
 
 15-1 
 
 261 
 
 273 
 
 9 
 
 87-55 
 
 ii.3 
 
 146.7 
 
 26.0 
 
 30.1 
 
 6.5 
 
 
 15-3 
 
 
 13.0 
 
 67.4 
 
 16.0 
 
 274 
 
 274 
 
 10 
 
 84.23 
 
 13.5 
 
 X45.2 
 
 26.1 
 
 30.0 
 
 5-3 
 
 
 11-3 
 
 
 12. 1 
 
 77.8 
 
 14.7 
 
 253 
 
 255 
 
 II Ditto. 
 
 82.50 
 
 20.5 
 
 144.5 
 
 26.2 
 
 29.9 
 
 4.5 
 
 
 9.1 
 
 
 9.9 
 
 101.9 
 
 13.5 
 
 235 
 
 237 
 
 12 
 
 82.13 
 
 23.6 
 
 145.3 
 
 26.4 
 
 30. 1 
 
 3.1 
 
 
 8.5 
 
 
 9.8 
 
 104.2 
 
 . ^^-s 
 
 232 
 
 235 
 
 13 CT3 . 
 
 91.20 
 
 36.1 
 
 143-7 
 
 24.7 
 
 30.2 
 
 2.6 
 
 4.7 
 
 6.4 
 
 5.4 
 
 5.9 
 
 154.2 
 
 14.4 
 
 249 
 
 244 
 
 14 °g^ 
 
 91.40 
 
 32.8 
 
 143.6 
 
 25-0 
 
 30.2 
 
 2.9 
 
 6.4 
 
 7-1 
 
 4-3 
 
 6.4 
 
 145-1 
 
 14.1 
 
 244 
 
 240 
 
 IS ^ >« > 
 
 91.82 
 
 29-3 
 
 143-2 
 
 25-2 
 
 30.5 
 
 3.0 
 
 5.6 
 
 7.6 
 
 4.9 
 
 6.1 
 
 137-0 
 
 143 
 
 246 
 
 243 
 
 16 ^-Ss 
 
 91.83 
 
 27-5 
 
 147.1 
 
 24.7 
 
 30.3 
 
 1.4 
 
 4-7 
 
 8.9 
 
 31 
 
 7.3 
 
 128.8 
 
 14.1 
 
 242 
 
 237 
 
 ^7 rt-r^£ 
 
 92.17 
 
 25-9 
 
 145.5 
 
 ^|-^ 
 
 30.4 
 
 3-2 
 
 4-5 
 
 8.2 
 
 4.7 
 
 5-7 
 
 125.8 
 
 14. 1 
 
 243 
 
 241 
 
 18 'J 
 
 92.57 
 
 21.9 
 
 143.7 
 
 26.4 
 
 30.6 
 
 3-4 
 
 6.8 
 
 7.1 
 
 4-1 
 
 7.7 
 
 120.2 
 
 14.6 
 
 256 
 290 
 
 258 
 
 <9 
 
 84.95 
 
 9-1 
 
 145.8 
 
 25.6 
 
 30.0 
 
 2.9 
 
 
 7.7 
 
 
 8.7 
 
 55-9 
 
 16.6 
 
 285 
 
 20 J. 
 
 84.03 
 
 13-9 
 
 144.5 
 
 26.4 
 
 29-9 
 
 2. 1 
 
 
 7.2 
 
 
 8.6 
 
 69-4 
 
 15.5 
 
 273 
 
 277 
 
 21 ^ ^ 
 
 83-35 
 
 15.6 
 
 144.9 
 
 25.6 
 
 29.8 
 
 2.2 
 
 
 6.8 
 
 
 8.0 
 
 72.8 
 
 15.5 
 
 273 
 
 269 
 
 22 ^-a 
 
 82.40 
 
 20.7 
 
 145-3 
 
 26.7 
 
 30.3 
 
 1.4 
 
 
 6.6 
 
 
 8.0 
 
 84.2 
 
 15-1 
 
 269 
 
 269 
 
 =^3-^2 
 
 81.40 
 
 27.3 
 
 144-2 
 
 24.7 
 
 29-7 
 
 1.3 
 
 
 7-7 
 
 
 5.6 
 
 97-4 
 
 15-2 
 
 267 
 
 261 
 
 24 ^~ 
 
 81.05 
 
 29.7 
 
 143-4 
 
 25.4 
 
 29.9 
 
 1.4 
 
 
 5.3 
 
 
 6.8 
 
 101.5 
 
 15.0 
 
 265 
 
 263 
 
 25 ■"" 
 
 80.28 
 
 34.9 
 
 143- 1 
 
 25.5 
 
 30.2 
 
 1.2 
 
 
 5.0 
 
 
 6.4 
 
 109.4 
 
 15-0 
 
 26 s 
 
 262 
 
 26 
 
 80.32 
 
 35.6 
 
 144.0 
 
 25.0 
 
 29.9 
 
 1 . 1 
 
 
 4.6 
 
 
 7-4 
 
 114.1 
 
 15-2 
 
 267 
 
 264 
 
 27 
 
 85.60 
 
 8.4 
 
 152.8 
 
 26.1 
 
 29.7 
 
 
 
 
 
 
 53-2 
 
 17.3 
 
 318 
 
 318 
 
 28 
 
 85.62 
 85.60 
 84.22 
 
 8-3 
 10.6 
 iv8 
 
 153-3 
 152-1 
 152.8 
 
 26.1 
 
 26.1 
 
 259 
 
 
 
 
 
 
 
 55-7 
 60.6 
 74-9 
 
 16.9 
 16.2 
 
 15-4 
 
 306 
 296 
 287 
 
 C508 
 
 29 
 
 29.9 
 29.8 
 
 
 
 
 
 
 297 
 
 <o 
 
 
 
 
 
 
 286 
 
 31 
 
 83 C3 
 
 21.3 
 
 152.0 
 
 26., 
 
 
 
 
 
 
 
 85-8 
 
 15. I 
 
 276 
 
 277 
 
 32 ./ 
 
 82.92 
 
 21.2 
 
 152.4 
 
 26.09 
 
 30.15 
 
 
 
 
 
 86.9 
 
 15.4 
 
 281 
 
 281 
 
 33 "S 
 
 82.55 
 83.32 
 82.67 
 81.78 
 82.92 
 81.52 
 81.57 
 81.40 
 81.50 
 
 21.0 
 24.1 
 
 29.5 
 29.1 
 28.7 
 30.7 
 31.8 
 35.6 
 33-8 
 
 1530 
 152.0 
 151-9 
 152-0 
 152. 5 
 151. 5 
 152.0 
 152-0 
 151.9 
 
 26.02 
 
 25-70 
 
 25-6 
 
 26.0 
 
 26.1 
 
 26.0 
 
 26.04 
 
 25-9 
 
 30.0 
 
 1 
 
 
 
 
 87.8 
 91.1 
 99-9 
 100.5 
 102.4 
 106.0 
 108.2 
 III. 2 
 112. 2 
 
 15-2 
 15-5 
 15-5 
 15-2 
 15-0 
 
 15-2 
 
 14-9 
 14-3 
 151 
 
 284 
 280 
 283 
 275 
 272 
 278 
 271 
 274 
 274 
 
 ?8^ 
 
 34 "i 
 
 
 
 
 
 
 ,278 
 
 35 •" 
 
 30.0 
 
 
 
 
 
 
 ?8o 
 
 37 ^ 
 
 
 
 
 
 
 273 
 
 29.9 
 29.9 
 
 
 
 
 
 
 
 38 
 
 
 
 
 
 
 278 
 
 39 
 
 
 
 
 
 
 
 40 
 
 30.1 
 30.26 
 
 
 
 
 
 
 274 
 
 41 
 
 
 
 
 
 
 i274 
 
 
 
 
 
 , 
 
 
266 
 
 ECONOMY OF STEAM-ENGINES 
 
 Table XXIV gives tests made on this engine without steam 
 in the jackets and with steam suppUed to the tubular reheaters; 
 the results of these tests will be discussed later. 
 
 Table XXIV. 
 
 TRIPLE-EXPANSION EXPERIMENTAL ENGINE AT THE MASSA- 
 CHUSETTS INSTITUTE OF TECHNOLOGY WITH TUBULAR 
 REHEATERS. 
 
 
 Condition. 
 
 I 
 
 It 
 1^ 
 
 li 
 
 la 
 
 §1. 
 
 .S-Sg 
 
 ill 
 
 n 
 
 Per cent of 
 steam used 
 in reheaters. 
 
 w 
 
 
 0^ 
 
 Hi 
 
 
 
 i 
 
 n3 
 
 
 I 
 
 Without 
 steam in 
 reheaters. 
 
 8i.8 
 8i.8 
 8i.6 
 
 8l.2 
 
 27 
 27 
 29 
 36 
 
 146.7 
 
 147-5 
 I47-0 
 148.2 
 
 26.4 
 26.1 
 25-9 
 25-9 
 
 30.6 
 30.4 
 30.5 
 30.2 
 
 
 
 88.6 
 
 87-5 
 
 89.7 
 
 103-3 
 
 16.0 
 16.0 
 16.0 
 
 15. 5 
 
 290 
 291 
 290 
 282 
 
 288 
 28 
 
 
 
 3 
 4 
 
 
 
 28 
 281 
 
 
 
 
 
 
 5 
 6 
 
 7 
 
 Steam in 
 
 first 
 reheater. 
 
 85. S 
 83.5 
 81.4 
 
 10 
 31 
 
 147-2 
 146.9 
 146. 1 
 
 25-5 
 23.8 
 25.8 
 
 30.0 
 30.2 
 30.2 
 
 
 13 
 14 
 12 
 
 66.5 
 
 84.9 
 112. 4 
 
 15-7 
 15.9 
 15.0 
 
 277 
 277 
 266 
 
 273 
 262 
 264 
 
 8 
 9 
 
 lO 
 
 II 
 
 12 
 
 Steam in 
 
 both 
 reheaters. 
 
 85.0 
 84.5 
 82.4 
 8i.9 
 82.0 
 
 8 
 10 
 21 
 27 
 28 
 
 147-3 
 146.9 
 147. 1 
 147.7 
 146.6 
 
 26.6 
 26.2 
 25.3 
 25-4 
 25-7 
 
 30.3 
 30.3 
 30.4 
 30.1 
 30.2 
 
 10 
 12 
 10 
 6 
 
 7 
 
 7 
 8 
 6 
 9 
 8 
 
 61.5 
 
 74.8 
 
 95-7 
 
 105.9 
 
 107.0 
 
 15-5 
 14.9 
 14.7 
 14.7 
 X4.5 
 
 269 
 261 
 258 
 259 
 256 
 
 274 
 260 
 252 
 254 
 254 
 
 Gain from Steam-jackets. — Much of the difference of opinion 
 concerning the advantage to be derived from the use of steam- 
 jackets is to be ascribed to indiscriminate comparison of tests 
 on various engines, or to the failure to obtain any advantage 
 from jackets which were not applied with discrimination. Should 
 any engine when properly tested and computed, show no advan- 
 tage from the use of a steam-jacket, it will be better to omit 
 that device in future constructions for the same conditions 
 unless there are constructive reasons for retaining it. 
 
 In order to obtain definite conclusions from tests made to 
 determine the advantage of the use of steam-jackets, such tests 
 should be made in definite series in which only one property is 
 varied at a time, and from these tests the best results under 
 
GAIN FROM STEAM-JACKETS 267 
 
 the most favorable conditions should be chosen when the engine 
 has steam in the jackets, and in like manner the best result 
 without steam in the jackets should be selected; a comparison 
 of two such selected tests has more weight than a haphazard 
 comparison of individual tests, however great the number of 
 such tests may be. An investigation of Delafond's tests in 
 Tables XXI and XXII and represented by Figs. 57 and 58, 
 gives such a comparison. The tests selected are those given in 
 Table X and give two pairs, with condensation and without. 
 Thus the best result with steam in the jacket and with conden- 
 sation is 16.9 pounds, and without steam in the jacket is 18. i; 
 the gain is 
 
 18. 1 — 16. Q 
 
 =0.07. 
 
 18. I ' 
 
 Without condensation the best results are 21.5 with steam in 
 the jackets and 24.2 without steam in the jackets; the gain is 
 
 24.2 — 2\X 
 
 -^ -^ = O.I I. 
 
 24.2 
 
 These results are probably too small, as the steam used in the 
 jackets should be collected and returned to the boiler with only 
 a moderate reduction of temperature below the temperature of 
 the steam in the boiler. The drip from the jackets was passed 
 through a trap, and as reported is probably too small, this being 
 the most questionable result from the tests. 
 
 Data for a similar comparison for compound engines are not 
 at hand, but the tests described on page 265 seem to be conclusive 
 for the triple engine. 
 
 From the diagram Fig. 59 the best results with steam in all 
 the jackets of the cylinders and without steam in, any of the 
 jackets are 233 and 274 b.t.u. per horse-power per minute, and 
 the gain from the use of the steam in the jacket is 
 
 274 — 2'\'\ 
 
 -^ "^^ X 100 = IS per cent. 
 
 274 
 
268 ECONOMY OF STEAM-ENGINES 
 
 These heat-consumptions correspond to 13.8 and 15.2 pounds 
 of steam per horse-power per hour, so that on the basis of steam- 
 consumption the gain from the use of steam in the jackets would 
 appear to be only 9 per cent, instead of the actual gain of 15 per 
 cent. This large difiference is due to the large percentage of 
 steam used in the jackets, amounting in all to 17 or 18 per cent 
 of the total steam-consumption. The steam used in an indi- 
 vidual jacket is, however, not excessive, being about 2.5 per cent 
 in the jackets of the high- pressure cylinder and 7 or 8 per cent in 
 the jackets of each of the other two cylinders. 
 
 The effect of jacketing the heads of the cylinders only is 
 surprisingly small, as from the diagram the best result is 262 
 B.T.u. per ^horse-power per minute, which compared with the 
 best result without steam in any of the jackets gives a gain of 
 only 
 
 274 — 262 
 
 ~ X 100 = 4 per cent. 
 
 274 
 
 The correspondence between this result and the experiments by 
 Callendar and Nicolson on the action of the cylinder walls, 
 has already been pointed out. 
 
 From the tests just discussed and compared it appears con- 
 servative to say that about ten per cent can be gained by using 
 steam-jackets on simple and compound engines and that fifteen 
 per cent can be gained by their use on triple-expansion engines; 
 provided that these conclusions shall not be applied to engines of 
 more than 300 horse-power. The saving on massive engines 
 of 1000 horse-power or more is likely to be smaller, and very 
 large engines may derive no benefit from steam-jackets. On 
 the other hand, a saving of 25 per cent may be obtained from 
 jackets on small engines of five or ten horse-power. Such trivial 
 engines are never provided with jackets unless for experimental 
 purposes, and the results of such experiments are of little value. 
 
 Intermediate Reheaters. — Many compound and triple- 
 expansion engines have some method of reheating the steam 
 on its way from one cylinder to another. Notable examples 
 
INTERMEDIATE REHEATERS 269 
 
 are the Leavitt pumping-engines, for which results are given in 
 Table X. The fact that these engines give the best economies 
 recorded for engines using saturated steam lead to the inference 
 that such reheaters may be used to advantage. The only direct 
 evidence, however, is not so favorable, for, as has been pointed 
 out on page 264, there was found a small but distinct disadvantage 
 from using steam in double walls or jackets on the intermediate 
 receivers of the experimental engine at the Massachusetts Institute 
 of Technology. It appears that this engine gives the best 
 economy when steam is supplied to the jackets on the cylinders 
 and not to the jackets on the reheaters, and, further, that when 
 steam is used in the receiver-jackets the steam in the low- 
 pressure cylinder shows signs of superheating, which may be 
 considered to indicate that the use of the steam-jacket is carried 
 too far. 
 
 After the tests referred to were finished the engine was fur- 
 nished with reheaters made of corrugated-copper tubing, so 
 arranged that one-third, two-thirds, or all of the reheating-surface 
 can be used, when desired. Table XXIV, page 266, gives the 
 results of tests made on the engine with and without steam in 
 the reheaters; in these tests the entire reheating-surface was used 
 when steam was supplied to a reheater. 
 
 For some reason the heat-consumption when no steam was 
 used in the reheaters is somewhat greater than that given in 
 Table XXIV for the engine without steam in any of the 
 jackets; the difference, however, is not more than two or two 
 and a half per cent and cannot be considered of much importance. 
 It is clear from the table that there is advantage from using one 
 reheater, and still more from using two. If the heat-consumption 
 for the engine without steam in the jackets and without steam 
 in the reheaters (taken from Table XXIV) is assumed to be 
 274 B.T.u. per minute, then the gain from using the reheaters 
 appears to be 
 
 274 — 2^2 „ 
 
 -^-^ ^— X 100 == 8 per cent, 
 
 274 
 
270 ECONOMY OF STEAM-ENGINES 
 
 which is scarcely more than half the gain from using steam in 
 the jackets. These tests cannot be considered conclusive, as 
 they are too few and refer only to one engine. 
 
 Superheating. — The most direct and effective way of reducing 
 the interference of the cylinder walls and of improving steam- 
 engine economy is by the use of superheated steam. About 
 1863-64 a number of naval vessels were supplied with super- 
 heaters by Chief Engineer Isherwood, and when tested by him 
 showed a marked advantage which led to the adoption of super- 
 heated steam for stationary and marine practice both in America 
 and in Europe. But the superheaters which were exposed to 
 dry steam on one side and to the flue gases on the other, rapidly 
 deteriorated, and after an experience lasting ten or fifteen years 
 the use of superheated steam was abandoned in favor of com- 
 pound and triple engines with high-pressure steam. 
 
 More recently improved forms of superheaters have been 
 introduced in Great Britain and Germany, which show good 
 endurance, and superheated steam appears to have been used 
 successfully for sufficient times to warrant the conclusion that 
 the application of superheated steam has been accomplished. 
 Two series of tests will be discussed, namely, some early tests 
 on a simple engine, and some recent tests on compound engines. 
 There appears to be no reason for extending the application of 
 superheated steam to triple engines. 
 
 Dixwell's Tests. — A small Harris- Corliss engine was fitted 
 up for making tests on superheated steam at the Massachusetts 
 Institute of Technology by Mr. George B. Dixwell. Six tests 
 with superheated and saturated steam were made on this engine 
 in 1877 in the presence of a board of engineers of the United 
 States Navy. 
 
DIX WELL'S TESTS 
 
 271 
 
 Table XXV. 
 
 DIXWELL'S TESTS ON SUPERHEATED STEAM. 
 
 CYLINDER DIAMETER 8 INCHES; STROKE 2 FEET. 
 
 Proceedings 0} the Society of Arts, Mass. Inst. Tech., 1887-88. 
 
 Diiration, minutes 
 
 Cut-off 
 
 Revolutions per minute 
 
 Boiler-pressure above atmosphere, pounds 
 
 per square inch 
 
 Back-pressure, absolute, pounds per sq. in 
 Temperatures Fahrenheit: 
 
 Near engine 
 
 In cylinder by pyrometer 
 
 Per cent of water in cvlinder : 
 
 At cut-off 
 
 At end of stroke 
 
 Horse-power 
 
 Steam per horse-power per hour, poimds, 
 B.T.U. per horse- power per minute. . . 
 
 Saturated Steam. 
 
 Superheated St 
 
 I 
 
 II 
 
 III 
 
 IV 
 
 V 
 
 127 
 
 83 
 
 63 
 
 180 
 
 108 
 
 0.217 
 
 0.443 
 
 0.689 
 
 0.218 
 
 0.439 
 
 61. s 
 
 60.4 
 
 58.0 
 
 61 .0 
 
 61.4 
 
 50.4 
 
 SO. 2 
 
 50.3 
 
 50.4 
 
 50.0 
 
 15-4 
 
 15-7 
 
 15.8 
 
 15-2 
 
 15-4 
 
 302 
 
 303 
 
 303 
 
 478 
 
 441 
 
 278-297 
 
 279-296 
 
 282—300 
 
 313 
 
 316 
 
 52. 2 
 
 35-9 
 
 27.9 
 
 27.4 
 
 13-6 
 
 32.4 
 
 293 
 
 23-9 
 
 18.3 
 
 13.6 
 
 7.65 
 
 12.7 
 
 15.68 
 
 6.83 
 
 12.37 
 
 48.2 
 
 42.2 
 
 45-3 
 
 35-2 
 
 31-7 
 
 796 
 
 696 
 
 747 
 
 631 
 
 546 
 
 VI 
 
 75 
 0.672 
 59-5 
 
 SO. 2 
 15-5 
 
 406 
 315 
 
 8.9 
 
 II. 5 
 
 15-63 
 
 35-8 
 
 621 
 
 A metallic thermometer or pyrometer was placed in a recess 
 in the head of the cylinder. When saturated steam was used 
 this pyrometer showed a large fluctuation, but when superheated 
 steam was used its needle or indicator was at rest. Even if a 
 part of the apparent change of temperature with saturated steam 
 is attributed to the vibration of the needle and the multiplying 
 mechanism, it is very clear that the use of superheated steam 
 reduces the change of temperature of the cylinder-head in a 
 remarkable manner. The effect of superheating on the action 
 of the cylinder walls is also indicated by the per cent of water 
 in the cylinder at cut-off and release. 
 
 The apparent gain by comparing the amounts of steam used 
 per horse-power per hour in favor of superheated steam is but 
 
 42.2 - 31.7 
 42.2 
 
 X 100 = 25 per cent; 
 
 this result is of course misleading, since the superheating required 
 additional coal. As the coal-consumption was not determined, 
 
272 ECONOMY OF STEAM-ENGINES 
 
 we must compare instead the b.t.u. per horse-power per minute, 
 giving a real gain of 
 
 696 — 546 ^^ 
 
 -^ — — ~ — X 100 =19 per cent. 
 696 
 
 This same Harris- Corliss engine afterwards showed a heat- 
 consumption of 548 B.T.U. per horse-power per minute when 
 supplied with saturated steam at 77 pounds pressure, which shows 
 why the earlier attempts at the use of superheated steam were 
 so easily set aside when it was found expedient to raise the steam- 
 pressure. 
 
 Though we have no tests with high-pressure steam and with 
 condensation on engines of two or three hundred horse- power, 
 it is probable that a very material saving could be made by the 
 use of superheated steam under such conditions ; if the saving in 
 heat were as much as fifteen per cent, it would reduce the steam- 
 consumption to a larger degree, perhaps by twenty per cent, 
 and would be likely to give from 14.5 to 15 pounds of superheated 
 steam per horse-power per hour. 
 
 The best results obtained from the application of superheated 
 steam in compound engines are reported by Professor Schroter, 
 in Table XXVI, for a tandem-engine with poppet-valves 
 built in Ghent. Five tests were made with varying cut-off and 
 with saturated steam, and five others also with varying cut-off 
 and with steam that was superheated about 250° F., the absolute 
 initial pressure in the cylinder being about 145 pounds, so that 
 the boiler- pressure was probably between 130 and 135 pounds by 
 the gauge. 
 
 This engine gave a remarkable economy both with saturated 
 steam and with superheated steam, its steam and heat-consump- 
 tion being only five per cent more than that of the triple-expansion 
 Leavitt engine recorded in Table X. The gain from using 
 superheated steam appears to be 
 
 213 - 199 
 
 ^^— o.oO, 
 
 213 
 
SCHROTER TESTS 
 
 273 
 
 which places it a little beyond the performance of the triple 
 engine mentioned. But since the uncertainty of the determina- 
 tion of power by the indicator is probably two per cent, we may 
 reasonably conclude that the effect of using superheated steam 
 in a compound engine is to place it on a level with a triple 
 engine, and the question is to be decided in practice by the 
 relative expense and trouble of supplying and using a superheater 
 instead of a third cylinder and higher steam-pressure. 
 
 It is somewhat remarkable that steam was supplied to the 
 jackets during the superheating tests, but not at all surpris- 
 ing that for those tests the jackets had a small effect, as is 
 made evident by noting the percentages of steam condensed in 
 them. 
 
 Table XXVI. 
 
 COMPOUND HORIZONTAL MILL-ENGINE. 
 
 CYLINDER DIAMETERS 12.8 AND 22 INCHES; STROKE 33.5 INCHES. 
 
 By Professor M. Schroter, Mitleilungen iiher Forschungsarheiten, 
 Heft 19, 1904. 
 
 Horse-power 
 
 Duration, minutes 
 
 Revolutions per minute . . 
 Cut-off, high-pressure cylinder 
 
 Total expansions 
 
 Initial pressure, absolute pounds per 
 
 so. in 
 Back-pressure, absolute pounds per 
 
 sq . in 
 
 Superheating, degrees F 
 
 Steam per horse-power per hour, 
 
 pounds 
 
 Per cent condensed in jackets . 
 B.T.U. per horse-power per min. 
 Mechanical efficiency .... 
 
 Saturated . 
 
 299 
 
 60 
 
 126 
 
 0.38 
 
 7-9 
 
 148 
 
 13-6 
 
 10.9 
 
 246 
 
 >.90i 
 
 II III IV V 
 
 263 
 
 61 
 
 126 
 
 0.31 
 
 9-7 
 
 146 
 
 12.8 
 
 II. 8 
 
 232 
 
 ).89i 
 
 211 
 
 57-5 
 
 126.5 
 
 0.22 
 
 13-5 
 
 147 
 
 12.3 
 
 12.9 
 
 222 
 
 ).872 
 
 160 
 55 
 
 127 
 
 0.15 
 
 20 
 
 13-7 
 
 213 
 
 3.842 
 
 50 
 
 128 
 
 o.io 
 
 30 
 
 14.4 
 
 216 
 
 ).786 
 
 Superheated. 
 
 VI VII VIII IX X 
 
 303 
 
 48 
 
 126 
 
 0.41 
 
 7-3 
 
 T48 
 
 1-3 
 246 
 
 10.9 
 
 2.1 
 
 223 
 
 3.902 
 
 258 
 
 60 
 
 126 
 
 0.33 
 
 9.1 
 
 149 
 
 i.o 
 
 257 
 
 3-5 
 
 215 
 
 0.890 
 
 112 
 
 51 
 
 126. 5 
 
 0.26 
 
 ii-S 
 
 149 
 
 1. 1 
 258 
 
 3» 
 
 206 
 
 0.872 
 
 161 
 64- 5 
 
 127 
 o. 16 
 18.7 
 
 146 
 
 256 
 
 9-7 
 4.4 
 201 
 .842 
 
 o. 10 
 
 30 
 
 .46 
 
 256 
 
 9.6' 
 
 4.6 
 
 199 
 
 0.790 
 
 Cut-off and Expansion. — It has already been pointed out on 
 page 256 in connection with Delafond's tests that the best point 
 of cut-off for a simple engine, whether jacketed or not, is about 
 
274 ECONOMY OF STEAM-ENGINES 
 
 one-third stroke when the engine is non-condensing, and it is 
 about one-sixth stroke when condensing. In general, other 
 tests on simple engines such as those on the Gallatin, and on 
 the small Corliss engine at the Massachusetts Institute of 
 Technology, confirm these conclusions. 
 
 The term total expansion for a compound or a triple engine 
 can properly have only a conventional significance; it is usually 
 taken to be the product of the ratio of the large to the small 
 cylinder by the reciprocal of the fraction of the stroke at cut-off 
 for the high-pressure cylinder. This conventional total expan- 
 sion is about 20 for all the tests on triple engines quoted in Table 
 X, except those on marine engines, w^hich show a relatively 
 poor economy. It may therefore be concluded that it is not 
 advisable to use much more expansion for any triple engine, 
 and that less expansion should be used only when the condi- 
 tions of service (for example, at sea) prevent the use of large 
 expansion. 
 
 The stationary compound engines given in Table X also 
 have about 20 expansions, and experience shows conclusively 
 that highest economy for such a degree of expansion is re- 
 quired. In practice somewhat less may frequently be found 
 advisable. 
 
 Variation of Load. — In general, an engine should be so 
 designed that it may give a fair economy for a considerable 
 range of load or power. Very commonly the engine will have 
 sufficient range of power with good economy if designed to give 
 the best economy at the normal load. In general, however, 
 it is well to assign a less expansion and consequently a longer 
 cut-off to the engine than would be determined from a con- 
 sideration of the steam- (or heat-) consumption alone. For, 
 in the first place, the best brake or dynamic economy is always 
 attained for a little longer cut-off than that which gives the 
 best indicated economy, and in the second place the economy 
 is less affected by lengthening than by shortening the cut-off. 
 The first comes from the fact that the frictional losses of the 
 engine increase less rapidly than the power, as will be shown 
 
VARIATION OF LOAD 
 
 275 
 
 in the next chapter; and the second is evident from consideration 
 of curves of steam-consumption as given by Fig. 59, page 262, 
 and Figs. 57 and 58, pages 252-253. 
 
 The allowable range of power for a simple engine is greater 
 than for a compound or a triple engine. Comparisons for a 
 simple and a triple engine may be made by aid of Figs. 58 and 
 59. The Corliss engine at Creusot when supplied with steam 
 at 60 pounds pressure, with condensation and with steam in 
 the jacket, developed 150 horse-power and used 17.3 pounds 
 of steam per horse-power per hour. If the increase be limited 
 to 10 per cent of the best economy, that is, to 19 pounds per 
 horse-power per hour, the horse-power may be reduced to about 
 92, giving a reduction of nearly 40 per cent from the normal 
 power. The triple engine at the Massachusetts Institute of 
 Technology with steam at 150 pounds pressure and using steam 
 in all the cylinder- jackets developed 140 horse-power and used 
 233 B.T.u. per horse-power per minute. Again, limiting the 
 increased consumption to ic per cent or to 254 b.t.u., the power 
 may be reduced to about 104 horse-power, giving a reduction of 
 26 per cent from the normal power. The effect of increasing 
 power for these engines cannot be well shown from the tests 
 made on them, but there is reason to believe that the simple 
 engine would preserve its advantage if a comparison could be 
 made. Though the tests which we have on compound engines 
 do not allow us to make a similar investigation of the effect of 
 changing load, there is no doubt that it is intermediate in this 
 respect between the simple and the triple engine. 
 
 When the power developed by a compound engine is reduced 
 by shortening the cut-off of the high-pressure cylinder, the cut-off 
 of the low-pressure cylinder must be shortened at the same time 
 to preserve a proper distribution of power and division of the 
 range of temperature between the cylinders. If this is not done 
 the work will be developed mainly in the high-pressure cylinder, 
 which will be subjected to a large fluctuation of temperature, 
 and the engine will lose the advantages sought from compounding. 
 A compound non-condensing engine, if the cut-off for the large 
 
276 ECONOMY OF STEAM-ENGINES 
 
 cylinder is fixed, is likely to have a loop on the low-pressure 
 indicator-diagram due to expansion below the atmosphere, if 
 the power is reduced by shortening the cut-off of the high-pressure 
 cylinder. Such a loop is always accompanied by a large loss of 
 economy; if the loop is large the engine may be more wasteful 
 than a simple engine, for the high-pressure piston develops 
 nearly all the power and may have to drag the low-pressure 
 piston, which is then worse than useless. 
 
 There is seldom much difficulty in running a simple engine at 
 any desired reduced power by shortening the cut-off or reducing 
 the steam-pressure, or by a combination of the two methods. 
 But a compound engine sometimes gives trouble when run at 
 very low power (even when attention is given to the cut-off of 
 the low-pressure cylinder), which usually takes the form just 
 discussed ; i.e., the power is developed mainly in the high- pressure 
 cylinder. Triple engines are even more troublesome in this 
 way. A compound or triple engine running at much reduced 
 power is subject not only to loss of economy and to irregular 
 action, but the inside surface of the low-pressure cylinder is 
 liable to be cut or abraded. 
 
 Automatic and Throttle Engines. — The power of an engine 
 may be regulated by (i) controlling the steam- pressure, or (2) 
 by adjusting the cut-off. Usually these two methods are used 
 separately, but in some instances they are used in combination. 
 Thus a locomotive-driver may reduce the power of his engine 
 either by shortening the cut-off or by partially closing the throttle- 
 valve, or he may do both at once. Stationary engines are usually 
 run at a fixed speed and are controlled by mechanical governors, 
 which commonly consist of revolving weights that are urged 
 away from the axis of revolution by centrifugal force and are 
 restrained by the attraction of gravity or by the tension of 
 springs. 
 
 The earliest and simplest steam-engine governor, invented by 
 Watt, has a pair of revolving pendulums (balls on the ends of 
 rods that are hinged to a vertical spindle at their upper ends) 
 which arc urged out by centrifugal force and are drawn down 
 
AUTOMATIC AND THROTTLE ENGINES 
 
 277 
 
 by gravity. When the engine is running steadily at a given 
 speed the forces acting on the governor are in equiUbrium and 
 the balls revolve in a certain horizontal plane. If the load on 
 the engine is reduced the engine speeds up and the balls move 
 outward and upward until a new position of equilibrium is 
 found with the balls revolving in a higher horizontal plane. 
 Through a proper system of links and levers the upward motion 
 of the balls is made to partially close a throttle- valve in the pipe 
 which supplies steam to the engine and thus adjusts the work of 
 the engine to the load. 
 
 Shaft-governors have large revolving- weights whose centrifugal 
 forces are balanced by strong springs. They are powerful 
 enough to control the distribution or the cut-off valve of the 
 engine, which, however, must be balanced so that it may move 
 easily. 
 
 Automatic engines, like the Corliss engines, have four valves, 
 two for admission and two for exhaust of steam. The admission, 
 release, and compression are fixed, but the cut-off is controlled 
 by the governor. Usually an admission- valve is attached to the 
 actuating mechanism by a latch or similar device, which can be 
 opened by the governor, and then the valve is closed by gravity 
 by a spring, or by some other independent device. The office 
 of the governor is to control the position of a stop against 
 which the latch strikes and by which it is opened to release the 
 valve. 
 
 Corliss and other automatic engines have long had a deserved 
 reputation for economy, which is commonly attributed to their 
 method of regulation. It is true that the valve-gears of such 
 engines are adapted to give an early cut-off, which is one of the 
 elements of the design of an economical simple engine, but their 
 advantage over some other engines is to be largely attributed 
 to the small clearance which the use of four valves makes con- 
 venient, and to the fact that the exhaust-steam is led immediately 
 away from the engine, without having a chance to abstract heat 
 after it leaves the cylinder. These engines also are free from 
 the loss which Callendar and Nicolson attribute to direct leakage 
 
278 ECONOMY OF STEAM-ENGINES 
 
 from the steam to the exhaust side of slide-valves, and to valves 
 of similar construction. 
 
 Every steam-engine should have a reserve of power in excess 
 of its normal power; and again it is convenient if not essential 
 that a single-cylinder engine should be able to carry steam 
 through the greater part of its stroke in starting. These condi- 
 tions, together with the fact that it is somewhat difficult to design 
 a plain slide-valve engine to give an early cut-off, have led to the 
 use of a long cut-off for engines controlled by a throttle-governor. 
 The tests on the Corliss engine at Creusot (Tables XXI and 
 XXII, pp. 250 and 251) show clearly the disadvantage of using 
 a long cut-off for simple engines. It has already been pointed 
 out that a non-condensing engine should have the cut-off at 
 about one-third stroke. With cut-off at that point and with 75 
 pounds steam- pressure the engine developed 209 horse-power 
 and used 24.2 pounds of steam per horse-power per hour when 
 running without steam in the jacket and without condensation.- 
 If the steam-pressure is reduced to 50 pounds and the cut-off is 
 lengthened to 58 per cent of the stroke, the steam-consumption 
 is increased to 30.2 pounds per horse-power per hour, the horse- 
 power being then 173. The gain from using the shorter cut- 
 off is 
 
 ^0.2 — 24.2 ^, ^ . 
 
 X 100 = 20 per cent. 
 
 30.2 
 
 A similar comparison for the same engine running with a 
 vacuum and with steam in the jacket shows even a larger differ- 
 ence. Thus in test 16 the steam- pressure is 84 pounds and the 
 cut-off is at 1 1.5 per cent of the stroke, the horse-power is 176, 
 and the steam-consumption per horse-power per hour is 16.9 
 pounds, while the consumption for about the same power in test 
 44 is 25.4 pounds of steam per horse-power per hour, the steam- 
 pressure being 35 and the cut-off at 58 per cent of the stroke; 
 here the gain from using the shorter cut-off is 
 
 21^.4 — 16.0 ^^ 
 
 -"^-^ X 100 = 33 per cent. 
 
 25.4 
 
EFFECT OF SPEED OF REVOLUTION 279 
 
 Considering also that automatic engines are usually well 
 built and carefully attended to, while throttling-engines are 
 often cheaply built and neglected, the good reputation of 
 the one and the bad reputation of the other are easily ac- 
 counted for. 
 
 It is, however, far from certain that an automatic engine will 
 have a decided advantage over a throttle-engine, provided the 
 latter is skilfully designed, well built and cared for, and arranged 
 to run at the proper cut-off. Considering the rapid increase in 
 steam-consumption per horse-power per hour when the cut-off 
 is unduly shortened, it is not unreasonable to expect as good if 
 not better results from a simple throttling-engine than from an 
 automatic engine when both are run for a large part of the time 
 at reduced power. 
 
 The disadvantage of running a compound or a triple engine 
 with too little expansion can be seen by comparing the steam- 
 consumptions of marine and stationary engines; on the other 
 hand, the great disadvantage of too much expansion is made 
 evident from the tests on the engine in the laboratory of the 
 Massachusetts Institute of Technology (Table XXIII, page 
 265). Considering that the allowable variation from the most 
 economical cut-off is more limited for a compound or a triple 
 engine, it appears that there is less reason for using an automatic 
 governor instead of a throttling governor for compound and 
 triple engines than there is with simple engines. Nevertheless 
 the most economical engines (simple, compound, or triple) are 
 automatic engines. 
 
 Effect of Speed of Revolution. — Though the condensation of 
 steam on the walls of the cylinder of a steam-engine is very 
 rapid, it is not instantaneous. It would therefore appear that 
 an improvement in economy might be attained by increasing the 
 number of revolutions per minute; but whatever might be thus 
 gained is more than offset by the increase of the dimensions of 
 valves, passages, and clearances that would accompany such a 
 change in speed, for it has already been pointed out that the evil 
 of initial condensation is much aggravated by increasing the 
 
28o - ECONOMY OF STEAM-ENGINES 
 
 surfaces exposed to steam in clearance spaces. As a matter of 
 fact, all engines which for various reasons have been designed 
 to run at very high rotative speeds have shown relatively poor 
 economy, in part from the reason given, and in part from the 
 fact that piston- valves are commonly used, and they are subject 
 to the kind of leakage described by Callendar and Nicolson on 
 page 234, even when they are in good condition. Very com- 
 monly the engine has a fly-wheel governor, which requires the 
 valve to be very free with the chance of excessive leakage. Mr. 
 Willans invented a single-acting triple-expansion engine to run 
 at high rotative speed, and succeeded in getting abundant steam- 
 passages without excessive clearances by using a hollow piston- 
 rod to carry the steam from cylinder to cylinder, all arranged 
 tandem. Tests on this engine (which are not quoted elsewhere 
 in this book) showed that an increase from 100 revolutions to 
 200 revolutions per minute reduced the steam-consumption 
 from 24.7 to 23.1 pounds per horse-power per hour, and a 
 further increase of speed to 400 revolutions gave a reduction 
 to 21.4 pounds; the engine was then running compound non- 
 condensing. This engine used 12.7 pounds of steam per horse- 
 power per hour, when developing 30 horse-power, at 380 revo- 
 lutions per minute under 170 pounds gauge-pressure, acting as 
 a triple-expansion condensing engine. 
 
 Binary Engine. — On page 180, under the subject '' Compound 
 Engines," attention was called to the possibility of extending the 
 range of temperature for vapor-engines by the use of two fluids; 
 the second fluid (for example, sulphur dioxide) being chosen so 
 that a good working back-pressure could be maintained at the 
 temperature of the available condensing water which acts as 
 the refrigerator for the combined engines. Considering only 
 the efficiency of Carnot's cycle for the customary range of 
 temperature for a steam-engine, and the efficiency for the 
 extended range, it appeared that a gain of 26 per cent might 
 be possible. 
 
 Recent investigations by Professor Josse on an experimental 
 engine in the laboratory of the Technical High School at Char- 
 
BINARY ENGINE 281 
 
 lottenburg give some insight into the possibilities of this method. 
 The engine is of moderate size, developing about 150 horse-power 
 as a steam-engine, and about 200 horse-power as a binary engine, 
 using steam at about 160 pounds by the gauge with 200° F., 
 superheating. The engine is a three-cylinder triple- expansion 
 engine, but can be run also as a compound engine, though it 
 probably is not proportioned to give the best economy under the 
 latter condition. 
 
 The general arrangement of the engine is as follows : the three 
 steam-cylinders are arranged horizontally side by side, and the 
 additional cylinder using the volatile fluid (sulphur dioxide) lies 
 on the opposite side of the crank-shaft, to which it is connected by 
 its own crank and connecting-rod. Steam is supplied from the 
 boiler and superheater to the steam-engine, and is exhausted 
 into a tubular condenser which acts as the sulphur dioxide 
 vaporizes ; the condensed steam is pumped back into the boiler, 
 and the vacuum is maintained by an air-pump as usual; a vacuum 
 of 20 to 25 inches of mercury was maintained in this condenser. 
 The vaporous sulphur dioxide at a pressure of 120 to 180 pounds 
 by the gauge was led to the proper cylinder, from which it was 
 exhausted at about 35 pounds by the gauge; this exhaust was 
 condensed in a tubular condenser by circulating water with a 
 temperature of about 50° F. at the inlet and about 65° F. at 
 the exit. 
 
 The drips from the steam-jackets of the steam-cylinders were 
 piped to the steam-condenser instead of being returned to the 
 boiler, but that cannot be of much importance because the 
 condensation in the jackets was probably less than five per cent 
 of the total steam supplied to the engine. The performance of 
 the engine is given in Table XXVIII in terms of steam per 
 horse-power per hour and in thermal units per horse-power per 
 minute; the latter I have calculated from the total heat of the 
 steam including the superheat, and the heat of the liquid at 
 the vacuum in the steam-condenser. Comparisons must be 
 made in terms of thermal units in order to take account of 
 the superheating. 
 
282 
 
 ECONOMY OF STEAM-ENGINES 
 
 Table XXVII . 
 
 BINARY ENGINE, STEAM AND SULPHUR DIOXIDE. 
 By Professor E. JosSE, Royal Technical High School, Charlottenburg. 
 
 Revolutions per minute . . . , 
 
 Steam-Engine: 
 
 Pressure at inlet, h.p. cylinder 
 
 by gauge pounds 
 
 Vacuum, inches of mercury . . . 
 Superheating, degrees Fahrenheit 
 
 Horse-power, indicated 
 
 Steam p^r h.p. per hour, pounds . 
 Thermal units per h.p. per minute 
 Sulphur- Dioxide Engine : 
 
 Pressure by gauge poimds: . . . 
 
 In vaporizer 
 
 In condenser 
 
 Temperature Fahr. at inlet to cyl- 
 inder 
 
 Temperature Fahr. at outlet from 
 
 condenser 
 
 of circulating water inlet . . . 
 outlet . . . 
 
 Horse-power, indicated 
 
 per cent of steam-engine power 
 Combined Engine: 
 
 Horse-power, indicated 
 
 Steam per h.p. per hour, pounds . 
 Thermal units per h.p. per minute 
 Mechanical eflSciency 
 
 Triple Expansion. 
 
 39.6 
 
 136.5 
 
 23 -9 
 
 17s 
 
 132. 1 
 
 12.5 
 
 244 
 
 132 
 31 
 
 132.0 
 
 66.2 
 49-6 
 59-9 
 
 45-3 
 34-4 
 
 177-4 
 
 9-7 
 
 183 
 
 85.5 
 
 136.3 
 
 156.5 
 
 24.1 
 
 219 
 
 125.2 
 
 II. 2 
 
 223 
 
 128 
 34 
 
 133-7 
 
 65.8 
 49.9 
 60.2 
 42.8 
 34-2 
 
 168 
 8.36 
 
 167 
 86.2 
 
 143 5 
 
 158 
 20.9 
 
 221 
 
 154-2 
 
 12.2 
 
 240 
 
 172 
 35 
 
 151. 7 
 
 67.6 
 49-9 
 62.4 
 56.8 
 37-0 
 
 211 
 8.92 
 
 176 
 83.8 
 
 137-4 
 
 156.5 
 
 25-4 
 
 214 
 
 101.6 
 
 14.4 
 
 289 
 
 III 
 31 
 
 123-7 
 
 64.4 
 50.2 
 60.2 
 31.0 
 30.3 
 
 132.6 
 
 11.05 
 
 215 
 
 87.5 
 
 145 
 
 156.5 
 
 23.8 
 
 210 
 
 145-3 
 
 13-6 
 
 270 
 
 142 
 36 
 
 137-3 
 
 68.5 
 50.2 
 63.8 
 50.1 
 34-5 
 
 195-4 
 
 10. 12 
 
 200 
 
 89.1 
 
 156-5 
 
 20.6 
 
 210 
 
 144-5 
 
 13-8 
 
 270 
 
 36 
 157. 1 
 
 67.6 
 50.2 
 63.8 
 57.6 
 40.0 
 
 202. 1 
 
 9.86 
 
 193 
 
 87 
 
 148 
 
 156.5 
 
 20.5 
 
 221 
 
 161. o 
 
 13.2 
 
 261 
 
 186 
 36 
 
 155- 1 
 
 68.0 
 50.2 
 63-4 
 61.3 
 37-9 
 
 223.2 
 
 9-55 
 
 189 
 
 90.8 
 
 149 
 
 165.3 
 20.4 
 
 156-3 
 
 16.4 
 
 283 
 
 181 
 38 
 
 IS3-S 
 
 70.0 
 50.2 
 65.1 
 , 66.0 
 42.1 
 
 222.3 
 
 ii-S 
 
 205 
 
 90. s 
 
 Com- 
 pound. 
 
 137 
 
 165-3 
 
 21.8 
 
 257 
 
 121. 8 
 
 13-5 
 
 271 
 
 178 
 33 
 
 152-8 
 
 64.6 
 50.2 
 61.2 
 48.0 
 39-4 
 
 169.8 
 
 9-7 
 
 195 
 
 89-8 
 
 148 
 
 163.7 
 
 20.7 
 
 247 
 
 140.5 
 
 13-4 
 
 266 
 
 183 
 35 
 
 155.4 
 
 66.0 
 50.2 
 63-3 
 55.6 
 39.5 
 
 196. 1 
 
 9.6 
 
 191 
 
 92 
 
 Before comparing the results of these tests to determine the 
 gain from working binary, it is interesting to see that the increased 
 range of temperature in this case appears to give a possible 
 advantage of 9 per cent. Thus, if the engine working as a 
 steam-engine only had a vacuum of 27 inches so that the lower 
 temperature was about 115° F., the efficiency of Carnot's cycle 
 would be 
 
 r - r 
 
 575 - 115 
 575 + 460 
 
 c^o, 
 
 in which 575 is the temperature of the superheated steam supplied 
 to the engine. On the other hand, with a back-pressure of 
 
BINARY ENGINE 283 
 
 about 35 pounds in the sulphur-dioxide cylinder and a tempera- 
 ture of about 65° F., the efficiency would be 
 
 T - T' 575 - 65 ' 
 
 T . 575 + 460 ^^ 
 
 - 0.55 - 0.50 
 
 and —"^ '^— ^ 0.00. 
 
 . 0-55 
 
 The results of the tests given in Table XXVIII are somewhat 
 difficult to use as a basis for the discussion of the advantage of 
 the binary system on account of certain discrepancies ; for example, 
 tests No. 3 and No. 7 have substantially the same total power, 
 steam-pressure, superheating and vacuum, and nearly the same 
 vapor- pressures in the sulphur-dioxide cylinder; in fact, the 
 advantage appears to lie slightly in favor of No. 7 ; nevertheless, 
 the latter test is charged with 189 thermal units per horse-power 
 per minute, and the former with 176, giving to it an apparent 
 advantage of about 7 per cent. A comparison of steam per 
 horse-power per hour gives nearly the same result. A com- 
 parison of tests No. 2 and No. 4 gives even a more striking 
 discrepancy, though the conditions vary more, and especially 
 the total power of the latter is much greater. 
 
 If we take 200 thermal units per horse-power per hour as the 
 best result from a steam-engine, then the result from the second 
 test appears to show a gain of 16 per cent, while the seventh 
 test shows a gain of 6 per cent, and the fourth test is distinctly 
 worse than the standard taken for the steam-engine. Under 
 these conditions it is necessary to await further information. 
 
 The last two tests made with the engine running compound 
 gave results that are a trifle better than those for the compound 
 engine using superheated steam but as it probably had not 
 the most favorable proportions the comparison is hardly fair. 
 
 Test No. 8 with saturated steam gave a record equivalent to 
 that of the best steam-engine, which is distinctly favorable so 
 far as it goes, as the steam-consumption for the steam-engine is 
 large even making allowance for so poor a vacuum. 
 
284 ECONOMY OF STEAM-ENGINES 
 
 Finally it appears probable that the best results for the 
 binary engine could be obtained from a correctly designed 
 compound engine, using superheated steam; or nearly as 
 good results might be expected for saturated steam at about 
 175 pounds gauge pressure with steam-jackets. Attention has 
 already been called to the fact that steam-jackets accomplish 
 but little with highly superheated steam, and appear to be 
 unnecessary and illogical. 
 
CHAPTER XIII. 
 
 FRICTION OF ENGINES. 
 
 The efficiency and economy of steam-engines are commonly 
 based on the indicated horse-power, because that power is a 
 definite quantity that may be readily determined. On the 
 other hand, it is usually difficult and sometimes impossible to 
 make a satisfactory determination of the power actually delivered 
 by the engine. A common way of determining the work con- 
 sumed by friction in the engine itself is to disconnect the driving- 
 belt, or other gear for transmitting power from the engine, and 
 to place a friction-brake on the main shaft; the power developed 
 is then determined by aid of indicators, and the power delivered 
 is measured by the brake, the difference being the power con- 
 sumed by friction. Such a determination for a large engine 
 involves much trouble and expense, and may be unsatisfactory, 
 since the engine-friction may depend largely on the gear for 
 transmitting power from the engine, especially when belts or 
 ropes are used for that purpose. 
 
 The friction of a pumping-engine may be determined from a 
 comparison of the indicated power of the steam-cylinders with 
 the indicated work of the pumps, or, better, with the work done 
 in lifting water from the well and delivering it to the forcing- 
 main. But the friction thus determined is the friction of both 
 the engine and the pump. Air-compressors and refrigerating 
 machines may be treated in the same way to determine the fric- 
 tion of both engine and compressor. Again, the combined 
 friction of an engine and a directly connected electric generator 
 may be determined by comparing the indicated power of the 
 engine with the electric output of the generator, allowing for 
 electricity consumed or wasted in the generator itself. 
 
 The friction of a steam-engine mav consume from 5 to 15 per 
 
 285 
 
.86 
 
 FRICTION OF ENGINES 
 
 cent of the indicated horse-power, depending on the type and 
 condition of the engine. The power required to drive the air- 
 pump (when connected to the engine) is commonly charged to 
 the friction of the engine. It is usual to consider that seven per 
 cent of the indicated power of the engine is expended on the 
 air-pump. Independent air-pumps which can be driven at the 
 best speed consume much less power; those of some United 
 States naval vessels used only one or two per cent of the power 
 of the main engines. But as independent air-pumps are usually 
 direct-acting steam-pumps, much of the apparent advantage just 
 pointed out is lost on account of the excessive steam-consump- 
 tion of such pumps. 
 
 Mechanical Efficiency. — The ratio of the power delivered by 
 an engine to the power generated in the cylinder is the mechanical 
 efficiency; or it may be taken as the ratio of the brake to the 
 indicated power. The mechanical efficiency of engines varies 
 from 0.85 to 0.95, corresponding to the per cent of friction given 
 above. 
 
 The following table gives the mechanical efficiencies of a 
 number of engines, determined by brake-tests, or, in case of the 
 
 Table XXIX. 
 
 MECHANICAL EFFICIENCIES OF ENGINES. 
 
 Kind of Engine. 
 
 Simple engines: 
 
 Horizontal portable 
 
 Horizontal portable Hoadley .... 
 
 High-speed, straight-line 
 
 Corliss condensing 
 
 Corliss non-condensing 
 
 Compound: 
 
 Portable 
 
 Semi -portable ... 
 
 Horizontal 
 
 Horizontal mill-engine 
 
 Schmidt, superheated steam .... 
 
 Leavitt pumping-engine 
 
 Triple-expansion Leavitt pumping-engine 
 
 Efficiency. 
 
 0.86 
 0.91 
 0.96 
 0.81 
 0.86 
 
 0.88 
 0.88 
 0.90 
 0.86 
 0.92 
 
 0-93 
 0.90 
 
INITIAL FRICTION AND LOAD FRICTION 287 
 
 pumping- engines, by measuring the work done in pumping 
 water. 
 
 Initial Friction and Load Friction. — A part of the friction of 
 an engine, such as the friction of the piston-rings and at the 
 stuffing-boxes of piston-rods and valve-rods, may be expected 
 to remain constant for all powers. The friction at the cross- 
 head guides and crank-pins is due mainly to the thrust or pull 
 of the steam-pressure, and will be nearly proportional to the mean 
 effective pressure. Friction at other places, such as the main 
 bearings, will be due in part to weight and in part to steam- 
 pressure. On the whole, it appears probable that the friction 
 may be divided into two parts, of which one is independent of 
 the load on the engine, and the other is proportional to the load. 
 The first may be called the initial friction, and the second, the 
 load friction. Progressive brake-tests at increasing loads con- 
 firm this conclusion. 
 
 Table XXX gives the results of tests made by Walther-Meun- 
 ier and Ludwig * to determine the friction of a horizontal-receiver 
 compound engine, with cranks at right angles and with a fly- 
 wheel, grooved for rope-driving, between the cranks. The 
 piston-rod of each piston extended through the cylinder-cover 
 and was carried by a cross-head on guides, and the air-pump was 
 worked from the high-pressure piston-rod. The cylinders each 
 had four plain slide-valves, two for admission and two for exhaust; 
 the exhaust- valves had a fixed motion, but the admission- valves 
 were moved by a cam so that the cut-off was determined by the 
 governor. 
 
 The main dimensions of the engine were : 
 
 Stroke 40.2 inches. 
 
 Diameter: small piston 21.2 " 
 
 large piston 31.6 " 
 
 piston-rods 3.2 " 
 
 Diameter, air-pump pistons 14.2 " 
 
 Stroke, air-pump 18.8 " 
 
 Diameter, fly-wheel 24.1 " 
 
 * Bulletin de la Snc. Ind. de Mulhouse, vol. Ivii, p. 140. 
 
288 
 
 FRICTION OF ENGINES 
 
 Table XXX. 
 
 FRICTION OF COMPOUND ENGINE. 
 
 Walther-Meunier and Ludwig, Bulletin de la Soc. Ind. de Mulhouse, 
 
 vol. Ivii, p. 140. 
 
 
 
 Horse-Powers— Chevaux aux Vapeur. 
 
 
 
 
 Condition. 
 
 Indicated. 
 
 Effective. 
 
 Absorbed 
 by Engine. 
 
 Friction. 
 
 Efficiency. 
 
 I 
 
 
 288.5 
 
 249.0 
 
 39-5 
 
 °-^37 
 
 0.863 
 
 2 
 
 
 276.9 
 
 238.9 
 
 38.0 
 
 0.138 
 
 0.862 
 
 3 
 
 Compound 
 
 265.6 
 
 228.9 
 
 36.7 
 
 0.139 
 
 0.861 
 
 4 
 
 condensing 
 
 243-7 
 
 208.8 
 
 34-9 
 
 0.144 
 
 0.856 
 
 5 
 
 with 
 
 222.7 
 
 188.7 
 
 34-0 
 
 0-153 
 
 0.847 
 
 6 
 
 air-pump. 
 
 201.5 
 
 168.6 
 
 32.9 
 
 0. 164 
 
 0.836 
 
 7 
 
 
 180.4 
 
 148.5 
 
 31-9 
 
 0.178 
 
 0.822 
 
 8 
 
 
 158. 1 
 
 128.4 
 
 29-7 
 
 0.189 
 
 O.811 
 
 9 
 
 
 136. 1 
 
 108.3 
 
 27.8 
 
 0. 205 
 
 0-795 
 
 10 
 
 
 153 -I 
 
 128.4 
 
 24-7 
 
 0. 161 
 
 0.839 
 
 II 
 
 High- 
 
 142.0 
 
 118. 3 
 
 23-7 
 
 0. 167 
 
 0.S33 
 
 12 
 
 130.9 
 
 108.3 
 
 22.6 
 
 0.173 
 
 0.827 
 
 13 
 
 pressure 
 
 cyHnder 
 
 only. 
 
 Condensing 
 
 with 
 
 120. 1 
 
 98 2 
 
 21.9 
 
 0.182 
 
 0.818 
 
 14 
 
 109.0 
 
 88.2 
 
 20.8 
 
 0. lOI 
 
 0.809 
 
 \l 
 
 97-5 
 86.3 
 
 78.1 
 68.1 
 
 19.4 
 18.3 
 
 0.199 
 0. 212 
 
 0.801 
 0.788 
 
 17 
 
 75-7 
 
 58.0 
 
 17.7 
 
 0.234 
 
 0.766 
 
 18 
 
 air-pump. 
 
 65-5 
 
 48.0 
 
 17-5 
 
 0.267 
 
 0-733 
 
 19 
 
 
 55-2 
 
 37-9 
 
 17-3 
 
 o-3^3 
 
 0.687 
 
 20 
 
 
 145-9 
 
 128.4 
 
 ^7-5 
 
 0. I20 
 
 0.880 
 
 21 
 
 
 135-7 
 
 118.3 
 
 17.4 
 
 0. 129 
 
 0.871 
 
 22 
 
 High- 
 
 125.2 
 
 108.3 
 
 16.9 
 
 0-135 
 
 0.865 
 
 23 
 
 pressure 
 
 114.4 
 
 98.2 
 
 16.2 
 
 0. 142 
 
 0.858 
 
 24 
 
 cylinder 
 
 103.9 
 
 88.2 
 
 15-7 
 
 0. 152 
 
 0.848 
 
 25 
 
 onlv. 
 
 93 -o 
 
 78.1 
 
 14.9 
 
 0. 160 
 
 0.840 
 
 26 
 
 Non- 
 
 82.0 
 
 68.1 
 
 13 9 
 
 0.170 
 
 0.830 
 
 27 
 
 condensing, 
 
 71.7 
 
 58.0 
 
 13-7 
 
 0. 191 
 
 0.809 
 
 28 
 
 no air-pump. 
 
 61.6 
 
 48.0 
 
 13-6 
 
 0.221 
 
 0.779 
 
 29 
 
 
 51-3 
 
 37-9 
 
 13-4 
 
 0.262 
 
 0.738 
 
 The engine during the experiments made 58 revolutions per 
 minute. The air-pump had two single-acting vertical pistons. 
 
 Each experiment lasted 10 or 20 minutes, during which the 
 load on the brake was maintained constant, and indicator- 
 diagrams were taken. The experiments with small load on the 
 
INITIAL FRICTION AND LOAD FRICTION 
 
 289 
 
 brake (numbers 9, 18, 19, 28, and 29) were irregular and uncer- 
 tain. 
 
 The first nine tests were made with the engine working com- 
 pound. Tests 10 to 19 were made with the high-pressure cyUn- 
 der only in action and with condensation, the low-pressure con- 
 necting-rod being disconnected. Tests 20 to 29 were made with 
 the high-pressure cylinder in action, without condensation. 
 
 The results of these tests are plotted on Fig. 60, using the 
 
 AR8CIS8AE, EFFECTIVE HORSEPOWER. 
 ORDINATES, FRICTION HORSEPOWER. 
 
 Fig. 60. 
 
 effective horse- powers for abcissae and the friction horse-powers 
 for ordinates. Omitting tests with small powers (for which the 
 brake ran unsteadily), it appears that each series of tests can be 
 represented by a straight line which crosses the axis of ordinates 
 above the origin; thus affording a confirmation of the assumption 
 that an engine has a constant initial friction, and a load friction 
 which is proportional to the load. 
 
 Now the initial friction which depends on the size and con- 
 struction of the engine may be assumed to be proportional to the 
 
tQO 
 
 FRICTION OF ENGINES 
 
 normal net or brake horse-power, P„, which the engine is designed 
 to deliver, and may be represented by 
 
 where a is a constant to be determined from a diagram like Fig. 
 60. If P is the net horse-power delivered by the engine at any 
 time, then the load friction corresponding is 
 
 bp, 
 
 where Z> is a second constant to be determined from experiments. 
 The total friction of the engine will be 
 
 F = aP, + bP, 
 
 so that the indicated power of the engine will be 
 
 I.H.P. = P + aP^ + bP = aP^ + (i + b)P, 
 
 The mechanical efficiency corresponding will be 
 
 I.H.P. - F P 
 
 ^m. — 
 
 I.H.P. I.H.P. 
 
 The compound condensing engine for which tests are repre- 
 sented by Fig. 60 developed 290 I.H.P. and delivered 250 horse- 
 power to the brake, so that 40 horse-power were consumed in 
 friction. The diagram shows also that the initial friction was 
 20 horse-power, and consequently the load friction was 20 
 horse-power. The values of a and b are consequently 
 
 a = 20 -4- 250 = 0.07; 
 
 b = (40 — 20) -^ 250 = 0.07. 
 
 The indicated horse-power for a given load P is 
 
 I.H.P. = o.o7P„ + 1.07P. 
 
 Similar equations can be deduced for the engine with steam 
 supplied to the small cylinder only; but as the engine is not then 
 in normal condition they are not very useful. 
 
 The maximum efficiency of this engine is 
 
 250 -f- 290 = 0.86; 
 
INITIAL FRICTION AND LOAD FRICTION 
 
 591 
 
 but at half load (125 horse-power) the indicated horse-power is 
 
 I.H.P. = 0.07 X 250 -f 1.07 X 125 == 151, 
 and the efficiency is 
 
 125 - 151 = 0-83- 
 
 Table XXXI. 
 
 FRICTION OF CORLISS ENGINE AT CREUSOT. 
 
 By F. Delafond, Annales des Mines, 1884. 
 
 Condensing with air-pump, tests 1-33. 
 Non-condensing without air-pump, tests 34-46. 
 
 
 
 
 
 Horse-Power — Cheval h Vapeur. 
 
 
 Cut-off Frac- 
 tion of 
 
 Pressure at 
 Cut-off, Kilos 
 
 Revolutions 
 per Minute. 
 
 
 
 
 
 
 
 
 Stroke 
 
 per Sq. Cm. 
 
 
 Indicated. 
 
 Effective; 
 
 Absorbed 
 by Engine. 
 
 I 
 
 0.039 
 
 0.64 
 
 64.0 
 
 27.8 
 
 16.3 
 
 II-5 
 
 2 
 
 0.044 
 
 2.40 
 
 68.5 
 
 60.0 
 
 37.6 
 
 22.4 
 
 3 
 
 0.044 
 
 2.90 
 
 65.0 
 
 67.2 
 
 45-2 
 
 22.0 
 
 4 
 
 0.065 
 
 4.90 
 
 64.0 
 
 117. 
 
 88.7 
 
 28.3 
 
 5 
 
 0.065 
 
 6.20 
 
 61.0 
 
 138. 5 
 
 106.3 
 
 32.2 
 
 6 
 
 0.065 
 
 7.10 
 
 64.0 
 
 163.2 
 
 129.2 
 
 34-0 
 
 7 
 
 0.065 
 
 7.60 
 
 64.0 
 
 185.0 
 
 144.6 
 
 40.4 
 
 8 
 
 O.IOO 
 
 0. 16 
 
 58.0 
 
 21.0 
 
 10.6 
 
 10.4 
 
 9 
 
 0.106 
 
 1.55 
 
 60.0 
 
 61.9 
 
 42.3 
 
 19.6 
 
 10 
 
 O.IOO 
 
 2.82 
 
 57-3 
 
 82:7 
 
 61.0 
 
 21.7 
 
 II 
 
 0.090 
 
 4.80 
 
 58.3 
 
 135-3 
 
 106.7 
 
 28.6 
 
 12 
 
 0.128 
 
 4.82 
 
 58.3 
 
 154.5 
 
 124.8 
 
 29.7 
 
 13 
 
 0.142 
 
 0.76 
 
 62.0 
 
 42.3 
 
 28.4 
 
 13-9 
 
 14 
 
 0. 137 
 
 0.71 
 
 60.6 
 
 44-3 
 
 28.7 
 
 15.6 
 
 IS 
 
 0.132 
 
 2.50 
 
 540 
 
 795 
 
 59.8 
 
 19.7 
 
 16 
 
 0.147 
 
 2.60 
 
 61.6 
 
 100. 
 
 78.2 
 
 21.8 
 
 17 
 
 0.155 
 
 4.65 
 
 60.0 
 
 177.2 
 
 145-0 
 
 32.2 
 
 18 
 
 0.167 
 
 0.22 
 
 61.0 
 
 40.2 
 
 27.9 
 
 12.3 
 
 19 
 
 0.197 
 
 2.55 
 
 57.2 
 
 no. 8 
 
 83-3 
 
 27. 5 
 
 20 
 
 0.273 
 
 0.40 
 
 62.3 
 
 50.2 
 
 33-8 
 
 16.4 
 
 21 
 
 0.264 
 
 1.57 
 
 633 
 
 89.1 
 
 61.8 
 
 27-3 
 
 22 
 
 0.240 
 
 1.64 
 
 62.0 
 
 87.2 
 
 63.1 
 
 24.1 
 
 23 
 
 0.245 
 
 3.25 
 
 56.0 
 
 1450 
 
 116. 
 
 29.0 
 
 24 
 
 0.260 
 
 4.76 
 
 58.0 
 
 209.4 
 
 178.0 
 
 31-4 
 
 25 
 
 0.335 
 
 0.25 
 
 590 
 
 47.2 
 
 32.5 
 
 14-7 
 
 26 
 
 0.339 
 
 1.94 
 
 58.3 
 
 III. 7 
 
 90.0 
 
 21.7 
 
 27 
 
 0.338 
 
 2.97 
 
 61.0 
 
 161. 8 
 
 1330 
 
 28.8 
 
 28 
 
 
 0.47 
 
 59.3 
 
 81.3 
 
 67.2 
 
 14. 1 
 
 29 
 
 
 0.47 
 
 6i.o 
 
 80.8 
 
 67.9 
 
 12.9 
 
 30 
 
 
 1.60 
 
 61.6 
 
 148.5 
 
 128.4 
 
 20. 1 
 
 31 
 
 J 
 
 2.70 
 
 61.5 
 
 216.5 
 
 191. 
 
 25-5 
 
 32 
 
 
 2.70 
 
 61.5 
 
 215-5 
 
 191. 
 
 24-5 
 
 33 
 
 0.50 
 
 0.70 
 
 61.5 
 
 15.8 
 
 0.0 
 
 15.8 
 
 34 
 
 0.120 
 
 6.00 
 
 60.0 
 
 132.5 
 
 107.5 
 
 25.0 
 
 35 
 
 0.106 
 
 7.00 
 
 53.0 
 
 125.0 
 
 103.0 
 
 22.0 
 
 36 
 
 0. 120 
 
 7.50 
 
 62.0 
 
 172.0 
 
 148.0 
 
 24.0 
 
 37 
 
 0. 150 
 
 4.57 
 
 S50 
 
 102.3 
 
 86.5 
 
 IS. 8 
 
 38 
 
 0.262 
 
 4- 50 
 
 590 
 
 149.2 
 
 132.3 
 
 16.9 
 
 39 
 
 0.293 
 
 4. 55 
 
 .59.0 
 
 171. 8 
 
 153-8 
 
 18.0 
 
 40 
 
 0.371 
 
 4.40 
 
 60.0 
 
 195. 3 
 
 177.2' 
 
 18. 1 
 
 41 
 
 0.348 
 
 2.75 
 
 58.0 
 
 85.1 
 
 73-1 
 
 12.0 
 
 42 
 
 0.348 
 
 2.75 
 
 58. 5 
 
 84.8 
 
 71. 1 
 
 13.7 
 
 43 
 
 0.440 
 
 3.48 
 
 62.0 
 
 151. 
 
 134-3 
 
 T6.7 
 
 44 
 
 O.III 
 
 330 
 
 62.0 
 
 12.8 
 
 0.0 
 
 12.8 
 
 45 
 
 0.50 
 
 1.20 
 
 62.0 
 
 12.3 
 
 0.0 
 
 12.3 
 
 46 
 
 1 
 
 0.50 
 
 62.0 
 
 10. 45 
 
 0.0 
 
 10.45 
 
292 
 
 FRICTION OF ENGINES 
 
 Table XXXI gives the results of a large number of brake- 
 tests made on a Corliss engine at Creusot by M. F. Delafond, 
 both with and without a vacuum, and with varying steam- 
 pressures and cut-off. The tests with a vacuum are plotted 
 on Fig. 61, and those without a vacuum are given in Fig. 62. 
 In both figures the abscissae are the indicated horse-powers, and 
 the ordinates are the friction horse-powers. Most of the tests 
 are represented by dots; those tests which were made with the 
 most economical cut-off (one-sixth for the engine with conden- 
 
 4U 
 
 35 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 * .^ 
 
 y 
 
 30 
 
 
 
 
 
 
 
 
 ^ 
 
 /"^ 
 
 
 
 
 
 
 . 
 
 + ' 
 
 • 
 
 y^ 
 
 • 
 
 
 25 
 
 
 
 
 
 
 
 y 
 
 
 
 ® 
 
 
 
 
 
 . 
 
 ^/^ 
 
 
 
 
 ® 
 
 20 
 
 
 
 
 • 
 
 •^ 
 
 ^- 
 
 
 
 
 
 
 
 
 d 
 
 
 
 
 
 
 
 15 
 
 
 
 + V 
 
 
 
 Absci 
 
 ssae^ in 
 
 dicatec 
 
 . horse] 
 
 )ower 
 
 
 y 
 
 K 
 
 c 
 c 
 
 ; 
 
 Ordin 
 
 ates, f r 
 
 iction 1 
 
 lorsepo 
 
 wer 
 
 10 
 
 ^ 
 
 5 
 
 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 20 
 
 40 
 
 60 
 
 100 120 
 Fig. 61. 
 
 140 
 
 160 
 
 180 
 
 200 
 
 sation and one-third without) are represente.d by crosses. A 
 few tests with very long cut-off, on Fig. 61, are represented by 
 circles. The straight lines on- both figures are drawn to represent 
 the tests indicated by crosses. In general the points representing 
 tests with short cut-off and high steam-pressure lie above the 
 lines, and points representing tests with long cut-off and low 
 steam-pressure lie below the lines, though there are some notable 
 exceptions to this rule. The circles on Fig. 61, representing 
 tests with cut-off near the end of the stroke, show much less 
 
INITIAL FRICTION AND LOAD FRICTION 
 
 293 
 
 friction than the other tests. The tests on this engine show- 
 clearly that both initial and load friction are affected by the 
 cut-off and the steam-pressure, and that friction tests should 
 be made at the cut-off which the engine is expected to have in 
 service. 
 
 25 
 
 20 
 
 15 
 
 10 
 
 
 
 
 
 
 
 
 
 • 
 
 
 
 
 
 
 
 • 
 
 
 
 
 + 
 
 
 
 ___^ 
 
 ^- 
 
 + 
 
 
 
 
 
 
 
 
 . 
 
 
 Al 
 Or 
 
 Dscissat 
 iinates 
 
 , in die 
 , fricti 
 
 ited ho 
 m hors 
 
 rsepow 
 jpower 
 
 ;r 
 
 
 
 
 
 
 
 
 
 
 
 20 
 
 4() 
 
 60 
 
 100 
 Fig. 62. 
 
 120 
 
 140 
 
 160 
 
 180 
 
 200 
 
 The initial friction was eight horse-power both with and 
 without condensation. But Fig. 61 shows that the engine 
 with condensation gave the best economy when it indicated 
 160 horse-power; the friction was then 30 horse-power, so that 
 the net horse-power was 130, which will be taken for the normal 
 horse-power P„. Consequently 
 
 a = S -^ 130 = 0.06; 
 ^ = (30 - 8) -^ 130 = 0.17. 
 .-. I.H.P. = o.o62P„ -f- 1.17P. 
 
 In like manner Fig. 62 shows the best economy without 
 condensation, for about 200 indicated horse-power, for which 
 the friction is 20 horse-power, leaving 180 for the normal power 
 of the engine. Consequently 
 
 = 8 -^ 180 = 0.045; 
 b = (20 — S) -T- 180 = 0.07. 
 .-. I.H.P. = o.o45P„ + 1.07P. 
 
 This engine with condensation had 36 horse-power expended 
 
294 
 
 PRICTION OF ENGINES 
 
 in friction, when developing 200 horse-power; without conden- 
 sation it had 20; consequently the air-pump can be charged with 
 
 (36 — 20) -^ 200 = 0.08 
 of the indicated power. The large percentage is probably due 
 to the high vacuum maintained. 
 
 Thurston's Experiments. — As a result of a large number of 
 tests on non-condensing engines, made under his direction or 
 with his advice, Professor R. H. Thurston * concluded that, 
 for engines of that type, the friction is independent of the 
 load, and that it can, in practice, be determined by indicat- 
 ing the engine without a load. 
 
 Table XXXII. ' 
 
 FRICTION (3F NON-CONDENSING ENGINE. 
 
 STRAIGHT-LINE ENGINE, 8 INCHES DIAMETER, 14 INCHES STROKE. 
 
 No. of 
 Diagram. 
 
 Boiler- 
 Pressure. 
 
 Revolutions. 
 
 Brake H.P. 
 
 I.H.P. 
 
 Frictional H.I\ 
 
 I 
 
 50 
 
 232 
 
 4.06 
 
 7.41 
 
 3-35 
 
 2 
 
 65 
 
 229 
 
 4.98 
 
 7.58 
 
 2.60 
 
 3 
 
 63 
 
 230 
 
 , 6.00 
 
 10.00 
 
 4.00 
 
 4 
 
 69 
 
 230 
 
 7.00 
 
 10.27 
 
 3-27 
 
 5 
 
 73 
 
 230 
 
 8.10 
 
 'I 75 
 
 3-65 
 
 6 
 
 77 
 
 230 
 
 9.00 
 
 12.70 
 
 3.70 
 
 7 
 
 75 
 
 230 
 
 10.00 
 
 14.02 
 
 4.02 
 
 8 
 
 80 
 
 230 
 
 TI.OO 
 
 14.78 
 
 3-78 ^ 
 
 9 
 
 80 
 
 . 230 
 
 12.00 
 
 15-17 
 
 3-17 
 
 10 
 
 •^5 
 
 230 
 
 13.00 
 
 [5.96 
 
 2.96 
 
 II 
 
 75 
 
 230 
 
 14. 00 
 
 t6.86 
 
 2.86 
 
 12 
 
 70 
 
 • 230 
 
 15.00 
 
 17.80 
 
 2.80 
 
 13 
 
 72 
 
 231 
 
 20. 10 
 
 22.07 
 
 r.97 
 
 14 
 
 75 
 
 230 
 
 25.00 
 
 28.31 
 
 S'Z^ 
 
 i5 
 
 60 
 
 229 
 
 29-55 
 
 33-04 
 
 3-40 
 
 16 
 
 58 
 
 229 
 
 34.86 
 
 37.20 
 
 2.34 
 
 17 
 
 70 
 
 229 
 
 39-85 
 
 43-04 
 
 3-19 
 
 18 
 
 85 
 
 230 
 
 45.00 
 
 47-79 
 
 2 78 
 
 19 
 
 90 
 
 230 
 
 50.00 
 
 52.60 
 
 2.60 
 
 20 
 
 «5 
 
 230. 
 
 55-00 
 
 57-54 
 
 2.54 
 
 Table XXXII gives the details of one series of tests. The 
 friction horse-power is small in all the tests, and the variations 
 are small and irregular, and appear to depend on the state of 
 
 * Trans, of the Am. Soc. of Mech. Engrs., vols, viii, ix, and x. 
 
DISTRIBUTION OF FRICTION 
 
 295 
 
 lubrication and other minor causes rather than on the change 
 of load. 
 
 Distribution of Friction. — As a consequence of his conclusion 
 in the preceding section, Professor Thurston decided that the 
 friction of an engine may be found by driving it from some 
 external source of power, with the engine in substantially the 
 same condition as when running as usual, but without steam in its 
 cylinder, and by measuring the power required to drive it by 
 aid of a transmission dynamometer. Extending the principle, 
 the distribution of friction among the several members of the 
 engine may be found by disconnecting the several members, 
 one after another, and measuring the power required to run the 
 remaining members. 
 
 The summary of a number of tests of this sort, made by Pro- 
 fessor R. C. Carpenter and Mr. G. B. Preston, are given in 
 Table XXXIII. Preliminary tests under normal conditions 
 showed that the friction of the several engines was practically 
 the same at all loads and speeds. 
 
 The most remarkable feature in this table is the friction of 
 the main bearings, which in all cases is large, both relatively and 
 absolutely. The coefficient of friction for the main bearings, 
 calculated by the formula 
 
 33,000 H.P. 
 pen 
 
 is given in Table XXXIV. p is the pressure on the bearings in 
 pounds for the engines light, and plus the mean pressure on 
 the piston for the engines loaded; c is the circumference of the 
 bearings in feet; n is the number of revolutions per minute, 
 and H.P. is the horse-power required to overcome the friction 
 of the bearings. 
 
 The large amount of work absorbed by the main bearings 
 and the large coefficient of friction appear the more remarkable 
 from the fact that the coefficient of friction for car-axle journals 
 is often as low as one-tenth of one per cent, the difference being 
 probably due to the difference in the methods of lubrication. 
 
296 
 
 FRICTION OF ENGINES 
 
 Table XXXIII. 
 
 DISTRIBUTION OF FRICTION. 
 
 Parts of Engine. 
 
 Main Bearings 
 
 Piston and Rod 
 
 Crank Pin . 
 
 Cross Head and Wrist Pin 
 
 Valve and Rod 
 
 Eccentric Strap 
 
 Link and Eccentric . . 
 Air-Pump 
 
 Total 
 
 
 Percentages of Total 
 
 Friction. 
 
 
 Straight-line 6 X " 
 Balanced Valve. 
 
 III 
 
 7" X 10" Lansing 
 Iron Works — Trac- 
 tion Locomotive 
 Valve-Gear. 
 
 12" X18" Lansing 
 Iron Works — 
 Automatic Bal- 
 anced Valve. 
 
 21" X 20" Lansing 
 Iron Works— Con- 
 densing Balanced 
 Valve. 
 
 47.0 
 
 35-4 
 
 35 -o 
 
 41. 6 
 
 46.0 
 
 32-9 
 
 25.0 
 
 21.0 
 
 49.1 
 
 
 6.8 
 5-4 
 
 5-1 
 
 4.T 
 
 a3.o 
 
 21.8 
 
 2-5 
 
 5-3 
 
 26.4 
 4.0 
 
 22.0 
 
 9-3 
 
 21.0 
 
 ... 
 
 
 9.0 
 
 
 12.0 
 
 100. 
 
 100. 
 
 100. 
 
 100.0 
 
 100. 
 
 Table XXXIV. 
 
 COEFFICIENT OF FRICTION FOR THE MAIN BEARINGS OF 
 STEAM-ENGINES. 
 
 Engine. 
 
 6"X 12'' Straight-line . 
 1 2" X 18'' Automatic (L. I 
 
 7''Xio"Traction(L. I.W.) 
 -' r''X 20'' Condensing (L. I. W.) 
 
 W.) 
 
 
 
 l_ 
 
 °'Z 
 
 M 
 
 (^ 
 
 
 
 1— > (U 
 
 2 £ 
 
 ^ 3 
 
 ^■?. 
 
 •§§ 
 
 §^ 
 
 og 
 
 ^a 
 
 5.2 
 
 a 
 
 
 
 Q 
 
 3 
 
 0.85 
 
 1500 
 
 3-70 
 
 2600 
 
 
 0.68 
 
 500 
 
 2I 
 
 3-30 
 
 4000 
 
 Sh 
 
 
 . 10 
 ■19 
 ■31 
 ,09 
 
 4) ^Tl 
 
 o.a 
 
 c6 
 
 05 
 08 
 
 ft" 
 11.2 
 
 u O 
 
 230 
 190 
 200 
 206 
 
 * The i2''Xi8'''' automatic engine was new, and gave, throughout, an exces- 
 .sive amount of friction as compared with the older engines of the same class and 
 make. 
 
DISTRIBUTION OF FRICTION 
 
 297 
 
 The second and obvious conclusion from Table XXXIII is 
 that the valve should be balanced, and that nine-tenths of the 
 friction of an unbalanced slide-valve is unnecessary waste. 
 
 The friction of the piston and piston-rod is alvv^ays considerable, 
 but it varies much with the type of the engine, and with differ- 
 ences in handling. It is quite possible to change the effective 
 power of an engine by screwing up the piston-rod stuffing-box 
 too tightly. The packing of both piston and rod should be no 
 tighter than is necessary to prevent perceptible leakage, and is 
 more likely to be too tight than too loose. 
 
CHAPTER XIV. 
 
 INTERNAL-COMBUSTION ENGINES. 
 
 Recent advances in the generation of power from heat have 
 been found in the development of internal-combustion engines 
 and of steam-turbines; the latter will be treated in Chapter XIX. 
 When first introduced the only convenient fuel for internal-com- 
 bustion or gas-engines was illuminating-gas, which limited their 
 use to small sizes, for which convenience and small cost of attend- 
 ance offset the cost of fuel. Twenty years ago an engine of fifty 
 horse-power was a large though not an unusual size. At that 
 time Mr. Dowson had succeeded in generating gas from anthra- 
 cite coal and from coke in his producer. Ten years ago engines 
 of 400 horse-power were built to use Dowson producer gas, but 
 as they had four cylinders the horse-power per cylinder was only 
 twice that of single-cylinder engines of a decade earlier; the 
 fuel used in the producer was a cheap grade of anthracite. At 
 the present time, gas-engines are in use which develop as much 
 as 1500 horse-power per cylinder; these engines are of the two- 
 cycle double-acting type. The application of gas-engines to 
 marine propulsion may now be considered to be fairly under 
 way, though as yet the vessels so propelled have been of small 
 displacement; certain British firms of shipbuilders have plans 
 matured for the application of such engines to the propulsion 
 of large ships. 
 
 Hot-air Engines. — Though the attempt to develop hot-air 
 engines on a large scale appears to be definitely abandoned, and 
 though the interest of this type of engine is mainly historical a 
 brief discussion of them has some advantage, for, after all, the 
 internal-combustion engine is a hot-air engine in which heat is 
 applied by burning fuel in the cylinder. 
 
 In the discussion of the second law of thermodynamics {see 
 
 298 
 
STIRLING'S ENGINE 
 
 299 
 
 page 39) it was pointed out that to obtain the maximum effi- 
 ciency all the heat must be added at the highest practicable tem- 
 perature, and the heat rejected must be given up at the lowest 
 temperature. The hot-air engine is the only attempt to follow 
 the example of Carnot's engine by supplying heat to and with- 
 drawing heat from a constant mass of working substance (air). 
 An attempt to obtain the diagram of Carnot's cycle from such 
 an engine would involve the difficulty that the acute angle at 
 which the isothermal and adiabatic lines for air cross, gives a 
 very long and attenuated diagram that could be obtained only 
 by an excessively large working cylinder, with so much friction 
 that the effective power delivered by the engine would be insigni- 
 ficant. This is illustrated by Problem 20, page 75. To obviate 
 this difficulty Stirling invented the economizer or regenerator 
 which replaced the adiabatic lines by vertical lines of constant 
 volume, and thus obtained a practical machine. His type of 
 engine is still employed, but only for very small pumping-engines 
 which are used for domestic purposes, as they are free from dan- 
 ger and require little attention. 
 
 Stirling's Engine. — This engine was invented in 1816, and 
 was used with good economy for a few years, and then rejected 
 because the heaters, which took the place of the boiler of a steam- 
 engine, burned out rapidly; the small engines now in use have 
 little trouble on this account. It is described 
 and its performance given in detail by Rankine 
 in his "Steam-Engine." An ideal sketch is 
 given by- Fig. 63. £ is a displacer piston filled 
 with non-conducting material, and working 
 freely in an inner cylinder. Between this 
 cylinder and an outer one from A to C is 
 placed a regenerator made of plates of metal, 
 wire screens, or other material, so arranged 
 that it will readily take heat from or yield 
 heat to air passing through it. At the lower 
 end both cylinders have a hemispherical head; that of the outer 
 cylinder is exposed to the fire of the furnace, and that of the 
 
 Fig. 63. 
 
300 
 
 INTERNAL-COMBUSTION ENGINES 
 
 inner is pierced with holes through which the air streams when 
 displaced by the plunger. At the upper end there is a coil of 
 pipe through which cold water flows. The working cylinder H 
 has free communication with the upper end of the displacer 
 cylinder, and consequently it can be oiled and the piston may 
 be packed in the usual manner, since only cool air enters it. 
 
 In the actual engine the cylinder H is double-acting, and 
 there are two displacer cylinders, one for each end of the working 
 cylinder. 
 
 If we neglect the action of the air in the clearance of the 
 cylinder H and the communicating pipe, we have the following 
 ideal cycle. Suppose the working piston to be at the beginning 
 of the forward stroke, and the displacer piston at the bottom of 
 its cylinder, so that we may assume that the air is all in the upper 
 part of that cylinder or in the refrigerator, and at the lowest tem- 
 perature 7^2, the condition of one pound of air being represented 
 by the point D of Fig. 64. The displacer piston is then moved 
 quickly by a cam to the upper end of the 
 stroke; while the working piston moves so 
 little that it may be considered to be at rest. 
 The air is thus all driven from the upper end 
 of the displacer cylinder through the regene- 
 rator, from which it takes up heat abandoned 
 
 Fig. 64. during the preceding return stroke, thereby 
 
 acquiring the temperature T^, and enters the 
 lower end of that cylinder. During this process the line AD oi 
 constant volume is described on Fig. 64. When this process is 
 complete, the working cylinder makes the forward stroke, and 
 the air expands at constant temperature, this part of the cycle 
 being represented by the isothermal AB oi Fig. 64. At the end 
 of the forward stroke the displacer piston is quickly moved 
 down, thereby driving the air through the regenerator, during 
 which process heat is given up by the air, into the upper part 
 of the displacer cylinder; this is accompanied by a cooling at 
 constant volume, 'represented by the line BC. The working 
 piston then makes the return stroke, compressing the air at con- 
 
STIRLING'S ENGINE 
 
 301 
 
 stant temperature, as represented by the isothermal Hne CD, and 
 completing the cycle. 
 
 To construct the diagram drawn by an indicator, we may 
 assume that in the clearance of the cylinder iJ, the communi- 
 cating pipe, and refrigerator there is a volume of air which flows 
 back and forth and changes pressure, but remains at the tempera- 
 ture T^. If we choose, we may also make allowance for a simi- 
 lar volume which remains in the waste spaces at the lower end 
 of the displacer cylinder, at a constant temperature T^. 
 
 In Fig. 65, let ABCD represent the cycle of operations, with- 
 out any allowance for clearance or waste spaces; the minimum 
 volume will be that displaced by the displacer piston, while the 
 maximum volume is larger by the volume displaced by the work- 
 ing piston. Let the point E represent the maximum pressure, 
 the same as that at ^ ; and the united volumes of the clearance 
 at one end of the working cylinder, of the communicating pipe, 
 
 p 
 
 E 
 
 
 1 ^ 
 
 tVa-v V 
 
 
 
 
 
 ^- C C' V 
 
 Fir,. 65. 
 
 of the clearance at the top and bottom of the displacer cylinder, 
 and the volume in the refrigerator and regenerator. Each part 
 of this combined volume will have a constant temperature, so 
 that the volume at different pressures will be represented by the 
 hyperbola EF. To fmd the actual diagram A'B'C'D', draw 
 any horizontal line, as sy, cutting the true diagram at u and X, 
 and the hyperbola EF at /; make uv and xy equal to st\ then 
 v and y are points of the actual diagram. The indicator will 
 draw an oval similar to A'B'C'D' with the corners rounded. 
 
 The diagram in Fig. 66 was reduced from an indicator-dia- 
 gram from a hot-air engine made on the same principle 
 
302 
 
 INTERNAI^COMBUSTION ENGINES 
 
 as Stirling's hot-air engine. To avoid destruction of the lubri- 
 cant in the working cylinder Stirling found it advisable to con- 
 nect only the cool end of the 
 displacer cylinder with the working 
 cylinder, and had two displacer 
 cylinders for one working cylinder. 
 
 It has been found that a good 
 
 Fig. 66. mineral oil can be used to lubricate 
 
 the displacer piston, and that the 
 hot end also of the displacer cylinder can be advantageously 
 connected with the working cylinders, of which there are two. 
 Thus each working cylinder is connected with the hot end of 
 one displacer cylinder and with the cool end of the other 
 displacer cylinder. 
 
 The distortion of the diagram Fig. 66 is due in part to the 
 large clearance and waste space, and partly to the fact that 
 the displacer pistons are moved by a crank at about 70 degrees 
 with the working crank. 
 
 A test on the engine mentioned by Messrs. Underbill and 
 Johnson * showed a consumption of 1.66 of a pound of anthracite 
 coal per horse-power per hour; but the friction of the engine is 
 large, so that the consumption per brake horse-power is 2.37 
 pounds. This engine, like the original Stirling engine, appears 
 to have given much difficulty from 
 the burning of the heaters. The 
 difficulty is likely to be more serious 
 with large than with small engines, 
 as the volume of the displacer cylin- 
 ders increases more rapidly than the 
 heating surface. 
 
 The action of the regenerator may 
 be best explained by redrawing the 
 diagram Fig. 64 on the temperature- fig. 67. 
 
 entropy plane as shown in Fig. 67, 
 where AB and CD are constant temperature lines representing 
 
 * 'Ihcsis, M. I. T. i88q. 
 
 T+AT M 
 
 d IV X a 
 
 C 
 
 yz b 
 
STIRLING'S ENGINE 
 
 303 
 
 isothermal expansion, and DA and BC take the place of 
 the constant volume lines on Fig. 64. To show that these 
 lines are properly drawn, we may consider the equation 
 
 d(j) = c„-+ (Cp- cj — 
 1 V 
 
 which was deduced on page 67. For the lines DA and 
 BC the volumes are constant, so that the equation reduces to 
 
 
 
 or transposing, 
 
 
 
 dt T . 
 
 but this last expression represents the tangent of the angle between 
 the axis O^ and the tangent to the curve. This angle increases 
 (but with a diminishing ratio) with the temperature, and as c^ 
 is constant for a gas, the angle depends only on the temperature 
 r, so that the curve BC is identical in form with the curve AD, 
 and is merely set off further to the right; in consequence, parts 
 like W X and ZY between a pair of constant temperature lines 
 are identical except in their positions with regard to the axis OT. 
 Suppose now that the material -of the regenerator has the 
 temperature T^ at the lower end and T^ at the upper end, and 
 that the temperature varies regularly from bottom to top. Sup- 
 pose further that the air when giving heat to the regenerator 
 (or receiving heat from it) differs from it by only an inappreci- 
 able amount. Then the diagram of Fig. 67 will represent this 
 ideal action correctly, and it is easy to show that its efficiency 
 is the same as that of Carnot's cycle ABC'D\ For the 
 amount of heat acquired by the regenerator during the opera- 
 tion represented by BC, corresponding to the down stroke of 
 the displacer piston, is measured by the area bBCc, and the 
 heat yielded during the up stroke DA, is represented by 
 the area dDAa; and these two areas are manifestly equal. 
 
304 INTERNAL-COMBUSTION ENGINES 
 
 Moreover, the small amount of heat gained during the operation 
 ZF at the temperature T is exactly counterbalanced by the 
 heat yielded during the operation XW at the same temperature, 
 so that there is no loss of efficiency; the small amounts of heat 
 mentioned are represented by the equal areas zZ Yy and wWXx. 
 
 It can be shown that one of the curves like DA may be drawn 
 at random, provided that the other curve like BC is made iden-' 
 tical and set off further to the right; but the matter is not of 
 importance enough to warrant its discussion. 
 
 In practice a regenerator must be at an appreciably lower 
 temperature than the air from which it receives heat, and at a 
 higher temperature than that to which it yields heat, as the flow 
 of air is rapid. The loss of heat stored and restored per cycle 
 of the original Stirling engine was estimated at five per cent to 
 ten per cent. It may be proper before passing from the subject 
 state that regenerators are not applicable to gas-engines in use 
 at the present day. 
 
 Gas-Engines. — The chief difficulty with hot-air engines is 
 to transmit heat to' and from the working substance. In gas- 
 engines this difficulty is removed by mixing the fuel with the 
 air (so that heat is developed in the working substance itself), 
 and by rejecting the hot gases after they have done their work. 
 The fuel may be illuminating-gas, fuel-gas, or vapor of a volatile 
 liquid like gasoline. It will be shown that the specific volume 
 and the specific heat of the mixture of air and gas, both before 
 and after the heat is developed by combustion, are not very 
 different from the same properties of air. The general theory 
 of gas-engines may therefore be developed on the assumption 
 that the working substance is air, which is heated and cooled in 
 such a manner as to produce the ideal cycles to be discussed, 
 as is done by Clerk.* 
 
 Experience has shown that in order to work efficiently, the 
 mixture of gas and air supplied to a gas-engine must be com- 
 pressed to a considerable pressure before it is ignited. This may 
 be done either by a separate compressor or in the cylinder of the 
 
 * The Gas and OH Engine : Dugald Clerk. 
 
GAS-ENGINE WITH SEPARATE COMPRESSOR 
 
 305 
 
 F 
 
 engine itself; the second type of engines, of which the Otto 
 engine is an example, is the only successful type at the present 
 time; the other type has some advantages which may lead to its 
 development. 
 
 Gas-Engine with Separate Compressor. — This engine has 
 a compressor, a reservoir, and a working cylinder. When run 
 as a gas-engine a mixture of gas and air is drawn into a pump or 
 compressor, compressed to several atmospheres, and forced into 
 a receiver. On the way from the receiver to the working cylinder 
 the mixture is ignited and burned so that the temperature and 
 volume are much increased. After expansion in the working 
 cylinder the spent gases are exhausted at atmospheric pressure. 
 
 The ideal diagram is represented by Fig. 68. ED represents 
 the supply of the combustible mixture to the jp 
 compressor, DA is the adiabatic compres- 
 sion, and AF represents the forcing into 
 the receiver. FB represents the supply 
 of burning gas to the working cylinder 
 BC represents the expansion, and CE the 
 exhaust. In practice this type of engine ^^'^^' 
 
 always has a release, represented by GiJ, before the expansion 
 has reduced the pressure of the working substance to that of the 
 atmosphere. 
 
 This type of engine has been used as an oil-engine by supplying 
 the fuel in the form of a film of oil to the air after it has been 
 compressed. In such case the compressor draws in air only, 
 and there is not an explosive mixture in the receiver. The 
 Brayton engine when run in this way could burn crude petroleum, 
 or, after it was started, could burn refined kerosene. Its chief 
 defect appears to have been incomplete combustion and conse- 
 quent fouling of the cylinder with carbon. 
 
 The effective cycle may be considered to be represented by 
 the diagram A BCD (Fig. 68), and may be assumed to be pro- 
 duced in one cylinder by heating the air from A to B, by cooling 
 it from C to D, and by the adiabatic expansion and compression 
 from B io C and from D io A. If T^ and Tf, are the absolute 
 
 o 
 
3o6 INTERNAI^COMBUSTION ENGINES 
 
 temperatures corresponding to the points A and B, then the 
 heat added from A to B is 
 
 c, {T, - rj, 
 and the heat withdrawn from C to P is 
 
 Cj, {T, - Ta), 
 so that the efficiency of the ideal cycle is 
 
 c, {T, - rj T,-T,- ^'"^ 
 
 But since the expansion and compression are adiabatic, 
 
 but p^ = pa and Pt = p„ therefore 
 
 I t — I 
 
 so that the equation for efficiency becomes 
 
 (178) 
 
 This discussion of ideal efficiency is due to Dugald Clerk,* and 
 has the advantage of replacing an exceedingly complex operation 
 by a simple ideal operation which has approximately the same 
 efficiency. How far the ideal cycle can be used to determine 
 the probable advantages of certain conditions depends on the 
 degree of approximation, — a matter which will be referred 
 to later. It must be admitted that the divergence of the 
 actual from the real cycle is much greater than the divergence 
 of the steam-engine cycle from that of a non-conducting 
 cylinder. 
 
 For example^ with the pressure in the reservoir at 90 pounds 
 
 * The Gas Engine, 1886; The Gas and Oil Engine, 1896. 
 
GAS-ENGINE WITH SEPARATE COMPRESSOR 
 
 307 
 
 above the atmosphere the efficiency is 
 
 1 .405 — I 
 
 .405 
 
 (^^^ = -43. 
 
 \14.7 + 90/ 
 
 When the cycle is incomplete the expression for the efficiency 
 is not so simple, for it is necessary to assume cooling at constant 
 volume from G to H (Fig. 68), and cooling at constant pressure 
 from H to D; so that the heat rejected is 
 
 c. {T, - Tn) + c, (T, - r,), 
 and the efficiency becomes 
 
 - (T, - T,) + {T, - T,) 
 e-^-- ^_-^r . . . .(179) 
 
 For example^ let it be assumed that the pressure at A is 90, 
 pounds above the atmosphere, that the temperature at B is 2500° 
 F., and that the volume at G is three times the volume at B. 
 
 First, the temperature at A is 
 
 provided that the temperature of the atmosphere is 60° F. 
 The temperature at G is 
 
 ^'=^'G;r'= ^960(^-^=1897, 
 
 and the pressure at G is 
 
 (I'.V /iy-405 
 
 - ) = (14.7 +9o)(-) - 22.4 pounds, 
 ^(/ ^3 ' 
 
 so that the temperature at H is 
 
 r.= r,^= .897X^:1.,,,,, 
 
 and finally the efficiency is 
 
 (1897 - 1247) + 1247 - 520 
 
 « = I ^^-^ 7 = 0.42.. 
 
 2960 — 917 
 
3o8 INTERNAI^COMBUSTION ENGINES 
 
 Gas-Engines with Compression in the Cylinder. — All success- 
 ful gas-engines of the present day compress the explosive mixture 
 in the working cylinder. Very commonly they take gas at one 
 end of the cylinder only, and require four strokes to complete 
 the cycle, so that there is one explosion for twa revolutions when 
 working at full power. Such engines are commonly known as 
 four-cycle engines. Some engines have the exhaust and filling 
 of the cylinder accomplished in some other way, and are known 
 as two-cycle engines; they have an explosion for every revolu- 
 tion when single-acting. Both four-cycle and two-cycle engines 
 have been made double-acting in large sizes. The first forward 
 stroke of the piston from the head of the cylinder draws in the 
 mixture of gas and air, which is compressed on the return stroke; 
 at the completion of this return stroke the mixture is ignited and 
 the pressure rises very rapidly; the next forward stroke is the 
 working stroke, which is succeeded by an exhaust-stroke to 
 expel the spent gases. In almost all engines these four strokes 
 are of equal length, for the advantage of making them of unequal 
 length, as required for the best ideal cycle, is more than coun- 
 terbalanced by the mechanical difficulty of producing unequal 
 strokes. 
 
 The most perfect ideal cycle, represented by Fig. 69, has 
 
 four strokes of unequal length so 
 arranged that the piston starts from 
 the head of the cylinder when gas 
 is drawn in, and the pressure in the 
 cylinder is reduced to that of the 
 atmosphere before the exhaust stroke. 
 Thus there is the filling stroke, 
 represented by EC\ the compression 
 stroke, represented by CD\ the 
 working stroke, represented hy AB; 
 ' Fig. 69. and the exhaust stroke, represented 
 
 by BE. 
 The effective cycle is ABCD, which may be considered to 
 be performed by adding heat at constant volume from D to A, 
 
GAS-ENGINES WITH COMPRESSION IN THE CYLINDER 309 
 
 and withdrawing heat at constant pressure from B to C, together 
 with the adiabatic expansion and compression AB and CD. 
 The heat added under this assumption is 
 
 cATa - T,), 
 
 and the heat rejected is 
 
 so that the efficiency is 
 
 c. {T, - Ta) T,-T, ^ ^ 
 
 If the temperature at A and the pressure at D are assumed, 
 then it is necessary to make preliminary calculations of the 
 temperatures at D and at B before using equation (180). Thus, 
 adiabatic compression from C to D gives for the temperature 
 at D 
 
 K — X 
 
 T,= T,{^ ...... (181) 
 
 in like manner adiabatic expansion from A io B gives 
 
 r» = r„ (|?l) (,82) 
 
 in which the value of pa may be calculated by the equation 
 
 p. = p, ~ (183) 
 
 since the pressure rises with the temperature at constant volume 
 from D \.o A. 
 
 For example, if the pressure at the end of compression is 
 90 pounds above the atmosphere, and the temperature at the 
 end of the explosion is 2500° F., then 
 
 0405 
 
 r,= (6o+46o)(li:I±^y"=9i7, 
 
 \ 14.7 ' 
 
3IO 
 
 INTERNAL-COMBUSTION ENGINES 
 
 provided that the temperature of the atmosphere is 60° F. 
 
 2500 + 460 
 917 
 
 pa = 104.7 — ^ \J^ = 338 pounds; 
 
 •405 
 
 (\ "-405 
 ^lll-j = 1199; 
 
 Fig. 70. 
 
 represented by GC. 
 
 338 
 
 IIQQ — S20 
 
 2960 — 917 
 
 If the expansion is not carried to the 
 atmospheric pressure, then the diagram 
 shows a release at the end of the stroke, 
 as in Fig. 70, and the cycle must be 
 considered to be formed by adding 
 heat as before at constant volume, but 
 by withdrav^ing heat at constant volume 
 to cause a loss of pressure from B to 
 G, and by ^withdrawing heat at con- 
 stant pressure, during the process 
 The heat rejected becomes, therefore, 
 
 and the efficiency is 
 
 _ cATg - Tg) -CAT, - TJ 
 
 ' pC^^ 
 
 Tc) 
 
 = I 
 
 c^ (Ta - Ta) 
 T, + K (T, - T,) 
 
 Ta 
 
 (184) 
 
 Assuming, as before, the pressure at D and the temperature 
 at ^, it becomes necessary to find the temperatures at B and at 
 G as well as the temperature at D\ this last may of course be 
 found by equation (181). If the pressure at B is assumed also, 
 then equations (182) and (183) may be used as before to find 
 7^5 ; and Ty may be found by the equation 
 
 T,= r> 
 
 (185) 
 
GAS-ENGINES WITH COMPRESSION IN THE CYLINDER 311 
 
 For example J let it be assumed that the expansion ceases 
 when the pressure becomes 20 pounds above the atmosphere, 
 the other conditions being as in the previous example. Then 
 
 40s 
 
 (2 
 
 500 + 460) f — i— — \ = 1536; 
 
 and 
 
 r,= 1536^ = 650; 
 
 34-7 
 
 e= J - 1536 - 650 + 1.405 (650 - 520) _ ^^^g^ 
 2960 — 917 
 
 Though not essential to the solution of the example, it is 
 interesting to know that the volume at C is 
 
 \ 14.7 / 
 
 4 + 
 
 times the volume at D, and that the volume at 5 is 
 
 <34-7/ 
 
 5 + 
 
 times the volume at A. 
 
 When, as in common practice, the 
 four strokes of the piston are of equal 
 length, the diagram takes the form shown 
 by Fig. 71; the effective cycle may be 
 considered to be equivalent to heating at 
 constant volume from D io A and cooling 
 at constant volume from B to C, together 
 with adiabatic expansion and compression 
 from ^ to ^ and from C to Z) 
 
 
 A 
 
 
 
 
 
 D 
 
 \^^^B 
 
 
 
 E 
 
 
 "~-^C 
 
 
 V 
 
 Fig. 71. 
 
312 INTERNAL-COMBUSTION ENGINES 
 
 The heat applied is 
 and the heat rejected is 
 so that the efficiency is 
 
 Since the expansion and compression are adiabatic, we have 
 the equations 
 
 T.v,'^-' = TgV,^-\ and T,v,^-' = T^ v^"-') 
 
 but the volumes at A and D are equal, as are also the volumes 
 at B and C; consequently by division 
 
 consequently 
 
 T, - n T, T, 
 
 
 and the expression for efficiency becomes 
 
 ft)- <■»') 
 
 e = I 
 
 which shows that the efficiency depends only on the compression 
 before explosion. 
 
 For example^ if the volume of the clearance or compression 
 space is one-third of the piston displacement, so that v^ is one- 
 fourth of Vc, then the efficiency is 
 
 0.405 
 
 e=^ 1 - \-j = 0.43. 
 
 The pressure at the end of compression is 
 
GAS-ENGINES WITH COMPRESSION IN THE CYLINDER 313 
 
 pounds absolute, or 88.4 pounds by the gauge. The calculated 
 efficiency is therefore not much less than the efficiencies found for 
 other examples; it is notable that the efficiency is nearly the 
 same as that calculated on page 307 for an engine with separate 
 compression to 90 pounds by the gauge. For the case in hand, 
 however, the pressure after explosion, which depends on the 
 temperature, may exceed 300 pounds per square inch. 
 
 The diagrams from engines of this type * resemble Fig. 72, 
 
 Fig. 72. 
 
 which was taken from an Otto engine in the laboratory of the 
 Massachusetts Institute of Technology. During the filling 
 stroke, the pressure in the cylinder is less than that of the atmos- 
 phere; the charge is ignited just before the end of the compression 
 stroke, and the explosion though rapid is not instantaneous, 
 as is indicated by the rounding of the corners of the diagram 
 at both the bottom and the top of the explosion line, and by 
 the leaning of that line to the right. Release occurs before the 
 end of the stroke, and there is considerable back pressure during 
 the exhaust stroke. The scale of the diagram is 150 pounds to 
 the inch, and the maximum pressure is 251 pounds. The atmos- 
 pheric line is omitted to avoid confusion. 
 
 In order to show clearly the conditions during the exhaust 
 and filling strokes, the diagram Fig. 73 was taken with a scale 
 
 * A description of a four-cycle gas-engine will be found on page 337, and may 
 be read for the first time in this connection. 
 
314 INTERNAL-COMBUSTION ENGINES 
 
 of 20 to the inch, and with a stop to limit the rise of the indicator- 
 piston; the upper part of the diagram consequently does not 
 appear in the figure. The mean back-pressure is about five 
 pounds, and the reduction of pressure in the cylinder is between 
 
 Fig. 73. 
 
 three and four pounds below the atmosphere. Reference to 
 the influence of the negative area of Fig. 73 on the effective 
 indicated horse-power will be made later. 
 
 The compression line does not differ very much in appearance 
 or in reality from an adiabatic line from air, though the air may 
 be expected to receive heat from the walls of the cylinder during 
 the first part of the compression stroke, and may part with heat 
 during the latter part. The expansion line has a resemblance 
 to the adiabatic line for air, but is usually less steep, especially 
 for large engines; but in reality the conditions in the cylinder 
 are very different, for the combustion does not cease at the max- 
 imum pressure, but continues more or less during the expansion 
 stroke, and may extend to the release; and at the same time 
 heat is taken up energetically by the walls of the cylinder, which 
 are cooled by a water-jacket to avoid overheating. These two 
 effects, after-burning and loss of heat to the water-jacket, deter- 
 mine the form of the expansion line and its resemblance to an 
 adiabatic line. 
 
 Characteristics of Gases. — There are three distinct kinds of 
 gases used in gas-engines: (i) illuminating-gas, (2) producer- 
 gas, (3) blast-furnace gas. Each class has fairly well-marked 
 characteristics, though there is considerable variation in a class. 
 The greatest variation is liable to be found in blast-furnace 
 gas, since the metallurgical operations are of the first importance, 
 
CHARACTERISTICS OF GASES 
 
 315 
 
 and, if the gas is to be used for generating power, the engines 
 and adjuncts must be adapted to the conditions. Producer- 
 gas is made from coke, anthracite, or from non-caking bituminous 
 coal, and consists mainly of hydrogen and carbon monoxide, diluted 
 with the nitrogen of the air, together with five or ten per cent 
 of carbon dioxide and a small percentage of hydrocarbons espe- 
 cially when bituminous coal is used. Illuminating-gas is now 
 commonly made by the water-gas process, which yields a gas not 
 very unlike producer-gas, but that gas is enriched with hydro- 
 carbons of varying composition; formerly illuminating-gas was 
 distilled from gas-coal, which was a rich bituminous coal yielding 
 a large percentage of hydrocarbons when distilled. 
 
 The general characteristics of illuminating-gas are represented 
 by the following analysis of Manchester coal-gas quoted from 
 the first edition of Clerk's Gas Engine, and used by him to 
 investigate the effect of combustion on the volume of the gas. 
 
 ANALYSIS OF MANCHESTER COAL-GAS. (Bunsen and Roscoe.) 
 
 CO 
 
 Hydrogen, H . . 
 Methane, CH^ . 
 Carbon monoxide 
 
 Ethylene, C2H4 
 
 Tetrylene, C4Hg 
 
 Sulphuretted hydrogen, H^S 
 
 Nitrogen, N 
 
 Carbon dioxide, CO, . . . 
 
 Vols 
 
 Total I 100.00 
 
 Vols. O lequired 
 
 for 
 
 Combustion. 
 
 22 
 
 79 
 
 69 
 
 8 
 
 3 
 
 32 
 
 12 
 
 24 
 
 14 
 
 28 
 
 
 
 43 
 
 
 
 Products. 
 Vols. 
 
 45 
 
 104 
 
 6 
 
 16 
 
 19 
 o 
 2 
 3 
 
 58, H,0 
 
 7> 
 
 64, CO2 
 
 32, CO2 & H2O 
 
 04, CO2 & H2O2 
 
 58, H2O & SO2 
 
 46 
 
 67 
 
 122.86 O 198.99, C02,H2 0& SO2 
 
 An analysis of illuminating-gas made by the water-gas process 
 at Boston gave: Hydrogen 27.9, methane 28.9, carbon monoxide 
 25,3, carbon dioxide 1.9, hydrocarbons 12.0, nitrogen 3.0, oxygen 
 i.o; the analysis being only proximate does not allow of a calcu- 
 lation of the oxygen required for combustion. 
 
 The following composition of producer-gas was taken from a 
 report of tests on a gas-engine by Professor Meyer, for which 
 
3i6 
 
 INTERNAL-COMBUSTION ENGINES 
 COMPOSITION OF PRODUCER-GAS. 
 
 
 Vols. 
 
 Vols, of 
 Oxygen for 
 Combustion. 
 
 Products 
 Vols. 
 
 Hydrogen, H . . 
 
 13-7 
 0.7 
 
 24.6 
 
 6.5 
 
 •5 
 
 54-0 
 
 6.8 
 1.4 
 12.3 
 
 
 
 
 13.7 H2O 
 2.1, CO2 &H2O 
 24.6, CO2 
 6.5. CO2 
 0.5,0 
 
 54-0, N 
 
 Methane, CH4 ......... 
 
 Carbon monoxide, CO .... 
 
 Carbon dioxide, COg 
 
 Oxygen, O 
 
 Nitrogen, N 
 
 
 
 100 
 
 20.5 
 
 101.4 
 
 details are given on page 350. Eight analyses are given in the 
 original paper, v^hich are here averaged. 
 
 Rich non-caking bituminous coals may shov^ a considerably 
 larger proportion of hydrogen. 
 
 In a paper on the use of blast-furnace gas Mr. Bryan Donkin 
 gives the composition of gases from five furnaces in England, 
 Scotland, and Germany, from which the average values in the 
 folio v^ing table vv^ere deduced: 
 
 COMPOSITION OF BLAST-FURNACE GAS. 
 
 
 Vols. 
 
 Vols, of 
 
 Oxygen for 
 
 Combustion. 
 
 Products. 
 Vols. 
 
 Hydrogen, H 
 
 Carbon monoxide, CO . . . . 
 
 Carbon dioxide, CO2 
 
 Nitrogen, N. 
 
 2-5 
 
 29.1 
 
 7.0 
 
 61.4 
 
 1-3 
 19.6 
 
 
 
 
 2.5, H2O 
 
 29.1, CO2 
 
 7.0, CO2 
 
 6i.4,N 
 
 
 
 100 
 
 20.9 
 
 TOO 
 
 Not only is there much variation in the composition of gases 
 from different blast-furnaces, but the variation v^ith the progress 
 of the metallurgical operations is so marked that it is customary 
 to mingle the gases from several furnaces in order to insure 
 that the gas is proper for use in gas-engines. 
 
CHARACTERISTICS OF GASES 
 
 317 
 
 The amounts of oxygen required for the combustion of a given 
 volume of any gas can be computed from the formulae rep- 
 resenting the chemical changes accompanying combustion, 
 together with the fact that a compound gas occupies tv^o volumes, 
 if measured on the same volumetric scale as the component 
 gases. Thus two volumes of hydrogen with one volume of 
 oxygen unite to form superheated steam as represented by the 
 formula 
 
 2H + O = Ufi, 
 
 and the three volumes after combustion and reduction to the 
 original temperature are reduced to two volumes; in this case, 
 to have the statement hold, the original temperature would need 
 to be very high, to avoid condensation of the steam into water. 
 But in the application to gas-engines this leads to no inconven- 
 ience, because the gases after combustion remain at a high tem- 
 perature till they are exhausted, and the laws of gases can be 
 assumed to hold approximately. A compound gas like methane 
 can be computed as follows: 
 
 CH, +40== CO2 + 2H2O. 
 Since the compound gas methane occupies two volumes and 
 requires four volumes of oxygen, it is clear that each cubic foot 
 of that gas will demand two cubic feet of oxygen; the total volume 
 may be reckoned as six before combustion, and in like manner 
 there will be six volumes after combustion, namely, two of 
 cairbon d^ioxide and four of steam. 
 
 In this way the oxygen required for combustion of the three 
 kinds of gas for which the compositions arc given, has been 
 computed, and also the volumes after combustion. For coal- 
 gas the contraction due to the combustion of hydrogen and 
 carbon monoxide is very nearly compensated by the expansion 
 due to the breaking up and combustion of the hydrocarbons. 
 A similar result may be expected for any illuminating-gas. On 
 the other hand, producer-gas if burned in oxygen would show a 
 contraction of 
 
 I20.t: — IOI.4 IQ 
 
 = -^- = 0.16; 
 
 120.5 ^20 
 
3i8 INTERNAI^COMBUSTION ENGINES 
 
 but in practice the producer-gas is mixed with 1.3 to 1.5 of its 
 volume of air, so that the contraction of 19 volumes takes place 
 in 230 to 250 volumes, and thus is therefore of yV to 8 per cent 
 contraction. 
 
 Clearly this matter has to do with the question raised on 
 page 306, as to the reliance to be placed on the ideal efficiencies 
 which assume heating of air instead of combustion of fuel. 
 For illuminating-gas that assumption appears unobjectionable, 
 and for producer- gas the discrepancy is not so great as to 
 destroy the value of the method. 
 
 Temperature after Explosion. — The most difficult question 
 concerning the theoretical thermal efficiency of gas-engines is 
 the determination of the temperature after explosion. Direct 
 determination is difficult both on account of the high tempera- 
 ture and the very short interval of time during which the maxi- 
 mum temperature can be considered to exist. 
 
 A comparatively simple calculation of the temperature after 
 explosion can be made from a diagram like Fig. 72, if the com- 
 pression can be assumed to be adiabatic, and if the laws of 
 perfect gases can be applied. The pressure on the compression 
 line measured on an ordinate through the point a of maximum 
 pressure, is 61 pounds, or 75.7 pounds absolute. If the tem- 
 perature of the gases in the cylinder at atmospheric pressure is 
 taken to be 70 degrees, adiabatic compression gives approxi- 
 mately 
 
 o) (1-^' 
 \i4.7/ 
 
 r,= (70 +460) U^) =847°. 
 
 The maximum pressure after explosion is 251 pounds, or about 
 266 pounds absolute. If the temperature at constant volume 
 is assumed to be proportional to the absolute pressure, we have 
 
 ^47 X-— =2975, 
 
 /5-7 
 
 or about 2500° F. This result, which depends on the assumption 
 that the properties of the charge in the cylinder of a gas-engine 
 
AFTER BURNING 
 
 319 
 
 are and remain the same as those of gases at ordinary tempera-, 
 tures, can be taken as a first approximation only. 
 
 In connection with tests on a gas-engine (see page 350) using 
 illuminating-gas, Professor Meyer makes a careful investigation 
 of the temperature which might be developed in the cylinder 
 of a gas-engine if the charge were completely burned in a non- 
 conducting cylinder. The results only will be quoted here. 
 The composition of the gas will be found on page 316, from 
 which it appears that it was probably coal-gas resembling 
 Manchester gas, and not differing very radically from Boston 
 gas, by use of which Fig. 72 was obtained. The pressure at 
 the end of compression was 69 pounds by the gauge, and after 
 explosion was 220 pounds, so that the conditions were not very 
 different from those of Fig. 72, except that the pressure on the 
 compression line is not on the ordinate for measuring the max- 
 imum pressure, and therefore the parallel calculation cannot be 
 made. 
 
 On the assumption of constant specific heats Professor Meyer 
 finds that complete combustion should give 4250° F. in a non- 
 conducting cylinder, but using Mallard and Le Chatelier's 
 equation for specific heats at high temperatures he gets 3330*^ F. 
 Those experimenters report that dissociation of carbon monoxide 
 begins at about 3200° F., and of steam at about 4500° F.; but 
 the dissociation is slight at those temperatures. Though the 
 subject is still obscure, it appears fair to assume that the failure 
 to reach the temperatures which can be computed for complete 
 combustion, can be charged in part to suppression of combustion 
 on account of the high temperature in the cylinder. 
 
 After Burning. — Accompanying the suppression of heat on 
 account of the approach to the temperature of dissociation is 
 the development of heat during expansion which extends in some 
 cases to release, as is indicated by a flicker of flame into the 
 exhaust; explosions in the mufflers of automobiles are attributable 
 to this action. The fact that the expansion curve approaches 
 the adiabatic line during expansion is indirect evidence of after- 
 burning, because the water-jacket withdraws heat at the same 
 
320 INTERNAL-COMBUSTION ENGINES 
 
 time. The actual expansion line is less steep than the adiabatic 
 for gas, and for large gas-engines can approach the condition 
 represented by the equation 
 
 pv ^'^ = const.; 
 
 but a part of this action can be attributed to the presence of 
 carbon monoxide and steam in the products of combustion, which 
 may reduce the exponent of the adiabatic Hne from 1.405 to 1.37. 
 
 Water-jackets. — All except very small internal-combustion 
 engines have the heads and barrels of the cylinder cooled by 
 w^ater-jackets ; large engines commonly have the pistons cooled 
 with water, and double-acting engines have the piston-rods and 
 stuffing-boxes cooled. Not uncommonly the valves of large 
 engines are cooled, and if such engines use rich gases, extra 
 cooling surface is provided in the charging space or cartridge 
 chamber; the latter device is to avoid pre-ignition, and the 
 former is in part for the same purpose. 
 
 Primarily, water-jackets are to protect the metal of the cylinder 
 and to make lubrication possible. The use of jackets and other 
 cooling devices has been considered a mechanical necessity, which 
 many inventors have sought to avoid; but it appears likely that 
 it is only a question whether the heat shall be withdrawn by a 
 water-jacket, or whether the heat shall be suppressed by dissocia- 
 tion and thrown out in the exhaust. Large engines, which have 
 less exposed area per cubic foot of cylinder contents, show a less 
 percentage of heat withdrawn by the jacket, but a larger per- 
 centage thrown on in the exhaust; the balance is, however, in 
 favor of large engines which show a better economy. 
 
 Economy and Efficiency. — It is customary and altogether 
 desirable to rate the economy of gas-engines and other internal- 
 combustion engines in thermal units per horse-power per minute; 
 this was found to be desirable, if not necessary, for studying 
 the means of improving the performance of steam-engines. But 
 as steam-engines are commonly rated in terms of steam per 
 horse-power per hour, so also gas-engines have been rated in 
 terms of cubic feet of gas per horse-power per hour, and gasoline- 
 
ECONOMY AND EFFICIENCY 
 
 321 
 
 and oil-engines have been rated in pounds of fuel per horse- 
 power per hour. The variation in the fuel used for such engines 
 makes the secondary methods less satisfactory than rating engines 
 on steam-consumption, so that it should be employed only when 
 the calorific capacity of the fuel cannot be determined or 
 estimated. 
 
 Since the heat-equivalent of a horse-power is 42.42 thermal 
 units per minute, the actual thermal efficiency of an internal- 
 combustion engine can be determined by dividing that figure 
 by the thermal units consumed by the engine per horse-power 
 per minute. For example, the engine tested by Professor Meyer 
 used about 170 thermal units per horse-power per minute, 
 and its thermal efficiency was 0.25, using the indicated horse- 
 power. The ratio of the cartridge space to the whole volume 
 
 was 
 
 — —, so that equation (187) gives in this case 0.42 for the 
 
 nominal theoretical efficiency; consequently the ratio of the 
 efficiencies is nearly 0.60. 
 
 By a somewhat intricate method Professor Meyer computed 
 the efficiency for two tests on the engine for which details are 
 given on page 350, on the assumption that complete combustion 
 occurred in a non-conducting cylinder. The ratio of gas to air 
 in one test was one to 8.9, and in the other one to 12. Assuming 
 that the specific heat of the mixture in the cylinder before and 
 after explosion, remained constant, he found for the first test 
 an efficiency of 0.398, and for the second 0.403; but making use 
 of Mallard and Lc Chatelier's investigations on specific heats at 
 high temperatures, he found for the efficiencies 0.297 and 0.318. 
 The values for constant specific heat differ but little from the 
 nominal theoretical efficiency; in fact, if the exponent be reduced 
 from 0.405 to 0.38, the nominal efficiency becomes 0.40, which 
 is a very close coincidence. But the efficiencies computed from 
 the heat-consumptions for these two tests are 0.253 ^-nd 0.249. 
 If then the nominal theoretical efficiency, or the efficiency which 
 Professor Meyer calculated on assumption of constant specific 
 
322 INTERNAL-COMBUSTION ENGINES 
 
 heat, be taken as the basis of comparison, the engine gave for 
 the ratio of actual to theoretical efficiency, 
 
 0.253 -^ 0.398 = 0.64, or 0.249 ^ 0.403 =^ 0.62. 
 If, however, we take his second values with variable specific heat, 
 we have 
 
 0.253 -J- 0.297 ^ o-^Sj or 0.249 H- 0.318 = 0.78. 
 
 Professor Meyer uses these computations to emphasize the 
 importance of better knowledge of the properties of the working 
 substance in the cylinder of an internal-combustion engine; 
 because, if the nominal theoretical efficiency be taken for the 
 basis of comparison, there appears to be room for material 
 improvement in the economy of the engine; whereas, if the 
 second set of computations is taken as the basis, there is little 
 prospect of improvement. In conclusion, attention is called to 
 the fact that these tests were on a small engine which developed 
 only ten brake horse-power. 
 
 In the discussion of efficiency we have thus far made use of the 
 heat-consumption per indicated horse-power, which is proper, 
 because the fluid efficiency (or the efficiency of the action of the 
 working substance) should for this purpose be preserved from 
 confusion with the friction and mechanical efficiency of the 
 engine. For the same reason, and also because the power of a 
 steam-engine can be determined satisfactorily by the indicator, 
 we used indicated horse-power in the discussion of steam-engine 
 economy. There is, however, a reason why the indicated power 
 is not a satisfactory basis for the discussion of the economy of 
 internal -combustion engines, namely, the fact that a series of 
 successive diagrams taken without removing the pencil from the 
 paper on the indicator drum, will show a wide dispersion, due 
 to the varying explosive action in the cylinder even when con- 
 ditions are most favorable. When the engine is governed by 
 omitting explosions, this difficulty is much aggravated on account 
 of the negative work of idly drawing in, compressing, and expel- 
 ling .air. 
 
 Fig. 74 shows a diagram taken from the same engine as Fig. 
 72, page 313, but with a fifty-pound spring and a stop to prevent 
 
ECONOMY AND EFFICIENCY 
 
 323 
 
 the indicator piston from rising too high which exhibits the 
 effects of an idle cycle and other features. A portion of the 
 expansion curve is shown, with oscillations due to the piston 
 suddenly leaving the stop. The exhaust of the spent gases is 
 
 Fig. 74. 
 
 shown by the curve ah, after which the engine draws a charge 
 of air (without gas) and compresses it on the upper curve from 
 c to d\ on the return stroke the indicator follows the lower 
 curve from d to c, so that the loop represents work done by the 
 engine; finally the air is exhausted, while the indicator draws 
 the line ce. To explain the difference between the exhaust lines 
 ah and ae with spent gas and with air only, it may be noted that 
 there is a marked drooping of the exhaust line a to about one- 
 fifth of the stroke from h] this feature is more marked in Fig. 73, 
 which shows the exhaust stroke to a larger scale. This droop 
 may be attributed to the inertia of the column of gas in the 
 exhaust pipe; the smaller volume of air which is exhausted with 
 gradually rising pressure does not happen to develop this feature 
 in such a way as to produce the result shown in Fig. 73. This 
 drop of pressure in the exhaust pipe may be accentuated by 
 adjusting the length of the exhaust pipe so as to give a partial 
 vacuum just before the engine takes its next charge; when this 
 action is obtained, the air-valve is opened before the gas-valve, 
 and fresh air is drawn through the cyhnder to produce a scav- 
 enging effect before the engine takes a new charge. At one 
 
324 INTERNAL-COMBUSTION ENGINES 
 
 time considerable importance was given to scavenging to clear 
 out spent gas, but it attracts less importance now for four-cycle 
 engines. 
 
 In indicating a gas-engine, allowance is, of course, made for 
 the negative work of exhaust and filling; if an explosion is missed, 
 allowance for the negative work for the operation shown on 
 Fig. 74 should be made for each idle cycle, and when the engine 
 has only a few working cycles the error of taking proper account 
 of the negative work may be very large. This is, of course, 
 another reason why comparisons are best based on brake horse- 
 power. As can be seen from Table XXXV on page 350, the 
 mechanical efficiency may range from 60 per cent to 80 per cent, 
 depending mainly on the power developed; these figures are for 
 continuous explosions, and the efficiency is liable to be much 
 reduced if explosions are omitted at reduced power. 
 
 Two-cycle engines commonly have a compression pump 
 which supplies the mixture of gas and air at a pressure of five or 
 ten pounds above the atmosphere; in such case the work of com- 
 pression must be determined separately and allowed for, in the 
 measurement of the indicated horse-power. 
 
 Valve-Gear. — The supply and exhaust parts for an internal- 
 combustion engine are always separate, so that there are at 
 least two valves (or the equivalent) for each working end of a 
 cylinder; there is also for a gas-engine a separate valve for 
 admitting or controlling the supply of gas. The valves are 
 usually plain disk or mushroom valves with mitered seats; in 
 some cases double-beat valves are used on large engines. Very 
 commonly two-cycle engines exhaust through ports cut through 
 the cylinder walls and opened by the piston itself, which over- 
 runs them near the end of its stroke; in at least one case the 
 exhaust-valves of a four-cycle engine are water-cooled hollow 
 piston-valves, but that construction appears to be exceptional. 
 
 The exhaust-valves are always positively controlled, since they 
 must remain closed against pressure in the cyHnder until the 
 proper time. The inlet valves may be operated by the pressure 
 of the operating fluid, opening during the suction stroke and 
 
STARTING DEVICES 
 
 325 
 
 remaining closed during the compression, expansion, and exhaust 
 strokes; but very commonly the admission valves both for air 
 and for gas (when the latter are separate) are positively con- 
 trolled, and for very high speeds this action is necessary. 
 
 From what has been said, it will be evident that the general 
 problem of the design of the valve-gear for an internal-combus- 
 tion engine resembles that for a four-valve steam-engine, espe- 
 cially that type of steam-engine valve-gear which uses simple 
 lift-valves. The solution which is most evident and most com- 
 monly chosen is some form of cam-gear; usually the valves are 
 held shut by springs, and are opened by cams on a cam-shaft 
 either directly or through linkages. This cam-shaft is conven- 
 iently placed parallel to the axis of the cylinder and driven* from 
 the main shaft through bevel-gears; the four-cycle engine has 
 the gear in the ratio of one to two, so that the cam-shaft makes 
 one revolution for two revolutions of the engine in order to 
 properly time the four principal operations of the cycle. The 
 spring closing a valve must be properly designed not only to 
 give the required pressure to hold the valve shut, but to provide 
 the proper acceleration so that the valves shall remain under 
 the control of the cam when closing. The cam-shaft, in addi- 
 tion to the cams for the normal action of the engine, carries cams 
 which facilitate starting the engine. 
 
 Starting Devices. — Since an internal-combustion engine must 
 do the work of drawing in and compressing its charge before 
 energy is developed by explosion, some special device is required 
 to start such an engine, involving the use of power from an 
 external source. It is seldom if ever convenient .to apply power 
 sufficient to start an engine under its load, and consequently 
 there must be some disengagement gear to allow the engine to 
 start without load, except in cases where the load is developed 
 only as the engine comes up to speed. 
 
 A small engine can be started by hand, by turning the fly- 
 wheel or by working a special hand-gear; the latter should have 
 a ratchet or clutch which will release or throw it out of gear 
 as soon as the engine starts. The engine is driven by hand until 
 
326 INTERNAL-COMBUSTION ENGINES 
 
 the operations of charging, compressing, and igniting are per- 
 formed, whereupon the engine should start promptly. Except 
 for very small sizes, there is a special cam that may be thrown 
 into action, and which holds the exhaust-valve open till the 
 piston has completed about half the compression stroke, during 
 which the charge is partially wasted ; by this device the labor of 
 compression is much reduced. When an engine is started in 
 this manner the ignition should be delayed until the piston is 
 past the dead-point, otherwise the engine is liable to start back- 
 ward. The disengagement clutch will not act in such case, 
 and there is great danger of an accident. 
 
 When electric or other external power can be substituted for 
 hand-power, this method can be used for starting engines of 
 large size. 
 
 A very common device is to start the engine with compressed 
 air from a tank at a pressure of loo to 200 pounds per square 
 inch. This air is supplied to the tank by a pump driven by 
 the engine when necessary. To start the engine the cylinder is 
 disconnected temporarily from the ordinary gas and air supply, 
 and is worked Hke a compressed-air engine until well under 
 way, whereupon the compressed air is shut off and the normal 
 action is restored. The air can be supplied from the tank by 
 valves controlled by hand or by a special gear. If the engine 
 has more than one cylinder, compressed air may be supplied to 
 one only, and the other cylinder (or cyUnders) may act in the 
 usual manner, except that the compression may be reduced till 
 the engine is started. 
 
 At one time gas was withdrawn from the cylinder during the 
 compression stroke, and stood in a reservoir to be used for start- 
 ing. Such gas could be used at a pressure of 60 to 90 pounds, 
 to start the engine as just described; or the piston could be set 
 beyond the dead-point ready to start, gas could be supplied 
 under pressure and ignited. There is, of course, some objection 
 to the storage of explosive mixtures, though there is no reason 
 why the reservoir should not be made able to endure an explosion. 
 
 Governing and Regulating. — There are four ways available 
 
GOVERNING AND REGULATING 
 
 327 
 
 for controlling the power of an internal-combustion engine: (i) 
 by regulating the proportion of air and fuel, (2) by regulating 
 the amount of air and fuel without changing the proportion, 
 (3) by omitting the supply of fuel during a part of the cycles, (4) 
 delaying ignition. 
 
 (i) Regulation by controlling the supply of fuel is the normal 
 method for engines working on the Joule or Brayton cycle with 
 compression in a separate cyUnder, for which a theoretical dis- 
 cussion is given on page 305. For this cycle there is no explo- 
 sion, but the gaseous or liquid fuel can be burned during admis- 
 sion in any proportion. 
 
 The Brayton engine had a double control for variation in 
 load. In the first place a ball-governor shortened the cut-off 
 for the working cylinder when the speed increased on account 
 of reduction in the load; this had the effect of raising the pres- 
 sure in the air reservoir into which the air-pump delivered, since 
 that pump delivered nearly the same weight of air per stroke 
 under all conditions. In the second place, there was an arrange- 
 ment for shortening the stroke of the little oil-pump when the 
 pressure increased; so that indirectly the amount of fuel was 
 proportioned to the load. A similar effect was produced when 
 the engine was designed to use gas. 
 
 For the Diesel motor, to be described later, the fuel supply 
 can be adjusted to the power demanded for all conditions of 
 service. 
 
 But for gas-engines it has not been found practicable to con- 
 trol the engine by regulating the mixture of gas and air except 
 within narrow ranges. This comes from the fact that very rich 
 or very poor mixtures of gas and air will not explode. Experi- 
 ments at the Massachusetts Institute of Technology show that 
 illuminating-gas will explode at atmospheric pressure with 
 the ratio of gas to air varying from 1 115 to i : 3.5. Weaker mix- 
 tures can be exploded in a gas-engine after compression. Again, 
 gas may be supplied in such a way that the mixture near the 
 point of ignition may be rich enough to explode promptly and 
 fire the remainder of the charge. The ignition of weak mix- 
 
328 INTERNAL-COMBUSTION ENGINES 
 
 tures should occur before the end of the compression stroke, so 
 that even though the explosion is slow it may be completed near 
 the beginning of the working stroke. 
 
 The tests on page 350 show that with the ratio of gas to air 
 varying from i :8 to i : 12 the power may vary from 10 to 6 
 brake horse-power. 
 
 This discussion of the possibility of varying the power by 
 varying the mixture of gas and air would appear to show that 
 for many purposes that should be a practicable way of governing 
 a gas-engine. Nevertheless it is used very little if at all, although 
 it was tried early. 
 
 (2) The common way of governing large gas-engines is to 
 vary the supply of the mixture without varying its proportions. 
 There are two ways of accomphshing this : in the first place the 
 charge may be throttled so that a less weight is drawn in at a 
 lower pressure; in the second place the admission valve may be 
 closed before the end of the filhng stroke, thus cutting off the 
 supply. The effect of throttling is to increase to a marked extent 
 the reduction of pressure during the filling stroke with a corre- 
 sponding increase in the negative work; the area of the loop 
 Hke that shown by Fig. 72, page 313, will increase. The effect 
 of closing the inlet-valve before the end of the filling stroke is 
 to produce a diagram similar to Fig. 70, page 310. The charge 
 is drawn in at a pressure a little below that of the atmosphere 
 as far as the point C; then the piston goes on to the end of the 
 stroke with an expansion that could be represented by produ- 
 cing the curve DC\ the return stroke produces a compression 
 that can be represented by retracing the produced part of the 
 curve from C and then drawing the true compression curve 
 CD. In practice the indicator diagram will show a small nega- 
 tive work due to the expansion and compression caused by the 
 early closing of the supply-valve, but the loss on that account is 
 less than by throtthng. 
 
 (3) The third way of controlling a gas-engine is to cut off 
 the gas supply so that the engine draws in a charge of air only 
 and makes an idle cycle, represented by Fig. 74, page 323. At 
 
IGNITION 329 
 
 small power the negative work of idle cycles very much reduces 
 the brake economy of the engine. Now, a single-acting four- 
 cycle engine has only one working stroke in four, and must fur- 
 nish between times the work of expulsion, filling, and compres- 
 sion, and even with a very heavy fly-wheel will show an irregu- 
 larity in speed of revolution that is very objectionable for many 
 purposes. This difficulty is very much increased if the engine 
 is governed by omitting explosions on the hit-or-miss principle. 
 
 (4) Delaying ignition is one of the favorite ways of reducing 
 the power of automobile-engines on account of its convenience; 
 it is little used for other engines, and is very wasteful of fuel, 
 as there is not time for proper combustion. 
 
 Ignition. — The ignition of the charge may be produced by 
 one of three methods: (i) by an electric spark, (2) by a hot tube, 
 or (3) by compression in a hot chamber. 
 
 (i) The electric spark may be produced in one of two ways, 
 — by the make-and-break method, or by the jump-spark method. 
 For the first method a movable piece is worked inside the cylin- 
 der walls, which closes a primary circuit some time before igni- 
 tion is desired; the slight closing spark has no effect. At the 
 proper time the moving mechanism breaks the circuit, and a 
 good spark is made between the terminals, which are tipped 
 with platinum. A coil in the circuit intensifies or fattens the 
 opening spark. The spark obtained by this method is likely 
 to be better than the jump-spark, but there is the great incon- 
 venience of a moving mechanism in a cylinder exposed to very 
 high pressure, and the motion must be communicated by a 
 piece which enters the cylinder through a stuffing-box. 
 
 The jump-spark between two platinum terminals in an insu- 
 lated spark-plug, screwed through the cyHnder wall, is a high- 
 tension spark in a secondary circuit made by a circuit-breaker 
 outside of the cylinder. The movable parts in this case are under 
 observation and can be adjusted, and the spark-plug can be 
 easily withdrawn for examination or renewal. Frequently there 
 are two plugs that can be worked individually or together, or 
 both make-and-break and jump-sparks may be supplied. 
 
330 INTERNAI^COMBUSTION ENGINES 
 
 The circuit may be supplied by a primary battery, or may be 
 generated by a small dynamo driven by the engine, or may be 
 supplied from any convenient source. When a dynamo is sup- 
 plied, the engine is usually started by aid of a battery. 
 
 The electric method of ignition was the earliest used in the 
 history of the gas-engine, and though it was at one time neglected, 
 now tends to become universal. 
 
 (2) The hot tube requires only a small iron tube, which is 
 kept red-hot by a Bunsen burner or other heating flame. The 
 tube comes out horizontally from the cyhnder, and sometimes 
 is turned upward for convenience in heating. At the proper 
 time the explosive mixture in the cylinder is admitted to the 
 tube by a valve which is worked by the engine. Sometimes 
 the tube has an inlet- valve at the outer end to ventilate the 
 tube with air drawn in during the filling stroke. This method 
 has been widely used in Great Britain, where the electrical 
 method has met with little favor, though the prejudice against 
 it is passing away. 
 
 (3) Ignition by compressing the charge in a hot chamber is 
 used exclusively in oil-engines, and is an ingenious example of 
 taking advantage of a condition that at first sight appears to be 
 undesirable. The mixture of air and kerosene oil in engines of 
 this class is produced by spraying oil into a chamber attached 
 to the cylinder and unprovided with a water-jacket, so that it 
 is maintained by the explosion at a red heat. The charge thus 
 produced is more likely to be exploded than a mixture of gas 
 and air, when it comes in contact w ith a hot surface, and under the 
 conditions stated explosion cannot be avoided. Much ingenuity 
 has been expended in adjusting sizes and proportions of parts, and 
 frequency of explosion, to obtain the explosion when it is desired. 
 
 The tendency to work large gas-engines with high com- 
 pression, in order to obtain great power without undue bulk 
 and cost, is likely to lead to the danger of premature explosion, 
 especially when rich gas is used. Any projecting part (a bolt- 
 head or part of a valve) may become sufficiently heated to 
 cause explosion; or a spongy spot in a casting may act in the 
 
GAS-PRODUCERS 
 
 331 
 
 same way. Premature explosion in a small engine after it is 
 started may be an inconvenience, but in a large engine it may 
 lead to an accident. 
 
 Gas-Producers. — A gas-producer is essentially a furnace 
 which burns coal or other fuel with a restricted air supply, so 
 that the combustion is incomplete and the products of combus- 
 tion are capable of further combustion. In its simplest form a 
 gas-producer will deliver a mixture of carbon monoxide and 
 nitrogen together with small percentages of carbon dioxide oxygen 
 and hydrogen. If a proper proportion of steam is supphed with 
 the air, its decomposition in contact with the incandescent fuel 
 will yield free hydrogen, and the gas will give a higher pressure 
 when exploded, and develop more power in the engine cylinder. 
 
 When gas is produced on a large scale in a stationary plant, 
 intricate devices may be used to rectify the gas and save the 
 by-products, which are likely to be so important as to control 
 the methods employed. The most important by-product at 
 the present time appears to be ammonium sulphate, which is 
 used as a fertilizer, and for this reason a coal is preferred which 
 has a relatively large proportion of nitrogen, x^t a certain 
 station a coal containing three per cent of nitrogen produced 
 crude ammonium sulphate that could be sold for half the price 
 of the coal. This branch of chemical engineering is a specialty 
 of growing importance, and an adequate treatment of it would 
 demand a separate treatise. Such plants, especially when the 
 gas is used for heating furnaces as well as for power, are worked 
 under pressure, the air and steam being blown into the furnace. 
 
 When a producer supplies gas for power only, there is a great 
 gain in simplicity and in certainty of control, if the producer is 
 worked by suction, the engine being allowed to draw its charge 
 directly from the producer. During the suction stroke there 
 must be a sufficient vacuum in the engine cylinder to work the 
 producer; this amounts to about two pounds below the atmos- 
 phere. There is no attempt in this case to save by-products, 
 and the fuel must be chosen so that comparatively simple rectify- 
 ing devices will give a gas that will not clog the engine. At 
 
332 
 
 INTERNAL-COMBUSTION ENGINES 
 
 the present time the fuels used are coke, anthracite, and non- 
 caking bituminous coal. At the Louisiana Purchase Exposi- 
 tion, at St. Louis in 1904, a very large variety of fuels, including 
 caking bituminous coal and lignite, were used in an experimental 
 plant, and it is likely that all kinds of fuel will eventually be 
 used in practice. 
 
 Fig. 75 gives the section of a Dowson suction producer, in 
 which A is the grate carrying a deep coal fire; at B is the charg- 
 ing hopper with double doors, 
 so that the vacuum is not lost 
 during charging; at C is a 
 vaporizer filled with pieces of 
 fire-brick, which are heated by 
 the hot gases from the furnace; 
 water is sprayed on to the fire- 
 brick through holes in a circular 
 water-pipe D, and flashes into 
 steam which mingles with the 
 air supply; the air for com- 
 bustion enters at F, and passing 
 through the vaporizer is charged 
 with steam and then flows 
 through the pipe L to the ash-pit. In the normal working 
 of the engine the gas passes through the pipe G and the 
 water-seat at J to the scrubber K, which is filled with coke 
 sprayed with water. From K the gas passes directly to 
 the engine. To start the producer, kindling is laid on the 
 grate and the furnace is filled; the fire is lighted through a 
 side door, and air is blown in by a fan driven by hand. At 
 first the gas is allowed to escape through the pipe /, until gas 
 will burn well at the testing-cock at H; then the pipe / is shut 
 off, and the gas is blown through the scrubber and wasted at a 
 pipe near the engine until it appears to be in good condition 
 when tested at that place. The engine is then started and the 
 fan is stopped. 
 
 The producer described is intended to burn coke or anthra- 
 
 FiG. 75- 
 
OTHER KINDS OF GAS 
 
 333 
 
 cite; those that burn bituminous coal must have some method 
 of dealing with tarry matter. Sometimes this is accomplished 
 by passing the gas through a sawdust cleaner; sometimes a 
 centrifugal extractor is added. Some makers remove the tar 
 by care in cooling before the gas comes in contact with water. 
 Others pass the distillate through the fire, and thus change it 
 into Hght gas or burn it ; with this in view, some producers work 
 with a down-draught. It is probable that different kinds of 
 fuel will need different treatments. 
 
 Blast-furaace Gas. — From the composition of blast-furnace 
 gas on page 316, it is evident that it differs from producer-gas 
 only in that it contains very little hydrogen, and therefore is 
 hke the gas that would be made in a producer working without 
 steam. During the operation of the furnace the composition 
 is liable to vary and the gas may become too weak; to remedy 
 this difficulty, it is desirable to mingle the gases from two or 
 more furnaces. Since the gas available from a furnace may 
 be equivalent to 2000 horse-power, it is evident that installations 
 to develop power from that source must be on a very large 
 scale. 
 
 The gas from a blast-furnace is charged with a large amount 
 of dust, some of which is metallic oxide, and readily falls out, 
 and the remainder is principally silica and lime which is very 
 fine and light. To remove this fine dust the gas should be 
 passed through a scrubber, which has the additional advantage 
 of cooling the gas. 
 
 Other Kinds of Gas. — Any inflammable gas that can be fur- 
 nished with sufficient regularity can be used for developing 
 power. The gas from coke-ovens is a rich gas resembling 
 producer-gas in its general composition. Natural gas consists 
 of 90 to 95 per cent of methane (CH4) with a small percentage 
 of hydrogen and nitrogen and traces of other gases. This gas 
 for complete combustion requires an equal volume of oxygen 
 and consequently about five times its volume of air; it is prob- 
 able that ten or twelve volumes of air can be used to advantage 
 with this gas in a gas-engine. 
 
334 INTERNAL-COMBUSTION ENGINES 
 
 Gasoline. — The lighter distillates of petroleum, known as gaso- 
 line, are readily vaporized at atmospheric pressure, and provide 
 the most ready means of supplying fuel to small engines; engines 
 of several hundred horse-power developed in several cylinders 
 have been built for small torpedo-boats, but, in general, the use 
 of gasoline has been Hmited by its price to comparatively small 
 craft and to automobiles; in both cases, whether for pleasure or 
 'for business, other things than cost of fuel determine the selec- 
 tion of the engines. The same is true for the engines of rela- 
 tively small power used for stationary plants. 
 
 The most vital feature of the gasoline-engine is the vaporizer 
 or carburetor, and this device has received much attention, 
 especially for automobile-engines which are run at very high 
 speed. 
 
 There are three types of carburetors that have been used for 
 gasoline-engines: (i) those depending on direct vaporization, (2) 
 those that depend on aspiration with a float, and (3) those 
 depending on aspiration without a float. The earliest types 
 depended on direct vaporization as air was drawn through the 
 mass of the fluid, or through or over fibrous material or a sur- 
 face of wire gauze; some of the latter devices depended on such 
 a regulation of feed that nearly all the fluid vaporized as it was 
 supplied, leaving only a remnant to return to the tank. But 
 in any case there was a chance of fractional vaporization which 
 resulted in the production of a heavier and less tractable 
 fluid. 
 
 The more recent carburetors depend on aspiration, the air 
 supply being drawn past an orifice (or orifices) to which gaso- 
 line is supplied, and from which it can be drawn by the air 
 more or less in proportion as required. For stationary and 
 marine engines the supply of gasoline to the aspirator can be 
 nicely regulated by a float which keeps a small chamber filled 
 just to the level of the aspirating orifices, so that the inrush of 
 air may draw out the gasoline in proper proportion. This 
 device has been tried on automobiles, but the shaking of the 
 machine disturbs the proper action of the float. 
 
KEROSENE OIL 
 
 335 
 
 A third form of carburetor is illustrated by Fig. 76. Here 
 the gasoline is supplied by a pipe E to a valve that may be set 
 to give good average action. Below is a fine conical valve at 
 the end of a vertical rod vi^hich is 
 held up by a light spring; at the 
 middle of the spindle is a disk- 
 valve which fit sloosely in a sleeve. 
 At aa are air-inlet valves, and at 
 A is the entrance to the cylinder. 
 During the suction or filling stroke 
 the spindle is drawn down, opening 
 the valve at the top of the spindle 
 and allowing the air to draw 
 gasoline by aspiration. Some of 
 the hot products of combustion 
 from the exhaust are circulated 
 around the aspirating chamber to 
 prevent undue reduction of tem- 
 perature. This type of carburetor 
 works well enough at moderate 
 speeds, but at very high speeds the inertia of the spindle 
 and disk-valve cannot be overcome rapidly enough by the air, 
 which is consequently throttled, so that there is not the increase 
 of power which might properly be expected at such speeds. 
 
 It is alleged that this type of vaporizer, or carburetor, can be 
 made to deal with kerosene oil and alcohol. 
 
 Kerosene Oil. — The use of kerosene oil has been developed 
 to the greatest extent in England, on account of former restric- 
 tions on the transportation and storage of gasoline. It has 
 been used in America where there is objection to gasoline. 
 
 There is much difficulty in vaporizing or spraying kerosene 
 oil so that it can be properly mixed with air at the temperature 
 for the supply to an engine. On the other hand, any attempt 
 to vaporize the oil at a high temperature results in the deposit 
 of a hard graphitic material. 
 
 One of the most successful English engineers frankly accepts 
 the latter alternative. The essential feature of the carburetor 
 
 Fig. 76. 
 
336 INTERNAL-COMBUSTION ENGINES 
 
 of this engine is shown in Fig. 77, which gives a vertical section 
 of the cylinder- head and of the vaporizer; the remainder of 
 the engine differs in no essential particular 
 from any horizontal gas-engine. This 
 vaporizer, which has a constricted neck, is 
 bolted to the cylinder-head; the forward 
 end is jacketed with water, as is also the 
 cylinder of the engine; but the after end, 
 pj^ which is ribbed internally, is not jacketed; it 
 
 consequently remains at a red-heat when 
 the engine is running. The oil for each explosion is delivered 
 into this hot end of the vaporizer, and is vaporized and mingles 
 with the hot spent gases; toward the end of the compression 
 stroke the charge of air which has been drawn in and com- 
 pressed enters the vaporizer and an explosion occurs. When 
 the vaporizer-head has become clogged, after 24 to 200 hours 
 running, depending on the kind of oil used, it is taken off and 
 the hard adherent deposit is removed; to avoid delay a second 
 head is put on for a corresponding run. This engine is 
 governed by controlling the oil supply; the governor opens a 
 bypass-valve on the oil supply-pipe and allows a part to return 
 to the tank. The hit-or-miss principle is not appHcable, as the 
 vaporizer would become too cool. Before starting, the vaporizer 
 must be heated to a dull red by aid of a kerosene or' gasoline 
 torch. The engine can burn also crude petroleum, or an 
 unrefined distillate resembling kerosene. 
 
 Alcohol. — The demand for gasoline maintains the price at 
 a point which makes it possible in some countries to use alcohol, 
 if it can be relieved from special taxation. To make alcohol 
 unfit for any but mechanical purposes it is mixed with a little 
 wood-alcohol and benzine; this process, called denaturizing, has 
 Httle if any effect on its combustion. For combustion the 
 amount of water brought over during distillation should be 
 limited to a small percentage. The use of alcohol for power in this 
 country has only recently been made possible under the internal- 
 revenue laws, so that we have no experience with it. There 
 
THE FOUR-CYCLE ENGINE 
 
 337 
 
 appears to be no reason why there should be trouble in the use 
 of some form of carburetor like those used for gasoline engines. 
 The Four-cycle Engine. — Fig. 78 gives a vertical section of a 
 Westinghouse four-cycle gas-engine built in various sizes, up to 85 
 horse- power with one cylinder, and up to 360 with three cylinders. 
 Massive engines of this type are horizontal with double- 
 acting pistons, having 
 two cylinders tandem 
 or four twin-tandem. 
 It is somewhat curious 
 that while massive 
 steam-engines tend to- 
 wards the upright con- 
 struction, large gas- 
 engines appear to be 
 all horizontal; it may 
 be for the convenience 
 of the tandem arrange- 
 ment. In Fig. 78 the 
 frame of the engine is 
 arranged to form an 
 inclosed crank - case, 
 which is somewhat 
 unusual for gas- 
 engines. The piston 
 is in the form of a 
 plunger, so that no 
 cross-head is needed; 
 
 a common arrangement for all except massive gas-engines. 
 The cylinder barrel and head are water- jacketed, the inlet 
 and exits being at H and K. Gas and air enter the mixer- 
 chamber M by separate pipes (not shown) and pass by N 
 to the inlet-valve 7; the engine is controlled by a throttle- valve 
 directly connected to a ball-governor beneath the chamber M, 
 but omitted from the figure. The valve is a piston-valve 
 with separate air and gas passages, which works in a sleeve 
 
 Fig. 78. 
 
338 INTERNAL-COMBUSTION ENGINES 
 
 that can be moved by hand; this sleeve may be set by hand 
 to give any desired mixture, and the proportion of the inlet 
 areas for gas and air having been once set, the relative 
 areas remain unchanged, while the governor adjusts the 
 piston-valve to give the amount of mixture that may be 
 demanded by the load on the engine. The inlet-valve / and 
 the exhaust-valve E are each moved by cams at B and at A as 
 indicated, the cams making one revolution for each double 
 revolution of the engine required for the four-stroke cycle. 
 Large sizes have the exhaust- valve water-cooled, to prevent 
 burning the valve, and to avoid danger of pre-ignition. Near A 
 there is a handle for shifting into action the starting-cam which 
 reduces compression when the engine is started. At F are two 
 low-tension make-and-break ignitors, either of which can be 
 thrown into action; they are worked by cams on the shaft that 
 operates the valve /. 
 
 Two-cycle Engines. — The two strokes of a four-cycle engine 
 which exhaust the spent charge and draw in the new charge are 
 performed with a pressure in the cylinder only a little higher or 
 lower than that of the atmosphere, and could be omitted with 
 advantage provided the operations could be performed in some 
 other way. The first successful attempt at a two-stroke cycle 
 was that by Dugald Clerk, who made the following changes: 
 (i) he cut a ring of exhaust ports through the cyhnder walls that 
 were over-run and opened by the piston near the end of the 
 expansion stroke, through which the major part of the spent 
 gases escaped during release; and (2) he provided a pump set 
 about half a stroke ahead of the engine piston, which compressed 
 the new charge to about ten pounds above the atmosphere; as 
 soon as the exhaust had sufficiently reduced the pressure in the 
 cylinder, this new charge opened the inlet-valve and entered the 
 cylinder, blowing the remainder of the spent gases out through 
 the ports in the cylinder walls. The piston closed these ports 
 and compressed the charge on the return stroke, so that only 
 two strokes were required to complete the cycle, and the engine 
 approximated the condition of a single-acting steam-engine in its 
 
TWO-CYCLE ENGINES 
 
 339 
 
 regularity of rotative velocity. The engine could also develop 
 twice as much power for its size as a four-cycle engine, and in 
 certain tests by Mr. Clerk, showed a slightly better economy 
 than the older type of engine. But the operation of replacing 
 the remnants of the spent charge by the fresh charge in engines 
 of this type is rather delicate, there being a chance that some of 
 the spent charge will remain, or that some of the fresh charge 
 will be wasted; it is likely that the charges mingle and that the 
 engine experiences both defects. Eventually the Clerk engine 
 was withdrawn from the market, but the principles are used for 
 two types of engines: (i) small gasoline engines for launches and 
 other small craft, and (2) large engines built for burning blast- 
 furnace gas. 
 
 Gasoline-engines of small power and moderate rotative speed 
 have been made on the two-cycle principle by enclosing the 
 crank- and connecting-rod in a casing, so that the piston may act 
 as the compressing-pump. On the up-stroke a charge of air 
 and gasoline is drawn into the crank-case, and it is slightly com- 
 pressed on the down-stroke. There are two sets of ports cut 
 through the cylinder w^alls near the end of the down-stroke and 
 are opened by the piston; these are on opposite sides of the 
 cylinder; one set, which is opened slightly earlier than the other, 
 forms the exhaust-ports and the other the inlet-ports which are in 
 communication with the crank-case, and therefore supply air 
 and gasoline to replace the spent charge. A barrier is cast on 
 the cylinder-head which prevents the fresh charge from flowing 
 directly across from the inlet to the exhaust, but nevertheless the 
 action is probably much inferior to that of Clerk's engine, which 
 had the charge supplied at the cylinder-head. These engines are 
 nearly valveless and can run in either direction, and on account 
 of the simplicity and small cost have found favor for propelling 
 small craft at moderate speeds. 
 
 If any attempt is made to run two-cycle engines at a high 
 rotative speed there is difficulty in obtaining proper exhaust 
 and supply, since both operations are performed under gaseous 
 pressure that cannot well be increased. Recently two-cycle 
 
340 INTERNAL-COMBUSTION ENGINES 
 
 engines have been introduced on automobiles to a limited extent. 
 Two German engineering firms have developed two-cycle engines 
 especially for burning blast-furnace gas on a large scale, as much 
 as 1500 horse-power in a single cylinder. 
 
 The Korting engine (built by the dc la Verne Machine 
 Company) is a double-acting engine which has a piston nearly 
 as long as the stroke of the engine. At the middle of the length 
 of the cylinder is a ring of exhaust-ports that are uncovered at 
 the end of each stroke, and discharge burnt gases from first 
 one end of the cylinder and then the other. By the side of the 
 engine-cylinder, and arranged in tandem so that they can be 
 driven by one crank (which has a lead of 110°), are two pumps, 
 one for compressing air, and the other gas. The capacities 
 of the two pumps are designed for the kind of gas to be 
 burned. 
 
 The air-pump compresses to eight pounds above the atmos- 
 phere and delivers air to the admission valves, which are lifted by 
 cams at the time when the release is completed. The governor 
 controls a bypass-valve which puts the two ends of the 
 pump in communication for about half of the discharge 
 stroke of that pump, which accomplishes two purposes. In 
 the first place the compression of the gas begins only when the 
 bypass-valve is closed, and consequently is to a less pressure 
 than that of the air; consequently the air backs up in the gas- 
 supply pipe, and when the engine admission valve is opened it 
 supplies only air which clears the cylinder of spent gases; after- 
 ward the cylinder receives its charge of mixed gas and air. By 
 careful design and adjustment it is attempted to fill the cylinder 
 without wasting gas at the exhaust-ports, but tests show an appre- 
 ciable percentage of unburned gas in the exhaust. And in the 
 second place the governor can regulate the closure of the bypass- 
 valve so as to adjust the amount of gas to the work. Since the 
 range of explosive mixture of blast-furnace gas is not wide, this 
 method of regulation appears to be adapted only to fairly uni- 
 form loads. 
 
 The Oechelhaiiser gas-engine has two single-acting pistons or 
 
THE DIESEL MOTOR 
 
 341 
 
 plungers in a long open-ended cylinder; these plungers are 
 connected to cranks at i8o° so that they approach or recede 
 from the middle of the cylinder simultaneously. The engine 
 has a cross-head at each end of the cylinder to take the cross- 
 thrust of the connecting-rod, so that the engine extends to a 
 great length on a horizontal foundation. Toward the crank- 
 end of the cylinder there is a ring of exhaust-ports uncovered by 
 the inner (or crank-end) piston, and toward the outer end of the 
 cylinder there is another row uncovered by the outer piston; a 
 part of these outer ports supply air, and a part gas. These air- 
 and gas-ports may be controlled by annular valves that are set 
 by hand when the engine uses blast-furnace gas. Under these 
 conditions the engine is regulated by a governor, which controls 
 the pumps that supply air and gas. These pumps, which are 
 driven from the outer cross-head, have bypass-valves which 
 connect the two ends and begin to deliver only when the 
 bypass- valves are shut by the governor, so that the charge is 
 adjusted in amount to the load. When the engine uses a rich 
 gas that has a wide explosive range, the governor controls the 
 annular valves at the gas-ports and varies the mixture. 
 
 The Diesel Motor. — A new form of internal-combustion 
 engine was described by Rudolf Diesel in 1893, which does 
 away with many of the difficulties 
 of gas- and oil-engines, and which 
 at the same time gives a much 
 higher efficiency. The essential 
 feature of his engine consists in 
 the adiabatic compression of 
 atmospheric air to a sufficient 
 temperature to ignite the fuel 
 which is injected at a determined 
 rate during part of the expansion 
 or working stroke. 
 
 The theoretical cycle is shown by 
 Fig. 79, which represents four strokes 
 of a single-acting piston or plun- 
 
 FlG 
 
342 
 
 INTERNAL-COMBUSTION ENGINES 
 
 ger. Atmospheric air is drawn in from a to b and is com- 
 pressed from Z> to c to a pressure of 500 pounds to the 
 square inch and a temperature of 1000° F. From c to d fuel 
 is injected in a finely divided form, and as there is air in 
 excess it burns completely at a rate that can be controlled 
 by the injection mechanism. Thus far the only fuel used 
 is petroleum or some other oil. At d the supply of fuel is 
 interrupted, and the remainder of the working stroke, de, 
 is an adiabatic expansion. The cycle is completed by a release 
 at e and a rejection of the products of combustion from b to a. 
 The cycle has a resemblance to that of the Otto engine, but 
 differs in that the air only is compressed in the cylinder and 
 the combustion is accompanied by an expansion. Diesel, in 
 his theoretic discussion of his engine, stipulates that the rate 
 of combustion shall be so regulated that the temperature shall 
 not rise during the injection of fuel, and that the line cd shall 
 therefore be very nearly an isothermal for a perfect gas. Since 
 the fuel is added during the operation represented by the line 
 cd, the weight of the material in the cylinder increases and its 
 physical properties change, so that the line will not be a true 
 isothermal. The fact that there is air in excess makes it prob- 
 
 FlG. 80. 
 
 able that these changes of weight and properties will be insig- 
 nificant. On the other hand, it is not probable that in practice 
 the rate of injection of fuel will be regulated so as to give no 
 
THE DIESEL MOTOR 
 
 343 
 
 rise of temperature, or that there is any great advantage in such 
 a regulation if the temperature is not allowed to rise too high. 
 
 The diagram from an engine of this type is shown by Fig. 80, 
 which appears to show an introduction of fuel for one-eighth 
 or one-seventh of the working stroke. It is probable that the 
 compression and the expansion (after the cessation of the fuel 
 supply) are not really adiabatic, though as there is nothing but 
 dry gas in the cylinder during those operations the deviation 
 may not be large. The sides and heads of the cylinders of all 
 the engines thus far constructed are water-jacketed, though 
 the use of such a water-jacket and the consequent waste of heat 
 was one of the difficulties in the use of internal-combustion 
 engines that Diesel sought to avoid by controlling the rate of 
 combustion. The statement on page 39 that the maximum 
 efficiency is attained by adding heat only at the highest tem- 
 perature has no application in this case. The real conditions 
 are that heat cannot at first be added at a temperature higher 
 than that due to compression (about 1000° F.), but as combus- 
 tion proceeds heat can be added at higher temperature and 
 with greater efficiency. The fuel may be regulated so as to 
 avoid temperatures at which dissociation has an influence and 
 after-burning can be avoided. 
 
 The oil used as fuel is injected in form of a spray by air that 
 is compressed separately in a small pump to 30 or 40 pounds 
 pressure above that in the main cylinder; of course it is neces- 
 sary to cool this portion of the air after compression to avoid 
 premature ignition. The engines that have been used are 
 described as giving a clear and nearly dry exhaust. In damp 
 weather the exhaust shows a little moisture, probably from the 
 combustion of hydrogen in the oil. The cylinder when opened 
 shows a slight deposit of soot on the head. It appears there- 
 fore that Diesel has succeeded in constructing an engine for 
 burning heavy oils with good economy and without the annoy- 
 ances of an igniting device. The engines have the further 
 advantage in that the work can be regulated by the amount 
 of fuel supplied, which amount is not controlled, as in explosive 
 
344 
 
 NTERNAL-COMBUSTION ENGINES 
 
 engines, by the necessity to form an explosive mixture. The 
 discussion of the theoretical efficiency of the cycle shows that 
 the efficiency increases as the time of injection of fuel is shortened. 
 In practice the engine shows a slight decrease in economy for 
 light loads, due probably to the losses by radiation and to the 
 water-jacket, which are nearly constant for all loads. 
 
 In the exposition of the theory of his motor, Diesel * claims 
 that all kinds of fuel, solid, liquid, and gaseous, can be burned 
 in his motor. As yet oil only has been used ; the choice of petro- 
 leum or other heavy oil has probably been due to the low cost 
 of such oils. It is evident that gas may be used in this type 
 of engine; the gas can be compressed separately to a pressure 
 somewhat higher than that in the main cylinder, much as the 
 air is which is used for injecting oil. It does not appear neces- 
 sary to cool the gas after compression, as it will burn only when 
 supplied with air. 
 
 There appears to be no insurmountable difficulty in supply- 
 ing powdered solid fuel to this engine. The presence of the 
 ash from such fuel in the cylinder may, however, be expected 
 to give trouble. Diesel claims that with a large excess of air 
 (for example, a hundred pounds of air for one pound of coal) 
 the ash will be swept out of the cylinder with the spent gases 
 and will not give trouble; but that claim has not as yet been 
 substantiated. 
 
 Diesel's original discussion of his motor contemplated a com- 
 pound compressing-pump, one stage to give isothermal compres- 
 sion, and the second stage to give adiabatic compression; also a 
 compound motor, the first cylinder having isothermal expansion 
 with a supply of fuel, and the second cylinder an adiabatic ex- 
 pansion. He gives with that discussion a theoretical diagram 
 approaching Carnot's cycle in appearance and efficiency. If 
 this variety of the motor were mechanically practicable it would 
 have the defects of Carnot's cycle for gas, namely, the diagram 
 would be very long and attenuated, and even with the very high 
 pressures contemplated would give a relatively small power. 
 
 * Ratiotml Heat Motor ; Rudolf Diesel, trans. Brvan Donkin. 
 
THE DIESEL MOTOR 
 
 345 
 
 A theoretical discussion of the efficiency of the cycle for the 
 simple engine as represented by Fig. 79 may be obtained by 
 considering that heat is added at constant temperature from c 
 to d and that heat is rejected at constant volume from e to 6, 
 bearing in mind that he and dc represent adiabatic changes. 
 
 From equation (75), page 63, the expression for the heat 
 supplied from c to d is, for one pound of working substance, 
 
 Q, = Ap^, log.^" = ART, log, J^. 
 
 The heat rejected at constant volume is 
 
 Since the expansion de is adiabatic, 
 
 but since the compression he is also adiabatic, 
 
 and consequenth' 
 
 '-•=-.(;:)■"■(?)■"■-'••©■"■ 
 
 for T'g = Vb. Replacing T^ by its value in the expression for 
 Q^, we have 
 
 «--'i-'K?r'--i 
 
 Finally, the efficiency appears to be 
 
 ■'■•S ©■"'-■( 
 
 e = Qi ~^^ = I '-^^ '-. (188) 
 
 Inspection of the equation shows that the efficiency may 
 be increased by raising the temperature T^ or by reducing the 
 
346 INTERNAL-COMBUSTION ENGINES 
 
 temperature T^. The latter is practically the temperature of 
 the atmosphere, but Tc may be made any desired temperature 
 by reducing the clearance of the cylinder and thus raising the 
 pressure at the end of compression. Again, the efficienc}- 
 may be increased by reducing the time during which fuel is 
 injected, that is, by reducing the ratio v^ : v^, as may be proved 
 by a series of calculations with different values for that ratio. 
 This is a very important conclusion, as it shows that the engine 
 will have in practice little if any falling off in efficiency at reduced 
 loads. 
 
 It is reported that a clearance of something less than 7 per 
 cent is associated with a compression to 500 pounds and a 
 temperature of 1000° F., or more. Taking the pressure of 
 the atmosphere at 14.7 pounds per square inch, adiabatic com- 
 pression to 500 pounds above the atmosphere or to 514.7 pounds 
 absolute requires a clearance of 
 
 I T_ 
 
 / V K y ^ \ 1.405 
 
 ^« = -I'b {-A = "^h {-^^^) = 0.0796 vi„ 
 
 so that the clearance is 
 
 0.0796 ^ \i — 0.079 J = 0.0865 
 
 of the piston displacement. 
 
 If the temperature of the atmosphere be taken at 70° F. 
 or 530 absolute, the temperature after adiabatic compression 
 becomes 
 
 i^ — t I-40S — T 
 
 absolute, or 1020° F. 
 
 If it be further assumed that fuel is supplied for one-tenth 
 of the working stroke, then 
 
 T;^ = O.I {Vf, - Va) +Va= [O.I (l - O.O796) + O.O796] T/j 
 
 = O.I 716 Vi,, 
 
ENGINES FOR SPECIAL PURPOSES 347 
 
 The equation for efficiency gives in this case 
 
 ^ = i__ = 0.58. 
 
 1-405 X 53.22 X 1480 loge ^'^^^ 
 
 0.0790 
 
 Engines for Special Purposes. — Small engines can be made 
 to give any required degree of regularity for electrical or other 
 purposes, by giving a sufficient weight to the fly-wheel; for 
 large power the same object can be attained by using a number 
 of cylinders, by making the engine double acting, by the con- 
 struction of two-cycle engines, or by the combination of two or 
 more of these devices. 
 
 The four-cycle engine has not as yet been made reversible, 
 and even if the complexity of valve-gear for running in both 
 directions could be accepted, it appears likely that a special 
 starting device would be required for every reversal. Reversing 
 launches and automobiles is done by aid of a mechanical revers- 
 ing gear, except that for some small boats a reversing propeller 
 is used. Such gear for large ships appears to be dangerous as 
 well as impracticable. 
 
 Two-cycle engines would not require much complication of 
 valve-gear to make them reversible, and would have some 
 advantage on account of the greater frequency of working 
 strokes; they also might require the use of a starting gear 
 for every reversal. Small launches with two-cycle engines 
 are readily reversed by hand, but such small craft can be 
 fended off, and a failure to reverse need not be serious. 
 
 The engine with separate compressing-pump discussed on 
 page 305, appears to show greater promise for marine or other 
 purposes where ready reversal is essential. Even with the 
 pump geared directly to the engine, it was found possible to 
 reverse a two-cylinder engine promptly with a valve-gear but 
 little more complicated than that for a steam-engine. But for 
 marine purposes the engines could be placed in two groups ; one 
 
348 
 
 INTERNAI^COMBUSTION ENGINES 
 
 group could be connected to the propeller shaft (or shafts) and 
 worked without compressor-pumps, and the other group at any 
 convenient place could drive the compressor- pumps for the 
 whole system. Such an arrangement should give practically 
 the same certainty of maneuvering as steam-engines. 
 
 The application of gas-engines to large ships cannot be 
 considered to be accomplished till producers have been made 
 that can use all grades of bituminous coal, including inferior 
 qualities. 
 
 Automobiles are commonly driven by four-cycle gasoline 
 engines, and have a rather formidable array of mechanical 
 devices, including clutches to release the engine for starting, or 
 when the carriage is standing still, several change-speed gears 
 for running slowly and climbing hills, and a reversing mechanism. 
 All of this entails weight, cost and depreciation, and while gaso- 
 line vehicles can be handled efficiently by skilled drivers they have 
 not the facility of control that is readily given to steam-carriages. 
 The speed and power can be controlled by throttling the charge 
 and by delaying the ignition; the mixture may be included in 
 the methods of control, but probably it is better left alone when 
 well adjusted. 
 
 Economy of Gas-Engines. — It will be convenient to consider 
 the economy of gas-engines before discussing the economy of 
 engines using special fuel like gasoline or oil, because it is only 
 this class of engines that can, by association with the gas-producer, 
 make use of all kinds of fuel, and especially of coal. 
 
 It will be convenient also to make such inquiry as may be 
 possible concerning the influence of various conditions on the 
 economy of gas-engines before trying to determine what economy 
 may properly be attributed to them. 
 
 There are five conditions that can be enumerated which have 
 an effect on the efficiency of gas-engines: 
 
 (i) Compression. 
 
 (2) Mixture. 
 
 (3) Size. 
 
 (4) Quality of gas. 
 
ECONOMY OF GAS-ENGINES 349 
 
 (5) Time of ignition. 
 
 (i) The influence of compression is indicated theoretically by 
 equation (187), page 312, which shows that the efficiency may be 
 expected to increase progressively with increasing compression. 
 To exhibit this feature and to compare it with the results obtained 
 in practice, the following table has been computed for tests 2, 5, 
 and 7 of Table XXXV, page 350. The composition of the illumin- 
 ating-gas used was similar to that on page 315; the original 
 detailed report of these tests shows little variation in composition. 
 
 Number of tests . . 
 
 2 
 
 5 
 
 7 
 
 Ratio of compression 
 
 . 4.98 
 
 4-59 
 
 3.84 
 
 Theoretical efficiency 
 
 . 0.479 
 
 0.461 
 
 0.420 
 
 Thermal efficiency 
 
 . 0.270 
 
 0.264 
 
 0.252 
 
 Ratio 
 
 . 0.564 
 
 0-573 
 
 0.600 
 
 Such a comparison is commonly considered to show that the 
 actual efficiency follows the theoretical efficiency, the former 
 being based on the indicated horse-power, and being obtained 
 by dividing 42.42 (the equivalent of one horse-power in thermal 
 units per minute) by the thermal units per indicated horse-power 
 per minute. But if the brake horse-power is taken as the basis 
 of comparison, as has already been shown to be proper, there 
 appears to be practically no advantage in the higher compression 
 for the illuminating-gas; for the power-gas there is no advantage 
 in a compression beyond four and a half. There is, however, 
 an advantage in that a higher compression gives a larger mean 
 efifective pressure and greater power. 
 
 (2) A stronger mixture of gas and air may in general be 
 expected to yield more work than a weaker one, as is shown b}- 
 comparing the trios of tests with the same compression both for 
 illuminating-gas and for power-gas; but there is usually some 
 mixture that will give the best economy. This mixture should 
 be selected from a proper series of engine- tests rather than by 
 some other method, but as this involves a large amount of exper- 
 imental work, a satisfactory discussion of this feature is not 
 always possible. The tests in Table XXXV show that for both 
 
350 
 
 INTERNAI^COMBUSTION ENGINES 
 
 kinds of gas the richest mixture used is the most economical, 
 basing the comparison on brake horse-power as should be done. 
 The first trio of tests shows a distinct minimum for a ratio of ten 
 
 Table XXXV. 
 
 GAS-ENGINE WITH ILLUMINATING- AND WITH POWER-GAS. 
 
 DIAMETER 8.6 INCHES; STROKE 1 3 INCHES. 
 
 Professor Meyer, Mitteilungen iiher Forschungsarheiten Heft 8, 1903^ 
 
 
 
 
 
 
 
 
 
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 Mr. 
 
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 202 
 
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 116 
 
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 222 
 
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 204 
 
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 117 
 
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 204 
 
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 8.6 
 
 118 
 
 87 
 
 281 
 
 174 
 
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 59 
 
 200 
 
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 102 
 
 87 
 
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 166 
 
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 24:0 
 
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 105 
 
 88 
 
 229 
 
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 59 
 
 202 
 
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 10.7 
 
 0.58 
 0.79 
 
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 108 
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 89 
 
 281 
 
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 84 
 
 207 
 
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 13-3 
 
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 86 
 
 213 
 
 168 
 
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 208 
 
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 87 
 
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 84 
 
 207 
 
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 28.0 
 
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 88 
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 275 
 
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 98 
 
 202 
 
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 12.6 
 
 0-73 
 
 107-5 
 
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 251 
 
 181 
 
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 4 
 
 98 
 
 294 
 
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 12.4 
 
 0.67 
 
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 107 
 
 80 
 
 247 
 
 164 
 
 12 
 
 CO 
 
 4 
 
 98 
 
 207 
 
 6.2 
 
 9-3 
 
 0.65 
 
 121. 5 
 
 1.78 
 I 13 
 
 III 
 
 81 
 
 282 
 
 178 
 
 33 
 
 4 
 
 59 
 
 201 
 
 S.S 
 
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 0-73 
 
 108.0 
 
 98 
 
 81 
 
 250 
 
 184 
 
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 59 
 
 203 
 
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 0.70 
 
 121. 5 
 
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 82 
 
 267 
 
 187 
 
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 59 
 
 202 
 
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 145 
 
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 83 
 
 302 
 
 186 
 
 16 
 
 3 
 
 84 
 
 204 
 
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 0-73 
 
 124.0 
 
 81 
 
 86 
 
 263 
 
 195 
 
 17 
 
 
 3 
 
 84 
 
 205 
 
 7-3 
 
 10.4 
 
 0.70 
 
 128.5 
 
 1-39 
 
 82 
 
 85 
 
 275 
 
 194 
 
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 3 
 
 84 
 
 205 
 
 (>-3 
 
 9-5 
 
 0.66 
 
 138.0 
 
 1 .64 
 
 81 
 
 85 
 
 292 
 
 190 
 
 to one; the minimum per brake horse-power will be found for a 
 richer mixture, on account of the better mechanical efficiency 
 which accompanies the larger power which such a mixture will 
 develop; it cannot be far wrong to assume that the mixture of 
 
ECONOMY OF GAS-ENGINES 351 
 
 eight to one will give the minimum per brake horse-power. The 
 remainder of the table is less conclusive, but it appears likely 
 that a ratio of eight volumes of illuminating-gas to one volume 
 of air is proper, and that for power-gas the ratio should be some- 
 what larger than unity. 
 
 (3) A committee of the Institution of Civil Engineers * tested 
 three gas-engines of varying size, but all having the same ratio 
 of compression, and tested under the same conditions. The 
 results that bear on the question of size are as follows : 
 
 Brake horse-power 5.2 20.9 52.7 
 
 Thermal units per horse-power per 
 
 ISO 1=^0 14^ 
 minute \ jy J ^o 
 
 It is to be remarked that the results just quoted are remarkably 
 low, but that the composition of the committee and the precau- 
 tions taken, place them beyond cavil. It is somewhat difficult to 
 account for the difference between the results just quoted, and 
 those given in Table XXXV, though part of it is due to the better 
 mechanical efficiency of the former. This was estimated to be 
 about 0.87, while that of the engine tested by Professor Meyer 
 was about 0.72; allowance for this difference may be estimated 
 to reduce the results of the first test in Table XXXV to 184 
 thermal units per brake horse-power per minute. This illus- 
 trates an inconvenience of using the brake horse-power as the 
 basis of comparison of tests on different engines, since it makes 
 the results depend on the mechanical condition of the engine; 
 however, this condition is one of the elements of practical 
 economy. 
 
 (4) It is likely that an engine will show a better heat economy 
 when using a richer gas, as is indicated by comparing the results 
 in Table XXXV with illuminating-gas and with power-gas; but 
 there is not sufficient information to make this feature decisive. 
 
 (5) It is customary to time the ignition so that the maximum 
 pressure shall come early in the stroke, and that is probably 
 conducive to good economy; delaying ignition, as is done on 
 automobiles lo reduce the power, is known to be very wasteful. 
 
 * Proc. Inst. Civ. Engrs., vol. clxii, p. 241. 
 
352 INTERNAL-COMBUSTION ENGINES 
 
 Professor Meyer made some subsidiary tests to determine 
 the influence of the time of ignition on illuminating-gas with the 
 results following: 
 
 Lead of ignition, 1.2 5.6 9.7 ii.o 10.9 14.2 20.7 
 
 Thermal units per indi- J 
 
 Gated horse-power per > 216 217 223 216 221 226 260 
 
 minute ) 
 
 This appears to show that any lead up to 15° would give about 
 the same result for this engine, but that a greater lead was 
 undesirable. 
 
 The question as to the economy to be expected from gas- 
 engines has been considered incidentally in our review of the 
 influence of various conditions on the economy of gas-engines. 
 The best result that is quoted is for an engine tested by the 
 committee of the Institution of Civil Engineers, which used 143 
 thermal units per horse-power per minute, when developing 52.7 
 brake horse-power. The gas used had the composition by 
 volume : 
 
 Hydrocarbons ... 4.74 Carbon dioxide . . 2.62 
 
 Methane CH4 ... 33.73 Oxygen 0.27 
 
 Hydrogen ..... 41.29 Nitrogen 10.22 
 
 Carbon monoxide . . 7.13 Total ...... 100 
 
 Its heat of combustion determined by aid of a Junker calori- 
 meter was 561 B.T.U. 
 
 The test of a producer gas-power plant at St. Louis given on 
 page 354 used 198 thermal units per brake horse-power per 
 minute. 
 
 An engine developing 728 metric horse-power at Seraing at 
 93 revolutions per minute, used 163 thermal units per brake 
 horse-power per minute; the mechanical efficiency being 0.82, 
 when tested by Hubert.* 
 
 A Producer- Gas Plant. — At the Louisiana Purchase Exposi- 
 tion at St. Louis in 1904, an extensive investigation was made of 
 various fuels from all parts of the United States, including the 
 
 * Bui. Soc. de VIndustrie Mineral, 3d series, vol. xiv, p. 1461. 
 
A PRODUCER-GAS PLANT 
 
 353 
 
 development of power by the combination of a Taylor gas-pro- 
 ducer with necessary adjuncts, and a three-cylinder Westinghouse 
 gas-engine; a detailed report of the tests is given by Messrs. 
 Parker, Holmes, and Campbell,* the committee in charge. 
 
 The gas-producer had a diameter of 7 feet inside the brick 
 lining, and at the bottom was a revolving ash table 5 feet in 
 diameter; the blast was furnished by a steam-blower supplied 
 from a battery of boilers used for other purposes; tests were 
 made to determine the probable amount of steam taken by the 
 blower, but the variation of steam-pressure acting at the blower 
 during tests made this determination somewhat unsatisfactory. 
 The cost of the steam in coal of the kind used for any test could 
 be estimated closely from boiler-tests made with the same coal. 
 
 The gas from the producer passed through a coke-scrubber, 
 and then through a centrifugal tar-extractor using a liberal 
 amount of water. From the extractor the gas passed through 
 a purifier filled with iron shavings to extract sulphur. On the 
 way to the engine the gas was measured in a meter. 
 
 The engine-cylinders were 19 inches in diameter and had 22 
 inches stroke. At 200 revolutions the engine was rated at 235 
 brake horse-power. The engine was belted to a direct-current 
 generator, and the energy was absorbed by a water-rheostat. 
 
 The results of a test on a bituminous coal from West Virginia 
 have been selected for presentation. The composition of the 
 coal by weight and the gas by volume are: 
 
 Coal. 
 Moisture . . . 
 Volatile matter 
 Fixed carbon . 
 
 Ash 
 
 Thermal units 
 per pound coal 
 
 Gas. 
 
 2.22 Carbon dioxide ... 8 
 
 31.05 Carbon monoxide . . 14 
 
 59.83 Oxygen 
 
 6.90 Hydrogen 9 
 
 Methane 6 
 
 [ 14224 Nitrogen 59 
 
 90 
 
 77 
 33 
 52 
 65 
 
 83 
 
 Thermal units per " 
 cu. ft. (62° F., I 
 14.7 pounds) 
 
 * U. S. Geological Survey, Professional Paper No. 48. 
 
 160.5 
 
354 INTERNAL-COMBUSTION ENGINES 
 
 Test on Producer and Engine. 
 
 Duration, hours 24 
 
 Total coal fired in producer, pounds 6,000 
 
 Coal equivalent of steam used by blower, pounds 835 
 
 Coal equivalent of power to drive auxiliary machinery 299 
 
 Total equivalent coal 7, 134 
 
 Thermal value of total, equivalent coal, b.t.u. 101,500,000 
 
 Total gas (at 62° F. and 14.7 pounds), cu. ft 415,660 
 
 Thermal value of total gas 66,700,000 
 
 Efficiency of producer 0657 
 
 Electrical horse-power i99-3 
 
 Mechanical efficiency, estimated o . 85 
 
 Brake horse-power 234 
 
 Gas per horse-power per hour, cubic feet . . . . ' 74.1 
 
 Thermal units per horse-power per minute 198 
 
 Thermal efficiency of brake-power 0.214 
 
 Coal per brake horse-power per hour 1.27 
 
 Combined thermal efi&ciency of producer and engine 0.14 
 
 It is interesting to compare these results of a test on a producer- 
 plant with the tests at the pumping-station at Chestnut Hill 
 from which the results quoted on page 239 were taken. 
 
 Test at Chestnut Hill Pumping Station. 
 
 Duration hours, ' 24 
 
 Coal required by plant, corrected 16,269 
 
 Thermal value of George's Creek coal, estimated 14,500 
 
 Heat abstracted from one pound of coal by boiler 10,690 
 
 ^Efi&ciency of boiler o . 74 
 
 Indicated horse-power, engine 576 
 
 Indicated horse-power, pump 530 
 
 Mechanical efi&ciency 0.920 
 
 Thermal units per pump horse-power per minute 222 
 
 Thermal efi&ciency pump-power 0.191 
 
 Combined thermal efi&ciency pump and boiler 0.14 
 
 Coal per pump horse-power per hour 1.21 
 
 If allowance is made for the higher thermal value of George's 
 Creek coal, the coal consumptions are very nearly equivalent. 
 
 A test on a Dowson suction producer by Mr. M. A. Adam * 
 gave an efficiency of 0.80 to 0.84 after the producer was well 
 started. If the thermal efficiency of an engine using the gas 
 may be estimated from 0.20 to 0.24, the combined efficiency may 
 be estimated from 0.16 to 0.20, which for anthracite coal would 
 
 * Proc. Inst. Civ. Engrs., vol. clviii, p. 320. 
 
ECONOMY OF A DIESEL MOTOR 
 
 355 
 
 correspond to one pound per brake horse-power per hour, or 0.9 
 of a pound per indicated horse- power; the makers of producer 
 power-plants are now ready to guarantee a consumption of 
 one pound of anthracite per brake horse-power per hour. 
 
 Economy of Oil- Engine. — An engine of the type described on 
 page 335 was tested by Messrs. A. E. Russell and G. S. Tower * 
 of the Massachusetts Institute of Technology. The engine 
 had a diameter of 11.22 inches and a stroke of 15 inches, and at 
 220 revolutions per minute developed ten brake horse-power; 
 the mechanical efficiency was about 0.72, so that the indicated 
 power was about 14; the clearance or charging space was about 
 0.44 of the piston displacement. 
 
 With kerosene the best economy was 1.5 pounds per brake 
 horse-power per hour; this kerosene weighed 6.52 pounds 
 per gallon, flashed at 104° F., and had a calorific power of 
 17,222 thermal units per pound. 
 
 The engine was also tested with a crude distillate which 
 comes from petroleum after the kerosene, weighing 6.66 pounds 
 per gallon, with a flash-point at 148° F., and having a calorific 
 power of 19,410 thermal units per pound; of this oil the engine 
 used 1.3 pounds per brake horse-power per hour. 
 
 The thermal units per horse-power per minute were 430 for 
 kerosene and 420 for the distillate; the thermal efficiencies corre- 
 sponding are 0.099 ^^^ o.ii on the basis of brake horse-power. 
 
 Economy of a Diesel Motor. — A 70 horse-power Diesel 
 motor using Russian petroleum, which had a calorific power of 
 18,450 thermal units per pound, was tested by Professor Meyer f 
 in 1904. The diameter of the cylinder was 15.75 inches, the 
 stroke was 23.7 inches, and the ratio of compression was 15.4. 
 The air-pump had a diameter of 2.2 inches and a stroke of 5.5 
 inches. At the normal load of 69.63 metric horse-power by the 
 brake (68.6 English horse-power) the oil-consumption was 0.429 
 pound per horse-power per hour, or 132 thermal units per brake 
 horse-pov/er per minute. The thermal efficiency was conse- 
 
 * Thesis, M. I .T. 1905. 
 
 t Mitteilungen uber Forschungsarbeiten Heft 17, p. 35. 
 
356 
 
 INTERNAI^COMBUSTION ENGINES 
 
 quently 0.32. At an overload amounting to 85.7 brake horse- 
 power, the oil-consumption was 0.42 pound, and at half load 
 (34.4 horse-power) the consumption was 0.50 of a pound. 
 
 Since oil for lubrication of the cylinder is liable to be burned 
 together with the fuel, it is specially necessary in tests of engines 
 of this type that error from the effect of excessive use of lubri- 
 cating-oil is to be guarded against. 
 
 Distribution of Heat. — A very interesting and instructive 
 matter in the discussion of tests on gas-engines is the distribution 
 of the heat, and especially of the heat that is not changed into 
 work. It cannot be considered that all of this lost heat is wasted, 
 because any heat-engine must reject heat, and that for the theo- 
 retical cycles, which are the limits for practical engines, the 
 major part of the heat is unavoidably rejected. 
 
 The following table is taken from a lecture by Mr. Dugald 
 Clerk.* 
 
 Dimension 
 
 Distribution of Heat. 
 
 of Engine. 
 
 Work. 
 
 Jacket. 
 
 Exhaust. 
 
 6.75 X 13.7 
 
 9.5 X 18.0 
 
 26 X 36 ^ 
 
 2 cyls. S 
 
 51.2 X 55.13 
 
 0.16 
 0.22 
 
 0.28 
 
 0.28 
 
 0.51 
 
 0.43 
 0.24 
 0.52 
 
 0.31 
 
 0-35 
 
 0.59 
 0.20 
 
 The first three show, together with a notable gain in efficiency, 
 a strong tendency to shift the waste heat from the water-jacket 
 to the exhaust, as the engine increases in size; the last test is 
 from an engine using blast-furnace gas, and which is liberally 
 cooled with water. The whole table, and especially the last 
 two examples, show that to a large extent an engineer may decide 
 in the design of an engine, whether he will withdraw heat by 
 thorough cooling, or allow the heat to be suppressed by disso- 
 ciation and thrown out in the exhaust. 
 
 Mean Effective Pressure. — In the design of a gas-engine the 
 
 * Forest Lecture. Inst. Civ. Eng. cxliii. p. 21. 
 
WASTE-HEAT ENGINES 357 
 
 first question to be determined is the mean effective pressure 
 that is desired or can be obtained. This must depend on the 
 fuel and its mixture with air, and on the degree of compression. 
 There does not at the present time appear to be information 
 that will serve as the basis of a working theory for determining 
 the mean effective pressure even when these features are 
 determined. 
 
 It is desirable, in order that the engine shall be powerful and 
 compact, that the mean effective pressure shall be high; English 
 engineers commonly make use of 90 to 100 pounds mean effective 
 pressure; but German engineers who have had experience with 
 very large engines for which pre- ignition is dangerous, have been 
 content with 60 pounds or less. 
 
 Waste-heat Engines. — On page 180 attention was called to 
 the fact that the exhaust-steam from a steam-engine could be 
 used for vaporizing some fluid like sulphur dioxide, and that 
 thereby the temperature range could be extended. The only 
 tests quoted failed to show the advantage that might be expected 
 when this method is used with steam-engines. But the exhaust 
 from a gas-engine is very hot, probably 1000° F., or over, and 
 there appears to be no reason why the heat should be wasted, 
 as it could readily be used to form steam in a boiler or for other 
 purposes. 
 
CHAPTER XV. 
 
 COMPRESSED AIR. 
 
 Compressed air is used for transmitting power, for storing 
 energy, and for producing refrigeration. Air at moderate 
 pressure, produced by blowing-engines, is used in the production 
 of iron and steel; and currents of air at slightly higher pressure 
 than that of the atmosphere (produced by centrifugal fan- 
 blowers) are used to ventilate mines, buildings, and ships, and 
 for producing forced draught for steam-boilers. Attention will 
 be given mainly to the transmission and storage of energy. The 
 production and use of ventilating currents require and are sus- 
 ceptible of but little theoretical treatment. Refrigeration will 
 be reserved for another chapter. 
 
 A treatment of the transmission of power by compressed air 
 involves the discussion of air-compressors, of the flow of air 
 through pipes, and of compressed-air engines or motors. The 
 storage of energy differs from the transmission of power in that 
 the compressed air, which is forced into a reservoir at high 
 pressure, is used at a much lower pressure at the air- motor. 
 
 Air-Compressors. — There are three types of machines used 
 for compressing or moving air: (i) piston air-compressors> (2) 
 rotary blowers, (3) centrifugal blowers or fans. 
 
 The piston air-compressor is always used for producing high 
 pressures. It consists of a piston moving in a cylinder with 
 inlet- and exit-valves at each end. Commonly the valves are 
 actuated by the air itself, but some compressors have their valves 
 moved mechanically. Blowing-engines are usually piston- 
 compressors, though the pressures produced are only ten or 
 twenty pounds per square inch. 
 
 Rotary blowers have one or more rotating parts, so arranged 
 that as they rotate, chambers of varying capacity are formed, 
 
 358 
 
FLUID PISTON-COMPRESSORS 
 
 359 
 
 which receive air at atmospheric pressure, compress it, and 
 deliver it against a higher pressure. They are simple and com- 
 pact, but are wasteful of power on account of friction and leakage, 
 and are used only for moderate pressures. 
 
 Fan-blowers consist of a number of radial plates or vanes, 
 fixed to a horizontal axis and enclosed in a case. When the 
 axis and the vanes attached to it are rotated at a high speed, air 
 is drawn in through openings near the axis and is driven by 
 centrifugal force into the case, from which it flows into the 
 delivery-main or duct. Only low pressures, suitable for ventila- 
 tion and forced draught, can be produced in this way. But 
 little has been done in the development of the theory or the 
 determination of the practical efficiency of fan-blowers. Some 
 ventilating-fans have their axes parallel to the direction of the 
 air-current, and the vanes have a more or less helicoidal form, 
 so that they may force the air by direct pressure; they are in 
 effect the converse of a windmill, producing instead of being 
 driven by the current of air. They are useful rather for moving 
 air than for producing a pressure. 
 
 Fluid Piston- Compressors. — It will be shown that the effect 
 of clearance is to diminish the capacity of the compressor; con- 
 sequently the clearance should be made as small as possible. 
 With this in view the valves of compressors and blowers are 
 commonly set in the cylinder-heads. Single-acting compressors 
 with vertical cylinders have been made with a layer of water or 
 some other fluid on top of the piston, which entirely fills the 
 clearance-space when the piston is at the end of the stroke. An 
 extension of this principle gives what are known as fluid piston- 
 compressors. Such a compressor commonly has a double-acting 
 piston in a horizontal cylinder much longer than the stroke of 
 the piston, thus giving a large clearance at each end. The 
 clearance-spaces extend upward to a considerable height, and the 
 admission- and exhaust- valves are placed at or near the top, and 
 the entire clearance-space is filled with water. The spaces 
 and heights must be so arranged that when the piston is at one 
 end of its stroke the water at that end shall fill the clearance 
 
360 COMPRESSED AIR 
 
 and cover the valves, and at the other end the water shall not 
 fall to the level of the top of the cylinder. There are conse- 
 quently two vertical fluid pistons actuated by a double-acting 
 horizontal piston. It is essential that the spaces in which the 
 fluid pistons act shall give no places in which air may be caught 
 as in a pocket, and that there are no projecting ribs or other 
 irregularities to break the surface of the water; and, further, 
 the compressor must be run at a moderate speed. The water 
 forming the fluid pistons becomes heated and saturated with 
 air by continuous use, and should be renewed. 
 
 Air-pumps used with condensing-engines or for other purposes 
 may be made with fluid pistons which are renewed by the 
 water coming with the air or vapor. In case the water thus 
 supplied is insufficient, water from without may be admitted, 
 or water from the delivery may be allowed to flow back to 
 the admission side of the pump. 
 
 Displacement Compressors. — When a supply of water under 
 sufficient head is available, air may be compressed in suitably 
 arranged cylinders or compressors by direct action of the water 
 on air, compressing it and expelling it by displacement. Such 
 compressors are very wasteful of power, and in general it is 
 better to use water-power for driving piston-compressors, prop- 
 erly geared to turbine- wheels or other motors. 
 
 Cooling during Compression. — There is always a considerable 
 rise of temperature due to compressing air in a piston air-com- 
 pressor, which is liable to give trouble by heating the cylinder 
 and interfering with lubrication. Blowing-engines which pro- 
 duce only moderate pressures usually have their cylinders lubri- 
 cated with graphite, and no attempt is made to cool them. All 
 compressors which produce high pressures have their cylinders 
 cooled either by a water-jacket or by injecting water, or by 
 l)oth methods. 
 
 Since the air after compression is cooled either purposely or 
 unavoidably, there would be a great advantage in cooling the 
 air during compression, and thereby reducing the work of com- 
 })ression. Attempts have been made to cool the air by spray- 
 
MOISTURE IN THE CYLINDER 361 
 
 ing water into the cylinder, but experience has shown that the 
 work of compression is not much affected by so doing. The 
 only effective way of reducing the work of compression is to 
 use a compound compressor, and to cool the air on the way 
 from the first to the second cylinder. Three-stage compressors 
 are used for very high pressures. It is, however, found that 
 air which has been compressed to a high pressure and great 
 density is more readily cooled during compression. 
 
 Moisture in the Cylinder. — If water is not injected into the 
 cylinder of an air-compressor the moisture in the air will depend 
 on the hygroscopic condition of the atmosphere. But even if 
 the air were saturated with moisture the absolute and the rela- 
 tive weight of water in the cylinder would be insignificant. 
 Thus at 60° F. the pressure of saturated steam is about one- 
 fourth of a pound per square inch, and the weight of one cubic 
 foot is about 0.0008 of a pound, while the weight of one cubic 
 foot of air is about 0.08 of a pound. It is probable that the 
 only effect of moisture in the atmosphere is to slightly reduce 
 the exponent of the equation (77), page 64. This conclu- 
 .sion probably holds when the cylinder is cooled by a water- 
 jacket. 
 
 When water is sprayed into the cylinder of a compressor 
 the temperature of the air and the amount of vapor mixed with 
 it vary, and there is no ready way of determining its condition. 
 But, as has been stated, the spraying of water into the cylinder 
 does not much reduce the work of compression, and consequently 
 it is probable we can assume that the compression always fol- 
 lows the law expressed by an exponential equation; such as 
 
 The value to be given to n is not well known; it may be as 
 small as 1.2 for a fluid piston-compressor, and it may approach 
 1 .4 when the cooling of the air is ineffective, as is usually the case. 
 
 Power Expended. — The indicator-diagram of an air-com- 
 pressor with no clearance-space is represented by Fig. 81. Air 
 is drawn in at atmospheric pressure in the part of the cycle 
 
362 
 
 COMPRESSED AIR 
 
 of operations represented by dc) in the part represented by ch 
 the air is compressed, and in the part represented by ha it is 
 expelled against the higher pressure. 
 
 If p^ is the specific pressure and v^ the 
 specific volume of one pound of air at atmos- 
 pheric pressure, and p^ and v^ corresponding 
 quantities at the higher pressure, then the 
 
 Fig. 81. 
 
 work done by the atmosphere on the piston 
 of the compressor while air is drawn in is p^v^. Assuming 
 that the compression curve ch may be represented by an expo- 
 nential curve having the form 
 
 pv"" = p^v^ = const., 
 
 then the w^ork of compression is 
 
 _ii 
 
 ^ MA 
 
 n- i\ \pj 
 The work of expulsion from 6 to a is 
 
 p.v^-pM^-p.vM'^ 
 
 The effective work of the cycle is therefore 
 
 n — 1 
 
 Equation (189) gives the work done to compress one pound 
 of air, p^ and p^ being specific pressures (in pounds per square 
 foot), and v^ the specific volume, which may be calculated by 
 aid of the equation 
 
 T r/ 
 
EFFECT OF CLEARANCE 363 
 
 in which the subscripts refer to the normal properties of air at 
 freezing-point and at atmospheric pressure. 
 
 If, instead of the specific volume i/^, we use the volume V^ of 
 air drawn into the compressor we may readily transform equation 
 (189) to give the horse-power directly, obtaining 
 
 H.P.= i44/>.F,. (/m""^_ ) 
 S300o(n - i) l\pj S 
 
 where p^ is the pressure of the atmosphere in pounds per square 
 inch, and n is the exponent of the equation representing the 
 compression curve, which may vary from 1.4 for dry-air com- 
 pressors to 1.2 for fluid piston-compressors. 
 
 Effect of Clearance. — The indicator-diagram of an air- 
 compressor with clearance may be represented by Fig. &2. 
 The end of the stroke expelling air is at a, 
 and the air remaining in the cylinder ex- 
 pands from a to d, till the pressure becomes 
 equal to the pressure of the atmosphere 
 before the next supply of air is drawn in. "^ "f^ZIZ" 
 The expansion curve ad may commonly be 
 represented by an exponential equation having the same expo- 
 nent as the compression curve cb, in which case the air in the 
 clearance acts as a cushion which stores and restores energy, 
 but does not affect the w^ork done on the air passing through the 
 cylinder. The work of compressing one unit of weight of air 
 in such a compressor may be calculated by aid of equation 
 (189), but the equation (190) for the horse- power cannot be used 
 directly. 
 
 The principal effect of clearance is to increase the size of the 
 cylinder required for a certain duty in the ratio of the entire 
 length of the diagram in Fig. 82 to the length of the line dc. 
 
 Let the clearance be — part of the piston displacement. At 
 
 m 
 
 the beginning of the filling stroke, represented by the point a, 
 that volume will be filled with air at the pressure p^. After the 
 expansion represented by ad the air in the clearance will have 
 
 a 
 
 I 
 
 b 
 
 ^ — « 
 
 
 1 
 
364 COMPRESSED AIR 
 
 the pressure p^y and, assuming that the expansion follows the 
 law expressed by the exponential equation 
 
 P'v'' = ^i^i" (190a) 
 
 its volume will be 
 
 
 m 
 
 part of the piston displacement. The ratio of the line dc to the 
 length of the diagram will consequently be 
 
 1 
 
 ac m \p^i 
 
 -=x-lgA%l (X9X) 
 
 m\pj m 
 
 and this is the factor by which the piston displacement calculated 
 without clearance must be divided to find the actual piston 
 displacement. 
 
 Temperature at the End of Compression. — When the air in 
 the compressor-cylinder is dry or contains only the moisture 
 brought in with it, it may be assumed that the mixture of air and 
 vapor follows the law of perfect gases, 
 
 PV_^ pj^Vi 
 
 T T^ ' 
 which, combined with the exponential equation 
 
 pv^=p,v,\ 
 gives 
 
 n—\ 
 
 from which the final temperature T^ at the end of compression 
 may be determined when T^ is known. When water is used 
 freely in the cylinder of a compressor the final temperature 
 cannot be determined by calculation, but must be determined 
 from tests on compressors. 
 
 Contraction after Compression. — Ordinarily compressed air 
 loses both pressure and temperature on the way from the com- 
 
VOLUME OF THE COMPRESSOR CYLINDER 365 
 
 pressor to the place where it is to be used. The loss of pressure 
 will be discussed under the head of the flow of air in long pipes ; 
 it should not be large, unless the air is carried a long distance. 
 The loss of temperature causes a contraction of volume in two 
 ways : first, the volume of the air at a given pressure is directly 
 as the absolute temperature; second, the moisture in the air 
 (whether brought in by the air or supplied in the condenser) in 
 excess of that which will saturate the air at the lowest temperature 
 in the conduit, is condensed. Provision must be made for 
 draining off the condensed water. The method of estimating 
 the contraction of volume due to the condensation of moisture 
 will be exhibited later in the calculation of a special problem. 
 
 Interchange of Heat. • — The interchanges of heat between 
 the air in the cylinder of an air-compressor and the walls of the 
 cylinder are the converse of those taking place between the steam 
 and the walls of the cylinder of a steam-engine, and are much 
 less in amount. The walls of the cylinder are never so cool as 
 the incoming air, nor so warm as the air expelled; consequently 
 the air receives heat during admission and the beginning of 
 compression, and yields heat during the latter part of com- 
 pression and during expulsion. The presence of moisture in 
 the air increases this effect. 
 
 Volume of the Compressor Cylinder. — Let a compressor 
 making n revolutions per minute be required to deliver Fg cubic 
 feet of air at the temperature t^ F., or 7^3° absolute, and at the 
 absolute pressure p^ pounds per square inch, at the place where 
 the air is to be used. Assuming that the air is dry when it is 
 delivered and that the atmosphere is dry when it is taken into 
 the compressor, then the volume drawn into the compressor per 
 minute at the temperature T^ and the pressure p^ will be 
 
 ^1= ^af^^ (193) 
 
 cubic feet; and this expression will be correct whatever may be 
 the intermediate temperatures, pressures, or condition of satura- 
 tion of the air. 
 
366 
 
 COMPRESSED AIR 
 
 If the compressor has no clearance the piston displacement 
 will be 
 
 -f (194) 
 
 if the clearance is — part of the piston displacement, dividing 
 fn 
 
 by the factor (191) gives for the piston displacement 
 
 2W 
 
 expressed in cubic feet. , 
 
 The pressure in the compressor-cylinder when air is drawn 
 in, is always less than the pressure of the atmosphere, and when 
 the air is expelled it is greater than the pressure against which 
 it is delivered. From these causes and from other imperfections 
 the compressor will not deliver the quantity of air calculated 
 from its dimensions, and consequently the volume of the cylinder 
 as calculated, whether with or without clearance, must be in- 
 creased by an amount to be determined by experiment. 
 
 Compound Compressors. — When air is to be compressed 
 from the pressure p^ to the pressure p^, but is to be delivered at 
 the initial temperature t^, the work of compression may be 
 reduced by dividing it between two cylinders, one of which 
 takes the air at atmospheric pressure and delivers it at an 
 intermediate pressure p' to a reservoir, from which the other 
 cylinder takes it and delivers it at the required pressure p^, 
 provided that the air be cooled, at the pressure p', between the 
 two cylinders. 
 
 The proper method of dividing the pressures and of pro- 
 portioning the volumes of the cylinders so that the work of 
 compression may be reduced to a minimum may be deduced 
 from equation (189) when there is no clearance or when the 
 clearance is neglected. 
 
COMPOUND COMPRESSOR 367 
 
 The work of compressing one pound of air from the pressure 
 
 p^ to the pressure p' is 
 
 » — 1 
 
 ^•-^•^';rhKA)"-4 • • • • ^'''^ 
 
 The work of compressing one pound from the pressure f to p^ 
 is 
 
 because the air after compression in the first cylinder is cooled 
 to the temperature t^ before it is supplied to the second cylinder, 
 and consequently fv' = p^v^. The total work of compression is 
 
 n — 1 n — 1 
 
 and this becomes a minimum when 
 
 n — 1 n — 1 
 
 w. 
 
 if) ' -e-) 
 
 becomes a minimum. Differentiating with regard to p^, and 
 equating the first differential coefficient to zero, gives 
 
 / = ^pj2 (199) 
 
 Since the air is supplied to each cyHnder at the temperature t^, 
 their volumes should be inversely as the absolute pressures p^ 
 and p'. This method also leads to an equal distribution of work 
 between the two cylinders, for if the value of p' from equation 
 (189) is introduced into equations (197) and (198) we shall 
 obtain 
 
 n — l 
 
 2n 
 
 W^^W, = p^v,^^\(^j "-.j. . .(300) 
 
 and the total work of compression is 
 
 w — 1 
 
368 COMPRESSED AIR 
 
 Three-Stage Compressors. — When very high pressures are 
 required, as where air is used for storing energy, it is customary 
 to use a compressor with a series of three cyHnders, through 
 which the air is passed in succession, and to cool the air on the 
 way from one cylinder to the next. If the initial and final pres- 
 sures are p^ and p^, and if f and p" are the pressures in the 
 intermediate receivers in which the air is cooled, the conditions 
 for most economical compression may be deduced in the follow- 
 ing way: 
 
 The work of compressing one pound of air in the several 
 cylinders will be 
 
 n — 1 
 
 W, 
 
 ^'""'^Aij) "-i • ■ • -(-4) 
 
 But since the air is cooled to the initial temperature on its way 
 from one cylinder to the other so that 
 
 p^v^ = p'v' = p"v"\ 
 the total work of compressing one pound of air will be 
 
 This expression will be a minimum when 
 
 n — 1 n — 1 n — 1 
 
 becomes a minimum; that is, when 
 
 J 
 
 hk n - 1 f "" n - 1 p' 
 
 pr P' ' 
 
 = o . . (206) 
 
FRICTION AND IMPERFECTIONS 369 
 
 and _L "-1 
 
 = r — ^ — ^ = o . , . (207) 
 
 Equations (206) and (207) lead to 
 
 f' = p^f^ ....... (208) 
 
 p'^'-^fp, ....... (209) 
 
 from which by eUmination we have 
 
 / = ^J^, • .(210) 
 
 and , 
 
 P" =^P.P.' •...».. (211) 
 Since the temperature is the same at the admission to each 
 of the three cylinders, the volumes of the cylinders should be 
 inversely proportional to the absolute pressures p^^ f, and p'' . 
 As w^ith the compound compressors, this method of arranging 
 a three-stage compressor leads to an equal distribution of work 
 between the cylinders. For, if the values of f and f' from 
 equations (210) and (211) are introduced into equations (202) to 
 (204), taking account also of the equation (190a) we shall have 
 
 n — \ 
 
 W,= W._ = W,= p,v, ^ j (^^) " - I j . (212) 
 and consequently the total work of compression is 
 
 n — \ 
 
 Friction and Imperfections. — The discussion has thus far 
 taken no account of friction of the compressor nor of imperfec- 
 tions due to delay in the action of the valves and to heating the 
 air as it enters the cyHnder of the compressor. 
 
 From comparisons of indicator-diagrams taken from^ the 
 steam- and the air-cylinders of certain combined steam-engines 
 and air-compressors at Paris, Professor Kennedy found a mechan- 
 ical efficiency of 0.845. Professor Gutermuth found an efficiency 
 of 0.87 for a new Riedler compressor. It will be fair to assume 
 an efficiency of 0.85 for compressors which are driven by steam- 
 
370 
 
 COMPRESSED AIR 
 
 engines; compressors driven by turbines will probably be affected 
 to a like extent by friction. 
 
 The following table given by Professor Unwin * shows the 
 effect of imperfect valve-action and of heating the entering air 
 as deduced from tests on a Dubois- Francois compressor which 
 had a diameter of i8 inches and a stroke of 48 inches. 
 
 RATIO OF ACTUAL AND APPARENT CAPACITIES OF AN 
 AIR-COMPRESSOR. 
 
 
 
 Ratio of air 
 
 
 
 delivered at 
 
 Piston speed, 
 feet per 
 minute. 
 
 Revolutions 
 
 atmospheric 
 pressure and 
 
 per minute. 
 
 temperature to 
 volume dis- 
 
 
 
 placed by 
 
 
 
 piston. 
 
 80 
 
 10 
 
 0.94 
 
 160 
 
 20 
 
 0.92 
 
 200 
 
 25 
 
 0.90 
 
 240 
 
 30 
 
 0.86 
 
 280 
 
 35 
 
 0.78 
 
 This table does not take account of the effect of clearance, 
 nor is the clearance for the compressor stated. It is probable 
 that five or ten per cent will be enough to allow for imperfect 
 valve-action after the effect of clearance is properly calculated. 
 The effect of clearance is to require a larger volume of cylinder 
 than would be needed without clearance. The effect of imper- 
 fect valve-action and of heating of the entering air is to require 
 an additional increase in the size of the cylinder of the air-com- 
 pressor and also to increase the work of compression. 
 
 Efficiency of Compression. — If air could 
 be so cooled during compression that the tem- 
 perature should not rise, the compression line 
 cb, Fig. 83, would be an isothermal line, 
 Fig. 83. and the work of compressing one pound of air 
 
 * Development and Transmission of Power, p. 182. 
 
EFFICIENCY OF COMPRESSION 
 
 371 
 
 would be 
 
 ^ = p2'^2 + Pi'^i log, 
 
 Pi'^i'^^ 
 
 but p^v^ = p^y^ for an isothermal change, and consequently 
 
 W = p,v, log, {^ 
 Pi 
 
 (214) 
 
 Some investigators have taken the v^^ork of isothermal com- 
 pression, represented by equation (214), as a basis of comparison 
 for com^pressors, and have considered its ratio to the actual work 
 of compression as the efficiency of compression. This throws 
 together into one factor the effect of heating during compression 
 and the effect of imperfect valve-action. 
 
 Professor Riedler * obtained indicator-diagrams from the 
 cylinders of a number of air-compressors and drew upon them 
 the diagrams which would represent the work of isothermal 
 compression, without clearance or valve losses. A comparison 
 of the areas of the isothermal and the actual diagrams gave the 
 arbitrary efficiency of compression just described. The following 
 table gives his results: 
 
 ARBITRARY EFFICIENCY OF COMPRESSION. 
 
 Type of compressor. 
 
 Pressures in 
 
 main, 
 atmospheres. 
 
 Lost work in 
 
 per cent of 
 
 useful work. 
 
 Arbitrary 
 efficiency. 
 
 CoUadon, St. Gothard 
 
 do. 
 
 Sturgeon 
 
 Colladon 
 
 Slide-valve 
 
 6 
 6 
 3 
 4 
 
 5 
 6 
 6 
 6 
 
 • 105 -o 
 92.0 
 
 94-3 
 
 38.15 
 
 49-3 
 
 42.7 
 
 40.2 
 
 12.07 
 
 0.488 
 0.521 
 
 0.515 
 0.772 
 0.670 
 0.701 
 
 0.713 
 0.892 
 
 Paxman 
 
 Cockerill 
 
 Riedler two-stage 
 
 A similar comparison for a fluid piston-compressor showed 
 an efficiency of 0.84. 
 
 * Development and Distribution of Power, Unwin. 
 
372 
 
 COMPRESSED AIR 
 
 There are three notable conclusions that may be drawn from 
 this table: (i) there is much difference between compressors 
 working at the same pressures, (2) a simple compressor loses 
 efficiency rapidly as the pressure rises, and (3) the compound 
 or two-stage compressor shows a great advantage over a simple 
 compresson. 
 
 Test of a Blowing-Engine. — Pernolet * gives the following 
 test of a blowing-engine used to produce the blast for Bessemer 
 converters at Creusot. The engine was a two-cylinder horizontal 
 engine, with the cranks at right angles. The piston -rod for 
 each cylinder extended through the cylinder-head and actuated 
 a double-acting compressor. The dimensions were: 
 
 Diameter, steam-pistons 47J inches 
 
 " air-pistons 59 " 
 
 Stroke 70-9 " 
 
 Diameter of fly-wheel 26 i feet 
 
 At 28 revolutions per minute the following results were 
 obtained : 
 
 Indicated horse-power of steam-cylinders .... 1078 
 
 " " " air-cylinders 986 
 
 Efficiency 0.92 
 
 Temperature of air admitted 50° F. 
 
 " '' delivered 140° F. 
 
 Pressure of air delivered, pounds per square 
 
 inch gauge 23.4 
 
 Pressure of air in supply-pipe, pounds per 
 
 square inch gauge 0.44 
 
 At 25 revolutions there was no sensible depression of pressure 
 in the supply-pipe. 
 
 The air from such a blowing-engine probably suffers little 
 loss of temperature after compression. 
 
 Hydraulic Air-Compressor. — The Taylor hydraulic air-com- 
 pressor makes use of water-power for compressing air at constant 
 
 * L'Air Comprime, 1876. 
 
HYDRAULIC AIR-COMPRESSOR 
 
 373 
 
 temperature. The essential features are an aspirator for charg- 
 ing the water with air, a column of water to give the required 
 pressure, and a separator to gather the air from the water after 
 compression. The water is brought to the compressor in a pen- 
 stock, as it would be to a water-wheel, and below the dam it flows 
 away in a tailrace; the power available is determined from the 
 weight of water flowing and the head in the penstock above the 
 tailrace, in the usual manner. Below the dam a shaft is exca- 
 vated to a depth proper to give the required pressure (about 
 2.3 feet depth per pound pressure), and then a chamber is exca- 
 vated to provide space for the separator. In the shaft is a 
 plate- iron pipe or cylinder, down which the water flows; after, 
 passing the separator the water ascends in the shaft and flows 
 away at the tailrace. 
 
 The head of the pipe is surrounded by a vertical plate-iron 
 drum into which the penstock leads, so that water is supplied 
 to the head all round the periphery. The head itself is formed 
 of two inverted conical iron-castings, so formed that the space 
 into which the water flows at first contracts and then expands; 
 the changes of velocity being gradual, no appreciable loss of 
 energy ensues. At the throat of the inlet, where the velocity is 
 highest, there is a partial vacuum, and air is admitted through 
 numerous small pipes so that the water is charged with bubbles 
 of air. The upper conical casting can be set by hand to control 
 the supply of water and air. 
 
 As the mingled column of water and air-bubbles goes down 
 the pipe, the air is compressed at appreciably the temperature 
 of the water. At the lower end, the pipe expands to reduce the 
 velocity, and delivers the air and water into a plate-iron bell; 
 the air gathers in the top of the bell, from which it is led by 
 a pipe, and the water escapes under the edge of the bell. Air 
 in solution is unavoidably lost, and forms the chief source of 
 loss of power in the device. The air is, of course, saturated with 
 moisture at the temperature of the water, but that is probably 
 the , condition of compressed air however produced. The 
 efficiency of the compressor may be taken as about 0.60 to 
 
374 COMPRESSED AIR 
 
 0.70; making allowance for loss in transmission and for the 
 efficiency of the compressed-air motors, the system appears to 
 be inferior to the ordinary turbine water-wheel. 
 
 Air-Pumps. — The feed-water supplied to a steam-boiler 
 usually contains air in solution, which passes from the boiler 
 with the steam to the engine and thence to the condenser. In 
 like manner the injection- water supplied to a jet-condenser 
 brings in air in solution. Also there is more or less leakage of 
 air into the cylinder communicating with the condenser and 
 into the exhaust-pipe or the condenser itself. An air-pump 
 must therefore be provided to remove this air and to maintain 
 the vacuum. The air-pump also removes the condensed steam 
 from a surface-condenser, and the mingled condensed steam and 
 injection-water from a jet-condenser. If no air were brought 
 into the condenser the vacuum would be maintained by the con- 
 densation of the steam by the injection, or the cooling water, 
 and it would be sufficient to remove the water by a common 
 pump, which, with a surface-condenser, might be the feed- 
 pump. 
 
 The weight of injection-water per pound of steam, calculated 
 by the method on page 149, will usually be less than 20 pounds, 
 but it is customary to provide 30 pounds of injection -water per 
 pound of steam, with some method of regulating the quantity 
 delivered. 
 
 It may be assumed that the injection- water will bring in with 
 it one-twentieth of its volume of air at atmospheric pressure, 
 and that this air will expand in the condenser to a volume inversely 
 proportional to the absolute pressure in the condenser. The 
 capacity of the air-pump must be sufficient to remove this air 
 and the condensed steam and injection-water. 
 
 An air-pump for use with a surface-condenser may be smaller 
 than one used with a jet-condenser. In marine work it is com- 
 mon to provide a method of changing a surface- into a jet-con- 
 denser, and to make the air-pump large enough to give a fair 
 vacuum in case such a change should become advisable in an 
 emergency. 
 
DRY-AIR PUMP 
 
 375 
 
 Seaton * states that the efficiency of a vertical single-acting 
 air-pump varies from 0.4 to 0.6, and that of a double-acting 
 horizontal air-pump from 0.3 to 0.5, depending on the design 
 and condition; that is, the volume of air and v^ater actually 
 discharged will bear such ratios to the displacement of the 
 pump. 
 
 He also gives the following table of ratios of capacity of air- 
 pump cylinders to the volume of the engine cylinder or cylinders 
 discharging steam into the condenser : 
 
 RATIO OF ENGINE AND AIR-PUMP CYLINDERS. 
 
 Description of Pump. 
 
 Description of Engine. 
 
 Ratio. 
 
 Single-acting vertical .... 
 
 Jet-condensing, 
 
 expansion i^ to 2 
 
 6 to 8 
 
 « <' 
 
 Surface- " 
 
 i^ to 2 
 
 8 to 10 
 
 " " . . . . 
 
 Jet- 
 
 3 to 5 
 
 10 to 12 
 
 " " . . . . 
 
 Surface- " 
 
 3 to 5 
 
 12 to 15 
 
 " " . . . . 
 
 " 
 
 compound . . . 
 
 15 to 18 
 
 Double-acting horizontal . . . 
 
 Jet-condensing, 
 
 expansion i^ to 2 
 
 10 to 13 
 
 << a 
 
 Surface- " 
 
 " i\ to 2 
 
 13 to 16 
 
 (( i( 
 
 Jet- 
 
 3 to 5 
 
 16 to 19 
 
 « (I 
 
 Surface- " 
 
 3 to 5 
 
 19 to 24 
 
 (t tc 
 
 (( <( 
 
 compound . . . 
 
 24 to 28 
 
 Dry-air Pump. — In the recent development of steam-engineer- 
 ing, especially for steam-turbines, great emphasis is given to 
 obtaining a high vacuum. For this purpose the old form of air- 
 pump which withdraws air and water from the condenser has 
 been replaced by a feed-pump which takes water only from the 
 condenser, and a dry-air pump which removes the air. The air 
 is necessarily saturated with moisture at the temperature in 
 the condenser, and allowance must be made for this moisture or 
 steam, in the design of the pump. For this purpose Dalton's law 
 is used, which says that the total pressure in any receptacle con- 
 taining air and vapor is equal to the sum of the pressures due 
 to the air and to the vapor. 
 
 * Manual of Marine Engineering. 
 
376 
 
 COMPRESSED AIR 
 
 If the amount of air brought by the water to a jet-condenser 
 can be determined or assumed, a calculation for a dry-air pump 
 can readily be made. The leakage to a surface-condenser can- 
 not be estimated, and consequently the only way of proportion- 
 ing the air-pump for a surface-condenser is that already given 
 on page 375. 
 
 To illustrate the method of calculation for a dry-air pump 
 use will be made of the data from the test of the Chestnut Hill 
 Pumping Station already quoted on page 239. 
 
 The vacuum in the condenser was 27.25 inches of mercury, 
 and the barometer stood at 30.25 inches reduced to 32° F., so 
 that the absolute pressure was 1.473 of a pound. The con- 
 densing water entered the surface-condenser at 5i°.9 F. and left 
 at 85°. 2 F.; had there been a jet-condenser this would have been 
 the temperature in the condenser and will be used for our 
 calculation. Making use of the equation for the quantity of 
 condensing water on page 150, we have, 
 
 H - gk _ iii7-i-53-3 _ 
 gk - gi 53-3 - 20 
 
 Since the engine used 11.22 pounds of steam per horse-power 
 per hour and developed 575.7 horse-power, the total condensing 
 water per hour would be 
 
 32 X 11.22 X 575-7 
 02,4 
 
 the denominator being the weight of a cubic foot of water. If 
 the water brings one-twentieth of its volume of atmospheric 
 air, the volume of air will be 166 cubic feet per hour. 
 
 Steam at 85°.2 F. has the pressure of 0.595 ^^ ^ pound abso- 
 lute; consequently the pressure 1.473 ^^ ^ pound in the con- 
 denser is made up of 0.595 steam-pressure and 0.878 air-pressure. 
 The atmospheric pressure is 30.25 inches of mercury or 14.85 
 pounds, so that taking account of the influence of the pressures 
 and absolute temperatures the volume of air (saturated with 
 moisture) to be removed from the condenser per hour is 
 
CALCULATION FOR AN AIR COMPRESSOR 377 
 
 ,66 X ^^"^-^ + ^^'' X '-^^ = 2980 cubic feet. 
 459-5 + 51-9 0-878 
 
 Assuming the air-pump to be single-acting and to be con- 
 nected directly to the engine which made about 50 revolutions 
 per minute, the effective displacement of the air-pump bucket 
 
 should be 
 
 2980 ^ (50- X 60) = 1.0 cubic foot. 
 
 To allow for the effect of the air-pump clearance, imperfection 
 of valve-action, and for variation in the temperature of condens- 
 ing water, this quantity may be increased by 50 to 100 per cent. 
 
 The engine had 3 J feet for the diameter and 6 feet for the 
 stroke of the low-pressure piston, so that its displacement was 
 nearly 50 cubic feet; the air-pump had a diameter of 2 feet and 
 a stroke of one foot, so that its displacement was 3.14 cubic 
 feet; the ratio of displacements was about sixteen. This discrep- 
 ancy shows that the conventional method of designing air-pumps 
 provides liberal capacity. 
 
 Calculation for an Air Compressor. — Let it be required to find 
 the dimensions of an air-compressor to deliver 300 cubic feet of 
 air per minute at 100 pounds per square inch by the gauge, and 
 also the horse-power required to drive it. 
 
 If it is assumed that the air is forced into the delivery-pipe 
 at the temperature of the atmosphere, and, further, that there 
 is no loss of pressure between the compressor and the delivery- 
 pipe, equation (193) for finding the volume drawn into the 
 compressor will be reduced to 
 
 V^ = V^-^ = 300 X — ^ = 2341 cubic feet. 
 Pi 14-7 
 
 If now we allow five per cent for imperfect valve-action and 
 for heating the air as it is drawn into the compressor the appar- 
 ent capacity of the compressor will be 
 
 2341 -^ 0.95 = 2464 cubic feet. 
 
 This is the volume on which the power for the compressor must 
 be calculated. 
 
378 COMPRESSED AIR 
 
 If the clearance of the compressor is 0.02 of the piston dis- 
 placement, then the factor for allowing for clearance will be 
 1^ i_ 
 
 i-~-^)H = 1 -— ^' ) + — = 0.0332 
 
 m\pj m 100 \ 14.7/ 100 
 
 if the exponent of the equation representing the expansion of 
 the air in the clearance is 1.4. Consequently the volume on 
 which the dimensions of the compressor must be based is 
 2464 ^ 0.9332 = 2640 cubic feet. 
 
 At 80 revolutions per minute the mean piston displacement 
 will be 
 
 2640 -^ (2 X 80) = 16.5 cubic feet. 
 
 Assuming a stroke of 3 feet, the mean area of the piston must be 
 (144 X 16.5) ^ 3 = 792 square inches. 
 
 Allowing 16 square inches for a piston-rod 4^ inches in diameter 
 gives a mean area of 800 square inches for the piston, which 
 corresponds very nearly to 32 inches for the diameter of the 
 piston. 
 
 The power expended in the compressor-cylinder may be cal- 
 culated by equation (190), using for Fj the apparent capacity 
 
 of the compressor, giving 
 
 1.4 — 1 
 
 H.P. = 144 X 14.7 X 2464 X 1-4 I lll^iS '•'' - A= 442. 
 
 33000 X (1.4 — i) (V14.7/ ) 
 
 If the friction of the combined steam-engine and compressor 
 is assumed to be 15 per cent the horse-power of the steam- 
 cylinder must be 
 
 442 -^ 0.85 = 520. 
 
 If the temperature of the atmosphere drawn into the com- 
 pressor is 70° F., then by an equation like (80), page 65, the 
 
 delivery temperature will be 
 
 n-i 1.4-1 
 
 r.-r,(fc)-=(4<.o+,o,(HM)-.,„, 
 
 absolute, or about 493° F. 
 
CALCULATION FOR AN AIR COMPRESSOR 379 
 
 The calculation has been carried on for a simple compressor, 
 but there will be a decided advantage in using a compound com- 
 pressor for such work. Such a compressor should have for the 
 pressure in the intermediate reservoir 
 
 p' = VP1P2 = v^ii4-7X 14.7 = 41.06 pounds. 
 
 The factor for allowing for clearance of the low-pressure 
 cylinder will now be 
 
 x-lg7H-i-=z-^(^Y"^+^ =0.9784. 
 m\pj m 100x14.7/ 100 
 
 The loss from imperfect action of the valves and for heating 
 of the air as it enters the compressor will be less for a compound 
 than for a simple compressor, but we will here retain the value 
 2464 cubic feet, previously found for the apparent capacity of 
 the compressor. The volume from which the dimensions of the 
 compressor will be found will now be 
 
 2464 ^ 0.9784 = 2518 cubic feet, 
 
 which with 80 revolutions per minute will give 15.74 cubic feet 
 for the piston displacement, and 755.5 square inches for the 
 effective piston area, if the stroke is made 3 feet, as before. 
 Adding 16 inches for the piston-rod, which will be assumed to 
 pass entirely through the cylinder, will give for the diameter of 
 the low-pressure cylinder 31! inches. 
 
 Since the pressure f is a mean proportional between p^ and 
 p^y the clearance factor for the high-pressure cylinder will be 
 the same as that for the low-pressure cylinder, and, as the volumes 
 are inversely proportional to the pressures p^ and f, the high- 
 pressure piston displacement will be 
 
 (15.74 X 14.7) -^ 41.06 = 5.64 cubic feet. 
 
 If we allow 8 inches for a rod 4J inches in diameter at one side 
 of the piston, then the mean area of the piston will be 278.7 
 square inches, which corresponds to a diameter of i8|- inches 
 for the high-pressure cylinder. In reality the piston-rod for the 
 compound compressor may have a less diameter than the rod for 
 
380 COMPRESSED AIR 
 
 a simple compressor, because the maximum pressure on both 
 pistons will be less than that for the piston of the simple com- 
 pressor. Again, the rod which extends from the large to the 
 small piston may be reduced in size. But details like these 
 which depend on the calculation of strength cannot properly 
 receive much attention at this place. 
 
 The power required to drive the compressor may be derived 
 from equation (190), replacing v^^, the specific volume, by V^, 
 the apparent capacity of the low-pressure cylinder. Using the 
 apparent capacity already obtained, 2464 cubic feet, we have 
 for the power expended in the air-cylinders 
 
 1.4 — 1 
 HP = 2 X 144 X 14-7 X 2464 X 1.4 < / II4-7 Y''''' 1^ = ^77- 
 33000 X (1.4 - i) I \i4.7/ ) 
 
 and, as before, allowing 15 per cent for friction of the engine 
 and compressor, we have for the indicated horse-power of the 
 steam-engine 
 
 377 -^ 0.85 = 444. 
 
 The temperature at the delivery from the low-pressure cylinder 
 will be for 70° F. atmospheric temperature 
 
 ''(^) 
 
 1.4 — 1 
 1.4 
 
 o 
 
 (460 + 70) r—- = 711 
 
 absolute, or 251° F. Since p' is a mean proportional between 
 p^ and p^, this will also be the temperature of the air delivered 
 by the high-pressure cylinder. 
 
 Friction of Air in Pipes. — The resistance to the flow of a 
 liquid through a pipe is represented in works on hydraulics by 
 an expression having the form 
 
 f— - (215) 
 
 2g m 
 
 in which ? is an experimental coefficient, u is the velocity in 
 feet per second, g is the acceleration due to gravity, I is the 
 length of the pipe in feet, and m is the hydraulic mean depth, 
 
FRICTION OF AIR IN PIPES 381 
 
 which last term is obtained by dividing the area of the pipe 
 by its perimeter. For a cylindrical pipe we have consequently 
 
 m = ln(P ^ nd =- Id . . <, . . . (216) 
 
 The expression (215) represents the head of liquid required to 
 overcome the resistance of friction in the pipe when the velocity 
 of flow is u feet per second. Such an expression cannot properly 
 be applied to flow of air through a pipe when there is an appre- 
 ciable loss of pressure, for the accompanying increase in volume 
 necessitates an increase of velocity, whereas the expression treats 
 the velocity as a constant. If, however, we consider the flow 
 through an infinitesimal length of pipe, for which the velocity 
 may be treated as constant, we may write for the loss of head 
 due to friction 
 
 ? ........ (217) 
 
 2g m 
 
 This loss of head is the vertical distance through which the air 
 must fall to produce the work expended in overcoming friction, 
 and the total work thus expended may be found by multiplying 
 the loss of head by the weight of air flowing through the pipe. 
 It is convenient to deal with one pound of air, so that the expres- 
 sion for the loss of head also represents the work expended. 
 
 The air flowing through a long pipe soon attains the tem- 
 perature of the pipe and thereafter remains at a constant temper- 
 ature, so that our discussion for the resistance of friction may be 
 made under the assumption of constant temperature, which 
 much simplifies our work, because the intrinsic energy of the air 
 remains constant. Again, the work done by the air on enter- 
 ing a given length dl will be equal to the work done by the air 
 when it leaves that section, because the product of the pressure 
 by the volume is constant. 
 
 Since there is a continual increase of volume corresponding 
 to the loss of pressure to overcome friction, and consequently 
 a continual increase of velocity from the entrance to the exit 
 end of the pipe, there is also a continual gain of kinetic energy. 
 
382 
 
 COMPRESSED AIR 
 
 But the velocity of air in long pipes is small, and the changes of 
 kinetic energy can be neglected. 
 
 The air expands by the amount dv as it passes through the 
 length dl of pipe, and each pound does the work pdv. This 
 work must be supplied by the loss of head, and, since there is 
 no other expenditure of energy, the work expended in the loss 
 of head is equal to the work done by expansion; consequently 
 
 pdv = ^ (218) 
 
 2g m 
 
 But from the characteristic equation 
 
 pv = RT (219) 
 
 we have 
 
 RT 
 
 P 
 which substituted in equation (217) gives 
 
 dv =- — dp, 
 
 ^u'dl RT . . , 
 
 ^ = — dp .... (220) 
 
 2gm P 
 
 If the area of the pipe is A square feet, and if W pounds of air 
 flow through it per second, then 
 
 Wv WRT , , 
 
 u = -—- = — - — (221) 
 
 A Ap ^ ^ 
 
 in which v is the specific volume, for which a value may be 
 derived from equation (219). Replacing u in equation (220) 
 by the value just derived, we have 
 
 WTR'dl _ _ RT^ 
 2gA^p^m p ' 
 
 2gA^m RT 
 
 Integrating between the limits L and o, and p^ and p^, we 
 have 
 
 ^ gA'm RT ■■■■■■ ^"3; 
 
FRICTION OF AIR IN PIPES 
 
 383 
 
 But from equation (221) the velocity at the entrance to the pipe 
 where the pressure is p^ will be 
 
 WRT , ,,/ ApM, 
 ^^=__ and W^-l^, 
 
 so that equation (223) may be reduced to 
 
 . A^p,^u,^L _ p,'-p : . 
 
 gA^mR^r RT ' 
 
 " ^gRTm pl ^^^^^ 
 
 Equation (224) may be solved as follows : 
 _ ( gRTm p^ 
 
 ^- = ^-^^ -- r \ (225) 
 
 \ ^L p, 
 
 ^^SRTn^pl-^ ^^^^^ 
 
 
 The first two forms allow us to calculate either the velocity 
 or the loss of pressure; the last form may be used to calculate 
 values of ffrom experiments on the flow through pipes. 
 
 From experiments made by Riedler and Gutermuth* Pro- 
 fessor Unwin f deduces the following values for ?: 
 
 Diameter of pipe, feet. f 
 
 0.492 0.00435 
 
 0.656 0.00393 
 
 0.980 0.00351 
 
 For pipes over one foot in diameter he recommends for use 
 
 f = 0.003. 
 
 * Neue Erjahrungen uber die Krajtversorgung von Paris durch Drticklujt, 1891. 
 t Development and Distribution of Power. 
 
•i 
 
 384 COMPRESSED AIR 
 
 Replacing the hydraulic mean depth m by id, its value for 
 round pipes, and using R = 53.22 and g = 32.16, we have in 
 place of equation (226) 
 
 ^-47o^r • • • (^^^) 
 
 All of the dimensions are given in feet, but from the form of 
 the equation it is evident that the pressures may be in any con- 
 venient units, for example, in pounds per square inch absolute. 
 
 For example, let us find the loss of pressure of 300 cubic feet 
 per minute if delivered through a six-inch pipe a mile long, the 
 initial pressure being 100 pounds by the gauge. 
 
 The velocity of the air w;ll be 
 
 (300 -^ 60) ^ — = 5 -^ -^ = 25.5 feet. 
 
 4 ,4 
 
 The terminal pressure will consequently be 
 
 ^ ( ^u.^L ) ( 0.0044 X 25.5 X S28o)^ 
 
 ^^ = ^>r-4l^h""-^ r 43°(46o+7o)i 1 
 
 = 107 pounds, 
 
 with 70° F. for the temperature of the atmosphere and with 
 
 ? = 0.0044. Consequently the loss of pressure is about eight 
 
 pounds. 
 
 Compressed-air Engines. — Engines for using compressed air 
 
 differ from steam-engines only in details that depend on the 
 
 nature of the working 
 fluid. In some instances 
 compressed air has been 
 used in steam-engines 
 without any change; for 
 example, in Fig. 84 the 
 dotted diagram was taken 
 from the cylinder of an 
 Fig. 84. engine using compressed 
 
 air, and the dot-and-dash 
 
 diagram was taken from the same end of the cylinder when 
 
FINAL TEMPERATURE 385 
 
 steam was used in it. The full line ab is a hyperbola, and the 
 line ac is the adiabatic line for a gas ; both lines are drawn through 
 the intersection of the expans^ion lines of the two diagrams. 
 
 Power of Compressed-air Engines. — The probable mean 
 effective pressure attained in the cylinder of a compressed-air 
 engine, or to be expected in a projected engine, 
 may be found in the same manner as is 
 used in designing a steam-engine. In Fig. 
 85 the expansion curve i 2 and the com- 
 pression curve 3 o may be assumed to be 
 adiabatic lines for a gas represented by 
 the equation 
 
 and the area of the diagram may be found in the usual way, and 
 therefrom the mean effective pressure can be determined. Hav- 
 ing the mean effective pressure, the power of a given engine or 
 the size required for a given power may be determined directly. 
 The method will be illustrated later by an example. 
 
 Air-Consumption. — The air consumed by a given compressed- 
 air engine may be calculated from the volume, pressure, and 
 temperature at cut-off or release, and the volume, temperature, 
 and pressure at compression, in the same way that the indicated 
 consumption of a steam-engine is calculated; but in this case 
 the indicated and actual consumption should be the same, since 
 there is no change of state of the working fluid. Since the 
 intrinsic energy of a gas is a function of the temperature only, 
 the temperature will not be changed by loss of pressure in the 
 valves and passages, and the air at cut-off will be cooler than 
 in the supply-pipe, only on account of the chilling action of the 
 walls of the cylinder during admission, which action cannot be 
 energetic when the air is dry, and probably is not very important 
 when the air is saturated. 
 
 Final Temperature. — If the expansion in a compressed-air 
 engine is complete, i.e., if it is carried down to the pressure in 
 the exhaust-pipe, then, assuming that there are no losses of 
 
386 COMPRESSED AIR 
 
 pressure in valves and passages, the final temperature may be 
 found by the equation 
 
 7-,= nf^M (229) 
 
 ^ '-if) 
 
 If the expansion is not complete, then the temperature at the 
 end of expansion may be found by the equation 
 
 Tr = T 
 
 m- <-) 
 
 in which Vc is the volume in the cylinder at cut-off and F^ at 
 release, Tj. is the absolute temperature at the end of expansion, 
 and T3 is the temperature at cut-off, assumed to be the same as 
 in the supply-pipe. T^ is not the temperature during back- 
 pressure nor in the exhaust- pipe. When the exhaust- valve is 
 opened at release the air will expand suddenly, and part of the 
 air will be expelled at the expense of the energy in the air remain- 
 ing — much as though that air expanded behind a piston, and 
 the temperature in the cylinder during exhaust and at the 
 beginning of compression may be calculated by equation (229). 
 The temperature in the exhaust-pipe will not be so low, for the 
 temperature of the escaping air will vary during the expulsion 
 produced by sudden expansion, and will only at the end of that 
 operation have the temperature T^, while the energy expended 
 on that air to give it velocity will be restored when the velocity 
 is reduced to that in the exhaust-pipe. 
 
 Volume of the Cylinder. — The determination of the volume 
 of the cylinder of a compressed-air engine which uses a stated 
 volume of air per minute is the converse of the determination 
 of the air consumed by a given engine, and can be found by a 
 similar process. We may calculate the volume of air, at the 
 pressure in the supply-pipe, consumed per stroke by an engine 
 having one unit of volume for its piston displacement, and 
 therefrom find the number of units of volume of the piston dis- 
 placement for the required engine. 
 
 Interchange of Heat. — The interchanges of heat between 
 
MOISTURE IN THE CYLINDER 387 
 
 the walls of the cylinder of a compressed-air engine and the air 
 working therein are of the same sort as those taking place between 
 the steam and the walls of the cylinder of a steam-engine; that 
 is to say, the walls absorb heat during admission and compression 
 if the latter is carried to a considerable degree, and yield heat 
 during expansion and exhaust. Since the walls of the cylinder 
 are never so warm as the entering air nor so cold as the air 
 exhausted, the walls may absorb heat during the beginning of 
 expansion and yield heat during the beginning of compression. 
 
 The amount of interchange of heat is much less in a com- 
 pressed-air engine than in a steam-engine. With a moderate 
 expansion the interchanges of heat between dry air and the 
 walls of the cylinder are insignificant. Moisture in the air 
 increases the interchanges in a marked degree, but does not 
 make them so large that they need be considered in ordinary 
 calculations. 
 
 Moisture in the Cylinder. — The chief disadvantage in the 
 use of moist compressed air — and it is fair to assume that 
 compressed air is nearly if not quite saturated when it comes 
 to the engine — is that the low temperature experienced when 
 the range of pressures is considerable causes the moisture to 
 freeze in the cylinder and clog the exhaust-valves. The diffi- 
 culty may be overcome in part by making the valves and passages 
 of large size. Freezing of the moisture may be prevented by 
 injecting steam or hot water into the supply-pipe or the cylinder, 
 or the air may be heated by passing it through externally heated 
 pipes or by some similar device. In the application of com- 
 pressed air to driving street-cars the air from the reservoir has 
 been passed through hot water, and thereby made to take up 
 enough hot moisture to prevent freezing. The study of gas- 
 engines suggests a method of heating compressed air which it is 
 believed has never been tried. The air supplied to a compressed- 
 air engine, or a part of the air, could be caused to pass through 
 a lamp of proper construction to give complete combustion, and 
 the products of combustion passed to the engine with the air. 
 Should such a device be used it would be advisable that the tem- 
 
388 COMPRESSED AIR 
 
 perature of the air should be raised only to a moderate degree 
 to avoid destruction of the lubricants in the cylinder, and the 
 combustion at all hazards must be complete, or the cylinder 
 would be fouled by unburned carbon. 
 
 Compound Air-Engines. — When air is expanded to a con- 
 siderable degree in a compressed-air engine a gain may be 
 realized by dividing the expansion into two or more stages in 
 as many cylinders, provided that the air can be economically 
 reheated between the cylinders. The heat of the atmosphere 
 or of water at the same temperature may sometimes be used 
 for this purpose. It is not known that machines of this con- 
 struction have been used. If they were to be constructed the 
 practical advantages of equal distribution of work and pressure 
 would probably control the ratio of the volumes of the cylinders. 
 
 Calculation for a Compressed-air Engine. — Let it be required 
 to find the dimensions for a compressed-air engine to develop 
 100 indicated horse-power at the pressure of 92 pounds by the 
 gauge and at 70° F. Assume the clearance to be five per cent 
 of the piston displacement, and assume the cut-off to be at 
 quarter stroke, the release to be at the end of the stroke, and the 
 compression at one-tenth of the stroke. 
 
 If the piston displacement is represented by /), then the volume 
 in the cylinder at cut-off will be 0.30 Z), that at release will be 
 1.05 Z>, and that at compression will be 0.15 D. The absolute 
 pressures during supply and exhaust may be assumed to be 
 106.7 ^^d 14.7 pounds per square inch. The work for one 
 stroke of the piston will be 
 
 w v^ /: .. r^ , 144X106.7X0.30^^ 
 1^=144X106.7X0.252) -{■ -^^ ^^^ 
 
 K — 1 
 
 V1.05/ 
 
 ^ 144 X 14-7 X o.i^D i /0.05V'-' ) 
 
 - 144 X 14.7 Xo.oZ) — ^-^ ^^ — ^i— — -] I 
 
 K — 1 ( \o.i5/ ) 
 
 = 144Z) (26.68 + 31.530 - 13.23 - 1.96) = 144 X 43.02D. 
 
 The corresponding mean effective pressure is 43.02 pounds per 
 square inch. If the engine is furnished with large ports and 
 
CALCULATION FOR A COMPRESSED-AIR ENGINE 389 
 
 automatic valve-gear the actual mean effective pressure may 
 be 0.9 of that just calculated, or 38.7 pounds per square inch. 
 
 For a piston displacement D the engine will develop at 150 
 revolutions per minute 
 
 144 X sS.yP X 2 X ISO , 
 
 • — ^ — horse- power; 
 
 33000 
 
 and conversely to develop 100 horse-power the piston displace- 
 ment must be 
 
 ^ 100 X 33000 , . . ^ 
 
 D= ^^ = 1.074 cubic feet, 
 
 144 X 38.7 X 2 X 150 
 
 and with a stroke of 2 feet the effective area of the piston will be 
 
 1.974 X 144 -^ 2 = 142. 1 square inches. 
 
 If the piston-rod is 2 inches in diameter it will have an area of 
 3.14 square inches, so that the mean area of the piston will be 
 143.7 square inches, corresponding to a diameter of 13 J inches. 
 
 We find, consequently, that an engine developing 100 horse- 
 power under the given conditions will have a diameter of 13^ 
 inches and a stroke of 2 feet, provided that it runs at 150 revo- 
 lutions per minute. 
 
 In order to determine the amount of air used by the engine 
 we must consider that the air caught at compression is compressed 
 to the full admission-pressure of 106.7 pounds absolute. Part 
 of this compression is done 'by the piston and part by the entering 
 air, but for our present purpose it is immaterial how it is done. 
 The volume filled by air at atmospheric pressure when the 
 exhaust- valve closes (including clearance) is 0.15 of the piston 
 displacement. When the pressure is increased to 106.7 pounds 
 the volume will be reduced to 
 
 l2±l) 
 \io6.7/ 
 
 of the piston displacement. The volume drawn in from the 
 supply-pipe will consequently be 
 
 0.25 +0.05 — 0.017 = 0.283 
 
390 
 
 COMPRESSED AIR 
 
 of the piston displacement. If the compression occurred suffi- 
 ciently early to raise the pressure to that in the supply-pipe 
 before the ad mission- valve opened, then only 0.25 of the piston 
 displacement would be used per stroke and a saving of about 13 
 per cent v^'ould be attained; in such case the mean effective 
 pressure would be smaller and the size of the cylinder would be 
 larger. 
 
 The air-consumption for the engine appears to be 
 2 X 150 X 0.283 X pist. displ. =2X150X0.283X1.974= 167.6 
 cubic feet per minute. The actual air-consumption will be 
 somewhat less on account of loss of pressure in the valves and 
 passages; it may be fair to assume 160 cubic feet per minute for 
 the actual consumption. 
 
 In order to make one complete calculation for the use of com- 
 pressed air for transmitting power, the data for the compressed- 
 air engine have been made to correspond with the results of calcu- 
 lations for an air-compressor on page 377 and for the loss of 
 pressure in a pipe on page 384. Since there is a loss of pressure 
 in flowing through the pipe at constant temperature, there is 
 a corresponding increase of volume, so that the pipe delivers 
 
 300 X 114.7 -^ 106.7 = 322.6 
 cubic feet per minute. Our calculation for the air-consumption 
 of an engine to deliver 100 horse-power gives about 160 cubic 
 feet, from which it appears that the system of compressor, con- 
 ducting-pipe, and compressed-air engine should deliver 
 100 X 322.6 -^ 160 = 200 -f horse-power. 
 
 If the friction of the compressed-air engine is assumed to be 
 ten per cent, the power delivered by it to the main shaft (or to 
 the machine driven directly from it) will be 
 
 200 X .9 = 180 horse-power. 
 
 The steam-power required to drive a simple compressor was 
 found to be 520 horse-power; it consequently appears that 
 
 180 -^ 520 = 0.34 
 of the indicated steam-power is actually obtained for doing work 
 
EFFICIENCY OF COMPRESSED-AIR TRANSMISSION 391 
 
 from the entire system of transmitting power. If, however, a 
 compound compressor is used, then the indicated steam-power 
 is 444, and of this 
 
 180 -^ 444 = 0.40 
 will be obtained for doing work. 
 
 If, however, we consider that the power would in any case be 
 developed in a steam-engine, and that the transmission system 
 should properly include only the compressor-cylinder, the pipe, 
 and the compressed-air engine, then our basis of comparison will 
 be the indicated power of the compressor-cylinder. For the 
 simple compressor we found the horse-power to be 442, which 
 gives for the efl&ciency of transmission 
 
 180 -^ 442 = 0.41, 
 while the compound compressor demanded only 3.77 horse- 
 power, giving an efficiency of 
 
 180 ^ 377 = 0.48. 
 
 It appeared that the failure to obtain complete compression 
 involved a loss of about 13 per cent in the air-consumption. 
 It may then be assumed that with complete compression our 
 engine could deliver 200 horse-power to the main shaft. In 
 that case the efficiency of transmission when a compound com- 
 pressor is used may be 0.53. 
 
 Efficiency of Compressed-air Transmission. — The preced- 
 ing calculation exhibits the defect of compressed air as a means 
 of transmitting power. It is possible that somewhat better 
 results may be obtained by a better choice of pressures or pro- 
 portions. Professor Unwin estimates that when used on a large 
 scale from 0.44 to 0.51 of the indicated steam-power may be 
 realized on the main shaft of the compressed-air engine. On 
 the other hand, when compressed air is used in small motors, 
 and especially in rock-drills and other mining- machinery, much 
 less efficiency may be expected. 
 
 Experiments made by M. Graillot * of the Blanzy mines 
 showed an efficiency of from 22 to 32 per cent. Experiments 
 
 * Pernolet, L'Air Comprime, pp. 549, 550. 
 
392 COMPRESSED AIR 
 
 made by Mr. Daniel at Leeds gave an efficiency varying from 
 0.255 to 0.455, with pressures varying from 2.75 atmospheres 
 to 1.33 atmospheres. An experiment made by Mr. Kraft* gave 
 an efficiency of 0.137 for ^ small machine, using air at a pressure 
 of five atmospheres vv^ithout expansion. 
 
 Compressed air has been used for transmitting pov^er either 
 where pov/er for compression is cheap and abundant, or v^here 
 there are reasons why it is specially desirable, as in mining and 
 tunnelling. It is now used to a considerable extent for driving 
 hand-tools, such as drills, chipping-chisels, and calking-tools, 
 in machine- and boiler-shops, and in shipyards. It is also used 
 for operating cranes and other machines where power is used 
 only at intervals, so that the condensation of steam (when used 
 directly) is excessive, and where hydraulic power is liable to give 
 trouble from freezing. 
 
 Compressed air has been used to a very considerable extent 
 for transmitting power in Paris. The system appears to be 
 expensive and to be used mainly on account of its convenience 
 for delivering small powers or in places where the cold exhaust 
 can be used for refrigeration. The trouble from freezing of 
 moisture in the cylinder has been avoided by allowing the air 
 to flow through a coil of pipe which is heated externally by a 
 charcoal fire. Professor Unwin estimates that an efficiency of 
 transmission of 0.75 may be attained under favorable conditions 
 when the air is heated near the compressor, but he does not 
 include the cost of fuel for reheating in this estimate. 
 
 Storage of Power by Compressed Air. — Reservoirs or cylin- 
 ders charged with compressed air have been used to store power 
 for driving street-cars. A system developed by Mekarski uses 
 air at 350 to 450 pounds per square inch in reservoirs having a 
 capacity of 75 cubic feet. The car also carries a tank of hot 
 water at a temperature of about 350° F., through which the air 
 passes on the way to the motor and by which it is heated and 
 charged with steam. This use of hot water gives a secondary 
 method of storing power, and also avoids trouble from freezing 
 
 * Revue universelle des Mines, 2 serie, tome vi. 
 
STORAGE OF POWER BY COMPRESSED AIR 393 
 
 in the motor-cylinders. Air at much higher pressures has been 
 used for driving street-cars in New York City, but the particu- 
 lars have not been given to the public. 
 
 The calculation for storage of power may be made in much 
 the same way as that for the transmission of power; the chief 
 difference is due to the fact that the air is reduced in pressure 
 by passing it through a reducing-valve on the way from the 
 reservoir to the motor. By the theory of perfect gases such 
 a reduction of pressure should not cause any change of tem- 
 perature, but the experiments of Joule and Thomson (page 69) 
 show that there will be an appreciable, though not an important, 
 loss of temperature when there is a large reduction of pressure. 
 Thus at 70° F. or 2i°.i C. the loss of temperature for each 100 
 inches of mercury will be 
 
 o°.92 X /^-^V= o°.79 C. = 11° F. 
 \294/ 
 
 Now 100 inches of mercury are equivalent to about 49 pounds 
 to the square inch, so that 100 pounds difference of pressure will 
 give about 3^° F. reduction of temperature, and 1000 pounds 
 difference of pressure will give about 35° F. reduction of tem- 
 perature. The last figures are far beyond the limits of the 
 experiments, and the results are therefore crude. Again, the air 
 in passing through the reducing-valve and the piping beyond 
 will gain heat and consequently show a smaller reduction of tem- 
 perature. The whole subject of loss of temperature due to 
 throttling is uncertain, and need not be considered in practical 
 calculations for air-compressors. 
 
 For an example of the calculation for storage of power let us 
 find the work required to store air at 450 pounds per square 
 inch in a reservoir containing 75 cubic feet. Replacing the 
 specific volume v^ in equation (213) by the actual volume, we 
 have for the work of compression (not allowing for losses and 
 imperfections) 
 
 W^^X 464.7 X 144 X 75 -^:4_j (464:1)'^' _) 
 
 1.4 - I (\ 14.7 / ) 
 
 = 20520000 foot-pounds. 
 
394 
 
 COMPRESSED AIR 
 
 If the pressure is reduced to 50 pounds by the gauge before it is 
 used, the volume of air will be 
 
 75 X 464.7 -^ 64.7 = 539 cubic feet. 
 The work for complete expansion of one pound to the pressure 
 of the atmosphere will be 
 
 i»'=ft«.+.-^|.-(;^r'i-f.. 
 
 © 
 
 1.4-1 
 
 and the work for 539 cubic feet will be 
 
 1 
 
 144 X 64.7 X 539 ^'^ ^ \ I - {^^ ^ = 5976000 
 
 foot-pounds, without allowing for losses or imperfections. The 
 maximum efficiency of storing and restoring energy by the 
 use of compressed air in this case is therefore 
 5976000 -j- 20520000 = 0.29. 
 
 In practice the efficiency cannot be more than 0.25, if indeed 
 it is so high. 
 
 Sudden Compression. — It may not be out of place to call atten- 
 tion to a danger that may arise if air at high pressure is suddenly 
 let into a pipe which has oil mingled with the air in it or even 
 adhering to the side of the pipe. The air in the pipe will be com- 
 pressed, and its temperature may become high enough to ignite the 
 oil and cause an explosion. That this danger is not imaginary is 
 shown by an explosion which occurred under such conditions in 
 a pipe which was strong enough to withstand the air-pressure. 
 
 Liquid Air. — The most practical way of liquefying air on a 
 large scale is that devised by Linde depending on the reduction 
 of the temperature by throttling. On page 69, is given the 
 empirical expression deduced by Joule and Kelvin for the 
 reduction in temperature of air flowing through a porous plug 
 with a difference of pressure measured by 100 inches of mercury, 
 
 0.92 
 
 m 
 
LIQUID AIR 395 
 
 in which 2 73°. 7 C. is taken to be the absolute temperature of 
 freezing, and T is the absolute temperature of the air. 
 
 A modern three-stage air-compressor can readily give a press- 
 ure of 2000 pounds per square inch, and if the above expression 
 is assumed to hold approximately for such a reduction in pressure, 
 it indicates a cooling of 
 
 2000 o ^ 
 
 0.02 X = 37°.S C. 
 
 ^ 100 X 0.491 
 
 or about 67° F. By a cumulative effect to be described, the air 
 may be cooled progressively till it reaches the boiling-point of its 
 liquid and then liquefied. Linde's liquefying apparatus consists 
 essentially of an air-compressor, a throttling-orifice, and a heat 
 interchange apparatus. 
 
 The air-compressor should be a good three-stage machine 
 giving a high pressure. The throttling-orifice may be a small 
 hole in a metallic plate. The heat interchange apparatus may 
 be made up of a double tube about 400 feet long, the inner tube 
 having a diameter of 0.16 and the outer tube a diameter of 0.4 
 of an inch ; these tubes for convenience are coiled and are then 
 thoroughly insulated from heat. The air from the compressor 
 is passed through the inner tube to the throttle-orifice and then 
 from the reservoir below the orifice, through the space between 
 the inner and outer tubes back to the compressor. The cumu- 
 lative effect of this action brings the air to the critical temper- 
 ature in a comparatively short period, and then liquid air begins 
 to accumulate in the reservoir below the orifice, whence it may be 
 drawn off. 
 
 The atmospheric air before it is supplied to the condenser 
 should be freed from carbon dioxide and moisture, which would 
 interfere with the action, and should be cooled by passing it 
 through pipes cooled with water and by a freezing mixture. 
 The portion of air liquefied must be made up by drawing air from 
 the atmosphere, which is, of course, purified and cooled. 
 
 The principal use of liquid air is the commercial production of 
 oxygen by fractional distillation ; several plants have been installed 
 for this purpose. 
 
CHAPTER XVI. 
 
 REFRIGERATING-MACHINES. 
 
 A REFRiGERATiNG-MACHiNE IS a device for producing low 
 temperatures or for cooling some substance or space. It may 
 be used for making ice or for maintaining a low temperature in 
 a cellar or storehouse. 
 
 Refrigeration on a small scale may be obtained by the solu- 
 tion of certain salts; a familiar illustration is the solution of 
 common salt with ice, another is the solution of sal ammoniac 
 in water. Certain refrigerating- machines depend on the rapid 
 absorption of some volatile liquid, for example, of ammonia by 
 water; if the machine is to work continuously there must be some 
 arrangement for redistilling the liquid from the absorbent. The 
 most recent and powerful refrigerating- machines are reversed 
 heat-engines. They withdraw the working substance (air or 
 ammonia) from the cold-room or cooling-coil, compress it, and 
 deliver it to a cooler or condenser. Thus they take heat from a 
 cold substance, do work and add heat, and finally reject the sum 
 of the heat drawn in and the heat equivalent of the work done. 
 These reversed heat-engines, however, are very far from being 
 reversible engines, not only on account of imperfections and losses 
 but because they work on a non-reversible cycle. 
 
 Two forms of refrigerating- machines are in common use, air 
 refrigerating- machines and ammonia refrigerating-machines. 
 Sometimes sulphur dioxide or some other volatile fluid is used 
 instead of ammonia. Carbon dioxide has been used, but there are 
 difficulties due to high pressure and the fact that the critical tem- 
 perature is 88° F. 
 
 Air Refrigerating-Machine. — The general arrangement of 
 an air refrigerating-machine is shown by Fig. 86. It consists 
 
 396 
 
AIR REFRIGERATING-MACHINE 
 
 397 
 
 of a compression-cylinder A, an expansion-cylinder B of smaller 
 size, and a cooler C. It is commonly used to keep the atmos- 
 phere in a cold-storage room at a low temperature, and has 
 certain advantages for this purpose, especially on shipboard. 
 The air from the storage-room comes to the compressor at or 
 about freezing-point, is compressed to two or three atmospheres 
 and delivered to the cooler, which has the same form as a sur- 
 face-condenser, with cooHng water entering at e and leaving at /. 
 The diaphragm mn is intended to improve the circulation of 
 the cooling water. From the cooler the air, usually somewhat 
 warmer than the atmosphere, goes to the expansion-cylinder J5, 
 
 Fig. 86- 
 
 in which it is expanded nearly to the pressure of the air and 
 cooled to a low temperature, and then delivered to the storage- 
 room. The inlet-valves a, a and the delivery-valves b, b of 
 the compressor are moved by the air itself; the ad mission- valves 
 Cy c and the exhaust-valves d, d of the expansion-cylinder are 
 like those of a steam-engine and must be moved by the machine. 
 The difference between the work done on the air in the com- 
 pressor and that done by the air in the expansion-cylinder, 
 together with the friction work of the whole machine, must be 
 supplied by a steam-engine or other motor. ♦ 
 
 It is customary to provide the compression-cylinder with a 
 water-jacket to prevent overheating, and frequently a spray 
 of water is thrown into the cylinder to reduce the heating and 
 the work of compression. Sometimes the cooler C, Fig, 86, 
 
398 REFRIGERATING MACHINES 
 
 is replaced by an apparatus resembling a steam-engine jet-con- 
 denser, in which the air is cooled by a spray of water. In any 
 case it is essential that the moisture in the air, as well as the 
 water injected, should be efficiently removed before the air is 
 delivered .to the expansion-cylinder; otherwise snow will form 
 in that cylinder and interfere with the action of the machine. 
 Various mechanical devices have been used to collect and remove 
 water from the air, but air may be saturated with moisture after 
 it has passed such a device. The Bell-Coleman Company use 
 a jet-cooler with provision for collecting and withdrawing water, 
 and then pass the air through pipes in the cold-room on the 
 way to the expansion-cylinder. The cold-room is maintained 
 at a temperature a little above freezing-point, so that the mois- 
 ture in the air is condensed upon the sides of the pipes and 
 drains back into the cooler. 
 
 When an air refrigerating- machine is used as described, the 
 pressure in the cold-room is necessarily that of the atmosphere, 
 and the size of the machine is large as compared with its per- 
 formance. The performance may be increased by running 
 the machine on a closed cycle with higher pressures; for example., 
 the cold air may be delivered to a coil of pipe in a non-freezing 
 salt solution, from which the air abstracts heat through the 
 walls of the pipe and then passes to the compressor to be used 
 over again. The machine may then be used to produce ice, or 
 the brine may be used for cooling spaces or liquids. A machine 
 has been used for producing ice on a small scale, without cooling 
 water, on the reverse of this principle; that is, atmospheric air 
 is first expanded and chilled and delivered to a coil of pipe in 
 a salt solution, then the air is drawn from this coil, after absorb- 
 ing heat from the brine, compressed to atmospheric pressure, 
 and expelled. 
 
 ' Proportions of Air Refrigerating-Machines. — The perfor- 
 mance of a refrigerating-machine may be stated in terms 
 of the number of thermal units withdrawn in a unit of time, 
 or in terms of the weight of ice produced. The latent heat of 
 fusion of ice may be taken to be 80 calories or 144 b.t.u. 
 
PROPORTION OF AIR OF REFRIGERATING-MACHINES 399 
 
 Let the pressure at which the air enters the compression- 
 cylinder be />p that at which it leaves be p^\ let the pressure at 
 cut-ofif in the expanding-cylinder be p^ and that of the back- 
 pressure in the same be p^\ let the temperatures correspond- 
 ing to these pressures be Z^, t^, /g, and t^, or, reckoned from the 
 absolute zero, T^, Tj, Tg, and T^- With proper valve-gear 
 and large, short pipes communicating with the cold-chamber 
 /)4 may be assumed to be equal to p^ and equal to the pressure 
 in that chamber. Also t^ may be assumed to be the tempera- 
 ture maintained in the cold-chamber, and /, may be taken to 
 be the temperature of the air leaving the cooler. With a good 
 cut-off mechanism and large passages p^ may be assumed to 
 be nearly the same as that of the air supplied to the expanding- 
 cylinder. Owing to the resistance to the passage of the air 
 through the cooler and the connecting pipes and passages, p^ 
 is considerably less than p^. 
 
 It is essential for best action of the machine that the expan- 
 sion and compression of the expanding-cylinder shall be complete. 
 The compression may be made complete by setting the exhaust- 
 valve so that the compression shall raise the pressure in the 
 clearance-space to the admission-pressure p^ at the instant 
 when the admission-valve opens. The expansion can be made 
 complete only by giving correct proportions to the expanding- 
 and compression-cylinders. 
 
 The expansion in the expanding-cylinder may be assumed 
 to be adiabatic, so that 
 
 Were the compression also adiabatic the temperature t^ could 
 be determined in a similar manner; but the 
 air is usually cooled during compression, 
 and contains more or less vapor, so that the 
 temperature at the end of compression cannot 
 Fig. 87. i^Q determined from the pressure alone, even 
 
 though the equation of the compression curve be known. 
 
400 REFRIGERATING MACHINES 
 
 Let the air passing through the refrigerating- machine per 
 
 minute be M; then the heat withdrawn from the cold-room is 
 
 Q, = Mc, {t, - U) (232) 
 
 The work of compressing M pounds of air from the pressure p^ 
 to the pressure p^ in a compressor without clearance is (Fig. 87) 
 
 W^, = M I p,v, + y pdv - p^v^ \ ; 
 
 n - 1 
 
 ••• W.= Mp,v^^^\{f-) " -X j . . . . .(.33) 
 
 provided that the compression curve can be represented by an 
 exponential equation. If the compression can be assumed to 
 be adiabatic, 
 
 K I 
 
 for in such case we have the equations 
 
 
 ^ = (^] ' AR = r,.-c. = c, " 
 
 If the expansion is complete in the expanding-cylinder, as 
 should always be the case, then the equation for the work done 
 by the air will have the same form as equation (233) or (234), 
 replacing /j and p by fi and />4, and t^ and p^ by /, and p^ ; so that 
 
 n — 1 
 
 W'.= KM,;^J(^)"-xj. . .(33s) 
 and for adiabatic expansion 
 
 W,= ^(1,-1,) (236) 
 
PROPORTION OF AIR OF REFRIGERATING-MACHINES 401 
 
 The difference between the works of compression and expan- 
 sion is the net work required for producing refrigeration; conse- 
 quently 
 
 W=W,-W,= ^U,-h-t,+t4 .(237) 
 
 or, replacing M by its value from equation (232), 
 
 TF = Si ^2 + ^4 - /, - ^3 ^2s8) 
 
 A /j — /4 
 
 The net horse-power required to abstract Q^ thermal units 
 per minute is consequently 
 
 33000 i,-h ^ ^^' 
 
 where l^ is the temperature of the air drawn into the compressor, 
 and ^2 is the temperature of the air forced by the compressor into 
 the cooler, and f^ is the temperature of the air supplied to the 
 expanding-cylinder, and U is the temperature of the cold air 
 leaving the expanding-cylinder. The gross horse-power devel- 
 oped in the steam-engine which drives the refrigerating- machine 
 is likely to be half again as much as the net horse-power or even 
 larger. The relation of the gross and the net horse-powers for 
 any air refrigerating- machine may readily be obtained by indi- 
 cating the steam- and air-cylinders, and may serve as a basis for 
 calculating other machines. 
 
 The heat carried away by the cooling water is 
 
 Q, = Q,+AW (240) 
 
 If compression and expansion are adiabatic, then 
 Q, = Mc^ (/, _ /^ + /^ -f- /, _ /^ _ Q = Mcp {t, - /g) . (241) 
 
 or, replacing M by its value from equation (232), 
 
 Q. = <2. 7^ (242) 
 
 ^1 — M 
 
 If the initial and final temperatures of the cooling water are 
 
402 REFRIGERATING MACHINES 
 
 /, and /*, and if qi and ^^ are the corresponding heats of the 
 liquid, then the weight of cooling water per minute is 
 
 G = — 2i_ == Q ^Z_3 . . . (24^) 
 
 The compressor-cylinder must draw in M pounds of air per 
 minute at the pressure p^ and, the temperature /j, that is, with 
 the specific volume v^\ consequently its apparent piston dis- 
 placement without clearance will be at N revolutions per minute, 
 
 Mv, MRT, , , 
 
 2N 2Np^ 
 
 for the characteristic equation gives 
 
 p,v, = RT,. 
 Replacing M by its value from equation (232), we have 
 
 Dc = ^^^^\. ' .. .... (245) 
 
 Since all the air delivered by the compressor must pass through 
 the expanding-cylinder, its apparent piston displacement will be 
 
 If ^j, the pressure of the air entering the compression-cylinder 
 is equal to />4, that of the air leaving the expanding-cylinder (as 
 may be nearly true with large and direct pipes for carrying the 
 air to and from the cold-room), equation (246), will reduce to 
 
 D. = r),'^ (247) 
 
 Both the compressor- and the expanding-cylinder will have 
 a clearance, that of the expanding-cylinder being the larger. 
 As is shown on page 363, the piston displacement for an air- 
 compressor with a clearance may be obtained by dividing the 
 apparent piston displacement by the factor 
 
 m \pj m 
 
CALCULATION FOR AN AIR-REFRIGERATING MACHINE 403 
 
 If the expansion and compression of the expanding-cylinder are 
 complete, the same factor may be applied to it. For a refriger- 
 ating-machine n may be replaced by fc for both cylinders. To 
 allow for losses of pressure and for imperfect valve action the 
 piston displacements for both compressor- and expanding- 
 cylinders must be increased by an amount which must be deter- 
 mined by practice; five or ten per cent increase in volume will 
 probably suffice. In practice the expansion in the expanding- 
 cylinder is seldom complete. A little deficiency at this part 
 of the diagram will not have a large effect on the capacity of 
 the machine, and will prevent the formation of a loop in the 
 indicator-diagram; but a large drop at the release of the expand- 
 ing-cylinder will diminish both the capacity and the efficiency 
 of the machine. 
 
 The temperature t^ and the capacity of the machine may be 
 controlled by varying the cut-off of the expanding-cylinder. If 
 the cut-off is shortened the pressure p^ will be increased, and 
 consequently Ti will be diminished. This will make D^, the 
 piston displacement of the expanding-cylinder, smaller. A 
 machine should be designed with the proper proportions for its 
 full capacity, and then, when running at reduced capacity, the 
 expansion in the expanding-cylinder will not be quite complete. 
 
 Calculation for an Air-refrigerating Machine. — Required 
 the dimensions and power for an air refrigerating- machine to 
 produce an effect equal to the melting of 200 pounds of ice per 
 hour. Let the pressure in the cold-chamber be 14.7 pounds per 
 square inch and the temperature 32° F. Let the pressure of 
 the air delivered by the compressor-cylinder be 39.4 pounds by 
 the gauge or 55.1 pounds absolute, and let there be ten pounds 
 loss of pressure due to the resistance of the cooler and pipes and 
 passages between the compressor- and the expanding-cylinder. 
 Let the initial and final temperatures of the cooling water be 
 60° F. and 80° F., and let the temperature of the air coming 
 from the cooler be 90° F. Let the machine make 60 revolutions 
 per minute. 
 
 With adiabatic expansion and compression the temperatures 
 
404 REFRIGERATING MACHINES 
 
 of the air coming from the compressor- and discharged from the 
 
 expanding-cylinder will be 
 
 qj 
 
 T^ = 492 (^)?= 714; ••• /, = 254° F. 
 
 \I4.// 
 
 T, = (460 + 90) (^ =402; .-. /4= -58° F. 
 
 \44.i/ 
 
 The melting of 200 pounds of ice is equivalent to 
 
 200 X T44 -^ 60 = 480 B.T.u. 
 
 per minute; consequently the net horse-power of the machine 
 
 is by equation (239) 
 
 P^ = 77861 /. + /4 - /. - /. 
 33000 t^ - /4 
 
 _ 778 X 480 .. 254 - 58 - 32 - 90 
 
 33000 32+58 
 
 = ^7^ X ^^^ X 74 ^ H. P., 
 
 33000 X 90 
 
 and the indicated power of the steam-engine may be assumed 
 to be 14 horse-power. 
 
 By equation (245) the apparent piston displacement of the 
 compressor without clearance will be 
 
 2l\Cj,p^ (^ - U) 
 
 2.33 cu. ft. 
 
 2Nc^p, (t, - U) 
 
 480 X .S3. 22 X .102 
 
 2 X 60 X 0.2375 X 144 X 14.7 (32 + 58) 
 
 By equation (247) the apparent piston displacement of the 
 expanding-cylinder without clearance will be 
 
 Dg = Dc-;=r = 2.33 X = 1.90 cubic feet. 
 
 ^1 492 
 
 If the clearance of the compressor-cylinder is 0.02 of its piston 
 
 displacement, then the factor for clearance by equation (191) is 
 
 i-i(^f+-^---^M'^-^ = o.979, 
 
 m\pj m 100 \i4.7/ 100 
 
COMPRESSION REFRIGERATING-MACHINES 
 
 405 
 
 SO that the piston displacement becomes 
 
 2.33 -^ 0.979 = 2.38 cubic feet. 
 If, further, the clearance of the expander-cylinder is 0.05 of 
 its piston displacement, the factor for clearance becomes 
 
 I — 
 
 100 
 
 (-) 
 
 + 
 
 5 _ 
 
 100 
 
 0.963, 
 
 which makes the piston displacement 
 
 1.90 H- 0.963 = 1.97 cubic feet. 
 
 If now we allow ten per cent for imperfections, we will get for 
 the dimensions : stroke 2 feet, diameter of the compressor-cylinder 
 15 J inches, and diameter of the expanding-cylinder 14 inches. 
 
 Compression Refrigerating-Machine. — The arrangement of 
 a refrigerating- machine using a volatile liquid and its vapor is 
 
 Fig. 
 
 shown by Fig. 88. The essential parts are the compressor A, 
 the condenser B, the valve D, and the vaporizer C. The com- 
 pressor draws in vapor at a low pressure and temperature, 
 compresses it, and delivers it to the condenser, which consists 
 of coils of pipe surrounded by cooling water that enters at e and 
 leaves at /. The vapor is condensed, and the resulting liquid 
 
4o6 REFRIGERATING MACHINES 
 
 gathers in a reservoir in the bottom, from whence it is led by a 
 small pipe having a regulating-valve D to the vaporizer or 
 refrigerator. The refrigerator is also made up of coils of pipe, 
 in which the volatile liquid vaporizes. The coils may be used 
 directly for cooling spaces, or they may be immersed in a tank 
 of brine, which may be used for cooling spaces or for making ice. 
 Fig. 88 shows the compressor with one singlcracting vertical 
 cylinder which has head-valves, foot-valves, and valves in the 
 piston. Small machines usually have one double-acting com- 
 pressor cylinder. Large machines have vertical compressors 
 which may be single-acting or double acting. 
 
 The cycle which has been stated for the compression 
 refrigerating- machine is incomplete, because the working fluid 
 is allowed to flow through the expansion-cock into the expanding- 
 coils without doing work. To make the cycle complete, there 
 should be a small expanding-cylinder in which the liquid could 
 do work on the way from the condenser to the vaporizing-coils ; 
 but the work gained in such a cylinder would be insignificant, 
 and it would lead to complications and difficulties. 
 
 Proportions of Compression Refrigerating-Machines. — The 
 liquid condensed in the coils of the condenser flows to the expan- 
 sion-cock with the temperature t^ and has in it the heat q^. In 
 passing through the expansion-cock there is a partial vaporiza- 
 tion, but no heat is gained or lost. The vapor flowing from the 
 expansion-coils at the temperature t^ and the pressure p^ is 
 usually dry and saturated, or perhaps slightly superheated, as it 
 approaches the compressor. Each pound consequently carries 
 from the expanding-coils the total heat H^. Consequently 
 the heat withdrawn from the expanding-coil by a machine using 
 M pounds of fluid per minute is 
 
 Q, = M(H^-q,) (246) 
 
 The compressor-cylinder is always cooled by a water-jacket, 
 but it is not probable that such a jacket has much effect on the 
 working substance, which enters the cylinder dry and is super- 
 heated by compression. We may consequently calculate the 
 
PROPORTIONS OF COMPRESSION 407 
 
 temperature of the vapor delivered by the compressor by aid of 
 equation (80), page 65, giving 
 
 -.'T.(f.y'r.{f.y . . .,.,. 
 
 This equation may be used because it is equivalent to the 
 assumption with regard to entropy on page 121. The value 
 of a is i for ammonia and 0.22 for sulphur dioxide as given on 
 pages 119 and 124. 
 
 As has already been pointed out, the vapor approaching the 
 compressor may be treated as though it were dry and saturated, 
 each pound having the total heat H^. The vapor discharged by 
 the compressor at the temperature /, and the pressure p^ will 
 
 have the heat 
 
 c^ (/, - /J + H^. 
 
 The heat added to each pound of fluid by the compressor is 
 consequently 
 
 and an approximate calculation of the horse-power of the com- 
 pressor may be made by the equation 
 
 ^_ 778M \c,{t, -t,) +H, - HJ 
 33000 
 
 or, substituting for M from equation (249), 
 
 ^ 778O. ic, (/.-/,) +H,-H,} 
 
 ■ 33000 (H,-?,) • • ^'^'> 
 
 The power thus calculated must be multiplied by a factor to 
 be found by experiment in order to find the actual power of the 
 compressor. Allowance must be made for friction to find the 
 indicated power of the steam-engine which drives the motor; for 
 this purpose it will be sufficient to add ten or fifteen per cent of 
 the power of the compressor. 
 
 The heat in the fluid discharged by compressor is equal to 
 the sum of the heat brought from the vaporizing-coils and the 
 heat-equivalent of the work of the compressor. The heat that 
 
 (250) 
 
4o8 REFRIGERATING-MACHINES 
 
 must be carried away by the cooling water per minute is con- 
 sequently 
 
 .-, Q, = M\c^{t, -K) ^r,\ (252) 
 
 where r^ is the heat of vaporization at the pressure p^. 
 
 If the cooling water has the initial temperature /„, and the final 
 temperature t' ^^ and if qy, and q'y, are the corresponding heats of 
 the liquid for water, then the weight of cooling water used per 
 minute will be 
 
 M[cJt, 
 
 ■^-, ^ (253) 
 
 G = 
 
 qw - q'w 
 
 If the vapor at the beginning of compression can be assumed 
 to be dry and saturated, then the volume of the piston displace- 
 ment of a compressor without clearance, and making N strokes 
 per minute, is 
 
 ^ = V • • • • ('54) 
 
 To allow for clearance, the volume thus found may be divided 
 by the factor 
 
 
 <p2 ' ^ 
 
 as is explained on page 363. The volume thus found is further 
 to be multiplied by a factor to allow for inaccuracies and 
 imperfections. 
 
 The vapors used in compression- machines are liable to be 
 mingled with air or moisture, and in such case the performance 
 of the machine is impaired. To allow for such action the size 
 and power of the machine must be increased in practice above 
 those given by calculation. Proper precautions ought to be 
 taken to prevent such action from becoming of importance. 
 
 Calculation for a Compression Refrigerating-Machine. — Let 
 it be required to find the dimensions and power for an ammonia 
 refrigerating- machine to produce 2000 pounds of ice per hour 
 from water at 80° F. Let the temperature of the brine in the 
 
FLUIDS AVAILABLE 409 
 
 freezing-tank be 15° F., and the temperature in the condenser 
 be 85° F. Assume that the machine will have one double- 
 acting compressor, and that it will make 80 revolutions per 
 minute. 
 
 The heat of the liquid for water at 80° F. is 48 b.t.u., and the 
 heat of liquefaction of ice is 144, so that the heat which must 
 be withdrawn to cool and freeze one pound of water will be 
 
 48 + 144 = 192 B.T.U. 
 
 If we allow 50 per cent loss for radiation, conduction, and 
 melting the ice from the freezing-cans, the heat which the machine 
 must withdraw for each pound of ice will be about 300 b.t.u.; 
 consequently the capacity of the machine will be 
 
 Q^ = 2000 X 300 -7- 60 = loooo B.T.U. per minute. 
 
 The pressures for ammonia corresponding to 15° and 85° F., 
 are 42.43 and 165.47 pounds absolute per square inch, so that by 
 equation (249) 
 
 r. = r,(fr =(15+460) (i^M7\i^668. 
 \pj V 42.43 / 
 
 .-. /, = 668 - 460 = 208° F. 
 The horse-power of the compressor is 
 
 P _ 778Q, s^.g--/,) + H, -H,\ 
 
 33000 {H^ - q^) 
 ^ 778 X loooo jo.50836 (208-85) -f 556 - 535 j _^ 
 33000 (535 - 58) 
 If we allow 10 per cent for imperfections, the compressor will 
 require 45 horse-power. If, further, 15 per cent is allowed for 
 friction, the steam-engine must develop 53 horse-power. 
 
 From equation (248) the weight of ammonia used per minute 
 
 is 
 M = Q^-r (H^- Q,) = loooo -r (535 - 58) = 21 pounds; 
 
 and by equation (254) the piston displacement for the com- 
 pressor will be 
 
 ^ Mv^ 21 X 6.03 1 . r . 
 
 D = — — ^ = —^^ = o.gi cubic feet. 
 
 N 2 X 80 ^ 
 
4IO 
 
 REFRIGERATING-MACHINES 
 
 If lo per cent is allowed for clearance and imperfect valve 
 action, the piston displacement will be one cubic foot, and the 
 diameter may be made loj inches and the stroke 20 inches. 
 
 Fluids Available. — The fluids that have been used in compres- 
 sion refrigeratmg- machines are ether, sulphur dioxide, ammonia, 
 and a mixture of sulphur dioxide and carbon dioxide, known as 
 Pictet's fluid. The pressures of the vapors of these fluids at sev- 
 eral temperatures, and also the pressure of the vapors of methylic 
 ether and carbon dioxide, are given in the following table: 
 
 PRESSURES OF VAPORS, MM. OF MERCURY. 
 
 Temperatures 
 
 Degrees 
 
 Centigrade. 
 
 Ether. 
 
 Sulphur 
 Dioxide. 
 
 287-5 
 
 Methyl - 
 Ether. 
 
 Ammonia. 
 
 Carbon 
 Dioxide. 
 
 Pictet's 
 Fluid. 
 
 - 30 
 
 
 576.5 
 
 866.1 
 
 
 585 
 
 — 20 
 
 68.9 
 
 479-5 
 
 882.0 
 
 1392. I 
 
 15142 
 
 745 
 
 — 10 
 
 114. 7 
 
 762.5 
 
 1306.6 
 
 2144.6 
 
 20340 
 
 1018 
 
 
 
 184.4 
 
 1 165. 1 
 
 1879.0 
 
 3183.3 
 
 26907 
 
 1391 
 
 10 
 
 286.8 
 
 1719.6 
 
 2629.0 
 
 4574.0 
 
 34999 
 
 1938 
 
 20 
 
 432.8 
 
 2462 . I 
 
 3586.0 
 
 6387.8 
 
 44717 
 
 2584 
 
 30 
 
 634.8 
 
 3431-8 
 
 4778.0 
 
 8701 .0 
 
 56119 
 
 3382 
 
 40 
 
 907.0 
 
 4670.2 
 
 
 11595-3 
 
 69184 
 
 4347 
 
 Ether was used in the early compression- machines, but at the 
 temperatures maintained in the refrigerator the pressure is 
 small and the specific volume large, so that the machines, Hke 
 air refrigerating-machines, were either feeble or bulky. More- 
 over, air was liable to leak into the machine and unduly heat the 
 compressor -cylinder. Sulphur dioxide has been used success- 
 fully, but it has the disadvantage that sulphuric acid may be 
 formed by the leakage of moisture into the machine, in which 
 case rapid corrosion occurs. Ammonia has been extensively 
 used in the more recent machines with good results. When 
 distilled from an aqueous solution it is liable to contain con- 
 siderable moisture. As is shown by the table, Pictet's fluid has 
 a pressure at low temperature intermediate between the pressures 
 of sulphur dioxide and ammonia, and the pressure increases 
 slowly with the temperature. It has been used by the inventor 
 
ABSORPTION REFRIGERATING APPARATUS 
 
 411 
 
 only, and does not appear in practice to have any advantage over 
 ammonia. 
 
 Absorption Refrigerating Apparatus. — Fig. 89 gives an 
 ideal diagram of a continuous absorption refrigerating appara- 
 tus. It consists of the following essential parts: (i) the gen- 
 erator B, containing a concentrated solution of ammonia in 
 water, from which the ammonia is driven by heat; (2) the con- 
 denser C, consisting of a coil of pipe in a tank, through which 
 cold water is circulated; (3) the valve F, for regulating the 
 pressures in C and in /; (4) the refrigerator /, consisting of a 
 coil of pipe in a tank containing a non-freezing salt solution; 
 (5) the absorber A, containing a dilute solution of ammonia, 
 in which the vapor of ammonia is absorbed; and (6) the pump 
 P for transferring the solution from the bottom of A to the top 
 of B\ there is also a pipe connecting the bottom of B with the 
 top oi A. It is apparent that the condenser and refrigerator 
 or vaporizer correspond to the parts B and C of Fig. 88, and 
 that the absorber and generator take the place of the compressor. 
 The pipes connecting A and B are arranged to take the most 
 
 B 
 
 c 
 
 1 
 
 
 1 ' "S 
 
 
 I 
 
 1 A 
 
 
 ^_ir-^ 
 
 
 Fig. 89. 
 
 concentrated solution from A to B, and to return the solution 
 from which the ammonia has been driven, from B io A. In 
 practice the generator B is placed over a furnace, or is heated 
 by a coil of steam-pipe, to drive off the ammonia. Also, arrange- 
 ments are made for transferring heat from the hot liquid flow- 
 ing from B io A io the cold liquid flowing from A to B. As 
 
412 
 
 REFRIGERATING-MACHINES 
 
 the ammonia is distilled from water in B the vapor driven off 
 contains some moisture, w^hich causes an unavoidable loss of 
 efficiency. 
 
 Tests of an Air Refrigerating-Machine. — An air refriger- 
 ating- machine, constructed under the Bell-Coleman patent, 
 was tested by Professor Schroter * at an abattoir in Hamburg, 
 where it was used to maintain a low temperature in a storage- 
 room. The machine is horizontal, and has the pistons for the 
 expansion- and compression-cylinders on one piston-rod, the 
 expansion-cylinder being nearer the crank. Power is furnished 
 by a steam-engine acting on a crank at the other end of the 
 main shaft and at right angles to the crank driving the air- 
 pistons. Both the steam-cylinder and the expansion-cylinder 
 have distribution slide-valves, with independent cut-off valves. 
 The main dimensions are given in the following table: 
 
 DIMENSIONS BELL-COLEMAN MACHINE. 
 
 
 Steam- 
 Cylinder. 
 
 Compression- 
 Cylinder. 
 
 Expansion- 
 Cylinder. 
 
 
 Head 
 End. 
 
 Crank 
 End. 
 
 Head 
 End. 
 
 Crank 
 End. 
 
 Head 
 End. 
 
 Crank 
 End. 
 
 Diameter of piston, cm 
 
 Diameter of piston-rod, cm 
 
 53 
 8.1 
 0.605 
 5-9 
 
 53 
 
 0.605 
 5.8 
 
 71 
 9.0 
 605 
 1-4 
 
 71 
 6.8 
 0.605 
 1-4 
 
 53 
 9.0 
 0.605 
 8 9 
 
 53 
 9.0 
 0.605 
 8, 
 
 Clearance, per cent of piston displacement . 
 
 Water is sprayed into the compression-cylinder, and the air 
 is further cooled by passing through an apparatus resembling 
 a steam-engine jet-condenser, after which it is dried by passing 
 it through a system of pipes in the cold-room before it passes 
 to the expansion-cylinder. 
 
 In the tests, indicators were attached to each end of the several 
 cylinders, and the temperature of the air was taken at entrance 
 to and exit from each of the air-cylinders. Specimens of the 
 indicator-diagrams from the air-cylinders show for the com- 
 pressor a slight reduction of pressure during admission and 
 some irregularity during expulsion, and for the expansion- 
 
 * Untersuchungen an Kdltemachinen , 188'/. 
 
TESTS OF AN AIR REFRIGERATING-MACHINE 
 
 413 
 
 cylinder a little wire-drawing at cut-off, and a good expansion 
 and compression, though neither is complete. No attempt 
 was made to measure the amount and temperatures of the cool- 
 ing water. 
 
 The data and results of the tests and the calculations are 
 given in Table XXXVI. 
 
 Table XXXVI. 
 
 tests on bell-coleman machine. 
 
 Number of test 
 
 Duration in hours 
 
 Revolutions per minute 
 
 Temperatures of air, degrees Centigrade : 
 
 At entrance to compression-cylinder 
 
 At exit from compression-cylinder . 
 
 At entrance to expansion-cylinder 
 
 At exit from expansion- cylinder 
 
 Mean effective pressure, kgs. per sq. cm.: 
 
 Steam-cj'linder: headend 
 
 crank end 
 
 Compression-cylinder: head end 
 
 crank end 
 
 Expansion -cj'linder: head end 
 
 crank end 
 
 Indicated horse-power : 
 
 Steam-cylinder 
 
 Compression-cylinder 
 
 Expansion- cylinder 
 
 Mean pressure during expulsion from compression-cylinder, kgs. . 
 Mean pressure during admission to expansion-cylinder, kgs. . . . 
 
 Difference 
 
 Calculation from compression diagram : 
 
 Absolute pressure at end of stroke, kgs 
 
 Absolute pressure at opening of admission- valve, kg.: 
 
 Head end . 
 
 Crank end 
 
 Volume at admission, per cent of piston displacement : 
 
 Head end 
 
 Crank end 
 
 Weight of air discharged per stroke, kg.: 
 
 Head end 
 
 Crank end 
 
 Weight of air discharged per revolution, kg. . , 
 
 Calculation from expansion diagram : 
 Absolute pressure at release, kgs. : 
 
 Head end „ 
 
 Crank end 
 
 Absolute pressure at compression, kgs. : 
 
 Head end 
 
 Crank end 
 
 Volume at release, per cent of piston displacement: 
 
 Head end 
 
 Crank end 
 
 Volume at compression, per cent of piston displacement: 
 
 Head end 
 
 Crank end . 
 
 Air used per stroke, kg. : 
 
 Head end 
 
 Crank end 
 
 Air used per revolution 
 
 Difference of weights, calculated by compression and expansion 
 
 diagrams, kg 
 
 In per cent of the former 
 
 Mean weight of air per revolution, kg 
 
 Elevation of temperature at constant pressure, degrees Centigrade. 
 Heat withdrawn per H. P. per hour, calories 
 
 6 
 6505 
 
 II. 
 
 1.63 
 61.2 
 
 III. 
 2.92 
 63.5 
 
 193 
 27.3 
 19.00 
 -47.0 
 
 175 
 
 26.8 
 
 16.6 
 
 — 47.0 
 
 19. 1 
 
 27.2 
 
 19. 1 
 
 — 47-0 
 
 2.263 
 2.239 
 
 i!869 
 1.592 
 1. 615 
 
 2.336 
 2.294 
 I. 861 
 1.825 
 1.589 
 1.594 
 
 2.343 
 
 1.870 
 1.906 
 1.626 
 1.624 
 
 85.12 
 128.8s 
 
 60.10 
 3-35 
 2.82 
 0.53 
 
 82.35 
 118-55 
 
 56.12 
 3-25 
 2.83 
 0. 42 
 
 85.71 
 
 126.01 
 
 59.46 
 
 0.56 
 
 1.04 
 
 1.04 
 
 1.04 
 
 0.783 
 0.765 
 
 0.788 
 0.749 
 
 0.764 
 0.76s 
 
 6.15 
 8.50 
 
 5-95 
 8.41 
 
 6.03 
 7-91 
 
 0.2744 
 0. 2716 
 0.546 
 
 0.2764 
 0.2742 
 0.551 
 
 0.2750 
 0.2730 
 0.548 
 
 I -32 
 I -45 
 
 1-31 
 
 1.44 
 
 1.33 
 1.46 
 
 I. 14 
 1.20 
 
 1. 14 
 1. 19 
 
 1. 17 
 1.22 
 
 104.65 
 106.1 
 
 104.7 
 106.3 
 
 104.8 
 106.4 
 
 16.5 
 19.8 
 
 16.0 
 19.6 
 
 16.6 
 20.6 
 
 0.234 
 0.254 
 0.488 
 
 0.233 
 0.254 
 0.487 
 
 0.238 
 
 0.2SS 
 
 0.493 
 
 0.058 
 10.6 
 
 0.064 
 II. 6 
 
 0.05s 
 10.0 
 
 0.514 
 66.3 
 371 
 
 0.519 
 64.5 
 354 
 
 0.520 
 
 66.1 
 363 
 
Table XXXVII. 
 
 TESTS ON REFRIGERATING MACHINES. 
 By Professor Schroter. 
 
 Number. 
 
 I 
 
 2 
 
 3 
 4 
 5 
 6 
 7 
 8 
 o 
 19 
 II 
 
 12 
 
 6 
 
 Dimensions of the steam 
 
 Dimensions of the 
 
 B 
 
 cylinder. 
 
 
 compression cylinder. 
 
 
 
 
 
 
 
 ■5 
 
 
 n 
 
 
 -o\ 
 
 ■^1 
 
 6 
 
 £ 
 
 
 
 
 
 
 <u c 
 
 
 i 
 
 tJ o 
 .2 a 
 
 Jls 
 
 
 J-s. 
 
 Hi 
 
 1 
 
 >. 
 
 Q 
 
 Q 
 
 m 
 
 P 
 
 Q 
 
 W 
 
 c^ 
 
 
 
 
 
 
 
 Linde. 
 
 371^25 
 
 55; 5 
 
 800 
 
 32 s 
 
 ^3 
 
 540 
 
 ;;' 
 
 400 
 
 .... 
 
 602 
 
 250 
 
 55 
 
 420 
 
 '' 
 
 330 
 
 52 
 
 740 
 
 " 
 
 " 
 
 " 
 
 Pictet. 
 
 450 
 
 68 
 
 900 
 
 " 
 " 
 
 430 
 
 ^5 
 
 900 
 
 36 min. 
 
 34 " 
 106 " 
 
 50 " 
 46 " 
 
 35 " 
 
 3 hrs. 
 3 " 
 3.5 " 
 11.08" 
 9- 83 
 4.00 " 
 
 Number. 
 
 
 
 "S e 
 
 
 11 
 
 
 3 8 
 
 a 
 
 I 
 
 64.8 
 59-8 
 
 53-6 
 66.1 
 
 
 2 
 
 45.9 
 
 a 
 
 54-7 
 55-1 
 
 
 26. 27 
 
 4 
 
 
 27.30 
 
 
 59- 1 
 49.6 
 65-15 
 
 
 
 6 
 
 
 
 7 
 
 26.1 
 
 18. 1 
 
 8 
 
 65.8 
 64.2 
 
 34-5 
 91.2 
 
 25.8 
 
 9 
 
 52.01 
 
 10 
 
 64.7 
 
 94-5 
 
 61.70 
 
 II 
 
 64.5 
 
 99.2 
 
 66.42 
 
 12 
 
 64.0 
 
 
 75.02 
 
 Absolute pressures of vapor, 
 kilos, per sq. centimeter. 
 
 ^ 
 
 
 
 1 g 
 
 ill 
 
 1 
 
 2|| 
 
 CI 
 
 C! 
 
 13 
 
 
 
 
 
 6.99 
 
 
 9.58 
 
 9.31 
 
 13-66 
 14.06 
 14. II 
 13-78 
 
 2.50 
 
 8.13 
 
 7.87 
 
 2.36 
 
 10.68 
 
 10.41 
 
 2.97 
 
 3-77 
 
 3.22 
 
 0.45 
 
 4. II 
 
 3-50 
 
 0.63 
 
 4- 23 
 
 3.62 
 
 0.73 
 
 5.81 
 
 5-11 
 
 0.67 
 
 Number. 
 
 I 
 
 2 
 
 3 
 4 
 S 
 6 
 
 I 
 
 9 
 10 
 II 
 12 
 
 Ice formed. 
 
 
 9.0 
 
 8.3 
 
 1.3 
 1.3 
 1-3 
 1-3 
 
 
 34.8 
 
 16.8 
 25.0 
 28.2 
 20.6 
 
 o V <u 
 
 Uri Cue 
 a"" 
 
 15.2 
 
 22.6 
 25.9 
 
 18. 5 
 
 2.76 
 2.64 
 
 4-851 
 
 4-55) 
 4.90) 
 4-53) 
 4.91 1 
 4-55) 
 4.27 I 
 .4.83I 
 2.63 
 3.24 
 0.82 
 1-03 
 i-iS 
 1.06 
 
 Cooling water. 
 
 aJ 
 
 2 
 
 
 k 
 
 fc 
 
 6 
 
 K 
 
 4J . 
 
 13 S 
 
 g| 
 
 c 
 
 u. 
 
 II . 19 
 
 22.56 
 
 II. 2 
 
 23.58 
 
 II. 2 
 
 23.04 
 
 II. I 
 
 26. 10 
 
 8.77 
 
 12.41 
 
 8.82 
 
 20.45 
 
 10. IS 
 
 14.0 
 
 10. 1 
 
 15-95 
 
 10.15 
 
 17.20 
 
 10.3 
 
 31 -t 
 
 Temperature of 
 
 water or brine 
 
 cooled. 
 
 -4.4 
 -5-9 
 
 —9.50 
 —3-1 
 —18.2 
 — 10. o 
 —9.7 
 — 6.0s 
 
 -4-4 
 -5-9 
 
 2-95 
 2.38 
 
 4.71 
 
 -9.97 
 
 -4.1 
 
 -18.2 
 
 -10. o 
 
 -9-7 
 
 -6.0s 
 
 S,K 
 
 ■y o o 
 
 4444 
 3120 
 
 3249 
 
 3367 
 
 3072 
 
 3263 
 
 3684 
 3086 
 1674 
 2385 
 2638 
 1958 
 
TESTS OF COMPRESSION-MACHINES 415 
 
 Tests of Compression-Machines. — In Table XXXVII are given 
 the data and results of tests on three refrigerating- machines 
 on the Linde system using ammonia, and of a machine on 
 Pictet's system using Pictet's fluid, all by Professor Schroter. 
 The tests on machines used for making ice were necessarily of 
 considerable length, but the tests on machines used for cool- 
 ing liquids were of shorter duration. 
 
 The cooling water when measured was gauged on a weir or 
 through an orifice. In the tests 3 to 6 on a machine used for 
 cooling fresh water the heat withdrawn was determined by 
 taking the temperatures of the water cooled, and by gauging 
 the flow through an orifice, for which the coefficient of flow was 
 determined by direct experiment. The heat withdrawn in 
 the tests 7 and 8 was estimated by comparison with the tests 
 3 to 6. The net production of ice in the tests i and 2 was deter- 
 mined directly; and in the test 2 the loss from melting during 
 the removal from the moulds was found by direct experiment 
 to be 8.45 per cent. By comparison with this the loss by melting 
 in the first test was estimated to be 7.7 per cent. The gross 
 production of ice in the refrigerator was calculated from the 
 net production by aid of these figures. In the tests 9 to 12 on 
 the Pictet machine the gross production was determined from 
 the weight of water supplied, and the net production from the 
 weight of ice withdrawn. 
 
 A separate experiment on the machine used for cooling brine 
 gave the following results for the distribution of power: 
 
 Total horse-power , . 57.1 
 
 Power expended on compressor 19.5 
 
 *' " " centrifugal pump 9.8 
 
 '* '' " water-pump 3.6 
 
 The centrifugal pump was used for circulating the brine 
 through a system of pipes used for cooling a cellar of a brew- 
 ery. The water-pump supplied cooling water to the condenser 
 and for other purposes. 
 
4i6 
 
 REFRIGERATING-MACHINES 
 
 A similar test on the Pictet machine gave: 
 
 Power of engine alone 7.9 H. P. 
 
 ' and intermediate gear 16.6 * ' 
 
 ' gear, and pump 20.0 " 
 
 < < (I 
 
 i i i i 
 
 In 1888 comparative tests were made by Professor Schroter, 
 on a Linde and on a Pictet refrigerating- machine, in a special 
 building provided by the Linde Company which had every 
 convenience and facility for exact work. The following table 
 gives the principal dimensions of the machines: 
 
 PRINCIPAL DIMENSIONS OF LINDE AND PICTET 
 REFRIGERATING-MACHINES. 
 
 Diameter of steam-cylinder, cm 
 
 compressor-cylinder, cm. . . . 
 
 steam piston-rod, cm 
 
 compressor-rod, cm 
 
 Stroke of steam-piston, cm 
 
 compressor, cm 
 
 Diameter of pipe in vaporizers, external, mm 
 
 internal, mm 
 
 Length of pipe in first vaporizer, m 
 
 second vaporizer, m 
 
 Diameter of pipe in condenser, external, mm 
 
 internal, mm. 
 Length of pipe in condenser, m 
 
 The Linde machine used ammonia and was allowed to draw 
 a mixture of liquid and vapor into the compressor, so that no 
 water-jacket was required. The Pictet machine used Pictet 's 
 fluid, which is a mixture of sulphur dioxide and carbon dioxide 
 and had the compressor cooled by a water-jacket. 
 
 The data and results of the tests are given in Table XXXVIII. 
 Five tests were made on each machine. The temperature of 
 the salt solution or brine, from which heat was withdrawn by the 
 vaporizers, was allowed to vary about three degrees centigrade 
 from entrance to exit. The entrance temperatures were intended 
 
TESTS OF COMPRESSION-MACHINES 
 
 417 
 
 Table XXXVIII. 
 
 TESTS ON REFRIGERATING-MACHINES. 
 By Professor M. Schroter, Vergleichende Versuche an Kdltetnaschinen. 
 
 Pictet machine. 
 
 Steam-engine : 
 
 Revolutions per minute 
 
 Indicated horse-power 
 
 Compressor : 
 
 Horse-power 
 
 Mechanical efficiency 
 
 Pressure in condenser, kilograms per square 
 
 centimetre 
 
 Pressure in vaporizer, kilograms per square 
 
 centimetre 
 
 Vaporizer : 
 
 Mean temperature of brine, entrance . . 
 Mean temperature of brine, exit .... 
 
 Specific heat per litre 
 
 Initial temperature of brine, entrance . . 
 
 Initial temperature of brine, exit 
 
 Final temperature of brine, entrance . . . 
 
 Final temperature of brine, exit 
 
 Condenser : 
 
 Mean temperature of cooling-water, entrance 
 Mean temperature of cooling-water from 
 
 condenser 
 
 Mean temperature of cooling-water from 
 
 jacket 
 
 Initial temperature of condensing-water, 
 
 entrance 
 
 Initial temperature of condensing-water, exit 
 Final temperature of condensing-water, 
 
 entrance 
 
 Final temperature of condensing-water, exit 
 
 Error in heat account, per cent 
 
 Refrigerative effect, calories per horse-power 
 
 per hour 
 
 One vaporizer. 
 
 57-0 
 21.81 
 
 16.82 
 0.771 
 
 3-99 
 
 1-47 
 
 6. 10 
 308 
 0.850 
 6.09 
 303 
 
 6. 11 
 305 
 
 965 
 
 19 72 
 
 15-5 
 
 9-57 
 19.71 
 
 9.67 
 19.71 
 -t-0.6 
 
 3507 
 
 56.8 
 
 16. 10 
 0.771 
 
 391 
 
 1.05 
 
 — 1 .96 
 —4.98 
 
 0.847 
 — 2.02 
 
 4.99 
 — 2.04 
 —4.98 
 
 9.60 
 
 19.70 
 
 15-6 
 
 9.64 
 19.72 
 
 957 
 19.64 
 + 0.6 
 
 2556 
 
 III 
 
 57-1 
 18.75 
 
 14.26 
 0.761 
 
 3 84 
 0.68 
 
 — 9.92 
 — 12.91 
 
 0.845 
 
 — 9.91 
 — 12.91 
 
 — 9-94 
 —12.88 
 
 9.61 
 
 19- 59 
 
 16.8 
 
 9- 58 
 1937 
 
 9.61 
 19-35 
 
 -Fo.4 
 
 1852 
 
 IV 
 
 57.6 
 iS-93 
 
 11.83 
 0.743 
 
 425 
 
 0.17 
 
 -17-93 
 -20.96 
 0.841 
 -18.00 
 -21.00 
 -18.00 
 
 9.68 
 
 19-51 
 
 16.7 
 
 9.68 
 19-52 
 
 9.72 
 19-59 
 -1-3 
 
 59-3 
 27.56 
 
 22.91 
 0.831 
 
 6.39 
 
 1.05 
 
 — 2.04 
 —5.01 
 
 0.846 
 —1.99 
 —5 02 
 —2.05 
 —4.96 
 
 9.68 
 
 35-18 
 
 18.6 
 
 9-73 
 35 -08 
 
 9.72 
 3SOI 
 + 89 
 
 1702 
 
 Linde machine. 
 
 Steam-engine: 
 
 Revolutions per minute 
 
 Horse-power 
 
 Compressor : 
 
 Horse-power 
 
 Mechanical efficiency 
 
 Pressure in condenser, kilograms per .square 
 centimetre 
 
 Pressure in vaporizer, kilograms per square 
 
 centimetre 
 
 Vaporizer : 
 
 Mean temperature of brine, entrance . . 
 
 Mean temperature of brine, exit .... 
 
 Specific heat per litre ; . . 
 
 Initial temperature of brine, entrance . . 
 
 Initial temperature of brine, exit 
 
 Final temperature of brine, entrance . . . 
 
 Final temperature of brine, exit 
 
 Condenser : 
 
 Mean temperature of cooling-water, entrance 
 
 Mean temperature of cooling-water, exit 
 
 Initial temperature of water, entrance 
 
 Initial temperature of water, exit . . 
 
 Final temperature of water, entrance 
 
 Final temperature of water, exit . . . 
 
 Error in heat account, per cent . . . 
 
 Refrigerative effect, calories per horse-power 
 per hour 
 
 15-53 
 0.856 
 
 3-89 
 
 6.00 
 
 2 89 
 
 0.850 
 
 5 98 
 
 2.89 
 
 5-97 
 
 2.94 
 
 9-56 
 19.76 
 
 9-56 
 19.74 
 
 9-57 
 19.74 
 
 4308 
 
 45-1 
 18.26 
 
 15-20 
 0.833 
 
 -5-02 
 
 0.846 
 
 —2.05 
 
 -5.02 
 
 2.04 
 
 5-04 
 
 9-54 
 19.63 
 
 9-SS 
 19.42 
 
 9-54 
 19-45 
 -1.8 
 
 3182 
 
 45-1 
 17-03 
 
 [4-31 
 0.840 
 
 -9.99 
 12.91 
 
 0.843 
 
 ■ 9-95 
 
 -12.94 
 
 9-97 
 
 12.89 
 
 9.61 
 19.84 
 
 9.61 
 19.82 
 
 9.60 
 19.89 
 - 1.9 
 
 2336 
 
 12.63 
 0.805 
 
 1-56 
 
 -17.92 
 -20.82 
 
 0.840 
 -17.97 
 -20.83 
 17.96 
 20.83 
 
 9.61 
 19.72 
 
 9.64 
 19.79 
 
 9-56 
 19.88 
 
 45-0 
 24.41 
 
 21.86 
 0.895 
 
 2.95 
 
 -2.03 
 - 5-OI 
 
 0.84s 
 
 -2.03 
 
 -5.00 
 
 2.03 
 
 501 
 
 9.68 
 35-33 
 
 9.68 
 35-45 
 
 9-65 
 35-44 
 -f I 
 
 2022 
 
4l8 REFRIGERATING-MACHINES 
 
 to be 6°C., - 2° C, - io° C and - i8° C. The cooling 
 water was supplied to the condenser at about 9^.5 C, for all 
 tests, and for all but one it left the condenser with a temperature 
 of nearly 20° C; the fifth test on each machine was made with 
 the exit temperature of the cooling water at about 35° C. 
 
 The pressure in the compressor depended, of course, on the 
 temperatures of the brine and the cooling-water. For all the 
 tests except the fifth on each machine, the maximum pressure 
 of the working substance was nearly constant: about 9 kilograms 
 per square centimetre for ammonia and about 4 kilograms for 
 Pictet's fluid. The fifth test had considerably higher pressure, 
 corresponding to the higher temperature in the condenser. The 
 minimum pressure of the working substance of course diminished 
 as the brine temperature fell. 
 
 The heat yielded per hour to the ammonia in the vaporizer 
 was calculated by multiplying together the amount of brine used 
 in an hour, the specific heat of the brine, and its increase of 
 temperature. But the initial and final temperatures were not 
 quite constant, and so a correction was applied. The heat 
 abstracted from the ammonia in the condenser was calculated 
 from the water used per hour and its increase of temperature. 
 The calculation for Pictet's machine involves also the jacket- 
 water and its increase of temperature. A correction is applied 
 for the variations of initial and final temperatures of the 
 cooling-water. If the heat equivalent of the work of the com- 
 pressor is added to the heat yielded by the vaporizer the sum 
 should be equal to the heat abstracted by the cooling-water. 
 The per cent of difference between these two calculations of 
 the heat abstracted by the cooling-water is a measure of the 
 accuracy of the tests. 
 
 The refrigerative effect is obtained by dividing the heat yielded 
 by the vaporizer by the horse-power of the steam-cylinder. The 
 first four tests with constant temperature in the condenser show 
 a regular decrease in the refrigerative effect for each machine 
 as the temperature of the brine and the minimum pressure of 
 the working substance is reduced. The fifth test, with a 
 
TESTS OF COMPRESSION-MACHINES 
 
 419 
 
 higher temperature in the condenser, shows a less refrigerative 
 effect than the second test, which has nearly the same brine 
 temperatures. These results are in concordance with the idea 
 that a refrigerating- machine is a reversed heat-engine; for a 
 heat-engine will have a higher efficiency and will use less heat 
 per horse-power when the range of temperatures is increased, 
 and per contra, a refrigerating-machine will be able to transfer 
 less heat per horse-power as the range of temperatures is 
 increased. 
 
 Table XXXIX. 
 
 TESTS ON AMMONIA REFRIGERATING-MACHINE. 
 By Professor J. E. Denton, Trans. Am. Soc. Mech. Engr., vol. xii, p. 326. 
 
 Pressure above atrnospliere, pounds per square inch : 
 
 Ammonia from compressor , 
 
 Ammonia back-pressure .' 
 
 Barometer, inches of mercury 
 
 Temperature, degrees Fahrenheit : 
 
 Brine, inlet 
 
 outlet 
 
 Condensing- water inlet 
 
 outlet 
 
 Jacket-water, inlet 
 
 Ammonia-vapor, leaving brine-tank 
 
 entering compressor 
 
 leaving compressor 
 
 calculated 
 
 entering condenser 
 
 Brine, pounds per minute 
 
 Specific gravity 
 
 Specific heat 
 
 Ammonia, lbs. per min. by metre 
 
 from compressor displacement . 
 Heat account, b.t.c per minute : 
 
 Given to ammonia by brine 
 
 compressor 
 
 atmosphere 
 
 Total received by ammonia 
 
 Taken from ammonia by condenser 
 
 jackets 
 
 atmosphere 
 
 Total taken from ammonia 
 
 Error, per cent 
 
 Power, etc. : 
 
 Revolutions per minute 
 
 Horse-power steam-cylinder 
 
 compressor 
 
 Mechanical efficiency 
 
 Refrigerative effect: 
 
 Tons of ice (melted) in 24 hours 
 
 B.T.U. abstracted from brine per horse-power minute 
 Pounds of ice (melted) per pound of coal 
 
 151 
 28 
 30.07 
 
 36.76 
 
 28.86 
 
 44-65 
 
 83.66 
 
 44-65 
 
 34-2 
 
 39 
 
 213 
 
 229 
 
 200 
 
 2281 
 
 I -163 
 
 0.82 
 
 14776 
 
 27860 
 
 140 
 
 17702 
 
 17242 
 
 608 
 
 182 
 
 18032 
 
 58.09 
 85.0 
 65.7 
 o.8r 
 
 74-8 
 
 174 
 
 24.1 
 
 II 
 
 152 
 
 8.2 
 
 29-59 
 
 6. 27 
 2.03 
 56.65 
 85-4 
 56.7 
 14.7 
 25 
 263 
 304 
 218 
 2173 
 1. 174 
 0.78 
 14.68 
 
 71876 
 
 2320 
 
 147 
 
 9653 
 
 9056 
 
 712 
 
 338 
 
 ioio6 
 
 5 
 
 57-7 
 71-7 
 54-7 
 0.83 
 
 .?6.43 
 197 
 
 III 
 
 147 
 
 13 
 
 29.87 
 
 14.29 
 2 .29 
 46-9 
 85.46 
 46.9 
 3-0 
 XO.I3 
 239 
 260 
 209 
 942.8 
 1. 174 
 0.78 
 16.67 
 
 8824 
 25x8 
 
 167 
 1 1 409 
 9910 
 
 656 
 
 250 
 10816 
 
 3-5 
 
 57.88 
 73-6 
 59-4 
 0.86 
 
 44-64 
 
 197 
 
 17.37 
 
 IV 
 
 161 
 
 .27-5 
 30.01 
 
 28.45 
 54.00 
 82.86 
 54-3 
 29.2 
 34 
 
 221 
 237 
 168 
 
 2374 
 
 I -174 
 0-78 
 28-32 
 34-51 
 
 14647 
 
 3020 
 
 141 
 
 17708 
 
 17359 
 406 
 252 
 
 18017 
 
 58.89 
 88.6 
 71.2 
 0.83 
 
 74 56 
 
 196 
 
 23-37 
 
 Table XXXIX gives the data and results of tests made by 
 Professor Denton on an ammonia refrigerating-machine. The 
 
420 REFRIGERATING-MACHINES 
 
 only items requiring explanation are the refrigerative effect 
 and the calculated temperature of the vapor leaving the con- 
 denser; the latter was calculated bv the equation 
 
 and shows both the cooling effect of the jacket and the error in 
 assuming an adiabatic compression. The exponent used here 
 is a trifle smaller than that of equation (249) page 407. The 
 refrigerative effect was obtained by dividing the b.t.u. given 
 to the ammonia in a minute by the horse-power of the steam- 
 cylinder. The tons per horse-power in 24 hours was obtained 
 by multiplying the refrigerative effect in thermal units per 
 minute by the number of minutes in a day and then dividing 
 the product by 2000 (the pounds in a short ton) and by 144 
 (the heat of melting a pound of ice). The pounds of ice per 
 pound of coal was based on an assumed consumption of three 
 pounds of coal per horse-power per hour, and was calculated 
 by multiplying the b.t.u. per horse-power per minute by 60 
 and dividing by 3 X 144. 
 
 The main dimensions of the machine were: 
 
 Diameter of ammonia cylinder (single-acting) 12 inches 
 
 Stroke of ammonia cylinder 30 " 
 
 Diameter of steam-cylinder 18 " 
 
 Stroke of steam-cylinder 36 " 
 
 Diameter of pipe for vaporizer and condenser i " 
 
 Length of pipe in vaporizer 8000 feet 
 
 condenser 5000 " 
 
 Test of an Absorption-machine. — The principal data and 
 the results of a test made by Professor J. E. Denton * on an 
 absorption ammonia refrigerating- machine are given in Table 
 XL. The machine is applied to chill a room of about 400,000 
 cubic feet capacity at a pork-packing establishment at New 
 Haven, Conn. In connection with this test the specific heat of 
 the brine, which served as a carrier of heat from the cold room 
 to the ammonia, was determined by direct experiment. The 
 
 * Trans. Am. Soc. Mech. Eng., vol. x, May, 1889. 
 
TEST OF AN ABSORPTION-MACHINE 
 
 421 
 
 Table XL. 
 
 TEST OF AN ABSORPTION-MACHINE. 
 Seven Days' Continuous Test, Sept. 11-18, 18 
 
 . f Generator 
 
 Average pressures j „ 
 
 above atmosphere "j p , 
 
 in lbs. per sq. in. (^ Absorber ! 
 
 Average tempera- 
 tures in Fahren- 
 heit degrees. 
 
 Atmosphere in vicinity of machine . . . . 
 
 Generator 
 
 ^ . (Inlet 
 
 ^""^ (Outlet 
 
 Condenser I ^"^^f^^- [[[[[[[]][ 
 
 Inlet 
 
 (Outlet 
 
 r Upper outlet to generator . . . . 
 Heater-^ Lovi^er " " absorber , . . . 
 
 Linlet from absorber 
 
 Inlet from generator 
 
 Water returned to main boilers from steam 
 coil . .• 
 
 Absorber 
 
 Average range off Condenser 
 temperature s"! Absorber . 
 Fahr. degrees. I Brine . . 
 
 Brine circulated per ( Cubic feet 
 hour. i Pounds . 
 
 Specific heat of brine 
 
 Cooling capacity of machine in tons of ice per day of 24 hours 
 Steam consumption per hour, to volatilize ammonia, and to 
 ojjerate ammonia pump pounds 
 
 British thermal 
 units: 
 
 Eliminated Pe^ P°^"d^«^ b""^ • ' ' ' 
 ( Total per hour 
 
 Of refrigerating effect per pound of steam 
 
 consumption 
 
 ^ . . J ( At condenser, per hour .... 
 
 ^ ^ I At absorber " .... 
 
 fOn entering generator 
 
 Per pound of steamy ^ , .■■'■■' 
 On leaving generator 
 
 I coil 
 
 Consumed by generator per lb. of steam 
 
 condensed 
 
 Condensing water per hour, in pounds 
 
 Equivalent ice production per pound of coal, if one pound of coal 
 
 evaporates ten pounds of steam at boiler 
 
 Calories, refrigerating effect per kilogram of steam consumed . . 
 Approximate c o i 1 r Condensing coil 
 
 surface in sq. ft. < Absorber " 
 
 ( Steam " 
 
 150-77 
 47.70 
 23.69 
 
 23-4 
 
 80 
 
 272 
 
 21 .2 
 
 16.16 
 
 54i 
 
 80 
 
 80 
 III 
 212 
 178 
 132 
 272 
 
 260 
 
 25i 
 
 5 13 
 
 1.633-7 
 119,260 
 
 0.800 
 40.67 
 
 1,986 
 
 4.1 
 481,260 
 
 243 
 
 918,000 
 
 1,116,000 
 
 1,203 
 
 271 
 
 932 
 36,000 
 
 17. 1 
 
 135 
 
 870 
 
 350 
 200 
 
422 REFRIGERATING-MACHINES 
 
 brine chilled and the cooling water used were measured with 
 meters, which were afterwards tested under the conditions of 
 the experiment. 
 
 It is interesting to compare the refrigerative effects expressed in 
 pounds of ice per pound of coal. On this basis the compression- 
 machine tested by Professor Denton has an advantage of 
 
 24.1 -17. 1 ^, 
 
 ' — X 100 = 10 per cent. 
 
 24.1 
 
 But this comparison is really- unfair to the compression- 
 machine, for its steam-engine is assumed to require a consump- 
 tion of three pounds of coal per horse-power per hour, while the 
 calculation for the absorption-machine is based on the assumption 
 that a pound of coal can evaporate ten pounds of water; but an 
 automatic condensing-engine of the given power should be able 
 to run on 20 or 22 pounds of steam per horse-power per hour. 
 
CHAPTER XVIL 
 
 FLOW OP^ FLUIDS. 
 
 Thus far the working substance has been assumed to be at 
 rest or else its velocity has been considered to be so small that 
 its kinetic energy has been neglected; now we are to consider 
 thermodynamic operations involving high velocities, so that the 
 kinetic energy becomes one of the important elements of the 
 problem. These operations are clearly irreversible and conse- 
 quently the first law of thermodynamics only is available, and if 
 any element of computation involves reference to equations that 
 were deduced by aid of the second law, care must be taken 
 that such computations are allowable. It is true that all prac- 
 tical thermal operations are irreversible for one reason or another; 
 for example, the cycle for a steam engine is irreversible, both 
 because steam is supplied and exhausted from the cylinder and 
 because the cylinder is made of conducting material. But all 
 adiabatic operations in cylinders (which serve as the basis of 
 theoretical discussions) are properly treated as reversible and all 
 the deductions from the second law may be applied to that part 
 of the cycle. In particular the limitations of the discussion of 
 entropy on page 32 have been observed. 
 
 Three cases of continuous thermal operations have been 
 discussed (i) flow through a porous plug, (2) the throttling 
 calorimeter, (3) friction of air in pipes; to which it may be well 
 to return now. In all, the velocity of the fluid has been so small 
 that its kinetic energy was neglected; in none of them was any 
 reference made to equations deduced by the aid of the second 
 law of thermodynamics. Rather curiously, all the operations 
 were adiabatic, using the word to mean that no heat was taken 
 from or lost to external objects; in the case of transmission of air 
 in pipes, this comes from the natural conditions of the case 
 
 423 
 
424 FLOW OF FLUIDS 
 
 and in the other two operations there was careful insulation 
 from heat. None of the operations are isoentropic; for instance, 
 the entropy of steam supplied to the calorimeter on page 192 
 is about 1.60 and the entropy of the superheated steam in the 
 calorimeter is about 1.72; but this does not enter into the solution 
 of the problem and is more curious than useful. 
 
 The flow of fluids through orifices and nozzles has become 
 even of more importance than formerly on account of the develop- 
 ment of steam turbines. Thus far all computations have been 
 based on adiabatic action, and when attempt is made to allow 
 for friction it is done by the application of an experimental 
 factor to results from adiabatic computations. 
 
 The following is the customary method of establishing the 
 fundamental equation. Suppose that a fluid is flowing from 
 
 the larger pipe A into the pipe B; 
 u , there will clearly be an increase in 
 
 l2— — p— velocity, with a reduction in pressure, 
 f The first law of thermodynamics 
 
 Fig. 90 as expressed by equation (16), page 14, 
 
 needs the addition of a term to take 
 
 account of the change in kinetic energy, and may be written 
 
 dQ = A {dE + dW + dK); 
 
 the last term in the parenthesis represents the increase of kinetic 
 
 energy. 
 
 Let it be supposed that there is a frictionless piston in each 
 
 cylinder; the piston in A exerts the pressure p^ on the fluid in 
 
 front of it, and the piston in B has on it the fluid pressure p^. 
 
 Each unit of weight of fluid passing from A through the orifice 
 
 has the work p^v^ done on it, while each pound entering the 
 
 cylinder B does the work p^v^. The assumption of pistons is 
 
 merely a matter of convenience, and if they are suppressed the 
 
 same conditions with regard to external work will hold. 
 
 If the velocity in A is V^ the kinetic energy of one unit of 
 
 72 y 2 
 
 weight in that cylinder is — ^ ; the kinetic energy in B is — ^ 
 
 2g 2g 
 
 for a velocity V^. 
 
TEST OF AN ABSORPTION-MACHINE 425 
 
 The intrinsic energies in A and B are E^ and E^. If there 
 is no heat communicated to or from the fluid the sum of the 
 intrinsic energy, external work, and kinetic energy must remain 
 constant, so that 
 
 this is the fundamental equation for the flow of a fluid. 
 
 If the walls of the pipes are well insulated there will not be 
 much radiation or other external loss even if the pipes have 
 considerable length, and in cases that arise in practice that loss 
 may properly be neglected. There is likely to be a considerable 
 frictional action even if the pipes are short, and the logical method 
 appears to call for the introduction of frictional terms at this 
 place. Such is not the custom, and a substitute will be dis- 
 cussed later. 
 
 Usually the velocity in the large cylinder A is small and the 
 term depending on it may be neglected. Solving for the term 
 depending on the velocity in B and dropping the subscript, 
 we have 
 
 ^ = £,-£, + p,v^ - p,v.^ .... (256) 
 
 Incompressible . Fluids. — There is little if any change of 
 volume or of intrinsic energy in a liquid in passing through an 
 orifice under pressure, so that the equation of flow becomes in 
 this case 
 
 V' 
 
 — = (/^l - P2>1 ' (257) 
 
 If the difference of pressure is due to a dift'erence of level or 
 head, hy we have 
 
 Pi — P2 ^ ^^' 
 
 where d is the density, or weight of a unit of volume, and is the 
 reciprocal of the specific volume; consequently equation (257) 
 reduces to 
 
 — = ^, (258) 
 
 2^ 
 
426 FLOW OF FLUIDS 
 
 which is the usual equation for the flow of a liquid through a 
 small orifice. 
 
 Flow of Gases. — The intrinsic energy of a unit of weight of 
 a gas is 
 
 pv 
 
 E = 
 
 fc — I 
 
 which depends only on the condition of the gas and not on any 
 changes that have taken or may take place. The equation for 
 the flow of a gas therefore becomes 
 
 At this place it is customary to use the equation 
 
 /'zV = Pi'^i" (259) 
 
 for the reduction of the equation (258) just as though we were 
 dealing with an adiabatic expansion in a non-conducting closed 
 cylinder. Now the fact that the isoenergic line and the iso- 
 thermal line are practically identical (page 63) shows that a 
 perfect gas has no disgregation energy and consequently for an 
 adiabatic change all the change in intrinsic energy is available 
 for doing outside work, which in this case is applied to increasing 
 the kinetic energy of the gas, instead of being applied to the 
 piston of a compressed air motor. If this analogy is allowed 
 equation (258) may be used, and will yield 
 
 K I 
 
 P2V2 = Z-.^. (^J~'= P'^'^ipj ' • ■ ■ (260) 
 
 so that equation (259) may be reduced to 
 
 YL 
 
 2g 
 
 ='.%-^[--(ff'] • ■ • ■<^-' 
 
FLOW OF GASES 427 
 
 This equation may also be deduced for the 
 work of air in the cylinder of a compressed 
 ^ air motor (Fig. 91). The work of admission 
 is p^v^\ the work of expansion is by equation 
 F»°- 9- (81), page 65. 
 
 &i--eri=s[--g;n 
 
 and the work of exhaust is 
 
 K T 
 
 so that the effective work is 
 
 which is readily reduced to equation (261). 
 
 For the calculation of velocities it is convenient to replace the 
 coefficient p^v^ in equation (261) by RT^, since pressures and 
 temperatures are readily determined and are usually given, thus 
 
 n.^r,-^r.-(fcpl . .(.6.) 
 
 2g '/C - I L \pj J 
 
 If the area of the orifice is a, then the volume discharged per 
 second is 
 
 aV, 
 
 and the weight discharged per second is 
 
 aV 
 
 w = — , 
 
 when v^ is the specific volume at the lower pressure and is equal 
 to 
 
428 FLOW OF FLUIDS 
 
 Substituting V from equation (262) and v^ from (263) and 
 reducing 
 
 The equations deduced for the flow of air apply to the flow 
 from a large cylinder or reservoir into a small straight tube 
 through a rounded orifice. The lower pressure is the pressure 
 in the small tube and differs materially from the pressure of the 
 space into which the tube may deliver. In order that the flow 
 shall not be much affected by friction against the sides of the 
 tube it should be short — not more than once or twice its diameter. 
 The flow does not appear to be affected by making the tube 
 very short, and the degree of rounding is not important; the 
 equations for the flow of both air and steam may be applied 
 with a fair degree of approximation to orifices in thin plates and 
 to irregular orifices. 
 
 Professor Fliegner * made a large number of experiments on the 
 flow of air from a reservoir into the atmosphere, with pressures 
 in the reservoir varying from 808 mm. of mercury to 3366 mm. 
 He used two different orifices, one 4.085 and the other 7.314 mm. 
 in diameter, both well rounded at the entrance. 
 
 He found that the pressure in the orifice, taken by means of 
 a small side orifice, was 0.5767 of the absolute pressure in the 
 reservoir so long as that pressure was more than twice the atmos- 
 pheric pressure; under such conditions the pressure in the orifice 
 is independent of the pressure of the atmosphere. 
 
 . If the ratio -^ is replaced by the number 0.5767 and if k, is 
 
 replaced by its value 1.405 in equation (264) we shall have for 
 the equation foi the flow of a gas 
 
 7£; = 0.4822a y^-^ (265) 
 
 * Der Civilingenieur, vol. xx, p. 14, 1874. 
 
FLIEGNER'S EQUATIONS FOR FLOW OF AIR 429 
 
 For the flow into the atmosphere from a reservoir having a 
 pressure less than twice the atmospheric pressure Fliegner found 
 the empirical equation 
 
 .■ = o.9644Vf- \/-^— ^' • • • 
 
 (266) 
 
 where p^ is the pressure of the atmosphere. 
 
 These equations were found to be justified by a comparison 
 with experiments on the flow of air, made by Fliegner himself, 
 by Zeuner, and by Weisbach. 
 
 Although these equations were deduced from experiments 
 made on the flow of air into the atmosphere, it is probable that 
 they may be used for the flow of air from one reservoir into 
 another reservoir having a pressure differing from the pressure 
 of the atmosphere. 
 
 Fliegner's Equations for Flow of Air. — Introducing the 
 values for g and R in the equations deduced by Fliegner, we have 
 the following equations for the French and English systems of 
 units : 
 
 French units. 
 
 p^ > 2p„ w = o.sgsa-^; 
 
 p,<2p,„ u>^ 0.790a v/ ^- ^\ ^"K 
 
 -* 1 
 
 English units. 
 P. 
 
 Pi > 2p„, W = 0.530a 
 
 Vr, ' 
 
 P, < 2P,, W = 1. 060a V^ ^' ^ ^"^ 
 
 p^ = pressure in reservoir; 
 pj = pressure of atmosphere; 
 
 T'j = absolute temperature of air in reservoir (degrees centi- 
 grade, French units; degrees Fahrenheit, English units). 
 
430 
 
 FLOW OF FLUIDS 
 
 In the English system p^ and pa are pounds per square inch, 
 and a is the area of the orifice in square inches, while w is the 
 flow of air through the orifice in pounds per second. If desired, 
 the area may be given in square feet and the pressures in pounds 
 on the square foot, as is the common convention in thermo- 
 dynamics. 
 
 In the French system w is the flow in kilograms per second. 
 The pressures may be given in kilograms per square metre 
 and the area a in square metres; or the area may be given in 
 square centimetres, and the pressures in kilograms on the same 
 unit of area. If the pressures are in millimetres of mercury, 
 multiply by 13.5959; ^^ ^^ atmospheres, multiply by 10333. 
 
 Theoretical Maxima. — From a discussion of the mean velocity 
 of molecules of a gas Fliegner deduces for the maximum velocity 
 through an orifice 
 
 V max = '^gRT^ = 16.9 Vr, 
 
 in metric units. His ratio of pressure 0.5767 inserted in equation 
 (262) gives 
 
 V max = 17. 1 Vrj. 
 
 The algebraic maximum of equation (264) occurs for the 
 ratio p2 -^ Pi = 0-5274, but this figure probably has no physical 
 significance. 
 
 Flow of Saturated Vapor. — For a mixture of a liquid and its 
 vapor equation (no), page 95, gives 
 
 £=-(? + ^f ), 
 
 so that equation (256) gives for the adiabatic flow from a recep 
 tacle in which the initial velocity is zero 
 
 — =7 (?1 - ?2 + ^iPl - ^2^2) + Pl'^l ~ P2'^2' (267) 
 2g /t 
 
 Substituting for v^ and v^ from 
 
 V = xu -\- 0-, 
 
 i 
 
FLOW OF SATURATED VAPOR 43 1 
 
 But 
 
 p + Apti = r; 
 
 .-. A —= x/j - x^r^ + ?i - ?2 + ^^ (Pi - p2)- (268) 
 2^ 
 
 The last term of the right-hand member is small, and fre- 
 quently can be omitted, in which case the right-hand member is 
 the same as the expression for the work done per pound of steam 
 in a non-conducting engine, equation (143), page 136, except 
 that as in that place the steam is assumed to be initially dry, x^ 
 is then ynity. The intrinsic energy depends only on the con- 
 dition of the steam, and consequently reference to the second 
 law of thermodynamics first comes into this discussion with 
 the proposal to compute the quality x^ in the orifice by aid of 
 the standard equation for entropy 
 
 
 2' 
 
 the acceptance of this method infers that the flow of steam 
 through a nozzle differs from its action in the cylinder of an 
 engine in that the work done is applied to increasing the kinetic 
 energy of the steam instead of driving the piston. 
 
 Values of the right-hand member of equation (268) may be 
 found in the temperature-entropy table which was computed 
 for solving problems of this nature. 
 
 The weight of fluid that will pass through an orifice having 
 
 an area of a square metres or square feet may be calculated by 
 
 the formula 
 
 aV 
 w = "-— (268). 
 
 The equations deduced are applicable to all possible mixtures 
 of liquid and vapor, including dry saturated steam and hot 
 water. In the first place steam will be condensed in the tube, 
 and in the second water will be evaporated. 
 
432 FLOW OF FLUIDS 
 
 If Steam blows out of an orifice into the air, or into a large 
 receptacle, and comes to rest, the energy of motion will be turned 
 into heat and will superheat the steam. Steam blowing into the 
 air will be wet near the orifice, superheated at a little distance, 
 and if the air is cool will show as a cloud of mist further from the 
 orifice. 
 
 Rankine's Equations. — After an investigation of the experi- 
 ments made by Mr. R. D. Napier on the flow of steam, Rankine 
 concluded that the pressure in the orifice is never less than the 
 pressure which gives the maximum weight of discharge, and 
 that the discharge in pounds per second may be calculated by 
 the following empirical equations: 
 
 p, = or > - pa, w = a^; 
 3 70 
 
 3 42 ( 2p, ) 
 
 in which p^ is the pressure in the reservoir, p^ is the pressure of 
 the atmosphere, both in pounds on the square inch, and a is the 
 area in square inches. 
 
 The error of these equations is liable to be about two per cent; 
 but the flow through a given orifice may be known more closely 
 if tests are made on it at or near the pressure during the flow, 
 and a special constant is found for that orifice. 
 
 Grashoff's Formula. — For pressures exceeding five-thirds 
 of the external or back pressure Grashoff gives the following 
 formula for the discharge of steam through a converging orifice, 
 
 w = 15.26 ap^-^"^ 
 
 the weight being in grams per second, the area in square centi- 
 metres and the pressure in kilograms per square centimetre. 
 For English units the equation becomes 
 
 w = 0.0165 ap^'^'' 
 
 the discharge being in pounds per second, the area in square 
 inches and the pressure in pounds absolute per square inch. 
 Rateau shows that this formula is well verified by his experiments 
 
FLOW OF SUPERHEATED STEAM 
 
 433 
 
 on the flow of steam, and that when the pressure is less than 
 that required by the formula the flow can be represented by a 
 curve which has for coordinates the ratio of the back pressure 
 to the internal pressure and for ordinates the ratio of the actual 
 discharge to that computed by the equation on the preceding page. 
 The following values were taken from his curves: 
 
 Ratio of back pressure 
 to internal pressure. 
 
 Ratio of actual to computed discharge. 
 
 Converging orifice. 
 
 Orifice in thin plates. 
 
 0-95 
 
 ■ 0.45 
 
 0.30 
 
 0.90 
 
 0.62 
 
 0.42 
 
 0.85 
 
 0-73 
 
 0.51 
 
 0.80 
 
 0.82 
 
 0.58 
 
 0-75 
 
 0.89 
 
 0.64 
 
 0.70 
 
 0.94 
 
 0.69 
 
 0.65 
 
 0.97 
 
 0-73 
 
 0.60 
 
 0.99 
 
 0.77 
 
 0.55 
 
 
 0.80 
 
 0.45 
 
 
 0.82 
 
 0.40 
 
 
 0.83 
 
 He further gives a curve for the discharge from a sharp-edged 
 orifice from which the third column was taken. 
 
 Flow of Superheated Steam. — Though there is no convenient 
 expression for the intrinsic energy of superheated steam, and 
 though the general equation (256) cannot be used directly, an 
 equation for velocity can be obtained by the addition of a term 
 to equation (268) to allow for the heat required to superheat 
 one pound of steam, making it read 
 
 2g Jt, 
 
 cdt + r^ + q^- xj,^ - q^. 
 
 (269) 
 
 The accompanying equation for finding the quality of steam x^ is 
 
 '^ cdt r^ 
 T T. 
 
 
 + e. 
 
 ^2^2 
 
 + ^, 
 
 (270) 
 
 Here / and T are the thermometric and the absolute temper- 
 atures of the superheated steam, t^ is the temperature of saturated 
 steam at the initial pressure, and t^ the temperature at the final 
 
434 
 
 FLOW OF FLUIDS 
 
 pressure, and the letters r^ and r^ and 0^ and 0^ represent the 
 corresponding heats of vaporization and entropies of the liquid. 
 
 Both equations apply only if the steam becomes moist at the 
 lower pressure, which is the usual case. They may obviously 
 be modified to apply to steam that remains superheated, but 
 such a form does not appear to have practical application. 
 
 The method of reduction of the integrals in equation (269) 
 and (270) is given on page 114; attention is called to the fact 
 that the temperature-entropy table affords ready solution of 
 equation (269), also of the velocity flow during which the steam 
 remains superheated. 
 
 Flow in Tubes and Nozzles. — The velocity of air or steam 
 flowing through a tube or nozzle with a large difference in pressure 
 is very high, reaching 3000 feet a second in some cases; and 
 consequently the effect of friction is marked even in short tubes 
 and nozzles. A test by Buchner * on a straight tube 3.52 inches 
 long and 0.158 of an inch internal diameter, under an absolute 
 pressure of 177 pounds to the square inch delivered only about 
 0.9 of the amount of steam calculated by the adiabatic method, 
 and the pressure in the tube fell gradually from 131 pounds near 
 the entrance to 14.5 pounds near the exit when delivering to a 
 condenser at about atmospheric pressure. If there were any 
 use for such a device in engineering the problem would appear 
 to call for a method of dealing with friction resembling that on 
 page 380 for flow of air in long pipes, but probably more difficulty 
 would be found in getting a satisfactory treatment. 
 
 From the investigations that have been made on the flow of 
 steam through nozzles it appears that they should have a well- 
 rounded entrance, the radius of the curve of the section at entrance 
 being half to three-fourths of the diameter of the smallest 
 section or throat; from the throat the nozzles should expand 
 gradually to the exit, avoiding any rapid change of velocity, 
 as such a change is likely to roughen the surface where it occurs. 
 The longitudinal section may well be a straight line joined to 
 the entrance section by a curve of long radius. The taper of 
 
 *MeiUeil ungen uber Forsehungrarheit Heft, i8, p. 43. 
 
FRICTION HEAD 
 
 435 
 
 the cone may be one in ten or twelve; this will give for the total 
 angle at the apex of the cone 5° to 6°; if the entrance to the nozzle 
 is not well rounded there will be a notable acceleration of the 
 steam approaching the nozzle and this acceleration outside of 
 the nozzle appears to diminish the amount of steam that the 
 nozzle can deliver. The expansion should preferably be suffi- 
 cient to reduce the steam to the pressure into which the nozzle 
 delivers; otherwise the acceleration of the steam will continue 
 beyond the nozzle, but the steam tends more and more to mingle 
 with the adjacent fluid through which it moves, and a poorer 
 effect is likely to be obtained. 
 
 If the expansion in the nozzle is not enough to reduce the 
 pressure of the steam to (or nearly to) the external pressure into 
 which the nozzle delivers, sound waves will be produced and 
 there will be irregular action, loss of energy, and a distressing 
 noise. On the other hand if the expansion in the nozzle reduces 
 the pressure of the steam below the external pressure at the 
 exit, sound waves will be set up in the nozzle with added resist- 
 ance. This latter condition is likely to be worse than the 
 former, and if the pressures between which the nozzle acts 
 cannot be controlled it should be so designed as to expand 
 the steam to a pressure a little higher than that against which 
 it is expected to deliver, allowing a little acceleration to occur 
 beyond the nozzle. 
 
 Friction Head. — In dealing with a resistance to the flow of 
 water through a pipe, such as is caused by a bend or a valve, 
 it is customary to assume that the resistance is proportional to 
 the square of the velocity and to modify equation (258), page 
 425 to read 
 
 h = h C — J 
 
 where C is a factor to be obtained experimentally. The term 
 containing this factor is sometimes called the head due to the 
 resistance or required to overcome the resistance, and the 
 equation may be changed to 
 
436 FLOW OF FLUIDS 
 
 it being understood that of the available head h, a certain portion 
 h' is used up in overcoming resistances and the remainder is 
 used in producing the velocity V. This aspect is well expressed 
 by shifting h^ to the other side of the equation and writing 
 
 1/2 
 
 ~ = h - h' ^ h 
 
 (.-f) = M.-,). 
 
 This method has been used by writers on steam turbines to 
 allow for frictional and other resistance and losses. It must 
 be admitted that it is a rough and unsatisfactory method, but 
 perhaps it will serve. The value of y probably varies between 
 0.05 and 0.15 for flow through a single nozzle or set of guide 
 blades or moving buckets in a steam turbine. 
 
 There is one difference between the behavior of water and 
 an elastic fluid like air or steam that must be clearly understood, 
 and kept in mind. Frictional resistance and other resistances 
 to the flow of water, transform energy into heat and that heat 
 is lost, or if it is kept by the water is not available afterwards 
 for producing velocity; on the other hand the energy which 
 is expended in overcoming frictional or other resistances of 
 like nature by steam or air, is changed into heat and remains in 
 the fluid, and may be available for succeeding operations. 
 
 Experiments on Flow of Steam. — There are five ways of 
 experimenting on the flow of steam through orifices and nozzles 
 that have been applied to test the theory of flow. Some of them, 
 used separately or in combination, can be made to give values 
 of the friction factor y, 
 
 (i) Steam flowing through an orifice or a nozzle may be 
 condensed and weighed. 
 
 (2) The pressure at one or several points in a nozzle may 
 be measured by side orifices or by a searching-tube; the latter 
 may be used to investigate the pressure in the region of the 
 approach to the entrance, or in the region beyond the exit, and 
 may also be used with an orifice. 
 
BUCHNER'S EXPERIMENTS 437 
 
 (3) The reaction of steam escaping from a nozzle or an orifice 
 may be measured. 
 
 (4) The jet of steam may be allowed to impinge on a plate 
 or curved surface and the impulse may be measured. 
 
 (5) A Pitot tube may be introduced into the jet and the 
 pressure in the tube can be measured. 
 
 Of course two or more of the methods may be used at the same 
 time with the greater advantage. It will be noted that none of 
 the methods alone or in combination can be made to determine 
 the velocity of the steam, and that all determinations of velocity 
 equally depend on inference from calculations based on the 
 experiments. 
 
 Formerly the weight of steam discharged was considered of 
 the greatest importance, as in the design of safety-valves, or in 
 the determination of the amount of steam used by auxiliary 
 machines during an engine-test. The first method of experi- 
 menting was obviously the most ready method of determining 
 this matter, and was first applied by Napier in 1869, and on his 
 results were based Rankine's equations. 
 
 Since the development of steam turbines much importance is 
 given to determination of steam velocities, though it is probable 
 that the determination of areas is still the more important 
 method, as on it depends the distribution of work and pressure, 
 while a considerable deviation from the best velocity will have 
 an unimportant influence on turbine efficiency. The first 
 experiments on reaction were by Mr. George Wilson in 1872, 
 but as his tests did not include the determination of the weight 
 discharged they are less valuable. 
 
 Biichner's Experiments. — A number of experimenters have 
 determined the weight of steam discharged by nozzles and tubes 
 and at the same time measured the pressure in side-orifices at 
 one or more places. The most complete appear to be those of 
 Dr. Karl Biichner * on the flow through tubes and nozzles. 
 Omitting the tests on tubes and on nozzles with a very small 
 
 * Mitteilungen uber Forschungsarbeiten Heft 18, p. 47. 
 
438 
 
 FLOW OF FLUIDS 
 
 taper, the nozzles for which results will be quoted have the fol- 
 lowing designations and dimensions: 
 
 NOZZLES TESTED BY DR. BUCHNER, 
 
 INCHES. 
 
 ALL DIMENSIONS IN 
 
 
 
 
 
 
 
 Distance 
 
 Designa- 
 
 Total 
 
 Cylindri- 
 
 Conical 
 
 Diameter 
 
 Taper 
 
 first side 
 orifice 
 from 
 
 tion. 
 
 length. 
 
 cal part. 
 
 part. 
 
 at throat. 
 
 one m. 
 
 
 
 
 
 
 
 entrance. 
 
 2a 
 
 1.97 
 
 0.36 
 
 1.61 
 
 0.158 
 
 20 
 
 0-33 
 
 2b 
 
 1.97 
 
 0.36 
 
 I. 61 
 
 0.158 
 
 13 
 
 0-33 
 
 3a 
 
 0-945 
 
 0.37 
 
 I 365 
 
 0159 
 
 7.2 
 
 0-34 
 
 3b 
 
 0-945 
 
 0-37 
 
 1-365 
 
 0.159 
 
 4-9 
 
 0.34 
 
 5c 
 
 1-37 
 
 0-37 
 
 I .00 
 
 0.200 
 
 20.3 
 
 0.24 
 
 5d 
 
 1-37 
 
 0-37 
 
 1. 00 
 
 0.200 
 
 14.2 
 
 0.24 
 
 Distance 
 
 last side 
 
 orifice 
 
 from exit . 
 
 0.17 
 0.17 
 0.14 
 0.14 
 O.II 
 O.II 
 
 All the nozzles had a cylindrical portion for which the length 
 is given in the above table including the rounding at entrance. 
 Excluding the rounding, this cylindrical portion was two or three 
 times the diameter at the throat and appears to have had consid- 
 erable influence on the distribution of the pressure. There were 
 from one to three additional side orifices evenly distributed; 
 from pressure in these orifices Biichner makes interesting com- 
 putations concerning the behavior of the fluid in the tube, but 
 the results are not different from those that are brought out by 
 the investigations of Stodola and are not included in this dis- 
 cussion. The data and results from such of the tests as appear 
 to bear on our present purpose of investigating the discharge and 
 friction of nozzles are given on page 439. 
 
 Steam for these tests was taken from a boiler through a sepa- 
 rator which probably delivered steam with a fraction of a per cent 
 of priming. The pressures were all measured on one gauge by 
 aid of an eight-way-cock. The steam from the nozzles was con- 
 densed and weighed; the experimenter estimates the error due 
 to uncertainty of draining the condenser at two per cent, which 
 appears to be the maximum error to be attributed to any, of the 
 
BUCHNER'S EXPERIMENTS 
 
 439 
 
 results. The discharge was also computed by Grashofif's 
 equation on page 432, and the ratio to the actual discharge is 
 that set down in the table; the variation from unity is not greater 
 than the probable maximum error. The method of the compu- 
 tation of velocities at throat and exit by the experimenter is not 
 very clear, but it was made to depend on the equation (268), using 
 the proper pressure and the discharge computed by Grashoff's 
 equation. 
 
 TESTS ON FLOW OF STEAM. 
 Dr. Karl Buchner. 
 
 Number 
 and 
 
 Pressure pounds absolute. 
 
 Ratio of 
 throat to 
 initial. 
 
 Dis- 
 charge 
 pounds 
 per 
 
 Ratio 
 of actual 
 to com- 
 puted 
 dis- 
 charge. 
 
 Velocity 
 at throat 
 
 Velocity 
 at exit. 
 
 Ratio 
 of actual 
 
 designa- 
 
 
 
 
 
 puted 
 
 
 Initial 
 
 Throat. 
 
 Exit. 
 
 External 
 
 
 second. 
 
 
 
 velocity. 
 
 i-2a 
 
 182 
 
 104.4 
 
 25-3 
 
 13-6 
 
 0-573 
 
 . 0503 
 
 
 i8co 
 
 3030 
 
 0.928 
 
 2-2 a 
 
 160.5 
 
 94.4 
 
 21.7 
 
 13-6 
 
 0-577 
 
 0.0449 
 
 ir.^ 
 
 1790 
 
 3020 
 
 0.930 
 
 3-2a 
 
 147-3 
 
 83.0 
 
 20.7 
 
 13-8 
 
 0.564 
 
 0.041 I 
 
 
 
 1820 
 
 2990 
 
 0.926 
 
 4-2a 
 
 131-3 
 
 75-1 
 
 i«-5 
 
 
 0.572 
 
 0.0370 
 
 
 1790 
 
 2990 
 
 0.929 
 
 5-2a 
 
 117. 1 
 
 67.6 
 
 16.8 
 
 13.8 
 
 0.577 
 
 0.0331 
 
 
 1780 
 
 2960 
 
 0.925 
 
 33-2b 
 
 180.2 
 
 92.1 
 
 16.5 
 
 14. 1 
 
 0.511 
 
 0.0494 
 
 
 I94t) 
 
 3260 
 
 0.920 
 
 2>^2>^ 
 
 149-9 
 
 76.8 
 
 21.2 
 
 13-6 
 
 0.529 
 
 0.0394 
 
 "^ 
 
 i860 
 
 3060 
 
 0.957 
 
 37-3a 
 
 131-5 
 
 70.4 
 
 19-5 
 
 13-8 
 
 0-535 
 
 0.0363 
 
 0^ +-• 
 
 1850 
 
 3020 
 
 0.950 
 
 3«-3a 
 
 II5-7 
 
 62.0 
 
 17-4 
 
 13-8 
 
 0536 
 
 0.0219 
 
 
 
 1850 
 
 3020 
 
 0.944 
 
 39-3 b 
 
 183.6 
 
 99.6 
 
 18.5 
 
 18.5 
 
 0.541 
 
 0.0501 
 
 
 1830 
 
 3430 
 
 0.987 
 
 41-5 1> 
 
 103.0 
 
 68.6 
 
 38.1 
 
 15-4 
 
 0.660 
 
 . 0483 
 
 
 1550 
 
 2190 
 
 0.932 
 
 42-5b 
 
 89-3 
 
 58.7 
 
 32.8 
 
 14.9 
 
 0.658 
 
 0.0419 
 
 00 f< 
 
 ^0 g 
 
 1550 
 
 2180 
 
 0.932 
 
 43-5^ 
 
 75-2 
 
 49-3 
 
 27-9 
 
 14.7 
 
 0.656 
 
 0.0343 
 
 1560 
 
 2150 
 
 0.923 
 
 44-5 b 
 
 61.0 
 
 37-6 
 
 22.3 
 
 14-5 
 
 0.643 
 
 0.0282 
 
 '-' 
 
 1560 
 
 2160 
 
 0.929 
 
 45-5 b 
 
 45-4 
 
 23. 
 
 16.9 
 
 14-5 
 
 0.618 
 
 0.021 1 
 
 
 1630 
 
 2130 
 
 0.923 
 
 47-5C 
 
 102.5 
 
 65-4 
 
 25-9 
 
 I5-0 
 
 0.637 
 
 0.0549 
 
 
 1630 
 
 2520 
 
 0.927 
 
 48-5C 
 
 88.8 
 
 55-7 
 
 22.2 
 
 14.8 
 
 0635 
 
 0.0410 
 
 r^ M 
 
 1630 
 
 2530 
 
 0.931 
 
 49-5C 
 
 74.2 
 
 46.9 
 
 18.5 
 
 14.6 
 
 0-633 
 
 0.0344 
 
 s 
 
 1620 
 
 2530 
 
 0.935 
 
 50-5C 
 
 59-2 
 
 37-1 
 
 14.9 
 
 14.4 
 
 0.625 
 
 0.0277 
 
 M ^ 
 
 1630 
 
 2490 
 
 0.932 
 
 The nozzles 3a and 36 had tapers of i 7.2 and i .'4.9 which were 
 probably too great, so that they may not have been filled with 
 
440 FLOW OF FLUIDS 
 
 Steam; this might account for the small ratio of the throat to the 
 initial pressure; the nozzle 26, which had a taper of 1:13, also 
 shows a small ratio of throat to initial pressure. 
 
 The most interesting feature of the tests is the ratio of the 
 ^•elocity at exit, computed by the method referred to above, from 
 the pressure at the side orifice near the exit from the nozzle. This 
 does not appear to depend on the throat pressure. Leaving 
 out tests on the nozzles 3a and 3^ the mean value of this ratio is 
 about 0.93 which corresponds to a value y = 0.14. 
 
 Rateau's Experiments. — These tests * have already been 
 referred to in connection with Grashoff's formula. They differ 
 from most tests oh the discharge from orifices and nozzles in 
 that the steam was condensed by a stream of cold water which 
 formed a jet condenser; the amount of steam was computed 
 from the rise of temperature and the amount of cold water used, 
 which latter was determined by flowing it through an orifice. 
 He estimates his error at something less than one per cent. The 
 number of tests is too large to quote here; it may be enough to 
 say that his diagrams show a very great regularity in his results, 
 so that whatever error there may be is to be attributed to the 
 method, which does avoid, as he claims, the uncertainty of 
 draining a condenser. 
 
 Kneass' Experiments. — In order to determine the pressure 
 in steam-nozzles such as are used in injectors, Mr. Strickland L. 
 Kneass | made investigations with a searching-tube, having a 
 small side orifice, both when the nozzles were performing their 
 usual function in an injector and when discharging freely into 
 the atmosphere. He also used side orifices bored through the 
 nozzles for the same purpose. The most interesting feature of 
 his investigation is that it makes practically no difference whether 
 the discharge is free or into the combining tube of an injector. 
 
 * Experimental Researches on Flow of Steam, trans. H. B. Brydon. 
 t Practice and Theory of the Injector. J. Wiley & Sons, 1894. 
 
ROSENHAIN'S EXPERIMENTS ^^I 
 
 For a well-rounded nozzle such as is used for an injector having 
 a taper of one to six, he found the following results : 
 
 Absolute Pressure. 
 
 
 Calculated Veloc- 
 
 litial. Throat. 
 
 Ratio. 
 
 ity at Throat. 
 
 135 82.0 
 
 0.606 
 
 1407 
 
 105 61.5 
 
 0-585 
 
 1448 
 
 75 42 
 
 0-559 
 
 149 1 
 
 45 24.5 
 
 0.546 
 
 1504 
 
 Stodola's Experiments. — In his work on Steam Turbines, 
 Professor Stodola gives the results of tests made by himself on the 
 flow of steam through a nozzle, having the following proportions : 
 diameter at throat 0.494, diameter at exit 1.45, and length from 
 throat to exit 6.07, all in inches. The nozzle had the form of a 
 straight cone with a small rounding at the entrance; the taper was 
 1 16.37. Four side orifices and also a searching-tube were used to 
 measure the pressure at intervals along the nozzle; the searching- 
 tube was a brass tube 0.2 of an inch external diameter closed at 
 the end and with a small side orifice. This orifice was properly 
 bored at right angles; two other tubes with orifices inclined, 
 one 45° against the stream and one 45° down stream, gave results 
 that were too large and two small by about equal amounts. 
 
 Stodola made calculations with three assumptions (i) with no 
 frictional action, (2) with ten per cent for the value oiy, and (3) 
 with twenty per cent ; comparing curves obtained in this way for 
 the distribution of pressures with those formed by experiments, 
 he concludes that the value of y for this nozzle was fifteen per cent. 
 
 Rosenhain's Experiments. — The most recent and notable 
 experiments on flow of steam with measurement of reactions 
 were made at Cambridge by Mr. Walter Rosenhain.* Steam 
 was brought from a boiler through a vertical piece of cycle- 
 tubing to a chamber which carried the orifices and nozzles at its 
 side; the reaction was counteracted by a wire that was attached 
 to the chamber passed over an antifriction pulley to a scale 
 pan, to which the proper weight could be added. Afterwards 
 he determined the discharge by collecting and weighing steam 
 
 * Proc. Inst. Civ. Eng., vol. cxl, p. 199. 
 
442 
 
 FLOW OF FLUIDS 
 
 under similar conditions. The steam pressure was controlled by 
 a throttle-valve. It is probable that there was some moisture in 
 the steam at high pressured and that at low pressures the steam 
 was slightly superheated. The following table gives the dimen- 
 sions of the nozzles: 
 
 ROSENHAIN'S EXPERIMENTS DIMENSIONS. 
 
 Designation. 
 
 Least Diameter. 
 
 Greatest Diameter. 
 
 Taper. 
 
 I 
 
 0.1873 
 
 
 . 
 
 II 
 
 0.1840 
 
 0.287 
 
 I : 20 
 
 IIA 
 
 0.1866 
 
 
 
 IIB 
 
 0.1849 
 
 0.287 
 
 I : 20 
 
 III 
 
 0.1882 
 
 0.368 
 
 I : 12 
 
 IIIA 
 
 0.1882 
 
 0.255 
 
 I : 12 
 
 IIIB 
 
 0.1882 
 
 0.241 
 
 I : 12 
 
 IV 
 
 0.1830 
 
 0255 
 
 I :3o 
 
 IVA 
 
 0.1830 
 
 . 2.42 
 
 I 130 
 
 IVB 
 
 0.1830 
 
 0.230 
 
 I : 30 
 
 IVC 
 
 0.1830 
 
 0.217 
 
 I :3o 
 
 IVD 
 
 0.1830 
 
 0.205 
 
 I 130 
 
 I was an orifice with sharp edge; IIA had a sharp edge at entrances; the 
 several orifices numbered III and IV had slightly rounded entrances. 
 
 DATA AND RESULTS. 
 
 
 
 
 
 Velocities. 
 
 
 
 N-zzle. 
 
 Ratio of 
 
 Proper initial 
 
 
 
 
 Coefficient 
 
 diameter. 
 
 pressure. 
 
 
 
 
 of friction. 
 
 
 
 
 Adiabatic 
 
 Expt. 
 
 Ratio. 
 
 
 II 
 
 1.56 
 
 150 
 
 2900 
 
 2740 
 
 0.946 
 
 0.105 
 
 III 
 
 
 96 
 
 275 
 
 3280 
 
 
 
 
 IIIA 
 
 
 36 
 
 97i 
 
 2600 
 
 2530 
 
 0.972 
 
 0.045 
 
 IIIB 
 
 
 28 
 
 80 
 
 2460 
 
 2220 
 
 0.903 
 
 0.185 
 
 IV 
 
 
 39 
 
 ^05 
 
 2630 
 
 2400 
 
 0.913 
 
 0.166 
 
 IVA 
 
 
 32 
 
 90 
 
 2520 
 
 2340 
 
 0.929 
 
 0.137 
 
 IVB 
 
 
 26 
 
 77i 
 
 2440 
 
 2200 
 
 0.901 
 
 0.188 
 
 IVC 
 
 
 19 
 
 62i 
 
 2220 
 
 2030 
 
 0.914 
 
 0.165 
 
 IVD 
 
 
 12 
 
 SO 
 
 2100 
 
 1920 
 
 0.914 
 
 0.165 
 
 A calculation has been made by the adiabatic method to 
 determine the pressures for which the several nozzles tested 
 would expand the steam down to the pressure of the atmosphere; 
 
PRESSURE IN THE THROAT ^^^ 
 
 a direct calculation cannot be made, but a curve can readily be 
 determined from which the pressure can be interpolated. The 
 velocities corresponding to these pressures have been taken from 
 Rosenhain's curves and the velocities were calculated also by the 
 adiabatic method. Since the diagrams in the Proceedings are to 
 a small scale the deduction of pressures from them cannot be very 
 satisfactory, but the results are probably not far wrong. The 
 table on page 442 gives the coefficient of friction obtained by 
 this method. 
 
 Lewicki's Experiments. — These experiments were made by 
 allowing the jet of steam to impinge on a plate at right angles 
 to the stream, and measuring the force required to hold the plate 
 in place; from this impulse the velocity may be determined. 
 It was found necessary to determine by trial the distance at 
 which the greatest effort was produced. One of his nozzles had 
 for the least diameter 0.237 and for the greatest diameter 0.305 
 of an inch or a ratio of 1.28, which is proper for a pressure of 80 
 pounds per square inch absolute. His experiments gave the 
 following results as presented by Biichner: 
 
 Steam pressure 77 99 108 
 
 Ratio of computed and } a a 
 
 expt. velocities i * * 
 
 Coefficient of friction .... 0.08 0.08 0.09 
 These experiments like those for reaction are liable to be vitiated 
 by expansion and acceleration of the steam beyond the orifice. 
 
 Pressure in the Throat. — Some of the tests by Biichner show 
 rather a low pressure in the throat of the nozzle, but in general 
 tests on the flow of steam show a pressure in the throat about 
 equal to 0.58 of the initial pressure provided that the back pres- 
 sure has less than ratio 3/5 to the initial pressure; this corresponds 
 with Fliegner's results and should be expected from his com- 
 parison with molecular velocity on page 430. The following 
 table gives results of tests made by Mr. W. H. Kunhardt * in 
 the laboratories of the Massachusetts Institute of Technology: 
 The excess of the throat pressure above 0.58 of the initial 
 
 * Transactions Am. Soc. Mech. Engs., vol. xi, p. 187. 
 
444 
 
 FLOW OF FLUIDS 
 
 pressure for the tests numbered i to 9 is to be attributed to the 
 excessive length of the tube. Longer tubes tested by Biichner, 
 showed the same efifect in an exaggerated degree. 
 
 FLOW OF STEAM THROUGH SHORT TUBES WITH ROUNDED 
 
 ENTRANCES. 
 Diameters 0.25 of an inch. 
 
 
 
 
 Pressure above at- 
 
 
 Ratio of 
 
 
 
 Flow in pounds 
 per hour. 
 
 
 
 
 
 mosphere, pounds 
 
 
 absolute 
 
 ^ 
 
 
 
 
 
 
 per square inch. 
 
 
 pressures. 
 
 
 
 
 
 
 i 
 
 JS 
 M 
 g 
 
 1 
 
 
 
 
 k 
 
 11 
 
 
 1 
 
 s . 
 
 II 
 
 u 
 
 c 
 .2 3 
 
 is 
 S1^ 
 
 
 k 
 
 
 1 
 1 
 
 > 
 
 u 
 
 JQ 
 
 9 
 
 V 
 
 
 II 
 
 ill 
 
 J 
 
 '2 V: . 
 
 m 
 
 
 
 If 
 
 <u u 
 
 It 
 
 fn 
 
 1.5 
 
 3 
 
 8" 
 1 
 
 If 
 
 1- 
 
 
 hJ 
 
 Q 
 
 < 
 
 M 
 
 <"" 
 
 cq 
 
 (^ 
 
 ci; 
 
 H 
 
 PM 
 
 n 
 
 
 
 u 
 
 tj 
 
 I 
 
 1.5 
 
 30 
 
 74.1 
 
 14.8 
 
 41.2 
 
 14.7 
 
 0.332 
 
 0.630 
 
 126.2 
 
 1.2 
 
 221.0 
 
 217.0 
 
 224 
 
 1.018 
 
 2 
 
 
 30 
 
 71.0 
 
 13.2 
 
 39.6 
 
 14.8 
 
 0.326 
 
 0.634 
 
 138.7 
 
 1.5 
 
 213.0 
 
 207.8 
 
 215 
 
 1.025 
 
 3 
 
 " 
 
 20 
 
 72.6 
 
 19.7 
 
 40.6 
 
 14.7 
 
 0.394 
 
 0.634 
 
 141.4 
 
 0.5 
 
 216.0 
 
 211. 4 
 
 220 
 
 1.022 
 
 4 
 
 " 
 
 20 
 
 75.9 
 
 20.4 
 
 42.6 
 
 14.7 
 
 0.387 
 
 0.632 
 
 139.8 
 
 0.7 
 
 228.0 
 
 219.3 
 
 227 
 
 1.040 
 1. 016 
 
 5 
 
 " 
 
 20 
 
 71.9 
 
 24-5 
 
 40.6 
 
 14.7 
 
 0.454 
 
 0.638 
 
 140.6 
 
 0.7 
 
 2I3-0 
 
 209.7 
 
 218 
 
 6 
 
 Oj5 
 
 30 
 
 72.8 
 
 14.8 
 
 39.0 
 
 14.8 
 
 0.338 
 
 0.614 
 
 138.7 
 
 0.3 
 
 225.0 
 
 213.6 
 
 221 
 
 1.053 
 1.056 
 1,046 
 
 7 
 
 
 20 
 
 72.1 
 
 20.4 
 
 38.8 
 
 14.8 
 
 0.405 
 
 0.617 
 
 142.2 
 
 0.5 
 
 223.5 
 
 211.7 
 
 219 
 
 8 
 
 " 
 
 30 
 
 72.6 
 
 24.7 
 
 39.0 
 
 14.8 
 
 0.452 
 
 0.616 
 
 144.0 
 
 0.5 
 
 223.0 
 
 213.1 
 
 220 
 
 C' 
 
 " 
 
 30 
 
 73-1 
 
 29.9 
 
 39-2 
 
 14.8 
 
 0.509 
 
 0.61S 
 
 145.2 
 
 0.5 
 
 225.5 
 
 213.0 
 
 222 
 
 1.054 
 1.054 
 
 10 
 
 0.2 s 
 
 30 
 
 72.6 
 
 24.8 
 
 36.1 
 
 14.9 
 
 0.454 
 
 0.583 
 
 143.8 
 
 0.4 
 
 225,0 
 
 213.5 
 
 220 
 
 II 
 
 
 30 
 
 72.6 
 
 19.9 
 
 36.1 
 
 14.9 
 
 0.398 
 
 0.583 
 
 141.6 
 
 0.4 
 
 225.0 
 
 213.5 
 
 220 
 
 1.054 
 1.066 
 1.058 
 1.060 
 
 12 
 
 <( 
 
 30 
 
 72.7 
 
 14.9 
 
 36.2 
 
 14.8 
 
 339 
 
 0.583 
 
 140. 5 
 
 0.4 
 
 227.0 
 
 213.0 
 
 220 
 
 13 
 
 " 
 
 30 
 
 126.3 
 
 27.8 
 
 69.0 
 
 14.7 
 
 0.295 
 
 0.594 
 
 155.C 
 
 0.5 
 
 358.8 
 
 338.9 
 
 355 
 
 14 
 
 
 30 
 
 125.0 
 
 40.8 
 
 67.9 
 
 14.7 
 
 0.398 
 
 0.59? 
 
 157.C 
 
 0.2 
 
 355.0 
 
 334-8 
 
 352 
 
 Design of a Nozzle. — Required the dimensions of a nozzle 
 to deliver 500 pounds of steam per hour with a steam pressure of 
 150 pounds by the gauge and a vacuum of 26 inches of mercury. 
 The vacuum of 26 inches can be taken as substantially equiva- 
 lent to 2 pounds absolute and the steam pressure may be taken 
 as 165 pounds absolute. The throat pressure is then nearly 
 96 pounds absolute. Assuming the steam to be initially dry, 
 the calculation can be arranged as follov^^s: 
 
 x,r,= T, (^+ 0^-e\ =784.1 (1.0367 +0.5235 -0.4704) =855.1 
 
 'V3 = ^3(j-+^i -^3) =585.8(i.o367+o.5235-o.i756)=8io.8 
 
 1', + q, - x,v^ - ^2 = 855.9 + 337-7 - 855-1 - 295-1 = 43-4 
 ^1 + 9i - ^3*^3 - ?3 = 855-9 + 337-7 - 810.8 - 94.3 = 288.5. 
 
DESIGN OF A NOZZLE 445 
 
 The quantities just obtained are the amounts of heat that 
 would be available for producing velocity if the action were 
 adiabatic. In order to find the probable velocity allowing for 
 friction, they should be multiplied by 1 — y, where y the coeffi- 
 cient for friction may be taken as 0.15 for the determination of 
 the exit velocity F3. As for the throat velocity, there are two 
 considerations, the frictional effect is small because the throat is 
 near the entrance, and all experiments indicate that orifices and 
 nozzles which are not ' unduly long deliver the full amount of 
 steam that the adiabatic theory indicates; therefore we may 
 make the calculation for that part of the nozzle by the adiabatic 
 method. The available heats for producing velocity may there- 
 fore be taken as 
 
 43.4 and (i - 0.15) 288.5 = 245, 
 and the velocities are therefore (see page 436) 
 
 v^ = V64.4 X 778 X 43.4 = 1480. 
 
 F3 = V64.4 X 778 X 245 = 3500. 
 
 The quahty of steam in the throat is 
 
 ^2 = ^■^2 ^ ^2 = 855-1 - 885.9 = 0-967- 
 
 To find the quality of steam at the exit we may consider that 
 if x^' is the actual quality allowing for the effect of friction we 
 have 
 
 ^ + ?i - ^>3 - ?3 = 245 
 
 ^z = (855-9 + 337-7 - 245 - 94.3) ^ 1026 = 0.833. 
 
 Though not necessary for the solution of the problem it is 
 interesting to notice that adiabatic expansion to the exit pressure 
 would give for 
 
 ^3 "" ^3^3 "^ ^3 == 810.8 ^ 1026 = 0.790. 
 
 Now 500 pounds of steam an hour gives 
 
 — 2 
 500 -^ 60 = 0.139 
 
446 FLOW OF FLUIDS 
 
 of a pound per second; consequently the areas at the throat and 
 the exit will be by equation (268), page 431, in square inches 
 
 x,u^ +0- 
 144^2 = 144 X 0.139 
 
 2""2 
 
 = 144 X 0.139 (0'9^7 ^ 4-55^ + 0.016) -T-1480 = 0.0597; 
 14403 = 144 X 0.139 i'^'^33 X 173-6 + 0.016) ^ 3500 = 0.827. 
 The diameters are, therefore, 
 
 ^2 = 0.280 ^^3 = 1.026. 
 
 If the taper is taken to be one in ten, the conical part will have 
 a length of 
 
 10 (1.026 — 0.280) = 7.46 inches; 
 
 and allowing for the rounding at the entrance and for a fair curve 
 joining the throat to the cone, the total length may be eight 
 inches. 
 
 A nozzle to expand steam to the pressure of the atmosphere 
 only, would have the computation for the exit made as follows : 
 
 •^3^3= T^\f + ^i -6'3J = 67i.5(i.o37o+o.5235-o.3i25)=838.o; 
 
 ^ + ?i - ^3^3 - ?3 = 855-9 + 337-7 - 838.0 - 180.3 = 175.3. 
 Taking the coefficient for friction as o.io the available heat 
 appears to be 158.0 and the velocity at exit will be 
 
 F3 = \/64.4 X 778 X 158 = 2810. 
 The quality of the steam comes from the equation 
 ^1 + ?i - <^3 - ?3 = 158.0. 
 •'. < = (855-9 + 337-7 - 158 - 180.3) -^ 965.8 = 0.885. 
 The area at the exit will now become 
 144^3 = 144 X .139 (0.885 X 26.64 + 0.016) -H 2810 = 0.168, 
 
 and the corresponding diameter is 0.462 of an inch. Taking 
 
 the taper as one in ten, the length of the conical part of the nozzle 
 
 becomes 
 
 10 (0.462 — 0.283) = 1.79 inches, 
 
 and its total length including throat and inlet may be 2.3 inches. 
 
CHAPTER XVIII. 
 
 INJECTORS. 
 
 An injector is an instrument by means of which a jet of steam 
 acting on a stream of water with which it mingles, and by which 
 it is condensed, can impart to the resultant jet of water a sufficient 
 velocity to overcome a pressure that may be equal to or greater 
 than the initial pressure of the steam. Thus, stearrf from a 
 boiler may force feed-water into the same boiler, or into a boiler 
 having a higher pressure. The mechanical energy of the jet of 
 water is derived from the heat energy yielded by the condensation 
 of the steam-jet. There is no reason why an injector cannot be 
 made to work with any volatile liquid and its vapor, if occasion 
 may arise for doing so; but in practice it is used only for forcing 
 water. An essential feature in the action of an injector is the 
 condensation of the steam by the water forced; other instruments 
 using jets without condensation, like the water-ejector in which 
 a small stream at high velocity forces a large stream with a low 
 velocity, differ essentially from the steam-injector. 
 
 Method of Working. — A very simple form of injector is shown 
 by Fig. 91, consisting of three essential parts; a, the steam-nozzle^ 
 bf the combining-tube, and c, the delivery -tube. Steam is supplied 
 to the injector through a pipe connected at d\ water is supplied 
 through a pipe at/, and the injector forces water out through the 
 pipe at e. The steam-pipe must have on it a valve for startjng 
 and regulating the injector, and the delivery-pipe leading to the 
 boiler must have on it a check-valve to prevent water from the 
 boiler from flowing back through the injector when it is not 
 working. The water-supply pipe commonly has a valve for 
 regulating the flow of water into the injector. 
 
 This injector, known as a non-lifting injector, has the water- 
 reservoir set high enough so that water will flow into the injector 
 
 447 
 
448 
 
 INJECTORS 
 
 through the influence of gravity. A lifting injector has a special 
 device for making a vacuum to draw water from a reservoir 
 below the injector, which will be described later. 
 
 To start the injector shown by Fig. 91, the steam- valve is first 
 opened slightly to blow out any water that may have gathered 
 above the valve, through the overflow, since it is essential to have 
 dry steam for starting. The steam-valve is then closed, and 
 the water- valve is opened wide. As soon as water appears at the 
 overflow between the combining-tube and the delivery-tube the 
 
 w<.sssss\w 
 
 Fig. 91. 
 
 Steam- valve is opened wide, and the jet of steam from the steam- 
 nozzle mingles with and is condensed by the water and imparts 
 to it a high velocity, so that it passes across the overflow space 
 between the combining-tube and the delivery-tube and passes 
 into the boiler. When the injector is working a vacuum is liable 
 to be formed at the space between the combining and delivery- 
 tubes, and the valve at the overflow closes and excludes air 
 which would mingle with the water and might interfere with 
 the action of the injector. 
 
 Theory of the Injector. — The two fundamental equations of 
 the theory of the injector are deduced from the principles of the 
 conservation of energy and the conservation of momenta. 
 
THEORY OF THE INJECTOR 449 
 
 The heat energy in one pound of steam at the absolute pressure 
 p^ in the steam-pipe is 
 
 where r^ and q^ are the heat of vaporization and heat of the liquid 
 
 corresponding to the pressure p-^\- is the mechanical equivalent 
 
 /\. 
 
 of heat (778 foot-pounds), and x^ is the quality of the steam; if 
 there is two per cent of moisture in the steam, then x^ is 0.98. 
 
 Suppose that the water entering the injector has the tempera- 
 ture /g, and that its velocity where it mingles with the steam is F/ ; 
 then its heat energy per pound is 
 
 and its kinetic energy is 
 
 2^ 
 where q^ is the heat of the liquid at t^, and g is the acceleration 
 due to gravity (32.2 feet). 
 
 If the water forced by the injector has the temperature ^4, and 
 if the velocity of the water in the smallest section of the delivery- 
 tube is Vy„ then the heat energy per pound is 
 
 j?« 
 
 and the kinetic energy is 
 
 V 2 
 
 Let each pound of steam draw into the injector y pounds of 
 water; then, since the steam is condensed and forced through 
 the delivery-tube with the water, there will be i + >' pounds 
 delivered for each pound of steam. Equating the sum of the 
 heat and kinetic energies of the entering steam and water to the 
 sum of the energies in the water forced from the injector, we 
 have 
 
 ^ (V. + ?.) + Ki ?3 + ^)Mi + ,) (^ ,. + ^) (.69) 
 
450 INJECTORS 
 
 The terms depending on the velocities VJ and F„ are never 
 large and can commonly be neglected. 
 
 To get an idea of the influence of the former, v^e may consider 
 that the pressure forcing water into a non-lifting injector is sel- 
 dom, if ever, greater than the pressure of the atmosphere, and 
 the corresponding pressure for a lifting injector is always less. 
 Now, the pressure of the atmosphere is equivalent to a head of 
 
 /?/ = 144 X 14.7 -r- 62.4 = 34 feet. 
 
 A liberal estimate of y (the pounds of water per pound of 
 steam) is fifteen. Therefore, 
 
 y '2 
 
 y _^^ = yl^f _ j^ X 34 = 510. 
 
 In order that an injector shall deliver water against the steam- 
 pressure in a boiler its velocity must be greater than would be 
 impressed on cold water by a head equivalent to the boiler- 
 pressure. Taking the boiler- pressure at 250 pounds by the 
 gauge, or 265 pounds absolute, the equivalent head will be 
 
 h = 144 X 265 -^ 62.4 = 610 feet. 
 
 Again taking fifteen for y^ the value of the term depending on Vy, 
 will be 
 
 V ^ 
 (i + y) — ^ = (i + 15) 610 = 9150. 
 2^ 
 
 But the steam supplied to an injector is nearly dry and at 
 265 pounds absolute 
 
 ^ + 9i = 826.2 + 379.6 = 1205.8, 
 so that the term depending on that quantity will have the value 
 778 X 1206 = 939000. 
 
 It is, therefore, evident that the term depending on F^, has 
 an influence of less than one per cent and that the term depending 
 on VJ can be entirely neglected. 
 
THEORY OF THE INJECTOR 451 
 
 For practical purposes we may calculate the weight of water 
 delivered per pound of steam by the equation 
 
 A 
 
 y = _j_i u ^ (270) 
 
 ?4 - ?3 
 
 This equation may be applied to any injector including double 
 injectors with two steam-nozzles. 
 
 The discussion just given shows that of the heat suppHed to 
 an injector only a very small part, usually less than one per cent, 
 is changed into work. When used for feeding a boiler, or for 
 similar purposes, this is of no consequence, because the heat 
 not changed into work is returned to the boiler and there is no 
 loss. 
 
 For example^ if dry steam is supplied to the injector at 120 
 pounds by the gauge or 134.7 pounds absolute, if the supply- 
 temperature of the water is 65° F., and if the dehvery-temperature 
 is 165° F., then the water pumped per pound of steam is 
 
 r, + J, — ^4 867. s + S2I.I — \\x.\ , 
 
 y = -^ ^ ^' = — '-^ ^ 7^^^^— = 10.5 pounds. 
 
 ^4 - ?3 I33-I - 33-i6 
 
 From the conservation of energy we have been able to devise 
 an equation for the weight of water delivered per pound of 
 steam; from the conservation of momenta we can find the relation 
 of the velocities. 
 
 The momentum of one pound of steam issuing from the steam- 
 nozzle with the velocity F, is F, -^ g\ the momentum of y 
 pounds of water entering the combining-tube with the velocity 
 VJ is >'F„' ^ ^; and the momentum of i -f >' pounds of water 
 at the smallest section of the delivery-tube is (i -^ y) Vu> -^ g- 
 Equating the sum of the momenta of water and steam before 
 mingling to the momentum of the combined water and steam 
 in the delivery-tube, 
 
 ■Vs + yVJ = (I +y) F,, (270) 
 
 This equation can be used to calculate any one of the velocities 
 provided the other two can be determined independently. Unfor- 
 
452 INJECTORS 
 
 tunately there is some uncertainty about all of the velocities so 
 that the proper sizes of the orifices and of the forms and propor- 
 tions of the several members of an injector have been determined 
 mainly by experiment. The best exposition of this matter is 
 given by Mr. Strickland Kneass,* who has made many experi- 
 ments for William Sellers & Co. The practical part of what 
 follows is largely drawn from his work. 
 
 Velocity of the Steam-jet. — Equation (269) gives 
 
 ^. = 1^ (^/l - -^^2 + ?l - ^2) I ) • • (272) 
 
 where r^ and q^ are the heat of vaporization and the heat of the 
 liquid of the supply of steam at the pressure p^, and r^ and q^ 
 are corresponding quantities at the pressure p^ for that section 
 of the tube for which the velocity is calculated; x^ is the quality 
 of the steam at the pressure p^ (usually 0.98 to unity) and x^ is 
 the quality at the pressure p^ to be calculated by aid of the 
 equation 
 
 ^^ 4- (9 = ^^^ + d . 
 
 rp ' \ rp ^ 2' 
 
 Here T^ and T^ are the absolute temperatures corresponding to 
 the pressures p^ and p^, and 0^ and 0^ are the entropies of the 
 
 liquid at the same pressure. Also — is the mechanical equivalent 
 
 Ji. 
 
 of heat and g is the acceleration due to gravity. 
 
 Some steam-nozzles for injectors are simple converging orifices 
 and others have a throat and a diverging portion. It will be 
 found in all cases including double injectors, that the pressure 
 beyond the steam- nozzle is less than half the pressure causing 
 the flow, and consequently the pressure at the narrowest part 
 of the steam-nozzle and also the velocity at that place, depend 
 only on the initial pressure. As was developed in the preceding 
 chapter, the pressure and velocity at any part of an expanding 
 nozzle depend on the ratio of the area at that part to the throat 
 area, and are consequently under control. Also, as was empha- 
 
 * Practice and Theory of the Injector, J. Wiley & Sons. 
 
VELOCITY OF THE STEAM-JET 453 
 
 sized by Rosenhain's experiments, the steam will expand and 
 gain velocity beyond the nozzle, if it escapes at a pressure higher 
 than the back-pressure. For an injector this last action is 
 influenced by the fact that the jet from the steam-nozzle mingles 
 with water and is rapidly condensed. Some injector makers 
 use larger tapers than those recommended in the preceding 
 chapter for expanding nozzles. The throat pressure may be 
 assumed to be about 0.6 of the initial pressure; with the informa- 
 tion in hand it is probably not worth while to try to make any 
 allowance for friction. 
 
 The calculation of the area at the throat of a steam nozzle by 
 the adiabatic method will be found fairly satisfactory; the calcu- 
 lation of the final velocity of the steam will probably not be 
 satisfactory, as complete expansion in the nozzle seldom takes 
 place, but it is easy to show that the velocity is sufficient to 
 account for the action of the instrument. 
 
 For example, the velocity in the throat of a nozzle under the 
 pressure of 120 pounds by the gauge or 134.7 pounds absolute is 
 
 ^.= I ^ (^/i - ^2^ + ?i - ?2) r 
 
 = !2 X 32.2 X 778 (867.5 - 0.967X894.6 H-32I. I -282.7)1^ 
 = 1430 feet per second, 
 
 having for x^ 
 
 ^2= 7^(^ + <^i - ^2)= j-^ (1-0719 + 0-5032 - 0.4546) 
 = 0.967, 
 
 provided that p^ = o.6p^ = 80.8 pounds absolute. 
 
 If, however, the pressure at the exit of an expanded nozzle is 
 14.7 pounds absolute, then 
 
 ^3 = 7Tb-^(i-°7i9 +0.5032 -0.3125) =0.877, 
 1.4390 
 
 and 
 
 V,= I2X 32.2X778 (867.5 -0.8775 X966.3-f 321. 1 -i8o.3)(^ 
 = 2830 feet per second. 
 
454 INJECTORS 
 
 which is nearly twice that just calculated for the velocity at the 
 smallest section of the steam-nozzle. Since there is usually a 
 vacuum beyond the steam-nozzle, the final steam velocity is 
 likely to be considerably larger, but this computed velocity will 
 suffice for explaining the dynamics of the case. 
 
 Velocity of Entering Water. — The velocity of the water in 
 the combining-tube where it mingles with the steam depends on 
 (a) the lift or head from the reservoir to the injector, (b) the 
 pressure (or vacuum) in the combining-tube, and (c) on the 
 resistance which the water experiences from friction and eddies 
 in the pipe, valves, and passages of the injector. The first of 
 these can be measured directly for any given case; for example, 
 where a test is made on an injector. In determining the pro- 
 portions of an injector it is safe to assume that there is neither 
 lift nor head for a non-lifting injector, and that the lift for a 
 lifting-injector is as large as can be obtained with certainty in 
 practice. The lift for an injector is usually moderate, and 
 seldom if ever exceeds 20 feet. 
 
 The vacuum in the combining-tube may amount to 22 or 24 
 inches of mercury, corresponding to 25 or 27 feet of water; that 
 is, the absolute pressure may be 3 or 4 pounds per square inch. 
 The vacuum after the steam and water are combined appears 
 to be limited by the temperature of the water; thus, if the tem- 
 perature is 165° F., the absolute pressure cannot be less than 
 5.3 pounds. But the final temperature is taken in the delivery- 
 pipe after the water and condensed steam are well mixed and are 
 moving with a moderate velocity. 
 
 The resistance of friction in the pipes, valves, and passages 
 of injectors has never been determined ; since the velocity is high 
 the resistance must be considerable. 
 
 If we assume the greatest vacuum to correspond to 27 feet of 
 water, the maximum velocity of the water entering the combining- 
 tube will not exceed 
 
 \^2gh = V2 X 32.2 X 27 = 42 feet. 
 
 If, on the contrary, the effective head producing velocity is as 
 small as 5 feet, the corresponding velocity will be 
 
SIZES OF THE ORIFICES 455 
 
 V2 X 32.2 X 5 = 18 feet. 
 
 It cannot be far from the truth to assume that the velocity of 
 the water entering the combining-tube is between 20 and 40 
 feet per second. 
 
 Velocity in the Delivery-tube. — The velocity of the water in 
 the smallest section of the delivery-tube may be estimated in two 
 ways; in the first place it must be greater than the velocity of 
 cold water flowing out under the pressure in the boiler, and in the 
 second place it may be calculated by aid of equation (271), 
 provided that the velocities of the entering steam and water are 
 determined or assumed. 
 
 For example, let it be assumed that the pressure of the steam 
 in the boiler is 120 pounds by the gauge, and that, as calculated 
 on page 451, each pound of steam delivers 10.5 pounds of water 
 from the reserv^oir to the boiler. As there is a good vacuum in 
 the injector we may assume that the pressure to be overcome is 
 132 pounds per square inch, corresponding to a head of 
 
 132 X 144 -, ^ 
 
 .^ , = 305 feet. 
 02.4 
 
 Now the velocity of water flowing under the head of 305 feet is 
 'V2gh = V2 X 32.2 X 305 = 140 feet per second. 
 
 The velocity of steam flowing from a pressure of 120 pounds 
 by the gauge through a diverging-tube with the pressure equal 
 to that of the atmosphere at the exit has been calculated to be 
 2830 feet per second. Assuming the velocity of the water enter- 
 ing the combining-tube to be 20 feet, then by equation (271) 
 we have in this case 
 
 I + y I 4- 10.5 
 
 this velocity is sufficient to overcome a pressure of about 470 
 pounds per square inch if no allowance is made for friction or 
 losses. 
 
 Sizes of the Orifices. — From direct experiments on injectors as 
 well as from the discussion in the previous chapter, it appears 
 
456 INJECTORS 
 
 that the quantity of steam delivered by the steam-nozzle can be 
 calculated in all cases by the method for the flow of steam, 
 through an orifice, assuming the pressure in the orifice to be -^^ 
 of the absolute pressure above the orifice. 
 
 Now each pound of steam forces y pounds of water from the 
 reservoir to the boiler; consequently if w pounds are drawn from 
 the reservoir per second the injector will use w ^ y pounds of 
 steam per second. 
 
 The specific volume of the mixture of water and steam in the 
 smallest section of the steam-nozzle is 
 
 where x^ is the quality, u^ is the increase of volume due to vapor- 
 ization, and o" is the specific volume of the water. The volume 
 of steam discharged per second is 
 
 — ^> 
 
 y 
 
 and the area of the orifice is 
 
 where F^ is the velocity at the smallest section. 
 
 For example, for a flow from 134.7 pounds absolute to 80.8 
 pounds absolute x^ is 0.9670 and Vg is 1430 feet, as found on 
 page 453. Again, for an increase of temperature from 65° F. 
 to 165° F., the water per pound of steam is 10.5. Calculating 
 the specific volume at 80.8 pounds, we have 
 v., = x^u^ -f- cr = 0.967 (5.38 — 0.016) -}- 0.016 = 5.20 cubic feet. 
 
 If the injector is required to deliver 1200 gallons an hour, or 
 
 1200 X 2^1 X 62.4 „ 
 ^ ^± == 2.78 
 
 1728 X 60 X 60 ' 
 
 pounds per second, the area of the steam-nozzle must be 
 
 WV„ 2.78 X 5.20 . r ^ 
 
 a, = -—-/- = — = 0.000062 square feet. 
 
 yV, 10.5 X 1430 
 
 The corresponding diameter is 0.420 of an inch, or 10.6 milli- 
 metres. 
 
SIZES OF THE ORIFICES 
 
 457 
 
 In trying to determine the size of the orifice in the delivery- 
 tube we meet with two serious difficulties: we do not know the 
 velocity of the stream in the smallest section of the delivery- 
 tube, and we do not know the condition of the fluid at that place. 
 It has been assumed that the steam is entirely condensed by 
 the water in the combining-tube before reaching the delivery- 
 tube, but there may be small bubbles of uncondensed steam still 
 mingled with the water, so that the probable density of the 
 heterogeneous mixture may be less than that of water. Since 
 the pressure at the entrance to the delivery-tube is small, the 
 specific volume of the steam is very large, and a fraction of a 
 per cent of steam is enough to reduce the density of the steam 
 to one-half. Even if the steam is entirely condensed, the air 
 carried by the water from the reservoir is enough to sensibly 
 reduce the density at the low pressure (or vacuum) found at the 
 entrance to the delivery-tube. 
 
 If V^ is the probable velocity of the jet at the smallest section 
 of the delivery-tube, and if d is the density of the fluid, then the 
 area of the orifice in square feet is 
 
 for each pound of steam mingles with and is condensed by y 
 pounds of water and passes with that water through the delivery- 
 tube; w, as before, is the number of pounds of water drawn from 
 the reservoir per second. 
 
 For example, let it be assumed that the actual velocity in the 
 delivery-tube to ov^ercome a boiler-pressure of 120 pounds by the 
 gauge is 150 feet per second, and that the density of the jet is 
 about 0.9 that of water; then with the value oi w = 2.78 and y = 
 10.5, we have 
 
 Wi+y) 2.78 X II. 5 . . 
 
 a,r = — „ , = — = 0.000361 sq. ft. 
 
 V,,dy 150 X 0.9 X 62.4 X 10.5 ^ ^ 
 
 The corresponding diameter is 0.257 of an inch, or 6.5 milli- 
 metres. If this calculation were made with the velocity 266 
 (computed for expansion to atmospheric pressure) and with 
 
458 INJECTORS 
 
 clear water the diameter would be only 0.183 of 2,n inch; this is 
 to be considered rather as' a theoretic minimum than as a prac- 
 tical dimension. 
 
 Steam-nozzle. — The entrance to the steam-nozzle should be 
 well rounded to avoid eddies or reduction of pressure as the 
 steam approaches; in some injectors, as the Sellers' injector, 
 Fig. 92, the valve controlling the steam supply is placed near 
 the entrance to the nozzle, but the bevelled valve-seat will not 
 interfere with the flow when the valve is open. 
 
 It has already been pointed out that the steam-nozzle may 
 advantageously be made to expand or flare from the smallest 
 section to the exit. The length from that section to the end may 
 be between two and three times the diameter at that section. 
 
 Consider the case of a steam-nozzle supplied with steam at 
 120 pounds boiler-pressure: it has been found that the velocity 
 at the smallest section, on the assumption that the pressure is 
 then 80.8 pounds, is 1430 feet per second, and that the specific 
 volume is 5.20 cubic feet. If the pressure in the nozzle is 
 reduced to 14.7 pounds, at the exit, the velocity becomes 2830 
 feet per second, the quality being x^ = 0.8775. The specific 
 volume is consequently 
 
 V^ = ^2^2 + O- = 0.877 (26.66 — 0.016) + 0.016 = 23.4 CU. ft. 
 
 The areas will be directly as the specific volumes and inversely 
 as the velocities, so that for this case we shall have the ratio of 
 the areas 
 
 5.20: 23.4 
 
 Q i = I- 2.27; 
 
 2830: 1430 
 
 and the ratio of the diameters will be 
 
 Vi • V2.27 = i: 1.5. 
 
 Combining-tube. — There is great diversity with different 
 injectors in the form and proportions of the combining-tube. 
 It is always made in the form of a hollow converging cone, 
 straight or curved. The overflow is commonly connected to a 
 space between the combining-tube and the delivery-tube; it is. 
 
EFFICIENCY OF THE INJECTOR 459 
 
 however, sometimes placed beyond the delivery-tube, as in the 
 Sellers' injector, Fig. 92. In the latter case the combining- and 
 delivery- tuhes may form one continuous piece, as is seen in the 
 double injector shown by Fig. 93. 
 
 The Delivery-tube. — This tube should be gradually enlarged 
 from its smallest diameter to the exit in order that the water in it 
 may gradually lose velocity and be less affected by the sudden 
 change of velocity where this tube connects to the pipe leading 
 to the boiler. 
 
 It is the custom to rate injectors by the size of the delivery- 
 tube; thus a No. 6 injector may have a diameter of 6 mm. at 
 the smallest section of the delivery-tube. 
 
 Mr. Kneass found that a delivery-tube cut off short at the 
 smallest section would deliver water against 35 pounds pressure 
 only, without overflowing; the steam-pressure being 65 pounds. 
 A cylindrical tube four times as long as the internal diameter, 
 under the same conditions would deliver only against 24 pounds. 
 A tube with a rapid flare delivered against 62 pounds, and a 
 gradually enlarged tube delivered against 93 pounds. 
 
 If the delivery-tube is assumed to be filled with water without 
 any admixture of steam or air, then the relative velocities at 
 different sections may be assumed to be inversely proportional 
 to the corresponding areas. This gives a method of tracing the 
 change of velocity of the water in the tube from its smallest 
 diameter to the exit. 
 
 A sudden change in the velocity is very undesirable, as at the 
 point where the change occurs the tube is worn and roughened, 
 especially if there are solid impurities in the water. It has been 
 proposed to make the form of the tube such that the change of 
 velocity shall be uniform until the pressure has fallen to that in 
 the delivery-pipe; but this idea is found to be impracticable, as 
 it leads to very long tubes with a very wide flare at the end. 
 
 Efficiency of the Injector. — The injector is used for feeding 
 boilers, and for little else. Since the heat drawn from the boiler 
 is returned to the boiler again, save the very small part which 
 is changed into mechanical energy, it appears as though the 
 
460 
 
 INJECTORS 
 
 efficiency was perfect, and that one injector is as good as another 
 provided that it works with certainty. We may almost consider 
 the injector to act as a feed-water heater, treating the pumping 
 in of feed-water as incidental. It has already been pointed out 
 
 Fig. 92- 
 
 on page 450 that the kinetic energy of the jet in the delivery- 
 tube is less than one per cent of the energy due to the condensa- 
 tion of the steam. On this account the injector is used wherever 
 cold water must be forced into a boiler, as on a locomotive, or 
 when sea-water is supplied to a marine boiler. Considering 
 only the advantage of supplying hot water to the boiler, it 
 almost seems as though the more steam an injector uses the 
 better it is. Such a view is erroneous, as it is often desirable 
 to supply water without immediately reducing the steam- 
 pressure and then it is necessary to use as little steam as may be. 
 It is, however, true that simplicity of construction and certainty 
 of action are of the first importance in injectors. 
 
 Lifting Injector. — The injector described at the beginning of 
 
DOUBLE INJECTORS 461 
 
 this chapter was placed so that water from the reservoir would 
 run in under the influence of gravity. When the injector is 
 placed higher than the reservoir a special device is provided for 
 lifting the water to start the injector. Thus in the Sellers' 
 injector, Fig. 92, there is a long tube which protrudes well into 
 the combining-tube when the valves w and x are both closed. 
 When the rod B is drawn back a little by aid of the lever H the 
 valve w is opened, admitting steam through a side orifice to the 
 tube mentioned. Steam from this tube drives out the air in 
 the injector through the overflow, and water flows up into the 
 vacuum thus formed, and is itself forced out at the overflow. 
 The starting-lever H is then drawn as far back as it will go, 
 opening the valve x and supplying steam to the steam-nozzle. 
 This steam mingles with and is condensed by the water and 
 imparts to the water sufficient velocity to overcome the boiler- 
 pressure. Just as the lever H reaches its extreme position it 
 closes the overflow valve K through the rod L and the crank at R. 
 
 Since lifting-injectors may be supplied with water under a 
 head, and since a non-lifting injector when started will lift 
 water from a reservoir below it, or may even start with a small 
 lift, the distinction between them is not fundamental. 
 
 Double Injectors. — The double injector illustrated by Fig. 93, 
 which represents the Korting injector, consists of two complete 
 injectors, one of which draws water from the reservoir and 
 delivers it to the second, which in turn delivers the water to the 
 boiler. To start this injector the handle A is drawn back to 
 the position B and opens the valve supplying steam to the 
 lifting- injector. The proper sequence in opening the valves 
 is secured by the simple device of using a loose lever for joining 
 both to the valve-spindle; for under steam-pressure the smaller 
 will open first, and when it is open the larger wfll move. The 
 steam-nozzle of the lifter has a good deal of flare, which tends 
 to form a good vacuum. The lifter first delivers water out at 
 the overflow with the starting lever at B\ then that lever is pulled 
 as far as it will go, opening the valve for the second injector or 
 forcer, and closing both overflow valves.. 
 
462 
 
 INJECTORS 
 
 Self-adjusting Injectors. — In the discussions of injectors 
 thus far given it has been assumed that they work at full capac- 
 ity, but as an injector must be able to bring the water-level 
 in a boiler up promptly to the proper height, it will have much 
 more than the capacity needed for feeding the boiler steadily. 
 Any injector may be made to work at a reduced capacity by 
 simply reducing the opening of the steam-valve, but the limit 
 
 Fig. 93. 
 
 of its action is soon reached. The limit may be extended some- 
 what by partially closing the water-supply valve and so limiting 
 the water-supply. 
 
 The original Giffard injector had a movable steam-nozzle to 
 control the thickness of the sheet of water mingling with the 
 steam, and also had a long conical valve thrust into the steam- 
 nozzle by which the effective area of the steam- jet could be regu- 
 lated. Thus both water and steam passages could be controlled 
 without changing the pressures under which they were supplied, 
 and the injector could be regulated to work through a wide 
 range of pressures and capacities. The main objection was 
 that the injector was regulated by hand and required much 
 attention. 
 
SELF-ADJUSTING INJECTORS 463 
 
 In the Sellers' injector, Fig. 92, the regulation of the steam- 
 supply by a long cone thrust through the steam-nozzle is 
 retained, but the supply of water is regulated by a movable 
 combining-tube, which is guided at each end and is free to move 
 forwards and backwards. At the rear the combining-tube is 
 affected by the pressure of the entering water, and in front it is 
 subjected to the pressure in the closed space O, which is in 
 communication with the overflow space between the combining- 
 tube and the delivery-tube, in this injector the space is only for 
 producing the regulation of the water-supply by the motion of 
 the combining-tube, as the actual overflow is beyond the 
 delivery-tube at K. When the injector is running at any regular 
 rate the pressures on the front and the rear of the combining-tube 
 are nearly equal, and it remains at rest. When the starting- 
 lever is drawn out or the steam-pressure increases, the inflowing 
 steam is not entirely condensed in the combining-tube as it is 
 during efficient action; lateral contraction of the jet therefore 
 occurs when crossing the overflow chamber, causing a reduction 
 of pressure in O, which causes the tube to move toward D and 
 increase the supply of water. When the starting-lever is pushed 
 inward, reducing the flow of steam, the impulsive effort is 
 insufficient to force a full supply of water through the delivery- 
 tube, and there is an overflow into the chamber O which pushes 
 the combining-tube backwards and reduces the inflow of water. 
 The injector is always started at full capacity by pulling the 
 steam-valve wide open, as already described; after it is started 
 the steam-supply is regulated at will by the engineer or boiler 
 attendant, and the water is automatically adjusted by the movable 
 combining-tube, and the injector will require attention only 
 when a change of the rate of feeding the boiler is required on 
 account of either a change in the draught of steam from the 
 boiler, or a change of steam-pressure, for the capacity of the 
 injector increases with a rise of pressure. 
 
 A double injector, such as that represented by Fig. 93, is to a 
 certain extent self-adjusting, since an increase of steam- pressure 
 causes at once an increase in the amount of water drawn in by 
 
464 
 
 INJECTORS 
 
 the lifter and an increase in the flow of steam through the steam- 
 nozzle of the forcer. Such injectors have a wide range of action 
 and can be controlled by regulating the valve on the steam- 
 pipe. 
 
 Restarting Injectors. — If the action of any of the injector 
 thus far described is interrupted for any reason, it is necessary to 
 
 shut off steam and start the 
 injector anew; sometimes the 
 injector has become heated 
 while its action is interrupted, 
 and there may be difficulty in 
 starting. To overcome this 
 difficulty various forms of 
 restarting injectors have been 
 devised, such as the Sellers, 
 Fig. 94. This injector has 
 four fixed nozzles in line, the 
 steam-nozzle 3, the draft-tube 
 II, the combining-tube 2, 
 and the delivery-tube at the 
 bottom. There is also a slid- 
 ing bushing 5 and an overflow 
 valve 15. The steam-nozzle has a wide flare and makes a vacuum 
 which draws water from the supply- tank under all conditions; the 
 water passes through the draught-tube and out at the overflow 
 until the condensation of steam in the combining-tube makes a 
 partial vacuum that draws up the bushing 5 against the draught- 
 tube and shuts off the passage to the overflow; the injector then 
 forces water to the boiler. If the injector stops for any cause 
 the bushing falls and the injector takes the starting position and 
 will start as soon as supplied with water and steam. 
 
 Self-acting Injector. — The most recent type of Sellers' injector 
 invented by Mr. Kneass and represented by Fig. 95 is both self- 
 starting and self-adjusting. It is a double injector with all the jets 
 in one line; a, b, and c are the steam-nozzle, the combining-tube, 
 and the delivery-tube of the forcer; the lifter is composed of the 
 
 Fig. 
 
INJECTORS 
 
 465 
 
466 INJECTORS 
 
 annular steam-nozzle d, and the annular delivery- tube e, sur- 
 rounding the nozzle a. The proportions are such that the lifter 
 can always produce a suction in the feed-pipe even when there 
 is a discharge from the main steam-nozzle, and it is this fact 
 that establishes the restarting feature. When the feed-water 
 rises to the tubes it meets the steam from the lifter-nozzle and 
 is forced in a thin sheet and with high velocity into the combining- 
 tube of the forcer, where it comes in contact with the main 
 steam-jet, and mingling with and condensing it, receives a 
 high velocity which enables it to pass the overflow orifices and 
 proceed through the delivery-tube to the boiler. 
 
 Like any double injector, the lifter and forcer have a con- 
 siderable range of action through which the water is adjusted 
 to the steam-supply; but there is a further adjustment in this 
 injector, for when a good vacuum is established in the space 
 surrounding the combining-tube, water can enter through the 
 check- valve /, and flowing through the orifices in the combin- 
 ing-tube mingles with the jet in it, and is forced with that jet 
 into the boiler. 
 
 The steam- valve is seated on the end of the lifter-nozzle, 
 and it has a protruding plug which enters the forcer-nozzle. 
 When the valve is opened to start the injector, steam is sup- 
 plied first to the starter, and soon after, by withdrawing the 
 plug, to the forcer: If the steam is dry the starting-lever 
 may be moved back promptly; if tHere is condensed water in 
 the steam-pipe, the starting-handle should be moved a little 
 way to first open the valve of the lifter, and then it is drawn 
 as far back as it will go, as soon as water appears at the over- 
 flow. The water-supply may be regulated by the valve g, 
 which can be rotated a part of a turn. The minimum delivery 
 of the injector is obtained by closing this valve till puffs of 
 steam appear at the overflow, and then opening it enough 
 to stop the escape of steam. 
 
 When supplied with cold water this injector wastes very 
 little in starting. If the injector is hot or is filled with hot 
 water when started, it will waste hot water till the injector is 
 
EXHAUST STEAM INJECTORS 
 
 467 
 
 cooled by the water from the feed-supply, and will then work 
 as usual. If air leaks into the suction-pipe or if there is any 
 other interference with the normal action, the injector wastes 
 water or steam till normal conditions are restored, when it 
 starts automatically. 
 
 Exhaust Steam Injectors. — Injectors supplied with ex- 
 haust-steam from a non-condensing engine can be used to 
 feed boilers up to a pressure of about 80 pounds. Above 
 this pressure a supplemental jet of steam from the boiler must 
 be used. Such an injector, as made by Schaffer and Buden- 
 berg, is represented by Fig. 96; when ^xviamst s.-^'lk'^ 
 
 used with low boiler-pressure this in- 
 jector has a solid cone or spindle in- 
 stead of the live-steam nozzle. To 
 provide a very free overflow the com- 
 bining-tube is divided, and one side is 
 hung on a hinge and can open to give 
 free exit to the overflow^ when the 
 injector is started. When the injector 
 is working it closes down into place. 
 The calculation for an exhaust-steam 
 injector shows that enough velocity 
 may be imparted to the water in the 
 delivery-tube to overcome a moderate 
 boiler-pressure. 
 
 For example, an injector supplied with steam at atmospheric 
 pressure, and raising the feed-water from 65° F. to 145° F., 
 will draw from the reservoir 
 
 Fig. 96. 
 
 _ ^1 + gi - g4 _ 966.3 + 180.3 - 1 13-0 _ J 
 
 2.9 
 
 pounds of water per pound of steam. In this case as the steam- 
 nozzle is converging we will use for computing the velocity the 
 pressure 
 
 0.6 X 14.7 = 8.8 pounds. 
 
468 INJECTORS 
 
 This will give 
 
 ^2= ^2(^ + ^1- ^2)= 646.8(1.4390+0-3125- .2746) =954.6, 
 
 consequently 
 
 = V2 X 32.2 X 778 (966.3 + 180.3 - 954.6 - 155.3 = 1370. 
 
 Assuming the velocity of the water entering the combining- 
 tube will give for the velocity of the jet in the combining-tube 
 
 136 feet. 
 
 _ 1370 + 12.9 X 30 
 I + 12.9 
 
 This velocity is equivalent to that produced by a static pressure 
 
 of 
 
 136' X 62.4 
 
 -f = 124 
 
 64.4 X 144 
 
 pounds absolute, or a gauge pressure of 109 pounds. No allow- 
 ance is made for reduction of density by bubbles of steam in 
 the combining-tube or for resistance of pipes and valves. If 
 
 Fig. 97- 
 
 such an injector can take advantage of further expansion either 
 in the steam-nozzle or beyond, the velocity may be greater than 
 that computed and a better action might ensue. 
 
 Unless the exhaust-steam is free from oil its use for feeding 
 
WATER-EJECTOR 469 
 
 the boiler with an exhaust-steam injector will result in fouling 
 the boiler. 
 
 Water-ejector. — Fig. 97 represents a device called a water- 
 ejector, in which a small stream of water in the pipe M flowing 
 from the reservoir R raises water from the reservoir i?" to the 
 reservoir R'. 
 
 Let one pound of water from the reservoir R draw y pounds 
 from i?", and deliver i + ^ pounds to R'. Let the velocity of 
 the water issuing from A he v; that of the water entering from 
 R" be v^ at A^; and that of the water in the pipe O be v^. The 
 equality of momenta gives 
 
 V + yv^= {1 + y)v^ (275) 
 
 Let X be the excess of pressure at M above that at A^ expressed 
 in feet of water; then 
 
 v' = 2g(H + x); 
 
 V^ = 2g (h + x) 
 Substituting in equation (275), 
 
 \^H + X + y ^x = (i + )') V/z + X) 
 
 Vh + X - Vh + X , ^. 
 
 .-. y = -==^ -= — . . . (276) 
 
 V h + X — ^ X 
 
 It is evident from inspection of the equation (276) that y 
 may be increased by increasing x; for example, by placing the 
 injector above the level of the reservoir so that there may be a 
 vacuum in front of the orifice A. 
 
 Q 
 
 If the weight G of water is to be lifted per second, then - 
 
 y. 
 
 pounds per second must pass the orifice A, G pounds the space 
 
 at N, and (1 -f —) G pounds through the section at O; which, 
 
 with the several velocities v, v^, and v^, give the data for the 
 calculation of the required areas. 
 
 Problem. — Required the calculation for a water-ejector 
 
470 INJECTORS 
 
 to raise 1200 gallons of water an hour, H = g6 ft., h = 12 ft. 
 
 .V = 4 ft. 
 
 Vx = ^4 = 2; Vif 4- .T= Vioo = 10; \^h + x = V^i6 = 4; 
 
 10 — 4 
 
 y = 
 
 The velocities are 
 
 V =V2 X 32.2 X 100 = 80.25 feet per second; 
 v^ =\^2 X 32.2 X 16 = 32.10 feet per second; 
 v^ =\^2 X 32.2 X 4 = 16.05 f^^t per second. 
 1200 gallons an hour = 0.04452 cubic feet per second. 
 The areas are 
 
 0.04452 o ., ^ 
 
 ^ ^ :ri^ — ^ 0.000185 square teet; 
 
 3 X 80.25 ^ ^ ' 
 
 4 X 0.04452 , o - . 
 ^ ^ 2 xi^ ^ 0.06185 square feet: 
 
 ' 3 X 32.10 
 
 0.04452 . ^ 
 
 a„ = — 7^^^^^ = 0.00277 square feet. 
 
 16.05 
 
 The diameters corresponding to the velocities v and v^ are 
 d = 0.18 of an inch; 
 d^ = 0.58 of an inch. 
 The area a^ is of annular form, having the area 0.4 of a square 
 inch. 
 
 Ejector. — When the ejector is used for raising water where 
 there is no advantage in heating the water, it is a very wasteful 
 instrument. The efficiency is much improved by arranging 
 
 the instrument as in Fig. 98, so 
 
 that the steam-nozzle A shall deliver 
 
 a small stream of water at a high 
 
 velocity, which, as in the water- 
 
 ^^* ^ ■ ejector, delivers a larger stream at 
 
 a less velocity. Each additional conical nozzle increases the 
 
 quantity at the expense of the velocity, so that a large quantity 
 
 of water may be lifted a small height. 
 
EJECTOR-CONDENSERS 471 
 
 Ejectors are commonly fitted in steamships as auxiliary pumps 
 in case of leakage, a service for which they are well fitted, since 
 they are compact, cheap, and powerful, and are used only in 
 emergency, when economy is of small consequence. 
 
 Ejector-condensers. — When there is a good supply of cold 
 condensing water, an exhaust-steam ejector, using all the 
 steam from the engine, may be arranged to take the place of 
 the air-pump of a jet-condensing engine. The energy of the 
 exhaust-steam flowing from the cylinder of the engine to the 
 combining-tube, where the absolute pressure is less and where 
 the steam is condensed, is sufficient to eject the water and the air 
 mingled with it against the pressure of the atmosphere, and thus 
 to maintain the vacuum. 
 
 For example, if the absolute pressure in the exhaust-pipe is 2 
 pounds, and if the temperatures of the injection and the delivery 
 are 50° F. and 97° F., then the water supplied per pound of 
 steam will be about 20 pounds. If the pressure at the exit of 
 the steam-nozzle can be taken as one pound absolute, the velocity 
 of the steam- jet will be 1460 feet per second. If the water is 
 assumed to enter with a velocity of 20 feet, the velocity of the 
 water-jet in the combining-tube will be 88 feet, which can over- 
 come a pressure of 50 pounds per square inch. 
 
CHAPTER XIX. 
 
 STEAM-TURBINES. 
 
 The recent rapid development of steam-turbines may be 
 attributed largely to the perfecting of mechanical construction, 
 making it possible to construct large machinery with the accuracy 
 required for the high speeds and close adjustments which these 
 motors demand. 
 
 An adequate treatment of steam-turbines, including details of 
 design, construction, and management, would require a separate 
 treatise; but there is an advantage in discussing here the thermal 
 problems that arise in the transformation of heat into kinetic 
 energy, and the application of this energy to the moving parts 
 of the turbine. For this purpose it is necessary to give attention 
 to the action of jets of fluids on vanes and to the reaction of jets 
 issuing from moving orifices, subjects that otherwise would 
 appear foreign to this treatise. 
 
 The fundamental principles of the theory of turbines are the 
 same whether they are driven by water or by steam; but the use 
 of an elastic fluid like steam instead of a- fluid like water, which 
 has practically a constant density, leads to differences in the 
 application of those principles. One feature is immediately 
 evident from the discussion of the flow of fluids in Chapter XVII, 
 namely, that ej^ceedingly high velocities are liable to be devel- 
 oped. Thus, on page 444 it was found that steam flowing from 
 a gauge pressure of 150 pounds per square inch into a vacuum 
 of 26 inches of mercury (2 pounds absolute) through a proper 
 nozzle, developed a velocity of 3500 feet per second, with an 
 allowance of 0.15 for friction. This range of pressure corre- 
 sponds to a hydraulic head of 
 
 163 X 144 -^ 62.4 = 376 feet; 
 
 472 
 
IMPULSE 473 
 
 and such a head will give a velocity of 
 
 V = V2 X 32.2 X 376 = 156 feet per second. 
 
 But so great a hydraulic head or fall of water is seldom, if ever, 
 applied to a single turbine, and would be considered inconvenient. 
 One hundred feet is a large hydraulic head, yielding a velocity 
 of 80 feet per second, and twenty-five feet yielding a velocity of 
 40 feet per second is considered a very effective head. 
 
 If heads of 300 feet and upward were frequent, it is likely 
 that compound turbines would be developed to use them; except 
 for relatively small powers, steam-turbines are always compound, 
 that is, the steam flows through a succession of turbines which 
 may therefore run at more manageable speeds. 
 
 The great velocities that are developed in steam turbines, 
 even when compounded, require careful reduction of clearances, 
 and although they are restricted to small fractions of an inch 
 the question of leakage is very important. Another feature in 
 which steam turbines differ from hydraulic turbines is that 
 steam is an elastic fluid which tends to fill any space to which it 
 is admitted. The influence of this feature will appear in the 
 distinction between impulse and reaction turbines. 
 
 Impulse. — If a well formed stream of water at moderate 
 velocity flows from a conical nozzle, on a flat plate it spreads 
 over it smoothly in all directions and exerts a 
 steady force on it. If the velocity of the stream ^^^ J 
 
 is Fj feet per second, and if w pounds of water are ^^ 
 
 discharged per second, the force will be very 
 nearly equal to 
 
 g 
 
 Here we have the velocity in the direction of the jet changed 
 from Fj feet per second to zero; that is, there is a retardation, or 
 negative acceleration, of V^ feet per second; consequently the 
 force is measured by the product of mass and the acceleration, 
 g being the acceleration due to gravity. A force exerted by a 
 jet or stream of fluid on a plate or vane is called an impulse. It 
 
474 STEAM-TURBINES 
 
 is important to keep clearly in mind that we are dealing with 
 velocity, change of velocity or acceleration, and force, and that 
 the force is measured in the usual way. The use of a special 
 name for the force which is developed in this way is unfortunate 
 but it is too well established to be neglected. 
 
 If the plate or vane, instead of remaining at rest, moves with 
 the velocity of V feet per second, the change in velocity or negative 
 acceleration will be V^ ~ V feet per second, and the force or 
 impulse will be 
 
 P =-{V,- V). 
 
 o 
 
 This force in one second will move the distance V feet and will 
 do the work 
 
 - (V,- V)V = - (VJ - V) . . . (276) 
 
 o o 
 
 foot-pounds. 
 
 Since the vane would soon move beyond the range of the jet, 
 it would be necessary, in order to obtain continuous action on a 
 motor, to provide a succession of vanes, which might be mounted 
 on the rim of a wheel. There would be, in consequence, waste 
 of energy due to the motion of the vanes in a circle and to 
 splattering and other imperfect action. 
 
 If the velocity of the jet of water is high it would fail to spread 
 fairly over the plate in Fig. 99, when it is at rest, and a crude 
 motor of the sort mentioned would show a very poor efficiency. 
 Now steam has exceedingly high velocity when discharged from 
 a nozzle, and the jet is more easily broken, so that adverse influ- 
 ences have even a worse effect than on water, and there is the 
 greater reason for following methods which tend to avoid waste. 
 Also, as pointed out on page 434, the nozzle must be so formed as 
 to expand the steam down to the back pressure, or expansion 
 will continue beyond the nozzle with further acceleration of the 
 steam under unfavorable conditions. ' 
 
 It is easy to show that the best efficiency of the simple action 
 of a jet on a vane, which we have discussed, will be obtained by 
 making the velocity V of the vane half the velocity F, of the jet. 
 
IMPULSE 
 
 475 
 
 For if we differentiate the expression (276) with regard to V 
 and equate the differential coefficient to zero we shall have 
 
 V,- 2F = o; V = iV,; 
 
 and this value carried into expression (276) gives for the work 
 on the vane 
 
 *^ 1 ' 
 4 g 
 
 but the kinetic energy of the jet is 
 
 1 w 
 
 2 g 
 
 so that the efficiency is 0.5. 
 
 If the flat plate in Fig. 99 be replaced by a semi-cylindrical 
 vane as in Fig. 99a, the direction of the stream will be reversed, 
 and the impulse will be twice as great. If the 
 vane as before has the velocity V the relative 
 velocity of the jet with regard to the vane will 
 be 
 
 V^ — V Fig. 99a. 
 
 and neglecting friction this velocity may be attributed to the 
 water where it leaves the vane. This relative velocity at exit 
 will be toward the rear, so that the absolute velocity will be 
 
 V - (V,- V) = 2V - F,. 
 
 The change of velocity or negative acceleration will be 
 
 V, - (2F - FJ = 2 (F, - F), 
 
 and the impulse is consequently 
 
 
 
 
 P 
 
 "^ /Tr 
 
 = -.(F.- 
 
 - V). 
 
 
 The work of the 
 
 impulse 
 
 becomes 
 
 
 
 
 
 w 
 2 
 
 .2 (F, - 
 
 - F) F = 2 
 
 1''' 
 
 ,v 
 
 The 
 
 maximum < 
 
 occurs when 
 
 
 
 
 
 d 
 dV 
 
 {V,V 
 
 - p) 
 
 = F, - 2 F 
 
 = 
 
 01 
 
 ■n ■ ■ (277) 
 
47< 
 
 STEAM-TURBINES 
 
 But this value introduced in equation (277) now gives 
 
 2 g 
 
 which is equal to the kinetic energy of the jet, and consequently 
 the efficiency without allowing for losses appears to be unity. 
 
 Certain water-wheels which work on essentially this principle 
 give an efficiency of 0.85 to 0.90. The method in its simplest 
 form is not well adapted to steam turbines, but this discussion 
 leads naturally to the treatment of all impulse turbines now 
 made. 
 
 Reaction. — If a stream of water flows through a conical 
 nozzle into the air with a velocity V^ as in Fig. 100, a force 
 
 g 
 
 (278) 
 
 Fig. 
 
 will be exerted tending to move the vessel 
 from which the flow takes place, in the 
 contrary direction. Here again w is the 
 weight discharged per second, and g is the 
 acceleration due to gravity. The force R 
 is called the reaction, a name that is so 
 commonly used that it must be accepted. 
 Since the fluid in the chamber is at rest, the velocity V^ is that 
 imparted by the pressure in one second, and is therefore an 
 acceleration, and the force is therefore measured by the product 
 of the mass and the acceleration. However elementary this may 
 appear, it should be carefully borne in mind, to avoid future 
 confusion. 
 
 If steam is discharged from a proper expanding nozzle, which 
 reduces the pressure to that of the atmosphere, its reaction will 
 be very nearly represented by equation (278), but if the expansion 
 is incomplete in the nozzle it will continue beyond, and the 
 added acceleration will effect the reaction. . On the other hand, 
 if the expansion is excessive there will be sound waves in the 
 nozzle and other disturbances. 
 
GENERAL CASE OF IMPULSE 
 
 477 
 
 The velocity of the jet depends on the pressure in the chamber, 
 and if it can be maintained, the velocity will be the same rela- 
 tively to the chamber when the latter is supposed to move. The 
 work will in such case be equal to the product of the reaction, 
 computed by equation (278), and the velocity of the chamber. 
 There is no simple way of supplying fluid to a chamber which 
 moves in a straight line, and a reaction wheel supplied with 
 fluid at the centre and discharging through nozzles at the cir- 
 cumference is affected by centrifugal force. Consequently, 
 as there is now no example of a pure reaction steam turbine, it 
 is not profitable to go further in this matter. It is, however, 
 important to remember that velocity, or increase of velocity, is 
 due to pressure in the chamber or space under consideration, 
 and is relative to that chamber or space. 
 
 General Case of Impulse. — In Fig. loi let ac represent the 
 velocity V^ of a jet of fluid, and let V represent the velocity of a 
 curved vane ce. Then the 
 velocity of the jet, relative 
 to the vane is V^ equal 
 to be. This has been drawn 
 in the figure coincident 
 with the tangent at the end 
 of the vane, and in general 
 this arrangement is desir- 
 able because it avoids 
 splattering. 
 
 If it be supposed that 
 the vane is bounded at 
 the sides so that the steam 
 cannot spread laterally and 
 
 if friction can be neglected, the relative velocity V^ may be 
 assumed to equal F2. Its direction is along the tangent at 
 the end e of the vane. The absolute velocity V^ can be found 
 by drawing the parallelogram efgh with ef equal to F, the 
 velocity of the vane. 
 
 The absolute entrance velocity F, can be resolved into the 
 
 Fig. ioi. 
 
478 STEAM-TURBINES 
 
 two components ai and ic, along and at right angles to the direc- 
 tion of motion of the vane. The former may be called the 
 xelocity of flow, Vf, and the latter the velocity of whirl, Vy,. 
 In like manner the absolute exit velocity may be resolved into 
 the components ek and kg, which may be called the exit velocity 
 of whirl F/, and the exit velocity of flow, V/. 
 
 The kinetic energy corresponding to the absolute exit velocity 
 V^ is the lost or rejected energy of the combination of jet and 
 vane, and for good efficiency should be made small. The exit 
 velocity of whirl in general serves no good purpose and should 
 be made zero to obtain the best results. 
 
 The change in the velocity of whirl is the retardation or nega- 
 tive acceleration that determines the driving force or impulse; 
 and the change in the velocity of flow in like manner produces 
 an impulse at right angles to the motion of the vane, which in 
 a turbine is felt as a thrust on the shaft. 
 
 Let the angle acd which the jet makes with the line of motion 
 of the vane be represented by a, and let /? and 7 represent the 
 angles bed and Ich which the tangents at the entrance and exit of 
 the vane make with the same line. 
 
 The driving impulse is in general equal to 
 
 P =-(V,, - VJ) ; (279) 
 
 ft 
 
 and the thrust is equal to 
 
 T=-(V,-V/) (280) 
 
 If there is no velocity of whirl at the exit the impulse becomes 
 
 7/1 
 p = _F^ cos a (281) 
 
 o 
 
 In any case the thrust is 
 
 r = - (F, sin a - F3 sin 7) . • • (282) 
 
 The work delivered to the vane per second is 
 
 W=-VV, COS a, (283) 
 
 g 
 
GENERAL CASE OF IMPULSE 
 
 479 
 
 and since the kinetic energy of the jet is wF/ -^ 2g the effi- 
 ciency is 
 
 V 
 e = 2 ■— cos a (284) 
 
 To find the relations of the angles a, /?, and 7, we have from 
 inspection of Fig. 102 in which el is equal to ef, 
 
 Fj sin a = Fj sin /? . . .' . . . (285) 
 
 P^ = F2 cos 7 . . . . 
 V ^ Vj^ cos a — Fg cos /?; 
 
 (286) 
 
 from which 
 
 Fj cos a 
 
 J, sm a „ 
 
 F, ■ . , cos ^■■ 
 
 sm a cos 7 
 
 and 
 
 sin /? *' sin /? 
 
 sin /5 cos a — cos ,5 sin a = sin a cos 7 
 
 sin {^3 — ci) = sin o: cos 7 
 
 The equations given above may 
 be applied to the computation 
 of forces, work, and efficiency 
 when w pounds of fluid are dis- 
 charged from one or several noz- 
 zles and act on one or a number 
 of vanes ; that is, they are directly 
 applicable to any simple impulse 
 turbine. 
 
 Example. Let Fj, the velocity 
 of discharge, be 3500 feet per 
 second as computed for a nozzle 
 on page 444, and let a = 7 = 30°. By equation (287) 
 
 sin (,/9 — a) = sin a: cos 7 = 0.5 X 0.866 = 0.433; 
 .-. 3 - a = 25 40'; /9 = 55° 40' 
 
 (287) 
 
 Vu: 
 
 F. 
 
 . sm a 
 
 ' sin /? 
 
 3500 
 
 0-5 
 
 2020 
 
 0.866 
 
 F = F2 cos 7 = 2020 X 0.866 = 1750 
 ^ = 2 X 1750 X 0.866 ^ 3500 = 0.866. 
 
48o 
 
 STEAM-TURBINES 
 
 No Axial Thrust. 
 
 Fig. 103. 
 
 The builders of impulse steam-turbines 
 attribute much importance to 
 avoiding axial thrust, which can 
 be done by making the entrance 
 and exit angles of the vanes 
 equal, provided that friction 
 and other resistances can be 
 neglected. This is evident from 
 equation (280), provided that 
 7 is made equal to /? and V^ 
 equal to V^, and also that V^ 
 sin a is replaced by V^ sin /?. 
 Or the same conclusion can be 
 drawn from Fig. 103 because 
 in this case 
 
 at 
 
 V^ sin a 
 
 V^ sin f^ 
 
 F, sin 7 = hi, 
 
 and consequently there is no axial retardation. 
 
 The de Laval turbine has only one set of nozzles which expand 
 the steam at once to the back pressure, and consequently the 
 velocity of the vanes is very high and even with small wheels 
 it is difficult to balance them satisfactorily. This difficulty is 
 met by the use of a flexible shaft, and consequently axial thrust 
 is likely to be troublesome; as a matter of fact the turbine is so 
 arranged that the axial force (if there is any) shall be a pull. 
 The importance of avoiding axial thrust in other types of impulse 
 turbines does not appear to be so great, and in some cases axial 
 thrust may be an advantage, for example in marine propulsion. 
 
 If 7 is made equal to /? in equation (287) we have 
 
 sin /9 cos a — cos /9 sin a 
 
 sm a cos 
 
 cot 1^ = i cot a 
 
 (288) 
 
 and from inspection of Fig. loi it is evident that V is half of the 
 velocity of whirl or 
 
 (289) 
 
 F = i 
 
 V^ COS, (X 
 
DESIGN OF A SIMPLE IMPULSE-TURBINE 481 
 
 If this value is carried into equations (28^) and (284) the 
 
 work and etficiency become 
 
 It' 
 W = h — V^ cos a (290) 
 
 o 
 
 and 
 
 e = cos^ a (291) 
 
 This freedom from axial thrust appears to be purchased 
 dearly unless the accompanying reduction of velocity of the 
 wheel is to be considered also of importance. 
 
 Example. If as in the preceding case the velocity of discharge 
 is 3500 feet per second, and if a is 30°, we have now the following 
 results, 
 
 cot;9 = I cot a = }y X 1.732 = 0.866 .'. ^3 = 49° 10' 
 V = i V\ cos a' = J X 3500 X 0.866 = 1515 
 e = cos" 30° = 0.75. 
 
 Effect of Friction. — The direct effect of friction is to reduce 
 the exit velocity from the vane; resistance due to striking the 
 edges of the vanes, splattering, and other irregularities, will 
 reduce the velocity both at entering and leaving. The effect of 
 friction and other resistances is two-fold; the effect is to reduce 
 the efficiency of the wheel by changing kinetic energy into heat, 
 and to reduce the velocity at which the best efficiency will be 
 obtained. There does not appear to be sufficient data to permit 
 of a quantitative treatment of this subject. Small reductions 
 from the speed of maximum efficiency will have but small effect. 
 
 The question as to what change shall be made in the exit 
 angle (if any) on account of friction will depend on the relative 
 importance attached to avoiding velocity of whirl and axial 
 thrust. If the latter is considered to be the more important, 
 then 7 should be made somewhat larger so that the exit velocity 
 of flow may be equal to the entrance velocity of flow. But if it 
 is desired to make the exit velocity of whirl zero, then 7 should be 
 somewhat decreased. 
 
 Design of a Simple Impulse Turbine. — The following compu- 
 tation may be taken to illustrate the method of applying the 
 
482 STEAM-TURBINES 
 
 foregoing discussion to a simple impulse turbine of the de Laval 
 type. 
 
 Assume the steam-pressure on the nozzles to be 150 pounds 
 gauge and that there is a vacuum of 26 inches of mercury ; required 
 the principal dimension of a turbine to deliver 150 brake horse- 
 power. 
 
 The computation on page 444 for a steam-nozzle under these 
 conditions gave for the velocity of the jet, allowing 0.15 for 
 friction, V^ = 3500 feet per second. The throat pressure was 
 taken to be 96 pounds absolute, giving a velocity at the throat 
 of 1480 feet per second. The dryness factor was 0.965 at the 
 throat; at the exit this factor was 0.833 ^^^ 0.15 friction and for 
 adiabatic expansion was 0.790. 
 
 The thermal efficiency for adiabatic expansion with no allow- 
 ance for friction or losses whatsoever, as for an ideal non-con- 
 ducting engine, is given by equation (144) page 136 as 
 
 e = i 2-^ = 1 — -— ^^ ^ — = 0.262 ; 
 
 ^1 + ?i - ?2 ^56.0 + 337-6- 94.3 
 
 the corresponding heat consumption is 
 
 42.42 -^ 0.262 = 162, 
 
 by the method on page 144. 
 
 Let the angle of the nozzle be taken as 30° as on page 479, 
 then the angle /? becomes 49° 10', the efficiency is 0.75 and the 
 velocity of the vanes must be 151 5 feet per second. 
 
 Suppose that ten per cent be allowed for friction and resistance 
 in the vanes, and that the friction of the bearings and gears is 
 ten per cent; then, remembering that 0.15 was allowed for the 
 friction in the nozzle, and that the efficiency deduced from the 
 velocities is 0.75, the combined efficiency of the turbine should 
 be 
 
 0.262 X 0.75 X 0.85 X 0.9 X 0.9 = 0.135; 
 
 which corresponds to 
 
 42.42 ^ 0.135 = 314 B.T.U. 
 
 per horse-power per minute. 
 
DESIGN OF A SIMPLE IMPULSE TURBINE 
 
 483 
 
 Now it costs to make one pound of steam at 150 pounds by 
 the gauge or 165 pounds absolute, from feed water at 126° F. 
 (2 pounds absolute) 
 
 ^ + 9i - ^2 = 856.0 + 337.6 - 94.3 = 1099 B.T.U., 
 
 consequently 314 b.t.u. per horse-power per minute correspond 
 to 
 
 314 X 60 -^ 1099 = 17.2 
 
 pounds of steam per horse-power per hour. 
 
 The total steam per hour for 150 horse-power appears to be 
 
 150 X 17.2 = 1580. 
 
 If the nozzle designed on page 444 be taken it appears that 
 five would not be sufficient, as 
 each would deliver only 500 
 pounds of steam per hour. But 
 if allowance be made for a mod- 
 erate overload, six could be 
 supplied. 
 
 Not uncommonly turbines of 
 this type are run under speed as 
 a matter of convenience. Sup- 
 pose, for example, the speed of 
 the vanes is only 0.3 of the 
 velocity of whirl, instead of 
 0.5; that is, in this case take 
 V = 1050. 
 
 This case is represented by Fig. 104, from which it is evident 
 that 
 
 Vj. = V/ = at = V^ sin 30° = 3500 X 0.5 = 1750 
 
 F«,= Fj cos 30^ = 3500 X 0.86 = 3030 
 
 tan p = ai ^ id = 1750-J- (3030 — 1050) = 0.884 
 
 /3 = 41° 3°'- 
 The two triangles aid and elh are equal, and 
 le = id = 3030 — 1050 = 1980; 
 
 Fig. 104. 
 
484 STEAM-TURBINES 
 
 consequently the exit velocity of whirl is 
 
 Wf = ek = 1050 — 1980 = — 930. 
 
 Consequently the work delivered to the vane is 
 
 -PV = -[3030 - (- 930)] 1050=- 3960 X 1050 
 
 00 o 
 
 w 
 = 416000 — • 
 
 g 
 
 But the kinetic energy is wV^^ -^ 2g, so that the efficiency is 
 
 2 
 
 416000 X 2 -r- 3500 = 0.68. 
 
 The combined efficiency of the turbine therefore becomes 
 
 0.262 X 0.68 X 0.85 X 0.9 X 0.9 = 0.123 
 instead of 0.135; ^-nd the heat consumption becomes 
 42.42 -f- 0.123 == 342 B.T.U. 
 
 per horse-power per minute; and the steam consumption increases 
 
 to 
 
 342 X 60 -^ 1099 = 18.7 
 
 pounds per horse- power per hour. The total steam per hour 
 appears now to be about 
 
 18.7 X 150 = 2800, 
 
 so that six nozzles like that computed on page 444 would give 
 only a margin for governing. 
 
 If the turbine be given twelve thousand revolutions per minute 
 the diameter at the middle of the length of the vanes will be 
 
 D = 1050 X 12 X 60 -^ (3.14 X 12000) = 20 inches. 
 
 The computation on page 444 gave for the exit diameter of 
 the nozzle 1.026 inches, and as the angle of inclination to the 
 plane of the wheel is 30°, the width of the jet at that plane 
 would be twice the exit diameter or somewhat more, due to the 
 natural spreading of the jet. The radial length of the vanes 
 may be made somewhat greater than an inch, perhaps i^^ inches. 
 The circumferential space occupied by the six jets will be about 
 
TESTS ON A DE LAVAL TURBINE 
 
 485 
 
 12J inches out of 62.8 inches (the perimeter), or somewhat less 
 than one-fifth. The section of the nozzle is shown by 
 
 Fig. 105. 
 
 Fig. 105, and the form of the vanes may be like Fig, 106. 
 In this case the thickness of a vane is made half the space 
 from one vane to the next, or one-third the 
 pitch from vane to vane. The normal width 
 of the passage is made constant, the face of one 
 vane and the back of the next vane being struck 
 from the same centre. The form and spacing 
 of vanes can be determined by experience only 
 and appears to depend largely on the judgment 
 of the designer. In deciding on the axial width pio. jo6 
 
 of the vanes it must be borne in mind that 
 increasing that width increases the length and therefore the 
 friction of the passage; but that on the other hand, decreasing 
 the width increases the curvature of the passage which may be 
 equally unfavorable. Sharply curved passages also tend to 
 produce centrifugal action, by which is meant now a tendency to 
 crowd the fluid toward the concave side which tends to raise 
 the pressure there, and decreases it at the convex side. Mr. 
 Alexander Jude,* for a particular case with a steam velocity of 
 1000 feet per second, computes a change of pressure from 100 to 
 107. 1 pounds on the concave side and a fall to 93.4 on the convex 
 side. Even if this case should appear to be extreme there is no 
 question that sharp curves are to be avoided in designing the 
 steam passages. 
 
 Tests on a de Laval Turbine. — The following are results of 
 tests on a de Laval turbine made by Messrs. J. A. McKenna 
 
 * Theory of the Steam Turbine, p. 49. 
 
486 
 
 STEAM-TURBINES 
 
 and J. W. Regan * and by Messrs. W. W. Ammen and H. A. C. 
 Small. t 
 
 Number of nozzles 
 
 Boiler pressure gauge . . . 
 Steam chest pressure .... 
 
 Vacuum, inches 
 
 Steam per brake, horse-power 
 
 per hour 
 
 B.T.u. per brake horse-power 
 
 per minute 
 
 Velocity of vanes 
 
 Velocity of jet 
 
 Ratio of velocities 
 
 Efficiency of electric generator 
 
 Regar 
 
 I and McKenna. 
 
 .Ammen and Sti 
 
 6 
 
 6 
 
 6 
 
 6 
 
 6 
 
 153 
 
 " 154 
 
 154.7 
 
 148.8 
 
 148.8 
 
 140 
 
 131-4 
 
 III. 9 
 
 136.9 
 
 78.8 
 
 24-3 
 
 25.2 
 
 25-1 
 
 26 
 
 26 
 
 19.7 
 
 18.0 
 
 20.9 
 
 19-3 
 
 23.2 
 
 355 
 
 326 
 
 379 
 
 350 
 
 426 
 
 
 1016 
 
 
 1056 
 
 1037 
 
 
 3740 
 
 
 3470 
 
 3770 
 
 
 0.271 
 
 
 0-305 
 
 0.275 
 
 0.903 
 
 0.900 
 
 0.864 
 
 0.914 
 
 0.885 
 
 150-7 
 140.4 
 
 26.4 
 
 21-5 
 
 374 
 
 0.880 
 
 Compound Steam-Turbines. — There are three ways in which 
 impulse-turbines have been compounded (i) the steam may be 
 expanded at once to the back-pressure and then allowed to act 
 on a succession of moving and stationary vanes, (2) the steam 
 may flow through a succession of chambers each of which has 
 in it one simple impulse- wheel or (3) a combination of these 
 methods may be made, the steam flowing through a succession 
 of chambers in each of which it acts on a succession of moving 
 and stationary vanes. The first method which gives a very 
 compact but an inefficient- wheel, is used for the backing-turbine 
 of the Curtis marine-turbine. The second method is used in the 
 Rateau turbine, which has usually a large number of chambers. 
 The third method is found in the Curtis turbine which has from 
 two to seven chambers in each of which are from two to four sets 
 of revolving vanes. 
 
 The Parsons turbine, which is an impulse-reaction wheel, has 
 a very large number of sets of moving vanes, i.e., from fifty to 
 one hundred and fifty. 
 
 The various forms of compound turbines have been devised 
 to reduce the speed of the vanes and the revolutions per minute 
 to convenient conditions without sacrificing the efficiency. 
 * Thesis, M.I.T. 1903. t Thesis, M.I.T. 1905. 
 
VELOCITY COMPOUNDING 
 
 487 
 
 Velocity Compounding. — In Fig. 107, let V^ represent the 
 velocity of a jet of steam that is expanded in a proper nozzle 
 down to the back-pressure. 
 Suppose it acts on an equal- 
 angled (,5 = 7) vane which has 
 the velocity V. The relative 
 velocity at entrance to that 
 vane is V^ and this velocity 
 reversed and drawn at V.^ may 
 represent the exit velocity, 
 neglecting friction. V4 is the 
 absolute velocity at exit from 
 the vane, which may be re- 
 versed by an equal- angled 
 stationary guide, and then 
 becomes the absolute velocity 
 F/ acting on the next vane. 
 The diagram of velocities for 
 the second moving vane is 
 composed of the lines lettered 
 F/, F/, F/ and* F/; the 
 last of these is reversed by a 
 stationary guide, and the 
 velocities of the third vane are 
 F/', F/', F3" and F/'. The 
 diagram is constructed by 
 dividing the velocity of whirl 
 
 Vy, = Fj cos ix 
 
 into SIX equal parts, and the final exit velocity F/' is vertical, 
 indicating that there is no velocity of whirl at that place. 
 
 It is immediately evident, since the velocity of flow is unaltered 
 in Fig. 107, and since there is no exit velocity of whirl that the 
 efficiency neglecting friction is the same as for Fig. 103, namely 
 
 e = cos^ a 
 
 as given by equation (291) page 481. 
 
488 STEAM-TURBINES 
 
 It is, however, interesting to determine the work done on each 
 vane; the sum of the works of course leads to the same result. 
 In Fig. 107 the velocity of whirl at entrance to the first vane is 
 
 Fj cos a 
 
 and the velocity of whirl at exit is • 
 
 — V4 cos /5 = — 7 Fj <^os a ; 
 
 consequently the work done on the vane is 
 
 - V^ cos a - ( — - V^ cos «) -^1 cos a, 
 
 because V was made equal to one-sixth of the velocity of whirl. 
 This expression reduces to 
 
 10 W Tr 2 2 
 
 — ^- F/ cos^ a. 
 36 g 
 
 The second and third vanes receive the works 
 
 -— - F/ cos^ a and -- - F/ cos"^ a 
 . 3^g 3^ g 
 
 so that the resultant work is 
 
 1 - F/ cos^ a 
 g 
 
 and the efficiency is evidently given by the expression already 
 quoted. The most instructive feature of this discussion is that 
 the relation of the works done on the three vanes is 
 
 5. 3. I- 
 
 A similar investigation will show that the distribution among 
 four vanes is 
 
 7. 5> 3. I- 
 
 The first figure in such a series is obtained by adding to the 
 number of vanes one less than that number; and each succeeding 
 term is two units smaller. Thus seven vanes give the distribu- 
 tion 
 
 i3» II. 9) 7> 5. 3. I- 
 
VELOCITY COMPOUNDING 489 
 
 It is considered that this type of turbine cannot be made to 
 give good efficiency in practice on account of large losses in passing 
 through a succession of vanes and guides, especially as the steam 
 in the earlier stages has high velocities. The turbine, however, 
 has certain advantages when used as a backing device for a 
 marine-turbine, in that it may be very compact, and can be placed 
 in the low-pressure or exhaust chamber, so that it will experience 
 but little resistance when running idle during the normal forward 
 motion of the ship. 
 
 In dealing with this problem it is convenient to transfer the 
 construction to the combined diagram at abij Fig. 107 ; diagrams 
 for guides like that made up of the velocities F3, F4 and V^ being 
 inverted for that purpose. It is clear that the absolute velocities 
 at exit from the nozzle and the guides are represented by Fj,F/ 
 and F/', while the relative velocities are V^, V^^ and F/' which 
 with no axial thrust are equal to F3, V/ and F3''. The absolute 
 velocity at exit from a given guide is taken as equal to the abso- 
 lute velocity at exit from the preceding vane, thus F/ is equal 
 to F4, etc. The last absolute velocity F/' is equal to at the 
 constant velocity of flow. 
 
 The angles a, /?, a^, /?j, a^ and /?2 are properly indicated as may 
 be seen by comparing the original with the combined diagram. 
 
 If the diagram is accurately drawn to a large scale, the velocities 
 and angles can be measured from it, or they may readily be 
 calculated trigonometrically. Thus 
 
 -J sin a ^ sin a ^ 
 
 tan /? = ; tana, =- etc., 
 
 t cos a I cos a 
 
 F2 = V^ sin a cosec j3; F/ = F^ sin a cosec a^, etc. 
 
 The radial length of the vanes and guides must be increased 
 inversely proportional to the velocities, using relative velocities 
 for the vanes and absolute velocities for the guides. 
 
 There appears to be no reason why the guides should be 
 relieved from axial thrust provided they can be properly sup- 
 ported. 
 
490 
 
 STEAM-TURBINES 
 
 Except that the passages in the guides might become too 
 long or too sharply curved, they might all be given the same 
 delivery angle as the nozzle, and thus a notable improvement 
 
 in economy could be 
 realized. In Fig. io8 
 the velocities Fj, V^ 
 and F4, are drawn in 
 
 the 
 
 Fig. 108. 
 
 the usual manner, 
 being equal to V^; 
 velocity F4 is laid off 
 along the same line as 
 Fj and is lettered F/ 
 and serves as the initial 
 velocity for a new con- 
 struction as indicated. F/ is in like manner laid off for F/', 
 and thus the diagram is completed. The velocity of the vanes 
 of course remains constant with the value F. 
 
 Following the problem on page 444 for a nozzle discharging 
 from 150 pounds by the gauge into 26 inches of vacuum we have 
 Fj = 3500 feet per second with y = 0.15. The value of F may 
 be taken as 620 feet per second, which gives a diagram with no 
 final velocity of whirl. 
 
 The exit velocity of whirl from the first set of vanes is — 1830 
 feet per second as measured on the diagram, and since the initial 
 velocity of whirl is 
 
 Fj cos a = 3500 X 0.866 = 3030 
 the retardation is 
 
 3030 - ( - 1830) = 4860. 
 The retardation for the second set of vanes is 
 2160 — ( — 880) = 3040, 
 and for the third set is 1320, so that the work of the impulse is 
 
 w 
 
 (4860 -I- 3040 -f 1320) X 620 — 
 
 o 
 
 w 
 1:720000— , 
 
 g 
 
EFFECT OF FRICTION 491 
 
 and as the intrinsic energy of the jet is 
 
 W y^ ^ - ^w , w 
 
 — Vi = h 3500 - = 6125000- 
 2g g g 
 
 the efficiency of this arrangement without losses and friction 
 
 appears to be 
 
 5720 -^ 6125 = 0.92. 
 
 Effect of Friction. — The effect of friction is to change some 
 of the kinetic energy into heat, thereby reducing the velocity and 
 at the same time drying the steam and increasing the specific 
 volume so that the length of the guides and vanes must be 
 increased at a somewhat larger ratio than would otherwise be 
 required. 
 
 A method of allowing for friction is to redraw the diagram of 
 Fig. 107, shortening the lines that represent the velocities to 
 allow for friction. 
 
 In order to bring out the method clearly an excessive value 
 will be assigned to the coefficient for friction, namely, y = 0.19, 
 so that the equation for velocity may have for its typical form 
 
 Vq = V2gh {1 — y) = 0.9 \^2gh. 
 
 Again the coefficient will be assumed to be constant for sake of 
 simplicity, more especially as but little is known with regard to 
 its real value. 
 
 The diagram shown 
 by Fig. 109 was drawn 
 by trial with V^ = 3500 
 and with a = 30°. It 
 appeared necessary to 
 reduce V to 380 feet 
 per second, instead of 
 505 feet, which would 
 be proper without fric- 
 tion, this latter quantity 
 
 being one-sixth of the fig. 109. 
 
 initial velocity of whirl, 
 
 V^ = Fj cos a = 3500 X 0.866 = 3030. 
 
492 STEAM-TURBINES 
 
 Starting with V^ the velocity of the jet, the triangle V^, F, V^ 
 is drawn to determine the initial relative velocity for the first set 
 of vanes. The exit velocity V^ is made equal to 0.9 Fj, and the 
 triangle F3, F, F4 is drawn to determine the absolute velocity 
 at exit F4 from the guides. This is taken to be the velocity at 
 entrance to the guides, but the exit velocity from them is taken to 
 be F/ = 0.9 F4. Two repetitions of this process complete the 
 diagram. The velocities of whirl at entrance to the three sets of 
 vanes as measured on the diagram are 
 
 3030 1780 800, 
 
 and the velocities of whirl at exit from those vanes are 
 
 — 1890 — 880 — o, 
 
 so that the negative accelerations are 
 
 4920 2660 800, 
 
 making a total of 8380. Since the velocity of the vanes is 380 
 feet per second the work delivered to the turbine is 
 
 w w 
 
 8380 X 380— = 3180000—, 
 
 g g 
 
 and consequently, using the kinetic energy already computed for 
 the jet on the preceding page, the efficiency is 
 
 3180000 -^ 6125000 = 0.52. 
 
 This method preserves the equality of the angles of the vanes 
 and guides, but does not avoid axial thrust, for Fig. 109 shows a 
 large reduction of the velocity of flow, and as there are no reversals 
 of flow, the reduction is a measure of the impulse producing 
 axial thrust. Nearly half of the thrust is borne by the fixed 
 guides, and it is to be borne in mind that the assumption of an 
 exaggerated coefficient for friction greatly exaggerates this 
 feature, which in practice may not be very troublesome. 
 
 To entirely avoid axial thrust it appears to be necessary only 
 to slightly increase the angle 7 at the exit from the vane; the 
 angles of the guides may be reduced if desired as an offset. 
 
PRESSURE COMPOUNDING 
 
 493 
 
 Fig. iio. 
 
 In Fig. no an attempt is made to avoid axial thrust on 
 the vanes, and at the same time to retain a fair efficiency 
 by making the 
 delivery angle of 
 the guides constant. 
 
 A calculation like 
 that on page 492 
 indicates that an 
 efficiency of 0.76 
 might be expected 
 in this case. It is 
 quite likely that 
 in practice there 
 might be difficulty 
 
 in making the delivery angle of the guide as small as 30°, 
 but it appears as though the common idea that it is practically' 
 impossible to make an economical turbine on this principle is 
 not entirely justified. 
 
 Pressure Compounding. — The second method of compounding 
 impulse turbines with a number of chambers each containing 
 a single impulse wheel like that of the de Laval turbine requires 
 a large number of stages to give satisfactory results. For sake 
 of comparison with preceding calculation we will take the 
 same initial and final pressure and the same angle for the nozzles, 
 namely, 150 pounds by the gauge and 26 inches vacuum, and 
 a = 30°. 
 
 Nine stages in this case will give approximately the same 
 speed of the vanes as in the problem on page 490. The temper- 
 ature-entropy table which was made for work of this nature 
 is most conveniently used with temperature, and in this case the 
 initial and final temperature can be taken as 366° F. and 126° F. 
 At 366° F. the steam is found to be nearly dry for the entropy 
 1.56 and that column will be taken for the solution of this 
 problem. The heat contents is 1 193.3 instead of 1 193.6 as 
 found for 366° F. in Table I of the " Tables of Prop- 
 erties of Steam." On the other hand the table gives at 
 
494 STEAM-TURBINES 
 
 126° for the heat contents 904.9, and the difference is 
 
 1193-3 - 904.9 = 288. 
 
 If we divide the available heat into nine portions we have 
 for each 
 
 288 ^ 9 = 32 B.T.U. 
 
 If again we take y = o.i which may be excessive in this case 
 since, as will be evident, simple converging nozzles will be 
 required, the velocity of the steam jet will be 
 
 F, = \/2 X 32.2 X 778 X 32 X (i - 0.1) = 1200 
 
 feet per second. This is of course the velocity for all the stages. 
 The choice of « = 30° gives for the velocity of whirl 
 
 1200 cos 30® == 1200 X 0.866 =- 1040, 
 
 and the velocity of the vanes to give the maximum economy is 
 half of this or 520 feet per second or somewhat less if allowance 
 be made for friction and other losses. 
 
 Since we have to deal with a single impulse wheel in each 
 chamber and since the wheels are usually designed to avoid axial 
 thrust, all the conclusions concerning that type of wheel may be 
 assumed at once as has already tacitly been done. 
 
 One of the important conclusions is that the efficiency without 
 friction as given by equation (291) page 481 is ^ 
 
 e = cos^ a; 
 
 with a = 30°, this gives e = 0.75. 
 
 It is but fair to say that a smaller angle of a is used for this 
 type of turbine and that the range of temperature is likely to be 
 extended at both limits, and that in particular great importance 
 is attached to securing a good vacuum; 28 inches of mercury, 
 corresponding to one pound absolute, is commonly obtained 
 in good practice with all compound turbines. 
 
 If the peripheral speed of the wheel must be kept down, this 
 type of turbine is likely to have a very large number of chambers. 
 For example, if the speed must be no more than 260 feet per 
 second (half of 520), there must be 36 chambers instead of 9. 
 
PRESSURE COMPOUNDING 
 
 495 
 
 This will give for the available heat for each chamber 8 
 thermal units, and using as before y = o.i we shall have 
 
 F, = V2 X 32.2 X 778 X 8 X 0.9 = 600 
 
 feet per second. With a = 30° the velocity of whirl is now 520 
 feet and the velocity of the vanes as stated is 260 feet per second. 
 
 The next question in the discussion of this turbine is the 
 distribution of pressure. If the coefficients for friction and 
 other losses are taken to be constant, then the pressure can be at 
 once determined by the adiabatic method. 
 
 In the problem already discussed 32 b.t.u. are assigned to 
 each stage, and if this figure be subtracted nine times in succes- 
 sion from the heat contents 11 94 at the initial temperature we 
 shall have the values which may be used in determining the 
 intermediate temperature and pressure from the temperature- 
 entropy table. Also from that table or from Table I in the 
 " Tables of Properties of Steam," the corresponding pressures 
 can be determined. The work is arranged in the following 
 table: 
 
 DISTRIBUTION OF PRESSURE. 
 
 
 Values of ocv-^-q. 
 
 Temperatures. 
 
 Pressures absolute. 
 
 Ratios of pressures. 
 
 
 
 1 193 
 
 366 
 
 165 
 
 0.68 • 
 
 I 
 
 I161 
 
 336 
 
 112 
 
 0.66 
 
 2 
 
 1 1 29 
 
 306 
 
 73-5 
 
 0.65 
 
 3 
 
 1097 
 
 278 
 
 47-8 
 
 0.64 
 
 4 
 
 1065 
 
 251 
 
 30.4 
 
 0.61 
 
 5 
 
 1033 
 
 224 
 
 18.6 
 
 0.61 
 
 6 
 
 lOOI 
 
 199 
 
 II 3 
 
 0.58 
 
 7 
 
 969 
 
 174 
 
 6.55 
 
 0-57 
 
 8 
 
 937 
 
 150 
 
 371 
 
 0-53 
 
 9 
 
 905 
 
 126 
 
 1.98 
 
 0. 
 
 The last column gives the ratio of any given pressure to the 
 preceding pressure, i.e. 112 :*i65 = 0.68. These ratios indicate 
 that simple conical converging nozzles will be sufficient for all 
 but the last stage. With the usual number of stages, twenty or 
 more, the ratios are certain to be larger than 0.6 in all cases, 
 indicating the use of converging nozzles throughout. 
 
496 STEAM-TURBINES 
 
 To determine the sizes of the nozzles or the passages in the 
 guides it is necessary to estimate the quality of the steam in 
 order to find the specific volume. To do this we may consider 
 that, of the heat supplied to a certain stage of the turbine, a 
 portion is changed into work on the turbine vanes, some part is 
 radiated, and the remainder is in the steam that flows from the 
 chamber of that stage; if there is appreciable leakage, special 
 account must be taken of it, but both radiation and leakage 
 can be left at one side for the present. 
 
 Now in the case under consideration, 32 thermal units were 
 assigned to each stage in the adiabatic calculation for the 
 distribution of pressure. But o.io part was assigned to y to 
 allow for friction so that only 0.9 was applied to the calculation 
 of velocity; of the kinetic energy of the jet 0.75 only was 
 assumed to be applied to moving the vanes without friction, the 
 remainder being in the kinetic energy of the flow from the 
 vanes which was assumed to be changed into heat again; and 
 further there was an allowance of o.i for losses in the vanes, 
 leaving a factor, 0.9, to be applied for that action. Conse- 
 quently instead of 32 thermal units changed into work per 
 stage, our calculation gives only 
 
 32 X 0.9 X 0.75 X 0.9 = 19.44 B.T.U. . 
 
 will be changed into work. A method of determining the quali- 
 ties and specific volumes at the several nozzles is illustrated in 
 the table on the following page. 
 
 The quantity of heat changed into work per stage is sub- 
 tracted successively, giving the apparent remaining heat contents 
 as set down in the tables. At a given temperature we may find 
 the quality by subtracting the heat of the liquid from the heat 
 contents and dividing the remainder by the value of r. The 
 specific volumes are determined by the equation 
 
 r ~ %u -\- a^ 
 
 but as X is in all cases large, the effect of <r may be neglected 
 altogether. 
 
PRESSURE COMPOUNDING 
 
 497 
 
 FIRST COMPUTATION OF QUALITIES AND VOLUMES. 
 
 
 Temper- 
 ature 
 
 (0 
 
 Heat 
 contents 
 (.vr+g) 
 
 II93 
 
 Heat of 
 liquid 
 
 Value 
 of 
 
 XT 
 
 Heat of 
 vapori- 
 zation 
 (r) 
 
 Quality 
 (v) 
 
 Specific volumes 
 isx) 
 
 o 
 
 366 
 
 338 
 
 855 
 
 855 
 
 I 
 
 2.78 
 
 2.78 
 
 I 
 
 336 
 
 I174 
 
 307 
 
 867 
 
 878 
 
 0.988 
 
 3 
 
 95 
 
 3 
 
 90 
 
 2 
 
 306 
 
 II54 
 
 276 
 
 878 
 
 899 
 
 0.978 
 
 5 
 
 79 
 
 5 
 
 66 
 
 3 
 
 278 
 
 1135 
 
 247 
 
 888 
 
 919 
 
 0.976 
 
 8 
 
 65 
 
 8 
 
 44 
 
 4 
 
 251 
 
 II15 
 
 220 
 
 895 
 
 939 
 
 0-953 
 
 13 
 
 3 
 
 12 
 
 7 
 
 5 
 
 224 
 
 1096 
 
 192 
 
 904 
 
 958 
 
 0.944 
 
 21 
 
 
 
 19 
 
 8 
 
 6 
 
 199 
 
 1076 
 
 167 
 
 909 
 
 975 
 
 0.932 
 
 34 
 
 I 
 
 31 
 
 8 
 
 7 
 
 174 
 
 1057 
 
 142 
 
 915 
 
 993 
 
 0.922 
 
 56 
 
 8 
 
 52 
 
 2 
 
 8 
 
 150 
 
 1037 
 
 118 
 
 919 
 
 lOIO 
 
 0.910 
 
 97 
 
 
 
 88 
 
 3 
 
 9 
 
 126 
 
 1018 
 
 94 
 
 924 
 
 1026 
 
 0.901 
 
 175 
 
 158 
 
 
 
 By the aid of the temperature-entropy table, the qualities 
 and specific volumes may be determined directly v^ith good 
 approximation, it being necessary only to follov^ the line of the 
 temperature to an entropy column, having nearly the proper 
 heat contents. 
 
 There is a serious objection to this method as applied, because 
 it does not take any account of the fact that as the steam passes 
 from stage to stage losing less heat than it v^ould with adiabatic 
 action, the entropy increases, and that with increased entropy 
 the difference of heat contents between two given temperatures 
 increases. This will be very apparent from inspection of a 
 temperature-entropy diagram or the temperature-entropy table. 
 This matter will be discussed more at length in connection with 
 the Curtis type of turbine. 
 
 It has been assumed that the same amount of heat should be 
 assigned to each stage for the adiabatic calculation and that the 
 values of y to allow for friction and losses remain constant. 
 As to the values that should be assigned to y, we have very little 
 published information; it may be noted in passing that our 
 allowance for friction in the nozzles and guides is probably too 
 large. It will be evident that there is no difficulty in maintaining 
 the amount assigned to each stage in its proper proportion even 
 
498 
 
 STEAM-TURBINES 
 
 though y shall be varied from stage to stage. For example, our 
 choice of o.i for both y and y^ gives 
 
 32 X 0.9 X 0.9 = 25.92 B.T.U., 
 
 which multiplied by 0.75, the efficiency due to the angles and 
 velocities, gives 19.44 b.t.u. as above. Let it be assumed for 
 the moment that the above product shall be kept constant, so as 
 to obtain the same velocity of jet in each stage. Then the 
 following table exhibits a way of accomplishing this purpose 
 while varying y and y^\ 
 
 Stage 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 y 
 
 y^ ..... 
 (i-y) (i-3'i) 
 
 B.T.U 
 
 0.08 
 0.088 
 0.839 
 309 
 
 0.085 
 0.091 
 0.832 
 31.2 
 
 0.09 
 0.094 
 0.824 
 315 
 
 0.095 
 0.097 
 0.817 
 31-7 
 
 0. 10 
 0. 10 
 0.81 
 32 
 
 0. 105 
 0. 103 
 0.803 
 
 32-3 
 
 0. II 
 0. 106 
 . 796 
 32.6 
 
 O.I15 
 0.109 
 0.787 
 33-0 
 
 0. 12 
 0. 112 
 0.781 
 33-2 
 
 The last line shows the proper assignment of thermal units 
 for this condition. For simplicity both y and y^ are assumed 
 to vary uniformly, but other variations can be worked out with 
 a little more trouble. Evidently the sum of the figures in the 
 last line should be equal to 
 
 9 X 32 -= 288; 
 
 it is a trifle larger in the table. 
 
 Now it is probable that the best values of the factor for friction 
 and resistance are to be derived from investigations on turbines 
 rather than from separate experiments on nozzles and vanes, 
 and it is evident that the use of the methods of representing 
 the friction by a factor y is rather a crude way of trying to attain 
 in a new design favorable conditions found in a turbine already 
 built. 
 
 Since the general conditions of this problem are the same as 
 those on page 481, the efficiency due to adiabatic action will be 
 the same as is also the efficiency due to the angles and velocities. 
 Taking the factors for friction in the guides and blades as each 
 
PRESSURE COMPOUNDING 499 
 
 O.I, the corresponding factors are 0.9 and 0.9. The efficiency 
 due to velocities is 0.75, and the mechanical efficiency may be 
 estimated as 0.9. The combined efficiency of t^he turbine is 
 
 0.262 X 0.75 X 0.9 X 0.9 X 0.9 = 0.143. 
 
 A computation like that on page 483 with this efficiency gives 
 for the probable steam consumption 16.2 pounds per brake 
 horse-power per hour. 
 
 Assume that the turbine is to deliver 500 brake horse-power; 
 then the steam consumption per second will be 
 
 16.2 X 500 -^ 3600 = 2.25 pounds. 
 
 We can now determine the principal dimensions of the turbine 
 to suit the conditions of its use. Suppose that it is desired to 
 restrict the revolutions to 1200 per minute or 20 per second ; 
 then with nine stages and a peripheral velocity of 520 for the 
 vanes the diameter will be 
 
 520 -^ 207Z = 8.28 feet. 
 
 For a turbine of the power assigned this diameter will be 
 found to be inconveniently large. If, however, the number of 
 stages can be made 36, the velocity will be reduced to 260 feet 
 per second as computed on page 495. This will give for the 
 diameter 
 
 260 -i- 207r =4.14 feet. 
 
 The remainder of our calculation will be carried out on these 
 assumptions, namely, that the power is to be 500 brake- 
 horsc-power, and that there are to be 36 stages. If the method 
 of the table on page 497 were applied to a turbine having the 
 full 36 stages now contemp ated, it would have 37 lines; namely, 
 the ten already set down, and three intermediate entries between 
 each pair of consecutive lines; but the temperatures found in 
 that table would be found in the more extended table together 
 with their specific volumes. We can, therefore, use that table to 
 calculate areas and lengths of vanes for 9 out of the 36 stages, 
 
SOO 
 
 STEAM-TURBINES 
 
 Fig. III. 
 
 which will suffice for illustration. Beginning with the lowest stage 
 
 the area to be supplied will be 
 
 2.25 X 158 -^ 600 = 0.592 square feet; 
 
 where 600 is the velocity of the jet computed on page 495. 
 
 The circumference of a circle having the diameter of 4.14 feet 
 
 is 13 feet; but of this a portion, one-fourth or one-third, must be 
 
 assigned to the thickness of the guides. If we take one-fourth 
 
 in this case the effective perimeter 
 becomes 9.75 feet. But as is evi- 
 dent from Fig. 11 1 the peripheral 
 space assigned to the distance 
 between guides must be multiplied 
 by sin a in order to find the effec- 
 tive opening. As a is taken to be 
 30°, the sine is one-half, so that the 
 total width of spaces between 
 guides is reduced to 4.88 feet. The 
 
 radial length of the guides for the last stage will consequently be 
 0.592 -^ 4.88 = 0.123 of a foot = 1.45 inches, 
 
 provided that there is full peripheral admission to the guides. 
 
 Now the angles for this case are the same as those on page 481 
 and /9 is 49° 10'. Consequently the relative velocity is 
 F2 = Fj sin a -^ sin ^ = 600 sin 30° -=- sin 49° 10' = 397 feet. 
 
 If the passages between the vanes are made of constant width, 
 as shown in Fig. iii, the effective perimeter will be the entire 
 perimeter of the wheel less the allowance for thickness. An 
 allowance like that for the guides will make the vanes shorter 
 than the guides in this case. Let us try making the thickness 
 equal to a space; then the effective perimeter will be 6.5 feet. If 
 the density of the steam is assumed to be constant for a given 
 stage, then the lengths of the guides and vanes will be inversely 
 as the product of the velocities by the effective perimeters, so 
 that the length of the vane will be 
 600 X 4."'^ 
 
 1.45 X 
 
 397 X 6.5 
 
 = 1.65 inches. 
 
LEAKAGE AND RADIATION 
 
 501 
 
 Conversely, if desired, the thickness of the vanes could be 
 adjusted to give the same length. Such a construction as this 
 leads to is likely to give too sharp a curvature to the backs of 
 the vanes, and it may be better to give only the thickness 
 demanded for strength and take the chance that the passage 
 between the vanes shall not be filled. If allowance is made for 
 friction and the consequent reduction in velocity the lengths of 
 the vanes should be correspondingly increased. 
 
 The lengths, of the guides for the other stages will be directly 
 proportional to the specific volumes in the table on page 497, 
 because the velocities have been made the same for all the stages. 
 For example, at 199° the length for full admission will be 
 
 1.45 X 31.8 ^ 148 = 0.312 inch, 
 
 which will be the proper length for the twenty-fourth stage. If 
 it is considered undesirable to further reduce the length we may 
 resort to admitting steam through guides for only a portion of 
 the periphery. Making the arc of admission vary as the specific 
 volumes, the fourth stage (line i of the table on page 497) will 
 have admission for 
 
 360 X 3.86 -^ 31.8 = 43°. 
 
 Intermediate lengths of vanes and arcs of admission may be 
 computed by filling out a table like that on page 497 for all the 
 stages, or a diagram may be drawn from which the required 
 information can be had by interpolation; the values on the line 
 numbered o are for this purpose, there being of course no corre- 
 sponding stage. In fact the method of computing at convenient 
 intervals and interpolating from curves is likely to be more accu- 
 rate as well as more convenient, as the error of adiabatic calcula- 
 tions for steam with small change of temperature is liable to be 
 excessive. 
 
 Leakage and Radiation. — This type of turbine, as will be seen 
 in the description of the Rateau turbine, has a number of wheels 
 each in its own chamber, and the chambers are separated by 
 stationary disks that extend to the shaft. Reduction of leakage 
 must be attained by a small clearance between the disk and the 
 
502 STEAM-TURBINES 
 
 shaft for a proper bearing or stuffing box cannot be placed in so 
 inaccessible a place. The leakage can be estimated by aid of 
 Rankine's equation on page 432 or from Rateau's experiments 
 on page 433 ; but both methods are likely to give results that are 
 too large, and a factor less than unity should be applied; but 
 the value of such a factor for a long, narrow, annular passage is 
 not known, and any estimate must be crude. For a turbine of 
 the Rateau type the leakage is likely to be less than five per cent 
 at- the high pressure end. Now the leakage is proportional 
 nearly to the difference of pressure between successive chambers, 
 and as the difference decreases so also does the leakage till it 
 becomes of no account at the lower end. To allow for leakage 
 the length of guides or the arc of admission may be increased at 
 the high pressure end of the turbine. There does not appear 
 to be any information concerning the radiation from steam- 
 turbines. On the one hand the area of radiating surface is 
 larger than for steam-engines and on the other the temperatures 
 are less for the greater part if not all of that area. For compact 
 steam-engines the radiation is likely to be from five to ten per 
 cent. For turbines of the Rateau and Curtis types the effect 
 of radiation is to require larger areas in guides and passages 
 at the high pressure end. 
 
 Lead. — Turbines with pressure-compounding usually have 
 some space between the vanes of one wheel and the next 
 set of guides or nozzles, and consequently the absolute exit 
 velocity is mainly if not entirely dissipated, so that the steam 
 enters those nozzles with no appreciable velocity. If this action 
 is complete it would appear to be of little consequence where the 
 guides or nozzles are placed. Nevertheless considerable impor- 
 tance is attached to locating the guides so that steam from the 
 wheel shall flow directly into them. Clearly, as it takes an 
 appreciable time to flow through the passages between the 
 vanes, the steam will be discharged at some distance from the 
 place at which it was received and the general path of the steam 
 is a spiral wound around the turbine case in the direction of 
 rotation. 
 
RATEAU TURBINE 
 
 503 
 
 Let abcde represent a vane which has steam entering it 
 tangentially with the velocity V^, while it has itself the velocity 
 V. Assuming that the relative velocity is 
 constant we may divide the curve into a 
 number of equal small parts that are approxi- 
 mately straight. From b lay off 
 
 bb' 
 
 , V 
 
 ab—, 
 
 ^ 2 
 
 Fig. 
 
 then 6' will be a point in the trajectory of the particle of steam. 
 In like manner 
 
 cc 
 
 V 
 
 2ab — , etc. 
 
 Casing 
 
 The path ab'c'd'e' may be taken as the trajectory of the steam, and 
 e^ is the lead as defined above. Properly a similar construction 
 should be made also for the back of the vane, and the mean path 
 should be taken to establish the lead. Extreme refinement is 
 probably neither necessary nor justifiable in this work. 
 
 Rateau Turbine. — The construction of this turbine, which is 
 
 of the pure pressure-compound 
 type is represented by Fig. 113, 
 which is a half section through 
 the shaft, wheels and casing. 
 The wheels are light dished 
 plates which are secured to 
 hubs that are pressed onto the 
 shaft and which carry the 
 moving vanes. The chambers 
 are separated by diaphragms 
 of plate steel, riveted to a rim 
 and to a hub casting. The 
 hubs are bushed with anti- 
 friction metal that is expected 
 to wear away if it by chance 
 touches the shaft. This tur- 
 bine is sometimes divided into 
 two sections to provide a middle bearing for the shaft, which 
 has considerable length and should preferably have a small 
 
504 
 
 STEAM-TURBINES 
 
 diameter to reduce leakage. The high pressure portion may 
 have a smaller diameter to facilitate arrangement of guides and 
 vanes. Sometimes t'here are three diameters for the same pur- 
 pose. But little extra complication of computation is introduced 
 by such change of diameter; all that is necessary is to make 
 the portion of available heat per stage larger in proportion to 
 the increase in peripheral speed. 
 
 TESTS ON RATEAU TURBINE. 
 Dr. a. Stodola.* 
 
 Duration minutes 
 
 Revolutions per minute 
 
 Steam pressure at stop valve absolute 
 pounds 
 
 Superheating degrees F 
 
 Steam pressure at first guides .... 
 
 Superheating degrees F 
 
 Absolute exhaust pressure 
 
 Effective power 
 
 Steam per horse-power per hour, ex- 
 clusion of air-pump . 
 
 40 
 
 50 
 
 35 
 
 180 
 
 2184 
 
 2181 
 
 2190 
 
 2101 
 
 176. 1 
 
 I75-I 
 
 170-5 
 
 168.4 
 
 5-2 
 
 9 
 
 14.8 
 
 20 
 
 44-7 
 
 639 
 
 95-4 
 
 119. 9 
 
 32.6 
 
 32.2 
 
 20.9 
 
 18.9 
 
 1.29 
 
 ^■33 
 
 I-5I 
 
 1 .64 
 
 172 
 
 257 
 
 417 
 
 531 
 
 19.0 
 
 17.6 
 
 15-7 
 
 156 
 
 30 
 
 2200 
 
 181. 1 
 
 14.6 
 
 143-7 
 17. 1 
 1.89 
 634 
 
 152 
 
 The accompanying table gives . results of tests on a Rateau 
 turbine by Professor Stodola. To compare with results from 
 steam-engines, these latter should be referred to brake horse- 
 power, with a mechanical efficiency of 0.85 to 0.90. 
 
 This type of turbine has been applied successfully to use 
 exhaust steam from reciprocating engines which for some purpose 
 exhaust at atmospheric pressure or into a poor vacuum. Such 
 application can, however, be but local or accidental. 
 
 Steam Friction of Rotating Disks. — The resistance which a 
 turbine wheel experiences while rotating in steam can be divided 
 into two parts : first, that due to the friction of the smooth disk, 
 and second, that due to the action of the vanes, which have an 
 effect comparable to that of a centrifugal pump. 
 
 From a consideration of tests made by Odell f on cardboard 
 disks, and by Lewecki J on a de Laval turbine wheel driven in 
 
 * Steam Turbines, trans. Dr. L. C. Lowenstein. 
 
 t Engineering, January, 1904. t Zeitschr. d, V. deutsch Ing., 1903. 
 
SIDE THRUST 505 
 
 its casing, and from tests of his own, Professor Stodola gives the 
 following equations for the horse-power required to drive smooth 
 wheels and to drive wheels with vanes forward: 
 Smooth wheels 
 
 H.P. =0.02295 a^ D'-' (— ) 7. 
 
 Wheels with vanes 
 
 H.P. = [0.02295 «i^'*' + 1.4346 ^2 L'-''] (—)\ 
 
 Vioo / 
 
 where D is the diameter in feet, L is the blade length in inches, 
 V is the peripheral speed in feet per second, and 7 is the density 
 of the medium. The values of the other factors are 
 
 «i = 3-14 «2 = 0-42. 
 
 These formulae explain why the backing turbine for marine 
 propulsion is always run in a vacuum when idle. 
 
 Turbines which have only a partial admission must be affected 
 by some such action for that part of the revolution during which 
 steam is not admitted; but this matter is obscure and such a 
 resistance must be combined with friction and other resistances. 
 It is therefore very difficult to assign the proper value to the fric- 
 tion factor y for steam in the vanes or in the guides and vanes of 
 a velocity-compound turbine. In particular any change of the 
 angle 7 (Fig. 103, page 480) to avoid end thrust must be made 
 with caution and should be checked by experiment. 
 
 Side Thrust. — If admission is restricted to only a part of the 
 periphery of a turbine, then in order to preserve a balance and 
 avoid unnecessary pressure ^on the bearings of the shaft, the arc 
 of admission should be divided into two equal portions, that are 
 diametrically opposite. Some builders, however, prefer to 
 ignore this effect, and concentrate the admission at one side, 
 because there is tendency for the steam to spread which will have 
 double the effect if the arc is divided as suggested. The amount 
 of side thrust can be estimated from the powers developed at 
 the several wheels, having partial admission, together with the 
 dimensions and speed of revolutions, making allowance of course 
 for the distribution of the torque over an arc of a circle. 
 
5g6 steam-turbines 
 
 Pressure and Velocity Compounding. — A favorable combina- 
 tion may be made of the two methods of compounding already 
 discussed; that is, the pressure and temperature range may be 
 divided between two or more chambers in each of which shall be 
 two or three sets of moving vanes. This has been done on a 
 large scale with the Curtis turbine which appears to have a wider 
 range of economical application than any other type. 
 
 Since the principles of each method have been discussed 
 already, we will illustrate the application to a comparatively 
 simple problem avoiding too great minutiae of detail. 
 
 Let us take for the principle conditions the delivery of 500 kilo- 
 watts of electrical energy, which, with an efficiency of the dynamo 
 of about 0.9, will correspond to nearly 770 brake horse-power. 
 
 Let the initial pressure be 150 pounds by the gauge, and the 
 vacuum be 28 inches of mercury. Let the angle of the nozzles 
 be rt = 20°. The absolute pressures will be about 165 pounds 
 and one pound absolute, and the compounding temperatures 
 are 366° and 102° F. Dry saturated steam at the given pressure 
 will have nearly 1.56 units of entropy, and for this the temperature- 
 entropy table gives for adiabatic expansion with the above limits 
 of temperature the heat contents as 1193 ^^^ ^7^- ^^^^ value 
 of ^2 is 70 at the lower temperature, and consequently x^^ 
 is equal to 801 b.t.u. 
 
 The thermal efficiency of adiabatic expansion without allowing 
 for any losses is 
 
 XJr^ 801 o 
 
 6=1 — ^~^ =1 = 0.285; 
 
 ^ + ^i - ^2 II23 
 
 the corresponding heat consumption is 
 
 42.42 H- 0.285 "^ 145 B.T.U. 
 
 per horse-power per minute. 
 
 The efficiency for the turbine without friction by equation 
 (291), page 481 is 
 
 e = cos^ a = 0.883. 
 
 The efficiency of the nozzles has already been determined to be 
 0.85 by the selection of 0.15 for y. Let us further assume that 
 
PRESSURE AND VELOCITY COMPOUNDING 507 
 
 the combined effect of losses in the vanes may be taken to be 
 equivalent to making y^ equal to 25 so that i — >'(j is 0.75; this 
 is in effect the efficiency factor for the vanes as affected by friction. 
 If, further, we take the mechanical efficiency of the machine as 
 0.9, then the combined efficiency for the turbine will be 
 
 0.285 X 0.883 X 0-85 X 0.75 X 0.9 = 0.144. 
 
 This corresponds to 
 
 42.42 ~ 0.144 =^ 295 B.T.U. 
 
 per horse-power per minute. Now it costs to make steam from 
 water at 102°, and at an absolute pressure of 165 pounds, 11 23 
 (r^ + 5^1 — ^2) thermal units, as already calculated in the deduc- 
 tion of the efficiency of adiabatic action. Consequently the steam 
 per horse-power per hour will be 
 
 295 X 60 ^ 1123 - 15.7 
 
 pounds per brake horse-power per hour. To this should properly 
 be added a fraction, to allow for leakage and radiation, amounting 
 to five or ten per cent; this added amount of steam will affect 
 the size of the high pressure nozzles only in this case, and as 
 extra nozzles are sure to be provided we will take no further 
 account of it than to say that the steam consumption may amount 
 to 16.5 to 17.3 pounds per brake horse-power per hour. 
 
 The heat contents which have already been found give for the 
 adiabatic available heat 
 
 1193 - 871 - 322, 
 
 and if this be divided equally we have 161 thermal units per 
 stage. Using 0.15 for y in the nozzles, the velocity of the jet 
 becomes 
 
 V =^2 X 32.2 X 778 X 161 X0.85 =2610 
 
 feet per second. 
 
 Assuming that we may use three sets of moving vanes the 
 velocity for them will be 
 
 2610 -- (2 X 3) = 435 
 feet per second. 
 
5o8 STEAM-TURBINES 
 
 If we choose a diameter of 4^ feet for the pitch surface of the 
 vanes it will lead to the use of 1850 revolutions per minute. 
 
 To find the intermediate pressure we may take for the heat 
 contents at that pressure 
 
 1193 - 161 = 1032, 
 
 which in the temperature-entropy table corresponds to 223° F., 
 or 18.2 pounds. Since the back- pressure for the nozzles is rela- 
 tively small in each case, the nozzles will have throats for which 
 the velocities must be determined in order to find the areas. 
 The throat pressures may be taken to be 
 
 165 X 0.58 = 95.6; 18.2 X 0.58 = 10.6, 
 
 and the corresponding temperatures are 324° and 196° F. 
 
 Since the rounding of the nozzle is likely to give but small 
 area for friction compared with the cone for expanding to the 
 back-pressure, we may assume adiabatic expansion to the throat 
 and allow the entire value of >' = 0.15 for the computation for 
 the exit. This appears to agree with tests showing that such 
 nozzles give nearly full theoretical discharge. The heat contents 
 by the temperature-entropy table at entropy 156 and 324° F. 
 amounts to 1149 b.t.u., the value of x is 0.964 and the specific 
 volume is 4.45 cubic feet. The apparent available heat is 
 
 1193 - 1149 = 44B.T.U., 
 
 giving a throat velocity of 
 
 V ^ V2 X 32.2 X 778 X 44 = 1480. 
 
 The. apparent available heat for producing velocity at the exit 
 with y taken at 0.15 is 
 
 0.85 X 161 = 137 B.T.U., 
 
 leaving for the available heat 
 
 1 193 - 137 = 1056 B.T.U. 
 The heat of the liquid is 191 so that with 959 for r we have 
 x' = xV ^ r' = (1056 — 191) -^- 959 -= 0.902. 
 
PRESSURE AND VELOCITY COMPOUNDING 509 
 
 The specific volume is 
 
 v= (xu -\- a) = 0.902 (21.6 — 0.016) + 0.016 = 19.5. 
 
 With 15.7 pounds of steam per brake horse-power per hour 
 and 770 horse-power the steam per second is 
 
 w = 15.7 X 770 -^ 3600 = 3.36 pounds. 
 
 The combined area of discharge of all the first stage nozzles 
 is therefore, with the velocity at exit equal to 2610 feet, 
 
 3.36 X 19.5 X 144 -^ 2610 = 3.62 square inches. 
 
 The nozzles of turbines of this type are sometimes made square 
 at the exit so as to give a continuous sheet of steam to act on the 
 vanes. If the side of such a nozzle were made half an inch 
 there would appear to be fourteen and a half such nozzles; the 
 turbines would probably be given 16 or 18 of them, which could 
 be arranged in two groups. Since the angle of the nozzle is 20° 
 the width of the jet measured along the perimeter of the wheel 
 will be 
 
 0.5 ^ sin 20° = 0.5 -^ 0.3420 = 1.46 inch. 
 
 Allowing one-fourth of the width of the orifice for the thickness 
 of the walls, the width occupied by eight nozzles would be 
 
 1.46 X 1.25 X 8 = 14J inches. 
 
 The combined throat area of all the nozzles will be 
 
 3.36 X 4.45 X 144 -^ 1480 = 1. 41 square inch. 
 
 Dividing by 14I, the number of necessary nozzles, gives for 
 the throat area of one nozzle 
 
 1. 41 -^ 14.5 = 0.0972 square inch, 
 
 so that the diameter will be about 0.35 of an inch. 
 
 A method of calculation for the second set of nozzles consistent 
 with the method of determining the intermediate pressure is as 
 follows: The pressure in the throat has already been found to 
 be 10.6 pounds, corresponding to 196° F., for which the tem- 
 perature-entropy table at 1.56 units of entropy gives for heat 
 
5IO 
 
 STEAM-TURBINES 
 
 contents 998. The heat contents at 18.2 pounds (223) has 
 already been found to be 1032, so that the available heat for 
 adiabatic flow appears to be 34 B;T.u., which gives for the 
 velocitv in the throat 
 
 V = \^2 X 32.2 X 778 X 34 = 1300 feet. 
 
 The next step is the determination of the qualities at the throat 
 and exit, and from them the specific volumes. Now of the 
 161 B.T.u. available for adiabatic flow in the first nozzles only 
 a part has actually been changed into work, because there was 
 allowed 0.15 for friction in the nozzle, and 0.25 for losses in the 
 guides and vanes, while the efficiency due to angles and velocities 
 was 0.883. The heat changed into work was therefore 
 
 161 X 0.85 X 0.75 X 0.883 = 90-6 B.T.u. 
 
 Consequently the heat left in the steam as it approaches the 
 second nozzle is 
 
 1193 — 91 = 1102 B.T.u. 
 
 per pound. Now r has the value 959 at 223 F., and q is 191, so 
 that the quality is 
 
 X = (1102 - 191) ^ 959 = 0.950. 
 
 If the flow from the entrance to the throat 34 b.t.u. are 
 assumed to be changed into kinetic energy leaving for 
 
 xr + q = 11*02 — 34 = 1068, 
 
 and as r is equal to 978 and q is 164 at 196° F., we have 
 
 X = (1068 — 164) -^ 978 = 0.925 
 
 at the throat of the second nozzle. 
 
 Allowing as before 0.15 for the friction of the nozzle there will 
 be 
 
 0.85 X 161 = 137 B.T.u. 
 
 changed into kinetic energy for the entire nozzle leaving 
 
 xr -\- q = 1 102 — 137 = 965 B.T.u.; 
 and at i pound or 102° F., the values of r and q are 1043 and 70 
 X = (965 - 70) -V- 1043 = 0,858 
 
PRESSURE AND VELOCITY COMPOUNDING 511 
 
 at exit from the second set of nozzles. The volume of saturated 
 steam at 102° is 335 cubic feet, and with x equal to 0.858 the 
 specific volume is 288 cubic feet. Consequently, with a weight of 
 3.36 pounds per second, and a velocity of 2610 feet, the united 
 areas of all the nozzles at exit will be 
 
 3.36 X 288 X 144 ^ 2610 = 55.6 square inches. 
 
 Now the perimeter of a circle having a diameter of 4J feet is 
 about 170 inches. Allowing for the sine of the angle 20° and 
 one-fifth for thickness of guides there will be about 43.5 inches 
 for the united width of passages between guides so that the 
 radial length will be 
 
 55-6 -^ 43-5 = 1-27 inch. 
 
 The specific volume of saturated steam at 197° is 36.2 cubic 
 feet, so that with x equal to 0.925 the specific volume is 33.5. 
 Now the areas are proportional to the specific volumes and 
 inversely as the velocities, consequently the length of guides at the 
 throat is 
 
 1.28 X ^-^^ X ^^ = 0.30 inch. 
 1300 285 
 
 The length of the vanes and guides can be found by the method 
 on page 500, using relative velocities for the vanes and absolute 
 velocities for the guides. The velocities decrease as indicated 
 by Fig. 107, page 487, and the lengths must be correspondingly 
 increased. In this case, however, there are two considerations 
 which influences the lengths that should be finally assigned to the 
 guides and vanes, (i) The thickness may be diminished, which 
 tends to decrease the length. (2) Friction reduces the velocity 
 which tends to increase the length. Friction of course diminishes 
 all velocities including the peripheral velocity of the wheel, but a 
 proper discussion of that matter would be both long and uncertain. 
 
 Attention has already been called to the defect of this method 
 of making all the calculations at a single value of entropy and 
 trying to allow for friction and other losses by simple factors. 
 The difficulty is aggravated in this case by the fact that the 
 
512 
 
 STEAM-TURBINES 
 
 second set of nozzles or guides have proper throats. The proper 
 method after having selected a set of intermediate pressures 
 appears to be to calculate the turbine step by step. The steam 
 supplied to the second set of nozzles (or guides) has been found 
 to have the quality 0.950, and this is probably a good approxima- 
 tion to the actual condition, even if allowance is made for radi- 
 ation and leakage. The temperature-entropy table gives for 
 steam having that quality and the temperature 223, the 
 entropy as nearly 1.66. At that entropy the heat contents at 
 the initial, throat and exit pressures, are given in the following 
 table with also the quality and specific volume at the throat; 
 the table also gives the quality and specific volumes at exit with 
 y equal to 0.15. 
 
 Pressure. 
 
 Tempterature. 
 
 Heat contents. 
 
 Quality. 
 
 Specific volume. 
 
 18.2 
 
 10.6 
 
 I .0 
 
 223 
 196 
 102 
 
 1 100 
 
 1063 
 
 927 
 
 0.92 
 0.85 
 
 3 33 
 28.5 
 
 The apparent available heat for adiabatic flow to the throat 
 is now 
 
 iioi - 1063 = 37, 
 
 which would give a velocity of 
 
 F = V2 X 32.2 X 778 X 37 =- 1360, 
 
 instead of 1280 as previously found. The apparent available 
 heat to the exit with 0.15 for the friction factor is now 
 
 (iioi - 927)0.85 = 147, 
 
 which gives for the exit velocity 
 
 V = V2X32T2X 778 X 147 = 2710, 
 
 instead of 2610 previously computed. 
 
 This comparison shows that the intermediate pressure deter- 
 mined by the customary method will be too high, and that to 
 obtain the desired distribution of temperature the factors for 
 
CURTIS TURBINE 
 
 513 
 
 the lower stages must be modified arbitrarily as may be deter- 
 mined by comparison with practice. 
 
 Curtis Turbine. — Fig. 114 shows a partial elevation and section 
 of the essential features of a Curtis turbine, which has four 
 chambers and two sets of moving vanes in each chamber. The 
 axis of the turbine is vertical which demands an end bearing, 
 the difficulties of which construction appear to have been met by 
 
 Fig. 114. 
 
 pumping oil under pressure into the bearing, so that there is 
 complete lubrication without contact of metal on metal. The 
 condenser is placed directly under the turbine, and the electric- 
 generator is above on a continuation of the shaft. The arrange- 
 ment appears to be convenient, and in particular to demand 
 small floor space only. 
 
 When used for marine propulsion the Curtis turbine has a 
 horizontal shaft from necessity, and has a large number of stages. 
 
514 
 
 STEAM-TURBINES 
 
 A turbine developing 8000 horse-power has seven pressure 
 stages, each of which but the first has three velocity stages, that 
 one has four velocity stages. The diameter is ten feet and 
 the peripheral velocity is 180 feet per second. 
 
 Tests on Curtis Turbines. — The following tables give tests 
 on two Curtis turbines, having two and four pressure stages, 
 respectively; both were made by students at the Massachusetts 
 Institute of Technology. 
 
 TESTS ON A TWO-STAGE CURTIS TURBINE. ' 
 
 Darling and Cooper.* 
 
 Duration minutes 
 
 Throttle pressure gauge .... 
 
 Throttle temperature F 
 
 Barometer inches 
 
 Exhaust pressure absolute pounds 
 
 Load kilowatts 
 
 Steam per kilowatt hour, pounds 
 Thermal units kilowatt minute . 
 
 120 
 
 120 
 
 120 
 
 120 
 
 146.3 
 
 145-3 
 
 143-2 
 
 143-9 
 
 512 
 
 520 
 
 464 
 
 502 
 
 29.8 
 
 29.9 
 
 29.9 
 
 29.9 
 
 0.82 
 
 0.79 
 
 0.92 
 
 0.84 
 
 161 .4 
 
 255-7 
 
 374.0 
 
 512.9 
 
 21.98 
 
 19.63 
 
 19.98 
 
 18.43 
 
 440 
 
 396 
 
 392 
 
 369 
 
 60 
 
 149-3 
 512 
 
 30.0 
 0.85 
 731-9 
 
 17-75 
 357 
 
 If the efficiency of the dynamo is taken at 0.9 and one kilowatt 
 is rated as 1.34 horse-power, the steam and heat consumptions 
 per brake horse-power are, for the best result, 
 
 1 1.8 pounds 239 B.T.u. 
 
 TESTS ON A FOUR-STAGE CURTIS TURBINE 
 
 COE AND TRASK.f 
 
 Duration minutes 
 
 Boiler pressure, pounds 
 
 Vacuum inches 
 
 Load kilowatts 
 
 Steam per kilowatt hour pounds 
 Thermal units per kilowatt (minute) 
 
 60 
 
 60 
 
 60 
 
 180 
 
 152 
 
 149.6 
 
 152-1 
 
 150 
 
 28.5 
 
 28.2 
 
 28.8 
 
 28.4 
 
 282 
 
 380 
 
 523 
 
 562 
 
 21.4 
 
 20.3 
 
 18.8 
 
 19-5 
 
 394 
 
 370 
 
 352 
 
 360 
 
 120 
 
 150.4 
 
 28.3 
 788 
 19-3 
 
 357 
 
 * Thesis, M. I. T., 1905. 
 t Thesis, M. I. T., 1906. 
 
REACTION TURBINES 
 
 515 
 
 m 
 
 Taking the efficiency of the dynamo as 0.9 and a kilowatt as 
 1.34 horse-power, the best result is equivalent to a steam con- 
 sumption of 12.6 pounds and a heat consumption of 237 thermal 
 units. 
 
 Reaction Turbines. — The essential feature of a reaction 
 turbine is a fall of pressure and a consequent increase of veloc- 
 ity in the passages among the vanes of the turbine. Since 
 such wheels commonly are affected by impulse also they are 
 sometimes called impulse-reaction wheels, but if properly under- 
 stood the shorter name need not lead to confusion. In conse- 
 quence of the feature named the 
 relative exit velocity V^ is greater 
 than Fj. Another consequence is 
 that steam leaks part the ends 
 of the vanes which are usually 
 open, and there is also leakage 
 past the inner ends of the guides 
 which are also open; this feature 
 is shown by Fig. 115. 
 
 The reaction turbine is always 
 made compound with a large 
 number of stages, one set of guides 
 and the following set of vanes 
 being counted as a stage. In 
 consequence the exit pressure either 
 from the guides or the vanes is 
 
 only a little less than the entrance pressure, and the passages 
 are all converging. 
 
 There is no attempt to avoid axial thrust, and therefore the 
 exit angle 7 from the vanes may be made small; it is commonly 
 equal to the exit angle a from the guides. A common value 
 for these angles is 20°. 
 
 The guides and vanes follow alternately in close succession 
 leaving only the necessary clearance; the kinetic energy due to 
 the absolute exit velocity from a given set of vanes is not lost but 
 is available in the next set of guides. The turbines are usually 
 
 Fig. 115. 
 
5i6 STEAM-TURBINES 
 
 made in two or three sections as shown by Fig. 117, page 526, 
 and it is only at the end of a section that the kinetic energy due 
 to the absolute exit velocity is rejected; at the end of a section 
 this kinetic energy is changed into heat and is in a manner 
 available for the next section; at the end of the turbine it is of 
 course wasted. Since there are usually sixty stages or more 
 the influence of the kinetic energy rejected is likely to be less 
 than five per cent and it may properly be combined with the 
 general factor to allow for friction and leakage past the ends of 
 the guides and vanes. Both influences reduce the change 
 of heat into work applied to the turbine and increase the 
 value of the quality x and also of the specific volume of the 
 mixture of steam and moisture. 
 
 Since the exit absolute velocity from the vanes is applied to 
 driving the steam into the next set of guides, there is no direct 
 advantage in avoiding velocity of whirl at this place; it is only 
 necessary to give the guides the proper angle at entrance to 
 receive the steam. Indirectly it is disadvantageous to have a 
 high velocity at the entrance to the guides, or, for that matter, in 
 any part of the turbine, as the friction is probably proportional 
 to the square of the velocity as has been assumed in the use of 
 the friction factor y. 
 
 The steam enters a set of guides with a certain velocity, i.e., 
 the exit absolute velocity from the preceding set of vanes. 
 On account of the loss of pressure in the guides a certain amount 
 of heat is .changed into kinetic energy and the equivalent increase 
 of velocity may be added to the entrance velocity to find the 
 exit velocity which is of course an absolute velocity. This abso- 
 lute velocity combined with the velocity of the guides gives the 
 relative entrance velocity to the vanes. To this entrance veloc- 
 ity is to be added the gain in velocity due to change of heat into 
 kinetic energy in the vanes, in order to find the relative exit 
 velocity. The ratio of the heat used in the vanes to that used 
 in the entire stage is called the degree of reaction. Commonly 
 the degree of reaction is one-half; that is, the amount of heat 
 used in the vanes is equal to that used in the guides; and 
 
CHOICE OF CONDITIONS 
 
 517 
 
 the gain of velocity in the vanes is equal to the gain in the 
 guides. 
 
 In Fig. 116 let V^ be the velocity of the steam leaving the 
 guides and V the velocity of the vanes; then V^ is the relative 
 velocity of the steam entering the vanes. V^ is the relative exit 
 velocity which is greater than V^ on account of the change of 
 heat into work. F4 is the absolute exit velocity from the vanes 
 with which the steam enters the next set of guides. If the con- 
 ditions for successive stages are the same, F4 is also equal to the 
 entrance velocity to the set of guides of the stage under discussion, 
 and if ce is laid off at ac' then c'b is the gain of velocity in the 
 
 Fir.. 116. 
 
 guides. Consequently to construct F3 we may lay off c^' equal 
 to ac and e'd equal to c'b. Now a and 7 are commonly made equal, 
 and therefore the triangles abc and cde are equal. Consequently 
 the angle 5 for the entrance to the guides is equal to /? at the 
 entrance to the vanes. In fact the guides and vanes have the 
 same form. 
 
 Choice of Conditions. — The foregoing discussion shows that 
 the designer is given a wider latitude in his choice of conditions 
 for the compound reaction turbines than appeared possible 
 for impulse turbines, though if the restriction of no axial thrust 
 were removed from the latter the comparison would be quite 
 different. 
 
5^8 
 
 STEAM-TURBINES 
 
 The most authoritative statement of the preferable conditions 
 in practice for reaction turbines of the Parson's type is formed 
 in a paper by Mr. E. M. Speakman,* but much of the infor- 
 mation in the hands of the builders " being based on long and 
 costly experiments, much reticence is observed regarding their 
 publication." The statement of practical conditions is therefore 
 based on such information as can be gleaned from his paper, 
 with obvious applications by ordinary methods. Factors for 
 friction and leakage are largely conjectural, as must in fact be 
 the case at present for all turbines, and for our purpose may 
 perhaps be limited to giving the student an idea of the nature of 
 the problems. 
 
 The ratio of the velocity of the vanes to the velocity of the 
 steam has varied in turbines built by the Parsons Company 
 from 0.25 to 0.85. In general the ratio may be taken as 0.6. 
 
 These turbines are usually built with two or three diameters 
 of the revolving cylinder or rotor as shown in Fig. 117. The 
 following tables give the practice of that company with regard 
 to peripheral speed and number of stages. 
 
 PARSONS TURBINES — ELECTRICAL WORK. 
 
 
 Peripheral speec 
 
 , feet per second. 
 
 
 
 Normal output 
 
 
 
 Number of 
 stages. 
 
 Revohitions 
 
 kilowatts. 
 
 
 
 per minute. 
 
 
 First expansion. 
 
 Last expansion. 
 
 
 
 5000 
 
 135 
 
 33° 
 
 70 
 
 750 
 
 3500 
 
 138 
 
 280 
 
 75 
 
 1200 
 
 2500 
 
 125 
 
 300 
 
 84 
 
 1360 
 
 1500 
 
 125 
 
 360 
 
 72 
 
 1500 
 
 1000 
 
 125 
 
 '250 
 
 80 
 
 1800 
 
 750 
 
 125 
 
 260 
 
 77 
 
 2000 
 
 500 
 
 120 
 
 285 
 
 60 
 
 3000 
 
 250 
 
 100 
 
 210 
 
 72 
 
 3000 
 
 75 
 
 100 
 
 200 
 
 48 
 
 4000 
 
 Trans. Inst. Eng. and Shipbldn., Scot., vol. xlxix, 1905-06. 
 
CHOICE OF CONDITIONS 
 
 19 
 
 PARSONS TURBINE — MARINE WORK. 
 
 Type of vessel. 
 
 High speed mail steamers . 
 Intermediate mail steamers 
 
 Channel steamers 
 
 Battleships and large cruisers 
 
 Small cruisers 
 
 Torpedo crafts 
 
 Peripheral speed, feet 
 per second. 
 
 H.P. 
 
 LP. 
 
 70-80 
 
 I 10-130 
 
 80-90 
 
 110-135 
 
 90-105 
 
 120-150 
 
 85-100 
 
 115-135 
 
 105-120 
 
 130-160 
 
 1 10-130 
 
 160-210 
 
 Ratio of 
 
 velocities, 
 
 vanes to 
 
 steam. 
 
 0.45-0 
 0.47-0 
 0.37-0 
 o . 48-0 
 
 0.47-0 
 0.47-0 
 
 Number 
 
 of 
 
 shafts. 
 
 4 
 
 3 
 4 
 
 3-4 
 3-4 
 
 The Westinghouse Company have used much higher veloc- 
 ities of vanes for electrical work than given in the above tables ; 
 as much as 170 feet per second for the smallest cylinder and 
 375 for the largest cylinder. 
 
 The blade height should be at least three per cent of the 
 diameter of the cylinder in order to avoid excessive leakage 
 over the tips. Mr. Speakman says that leakage over the tips 
 of the blades is perhaps not so detrimental on account of actual 
 loss by leakage as because it upsets calculations regarding 
 passages by increasing the steam volume. 
 
 The following equation represents Mr, Speakman's diagram 
 for clearances over tips of vanes, 
 
 clearance in 
 inches 
 
 o.oi + 0.008 diam. in feet. 
 
 The proportions of blades may be taken from the following 
 
 table: 
 
 PROPORTIONS OF BLADES— INCHES. 
 
 Height 1 
 
 Width ^ 
 
 Pitch i| 
 
 Axial clearance ^ 
 
 Mr. Parsons * gives for the efficiency of the steam in the 
 turbine blades themselves 0.70 to 0.80. 
 
 * Jnst. Naval Arch., 1903. 
 
 2 
 
 3 
 
 4 
 
 6 
 
 8 
 
 ID 
 
 12 
 
 M 
 
 18 
 
 21 
 
 24 
 
 .30 
 
 -i 
 
 
 \ 
 
 h 
 
 f 
 
 * 
 
 i 
 
 i 
 
 I 
 
 I 
 
 I* 
 
 li 
 
 1* 
 
 li 
 
 a 
 
 I'i 
 
 2* 
 
 2i 
 
 ^ 
 
 2^ 
 
 ,ii 
 
 ^\ 
 
 ^% 
 
 4 
 
 A 
 
 i 
 
 tV 
 
 -i 
 
 tV 
 
 h 
 
 \ 
 
 ^ 
 
 h 
 
 f 
 
 W 
 
 i 
 
520 
 
 STEAM-TURBINES 
 
 In addition to the leakage past the tips of the blades which 
 cannot in practice be separated in its effects from friction, 
 there is likely to be a considerable leakage past the balance 
 pistons which will be described in connection with Fig. 117. 
 This leakage is in the end direct to the condenser, and no account 
 need be taken of it in the design of the blading of the turbine; 
 but allowance should be made in comparing theoretical calcula- 
 tions with results of tests. 
 
 Design for a Reaction Turbine. — Let us take for the principal 
 conditions the delivery of 500 kilowatts of electrical energy, which 
 with an efficiency of the dynamo of about 0.9 will correspond 
 to 770 brake horse-power, as for the calculation on page 506. Let 
 the initial pressure be 150 pounds by the gauge, and the vacuum 
 be 28 inches. The absolute pressures corresponding are 165 
 pounds and one pound, and the temperatures are 365°.9 and 
 102° F. The calculation referred to gives for the thermal 
 efficiency of adiabatic action 0.285, which corresponds to 
 145 B.T.u. per horse-power per minute. If we allow 0.60 for 
 the turbine efficiency, and ten per cent for leakage to the con- 
 denser and radiation, and take 0.9 for the mechanical efficiency 
 we shall have for the combined efficiency of the turbine 
 
 0.285 X 0.60 X 0.9 X 0.9 = 0.139. 
 
 This will give for the heat and steam consumption per horse- 
 power, 16.3 pounds per hour and 305 b.t.u. per minute. These 
 are to be compared with results of tests to determine whether 
 the constants assumed are proper. 
 
 For the estimate of the weight of steam to be used in deter- 
 mining the dimensions of the turbine we should omit the factor 
 for leakage to condenser and radiation, which will give for the 
 steam per horse-power per hour 14.7 pounds. The weight of 
 steam per second to be used in computing passage therefore 
 becomes 
 
 w = 14.7 X 770 -^ 3600 = 3.15 pounds. 
 
 Let the peripheral speed of the smallest cylinder be taken as 
 225 feet per second, and let the intermediate and low-pressure 
 
DESIGN FOR A REACTION TURBINE 521 
 
 cylinders be i J and 2 J times the diameter of the small cylinders. 
 Let the peripheral speed be 0.75 of the steam velocity, then the 
 latter will be 300 feet per second. If the exit angles for guides 
 and vanes be taken as 20° and if the degree of reaction is 0.5, 
 the velocities and angles will be represented by Fig. 116, page 
 517. In that figure 
 
 gb = Fj cos 20° = 0.940 V^ ; 
 
 and as V is 0.75 V^, 
 
 we have gc = (0.940 - 0.75) V^ = 0.190 V^. 
 
 But ag = Fj sin 20° = 0.342 F^; 
 
 and tan /? = 0.342 -^ 0.190 = 1.800 .•. /? = 61°. 
 
 The angle /? is given to the backs of the blades, and the angle at 
 the faces is somewhat larger, as will appear by Fig. 115, page 516; 
 in consequence there is some impulse at the entrance to the vanes. 
 To get the relative velocity we have 
 
 ^2 = ^S + ^^ = (0-342 + 0.190 ) F^' 
 .-. F, = 0.392 Fj. 
 
 But it is shown on page 518 that for the conditions chosen the 
 increase of velocity in either guides or vanes is equal to 
 
 Fj - F2 = (i - 0.392) F^ = 0.608 X 300 = 182 
 
 feet per second. 
 
 Now the equation for velocity when h thermal units are avail- 
 able is 
 
 F = V2 X 32.2 X 778/^, 
 and conversely 
 
 h = 182' ^ (64-4 X 778) = 0.661 B.T.U. 
 
 This is the amount with allowance for friction and leakage 
 past the ends of the blades which has been assigned the factor 
 0.6, so that for the preliminary adiabatic computation we may 
 take for one set of blades 
 
 0.661 ^ 0.6 = I.I B.T.U. , 
 
522 STEAM-TURBINES 
 
 and for a stage, consisting of a set of guides and vanes, we may 
 take for the basis of the determination of the proper number of 
 stages 2.2 B.T.u. per pound of steam used. 
 
 It appears on page 508 that adiabatic expansion from 165 
 pounds absolute to one pound absolute gives 322 thermal units 
 for the available heat. If this is to be distributed to the stages 
 of a turbine with 2.2 units per stage, then the total number of 
 stages will be 
 
 322 -7- 2.2 = 146 
 
 stages. This is under the assumption that the turbine has a 
 uniform diameter of rotor with 225 feet for the velocity of the 
 vanes; we have, however, taken the intermediate diameter ij 
 times the high-pressure and the low-pressure 2 J times. The 
 peripheral velocities will have the same ratios, and the amounts 
 of available heat per stage will be proportional to the squares of 
 those ratios, namely, 2.25 and 6.25. Consequently the amounts 
 of heat assigned per stage will be as follows : 
 
 High-pressure Intermediate Low-pressure. 
 
 2.2 4.95 13.75 
 
 If we decide to use ten low-pressures and twenty intermediate 
 stages they will require 
 
 10 X 13.75 + 20 X 4.95 = 236.5 B.T.U., 
 
 leaving 84.5 thermal units which will require somewhat more 
 than 38 stages. Reversing the operation it appears that one 
 distribution calls for 
 
 10 X 13.75 + 20 X 4-95 + 38 X 2.2 - 320 B.T.u. 
 
 For convenience of manufacture it is customary to make 
 several stages identical, that is, with the same length of blades, 
 clearances, etc.; this of course will derange the velocities to some 
 extent and interfere with the realization of the best economy. 
 That part of the cylinder which has the same length of blades 
 is known technically as a barrel. Let there be three barrels for 
 each cylinder, making nine in all, which may be conveniently 
 numbered, beginning at the high-pressure end and may have 
 
DESIGN FOR A REACTION TURBINE 
 
 523 
 
 the number of stages assigned above. In that table is given also 
 the number of the stage counting from the high-pressure end, 
 which is at or near the middle of the length of the barrel, for 
 which calculations will be made. The values of the heat con- 
 tents xr + q are readily found for each stage given in the table 
 by subtracting the amounts of heat changed into kinetic energy, 
 down to that stage, allowing 2.2 for each stage of the high- 
 
 COMPOUND REACTION TURBINE. 
 
 
 
 
 
 
 
 fli 
 
 •§ 
 
 •a 
 
 § 
 
 
 
 
 
 
 m 
 
 
 
 
 % 
 
 ^ 
 
 •3 
 
 ft 
 
 
 
 8 
 
 
 
 1 
 
 
 3 
 
 
 42 
 
 u 
 
 4) « 
 
 1 
 
 1 
 
 
 Specific 
 volumes. 
 
 3 
 
 1 
 
 1 
 
 1 
 
 E 
 
 3 
 
 1 
 
 .•2 
 
 1 
 
 a, 
 
 H 
 
 g 
 
 
 o«< 
 
 32 
 
 "o 
 
 i 
 
 1 
 
 a 
 
 
 u 
 
 I — 
 
 14 
 
 S 
 
 / 
 
 P 
 
 xr+Q 
 
 x'r+q 
 
 Q 
 
 r 
 
 x' 
 
 S V 
 
 
 I— 
 
 7 
 
 350 
 
 135 
 
 1178.6 
 
 ii8s 
 
 321 
 
 867 
 
 0.985 
 
 3.32 
 
 3-27 
 
 0.415 
 
 
 2 — 
 
 12 
 
 20 
 
 323.5 
 
 93.5 
 
 1150.0 
 
 1168 
 
 294 
 
 887 
 
 
 
 985 
 
 4.65 
 
 4.57 
 
 0.578 
 
 
 3— 
 
 12 
 
 32 
 
 300 
 
 67.2 
 
 1123.6 
 
 1152 
 
 270 
 
 904 
 
 
 
 976 
 
 6.39 
 
 6.22 
 
 0.787 
 
 II— 
 
 4— 
 
 8 
 
 42 
 
 271 
 
 42.6 
 
 1090.6 
 
 1132 
 
 240 
 
 924 
 
 
 
 965 
 
 9-79 
 
 9.43 
 
 0.532 
 
 
 5— 
 
 6 
 
 49 
 
 241 
 
 25.4 
 
 1056.0 
 
 IIIO 
 
 210 
 
 945 
 
 
 
 954 
 
 15.9 
 
 15.2 
 
 0.854 
 
 
 6— 
 
 6 
 
 55 
 
 217.5 
 
 16.4 
 
 1026. 3 
 
 1093 
 
 186 
 
 962 
 
 
 
 940 
 
 24.1 
 
 22.7 
 
 1.252 
 
 ni— 
 
 7— 
 
 4 
 
 60 
 
 184 
 
 8.19 
 
 983.9 
 
 1068 
 
 153 
 
 986 
 
 
 
 929 
 
 46.2 
 
 42.7 
 
 0.867 
 
 
 8— 
 
 3 
 
 64 
 
 147 
 
 3.44 
 
 935.8 
 
 1039 
 
 IIS 
 
 1012 
 
 
 
 913 
 
 104 • 
 
 94.4 
 
 1.92 
 
 
 9— 
 
 3 
 
 67 
 
 117 
 
 1-55 
 
 894.5 
 
 1014 
 
 85 
 
 1033 
 
 0.901 
 
 221 
 
 199 
 
 4.04 
 
 pressure cylinder, 4.95 for each intermediate stage and 13.75 ^^^ 
 each low-pressure stage. For example, the forty-ninth stage has 
 its heat contents found by subtracting from the initial heat con- 
 tents 1 1 93, the amount 
 
 38 X 2.2 + II X 4-95 = 138, 
 
 leaving for the heat contents after that stage 1055 thermal units. 
 The probable heat contents allowing for friction and leakage is 
 found by subtracting the product of the above quantity by the 
 factor 0.6. Giving 
 
 1 193 — 138 X 0.6 = 1111 B.T.U. 
 
 Having the values oi odr ■\- q obtained in this way, the values of 
 xf can be found by subtracting the heat of the liquid q^ and 
 
524 STEAM-TURBINES 
 
 dividing the remainder by r. Finally the specific volumes are 
 computed by the equation 
 
 V = x'w + t; 
 
 but in practice cr may be neglected giving 
 
 u = x's 
 
 because we have either x nearly equal to unity or else s will be 
 larger compared with cr. 
 
 The steam velocity for the first cylinder is 300 feet per second, 
 the weight of steam per second is 3.15 pounds and thes pecific 
 volume at the seventh stage, i.e., the middle of the first barrel, 
 is 3.27 cubic feet. The effective area must therefore be 
 
 WV 'l.\^ X S-27 . ^ 
 
 a = 144 -— = 144 - — - — ^ ' =4.94 square mches. 
 V 300 
 
 To this must be added a fraction of one-third or one-fourth to 
 allow for the thickness of the blades, and the result must be 
 divided by sine a in order to find the area of the peripheral 
 ring through which the steam will flow. Taking one-fourth 
 for the fraction in this case, and 20° for a, we have 
 
 4.94 X 5 o . , 
 
 -^-^-^ ^ = 18.1 square mches. 
 
 0.342 X 4 
 
 It is recommended that the height of the blades shall be 0.03 
 of the diameter, which gives for the expression for the peripheral 
 ring 
 
 0.03 Tzd"^ = 18. 1. 
 
 .'. d = V 18.1 -^ 0.03 n = 13.85 inches. 
 
 The diameters of the intermediate and low-pressure cylinders 
 will be 
 
 d^ = 13.85 X 1.5 = 20.77 in.; d^ = 13.85 X 2^ = 34.62 in. 
 
 The length of blade at the seventh stage will be 
 
 0.03 X 13.85 = 0.415 inch. 
 
DESIGN FOR A REACTION TURBINE , 525 
 
 and this length will be assigned to all the blades of the first 
 barrel. The blades of the second and third barrels will have 
 their lengths increased in proportion to the specific volumes at the 
 middle of those barrels, as set down in the table. The effect 
 of increasing the diameters of the intermediate and low-pres- 
 sure cylinders is to increase the steam velocity, and the peripheral 
 length of the steam passage, both in proportion to the diameter. 
 Consequently the lengths of the blades for these cylinders are 
 directly proportional to the proper specific volumes and inversely 
 proportional to the squares of the diameters. Thus the length 
 of the blades at the forty-second stage, i.e., the middle of the 
 fourth barrel is 
 
 0.415 X 9.43 . , 
 
 — ^^-^ ^£^ = 0.532 mch. 
 
 3-27 X 1.5 
 
 The lengths are computed for the other barrels in the same way, 
 using 2.5 for the ratio of the low-pressure diameter. 
 
 Since the diameter of the small cylinder is 13.85 inches and 
 the speed of the vanes on it is 225 feet per second, the revolutions 
 per minute are 
 
 22s X 60 X 12 
 
 Parsons Turbine. — The essential features of the Parsons 
 turbine are shown by Fig. 117. Steam is admitted at A and 
 passes in succession through the stages on the high-pressure 
 cylinder, and thence through the passage at E to the stages of 
 the intermediate cylinder; after passing through the intermediate 
 stages it passes through G to the low-pressure stages and finally 
 by B to the condenser. 
 
 The axial thrust is counterbalanced by the dummy cylinders, 
 C, C, C, the first receiving steam from the supply directly, the 
 second from the passage between the high and intermediate 
 cylinders through the pipe F, and the third through the pipe near 
 G from the passage between the intermediate and low-pressure 
 cylinders. Leakage past the dummy cylinders is checked by laby- 
 rinth packing, which is variously arranged to give a succession 
 
S26 
 
 STEAM-TURBINES 
 
 Fig. 117. 
 
 of spaces through which the steam must pass with narrow pass- 
 .ages, which throttle the steam as it passes from chamber to 
 chamber. One method is to let narrow strips of brass into 
 the surface of the cylinder and into the surface of the case; 
 these strips are adjusted to leave a very small axial clearance, 
 so that the steam is strongly throttled as it passes through. It 
 is reported that the labyrinth clearance is entirely successful in 
 reducing the leakage past the dummy cylinder to a small amount. 
 It is pointed out by Mr. Jude that the most effective throttling 
 is at the last section of the labyrinth, and that the other sections 
 are comparatively inefficient. This feature will be evident if an 
 attempt is made to calculate the loss by continual application of 
 Rankine's equations, page 432. Of course such a method can be 
 but crude, and yet its indications should be of value for estimating 
 leakage which should be small. 
 
 When applied to marine propulsion the dummy pistons are 
 omitted and the axial thrust is usefully applied to the propeller- 
 shaft. Since an absolute balance cannot be obtained, a thrust- 
 bearing is provided but it may have small bearing area and will 
 have but little friction. Stationary turbines also have a bearing 
 for residual unbalanced thrust. 
 
 Test on a Parsons Turbine. — A test on a Westinghouse- 
 
TEST ON A PARSONS TURBINE 
 
 527 
 
 Parsons turbine in Savannah was made under the direction of 
 Mr. B. R. T. Collins and reported by Messrs. H. O. C. Isenberg 
 and J. Lage,* which is interesting because the steam consumption 
 of the auxiliary machines was determined separately. The 
 data and results of tests on the turbine are given in the following 
 table. 
 
 The tests made at full load with varying degrees of vacuum 
 show clearly the advantage obtained in this machine from a 
 good vacuum, which amounted to a saving of 
 
 289 — 279 _ 
 289 
 
 0-035- 
 
 TESTS ON WESTINGHOUSE-PARSONS TURBINE. 
 Collins, Isenberg and Lage. 
 
 Duration minutes 
 
 Steam pressures, gauge . 
 
 Vacuum inches 
 
 Revolutions per minute . . 
 
 Load kilowatts 
 
 Steam consumption, pounds 
 
 per kilowatt-hour .... 
 
 per electric h.p. per hour . 
 Heat consumption b.t.u. 
 
 per kilowatt-minute 
 
 per horse-power per minute 
 
 i load. 
 
 J load. 
 
 Full load. 
 
 ij load. 
 
 60 
 
 60 
 
 60 
 
 60 
 
 60 
 
 45 
 
 131 
 28.1 
 3616 
 260 
 
 129 
 28.1 
 3601 
 
 379 
 
 128 
 
 25-7 
 3602 
 
 493 
 
 127 
 26.7 
 3612 
 501 
 
 128 
 28.0 
 3562 
 499 
 
 127 
 26.7 
 3540 
 629 
 
 243 
 18. 1 
 
 21.2 
 15-8 
 
 20.7 
 15,6 
 
 19.8 
 14.8 
 
 19.7 
 14.7 
 
 19.8 
 14.7 
 
 462 
 345 
 
 403 
 301 
 
 494 
 289 
 
 375 
 284 
 
 374 
 279 
 
 373 
 278 
 
 li load. 
 
 45 
 125 
 26.6 
 
 3537 
 733 
 
 20. 2 
 15-1 
 
 381 
 283 
 
 A great importance is attributed by turbine builders to obtaining 
 a low vacuum, in many cases special air-pumps and other devices 
 being used for that purpose. Unless discretion is shown both 
 in the design and operation of this auxiliary machinery, its size 
 and steam consumption is likely to be excessive, and what appears 
 to be gained from the vacuum may be entirely illusory. 
 
 * Thesis, M.I.T. 1906. 
 
528 STEAM-TURBINES 
 
 The steam consumption in pounds per hour for the several 
 auxiliary machines was as follows: 
 
 Centrifugal pump for circulating water .... 88i 
 
 Dry vacuum pump 212 
 
 Hot-well pump 42.8 
 
 II35-8 
 
 This total was equivalent to 0.115 of the steam consumption 
 of the turbine at full load and with 28 inches vacuum. Some 
 tests of turbine installations show twice or three times this 
 proportion. 
 
INDEX. 
 
 PAGE 
 
 Absolute temperature 56 
 
 Absorption refrigerating apparatus 411 
 
 Adiabatic for gases 63 
 
 for liquid and vapor 100 
 
 lines 17 
 
 Adiabatics, spacing of 31 
 
 After burning 319 
 
 Air-compressor, calculation ... 377 
 
 compound 366 
 
 cooling during compression . . 360 
 
 effect of clearance 363 
 
 efficiency 370 
 
 friction 369 
 
 fluid piston 359 
 
 moisture in cylinder 361 
 
 power expended 362 
 
 three-stage 368 
 
 Air, flow of 429 
 
 friction in pipes 380 
 
 pump 374,375 
 
 thermometer 368 
 
 Alternative method 49 
 
 Ammonia 123 
 
 Automatic and throttle engines . 276 
 
 Bell-Coleman refrigerating ma- 
 chine 413 
 
 Binary engines 180, 280 
 
 Blast-furnace gas-engine .... 335 
 
 Boyle's law 54 
 
 British thermal unit 5 
 
 Buchner 437 
 
 Calorimeter 191 
 
 separating 194 
 
 Thomas 195 
 
 throttling 161 
 
 Calorie 5 
 
 Callendar and Nicolson .... 231 
 
 PAGE 
 
 Carnot's engine 22 
 
 function 28 
 
 principle 26 
 
 Characteristic ec] nation 2 
 
 for gases 55 
 
 for superheated vapors .... no 
 
 Chestnut Hill, engine test .... 239 
 
 Compound air-compressor . . . 366 
 
 air-engine 384 
 
 Compound-engines 156 
 
 cross-compound 169 
 
 direct-expansion 163 
 
 indicator diagrams 162 
 
 low-pressure cut-off 161 
 
 ratio of cylinders 162 
 
 total expansions r6o 
 
 with receiver 159 
 
 without receiver . .' 158 
 
 Compressed-air 358 
 
 calculation 377 
 
 compound compressor .... 366 
 
 effect of clearance 363 
 
 friction, etc 369 
 
 hydraulic compressor .... 372 
 
 interchange of heat 365 
 
 storage of power 392 
 
 temperature after compression . 364 
 
 transmission of power .... 391 
 
 Compressed-air engine 384 
 
 calculation 388 
 
 compound 388 
 
 consumption 385 
 
 final temperature 385 
 
 interchange of heat 386 
 
 moisture in cylinder 3O1 
 
 volume of cylinder 386 
 
 Condensers 149 
 
 cooling surface 151 
 
 ejector 471 
 
 529 
 
530 
 
 INDEX 
 
 PAGE 
 
 Carburetors 334 
 
 Creusot, tests on engine .... 248 
 
 Critical temperature 71 
 
 Cut-off and expansion 273 
 
 Cycle, closed 25 
 
 non-reversible 40 
 
 reversible 24 
 
 Delafond 248 
 
 Oenton 4i9.»20 
 
 Density at high-pressure .... 71 
 
 Dry ness-f actor 86 
 
 Designing steam-engines . . 152, 179 
 
 Diesel motor 341 
 
 economy 355 
 
 Differential coefl&cient dpfdt . . 79 
 
 Dixwell's tests 270 
 
 Dynamometers 186 
 
 Economy, methods of improving. 245 
 
 compounding 257 
 
 expansion 256 
 
 increase of size 255 
 
 intermediate reheaters .... 268 
 
 of steam-engines 237 
 
 raising pressure 247 
 
 steam-jackets 261, 266 
 
 superheating 270 
 
 variation of load 274 
 
 Effectof raising steam-pressure, 148, 247 
 
 Efficiency 25 
 
 mechanical 287 
 
 of reversible engines ^^ 
 
 of steam-engine 130, 144 
 
 P^fficiency, maximum 39 
 
 of superheated steam .... 115 
 
 Ejector 470 
 
 condenser 471 
 
 P^ngine, Carnot's 22 
 
 compressed-air 384 
 
 friction of 285 
 
 hot-air 298 
 
 internal combustion 298 
 
 «il 335 
 
 reversible 24 
 
 P^ntropy 000 
 
 VAGB 
 
 Entropy — Continued. 
 
 due to vaporization 99 
 
 expression for 35 
 
 of a liquid 97 
 
 of a liquid and vapor .... 99 
 
 of gases 67 
 
 scale of 31 
 
 Exponential equation 66 
 
 First and second laws combined 49 
 
 First law of thermodynamics 13 
 
 application of 45 
 
 application of vapors 88 
 
 Flow in tubes and nozzles . . . 434 
 
 Buchner's experiments .... 437 
 
 design of a nozzle 444 
 
 experiments 436 
 
 friction head 435 
 
 Kneass' experiments 440 
 
 Kuhhardt's experiments . . . 443 
 
 Lewicki's experiments .... 442 
 
 Rateau's experiments .... 440 
 
 Rosenhain's experiments . . ' 441 
 
 Stodola's experiments .... 441 
 
 Flow of air, Fliegner's equations . 429 
 
 in pipes 380 
 
 maximum velocity 430 
 
 through porous plug 69 
 
 P'low of fluids 423 
 
 of gases 426 
 
 of incompressible fluids . . . 425 
 
 of saturated vapor 430 
 
 of superheated steam .... 433 
 
 French and English units .... 56 
 
 Friction of engines 285 
 
 distribution 295 
 
 initial and load 287 
 
 Gas-engine 304 
 
 after burning 319 
 
 blast-furnace gas 333 
 
 economy and efficiency . . 320, 348 
 
 ignition 329 
 
 starting devices 329 
 
 temperature after explosion . . 318 
 
 valve-gear 324 
 
 water jackets 320 
 
INDEX 
 
 531 
 
 I'AGi; 
 
 Gas-engines — Continued. 
 
 with compression in cylinder . 308 
 
 with separate compression . . 305 
 
 (ias-engines four-cycle 337 
 
 two-cycle 338 
 
 Cjases 54 
 
 adiabatic equations 64 
 
 characteristic equation .... 55 
 
 characteristics for gas-engines . 314 
 
 entropy 67 
 
 general equations 61 
 
 intrinsic energ)' 66 
 
 isoenergic equation 63 
 
 isothermal equation 61 
 
 special method 60 
 
 specific heats 59 
 
 specific volumes 57 
 
 Gasoline engine 334 
 
 Gas-producers 331^352 
 
 Gauges 186 
 
 Gay-Lussac's law 54 
 
 ( xraphical representation of change 
 
 of energy 20 
 
 of characteristic equation ... 4 
 
 of efficiency 33 
 
 (irashoff's formula 432 
 
 Hall's investigations 230 
 
 Hallauer's tests 219 
 
 Heat of the liquid 82 
 
 Heat of vaporization 85 
 
 Him engine, tests on 220 
 
 Hirn's analysis 205 
 
 Hot-air engines 298 
 
 Ignition 329 
 
 Indicators 187 
 
 Influence of cylinder walls ... 199 
 
 Callendar and Nicolson ... 231 
 
 Hall 230 
 
 Hirn's analysis 205 
 
 representation 202 
 
 Injector 447 
 
 combining-tube 458 
 
 delivery-tube 459 
 
 double 461 
 
 PAGU 
 
 Injector — Continued. 
 
 efliciency of 459 
 
 exhaust steam 467 
 
 Korting 462 
 
 lifting 460 
 
 restarting 464 
 
 self-adjusting 462 
 
 Seller's 460 
 
 steam-nozzle 458 
 
 theory 448 
 
 velocity in delivery tube ... 455 
 
 velocity of steam -jet 452 
 
 velocity of water 454 
 
 Internal combustion engines . . 298 
 
 Internal latent heat 87 
 
 Intrinsic energy 14 
 
 of gases 66 
 
 of vapors 95 
 
 Isoenergic or isodynamic line . . 17 
 
 for gases 63 
 
 Isothermal lines 16 
 
 for gases 61 
 
 for vapors 94 
 
 Josse, tests on binary engine . . 282 
 
 Joule and Kelvin's experiments . 69 
 
 Kelvin's graphical method ... 29 
 
 Kerosene-oil engine 335 
 
 Kilogram 56 
 
 Kneass 440-452 
 
 Knoblauch no 
 
 Kuhhardt 443 
 
 Latent heat of expansion ... 6 
 Laws of thermodynamics . . . 13, 22 
 
 application to gases 59 
 
 application to vapors 88 
 
 Lewicki . . '. 442 
 
 Lines, adiabatic 17 
 
 isoenergic 17 
 
 isothermal 16 
 
 of equal pressure 16 
 
 of equal volume 16 
 
 Meyer 350 
 
 Mass. Inst. Technology, engine 
 
 tests 262 
 
532 
 
 INDEX 
 
 PAGE 
 
 Mechanical efficiency 286 
 
 Mechanical equivalent of heat . . 8t 
 
 Meter ..." 56 
 
 Non-reversible cycles 40 
 
 Oil-engine economy 355 
 
 Oil-engines 335 
 
 Porous plug, flow through ... 69 
 
 Pressure of saturated steam ... 77 
 
 of vapors 77 
 
 specific 2 
 
 Quality 86 
 
 Rankine's equations for flow of 
 
 steam 432 
 
 cycle 134 
 
 Rateau 440 
 
 Ratio of cylinders, compound en- 
 gines 162 
 
 Refrigerating machines 396 
 
 absorption 411 
 
 air 396 
 
 calculations for 403, 408 
 
 compression 405 
 
 fluids, for 409 
 
 proportions 398, 406 
 
 tests 412, 413, 417 
 
 vacuum 398 
 
 Regnault's equations for steam . 77 
 
 Relations of thermal capacities . 12 
 
 of adiabatics and isothermal lines 18 
 
 Reversible cycle 24 
 
 engine 24 
 
 Rontgen's experiments 72 
 
 Rosenhain 441 
 
 Rowland 81 
 
 Saturated vapors 76 
 
 adiabatic equations 100 
 
 entropy 97> 99 
 
 flow of 430 
 
 general equation 87 
 
 intrinsic energy 95 
 
 isoenergic equation 95 
 
 isothermal equation 94 
 
 pac;e 
 
 Saturated vapors — Continued. 
 
 pressure of 77 
 
 specific heats 93 
 
 specific volumes 91 
 
 Saturated vapors, special method . 90 
 Schroter's tests of refrigerating 
 
 machines 412, 417 
 
 tests of steam-engines .... 273 
 Seaton's multipliers for steam- 
 engine design 179 
 
 Second law of thermodynamics 22, 27 
 
 application of 47 
 
 application to vapors 89 
 
 Specific-heat 6, 58 
 
 of gases 58 
 
 of liquids 83 
 
 of superheated steam .... 93 
 
 of water 80 
 
 Specific -heats, ratio of 59 
 
 Specific -pressure 56 
 
 Specific-volume 3 
 
 of gases 57 
 
 of liquids 85 
 
 of vapors 91 
 
 Starting devices 325 
 
 Steam-engine 128 
 
 actual 142 
 
 Carnot's cycle 128 
 
 compound 156 
 
 designing 152, 179 
 
 economy 245 
 
 efficiency 130 
 
 Hirn's analysis 205 
 
 indicators 187 
 
 influence of the cylinder walls . 190 
 
 leakage of valves 234 
 
 variation of load 274 
 
 Seaton's multipliers 179 
 
 triple-expansion 172 
 
 with non-conducting cylinder . 134 
 
 Steam turbines 47^ 
 
 compound 4^6 
 
 compounding velocity .... 487 
 
 " pressure .... 493 
 
 " pressure and velocity 506 
 
INDEX 
 
 533 
 
 PAGE 
 
 Steani turbines — Continued. 
 
 Curtis 513 
 
 effect of friction .... 481, 491 
 
 impulse , . 473 
 
 " general care .... 477 
 
 friction of rotating disks . . 504 
 
 lead 502 
 
 leakage and radiation .... 501 
 
 noaxial thrust 480 
 
 Rateau 503 
 
 reaction 476, 515, 520 
 
 Stirling's hot-air engine .... 299 
 
 Stodola 441 
 
 Sulphur dioxide 117 
 
 Superheated vapors no 
 
 characteristic equation .... 121 
 
 entropy 115 
 
 specific-heat 112 
 
 total heat 114 
 
 Temperature 3 
 
 absolute scale 29 
 
 standard 5, 81 
 
 Temperature-entropy diagram 
 
 35, 104, 131, 137 
 table 106, 139 
 
 PAGE 
 
 Testing steam-engines 183 
 
 Tests of steam-engines 237 
 
 examples of economy .... 238 
 
 marine engines 241, 242 
 
 simple engines 250 
 
 steam-pumps 244 
 
 superheated steam .... 270, 273 
 
 Thermal capacities 1,7 
 
 of gases 61 
 
 relations of 9 
 
 Thermal lines 16 
 
 and their projections .... 19 
 
 Thermal unit 5 
 
 Thomas 112 
 
 Thurston 294 
 
 Total heat of steam 84 
 
 of superheated steam .... 114 
 
 of vapors . 85 
 
 Triple-expansion engines .... 172 
 
 Tumlirz in 
 
 Value of i? 57 
 
 Waste-heat engine 357 
 
 Weirs 191 
 
 Zeuner's equations . 51 
 
OCT 1^'inn7