^.y^' ^ p: •..- 'ih'^- -.K/iy , .. ■ ■^■v , ' ■ If, V'''V iifrilTriii Class Book .5 6 COP^-RIGHT DEPOSm MECHANICAL LABORATORY METHODS THE TESTLNG OF INSTRUMENTS AND MACHINES IX THE MECHANICAL ENGINEERING LABORATORY .\XD IX PRACTICE BY JULIAX C. SMALL WOOD, M.E. Fdlow, Johns Hopkiris University, and Sometime Associite Professor of Experimental Engineering, Syracuse University; Member American Society of Mechanical Engineers 11 A ILLUSTRATIONS SECOND EDITION IlEYISED AXD ENLARGED NEW YORK D. VAN NOSTRAXD COMPANY 25 Park Place 1918 r -■ v^ Copyright, 1914, 1918 BY D. VAN NOSTRAND COMPANY « • • ^Pff -3 IBIB PRICE, S.......^lQO_ NET. PRESS OF BRAUNWORTH & CO. BOOK MANUFACTURERS BROOKLYN. N. Y. Y ^C{.A4U44()8 n^i^ I PREFACE TO THE SECOND EDITION This work has been enlarged and modified according to the requirements indicated by its use. The section dealing with in- struments contains a number of subjects not covered before, notably on recorders. The treatment of valve setting and steam engine testing is enlarged and improved. Under the heading of steam auxiliaries, the testing of condensers and feed water heaters is described. A new section is added on the testing of refrigerat- ing machinery, ammonia absorption and compression systems. Among the other newly included tests is one for the horse-power output of electric motors, which, it is believed, will be found of convenience in connection with the testing of motor-driven me- chanical units. In all there are described twelve additional tests. Sufficient tabular matter is appended in this edition to enable the user to calculate all the results sought by the various tests. This includes tables of the properties of steam and ammonia, a MoUier diagram, tables of areas of circles in three figures for cyHnder cal- culations, etc., four place logarithms, densities of water, and a sec- tion on hygrometry, together with all explanations necessary. All old and new numerical data and answers to problems have been thoroughly checked, and mistakes thus found corrected. The author wishes to express his obKgation to the various users of the first edition who have suggested improvements and additions. Such suggestions have been considered almost exclu- sively in the work of revision. It is modestly believed, therefore, that the book is materially bettered through this cooperation. Julian C. Small wood. Johns Hopkins University, January, 1918. iii r PREFACE TO THE FIRST EDITION In considering how best to describe what this book is intended to be, the author finds thoughts uppermost of what it is intended not to be. He has undertaken a subject already treated by a few admirable texts because there appeared in his own teaching the need of a brief work on the broad principles of experimental apparatus and methods. Therefore this book does not contain lengthy and detailed descriptions, nor does it attempt to cover all the instruments or methods of any class so that the student will understand them in all their details before commencing his work in the laboratory. It is obvious that the average student can learn details of instruments and apparatus much more readily by actual examina- tion of them than he can from printed and pictured descriptions. He should, of course, know the principles and purposes before- hand; then any deficiency of information may be made good by maker's pamphlets or by personal instruction in the laboratory. In dealing with any class of instruments, therefore, the text of this .book explains the principles of that class, or a subdivision of it, so that a brief explanation covers any specific instrument. Illustrations to help such explanations are diagrammatic, and not detailed drawings, the purpose being to make a simple pre- sentation. Instructions on how to operate engines, boilers, etc., have been omitted. The practicing engineer, presumably, does not need them. The student rarely memorizes them from a book, but he does grasp and remember them if imparted at the time ^'1 PREFACE when they may be associated wath the practice. It is believed that it is essential in any case to give such instructions per- sonally in the laborator3\ The principles of all except a few types of engines, descrip- tions of engines of differing types, and topics such as thermo- dynamics, etc., have not been included. It is assumed that the reader knows how the usual engines work before he is required to test them; at all events, if he does not, there are many texts open to him on these subjects. Ordinarily the college student of mechanical engineering has received a working knowledge of them from his other courses. This book is therefore on the subject of testing exclusively. The standards of the codes of the A.S.M.E. have been adopted in almost all instances, even where the author preferred other standards, for the sake of uniformity. The codes have not been quoted at length, however, because, in the first place, they are accessible to anyone, and secondh', their numerous items and many different expressions for practically the same results confuse, rather than help, the student. The value of such a book as this is intended to be depends largely upon the clarity of its presentation. The author has had exceptional opportunities in this particular, through nu- merous rearrangements of the subjects dealt with; the object being always to make them most easily understood by the student. The two main divisions deal with the testing of instruments and of machines, respectively. The first of these is subdivided so as to deal sc^parately with a group of instruments of a single type for a given purpose. Under each sub-division the prin- ciples of the instruments considered are first related, and then are given the methods of testing them. A number of problems are included, by the working of which the student may famil- iarize himself with the principles of the instrument before experi- menting with it. PREFACE vii The main division dealing with the testing of machines is similar in treatment; the principles introducing each sub- division in this case applying to the quantities usually sought in a test of the machine considered. The table of contents may be used as a synopsis of experi-' ments which may be referred to for the quantities to be meas- ured in the test of a given instrument or machine. A number of the testing methods described have not appeared elsewhere in book form. For some, the author is indebted to his former association with the University of Pennsylvania; for example, the method of setting the slide valve by the Bilgram diagram, the application of the method of least squares to indi- cator spring calibration, etc. Other of the methods, the author has developed at Syracuse University; notably those of testing indicator drum motion and reducing wheels. A number of original formulas are presented for the simplification of calcu- lations from test data. Upon such depend the methods given for testing gas engines and producers. Among others may be mentioned the formulas for the products of combustion of fuels, those for simplifying indicated horse-power determinations, etc. The sections dealing with these subjects, in somewhat different form, have been previously published in Power. Thanks are due to its editor, Mr. Fred. R. Low, for his courtesy in allowing their use here. To proportion such a work as this aims to be is difficult. One cannot help but be influenced by his personal inclinations toward one branch or another. Further, the field is too vast for one man to have covered thoroughly in all its branches through per- sonal experience. In view of these facts, the author states, in conclusion, that he would appreciate information concerning errors or defects from any who may use the book. Julian C. Smallwood. Syracuse University, January, 1914. r CONTENTS INTRODUCTION The Principles of Experimental Measurements PAGE ClassevS of errors. Limitations of instruments. Standards. Measure- ment of compound and variable quantities. Combining discordant observations. Rules for testing > . 1 PART I. THE TESTING OF INSTRUMENTS Weights and Forces 12 1. Calibration of Platform Scales. Principles, (a) Sensitiveness of scales. (6) Beam calibration, (c) Determination of leverage ratio, (d) Poise weight calibration, (e) Beam calibration by test of rider 13 2. Evaluation of a Spring. Principles, (a) Spring scale by graphic method, (h) Spring scale by method of least squares 18 Pressure 22 3. Calibration of a Bourdon Gage. Principles, (a) Determination of the constants of the dead weight apparatus, (b) Calibration, (c) Adjustment of the scale, (d) Calibration of a recording pressure gage : . . . 23 4. Calibration of a Draft Gage. Principles, (a) CaHbration by cal- culation. (6) Calibration by comparison 27 ix X CONTEXTS PAGE Angular Velocity 29 5. Calibration of a Tachometer. Principles and i}^es. (a) Calibra- tion against a continuous counter, (b) Calibration against a chro- nograph, (c) Cahbration of a recording tachometer 31 Power 33 6. The Constants of Friction Brakes. Principles, (a) Determination of the unbalanced weight, three methods, (b) Determination of the horse-power per pound thrust per revolution 34 7. Cahbration of a Fan Brake. Principles, (a) Calibration against a transmission dynamometer, (b) Against a cahbrated motor, (c) Use of the horse-power constant 3>^ 8. Calibration of a Transmission Dynamometer (Weight-arm Type). Principles, (a) Determination of constants. (6) Torque calibration by calculation, (c) Allowance for friction, etc. (d) Cahbration by comparison with prony brake 40 9. Calibration of Transmission Dynamometer (Spring Type). Principles, (a) Static cahbration. (b) Allowance for friction, windage, etc. (c) Cahbration by comparison with prony brake. ... 45 The Engine Indicator — Reducing Motions 50 10. Calibration of the Indicator Spring and Pencil Motion. Principles. (a) Parallelism of the motion. (6) Ascending, descending, and combined spring scales by graphic method. (c) By method of least squares, (d) Methods of applying cahbration results to correct indicator diagrams, (e) Sampling 52 11. Testing the Motion of the Indicator Drum. Principles, (a) Deter- mination of spring tension. (b) Of drum friction, (c) Testing indicator cord, (d) Adjustment of drum spring from overtravel. (e) Testing dram motion with motion tester. (/) Correction of diagrams from motion tester records 57 12. Testing of Reducing Motions (Link Type). Principles, (a) Deter- mination of errors by line diagram, (b) By direct measurement. 64 CONTENTS xi PAGE 13. Testing of Reducing Wheels. Principles, (a) Determination of spring tension and of friction. (6) Determination of errors by the drum tester, (c) Correction of diagrams 67 Irregular Areas and Mean Heights 76 14. The Polar Planimeter. Principles, (a) Determination of the zero circle, two methods. (6) Comparison of direct readings with known areas, fixed center within and without the areas, (c) Comparison of readings to scale with known areas, (d) Arm adjustment to a required scale 76 15. The Coffin Planimeter. Principles, (a) Comparison of records with known mean heights 85 16. Averaging Circular Charts, (a) The radial planimeter. (h) Approx- imate average with polar planimeter 88 Fluid Velocities — Meters 91 17. Calibration of a Volume Water Meter. Principles, (a) Calibration against caHbrated scales or tank, (h) Correction factors 92 18. Calibration of a Volimie Gas Meter. Principles, (a) Calibration with air measured by displacement. (6) Correction factors 93 19. Weir Calibration. Principles, (a) Determination of the zero of the hook gage, (b) Of quantity rates and corresponding heads. (c) Of the coefficient of discharge at various rates 96 20. Calibration of a V-notch Recorder, (a) Zero level of weir. (6) Cali- bration, (c) Sensitiveness 101 21. Calibration of Nozzles. Principles, (a) Determination of quan- tity rates at different heads, (b) Coefficient of discharge 104 22. Calibration of a Venturi Meter (Water). Principles, (a) Deter- mination of quantity rates at various pressure differences, (b) Of coefficient of discharge 107 23. Calibration of a Venturi Meter (Gas). Same as 22 Ill 24. Calibration of a Pitot Tube for Water. Principles, (a) Determi- nation of velocities and quantity rates by traversing, (b) Location of the point of mean velocity 112 xii CONTENTS PAGE 25. Calibration of a Pitot Tube for Gas. Principles, etc., same as 24. . . 115 26. Calibration of an Orifice for Water. Principles, (a) Determination of quantity rate at various heads, (h) Of coefficients 119 27. Calibration of an Orifice for Gas. Principles, etc., same as 26 121 28. Calibration of an Anemometer. Principles, (a) Calibration against velocity in still air. (b) Curve of correction factors 124 29. Test of a Calorimetric Apparatus for Measuring Gas. Principles. (a) Examination of instruments. (6) Determination of radiation 125 30. Calibration of a Steam Meter. Principles and types, (a) Cali- bration by weighing condensate, (b) Sensitiveness of recording meters 127 Thermometry , 131 31. Calibration of High Reading Thermometers and Pyrometers. Principles and types, (a) Calibration against a standard. (6) Cal- ibration against steam temperatures, (c) Calibration against melt- ing and boiling points, (d) Stem corrections 133 Heat of Steam — Calorimetry — Sampling 139 32. The Throttling Calorimeter. Principles, (a) Determination of radi- ation correction 145 33. The Separating Calorimeter. Principles, (a) Calibration of the dry steam meter. (6) CaUbration of the water gage, (c) Radiation correction 148 34. The Condensing Calorimeter. Principles, (a) Determination of the water equivalent, {b) Of radiation correction 151 Friction 154 35. Oil Testers. Principles and types, (a) Determination of con- stants f 156 36. Belt Testers. Principles, (a) Determination of constants 158 CONTEXTS xiii PART 2. THE ANALYSIS OF COMBUSTION PAGE The Constituents of Fuels 163 37. The Proximate Analysis of Coal. Sampling, (a) Determination of moisture, volatile matter, fixed carbon, and ash. (b) Estimation of total carbon and hydrogen 165 The Heat Value of Fuels 170 38. Determination of the Heat Value of Coal. Principles, Sampling. Determination by coal calorimeter. (6) By calculation from analysis 172 39. Determination of the Heat Value of Gas and Oil Fuels. Principles. Samphng. (a) Higher heat value by Junker calorimeter, (b) Lower heat value, (c) Calculation of heat values of gas fuel from its analysis 177 The Products of Combustion 180 40. Exhaust Gas Analysis. Principles. CO2 recorders. Peagents. Sampling, (a) Determination of CO2, O2, CO, and N2. Precautions in operating. (6) Calculations from the analysis 189 PART 3. THE TESTING OF P0\\:ER PLANT UNITS Steam Engine Testing 41. Determination of Cylinder Clearance. Principles, (a) Linear and volumetric clearance by Hnear measurements. (6) Volumetiic clearance by water measurement, (c) Volumetric clearance of a gas engine from indicator diagrams 205 42. Valve Setting of a Simple Slide Valve Engine. Principles, (a) Measurement of lead, (b) Setting for equal leads, (c) For equal cut-offs by the Bilgram diagram, (d) By the indicator, (e) Study of steam distribution by Bilgram or Zeaner diagrams 210 43. Setting of a Corliss Valve Gear. Principles, (a) Adjustment of laps and leads. (6) Adjustment of goy.ernor rods, (c) Of dash-pot rod. (d) Checking by indicator 220 xiv CONTENTS PAGE 44. Mechanical Efficiency Test of a Steam Engine. Principles, (a) DeterminatioQ of ths indicated horse-power at various values of the brake horse-power. (6) Of the friction horse-power, (c) Of efficiency, (d) Of speed regulation 223 45. Economy Test of a Steam Engine. Principles. Duration, (a) Steam consumption from the indicator diagram, by condenser, by steam meter, or by feed water measurement. Willan's Line. (6) CyHnder condensation, (c) Thermal efficiencies, British standard and Clausius 227 46. Test of a Multiple Expansion Engine. Principles, (a) I.h.p., B.h.p., F.h.p., and mechanical efficiency. (6) Steam consumption, (c) Thermal efficiency, (d) Equivalent and aggregate IVI.e.p. (e) Steam accounted for by indicator diagrams. (/) Combined diagram (g) Ratio of Expansion, (/i) Diagram factor 236 47. Economy Test of a Steam Turbine. Principles, (a) Determina- tion of useful horse-power. (6) Steam consumption, per horse- power- or kilowatt-hour. Willan's Line, (c) Thermal efficiencies, British standard and Clausius. (d) Separation of losses 242 48. Economy Test of a Steam Power Plant. Principles, (a) Steam and heat consumption of engine and auxiliaries. (6) Heat added to feed water, (c) Heat lost to leakage and drips, (d) Heat balance 246 Steam Pump Testing 49. Valve Setting of a Duplex Steam Pimip. Principles, (a) Adjustment of lost motion of valve, (b) Readjustment after trial 250 50. Mechanical Efficiency Test of a Reciprocating Steam Pump. Prin- ciples, (a.) Determination of indicated horse-power at various values of water horse-power, (b) Of mechanical and fluid losses. (r) Of efficiency. ((/) Of slip, (e) Of capacity 252 51. Economy Test of a Steam Pump. Principles, (a) Steam con- sumption. (6) Thermal efficiency, (c) Duty 256 52. Economy Test of an Injector. Principles. Selection of the inde- l)ondcnt variable, (a) Determination of the ratio of water pumped to steam used, (b) Of steam consumption, (c) Of efficiency, (rf) Of duty, (e) Of capacity 257 53. Economy Test of a Pulsometer. Principles, etc., same as 52 202 CONTENTS XV Boiler Testing PAGE 54. Test of a Steam Boiler. Principles. Duration. Starting and Stop- ping. Sampling, (a) Determination of total coal and refuse. (6) Of total water evaporated, (c) Quantities to be found prior to calculations of results, (d) Determination of equivalent evapora- tion, per pound of coal, etc. (e) Over-all efficiency. (/) Heat lost to carbon wasted in refuse, (g) To dry exhaust gases, (h) To water vapor in the exhaust, (i) To incomplete combustion, (j) To radiation, (k) Other results, efficiencies, horse-power, etc 262 • Testing Steam Auxiliaries 55. Test of a Surface Condenser. Principles, (a) Ideal and actual vacuums. (6) Rate of heat transmission, (c) Effectiveness of heat transmission, (d) Weight of condensing water per pound of condensate 276 56. Test of a Jet Condenser. Principles, (a) Ideal and actual vacuums. (b) Rate of heat transmission, (c) Weight of condensing water per pound of condensate 280 57. Test of a Feed-water Heater. Principles, (a) Useful heat trans- mitted. (6) Effectiveness of heat transmission, (c) Available heat. 281 Gas Engine Testing 58. Testing the Adjustment of an Internal Combustion Engine. Prin- ciples, (a) Timing the valves. (6) Timing the ignition. (c) Adjustment of fuel mixture, (d) Adjustment of carburetors, (e) Test of timing by indicator 282 59. Mechanical Efficiency Test of a Gas Engine. Principles, (a) Determination of indicated horse-power at various values of brake horse-power. (6) Of friction horse-power, (c) Of efficiency, (d) Of speed regulation 288 60. Economy Test of a Gas Engine. Principles. Sampling. Dura- tion, (a) Fuel consumption. (6) Heat supphed. (c) Heat con- verted into useful work, (d) Heat lost to mechanical friction, (e) xvi CONTENTS PAGE To jacket water. (/) Determination of the volume of dry exhaust gas per cubic foot of fuel, (g) Heat lost to dry exhaust gas. (h) To water vapor in exhaust, (i) To incomplete combustion. (J) To radiation, (k) Determination of ratio of air to fuel gas 290 61. Economy Test of an Automobile Engine. Principles, (a) Deter- mination of torque and brake horse-power at different speeds, (h) Of fuel consumption 300 62. Test of a Gas Producer. Principles. Starting and stopping. Duration. SampHng. (a) Quantities to be found prior to calcula- tion of results. (6) Useful heat in the cool gas. (c) Sensible heat in the dry gas. (d) Heat lost to excess steam, (e) Heat transferred to scrubber water. (/) Heat lost to carbon in ash. (g) To radia- tion, etc. (h) Other efficiencies and results 302 Testing Refrigeration Machinery 63. Test of a Refrigeration Plant. (Ammonia Compression.) Principles, and definitions, (a) Refrigerating effect by measurement of the brine, (b) By ammonia measurements, (c) By approximate cal- culation, (d) Ice-melting capacity, (e) Coefficient of performance, actual. (/) Ideal, (g) Gallons of cooling water per minute per ton. (Ji) Overall economy 313 64. Test of a Refrigeration Plant. (Ammonia Absorption.) Principbs. (a) Refrigerating effect. (6) Ice-melting capacity, (c) Ideal co- efficient of performance, {d) Gallons of cooling water per minute per ton. {e) Steam consumed by the generator. (/) Steam used by ammonia and brine pumps, (g) Work of ammonia pump, (h) Weight of anhydrous NH3 circulated per minute, (i) Concen- tration and specific gravity of the aqua, (j) Calculation of aqua and anhydrous weights 321 66. Heat Balance of a Refrigeration Plant. (Ammonia Absorption.) Principles, (a) Weight of weak aqua per pound of anhydrous. (6) Heat added to XH3 and aqua in generator, (c) Steam-heat quan- tities, (d) Heat transfers in absorber, (e) Heat removed by con- denser water 329 CONTENTS xvii Testing of Air Machinery PAGE C6. Test of a Fan Blower. Principles. Selection of the independent variable, (a) Determination of the horse-power supphed. (6) Of capacity, (c) Of horse-power supphed per thousand cubic feet of free air per minute, (d) Of air horse-power, (e) Of mechanical efficiency 336 67. Test of a Reciprocating Air Compressor. Principles, (a) Deter- mination of capacity. (6) Mechanical efficiency, (c) Volumetric efficiency, (d) Efficiency of compression, (e) Over-all efficiency. (/) Separation of losses, (g) Heat measurements 340 Testing of Water Motors 68. Test of a Hydraulic Turbine. Principles. Selection of the inde- pendent variable. (a) Determination of available horse-power. (b) Of hydraulic efficiency, (c) Of best operating speed 347 69. Test of a Hydraulic Ram. Principles. Selection of the independent variable. (a) Determination of capacity. (h) Of efficiencies, Rankine's and D'Aubisson's. (c) Curves 350 Miscellaneous Tests 70. Test of a Centrifugal Pump. Principles. Selection of the inde- pendent variable, (a) Determination of capacity. (6) Of horse- power supphed. (c) Of water horse-power, (d) Of efficiency, (e) Curves 352 71. Test of a ** Power " Pump. Principles, (a) Water horse-power. (b) Available horse-power, (c) Mechanical and fluid losses and efficiencies, {d) Slip and capacity 356 72. Test of a Hoist. Principles. (a) Determination of the ideal mechanical advantage, (b) Of the actual mechanical advantage at various loads, (c) Of corresponding efficiencies 358 73. Tests of Lubricating Oils. Principles. (a) Determination of specific gravity. (6) Of viscosity, (c) Of flash, burning, and chill points. (cZ) Of the coefficient of friction, (e) Endurance tests 358 xviii CONTENTS PAGE 74. Horse-power Test of an Electric Motor. Principles, (a) Determi- nation of horse-power output. (6) Of efficiency 362 APPENDIX Logarithms, Diameters and Areas of Circles, Densities of Water, Steam-vajoor Tension Tables, Properties of Steam, Tables and Diagram, M oilier Diagram, Properties of Ammonia, Hygrometry 365 Reports of Engineering Tests 384 A Method of Conducting Students' Tests 388 I L MECHANICAL LABORATORY METHODS INTRODUCTION THE PRINCIPLES OF EXPERIMENTAL MEASUREMENTS The science of experimental engineering rests primarily upon the art of measurement. Conclusions relating to general laws or specific operating conditions, formed from test results, stand or fall according to the accuracy of measurement. Absolute Accuracy. There is no such thing as absolute accuracy of measurement except by accident. For instance, the length of a bar, measured with a scale graduated to one-hun- dredths of an inch, may appear to be 3 ins. By chance, it may be that the bar is 3 ins. long exactly, neither more nor less by an infinitesimal fraction. This, however, is very improbable. A micrometer may show it to be 3.005 ins. long. An instrument of still nicer capability might yield another decimal place, and so on. Thus, absolute accuracy presupposes an instrument with graduations corresponding to infinitely small fractions of a unit. Assuming that this condition could be sensibly complied with, it would still be necessary to prove the correctness of the instrument within its own graduations, and this could only be done by comparison with absolute standard lengths, that is, material objects known to have definite linear dimensions. But this implies measurement by an absolutely accurate instru- 2 PRINCIPLES OF MEASUREMENTS ment. Thus, to create such an instrument, it is necessary to have the very article desired. Accidental Errors. Aside from instrumental limitations, accidental causes of error are a sufficient bar to absolute accuracy. Accidental errors are all those that cannot be eliminated by instru- mental or other corrections. They are due entirely to chance and are not s^^stematic except according to the law of probability and chance. Such errors are incurred in the calipering of a bar, for example, when the calipers are held on a slant instead of on a true diameter, when the calipers are held with var^dng degrees of pressure, when temperature changes momentarily affect the instrument, and so forth. Accidental errors are equally likely to be positive or negative from which it follows that in a series of observations upon the same quantity the probabilities are that the errors of excess will equal those of deficienc3\ Personal Errors. There is another class of errors knoTMi as *' personal errors ^' whereby a particular observer, by reason of his character, habitually reads too high or too low. This error may be estimated scientifically, the result being what is known as the '^ personal equation.'' Generally, in mechanical experi- mentation, this quantity is not an important one, being small in comparison with the usually unavoidable errors. We have, then, to consider two classes of errors which are bars to absolute accuracy in an}' measurement, namely, instru- mental and accidental. From an engineering standpoint, how- ever, absolute accuracy is neither necessary nor desirable, for it would be too laborious and cumbersome. It is not worth while to produce a result with ten or twenty significant figures when three or four are enough for practical requirements. Only that degree of accuracy is sought which accords with the dictates of common sense. Per Cent of Error. When a result is represented by three significant figures the error occurring through the omission of PRINCIPLES OF MEASUREMENTS 3 the fourth Is less than one half of one per cent. Thus, the quan- tities 1010, 101.0, etc., may be correctly expressed 1015, 101.5, etc., but in each case the error is less than 5 parts in 1000 or one half of one per cent. With the higher digits the per cent error is correspondingly less, as when 999.0 is used for 999.5, the error then being about 0.05 per cent. In most cases we cannot secure results with less than 1 per cent of error, so that three significant figures are ample for their presentation. In many cases even less accuracy than this is consistent with the object or the conditions of the test. The Precision and Accuracy of Instruments should be examined before using them for experimental measurements. Precision has reference to the fineness of graduations, accuracy to their correctness. The value of the smallest graduation of an instru- ment is called its '^ least count.'' Suppose, as an illustration, we wished to weigh separately a number of objects of approximately 100 lbs. so as to secure less than 1 per cent of error, that is, an error of less than 1 lb. A scales with a least count of 2 lbs., would do since a half a graduation could be estimated by eye with less probable error than 1 lb. A scales of any less precision however, would not be adequate. Standards. The accuracy of an instrument is established only by comparison with some ^^ standard unit,'' itself a copy, or a copy of a copy, of the ^' primary standard " kept at Wash- ington. The details of this sort of testing are given in Part I, but it is well to emphasize here that the necessary closeness of the approximation of any standard used to the primary standard depends entirely upon the least count of the instrument to be tested. Generally the standard is sufficiently accurate if it is correct within one quarter of this least count, and, if the standard is an instrument, its least count need not be less than one-half that of the instrument tested. It is thus seen that the word standard must be accepted with a relative sense, and that for engineering purposes secondary standards may be improvised 4 PRINCIPLES OF MEASUREMENTS which are just as useful as the most accurate standard obtainable. Assuming instrumental co: ectness as great as consistent with the least count, there are two ways of securing greater accuracy of measured results: first, by using an instrument of finer graduations, and second, by making numerous repetitions of the measurement. When the latter is done a result with less probable error is obtained from the average of the observations than from any one of them. This is because by so doing the accidental errors previously mentioned are to some extent eliminated. Intrinsic Evidence of Accuracy. In experimental engineer- ing one of the greatest aids to accuracy is repetition. It is only by repeated trials that accurate conclusions can be framed because, not only are there variations due to erroneous measurement, but the quantities measured are generally variable ones, them- selves subject to chance. Under such circumstances, a single determination proves nothing and indicates little. On the other hand a series of determinations not only reduces the prob- able error of the result, but furnishes intrinsic evidence of its value. Consider, for example, a series of four measurements made upon a single constant quantity by an observer, A. These are 103, 98, 101, 98, the average of which is 100. Assuming 100 to be the correct result (it is the best obtainable consistent with the observations, although, of course, not correct) then the error of each observation is the difference between it and the mean, or +3, —2, +1, —2, the plus and minus signs indicating whether the errors make the individual determinations greater or less than the mean. Now% If another observer measures the same quantity with the results 101, 100, 102, 101, averaging 101, the errors of his determinations will be 0, —1, +1, 0. It would be concluded at once that B^s measurements and result of 101 were more accurate than A's because his errors, figured from the mean, are less than A's. PRINCIPLES OF MEASUREMENTS 6 Compound Quantities. Most engineering measurements are upon compound quantities, the components of which are variable. The following parallel illustrates this case and also the graphic method later to be described. Fig. 1 represents the floor of a. room; and the solid diagonal line, the path of a ball that rolls across it. It is desired to locate as exactly as may be the path as it is traversed by the ball. The only exact data we have are that it is a straight line and starts at 0. At a given instant, one observer measures the distance of the ball from the wall OX and another from OY. These distances, x and y, are suf- ficient to locate one of the posi- tions of the ball and therefore its path, provided they are accurately determined. Acci- dental errors prevent this, how- ever, so that the path is falsely located on the line Oa. Obvi- ously, if a number of points^ instead of only one, could be located, a better result would ensue. 6, c, and d are such Acival Pafh-^. points. It is then found that Fig. 1. these points do not lie on the same straight line, the distances from the true path being the errors of their determinations. The question now arises how should these discordant observations be made to agree upon one result, which, though perhaps not the true one, is in best accord with the data. It is possible to locate a different line with each pair of observations, x-^y locating one, xi-^yij another, and so on. One might conclude that the average value oi x-iry would be best, but it can be shown by the theory of errors that the arithmetical mean does not yield the best result upon indirectly determined quantities. In this case, the result is obtained by measuring two other quantities; the determination 6 PRINCIPLES OF MEASUREMENTS is therefore indirect. The best result (referred to generally as *' most probable '') is a line so located that the sum of the squares of the distances from it of the points a, 6, c, and d shall be a minimum. Such a line can be determined mathematically, but it is generally drawn by eye judgment. Variables, Independent and Dependent. A large part of mechanical experimentation is parallel to this simple illustration. Two variables, bound together by a more or less rigid law, are measured, and from the result the law is deduced. The law is not always represented by a straight line, but often by a curve. Whichever it is, it is the business of experimentation to find. One of the variables can always be controlled; the other then follows it according to the law binding them. For example, w^hen a spring is extended by a force, there are two quantities, namely, the force and the extension, which combined give the law of the spring. In their measurement we may add predeter- mined increments of weight and let the extension vary as it may, or we may add weight enough to cause predetermined increments of extension and let the weight yV c / •J y« I <0 rorce. Poundi Fig. 2. 15 lbs. applied to a spring and 1 increase as it may. The pre- determined quantity is called the ^^independent variable"; the other, '' dependent.'' It is almost always desirable to present such measurements as points and to locate by them a smooth curve. This is done by adopting a pair of rectangu- lar axes, OX and OY and scaling them according to the units measured. In Fig. 2, for instance, 1 in. along OX represents 10 in. along OY represents \ in. of PRINCIPLES OF MEASUREMENTS 7 spring extension. The observations 7.5 lbs. and 0.375 in. are thus shown by the point indicated, and so on. In many cases there are three variables, as the pressure, temperature and volume of a gas. It is then customary to keep one of them constant throughout a test, arbitrarily control another, constituting the independent variable, and let the third vary as it may. If the relation between the variables appears to be satisfied by some other curve than a straight line, such a one is drawn. Intrinsic Evidence of Accuracy. If any point of a plotted series lies markedly off the line, it may be concluded logically that its determination contained some large error, or mistake, and it may be thrown out of consideration entirely. Similarly, the value of a set of measurements may be judged by the closeness of the plotted results to a smooth curve. It will be readily seen that the value of graphic presentation of results lies in the fact that their relative variation is visuaUzed and can therefore be grasped by the mind much more easily than could mere columns of figures. Conventions for Plotting. The independent variable, as a matter of convention, is plotted horizontally, the other vertically. Exceptions to this rule are calibration curves and stress-strain diagrams of materials; the one having instrument readings, the other, deformations, plotted as abscissas. Compound Variable Quantities. In the case of the spring the two variables, when combined, give a constant quantity, namely, the number of pounds per inch of extension. It is not often that the required compound quantity is a constant one, although it is sought to keep it so throughout one set of measure- ments. As an example, the mechanical efficiency of a steam engine depends upon the amount of work it is doing; the greater its output, within its capacity, the greater its efficiency. Sup- pose it is desired to measure the efficiency at a given output. The engine is operated to deliver this horse-power, no more and 8 PRINCIPLES OF MEASUREMENTS no less. But, owing to variations in steam pressure, governor action, and the like, it is possible to keep the horse-power out- put only approximately constant; it fluctuates somewhat through accidental causes more or less outside our control. Further, even if it were possible to keep it constant, the internal friction of the engine varies and this causes the ^vork done in the cylinder to vary. Consequently, the efTiciency, which is the delivered horse-power divided by the power developed in the cylinder, will vary. So aside from variations in the results produced by unavoidable errors of measurement, there are accidental varia- tions in the true value of the result, even when all the controllable conditions are kept as constant as possible. It is hke measuring the height of a small spot of light which persists in fluctuating up and down through a limited space. Clearly, a single measure- ment w^ould be altogether insufflcient, for it might represent a high or a low value, even if accurately made. Obviously, the best that can be done is to keep controllable conditions as con- stant as possible w^hile taking not one but a number of measure- ments. It may now be understood how such conditions will determine the precision necessary, because of the uncertainty of the true value of the result. Rules for Testing. The following rules should be observed when measuring variable compound quantities. First, For one value of the independent variable, the series of measurements made of each separate quantity may be averaged. All such averages may be used in a single calculation of the desired result. Second, Observations of fluctuating quantities should be made at equal time intervals to secure a true average. Third. The number of observations necessary of any quan- tity depends upon the constancy of the quantity. Fourth, Tests of time rates should cover a sufficient duration of time to reduce the error of initial and final measurements to 1 per cent of the total quantity. PRINCIPLES OF MEASUREMENTS 9 Fifth. In time rate tests, intermediate time readings should be taken to check rate constancy. Constancy of Conditions. Referring to the third rule, if all the conditions of a test could be kept absolutely constant, only two sets of readings would be necessary. The two would give identical results; the second would be made only to check the accuracy of measurement of the first. In some cases this condition is approximated, as, for instance, electric motor driven blowers. In other cases some of the quantities fluctuate more than the rest; under these circumstances the time interval between measurements of these quantities should be smaller than for the others, so that there may be more values obtained for them. Duration of Time Rate Tests. The fourth rule may be illustrated as follows. In measuring the pounds of water per minute flowing into a tank, the cross-section of the tank is measured, and the difference of water in it before and after an observed time interval is figured by noting the corresponding difference of the water levels. The water level is measured with a scale graduated to tenths of an inch. With such a scale, it is possible to make an error of gV in. (half a division) at each measurement, totaling iV in. It would be necessary, then, to make the duration of test long enough that yV in. be 1 per cent of the total rise in water level, that is, long enough for the w^ater to rise 0.1 in. -r- 1.0 per cent = 10 ins. This calculation allows for the maximum error probable, but it is on the safe side. Intermediate Readings. The table of observations on p. 10 illustrates the fifth rule. If the column of differences shows approximately equal values corresponding to equal time inter- vals, the result is valid. Any marked departure from constancy should throw suspicion upon the result. If the readings at 3:00 and 3:10 only had been taken, we should be ignorant as to rate constancy. As has been pointed out, the reliability of the result depends upon constancy of conditions. 10 PRixciPLES OF ^^EAsrRE^rE:xTs Time Height DifFerences 3:00 5.0 in 0.95 in. 3K)2 5.95.. 1.05 S.-Oi 7.00 1.05 Sm 8.05 1.00 3.-08 9.05 1.05 3:10 10.10.. A further advantage from intermediate readings is that they strengthen the determination against mistakes. This was shown in the illustration of the path of the ball. From the obsenations just cited, the result ordinarily would be figured thus f 10.1 -5.0) X area ,• • u 77- — : = cubic mches per mm. 10 mm. which is the same as though no intermediate readings had been taken. If, however, a mistake in measurement were incurred in the first or the last reading, as 6.0 instead of 5.0 ins., or 20.1 instead of 10.1 in^^., this mistake would not be apparent, and the result misleading or worthless. Intermediate readings would disclose such a mistake, and the set of observations involved could be discarded without sacrificing the others. Id time quantity measurements it is always best to record the time of day instead of time interv'als merely. This insures a correct record of the time. Otherwise it is easy to note an interval such as three minutes when two or four actually have elapsed. A further advantage is that possible irregularities in results may then be accounted for by related happenings that might be associated only by a knowledge of the time of occurrence. PRINCIPLES OF MEASUREMENTS 11 Before closing the general subject, it is well to emphasize the importance of figuring in the laboratory rough results from the observations as soon as obtained. This appHes to commercial as well as student work. By so doing, many faults in operation and in the appUcation of instruments may be detected and remedied in time. It is especially valuable to plot a curve of the variables as the test progresses, for it will reveal the accuracy or error of the determinations at the time when such knowledge is most valuable. Problem Ii. Temperatures of liquid in a pipe are read as follows: At 11:00 A.M., 90°; at 11:05, 100°; 11:15, 100°; 11:20, 90°. Compare the average of these four readings with the probable average if a reading had been taken at 11:10. Ans., 95°, 96°. Problem L. If the thermometer used in Problem li has a least count of 2°, what is the probable percentage of error in each reading? Ans., 1.1%, 1%. Problem I3. In a specific heat determination, two thermometers are used reading about 50° and 70°, respectively. What should be their least count that the probable error of the result be less than 2 per cent? Ajis.y 1°, or less. Problem I4. The rate of water flowing into a tank placed on a platform scales is to be determined by taking weighings and timing. If the rate is about 20 lbs. per minute and the probable error in reading the scales at starting and stopping is ±| lb., how long should the test be continued to secure less than 1 per cent of error? How many intermediate readings could be conveniently taken in this time? Arts., about 5 min. r PART ONE THE TESTING OF INSTRUMENTS WEIGHTS AND FORCES These are measured by comparison with known weights with the aid of a system of levers such as in a beam balance, or by reference to the amount they t „ deform some elastic object, as a spring, ^ I =J which has been previously calibrated /\ against standard weights. When a ^^-fe^^J-N leverage system is used so that a YiQ, 3. large force may be measured by com- parison with a small known weight, it is necessary to know the ratio of the lever arms. In Fig. 3, for instance, the force F is measured by the relation W = -F m 71 in which — may be referred to as the ^' leverage ratio/' The calibration of any force measuring appratus rests primarily upon the force of gravity as a standard. " Standard weight '' is a misnomer in that the weight of the body so called, being the 12 SCALES AND PRESSURE GAGES 13 force of gravity between it and the earth, actually varies with the locality of the body. Standard mass is a better term. A standard mass establishes a standard force when the accelera- tion of gravity at the given locality is known. 1. Calibration of Platform Scales Principles. The platform scales Fig. 4^ is arranged so that a large weight, W to be measured, may be balanced by a small Bh. ^ j< , a — >K-b-:4 Inolicafes a Fulcrvm. w W i I >lc* < I 1 .i-^ J Fig. 4. — Platform Scales. weight on the beam, B. The small weight is either or both P on the poise or i?, the rider, acting at .a variable distance from the beam fulcrum. If P balances IF, then by the principle of moments, fxf=^=?4+f^7>^f w ?^ 14 SCALES AND PRESSURE GAGES It is arranged that - = -> X- so that ^ c f c ^ d ^^^ d b c W ac and ^T = r^ = the leverage ratio. /^ ba (a) The Sensitiveness of the Scales. This is determined by placing a large weight on the platform, weighing it, and then finding the smallest additional weight that will cause a deflec- tion of the beam which gan be nicely balanced by the rider. This additional weight is also a measure of the precision of the scales, provided the beam graduations are small enough to take cog- nizance of it. (b) Beam Calibration. Readings of the beam are taken corresponding to a number of standard weights. These should be sufficient to cover fairly the range of the beam. If standard weights of convenient size are not available, a number of small weights may be standardized for the purpose by using a calibrated scales with slightly greater precision than that of the scales to be tested. (See p. 3.) If the instrument readings do not agree with the true weights a calibration curve should be plotted, having the instrument readings as abscissas and the true weights as ordinates. This curve may be used to get corrected values at any part of the beam. (c) The Leverage Ratio may be found by measurement of the lever arms, but this method is difficult and subject to error. A better one consists of balancing a standard weight on the poise with a standard weight on the platform, then calculating the ratio of these weights. The nominal leverage ratio may be learned by examination of the poise weights. They are marked with their actual weights and the weights they are intended to balance, as, for instance, 1 Ib.-lOO lbs. This gives a nominal leverage 1 SCALES AND PRESSURE GAGES 15 ratio of 100. To test the accuracy of this, place, for example, a standard ^-Ib. weight on the poise and a standard 50-lb. weight on the platform. If they do not balance, add enough weight (shot is convenient) to either one or the other until a balance is secured. This additional weight may then be accurately measured and the true leverage ratio found. (d) Poise Weight Calibration. The indications of the poise weights are accurate if the leverage ratio is true and if the actual weights of the poise weights are as marked. They should there- fore be weighed by a calibrated scales of sufficient precision. It should be noted that any error in the poise weight is multiplied in the instrument reading by the leverage ratio. The standard scales should therefore weigh these weights to within an amount equal to the precision of the scales to be tested divided by its leverage ratio. If the actual weight of a poise weight is not as marked, or if the leverage ratio is not true, then the weight balanced on the platform is Actual weight of poise weight X actual leverage ratio instead of the amount indicated by the marking. For instance, if the poise weight intended to measure 100 lbs. actually weighs 0.99 lb. instead of 1 lb., and if the leverage ratio is 99.5 instead of 100, then the weight on the platform balanced by it is 0.99X99.5 = 98.5 instead of 100 lbs. In this way the true weight balanced by each poise weight may be found. (e) Beam Calibration by Test of Rider. In some types of platform scales, there are no poise weights, a number of riders on different beams being used. In such cases, the following method may be used : The weighing beam to be tested is represented by Fig. 5. With no load, the rider is in the position shown, its pointer being at the zero graduation, and its beam floating. With a load W on the table, the rider must be moved through a distance d to 16 SCALES AND PRESSURE GAGES 1 secure balance. If the scales are correct, the weight of the rider must be such that the distance d will be that between the zero and the graduation marked W, Now, instead of using the rider, another weight could be applied at any convenient part of the beam as shown by S, of such amount as to secure a balance when the load W is on the table. Therefore, the moment of the weight S about the fulcrum / must equal the moment of r- ■i:::::::::tz^:::::- ^ d ^ *• 1 ®);^ h) ' I ' I ' I ' I ' I Ol ' !| ' I ' I ■ »' I H I I t^ I * Fig. 5. the rider which is replaced. Letting R denote the weight of the rider, SXD=RXd Let the ratio of the load on the platform to the balancing weight S be L. Then W Substituting this in the first equation, and simplifying, we find the weight which the rider must have in order to suit the existing graduation of the beam : To apply this relation to the calibration, a value of W is chosen, and the distance between the beam graduation marked W and the zero graduation is carefully measured. This deter- mines W and d. A point is then chosen to represent 2), and its distance measured from the fulcrum /. To find the ratio L, it is not necessary to apply the full weight W to the platform. 1 SCALES AND PRESSURE GAGES 17 since the ratio W : aS is constant for all values of TT, the ratio of levers being established by the selection of D. Therefore the following procedure is used. An appreciable, but not in- convenient, number of weights is placed on the platform, these having been previously measured with a standard scales. They may consist of anything available that may be readily moved. A balance pan, improvised from paste-board and wire, is then attached to the beam at the distance D from the fulcrum, and to this pan are added shot or other small weights until a balance is secured. If desired, the weight of the pan may be previously balanced by the usual beam counterweight so that the experi- menter need deal with the added weight only. The latter should then be accurately weighed. This result, divided into the weight applied to the table, gives the desired ratio L. The value thus obtained completes the data necessary to calculate the weight of the rider according to the equation previously deduced. The rider is then removed from the beam and weighed; if the actual checks the calculated weight, the instrument is proved at the graduation marked W. Any other graduation may then be checked by proportion, since the distances of the graduations from the zero mark must vary directly with the indicated loads. Problem li. Five weights of about 10 lbs. each are to be standardized in order to calibrate a beam up to 50 lbs. How closely should these secondary standards be weighed, if the least count of the beam to be calibrated is 4 oz.? (Note. Have regard for the cumulative error.) Problem I2. Referring to division (c), how closely should the shot be weighed for less than 1 per cent of error in the determination of the leverage ratio? Problem I3. The least count of a scales to be calibrated is 4 oz. Its leverage ratio is 100 : 1. How closely should the poise weights be weighed so that their calibration shall be within the precision of the beam? See {d). Problem I4. Prove that it makes no difference in the instrument indica- tions where W is placed on the platform. Problem I5. If the rider, R^ is too light, will the resulting error be con- stant at all indications of the beam or will it vary and why? Will the error be plus or minus? Problem le* If the poise is too light to bring the beam down with nothing 18 SCALES AND PRESSURE GAGES 2 on the platform, can a scales, otherwise accurate, be used for correct results ^s-ithout pre\'ious calibration, and how? If too hea\'>'? Problem l;. Calculate the proper weight of the rider and check by weighing it. Problem li. Examine a scales to find if its leverage ratio may be ad- justed. 2. Evaluation of a Spring Principles. In a large class of instruments, it is necessary to know the amount of force required to extend, compress, or tw-ist a spring per unit of deformation. This quantity is called the '' spring scale.'' According to Hooke's law, it is a constant \nthin the elastic limit of the material. In many cases the movable end of the spring is attached to bome combination of links and gears designed to indicate, magnify, or translate the motion. When the applied force is increasing, the friction of such links or gears makes the instrument read low, since the indicator is moving up the scale and friction tends to hold it back. With a decreasing force, the instrument reads high for a similar reason. Suppose an external force F is applied to a spring instrument, which is correct except for the effect of friction, first by increasing the external force to the value F, and then by decreasing it to this value. Then, if S is the spring scale, Ei and E2, the extensions in the two cases, and X the friction, F = SxEi+X Adding F = SXE2-X 2F = S(Ei+E2) ^ S(E,+E2) • ^ = 2 That is, the effect of friction may be eliminated by taking increas- ing and decreasing readings at each load applied, dividing the sum of the extensions thus found by two, and using the result as the extension caused by the external force. SCALES AND PRESSURE GAGES 19 (a) Spring Scale by Graphic Method. Take as an example the following measurements of force and extension. Force lbs. Extensions Increasing In. Decreasing In. Average In. 10 20 30 40 50 0.32 0.64 1.02 1.32 1.68 0.34 0.70 1.08 1.36 1.70 0.33 0.67 1.05 1.34 1.69 These are plotted as points on coordinating paper, and then is drawn what appears to the eye as the best straight hne to satisfy each of the three sets of points.* Fig. 6 shows the hne for the increasing readings; the other two curves are similar. When it is desired to apply a calibration only to increasing readings, the ascending line is used, and similarly wath the descending. The combined line gives the best results when the instrument is used for measurement of a fluctuating quantity. To figure one of the spring scales, as for instance the ascend- ing, the line for which is shown by Fig. 6, a point is selected near its extremity, asFi— i/i, this point not necessarily repre- senting a pair of observations. It should, however, lie on the line. Then the spring scale equals S (ascending) = El or, using numerical values, 47.4 — 1.0 = — T-n?: — = 29.0 lbs. per inch * Certain researches of the author indicate that the decreasing values of force and extension do not follow Hooke's law within appreciable amounts and that, theoretically, they must follow a curved line. (Physical Review, October, 1911.) To represent them by a straight line is therefore merely a convenient approximation. 20 SCALES AND PRESSURE GAGES to be used when the readings of the instrument increase; sim- ilarly with the other two spring scales. Note that the intercept, k, is taken into account. If the curve does not pass through the origin it is because of friction or backlash of the indicating mechanism or to a false zero reading of the extension. DU F,-47.4 L /sS> 40 1" / / / 15 / 5 £20 / / to / ^ / / To a40 0.80 1.20 Extension, in Inches IGO LOO Fig. 6. (b) Spring Scale by Method of Least Squares. The theory of errors shows that the most probable straight line to fit such data is one so located that the sum of the squares of the distances of the plotted points from the line shall be a minimum. This can be calculated as follows. The equation of the line may be written 2 SCALES AND PRESSURE GAGES 21 in which k and S are unknown, and F and E are represented by a number of more or less discordant observations. This equation may be multiphed through by the coefficient of each unknown, thus F=SE+k EF = SE^+Ek. In each equation the corresponding values of E and F are sub- stituted thus forming two series of equations. Each series is summed and the resulting equations are known as the " normal equations ^^ oi k and >S respectively. These may be solved as simultaneous equations to obtain the most probable value of S. Using the data of the ascending scale tabulated, F=ES+k EF=E^S-{-Ek 10 = 0.32>S+/c 3.2=0.1024*S+0.32/c 20=0.64>S+/c 12.8=0.4096aS+0.64A; 30 = 1.02S^k 30.6 = 1.0404aS+1.02A: 40 = 1.32iS+/c 52.8 = 1.7424aS+1.32/c 50 = 1.68/S+/c 84.0 = 2.8224iS+1.68/c 150 = 4. 98^+5/c 183.4 = 6.1172^+4.98/0 Normal equation of k. Normal equation of S, From these, by eliminating fc, it is found that aS = 29.38 lbs. per inch. The descending scale is found similarly and the combined scale is obtained by adding the corresponding normal equations from the ascending and descending values. Note that the numerical values in the equations should be figured to four or five significant figures since, when the equa- tions are solved, the first two or three figures disappear by subtraction. Labor can be saved by using multiples of ten, or simple figures, for the independent variable F, and by using a pocket-book table of squares to obtain the values of E^. Problem 2i. Calculate the descending and combined scales for the example given by methods (a) and (b). Compare them. 22 SCALES AND PRESSURE GAGES Problem 22. Prove from the fact that the area under each curve equals work done that the descending curve cannot be a straight line. Problem 2^, From the ascending data of the example given, figure and compare the different results for the ascending spring scale obtained by the following (faulty) methods. 50^-1.68. The average of all the F's-^ average of £"s. The average of F-^E, The average of each increment of F-j- cor- responding increment of extension. The average increment of F divided by average increment of E, PRESSURE The measurement of pressure is a special case of force measure- ment, wherein the area over which the force is distributed is taken into account. Pressure is a compound unit being the number of units of force per unit area. In cahbrating pressure measuring devices, the standard force is that of gravity acting on some standard mass. Pressure is usually expressed in pounds per square inch. Its measurement is always relative, that is, based upon some other pressure as a datum. A pressure gage reads so man}- units above atmospheric pressure, for instance, and a vacuum gage, so many below. Absolute pressure, or pressure counted from zero, is an abstract conception and cannot be measured directly by instruments. Wt--a0561 Lb. Area'1 Sc[. In. Pr.^a036tLh pcrScf.In. Fig. 7 wt^o. Area' Pk' 0.0561 ^ 0722 Lb. 2 Sq. In. LtxpcrScf-fn. Wt'a0722LtA AreO'tSo/Jn Pr.-a0722Lb perSq. In. 2" ->^ Fig. 8. Pressure Produced by Water. Fig. 9. >•' Another measure of pressure is the height of water or other liquid which by its weight balances the pressure to be measured. •=C\ i 3 SCALES AND PRESSURE GAGES 23 Fig. 7 represents a cubic inch of water. At 60° F., this weighs 0.0361 lb. Since the area this force acts upon is one square inch, the pressure produced is 0.0361 lb. per square inch. Two cubic inches of water, arranged as in Fig. 8, would have twice the weight, but it would be imposed upon twice the area; hence the pressure would be the same. Arranged as in Fig. 9, however, the area would be one square inch, and therefore the pressure would be twice that shown by Fig. 7. It follows that the pres- sure produced by a given mass of water varies directly with its height and is independent of its cross-section. Hence, inches or feet of water may be regarded as units of pressure. Fig. 10 shows the application of this prin- ^ ^YJ ciple in the ^^ manometer. ^^ The pressure in the chamber C is said to be ^' X inches of water ^^ and this equals 0.0361 XX lbs. per square inch. The absolute pressure in C equals this Fig. 10. quantity plus the pressure of the atmosphere Manometer, represented by the arrow at A . Mercury is also used in manometers, and since its specific gravity is about 13.6 at 60° F., the equivalent is 1 in. of mercury = 0.0361 X 13.6 = 0.49 lbs. per square inch. 3. Calibration of a Bourdon Gage Principles. The Bourdon gage consists essentially of a hollow circular spring which is deformed when subjected to internal fluid pressure, the deformation causing a pointer to rotate upon a graduated dial. (See Fig. 11.) The pointer is readily removed so that it can be set at any part of the dial to correspond to an applied known pressure. It should be noted that the deformation of the hollow tube is proportional not to the absolute pressure within the tube, but to the difference of pressure within and without. The Bourdon pressure gage, therefore, always indicates pressures above at- 24 SCALES AND PRESSURE GAGES SECTION OF TUBE Fig. 11 ■Mechanism of Bourdon Gage. mosphere, since the outer surface of the tube is subjected to atmospheric pressure; and to convert its readings into absolute pressures, one must add the baro- metric pressure expressed in the same units. The vacuum gage works on the same principle as the one just de- scribed, the only difference being that the excess of pressure is on the outside of the tube (Fig. 11) causing a contraction of the coil, instead of an expansion, which is indicated, generally, in inches of mercury less than the barometric. The testing apparatus consists of a chamber in which any desired pressure may be obtained and to which is attached some accurate device for measuring it. The pressure is generally obtained by some simple form of hand pump. The measuring device is either a ^^ test gage,'^ a column of mercury, or a set of weights acting on a plunger of known area arranged to produce the pressure desired. The test gage is not a desirable standard as it needs calibrating itself from time to time. The mercury column is a cumbersome and expensive apparatus for pressures above a few pounds, although it is the most accurate method of measuring the true pressure. Besides, a high degree of accuracy is not needed since the least count of commercial gages is generally not less than 5 lbs. It is neces- sary, however, to use the mercury column when testing vacuum gages, and con- venient since they are graduated in inches of mercury and not in pounds per square Fig. 12. — Vacuum Gage Tester. inch. (See Fig. 12.) The standard weight SCALES AND PRESSURE GAGES 25 method is convenient but the friction of the plunger prevents true records. Fig. 13 shows an apparatus of this type. Weicjfrh for J Measur'inq Pressure For Acijusfmenf\^ Fig. 13.— Dead Weight Gage Tester. (a) The Constants of the Standard Weight Apparatus are the area of the plunger and the actual weights of the test weights, from which may be figured the actual pressures produced by them. The area is measured by cahpering the plunger. The weights should be determined by comparison with standard weights with a degree of precision compatible with the least count of the gage to be tested. Note that the pressure produced by the plunger and attached pan is always applied. (b) Calibration. Set the pointer to read accurately at the division most used and then take a series of readings of true pressures and instrument readings increasing and decreasing, from which plot a calibration curve. Convenient procedure is as follows. With the weights appUed to produce the desired 26 SCALES AND PRESSURE GAGES 3 is as follows. With the weights apphed to produce the desired pressure, depress the plunger a trifle by hand and close the cock between the gage and the pressure chamber, thus confining in the gage a pressure slightly greater than produced by the weights. The pan and weights are now revolved to reduce friction at the plunger and the cock slowly opened. The pressure indicated by the gage will then slowly decrease and a reading may be taken. For increasing values, the pan is raised a trifle, otherwise the procedure is the same. The two readings thus found are added and divided by tw^o to ehminate the effect of friction. If the gage is to be used for ascending pressures, then the calibration resulting from them only should be used. Gen- eralh^ this is not the case and the calibration from the combined readings is preferable. (c) Adjustment of the Scale. When the calibration curve is plotted, if the instrument is in error, it will be noted that the indications either increase or decrease with relation to their true value. Inside of the gage will be found an adjustable link, by means of which the travel of the pointer may be made greater or smaller for a given motion of the tube. This link should be changed in length until a correct motion of the pointer on the scale is found, as proved by a calibration curve. (d) The calibration of a vacuum gage is essentiall}- the same as for a pressure gage, an air pump and mercury column being used instead of the apparatus described. (e) Calibration of a Recording Pressure Gage. The working principle of the usual pressure recorders is that of the Bourdon tube, the tube being helical in form instead of circular. This provides a sufficient motion to the free end of the tube, to which a pen arm is attached; and magnification by links is not needed. The pen arm swings over a circular chart which is uniformly rotated by clockwork. The curve traced by the pen is thus one of pressure shown radially against time circumferentially. (See Fig. 14.) SCALES AND PRESSURE GAGES 27 When calibrating, the clock should be stopped, and the instru- ment read the same as a simple indicating gage. The dead- weight apparatus may be used, the pen arm first being set to indicate accurately at the desired point on the chart scale. Recorders are often set at a con- siderable distance from the points at which the pressure is to be ascertained. If the gage is either above or below such a point, and the connecting tube is full of liquid (such as condensed steam when the gage is below a steam pipe whose pressure is sought) then a correction for the head of liquid must be applied. Since 2.3 feet head is equivalent to 1 pound per square inch, the correction for a difference of height of H feet is J7/2.3 lbs. per square inch, and this should be subtracted from the instrument indications when the gage is set below the point of measured pressure, and added when above. Problem 3i, If the table and plunger of the test apparatus weigh 15| oz., how much pressure does their weight produce in pounds per square inch, the diameter of the plunger being 0.50 inch? Is the difference between this and 5 lbs. per square inch worth considering? Problem 82. If the area of the plunger of the test apparatus is about \ square inch, how closely should the test weights be weighed to come within the precision of a gage having a least count of 5 lbs.? Fig. 14. — Mechanism of Pressure Rec:rder. 4. Draft Gage Calibration Principles. Draft gages are generally special forms of manom- eters used to measure the reduced pressure (less than atmosphere) in chimne3^s, which creates the draft. This is expressed in inches of water and, as it is usually only a few tenths, the ordinary 28 SCALES AND PRESSURE GAGES 4 U-tube will not do. Fig. 15 shows a favored type. It is the ordi- nary manometer with one leg on a slant, so that the travel of the r-r _<---yn level of the liquid used is magnified. In use, the instrument should be set true to its designed level and the hquid adjusted so that the level in Fig. 15.— Draft Gage. the inclined tube standsat zero when there is no difference of pressure. Calibration of a draft gage can be made by examination of its graduations and the weight of the liquid, or by comparison with a standard instrument. (a) Calibration by Calculation. Having set the gage to its designed level, a horizontal line H-H^ is drawn wdth a spirit-level through the zero of the scale. The vertical distance T^ from the last graduation on the scale to this line is then measured. The level of the liquid in the inclined tube will fall this distance for the whole scale, but the level in the enlarged tube will rise an amount equal to the length S of the scale in inches multiplied by the ratio of the squares of the diameters of the bores of the small to the large tube. If water is the liquid, the sum of the rise and fall thus calculated equals the inches of water, pressure. The true pressure corresponding to any other graduation can now be found by proportion. The calculation of the rise of level in the enlarged tube assumes that the bores are uniform. Commercial forms of this i\\)Q of gage generally use oil for the liquid, having a definite specific gravity less than one. When such a gage is cahbrated, the total vertical difi"erence of level is found as before. The corresponding height of water is then found by dividing this by the specific gravity of the partic- ular liquid used. The specific gravity may be obtained by using a hydrometer or by weighing a known volume of the liquid. (b) Calibration against a Standard Gage. Connect the gage to be tested with a piece of rubber tubing to the standard SCALES AND PRESSURE GAGES 29 gage as in Fig. 16. The pressure in this tube may readily be reduced to any desired amount by applying the lips to the branch B, the pinch-cock serving to confine the suction when obtained. Enough readings for a calibration curve should be taken. For the standard gage, an impromptu instrument is easily made by using an inclined tube of generous length. Fig. 16. — Arrangement for Testing. Fig. 17.—Kent's Draft Gage. Problem 4i. If a draft gage using water at 70° F. is correct, calculate the rise in temperature that would produce 1 per cent of error. (See p. for weight of water.) Ans. 60°. Problem 42. In the type of gage shown by Fig. 17, the reduced pressure inside the inverted can M causes it to descend against the resistance of the spring (neglecting the buoyancy of the water). If the area of the inverted can is 50 square inches and if the pressure within is tu inch of water less than without, what is the total downward force on the can? How much will the spring extend because of this force if the spring scale is 0.2 lb. per inch? Ans., 0.9 in. Problem 43. Deduce an equation for the gage shown by Fig. 17, neglect- ing buoyance, to show the relation between the extension of the spring and the draft, lq inches of water, causing it. ANGULAR VELOCITY The units are usually whole revolutions per minute, abbreviated R.p.m. The simplest form of instrument to measure this quan- tity is the hand counter. This consists of a worm and wheel. The worm is part of a small spindle tipped with rubber so that, 30 ANGULAR VELOCITY METERS 4 if held against the end of a revolving shaft, it turns with the shaft, thus giving a circular motion to the worm wheel. The wheel is graduated so as to indicate the number of turns of the spindle. In operation, the hand counter is applied during a period of time measured with a watch, and from the readings of watch and coun- ter, the revolutions per minute of the shaft are calculated. The Continuous Counter, or cyclometer, is a variation of the hand counter in that its spindle is geared to a series of wheels with numbered faces, partially exposed, so as to show at any time the total number of revolutions. Some forms of continuous counter are driven by a reciprocating lever instead of a revolving spindle. In both forms, the instrument usually receives its motion from a small pin on the end of the shaft whose revolu- tions are to be measured, which pin acts as a crank. The Tachometer gives instantaneous indications of revolu- tions per minute without measuring time. The spindle trans- mitting the speed bears a pair of weights so linked that they move outward from the spindle by centrifugal force, and against the restraint of a spring. In so doing they actuate a pointer on an appropriately graduated dial. As the centrifugal force, and therefore the motion of the weights, are proportional to the speed, the pointer may register the speed instantaneously. On account of the variation in their internal friction and in the stiffness of their springs wdth use, tachometers should be calibrated before using on important work. Recording Tachometers are made in a variety of forms, and, for the greater part, depend upon the action of centrifugal force on a solid or fluid mass. Thus, the simple tachometer just described may be made as a recorder if the centrifugal weights actuate a pen arm (instead of a dial pointer) which travels over a clock-work driven chart. An example of the centrifugal fluid tachometer is the Bristol. This consists of a small air blower which is driven by the shaft whose speed is to be found. The blower creates a partial vacuum which increases as the speed 5 ANGULAR VELOCITY METERS 31 increases, and vice versa. The vacuum is transmitted to and recorded by a pressure recorder, the chart of which is graduated in revolutions per minute. Still another recording tachometer consists of a small generator, driven by the shaft considered, whose speed variations are evidenced by the generator voltage. This is recorded in terms of revolutions per minute upon a time chart. The Chronograph is an instrument by which a graphic record of time is made. Fig. 18 shows a form. Paper is caused to roll over a drum, D, by clockwork, and in contact with the paper is a pen on a light arm, A, which is caused to vibrate at regular time intervals by connection, electrical or otherwise, with a standard clock. Another arm, A\ is similarly actuated by connection with the shaft ^^^' 18.— Chronograph, the speed of which is to be measured, so that it vibrates once each revolution. Thus, there are drawn two lines, one broken at intervals representing time, the other, revolutions; from which may be obtained angular velocity. The Tachagraph is a very sensitive tachometer, arranged to give an autographic diagram of angular velocity. It is used to measure minute changes of speed within a revolution, 5. Calibration of a Tachometer Principles. The standard should be either a continuous counter or a chronograph. In either case it is necessary to have a revolving shaft of variable and controllable speed to cover the whole range of operation of the tachometer. A small steam engine of variable speed may be used, or a water wheel, or a series wound electric motor. A shunt woimd motor will do if a rheostat is put in series with its armature circuit. A small water rheostat is convenient as it giver a wide range of resistance. (a) Calibration against a Continuous Counter. Increasing and decreasing readings of the tachometer should be taken at 32 ANGULAR VELOCITY METERS 5 each speed. The mean of these readings is plotted against the speed as shown by the counter for the cahbration curve. If the continuous counter is arranged on the variable speed shaft so that it can be applied at the same time as the tachometer, the procedure is as follows. Starting with a slightly lower speed than is required, the tachometer is connected and the speed raised to the desired amount. Time and counter readings are then taken wth the tachometer still connected. If the speed remains constant as indicated by the tachometer, the observations are valid after the second readings of time and counter are taken. The decreasing readings are o])tained similarly. When the speed is high the counter becomes difficult to read. This may be obviated by an arrangement for throwing the counter in or out of connection with the variable speed shaft. A hand counter may be used if it can be applied to one end of the shaft while the tachometer is at the other. It is inadvisable to take readings of the two instruments at other than the same time as the speed may vary. The time during which the revolutions are counted should be of sufficient length to reduce the error of starting and stopping to less than the precision of the tachometer. For instance, if the tachometer cannot be read closer than 5 R.p.m., at any part of its scale, then at 250 R.p.m. the error in reading the in- strument is 2 per cent, and the error in reading the time should l:>e made less than this, say 1 per cent. Now a moving number is unlikely to be timed with an ordinary watch closer than one- half second; therefore the counting should proceed through at least 50 seconds to get the desired precision. Similarly, at 500 R.p.m., the error in reading the instrument is 1 per cent; the starting and stopping error should be reduced to ^ per cent, and the timing should proceed through 100 seconds. The use of a stop-watch will greatly reduce this time, as it reduces the starting and stopping error to one-tenth of a second or less. (b) Calibration against a Chronograph. With this apparatus the tachometer may be left in connection with the variable speed 5 ANGULAR VELOCITY METERS 33 shaft, and the speed first increased and then decreased in a series of steps at constant speed. The moving record may be stopped while the speed is being adjusted. The time for counting may be very much reduced, as the chronograph shows the whole number and fraction of turns of the shaft that occur during a time beat which may be as small as desired. (c) Calibration of a Recording Tachometer. The principles to be observed are exactly the same as given under (a) and (b). It should be observed that certain types of this instrument have a time lag in their indications behind the true R.p.m. of shaft whose speed it is intended to measure. That is, when this shaft changes in speed, a certain interval is required before the change is felt at the recorder. This interval should be noted and reported. Problem 5i. Using an ordinary watch, how long should a continuous counter be timed when calibrating a tachometer witl a range from 600 to 1200 R.p.m., at the even hundreds, if the least count is 10 R.p.m.? How long, if a stop-watch is used? POWER Power is defined as the time rate of work. Quantitatively, w^ork is the product of a force and the distance through which it acts, the unit being foot-pounds. A horse-power is defined as 33,000 foot-pounds of work done in one minute. If an engine can deliver 33,000 foot-pounds of work in one minute it is rated as 1 horse-power; if 66,000, 2 horse- power; and so on. Generally engines deliver a rota- tive effort. Suppose, for example, that an engine transmits an average Fig. 19. tangential force of F pounds at its crank pin. (See Fig. 19.) In one revolution, this force will act through a distance equal to the circle through which the crank pin has passed, or 27rr, r being the radius of the crank in feet. 34 dyna]mo:meters 6 The foot-pounds of work per revolution are then 2-rXFy and if there are N revolutions per minute, the work done per minute will be 27rrFxX, and the horse-power will be 2xrFAr 33,000* The quantity rF is called the '' torque/' Dynamometers are used for measuring power. Generallj^ the speed is measured independently of the dynamometer bj' a hand counter or otherv\'ise, so the dj^namometer is apphed only to measure the torque. This is done by balancing the torque by a measured force acting at a kno^Ti distance from the center of rotation. There are two broad classes of d^mamometers: absorption by w^hich the power to be measured is converted into some form in which it cannot be used; and transmission j by which the power is passed on unchanged. 6. Constants of Friction Brakes Principles. Friction brakes ma}^ be used as absorption dynamometers, and of these the Prony brake is the commonest and most accurate form. (See Fig. 20.) It consists of a band wrapped around a pulley on the shaft whose power is to be measured, so arranged that by tightening a hand wheel, H, the friction between the wheel and band can be controlled. The band is held from turning by means of an arm, A, attached to it, and supported by some force measuring device at its free end. Considering the friction between the band and wheel as a single force,/, then the horse-power developed is 27rr7.Y-^ 33,000; r' being the radius of the wheel in feet. Now since the force W exerted by the scales, S, produces equihbrium, by the prin- ciple of moments RW = r% . DYNAMOMETERS 35 and therefore by substituting in the expression for horse-power just given 33,000 In practice, if the force, TF, and the revolutions per minute, Ny are measured, the horse-power may be calculated, the length of the arm being known. B is called the '^ brake constant/' Fig. 20.— Prony Brake. It should be noted that the arm, A, by its weight produces a force acting on the scales which should not be included in the force balancing the frictional effort. This should be allowed for by determining the ^^ unbalanced weight '' of the brake, or " brake zero,'' and subtracting it from the scale readings. Methods of determining the brake zero will be given later. The rope brake is a modified form of prony brake. Fig. 21 shows such a one, the friction between the rope and the wheel being balanced by the force of the scales on the right less the weight on the left. The difference between these quantities is / 36 DYXAMOMETERS the value of W in the formula, and the value of R is the radius of the wheel plus the radius of the rope. There is no unbalanced weight if the lengths of rope on each side of the pulley are equal. The friction, and therefore the horse- power, ma}' be varied by increasing the weight on the left or by taking more turns of the rope about the wheel; either procedure greatly in- creases the friction. Fig. 22 gives two other arrangements of rope brake and their equations. In operation, the heat generated by the friction is removed by circulating water within the brake wheel, the latter being provided vdth. internal flanges for that purpose. It is generally 7J^7m777777777777?77^77777Tr77777T7p77 Fig. 21. — Rope Brake. ^///■V'-." w///////////////////////////////// Torque = (5 -Brake Zqxo)R Torque = (TF->S-w;)i2 Fig. 22.— Rope Brakes. suflBcient to feed the water at a rate just equal to the loss by steaming. Hydraulic friction brakes are the same as those just described in principle though quite different in detail. A series of discs mounted on the power shaft revolve in a casing filled with water under pressure, the casing being free to revolve about the shaft. The friction between the discs and the water causes a turning 6 DYNAMOMETERS 37 effort upon the casing which is balanced by a force measuring device the same as with the common prony brake. Regulation is secured by varying the water pressure. The constants are the same as for the other types, but in most cases there is no unbal- anced weight. (a) Determination of Unbalanced Weight. If friction could be entirely eliminated between the band and 13 y wheel, the unbal- anced weight would be the reading of the scale, Fig. 20. But, no matter how loose the band is, there is always some friction between it and the wheel tending to hold up the brake arm when the wheel is stationary. If the brake is removed from the wheel and supported by a knife edge or circular pin at the point k, Fig. 20, the other end being supported by the scales as in opera- tion, then the scales will indicate the unbalanced weight pro- vided that the flexible band does not change in its weight dis- tribution. This is one method of finding this quantity. Another method consists in revolving the brake wheel first in one direction and then in the other, and noting the corresponding readings of the brake scales. With the wheel revolving clockwise, Fig. 20, the scales will indicate the unbalanced weight plus the force necessary to balance the friction at the band. Anti-clock- wise, it indicates the unbalanced weight minus this force, since the friction is reversed. Calling the force balancing friction X, Unbalanced Wt.+^ = lst reading Unbalanced Wt. — X = 2d reading Adding, Unbalanced Wt. = (lst+2d reading) -^2. When applying this method it is necessary that X remain con- (Btant. The band should be quite loose, the bearing blocks wet with oil, and the wheel turned at a uniform rate. The third method is the same in principle as the second, but the brake is revolved instead of the wheel. The spring balance. Fig. 20, is first drawn upward giving the weight +X reading; then the weight of the brake is allowed to draw it 38 DYXAMOMETERS 6 dowTi for the weight —X reading. Note that if the spring balance is slanted out of its correct position relative to the brake, a component force will be indicated. (b) Determination of the Horse-power per Pound of Thrust per Revolution. This is the '' brake constant " or 2-i?-=- 33,000. R should be measured with a tape or measuring rod. Note that R is the perpendicular distance from the center of the brake- wheel to the Une of the balancing force TF, Fig. 20. Problem 6i. \Miat is the brake constant ii R = 5 ft. 3 J in.? If unbal- anced weight of the brake is 2.5 lbs., what scale reacUng would be necessary to balance 40 H.P. at 160 R.p.m.? Aws., .001; 252.5 lbs. Problem 6^. By the third method, the scales indicate 10 lbs. when the brake is pulled up. (Fig. 20.) Its weight is not enough for it to drop, con- sequently the balance is reversed and the brake pulled down, for the weight — X reading. The scales then indicate 2 lbs. What is the unbalanced weight? Ans., 4 lbs. Problem 63. If the unbalanced weight is 5 lbs., where should weight be added to balance the brake, and how much? Problem 64. Given an arrangement like Fig. 20 except that the wheel turns anti-clockwise and the spring balance is inverted. If the R.p.m. = 100, arm = 4 ft., unbalanced weight = 14 lbs., and the balance reads 20 lbs., what is the horse-power? Ans., 2.59 H.P. 7. Calibratiox of a Fan Brake Principles. Fan brakes are convenient for measuring the output of high speed motors that operate at variable speed, such as automobile engines. Fig. 23 shows such a one. The energy of the shaft is absorbed by imparting kinetic energy and heat to the air. With a fixed set of vanes the power thus absorbed varies as the cube of the speed. The capacity of the brake at a given speed of rotation can be changed in only two ways, namely, by changing the size of the vanes or their distance from the cen- ter of the shaft. The first method may be taken by swinging the vanes around on their arms so that the effective area resist- DYNAMOMETERS 39 O O o o o o o o o ]> Fig. 23.~Fan Brake. ing motion is lessened. For the second method, the fastenings of the vanes to the arms may permit the desired radial variation. This type of dynamometer is sometimes mounted on a frame independent of the engine shaft and driven by a belt. In this case, the belt losses and brake journal friction (more or less iiideterminate quan- tities) are added to the resisting effort. (a) Calibration against a Transmission D3mamometer. By means of a transmission dynamometer, simultaneous values of torque necessary to drive the fan and revolutions per minute are determined for a given adjustment of the vanes. From these values, the horse-power absorbed at each speed may be calculated, and a curve of horse-power vs. revolutions per minute plotted. This curve may be used for finding the horse-power, when the brake is in usual operation, from readings of the rotative speed. (b) Calibration against a Calibrated Motor. If the fan brake is belt driven, it may be run by a variable speed electric motor, through the same belt and pulleys to be used when the fan measures power. At a definite speed of the fan, readings of the armature and field currents of the motor and of its speed are taken. The belt is then removed, a prony brake applied to the motor pulley, and the horse-power of the motor measured under the same conditions of current and speed. If all controllable conditions are the same, this horse-power will be the same as that absorbed by the fan at the applied speed. A series of similar trials at different speeds will give data for a calibration curve. This calibration will be somewhat in error owing to the fact that the reaction on the motor bearing caused by the prony brake thrust is somewhat different from the reaction due to the belt pull; hence the friction of the motor under the two loads will be slightly different. .^ 40 DYNAMOMETERS 7 (c) Use of the Horse-power Constant. The power absorbed by the fan for a given setting of tlie vanes equals KX density of the airX(R.p.m.)''^ in which i? is a quantity very nearly constant. Assuming that the density of the air also is nearly constant, the product of K and the density may be found experimentally at a convenient speed. Then the horse-power at any other speed may be found, approximately, by multiplying this product by the cube of the speed. The experimental determination of K times air density is made by taking readings according to either method (a) or (6). Then the desired value equals the horse-power divided by the cube of the apphed speed. Variations in belt losses and in the value of K make this method inexact. Problem 7i. WTiat percentage of error will be caused by the density of the air changing from that corresponding to a barometer of 29.5 in. of mercury, at which the fan is calibrated, to 30 in.? What percentage by a change of temperature from 60 to 80° F.? Atis., 1.6%; 3.8%. 8. Calibration of a Transmission Dynamometer, Weight-arm Type Principles. The weight-arm type of transmission dj^namora- eter consists of some device by which the torque of a revolving shaft can be balanced by a standard weight or weights acting with a known leverage. The balancing torque caused by the weights is thus a measure of the horse-power when the revolutions per minute are known. There are many forms of this type of d}Tiamometer differing mainly in mechanical details. Belt dynamometers of different kinds are in the weight-arm class, of which Fig. 24 represents one. The torque of the trans- DYNAMOMETERS 41 mission shaft is equal to the effective^belt pull, T1-T2, multipHed by the radius at which it acts, r. Disregarding the friction at the bearings of the pulleys, p and p', the reactions at these bearings will be 2Ti and 27^2, respectively, as will be seen from a consideration of the belt forces. Taking moments about the fulcrum /, and disregarding the weight of the arm A, we have WR +2T2a =2Tia from which Ti- T2 =WR-^2a and the torque = r{Ti -T2)=rWR-^2a. ^'Transmission Shaft ]' P/aiform \ Scales Fig. 24. — Belt Dynamometer. Fig. 25. — Pillow Block Dynamometer. Thus by balancing the belt torque by a known weight W, the power may be measured if R/a is known and if a suitable allow- ance is made for friction. A pillow block dynamometer is shown by Fig. 25, consisting of three gear wheels the middle one of which is mounted on a pillow block, so as to bear freely on a weighing device. The turning force of the driver, F, produces an equal resisting force at the gear on the transmission shaft, barring friction. The reaction W, which can be weighed by the scales, thus equals 2Fj and hence the torque of the transmission shaft is W Fr^^Xr. 42 DYNAMOMETERS 8 The reaction W may also be measured by hanging the middle wheel from one arm of a lever above the other carr>dng a balanc- ing weight. Some forms of pulley block dynamometer omit the middle wheel and weigh the reaction of the bearing on the transmission shaft directl3\ When this is done, the transmission shaft must be arranged to rest freely on the weighing de\dce. The Webber differential dynamometer is a variation of Fig. 25, but similar in principle. It is shown diagrammatically by Fig. 26, which represents three bevel gears, the middle one being Fig. 26. — Webber Dynamometer. supported by a lever whose fulcrum lies on the common axis of the driver and transmission shafts, Similar to the principle showTi by Fig. 25 the net force on the middle gear is 2F, This is balanced by the dead weight T7 acting with a lever arm of R feet. Taking moments of the forces acting on the lever around its fulcrum, we have 2Ft = WR from which, torque transmitted = Fr=ffl. As actually constructed there is another gear on the lever-arm, as indicated by the dotted line. This does not change the relation, merely substituting for the moment 2Ft two moments, 8 DYNAMOMETERS 43 Fr+Fr. Also there is a jockey weight on the arm in addition to the pan weights similar to the arrangement of a platform scales. The Emerson power scale is a dynamometer by which the torque is passed to a transmission pulley on the driver shaft through a lever system so arranged that a thrust in an axial direction is given to a non-revolving sleeve on the shaft. This thrust is balanced by dead weights which consequently measure the torque. Friction of the moving parts of the dynamometer itself has not been accounted for in the equations. Generally the dyna- mometer indicates the torque necessary to overcome its own f ricton ' and windage in addition to the external torque on the transmission pulley which alone it is the purpose to measure. (a) The Constants of a Djrnamometer of the Weight-arm Type are first, the true values of the dynamometer weights; second, the unbalanced weight of the arm or lever system; and third, the leverage ratio produced by the arm or lever system. The true values of the weights should be determined with a scales sufiiciently precise to keep within a reasonable percentage of error. The unbalanced weight of the arm may be found as for a prony brake, by revolving the driver shaft in first one direction and then the other by hand, and noting the resulting force at the end of the arm where the weights are to be applied. A spring balance may be used for this purpose. Half the sum of the two readings equals the unbalanced weight. The ratio of levers may be obtained generally by direct measurement. In the case of the Webber dynamometer, for instance, only the length of R, Fig. 26, is necessary. For the arrangement of Fig. 24, the ratio is R a, as shown by the equation. (b) Calibration by Calculation. The torque equivalent to each dynamometer weight acting at the previously determined leverage is found by multiplying its value in pounds by the lever- 44 DYNAMOMETERS 8 age ratio as shown In the equation for the dj^namometer in ques- tion. A series of such determinations furnishes data by which the horse-power corresponding to any weight may be found when the d\'namometer is in usual operation. The torque equivalent to the unbalanced weight of the arm should be added to that indicated b}^ the weights applied if the turning effort of the driver on the arm is upward. If it is down- ward, the power being then gaged by scales instead of weights simpl}^, the torque equivalent to the unbalanced weight of the arm should be subtracted. (c) Allowance for Friction, Windage, and Centrifugal Force. To allow for friction, a crude but convenient approximation is based upon the assumption that the frictional resistance is the same under all conditions of external torque. If, then, the dynamometer is run with the transmission shaft entirely free, the weight to balance the arm gives the correction to be sub- tracted from the readings in usual operation. Windage is included in this, but if the dynamometer is to be used at various speeds, similar corrections should be determined at these speeds to allow for the varying value of the windage. With some dynamometers having revolving levers, bell- cranks, and the like, such as the Emerson power scale, centrifugal force acting on these .-parts may cause a distortion of the indica- tions. This is allowed for under the windage corrections. (d) Comparison with Prony Brake Measurements is the most valid means of calibrating any transmission dvnamometer. To do this, a prony brake is fitted to the transmission pulley and is adjusted so as to balance each K R---.-> ^Ploi fe carry irtof pulleys, free to turn on center Fig. 27. — Belt Dynamometer. dynamometer weight in turn, power being delivered as in usual DYNAMOMETERS 45 operation. The torque shown by the prony brake is the true torque measured by the corresponding weight. When a jocky w^eight is used as for the Webber dynamometer, a calibration curve of torque against jockey weight positions is convenient. If the dynamometer is to be used at various speeds, it should be calibrated at a number of them, the results to be in terms of either horse-power or torque, as shown by the brake, correspond- ing to each dynamometer weight. In this way friction, windage, and centrifugal force may be taken into account. Problem 81. Deduce the torque equation for Fig. 27. 9. Caijbration of a Transmission Dynamometer, Spring Type Principles. Spring dynamometers differ from the weight- arm type in that the torque to be measured is balanced by a a spring or springs through which the torque is passed. The spring is consequentl}^ deformed by either a tensile, compressive, or twisting stress. If the constant of the spring is known (that is, the number of pound-feet of torque necessary to cause a unit deformation) then by noting the deformation, the horse-power may be determined. Fig. 28 shows, in part, the principle of the Van Winkle dyna- mometer. Power is taken off at the loose pulley P which is driven through springs by the disc attached to the driver shaft. The resulting deformation of the springs permits a change of position of the pulley relative to the disc, and this operates a bell-crank lever (not shown) which in turn actuates a pointer on a stantionary dial. The dial is arranged to indicate horse-power direct. Another spring dynamometer, made by the Central Laboratory Supply Company, is shown by Fig. 29. Two shafts are connected by a spring through which the power to be measured is passed. These shafts are provided with discs arranged as commutators. 46 DYNAMOMETERS being insulated from the shafts except at the shaded portions showTi under the brushes. In this position, an electric circuit is —Loose Trans, Pultetj •f/,river Fig. 29. — Central Laboratory D>Tiamometer. completed causing a click in a telephone receiver. The right-hand brush is stationary, but the one on the left is so arranged that it may be swung around the shaft. In operation, the latter is 9 DYNAMOMETERS 47 manipulated until a click is heard in the receiver, indicating that both contact pieces are passing under the brushes at the same time. Then the angular motion of the left-hand brush shown on the dial and measured from its clicking position when there is no torque delivered, is equal to the twist of the spring, and hence is a measure of the torque. In usual operation small variations of the torque, due to belt flapping, etc., make the clicking position somewhat variable. It is therefore convenient to read the maximum and minimum angles at which no click is heard and to take the average of these as the twist of the spring. The Flather dynamometer (Fig. 30) differs from the foregoing in that the torque is communicated to the transmission pulley through small pistons, p, working in cylinders filled with oil. ^V//^Wy777j^ "Loose Trans. Pulley <— Arm, Keyed Fig. 30. — Flather Dynamometer. The fluid pressure* thus produced is transmitted through tubes, t, and a longitudinal hole through the center of the driver shaft. Connecting with this hole at the end of the shaft is an indicator by which a graphic record of the pressure is made. Since this pressure is proportional to the torque (being produced by the driving force at the cylinders, c, acting at a constant distance from the shaft center) it is a measure of the horse-power. 48 DYNAMOMETERS 9 Friction affects the indications of a spring dynamometer in two ways. First, since the friction of the loose transmission pulley or of the transmission shaft on its bearings always acts against the motion, it makes the indicated torque greater than the true external torque. Second, friction of the indicating mechanism makes the indications for increasing torques low, and for decreas- ing high, similar to the action of friction in a pressure gage. Generally the first effect is greater than the second. (a) Static Calibration. With the driver shaft clamped, the transmitting shaft may be twisted with a series of known weights acting at a measured distance from the center of the shaft. Thus a series of values of torque may be obtained with the correspond- ing instrument indications, the latter being either in dial gradua- tions, degrees of twist, or height of an autographic diagram, as may be appropriate to the instrument tested. To apply the static torque, the transmission pulley may be used as the arm, a rope being tied to a spoke and passed over the pulley face from which to hang the weights. If the necessary number or size of standard weights are not available; a lever may be clamped to the transmission shaft, and a single weight applied at various distances from the center. In this case, the moment of the lever should be accounted for. Increasing and decreasing values of the torque should be applied and corresponding readings taken to eliminate the effect of fric- tion. For the increasing readings, the weights are caused to bring up the torque gradually to the desired amount. For decreasing, extra torque is brought upon the shaft by bearing on the weights by hand; then gradually removing the hand pres- sure so that the torque will decrease to the desired value. The average of each pair of readings is then plotted against torque for a calibration curve. By this procedure, for increasing values, the motion of the transmission pulley or shaft is opposite to that for decreasing values. Hence both effects of friction, previously noted, are eliminated. K^i. 9 DYNAMOMETERS 49 For dynamometers with which the angle of torsion is read, the curve of torque vs. degrees may be used to get the spring constant. Then if S is this constant in pound-feet per degree of twist and A the torsion angle noted in usual operation, horse-power = .00019 XaSX A XR.p.m. which is the horse-power delivered by the dynamometer pulley. (b) Allowance for Friction, Windage, and Centrifugal Force. The readings of the dynamometer should be reduced by an amount corresponding to the torque necessary to overcome these forces. The values of the corrections may be determined as for weight- arm dynamometers. For recording instruments, a line should first be made on the chart with the dynamometer running free. The diagram under load should then be measured from this friction line as a datum. For dynamometers using a measurement of the torsion angle, the correction is made in degrees, being subtracted from the reading observed in operation. (c) Comparison with a Prony Brake may be made in exactly the same way as for weight-arm dynamometers. (Test 8 (d).) Problem 9i. The reading of a spring dynamometer running at 450 R.p,.m. is 26 degrees. If the spring constant is 3 lb. -ins. per degree, and if the cor- rection for windage, friction, etc., is 5 degrees, how many foot-pounds of work will be done in ninety seconds? What will be the horse-power trans- mitted? Ans. 22,200 ft.-lbs.; 0.45 H.P. Problem 82. Same data as Problem 9i, except that the friction of the transmission shaft is separately determined, the correction being 4 degrees, and the correction for friction of the indicating device is 1 degree. What is the transmitted horse-power when the torque is increasing? When it is decreasing? Problem 9.3. The axis of the piston p (Fig. 30) is 15 inches from the cen- ter of the driver shaft, and the diameter of the piston is 2 ins. Disregarding friction, what fluid pressure is produced when the horse-power is five, at 150 R.p.m.? Ans. 44.0 lbs. per sq. in. 50 THE ENGINE INDICATOR 10 THE ENGINE INDICATOR- REDUCING MOTIONS The engine indicator is an instrument which makes a graphic diagram giving the relation between the pressure and volume of the fluid in an engine cylinder under working conditions. Since the area of such a diagram is proportional to work, the indicator is a dynamometer of a special type. It is shown in principle by Fig. 31. C is a small cyUnder with a close fiUing piston P which is subject to the same fluid pressure as in the engine cylinder, being connected to it by a short pipe. This pressure compresses the spring S until the force of the spring balances the pressure. Thus the motion of the piston is proportional to the pressure. The piston motion is communicated and magnified by means of a linkage L bearing a pencil point at ^4. Z) is a metal drum free to oscillate on a spindle and carrying the paper on which the record is to be made. The drum is actuated by the engine cross-head through a cord K, a spring within the drum serving to bring it back upon the return stroke. Thus the motion of the drum is proportional to the engine pis- ton and therefore to the volume in the engine cyhnder behind dj the piston. The diagram made by the pencil point on the record paper is one of pressure shown vertically and volume (or piston stroke) horizontally. The principal use to which the indicator is put is the find- ing of the mean ejfedive pressure in an engine cylinder through- out its working stroke, from which quantity the cylinder or Fig. 31. — Engine Indicator. 1 10 THE ENGINE INDICATOR 51 indicated horse-power may be calculated. (See Test 43.) Fig. 32 is a typical indicator diagram from a steam engine. The average pressure on the forward stroke is the mean height, to scale, of the curve ahc. On the return stroke, the average pres- sure {hack pressure) is the mean height of cde. The effective pressure is the difference between these two, or the mean height of the indicator diagram. This may be found by dividing its area in square inches by its length in inches, and multiplying the quotient by the scale of pressure. The scale of pressure is Steam Line d Steam Valyei^ Closes-" \ ^ .t •^ A^t 1 t <9 1 ^^#^ e ^rSham Vctlve "^"^"^"---^ I. Opens Q. Exhaust Yalve T X Opens ■-" \ Vv c '^ Exhaust Valve <^fe<--. y'" Closes ^ RETURN STROKE ^ d Exhaust Line Atmospheric Pressure Line—^ Vo\ume Fig. 32. — Indicator Diagram from Steam Engine. the number of pounds per square inch on the indicator piston necessary to produce one inch of rise of the pencil, and is referred to as the spring scale. The indicator is equipped with a number of springs of different stiffnesses so that one appropriate to given conditions may be selected. The drum spring is adjustable so that a greater tension may be operative at higher rotative speeds to provide proper accelera- tion of the drum upon the return stroke. 52 THE ENGINE INDICATOR 10 The cord actuating the drum does not receive its motion directly from the engine cross-head, but from a reducing motion^ the function of which is to reproduce the engine stroke on a small, but always proportionate scale. A pantagraph is often used for this purpose. Under Tests 12 and 13 are described various types. 10. Calibration of the Indicator Spring and Pencil Motion Principles. There are four causes of error in the ordinates of an indicator diagram. First, when applied to high speed engines, the inertia of the indicator piston and attached linkage causes a variation from correct positions. Second, at high speed, the pressure in the indicator cylinder lags behind that operating on the engine piston, because of the inability of the steam immediately to traverse the passages to the indicator. Third, the mechanism actuating the pencil may incorrectly magnify the motion of the indicator piston. Fourth, the spring scale may not be exactly known. Friction of the indicator piston and linkage causes a variation of the spring scale, since because of it the pencil is too low when rising and too high when falling. (See Test 2, principles.) The first of these errors may be avoided, or reduced, by the use of stiffer springs than are appropriate to low rotative speeds. With a stiffer spring, the total rise of the pencil is less, and there- fore the velocity and inertia of the pencil motion parts are decreased. The second cause of error, lag in the fluid pressure, may be reduced by the use of short and direct pipe connections between the indicator and engine cylinders. Errors due to the third and fourth causes may be corrected as will be described. 10 THE ENGINE INDICATOR 53 (a) The Pencil Motion may be Tested as Follows: With the indicator spring removed, a horizontal line is drawn on a piece of record paper placed on the drum, by revolving it by hand, the pencil bearing against the paper at a^low position of the linkage. Then, with the drum held stationary, a vertical line is made by moving the pencil and Hnkage up by hand. This is repeated with the drum in a second position. The two vertical lines should be parallel and straight, and perpendicular to the horizontal line, if the pencil motion is true. (b) Determination of Ascending, Descending, and Combined Spring Scales by Graphic Method. It is necessary to get a series of values of true pressures and corresponding heights of indicator pencil. The apparatus for varying and measuring the pressure should preferably be one using the same working fluid to which the indicator is subjected in practice, so as to duplicate the conditions of temperature and friction. Dead weights applied directly to the indicator piston are sometimes used, but these do not correctly reproduce the working conditions. Fig. 33 represents a calibration apparatus using steam. The pres- sure is varied by manipulating valves A and B, an opening of A and closing of B having the effect of increasing the pressure in the large steam chamber, and vice versa. The measuring device is a set of known weights acting on a plunger of known area, from which the pressure balancing the weights may be figured. An accurate and precise Bourdon gage would serve the purpose as well. The gage shown in Fig. 33 is used to indicate the pressure in the chamber when the weights are not balanced, for convenience in manipulating the valves A and B, Using the caUbration apparatus, a diagram similar to Fig. 34 is made on an indicator card. For the ascending pressures, the weight table must be balanced and rising very slowly when the line is drawn. Similarly, for descending pressures, the table should be gently falling. The table is revolved by hand to reduce friction at the plunger. 54 THE ENGINE INDICATOR 10 The heights of the Unes from the atmosphere Une are then measured to j^o in., and recorded on the diagram with corre- sponding pressures as in Fig. 34. These data are then plotted and results obtained as for Test 2 (a). (c) Spring Scales by Method of Least Squares. The same experimental data are used, but the results are calculated as for Test 2 (b), the value of F in the equations then being the observed frvfn Sfeam Line j Fig. 33.— Indicator Spring Testing Apparatus. ,.68" -JJ0l-5d 13J" 1:56 — 40 ,02. — !:°s:-3o 0.^ ^i2Lja 0.32 0.34' Atmo sphere v 10 Fig. 34.— Calibration Records. pressure in pounds per square inch, and £, the height of the indicator pencil in inches. (d) Correction of Indicator Diagrams. Various methods, more or less accurate and laborious, have been proposed for applying calibration results to indicator diagrams. Generally, it is suf- ficient to use the combined spring scale with which to multiply the mean height to get the mean effective pressure, the error involved being within the limit of accuracy of power tests. But the combined spring scale represents the true scale of the spring 10 THE ENGINE INDICATOR 55 more nearly than it does actual conditions, since the method of figuring it eliminates friction. Strictly speaking, the ascending and descending scales should be used separately on the diagram, the former applied to the mean height of cde. Fig. 32, since the pencil is rising on that line; and the latter to the mean height of abc since there the pressure falls. But when the back pressure line is horizontal in large part, as it almost always is, the descend- ing scale applied to the whole diagram will yield a fair result. The indicator is sometimes applied to other than power measurements, for which a high degree of accuracy is desirable. Pressure Fig. 35. Fig 36. Correction of Indicator Diagrams. It is then necessary to reconstruct the diagram to get correct results. A method of doing this is as follows. Calibration data are obtained as previously described, and plotted as shown by Fig. 35. The range of pressure P for the calibration must be the same as that in the indicator diagrams to be corrected, and all operating conditions of the indicator during its test the same as when the diagrams are taken. It will be noticed that the descending curve of Fig. 35 is not straight, and is joined to the ascending curve. Careful experimentation will reveal these characteristics. Actually, there can be no unfilled gap between 56 THE ENGINE INDICATOR 10 the two curves, as there would be under the assumption that both are straight lines, an assumption, as was pointed out under Test 2, made only for convenience in approximately figuring the scales. Having plotted the curves according to Fig. 35, the ascending scale should then be obtained by either of the two methods (a) or (6) previously given. The caHbration curve is next laid alongside of the indicator diagram to be corrected as shown by Figs. 35 and 36. Now, the back pressure line is shown correctly to the ascending scale determined from the calibration. To represent a point a of the indicator diagram on this scale, the construction abbiai^ is used, the point ai, being the required corrected position of a. Enough points are corrected in this way to reconstruct the pressure line of the indicator diagram. The ascending scale will then apply correctly to the whole diagram. (e) Sampling. When there are a large number of diagrams for a single engine test, a few representative ones only are selected for reconstruction. Suppose, for instance, that there are 24 diagrams and that the average of all their mean heights is H inches. Three of these should be selected as near as possible to this average mean height, and fairly representative in general proportions. These three diagrams are reconstructed and then the desired results obtained from them. To get the average of the mean effective pressure from all the diagrams without reconstructing all of them, the value H may be reduced in the proportion that the mean height of the three sample diagrams is reduced after reconstruction. The corrected value of H when multiplied by the ascending spring scale gives the corrected mean effective pressure. Problem lOi. The pencil of an indicator throws 2 ins. If the boiler pressure is 145 lbs., what should the spring scale be to give as high a diagram as possible? Ans.y 80. Problem 10:. The ratio of the pencil motion to the piston motion of an indicator is 6 : 1. The area of the piston is | sq. in. With a 30-lb. spring, the difference between ascending and descending positions of the pencil at 11 THE ENGINE INDICATOR 57 a given pressure is 0.04 in. If the friction is all at the piston, how much is it in pounds? Arts., 0.3 lb. Problem IO3. With the same indicator and spring at last problem, if the friction between the pencil point and the paper is 2 oz., how much differ- ence in the height of the pencil will this make? Ans. 0.042 inch. Problem IO4. With the apparatus of Fig. 33, what is the effect of friction at the plunger upon the apparent true pressure? What effect has this upon the calibration records? 11. Testing the Motion of the Indicator Drum* Principles, When an indicator drum is driven by a cord attached to a reducing motion mechanically correct, the motion imparted to it is approximately simple harmonic. Upon the forward stroke of the engine, the cord is pulling the drum, and upon the return stroke, the drum spring is stressing the cord to keep it taut. Thus the cord is always under stress. If the stress varies, the cord will stretch according to such variation, and consequently the drum will not assume the correct positions it would have if driven by an inelastic connector. Stress in an indicator cord is the resultant of three distinct forces: namely, the drum spring tension, the force required to overcome the inertia of tlie drum, and the force to overcome friction at the drum spindle and at any guide pulleys used to guide the cord. The force of the spring increases with the for- ward stroke of the drum (the spring being wound up) and decreases upon the return. The variation is usually uniform with the motion. In general, at the beginning of the forward stroke, inertia increases the cord stress since, as the speed is increasing from zero to a maximum at mid-stroke, inertia effects a tendency of the drum to lag. Beyond mid-stroke, however, the speed is decreasing, and as the drum tends to exceed the velocity induced * For a more complete discussion of this subject see author's article in Power, Aug. 20, 1912. 58 THE ENGINE INDICATOR 11 by the cord, a slackening results. Upon the return stroke the force of acceleration varies in the same way as on the advance. The force of friction is always opposite to the drum motion and therefore changes its direction at each stroke. During the forward stroke it tends to increase the cord stress, and upon the return, to decrease it. These three forces are represented graphically by Fig. 37. The resultant stress in the cord equals their algebraic sum at any drum position. At low speeds, the force of acceleration Positions of Drum Crank End Resultant e oc=os*od-of. Head End ■I — I _ J^^'^'^fS——~(£^'PJl. ■^-U i2 O^r Of: k - Forwanjl Stroke-- —Return Stroke ->H^g Fig. 37. — Variation of Forces on Indicator Card. is practically negligible; hence the resultant cord stress increases on the forward stroke, and decreases on the return with lowered values due to the reversal of friction. At high speeds, the force of acceleration reverses this variation as shown by Fig. 37. At some intermediate speed the force of acceleration and the spring tension nearly balance, so that the cord stress is approximately constant during each stroke, but a trifle less on the return because of friction. This is the speed at which the indicator drum is best adapted to work, since the more nearly constant the cord stress is, the less is its stretch and the consequent error. 11 THE ENGINE INDICATOR 59 Let us now compare the effects of a higher speed than this with the ideal condition of constant cord stress. The effect of speed is to increase the stress at the head end and decrease it at the crank end (see Fig. 37). At the head end, therefore, the cord is longer and the drum travels further in this direction. Similarly, at the crank end, the cord is shorter and the drum is pulled further toward that end. The net effect is to pull out the indicator diagram. Now, if the diagram were lengthened uniformly its proportions would remain correct, and there would be no error. Accordingly, if the cord were subjected to a uni- formly decreasing and increasing stress, and if its stretch varied directly with the stress, a correct diagram would result. It follows that, lacking such uniformity, the error of any point of the diagram should not be judged by the absolute stress or stretch at that point, but by the difference between this stress or stretch and that necessary to produce a uniform lengthening. It is seen from Fig. 37 that the resultant cord stress is greater than that necessary for uniformity on the forward stroke and less on the return. Hence, during the forward stroke, the cord is too long and a point on the indicator diagram is to the left and behind its correct position. During the return stroke the cord is too short; a point on the indicator diagram is to the right and again behind its correct position, since the motion is reversed. The net effect of the stretch of the cord, then, is to make the mean effective pressure appear smaller, and the cut- off, compression and release earlier than their true values. (a) Determination of Spring Tension. Since this varies through the drum stroke, its value at mid-stroke may be measured, or the average of the values at the ends of the stroke may be used. A spring balance of between 5 and 10 lbs. capacity should be fastened to the cord leading from the drum, and through it the drum pulled past the position at which it is desired to measure the spring tension. The reading of the balance is noted at the instant of passing this position. This equals the spring tension 60 THE ENXtIXE INDICATOR 11 plus friction. The spring is then allowed to reverse the motion, and another reading is taken, equal to the tension minus friction. The sum of these readings divided by two is the spring tension. (b) Determination of Dnmi Friction. The same method is used as for measuring the spring tension. The friction equals the difference of the readings divided by two. With an indicator properly lubricated and adjusted, and of good make, the friction should not exceed 5 or 10 per cent. When the cord rims over guide pulleys, however, the friction is greatly increased. When the friction is high, the cause should be looked for and remedied. (c) Testing Indicator Cord. Tie one end of about four feet of the cord to be tested to a fixed point on a bench or table, and the other end to a spring balance. Mark this end a few inches from the balance with a fine ink line, and under this line place a piece of paper or a foot-rule. Stretch the cord by pulling the balance horizontally until about 5 lbs. are indicated. Now reduce the force to about 1 lb. and repeat this procedure a few times. The elongation may then be noted for the applied range of stress. As the cord in the operation of the indicator is generally not stressed more than 5 lbs. or less than 1 lb., this range is appropriate. A good cord should not stretch more than 0.01 in. per foot per pound, but grades will be found with four times this stretch and more. The elongation and contraction of the cord are very much greater at stresses less than 1 lb. On this account there may be marked^overtravel at the crank end of the drum motion ^sithout a visible slackening or vibrating of the cord when the indicator is in usual operation. (d) Adjustment of Drum Spring Tension. The indicator is put in working adjustment on the engine to be indicated, the piston spring omitted. Then b\' putting the engine on first one dead center and then the other, two vertical lines may be made on an indicator card to mark the extremes of travel of the 11 THE ENGINE INDICATOR 61 drum. When the engine is run, a horizontal Hne will overtravel the vertical ones, as was previously demonstrated, if the speed is enough to cause any inertia effect. The overtravel at the crank end should not be greater than 0.01 in. for each foot of cord, the cord being of good quahty. If the overtravel exceeds this, the spring should be tightened, until it is reduced to the named amount. The spring should not be any tighter than necessary, as this would increase the reaction on the drum spindle and therefore the friction. For different speeds, different spring tensions should be used. (e) Testing Drum Motion with the Drum Motion Tester. The apparatus shown by Fig. 38 was devised by the author for Tmrnnntmn mruimmm Fig. 38. — Smallwood's Drum Motion Tester. this purpose. A shaft S, the rotary speed of which may be con- trolled by a variable speed motor, actuates two similarly pro- portioned crank trains E and C, set exactly 90 degrees apart. The motions of the two cross-heads are thus exactly proportional at all parts of their strokes. The indicator drum D is oscillated by fastening its cord to a bracket B carried on an extension of the horizontally moving cross-head. The cross-head with vertical travel carries a pencil point P which traces a diagram on a card on the drum. A diagram thus obtained is one of cross-head motion shown vertically and drum motion horizontally. If a rigid connector between the drum and the bracket were used instead of the indicator cord, the motion of the drum would be exactly proportional to that of the pencil, and the diagram 62 THE ENGINE INDICATOR 11 would be an inclined straight line. The effect of an elastic connector, as cord, variously stressed, is to give a curved Une. If a straight line is drawn between the highest and lowest points of this curve, then the horizontal departure of any point on the curve from the straight line shows the error in the drum motion at that point. When testing a drum motion for errors in an indicator diagram previously obtained, great care should be taken to reproduce all the operating conditions, relative to speed, spring tension, length of diagram, length of cord, general adjustment, and ^^"^v^^.-.-Lenafh o-fDrum Motion, tio Speed— ->\ , W-^ Oyer-trdvel>\ K- Fu]l'6ffvk€~oTCro66l^e7oi Error on Return 6iroke'y\ K •• ** Forward " ->|l<| Head End Drum Mo+i /Forward '0" I Return Crank End Fig. 39. — Error Diagram from Drum Motion Tester. friction. Special care should be taken to reproduce the arrange- ment of guide pulleys. The effect of guide pulleys, especially if near the indicator, is similar to that of drum spindle friction and imposes an additional tightening force on the forward stroke and slackening one on the return. Fig. 39 shows a typical error diagram taken with the drum motion tester and is self explanatory. In some cases the drum advances its correct position instead of lagging behind it on the return stroke. This is caused by the departure of the acceleration force from the variation assumed in Fig. 37, because of abnormal stretch of the cord and the con- sequent change in the drum velocities. 11 THE ENGINE INDICATOR 63 (f) The Correction of Indicator Diagrams from Drum Motion Tester Records may be accomplished as shown by Fig. 40, which needs no comment. Samphng of the diagrams may be done as indicated under Test 10 (e). ERROR DIAGRAM Full lines ^How di a of rams as fdkcn. Doffeof lines sS ho yv corrected oliaofrdms. Fig. 40. — Correction of Indicator Diagrams. Problem lli. The force of acceleration of the indicator drum varies directly with its stroke and the square of the engine R.p.m. If a drum motion with a 4-in. stroke is designed correctly to operate at 200 R.p.m., how long should the stroke be to operate correctly at 250 R.p.m.? At 300 R.p.m.? Ans., 2.56 in.; 1.78 in. Problem II2. What should be the constant of a drum spring (pounds per inch of extension measured on the card) to balance throughout a 4-in. stroke a force of acceleration which has a maximum value of -fl lb. at the 64 THE ENGINE INDICATOR 12 head end, and —1 lb. at the crank end? If the engine R.p.m. is doubled, what should be the constant of the spring? Arts., 0.5 and 2.0 lbs. per in. 12. The Testing of Link Type Reducing Motions Principles. The pantagraph in various forms has been much used to reduce engine cross-head motion for the purpose of driving indicators. Fig. 41 shows a number of them, diagrammatically. In these and in the following two figures, the letter F denotes the fixed center of the linkage; R, the point at which the indicator cord is attached; and C, the point of attachment of the hnkage to the engine cross-head. R Fig. 41. — Pantagraph Reducing Motions. There are two conditions necessary to the proportionaUty of motion of the points R and C. First, they must lie on a straight line passing through F, and second, the links that are parallel in one position must remain so in all positions. Fig. 41 A and B are familiar forms, the reduction of motion being in the proportion of FR to FC. The identity of Fig. 41 C may be established by the dotted lines, the linkage thereby repre- sented being replaced by the sliding bar on which the point R is centered. With this arrangement, the ratio of the long to the short link below F must be equal to the corresponding ratio above, in order to fulfill the condition of parallelism. This reduc- ing motion is appropriate to high speed engines since by it only 12 THE ENGINE INDICATOR 65 a short length of cord need be used. Fig. 41 D is a convenient form of pantagraph made by attaching to the engine crank shaft a small eccentric and rod, or crank and rod, the throw of which is equal to the desired drum stroke. It will be seen that for a correct reduction, the eccentricity must be in line with the engine crank; and the ratio of the lengths of eccentric rod to eccentricity must equal the ratio of the engine connecting rod to crank length. Fig. 41 £' is a modification of this, the motion being the same as that of a Scottish yoke, that is, a crank train with infinitely long connecting rod. The motion is therefore inaccurate. In each case, the proportional motion of R is parallel to that of C. Therefore, the indicator cord should be led from the reducing motion parallel to the cross-head guides; if on a slant, the drum motion will not be proportional to the cross-head motion. Reducing motions of the pendulum type are represented by Fig. 42. By A is shown the slotted pendulum. The shorter — R ^-« — Fig. 42.— Pendulum Reducing Motions. is the indicator cord, the greater will be its angularity due to the circular motion of R, The motion of R is not truly proportional to C since the ratio of FR to FC varies. Fig. 42 B shows the slotted cross-head, a correct motion except for the angularity of the cord. Fig. 42 D is the same as C except that a ^' brumbo '' pulley is attached, by which the cord may be led off at an angle with less error than if the pulley were not used. With a horizontal 66 THE ENGINE INDICATOR 12 cord, the pulley causes more error than would be obtained with- out its use. The errors of these reducing motions are kinematic and mechanical. Mechanical errors are due to lost motion in the joints, or flexing of the links. Kinematical truth or errors depend on the design. (a) Calibration by Line Diagram. The crosshead motion is laid out to scale as shown by XY, Fig. 43, and divided into a number of equal parts. The centers of \^ the reducing motion are then located to l\ represent it in an extreme position, and \\ "^"^ ^ point D to show the corresponding I \ position of the indicator drum. A second \ \ position of the reducing motion is tlien l \ drawn and a second drum position marked, \ \ and so on. It is then an easy matter — -'^-t^tt: ^^-^^-^^^^ c ^o measure the error of any of the drum positions since the distances between them Fig. 43. should be equal for exact proportionality of motion. If desired, the data may be plotted the same as Fig. 39, from which indicator diagrams may be corrected according to Test 11 (/). (b) Calibration by Direct Measurement. The indicator and reducing motion are set up as in actual use. The dead center positions of the engine cross-head are marked on the cross-head guides against a datum line on the cross-head. With the cross- bead placed at any part of its stroke, its position may then be readily measured from either dead center and expressed in per cent of the stroke. For a proportional motion, the indicator drum should have moved from its corresponding dead center position (located by marking with the indicator pencil a vertical line on a card on the drum) the same percentage of its stroke. A number of such measurements at different parts of the strokes furnish data which may be applied the same as under (a). L 13 THE ENGINE INDICATOR 67 Care should be taken that motion is not lost through stretch of the indicator cord. For rehable results, wire should be used between the reducing motion and the indicator drum. If the wire is not sufficiently flexible to pass around the drun, a few inches of cord tied to the wire may be used for this purpose. Problem 12i. The stroke of the drum given by the reducing motion of Fig. 41 £' is 4 ins. The ratio of the engine connecting rod to crank length is 5:1. Figure from the kinematic formulas the maximum error in the drum motion. Problem 122. Is the best arrangement of Fig. 42 C with the lower link always above the horizontal, always below it, or partly above and partly below? Why? What effect has the length of this link upon the accuracy of the motion? Problem I23. Draw two indicator diagrams, superimposed, to show the effect of twisting the eccentric of Fig. 42 D ahead of the crank by 10 degrees. 13. The Testing of Reducing Wheels* Principles. Link reducing motions have been largely sup- planted by reducing wheels on account of the latter's ready adaptability. This type of motion consists, in general, of two drums of different diameters mounted on separate shafts that are connected together with gears. Fig. 44 shows them on the same shaft for simplicity. The indicator cord is led from the engine cross-head to the larger drum to which it is fastened. Another cord connects the smaller drum to the indicator drum. It will be seen that the velocity of the one cord is to the other as the ratio of the drum diameters of the reducing motion. The reduc- ing wheel is supplied with a spring which acts the same as the indicator drum spring. One of the reducing motion drums is made interchangeable with others of various diameters so that different reductions may be made. * For a more complete discussion of this subject, and experimental results, see author's article in Power, Sept. 24, 1912. 68 THE ENGINE INDICATOR 13 In the operation of a reducing wheel the same forces are at work as in the case of the indicator drum (Test 10, principles), namely, spring tension, friction, and the force due to inertia. Since the indicator drum and wheel masses are connected by a short cord having inconsiderable stretch, they may be regarded as one mass producing a single inertia effect. Likewise, the Fbrward stroke ' -Indicaivr Drum Head End Midsfrt>ke Crank End V- -Yelociiy Increa^irfG^ - ->j— -Vdocify Decreaiincf- - ->j CD Enofine Cro6shead Inerfia • Sprinof Tension Friction ■ Resultant on Cord <- Forces a+ Wheel 'Return Stroke k - Velocity Decreasing ^ - Vehciiy Increasing -iA Inertia Sprincf Tension Friction ^0 Resultant on Cord ^-^ Fig. 44. — Forces on Cord Driving Reducing Wheel. two springs may be considered as exerting a single force. In Fig. 44, the component forces are shown as they are felt at the cord at three parts of each forward and return stroke. The arrows represent roughly by their length the comparative magnitude of the forces. At the beginning of the forward stroke, the cord exerts a maximum force in overcoming friction, inertia and spring ten- L 13 THE ENGINE INDICATOR 69 sion, but as most of the cord is wound on the wheel, its stretch and the consequent lag of the drum are inappreciable. As the cross-head advances, the length of cord free to stretch becomes greater, but, as the velocity of the moving parts approaches its maximum in the neighborhood of mid-stroke, the effect of inertia is to lessen the force exerted by the cord and therefore its stretch. This continues throughout the for- ward stroke; as the length of the cord increases its stress decreases, and the net effect is to maintain a reasonably uniform total stretch and consequently to give a correct drum motion. On the return stroke, however, the spring tension is required to accelerate the wheel sufficiently so that the cord does not slacken, and it must do this not only against inertia, but against the frictional resistance. As the friction is large, the spring may not be able to do this at a rate equal to that at which the cross-head is being accelerated, particularly at the beginning of the stroke, as here the acceleration is greatest. The stretch of the cord is therefore released at the beginning of the return stroke, if not entirely slackened, as evidenced by whipping. Beyond mid-stroke, the moving parts of the wheel have gained sufficient momentum to draw up the cord again, and this momentum keeps it taut to the end of the return stroke. Under ordinary circumstances, then, a marked distortion of the drum motion may be expected only through the return stroke and greatest at its beginning. Obviously the length of the cord free to stretch, i.e., that part of it not wrapped around the wheel, has a decided influence upon the correctness of the motion. In practice this length at its minimum and maximum is determined by the engine stroke. Ordinarily, at the head end, the length of cord free to stretch is about equal to the stroke, and at the crank end twice as long. Experiments upon reducing wheels will disclose the following characteristics. 70 THE ENGINE INDICATOR 13 First. The overtravel of the indicator drum is small at both ends of the stroke. Second, The distortion of the return-stroke motion is very marked and follows a characteristic wave. The forward motion is in all cases very closely true. Third, The piston speeds producing whipping and therefore limiting the operation of the wheel, are much greater at the longer strokes. The first effect is largely due to friction which helps the springs to check the velocity of the wheel at the end of the for- ward stroke. Much overtravel at the crank end would be evidenced by whipping of the cord. For instance, if the drum motion were 4 ins. and the engine stroke 24 ins., an overtravel of the drum of J in. would mean a slackening of the cord six times that amount, or f in., since any distortion of the drum motion is multiplied at the wheel by the ratio of the motions. This is enough to cause whipping unless the cord is very stretchable. At the head end the overtravel is subdued not only by friction but l3y the positive resistance of the cord, the stretch of which is a minimum at this end because of its reduced length. Overtravel of the drum motion does not indicate error with reducing wheels, as it is always small, exists for even low speeds when the motion is actually accurate, and may not exist at all when the friction is such as to cause large error. The second effect is due not only to friction, but is increased because an indicator cord varies very considerably in length for changes of stress below 1 lb., although above that amount the stretch is comparatively small and uniform with increasing stress. Also the cord will contract markedly when the stress reduces to zero, and sometimes has been observed to continue contracting after the stress was entirely removed. If the fric- tional resistance to motion of the reducing wheel prevents the spring from properl> accelerating it upon the return stroke, the cross-head motion gains upon the wheel motion, thus reduc- 13 THE ENGINE INDICATOR 71 ing the stress in the cord, perhaps to only a few ounces. The cord accommodates itself to this change in length because it con- tracts markedly at low stresses, and not until the distortion of, the drum motion is quite pronounced is the speed of contraction exceeded by the cross-head speed, as evidenced by whipping. The lag of the drum motion just after passing the crank- end dead center is only momentary at moderate speeds because the force required to accelerate the wheel is a maximum at dead center; when it has once started upon the return stroke less force is needed to continue the motion and this the spring is able to deliver. At higher speeds the action of the spring is further delayed, so that the late acquired momentum of the parts causes them to overshoot the mark and fetch up against the positive resistance of the cord, resulting in the wave effect. The third effect follows from the limitations caused by inertia. It may be explained by the fact that at a given piston speed the oscillations per minute of the wheel are greater the smaller the engine stroke, and therefore the effect of inertia is greater Avith the small strokes. Obviously, it is more difficult to oscillate a mass moving at a fixed average speed, the more frequent are the oscillations. This also follows from the mathematical value for the force required to accelerate a reducing wheel at the ends of the stroke (assuming harmonic motion) v/hich may be expressed as follows: A = WXLX N^ X a constant in which A = Force of acceleration referred to the cord; W^ = Weight of moving parts referred to the cord; L = Length of engine stroke; A/' = Revolutions per minute. In this expression LN is proportional to the piston speed. The force A cannot be greater than a certain value which Umits the 72 THE ENGINE INDICATOR 13 operation of the wheel. The product LN will have a maximum value, corresponding to the limiting value of ^, by increasing^L rather than A^, since A varies as the first power of L, and as the square of N, This analysis does not consider the inertia of the indicator drum. The throw of the drum is practically constant at all strokes, so the force required to accelerate it at the ends of the stroke is a = u; X Z X A^^ X a constant or a = ir X y^ X a constant in which w is the weight of the drum and I its stroke. Thus, a varies with the square of the R.p.m. onl3\ The total force of acceleration of drum and wheel is the sum of these forces a and A, but as the drum spring is strong enough to meet the drum inertia at the highest speed of oscillation possible with the usual reducing wheel, the force a generally need not be considered. If the wheel velocities are low so that inertia is not material, the frictional resistance to motion, if excessive, may cause a mate- rial lag of the drum behind its correct position throughout both strokes, since it effects a stretch of the cord upon the forward and a slackening upon the return stroke. If the variation of stress in the cord is the same for different engine strokes, the distortion of the drum motion is the same. This is because any error in the motion of the wheel is reduced at the drum in the ratio of the drum travel to the wheel travel. For example, if the stresses are the same, the stretch of the cord on a 4-ft. engine stroke is doul)le that of a 2-ft. stroke, since the cord is twice as long, but as the resulting drum distortion is Vu of the stretch in the one case (drum stroke being equal to 4 ins.) and \ in the other, the effect is the same. 13 THE ENGINE INDICATOR 73 (a) Determination of Spring Tension and Friction. The method is the same as described under Test 10 (a) and (6). The friction in a well designed wheel is not likely to be less than 20 per cent of the spring tension, and may be as much as 50 per cent in poor designs or when the reducing wheel is badly assembled. As the greatest source of error is in friction, this test is an important one and furnishes a good indication of the merit of a reducing wheel. When the wheel spring tension cannot be made great enough to accelerate the parts correctly, the deficiency may be made good by tightening the indicator drum spring, to a limited extent only. The drum spring acts upon the wheel at a mechanical disadvantage on account of the reduction of motion, and therefore has only a small effect to accelerate it. On the other hand, tightening the drum spring increases the reaction on the drum spindle, and therefore the friction to be overcome throughout the stroke, and this may cause even more distortion. As a gen- eral rule, it is best that the indicator drum spring have only just sufficient tension to overcome its own inertia. The wheel spring tension should be as high as possible if its ability to accelerate the wheel parts is doubted. (b) Testing Reducing Wheels with the Drum Motion Tester. To adapt this device. Fig. 38, to reducing wheels, a bracket, or some equivalent attachment is necessary with a long stroke to duplicate an engine cross-head motion; and, to make the apparatus cover all operating conditions, the stroke should admit variation. This is conveniently accomplished by coupling an extension rod to the motion tester, carrying at its outer end a rack meshing with a pinion on a vertical shaft. This shaft Sj Fig. 45; carries a wooden disc replaceable by others of different diameters. When the rack is reciprocated, the disc is given an oscillating motion. An extension of the indicator cord from the reducing wheel being fastened to a point on the circum- ference of the disc, the cord will be reciprocated through a stroke ^ 74 THE ENGINE INDICATOR 13 the length of which depends upon the diameter of the disc. By using different discs, a reducing wheel may thus be operated through any desired stroke. The reducing wheel to be tested is connected to an indicator and the whole set in place on the tester. The wheel may then be operated at any required conditions of stroke, speed, and cord length; and error diagrams similar to Fig. 39 taken. The cord length may be fixed by tying the desired length to a piece of stranded wire the other end of which is attached to the disc PLAN -Wire fasfemed here Dnvincf Shaif -W^ Variable Speed [-'-^ a=^ ELEVATION (Pencil ortE Indicator rt-y^A K; Wf^'-Rack TTTTTmmTTTTTTTTTTm TmrrTTTTTTumnTmrn jujurn ;/;/n/i/;//i///////;/// Fig. 45. — Smallwood's Drum Motion Tester Applied to Reducing Wheels. of the tester. The wire being practically inextensible, the effect is to reciprocate the cord through the desired lengths as by an engine cross-head at A', Fig. 45. Fig. 46 shows a number of error diagrams taken in this way. (c) Correction of Indicator Diagrams. This may be done as described under Test 11 (/j. The reducing wheel is reasonably accurate on short engine strokes and moderate piston speeds, and on long engine strokes at all usual piston speeds if properly designed to avoid friction. The drum motion resulting from its 13 THE ENGINE INDICATOR 75 use has its maximum error, when the friction is small, at a part of the stroke where usually it would affect the indicator dia- gram little if any, namely, at the beginning of the return stroke where either the steam line on the crank end or the exhaust line Overfrcxvef mecxsured from this line Fig. 46. — Error Diagrams from Reducing Wheels. on the head end diagram is described. As these lines are generally horizontal, or nearly so, errors upon them would not appear, except at their ends. 76 PLANIMETERS 14 IRREGULAR AREAS AND MEAN HEIGHTS Numerous engineering instruments, of which the engine indicator is one, have been devised to give an autographic diagram of the measured quantity expressed as an ordinate, the abscissae being generally time or in linear units simply. From such a diagram it is often desired to get the mean value of the measured quantity, that is, the mean ordinate of the diagram to scale. For this purpose, planimeters are used. Some planimeters measure the mean ordinate directly; others measure the area of the diagram, from which the mean ordinate may be found by dividing by the length. The best known of these two types are the Amsler Polar planimeter and the Coffin averaging instru- ment. The former is used to measure any irregular area; the latter is applied chiefly to the determination of the mean height of indicator diagrams. 14. The Polar Planimeter Principles. Fig. 47 shows in diagram the Amsler planimeter. When the tracing point traverses any closed curve, 1-2-1 the record wheel follows in a certain -n^^ en er i^2ii\\ and, through contact with the surface upon which it bears, is given a motion partly rolling and partly sliding. The principle upon which the instrument depends is that the ^'hed- \ J^^^^ rolling motion of the wheel is directly proportional to the area circum- jracin^^Point-' scribcd by the traciug poiut. If, then, Fig. 47.-Polar Planimeter. ^lie wheel is properly graduated, the area may be read directly. When the area to be measured is comparatively large, the 14 PLANIMETERS 77 fixed center of the instrument is placed within the area, thus securing a greater reach of the tracing point. (See Fig. 51.) In this case, the readings of the wheel must be interpreted dif- ferently and the constant known as the zero circle must be known. The zero circle maybe defined as one of such size i j\\^n;^ zero that if the fixed center of the planimeter ■ ^ ^ ^^■ is placed at its center, and if the tracing point then traverses its circumference, there will be no. motion of the record wheel. It may be seen from Fig. 48 that this condition requires that the plane of the record wheel shall pass through the fixed center, for in this position the wheel will travel in the direction of its own axis and there can therefore be no rolling. The algebraic expression for the radius of the zero circle may be deduced as follows. (See Fig. 48.) ro^=x^ +(6+c)2 -(a2~62) + (52+2&c+c2) = a^+(P+2bc (1) To deduce the mathematical relation between the area cir- cumscribed by the tracing point and the circtunferential motion of the record wheel. There are two cases, namely, the fixed center within and the fixed center without the area circum- scribed. The following paragraph gives an outline of the deduc- tion for the first case. 1. The motion of the tracing point is referred to polar coordi- nates whose pole is at the fixed center of the instrument. A polar differential of area is considered as the one circumscribed by the tracing point. An algebraic expression for this area is obtained in terms of the polar coordinates. 2. An expression is deduced for the motion of a point on the record wheel circumference in 78 PLANIMETERS 14 terms of the constants of the instrument. The motion is that which takes place when the tracing point has outhned the differ- ential of area. 3. By comparing the two expressions (for the area and for the motion of the wheel) the desired relationis obtained. Fig. 49 shows the differential of area, marked 4-5-6-7. Using the notation of the figure, Area 1-4-5 = ^r • rdK = \rHK Areal-7-G = ^n^K Subtracting, Area 4-5-6-7= \dK{r'^-ri^), ... (2) This is the expression for the differential of area. Consider now the corresponding motion of the record wheel. It is to be observed first that this is not affected by the radial motion of the tracing point. The angle between the arms when the point is at 4 (Fig. 49) is the same as that at 5. The same applies to points 6 and 7. Hence, the motion of the wheel when the tracing point passes on the radial from 5 to 6 is the same as that when it passes from 7 to 4. But as these two motions are opposite, they neutralize each other. The same reasoning applies to any irregular area as in Fig. 47. The radial component of the motion from 1 to 2 is the same in amount as that caused in passing from 2 to 1, but opposite in direction. So we may altogether disregard the motion of the wheel produced by the radial motion of the point. Considering again the differential of area of Fig. 49, it is seen that the motion of the tracing point from 4 to 5 is greater than that from 6 to 7, and that the angle made by the arms is different when the point traverses the two arcs. Hence the circular component of the motion of the tracing point when traver- sing a closed curve produces a record on the wheel. We have, then, to consider the effect of this component. 14 PLANIMETERS 79 See Fig. 50. The record wheel moves from 2 to 2' when the tracing point passes from 4 to 5. The rectangular component of the motion, 2-2', causing rotation of the wheel, is represented by the line m, perpendicular to the wheel axis, m is therefore Fig. 50. the distance moved through by any point on the record wheel circumference relative to its axis. From 1-2-3, From 1-2-4, Subtracting, From which. From (1), m = XdK sin (A -90°) = —X cos AdK a2 = 62 +X^-2bXcosA. r2 = (6+c)2+Z2-2(6+c)XcosA. q2_j,2 =,_25c — c^ +2cXcosA. XcosA= y(a2+c2+26c-r2). 1 = 2c^ro^-r^) (3) (4) 80 PLANIMETERS 14 Combining (3) and (4) m = ^(r^-ro^), (5) which is the value for the rotation of a point on the circumference of the record wheel when the tracing point moves from 4 to 5. Similarly, when it moves from 6 to 7, the motion is The difference between these two motions, m and mi, is the resultant motion M of a point on the circumference of the record wheel when the whole area has been circumscribed, or M=m—mi = Comparing (2) and (6) 2c (6) Area 4-5-6-7 =^{r^- n^) • - 2 c = Mc, (7> Fig. 51. which is the required relation. The deduction of the relation for the second case, namely, when the fixed center is within the area to be evaluated, is similar. Under this con- dition, however, the circular component of the tracing point is always in one direction. Hence there is no subtrac- tion as indicated by equation (6) and the differential expression is M = — (r2 — ro^). 14 PLANIMETERS 81 Integrating this for the entire circumferential motion of a point on the circumference of the record wheel, ^=r' dK r2 n 2c Jo 2c -f: 'rf(area) c T 2c area c 2W. 2c From which, Area = --Mc-\-irr(?, • • • • • • • (8) which is the required relation. From these two deductions it is seen that, First. When the fixed center of the planimeter is without the area to be integrated the motion of a point on the circum- ference of the record wheel, relative to its axis, multiplied by the length of the arm c, equals the desired area. Second. When the fixed center of the planimeter is within the area to be integrated, this product added to the area of the zero circle equals the desired area. With the working form of the instrument, the multiplication Mc is not necessary, the wheel being graduated in terms of square inches, or other units of area. In some types of polar planimeter, the arm c is made adjust- able in length, so that areas drawn to various scales may be read directly. (a) Determination of the Zero Circle. If the lengths of the arms, a, 6, and c, are carefully measured, the radius of the zero circle may be computed by means of the relation given by equation (1), and from this the area. If the axis of the wheel is in a perpendicular plane through the arm c, the graphic method suggested by Fig. 48 may be used. Two lines are drawn at right angles to each other, the fixed center placed on one, the tracing point on the other, and the point of contact of the wheel and the paper at the intersec- M^ 82 PLANIMETERS 14 tion of the lines. The radius of the zero circle is then the dis- tance between the fixed center and the tracing point. If the axis of the wheel does not lie in a vertical plane through the arm c (as is sometimes the case) the construction must be altered to allow for this difference. Another method consists in comparing the indications of the planimeter with the calculated area of a circle larger than the zero circle, the arms of the instrument being clamped for con- venience when describing the circle with the tracing point. If the indication of the planimeter be subtracted from the cal- culated area, the result will be the area of the zero circle. This follows from equation (8). When traversing a large circle, the fixed point being at the center, the clamping of the arms may be accomphshed by placing the fixed and tracing points in two holes pierced in a strip of manilla paper; these holes being distant from each other an amount equal to the radius of the traversed circle. (b) Comparison of Instrument Indications with Known Areas. For this purpose may be used a check rule, an in- strument by which the tracing point of the planimeter may be swung through a circle of known radius. Initial and final readings of the record wheel are taken; the difference between these readings should equal the area traversed. When the fixed center of the planimeter is inside the area, the difference between the readings should be added to the area of the zero circle. If the instrument indications do not correspond to the actual areas, the length of the arm, c, should be adjusted. Notice that the wheel reads positively if the direction of the tracing point is clockwise, with the single exception of the case when the area to be integrated is less than the zero circle and the fixed center is inside the area. It is well always to traverse the area in a clockwise direction and to use the following forms : 14 PLANIMETERS 83 Area = second reading — first reading, or Area = second reading — first reading+xro^. As an exercise record the results of two or three area readings of the following and compare with their calculated values. Small circle, fixed center outside. Circle > zero circle, fixed center inside. Circle < zero circle, fixed center inside. Note Carefully. Do not put down the result of an area only, but record in tabular form, as follows: 1st Reading. 2d Reading. Result. (c) Comparison of Instrument Indications with Areas to Scale. Planimeters with adjustable arms generally are arranged to be applicable to various scales. For instance, for a certain adjustment, each graduation of the wheel may indicate one square foot on an area drawn to a linear scale of | in. equals 1 ft. For comparison the check rule may be used, its area in square feet on a f-in. scale being figured by multiplying its area in square inches by the square of the linear scale, that is, 16. As an exercise, compare the planimeter and calculated results of a circle larger than the zero circle, using the scale setting. (d) Arm Adjustment to a Required Scale. Suppose it is required to read areas to a scale not provided for by the markings of the adjustable arm. The necessary length of the arm c may be calculated from equation (7). In this equation, we may assume the area to be one square inch. Then the motion M equals the length of one graduation on the wheel multiplied by the number of graduations previously selected to represent the scale units in one square inch. 84 PLANIMETERS U Let w = diameter of record wheel, inches. G = number of graduations on the record wheel. X = number of graduations representing one scale unit of area. Y = number of scale units of area in one square inch. Then, length of one graduation = -^ in inches. When the tracing point traverses one square inch of area, the number of graduations corresponding to the motion, ilf , will be XY; and M='^XY. (jT From (7) ^XYc = 1 sq. in., and c = TTWXY' in which everything is known except c, which may be found. A convenient application of this principle is in the direct determination of horse-power from indicator diagrams, for which purpose the arm c should be adjusted to the length given by the following formula. 10500Z^ ^" SKwX' ^^^ in which G, Wj and X are as previously defined, and Z= length of the indicator diagram, inches, *S = scale of the indicator spring, K = product of LAN in the PLAN formula (see Test 43). 14 PLANIMETERS 85 Problem 14i. Deduce the equation for the zero circle of a planimeter having the record wheel between the pivot and the tracing point instead of as shown by Fig. 48. Problem 142. If a is 5 ins.; 6, 2 ins.; and c, 3 ins., what is the area of the zero circle applicable to an arm adjustment for a J in. = 1 ft. scale? Arts., 2310 sq. ft. Problem 143. The fixed center of a planimeter is inside an area to be integrated which is smaller than the zero circle; consequently the wheel rotates backward. The first reading is 29.23 sq. ins.; the second, 48.73 sq. ins. What is the area if the zero circle area is 212 sq. ins.? Ans. 132.5 sq. ins. Problem 144. Integrate the area enclosed by a loop like a figure 8, first by finding separately the areas of the loop, and second by tracing the loop in the direction of its curve. Account for differences. Problem 145. The arm c of a planimeter is 2.0 ins. long and the diameter of its record wheel is 0.79 in. How many turns will the wheel make when the tracing point circumscribes 117 sq. ft. to a |-in. = 1 ft. scale? Ans. 13.1. Problem 146. If the wheel diameter is 0.79 in., what should be the length of the arm c so that one revolution corresponds to 1000 square miles on a hnear scale of i in. = 1 ft., there being 100 graduations? Ans.j 6.25 ins. Problem I47. Deduce equation (9). Problem 148. Find the mean height of a given indicator diagram with a planimeter. Calculate the horse-power. Find the horse-power by adjust- ing the arm as described under (d). Compare results. 15. The Coffin Planimeter Principles. Fig. 52 represents this planimeter. It consists of a single arm one end of which carries the tracing point, the other end bearing on a pin which sUdes in a guide represented by the line gg. The record wheel is mounted on the arm as shown. An examination of Figs. 52 and 47 will show that the Coffin planimeter is the same in principle as the polar; the mechanical difference being that the arm a of the former is infinitely long, so that the pivot swings in a right line instead of the arc of a circle. The relation Mc = area therefore applies (see Test 14, principles). The instrument may be used for finding areas, but its chief use is in determining the mean heights of indicator diagrams. 86 PLANIMETERS 15 --Record Wheel ^■■^Udincj Pin Fig. 52. Coffin Planimeter. For this purpose the indicator diagram is arranged as shown by Fig. 53, with its left-hand extremity in the line of the guide, and its base perpendicular to the line of the guide. The tracing point of the planimeter is then placed at the extreme right-hand point of the diagram, 1, and an initial reading taken. Next, the figure is traced in a clockwise direction, until the tracing point comes back to the point, 1. If now the tracing point is moved on a line parallel to the guide line until the wheel indi- cates again its initial reading, the distance 1-2 thus traveled by the tracing point equals the mean height of the indicator diagram in inches. To prove this, it should first l)e mentioned that the motion of the wheel corresponding to the motion of the point from 1 to 2 is the same as that corre- sponding to the motion of the point around the area, since the wheel returns backward to its initial position during the mo- tion 1-2. In Fig. 53, the motion 1-2 of the point causes a change of position of the wheel from 5 to 6. The line 6-7 is the component of this motion which causes roUing of the wheel. Since this rolling is the same as that taking place when the area is circumscribed, it equals M in the formula Mc = area, the area being that of the indicator Fig. 53 15 PLANIMETERS 87 diagram, and c the length of the planimeter arm (see Test 14, principles). Also, area = /iXZ in which h is the mean height and I the length of the diagram. Hence Mc Mc = hl, from which h = —j-. From the similarity of triangles 1-3-4 and 6-7-5, -yr =~j J from which S = —j-. Hence S = /i, that is the distance 1-2 equals the mean height of the indicator diagram. (a) Comparison of Records with Known Mean Heights. Instead of an indicator diagram, a carefully laid out rectangle may be used. The tracing point should be started in the lower right-hand corner, and the figure traced back to this starting point. The parallel motion necessary to bring the wheel back to its initial reading will take the point back to the upper right-hand corner of the rectangle, if the instrument indicates correctly. This test should be repeated several times, care being taken that the point pursues the path of the rectangle closely. If the instrument does not indicate correctly, it may be because the length of the arm has been altered, through bending of the tracing point or otherwise, because of faulty graduations of the wheel, or because of the wheel sticking instead of revolving freely. Problem 15i. If the length of the arm c is 5 ins., what should be the diameter of the wheel so that one revolution corresponds to 10 sq. ins. of area? Ans., 0.636 in. Problem 152. If the test under (a) gives results uniformly 8 per cent too small, is the arm too long or too short, and how much should it be changed if its length is 6.12 ins.? Ans., 0.45 in. Problem 163. Using the indicator diagram of Problem 148, find the mean effective pressures by the Coffin planimeter, and compare results with those from the Amsler. 88 PLAXIMETERS 16 16. The A^-eragixg of Circular Charts Principles. The growing use of autographic instruments of precision yielding circular charts has led to the development of appropriate methods of averaging and integrating. Recording instruments are used both for the measurement of quantities which need not be totaled, such as pressures, temperatm^es, CO2 percentages; and for time rates, such as cubic feet of steam or pounds of water per minute. It is often desirable to a\'erage such records, and it is essential, in the case of time-rate ones, to gei total quantities. The latter may alwaj'S be had, when the average rate is known, by multiplying this rate by the time. The problem, then, resolves itself into one of finding averages. It should be noted, however, that there are available special planimeters yielding total quantities from time rate charts, and that man}^ recorders are equipped with automatic ones, so arranged as to be driven by the same mechanism that moves the chart. Averaging methods only will be considered here. Circular diagrams always have uniform angular coordinates, since they are obtained by clockwork moving in proportion to time. The radial coordinates, on the other hand, may be uniform or non-uniform, depending upon the law controlling the pen movement and its mechanism. When the ordinates are non- uniform, the usual methods of averaging do not appl3\ (a) The Radial Planimeter. Fig. 54 illustrates the prin- ciple of the Bristol-Durand instrument for averaging circular charts. This consists of an arm carr\4ng a record wheel and tracing point at one end, arranged to slide in a pivoted sleeve. With the pivot set at the center of a circular chart, the tracing point can traverse an}^ curve on the chart, the arm shding in the sleeve when the point moves radially. Since the record wheel axis is set on a radial line, the motion of a point on the wheel circumference with relation to its axis w^ill be due only .to circum- ferential motion of the tracing point. Radial motion of the 16 PLANIMETERS 80 tracing point will cause no motion of the wheel on its axis. Thus it is seen that it is only the circumferential component of the motion of the tracing point which causes rolling of the wheel, and since the circumferential component is proportional to the radius, it follows that the rolling will be proportional to the radius. Bc7se Circle Fig. 54. — Radial Planimeter. To deduce the equation of the instrument, let iJ = average distance of tracing point to pivot center = average radius of curve, inches ; r = distance between tracing point and plane of wheel, inches; ro = distance between center of chart and zero of circular coordinates, inches; d = diameter of wheel, inches; n = number of turns of wheel when tracing point traverses a given curve; /= fraction of the time included between the curve limits to the time represented by a complete revolution of chart; 90 PLANIMETERS 16 Then the motion of a point on the wheel circumference will be 7rdn = 27r{R-r)Xf, the quantity on the right being the circumferential component of the wheel motion which exclusively produces rolling. Trans- posing If r is made equal to Tq (adjustment for this is provided), then the value oi R — r above is the average radius of the curve in inches, measured from the base circle. Multiplying by the scale of radial coordinates gives the desired mean. If the tracing point is between the wheel and the pivot, the equation becomes To get the mean height from the base circle, in this case, it is necessary to multiply the number of turns, n, by d/2f and subtract from their product r and ro. Calibration curves can be made for ready use with charts of given form. When the radial coordinates are curved (that is, produced b}^ a pen swing around a center), an error will result if the ends of the curve do not join. To obviate this, the tracing point must be brought back to the same radial distance from the chart center, at the finish as that at the start; and this closing must be made by following a curved radial coordinate. The instrument may be tested for accuracy, first, by tracing a circle of known radius; and, second, by noting whether a wholly radial movement of the tracing point rolls the wheel. (b) Approximate Average with Integrating Planimeter. This instrument is not appropriate to circular diagrams as might at first appear. If the area of such a diagram be found with the 6 FLOW METERS 91 polar planimeter and divided by its angular measure expressed in radians, and the square root of this quotient taken, the result will be the square root of the mean of the squares of the radii, instead of the arithmetical mean. However, in cases where the record is not that of a very variable quantity, these two values are not materially different, so that the one can be taken in heu of the other. The procedure is as follows : Close the gap at the ends of the curve to be averaged by radial lines, and then find the area bounded by the curve and the radials. Then, if / is the fraction of the time included between the radials to that represented by a complete chart revolution, the mean height of the curve from the center of the chart is (approximately) ^ /Area -/ The average quantity in scale units is now found by noting the value of a division on the chart at a distance from the center equal to this mean height. FLUID VELOCITIES— Meters Meters for the measurement of fluid quantities are of two broad types: those that measure volume or weights directly and those that measure velocities. Volume meters are so arranged that all of the measured fluid passes through them, alternately filling and emptying com- partments and thereby displacing a moving part which registers through a gear and counter combination, the quantity passed. This type of meter gives the total quantity at any time. To get rates it is necessary separately to count the time. Velocity meters measure quantity by means of the relation that the flow in volume units per unit of time is equal to linear velocity multiplied by the cross-sectional area of the fluid. Such 92 FLOW METERS 17 meters are dependent upon the uniformity of velocity throughout the cross-section, or upon the correctness of an estimated average velocity when it is not uniform. They may be calibrated to give volumes or weights per unit of time. To get total quantities, it is necessary to multiply by the time. 17. Calibration of a Volume Water Meter Principles. In some types of water meter, the moving part is a piston or disc which is displaced by the water entering the compartment of which this moving part is a wall. There may be leakage past the moving part or the valve motion which controls it. This leakage will increase with the pressure drop through the meter. The greater the pressure urging the water through the meter, the faster is the flow. Hence, the accuracy of a water meter will vary with the rate of flow. Other types of water meter, which may be arranged to avoid such leakage, still will have variable accuracy owing to the effect of inertia, etc., at different rates. For a complete calibration, then, a meter should be tested at enough different rates to cover its range. (a) Calibration against a Calibrated Tank cr Scales. The meter is arranged so that the water passing through it can be weighed in a tank placed on a platform scales or measured in volume from the known dimensions of the tank. If the volume is measured and the instrument reads in pounds, or vice versa, it is necessary to know the density of the water with reference to its tem])erature. Enough readings of both the true quan- tity as shown l^y the scales or tank and of the meter should be taken to get fair values of the rates of flow. In this connec- tion, rules 4 and 5 given on page 8, should be carefully followed. From the observations, should be figured a series of ^^ true rates ^' in pounds, gallons, or cubic feet per unit of time, and of *' rates by the meter '^ in the same units. If desired, these may be plotted for a calibration curve. 17 FLOW METERS 93 (b) Curve of Correction Factors. This is more convenient to use with a volume meter than a caUbration curve, because the instrument is not as a rule used to get rates, but total quantities. The correction factor at any rate of flow is that number by which the total quantity as shown by the meter for any length of time is multiplied to get the true quantity. Consequently, the cor- rection factor is the ratio of the true rate to that shown by the meter. A series of values of the factor may be calculated from the calibration curve and plotted against the rate by the meter. In using the curve, to select the appropriate correction factor, a rough value of the rate by the meter is figured, and from the curve the corresponding factor is obtained. The true quantity for the total time is then readily determined. Problem 17i. Discuss the following observations taken from the test of a meter, and from them figure the true rate, the rate by the meter, and the correction factor. Time. True Weight. Weight by Meter. 2:10 50.5 lbs. 10.0 lbs. 2:15 68.8 20.8 2:20 80.1 31.5 2:25 91.3 42.1 The first true weight is that of an empty tank on a platform scales. Ans., 2.25 and 2.13 lbs. per min.; 1.06. Problem 172. If a water meter of the volume or displacement type is accurate at all rates when the water is 60° F., draw its calibration and correc- tion factor curves to be used when the water is at 120° F. (See p. 369.) 18. Calibration of a Volume Gas Meter Principles. The gasometer is the most accurate instrument of this t^^pe. It is represented by Fig. 55, and consists of two tanks as shown, the upper one being movable vertically and properly counterbalanced. This arrangement makes a chamber of variable size and water sealed. When the upper tank is raised, gas is drawn through the inlet pipe, the valve being closed and / open. When lowered, the gas is discharged, the valve control 94 FLOW METERS 18 being reversed. The volume of gas thus displaced is measured by the vertical motion of the upper tank, its cross-section being known. '6a 6 Pipe-'^ Out In Fig. 55. — Gasometer It will be noted that the gasometer cannot be used for measure- ing continuous flow unless two are operated, one to fill and one to discharge, alternately. Another form of gasometer is shown by Fig. 56. Gas is drawn into the cylindrical chamber C by allowing water to flow out through the outlet pipe. This gas is then displaced through the gas outlet Ijy causing water to enter through the water inlet, the valves being properly adjusted. The gas displaced is measured by the rise of water level in the gage glass. Commercial forms of gas meter are generally of the '^ dry meter ^^ t3'pe and are arranged to measure continuous flow. In this type there are two bellows chambers which are alternately filled and emptied. One side of each bellows being stationary, 18 FLOW METERS 95 the other one is thus given a motion which actuates through a linkage the valve control and the recording mechanism. Gas tnJeh .•Manomefer Fig. 56. — Gasometer. As gas meters in general record volumes under the exist- ing conditions of pressure and temperature, these conditions should be noted if it is desired to translate the readings into weights or into volumes under standard conditions. (See p. 171.) (a) Calibration against a Gasometer. The meter to be tested is arranged as shown by the dotted lines of Fig. 56. The gas used for testing may be air; the gas inlet may then draw through an open pipe. The gasometer being full of air, water is caused to enter through the water inlet, its rate of flow being the desired gas rate. This is obtained by manipulating the water inlet and noting the time of rising in the gage glass. The valve in the outlet pipe at the meter is then adjusted so as to give a constant air pressure as shown by the manometer which, if equal to that usual in city gas mains, should be about four inches of water. For other details, see Test 17 (a). 96 FLOW METERS 19 (b) Curve of Correction Factors is obtained the same as for a water meter, Test 17 (6). Problem 18i. In calibrating a gas meter the capacity of which is 500 cu. ft. per hour, what rates should be appHed, and how long should each trial be so that the error due to reading the gage glass is no more than 1 per cent? The diameter of the gasometer is 3 ft. Problem I82. What should be the capacity of a gasometer to calibrate a meter of 2000 cu. ft. per hour capacity? 19. Calibration of a Weir Principles. A weir is a water meter of the velocity type. It is formed by a notch made in a dam like obstruction in a stream of water through which notch all of the water is caused to flow. The level of the water behind the dam stands above the bottom edge or sill of the notch, and according to a definite difference in these levels, a definite velocity is attained by the water, and hence the quantity passed in a unit of time. If it is arranged that the difference of level be measured by a precise instrument, such as a hook gage, then the flow may be calculated; or, if the weir has been calibrated, the flow may be obtained from the calibration curve. Fig. 57 shows a weir, the height of the water level above the sill being represented by H. The pressure to which the particles of water at the sill are subjected is equal to // ft. of water. W^hen this pressure is reduced to zero by emergence of the water into the atmosphere, the work done is WH ft.-lbs. per second, W being the weight of w^ater in pounds per second. This work is transformed into kinetic energy, the Try2 expression for which is — — , V being the Fig. 57. Weir and Hook Gage. 19 FLOW METERS 97 velocity in feet per second, and g the acceleration of gravity. Consequently, WH = WV^/2g and, The velocity of the particles of water at levels above the sill is less than this since they are at less pressure, and it may be shown that the average velocity is f F or f X v 2gH, If the breadth of the weir is B ft., then the cross-sectional area to which this average velocity applies under ideal conditions is BH sq. ft. Then, since Quantity = area X velocity, it follows Q' = BH Xl^2gH = lBV2gIP, Q' being in cubic feet per second. This is for ideal conditions. Actually, the velocity is some- what less than the ideal because of eddies and friction of which the theory takes no account. So we may write Actual velocity = CiX ideal velocity. Ci is less than unity and is called the ^^ coefficient of velocity." Also the actual water section is less than BH since there is generally a contraction due to a fall at the top and a narrowing at the edges of the weir on account of the tendency of the water at the sides to continue in the plane of the weir. Hence, Actual area = C2 X BH in which C2 is the '' coefficient of contraction." Mi 98 FLOW METERS 19 It follows that the actual quantity Q = iCiC2BV2gH\ C being called the ^' coefficient of discharge/' For rectangular weirs with sharp edges, C equale about 0.62, depending upon the size of the weir and the head. When the stream behind the weir is small in cross-section, its velocity is relatively high. The so-called velocity of approach will then appreciably increase the velocity of the water through the weir since it acts in addition to gravity, and should be allowed for. The average velocity of approach may be calculated by multiplying the velocity through the weir by the ratio of water sections at the weir and in the flume behind the weir. The additional head urging the water through the weir is then (Velocity of ap proach ) ^ which may be added to H for use in the formula for Q. This is an approximation since the velocity in the flume is very variable throughout the cross-section. The actual velocity of approach is greater since the water in the middle of the stream, having greatest influence on the passage through the weir, is of higher velocity than at the sides and bottom. It is more correct, then, to multiply the velocity head as just given by a number greater than unity which, according to Hamilton Smith, lies between 1.0 and 1.5. Many modifled formulas have been proposed for weirs to allow for the variations of C2 and C. The most notable, perhaps, is Francis^ Q = 3.33 {B-0.2H)V]p^ 19 FLOW METERS 99 in which 3.33 equals C iV2g. In this, it is regarded that each end contraction increases with the head and equals O.IH. There is thus less variation in the applied value of C which remains approximately equal to 0.62. This formula may be used for uncalibrated weirs having B greater than 4 ft. when the head, //, exceeds 5 ins. ; wath less than 1 per cent of error. Other shapes of weir notches are the V-notch and the trape- zoidal. For the former the equation is Q = C^,V2gH' when the sides of the notch make a right angle. See Test 20. There is less variation in the coefficient of contraction for this type of weir than the rectangular. Also it is useful for variable flow and small quantities since the head diminishes at a rapidly decreasing rate with the quantity. Merriman recommends an average value of C, 0.592, which gives Q = 2.5W1p, F-notch weirs are now made with elaborate indicating and recording apparatus to register the flow. (See Test 20.) The trapezoidal weir may be arranged so that the extra breadth due to the slope of the sides as the head rises balances the increased contraction of section so that the product of the breadth B at the sill and the coefficient of contraction remains nearly constant. The slope of the sides should then be 1 to 4. The value of C may be taken as 0.62, and we have, as for a rectangular weir without end contractions, Q = 3.33BV1p. The difference of level, H, is generally measured by the hook gage, Fig. 57, by which minute differences of level may be detected. 100 FLOW METERS 19 In use, the hook is started just below the water level, then raised slowly until it barely breaks the water surface, fastened in that position and then read at the graduated scale. (a) The Zaro of the Hook Gage is its reading at a given datum plane. For a weir, this plane is the horizontal one through the lowest edge of the notch. To get the zero of the hook gage for a weir, a straightedge should be placed with one end at the lowest point of the notch and the other end on the point of the hook, and so balanced that very little weight comes on the hook, to prevent springing it. The hook is then raised or lowered until a spirit-level placed on the straightedge show^s the horizontal, and a reading taken. The straightedge and level are then turned end for end and the procedure repeated. By averaging the two readings, any untruth of the straightedge or level is eliminated. (b) To Calibrate a Weir, a series of readings of head and corresponding quantity rates in cubic feet per minute or second should be obtained and plotted. To get the quantity rate, the water may be discharged into a calibrated tank, the rate of rising in which will give the volume per minute. When the weir is at the end of a flume of uniform horizontal cross-section, a convenient method is to start with it empty, and then adjust the incoming water to the desired rate of flow. The rate can be ascertained as the flume is filling by readings of the hook gage taken at equal in- crements of time. When the water level has reached its highest position, uniform flow through the weir being established, a final reading of the hook gage gives the head corresponding to the rate thus previously ascertained. With this method, it is especially important that the rate be constant toward the end of each run. (c) The Coefficient of Discharge varies with the rate. For any rate, it may be found from the quantity formula, the values of // and Q being known. Problem 19i. Find the coefficient of discharge from the following experi- mental data obtained from a rectangular weir. Size of flume 18 ft. long 20 FLOW METERS 101 by 3 ft. wide. Kate of rise, 0.12 ft. in 5 sec. Head on the weir, 5 ins. Breadth of weir, 18 ins. Arts., 0.6. 20. Calibration of a V-notch Recorder Principles. This instrument, largely used for measuring boiler feed, is illustrated diagrammatically by Fig. 58. A float • Recorder Drum 'PenCarnaq^e PJcfte Cam Fig. 58. — Principle of Cochrane V-notch Reccrder. is situated in a weir tank in such a way as to be in a quiet level. A vertical spindle on the float communicates the rise and fall of the water to a plate cam by means of a steel cable wound around a drum on the cam shaft. As the cam revolves, it engages a pin on a carriage so as to move the carriage from left to right according to the height of the float, and, therefore, the rate of flow. The 1 102 FLOW METERS 20 cam groove is a polar curve having the equation of flow; conse- quently the motion of the carriage is directly proportional to the flow and not to the head causing the flow. The carriage carries a pen which records on a drum chart. The Lea V-notch recorder is much the same in general prin- ciple, but a cylindrical cam is used. Another type of V-notch recorder makes use of a specially shaped weighing float, the vertical motion of which is proportional to the rate of flow. The equation cited under Test 19 for a 90° notch isQ = 2.53V IP in which Q is in cubic feet per second, and H is in feet. If h is the head in inches, and q the cubic feet per minute, then g = 3.04\/p. These meters are generally graduated to read in pounds, in which case there may be an error because of change of density of the water. This error is partly compensated for, in that, at a higher temperature, for a given head, a lesser weight of water will pass, but, on the other hand, the float will stand lower in the hot water, thus making the recording pen indicate less. If the flow were proportional to the head, the correction would be exact. (a) Zero Level of Weir. Some forms of these meters are provided with an inside and outside pointer indicating this level, the outside one being adjustable. If there is none, the hook gage can be set as described under Test 19, if convenient. When the hook gage, with which the calibration is to be made, is outside the weir tank (it is often located in a vertical pipe con- nected at the bottom with the tank, for convenience in handling, and securing still water), the following procedure may be used. The weir is blanked off with some boards, as indicated by Fig. 59. A gage, <;, of a convenient height, say 1 in., is set in the weir as indicated. The water level should now be brought to the point of this gage, and a reading of the hook gage taken. The zero level of the weir is then 1 in. below this reading. 20 FLOW METERS 103 (b) Calibration. Since the coefRcient in the formula q = 3.04:\/H^ is very well established, and is practically con- stant under usual operation (ranging about 1 per cent above and below), this formula furnishes a ready means of calibra- FiG. 59. — Gage Pointer for Finding Zero Level. tion. It is only necessary to measure the head corresponding to any instrument record, and from this calculate the actual flow. The mechanism should first be set to register zero when under a zero head as located by method outlined in (a). Note, that the height of the float should not be used for obtaining heads. Temperatures should be taken to enable the calculation of the flow in pounds. The coeflficient, 3.04, applies to a 90° notch. 54° notches also are used. This angle gives half the area of the right-angle notch. The coeflficient is a little greater than half that of the latter, and may be taken equal to 1.55. (c) Sensitiveness. With the hook gage set at a convenient height, start with a low level behind the weir, and gradually increase it until the gage is just submerged. At this instant a reading of the recorder should be noted. The procedure should be repeated, the hook gage position unchanged, with the head 104 FLOW IMETERS 21 decreasing. The difference between the readings represents twice the lag due to friction of the recording mechanism. 21. Calibration of a Nozzle Principles. A nozzle makes a very convenient form of velocity water meter when the water to be measured may be discharged from a pipe into the atmosphere. The prin- ciple upon which this meter depends is similar to that of a weir, that for a definite pressure behind the opening there will be a definite flow through it. Then, if it is arranged that this pressure be measured, the flow may be ascer- tained in cubic feet or pounds per unit of time either by calculation or from a calibration curve. The equation of a nozzle ma}^ be obtained from a consideration of the energy appearing in the water. In Fig. 60 the energy at the section a is in two forms, pressure and velocit3% neglect- ing the small amount of potential energy due to the height at a above the opening at 6. All the energy at a is converted into velocity at 6, since the pressure at h is nil, except that used to overcome fluid friction between the points a and h. Let W equal the weight of water passing per second. Then the available energy at a is WH+— — , H being the pres- sure in feet of water and V the velocity in feet per second at a. The expression ^ is the kinetic energy at a, and WH the Fig. 60.— Nozzle. 2^ pressure energy. Likewise, the energy delivered at h is 23' 21 FLOW METERS 105 If vi is the velocity at b under the ideal condition of no losses, then in which C is a coefficient less than unity. Since energy is propor- tional to the square of the velocity, C^X available energy = delivered energy. Substituting in this the values of the energies as previously noted, We also have the relation that the velocities are inversely propor- tional to the cross-sectional areas, or V_ 4 ^rf2 i;~7rZ)2~Z)2- Combining these last two equations we have Since the quantity, Q, in cubic feet per second, equals the velocity times the area of the stream, Q = 0.7854d2^^?fg. ..^^ 106 FLOW METERS 21 For convenience, this may be expressed Q = 6.3C , Vg, in which JS is the ratio of D to d. Note that the units of D are feet. The value of C for a well-designed nozzle is between 0.95 and 0.99. It is thus seen that such a nozzle may be used as a meter without material error if it is uncalibrated. A convenient method of measuring the pressure is by a mer- cury manometer as shown in Fig. 60. The difference in level of the mercury in inches should then be multiplied by -^ to con- vert into feet of water. The lower level of mercury should be referred to the datum plane through the end of the nozzle (when the nozzle is vertical) as this allows for the potential energy between the sections a and h which was neglected in the formula; the column of water in the right-hand leg of the manometer balanc- ing that within the nozzle. If the mercury descends below the datum plane, the reading of the manometer must be corrected for the head of water between the lower mercury level and the datum. When the nozzle is horizontal, the datum plane should be through the axis of the nozzle. (a) Calibration at Various Rates. The rate may be varied by turning a stop valve in the pipe to which the nozzle is affixed, and the rate may be measured by discharging the water into a calibrated tank or by weighing it. If the pressure measuring device is a manometer, the tube connecting it with the nozzle should be full of water as any air in it will cause the apparent water head to be different from the actual by amounts varying with the pressure. The water head below the datum plane may be corrected for by translating it from inches of water to 21 FLOW METERS 107 inches of mercury and subtracting from the manometer read- ing; or the manometer may be raised each time it is read so that the lower mercury level is at the datum plane at the instant of reading. The determinations of rate in the desired units should be plotted against pressures in inches of mercury. Rules 4 and 5, page 8, should be carefully observed. (b) The Coefficient of Discharge varies somewhat with the rate, at any value of which it may be found from the quantity formula, the values of H and Q and the diameters of the nozzle being known. Problem 21i. What is the discharge in cubic feet per second from a nozzle having a diameter ratio of 2 to 1, the smaller diameter being \ inch, if the manometer shows 5 ins. of mercury with its lower level 7 ins. below the nozzle mouth? Assume C = 0.97. Ans.y 0.0246 cu. ft. per sec. Problem 2I2. Assuming that a nozzle has been caUbrated with water at 60°, will more or less water (weight and volume) emerge for a given reading of the U-tube when the water is at 120°? Why? 22. Calibkation of a Venturi Meter for Water Principles. The Venturi meter is similar in principle to the nozzle. It is, in fact, a nozzle discharging into a closed and properly shaped pipe instead of into the atmosphere. See Fig. 61. The water passing through the pipe shown carries a certain amount of energy in the form of pressure and velocity. When the water reaches the contracted section 6, its velocity is increased, and therefore its pressure must be decreased, since the total energy, barring losses, remains constant. The drop in pressure between sections a and h thus becomes a measure of velocity and hence quantity. To deduce the equation for the Venturi meter it is only necessary to equate the expressions for energy at the two sec- 108 FLOW METERS 22 •Dia. ' D tions a and h. Thus, if V and y are the velocities in feet per second, and H and h the pressures in feet of water at the sections a and 6, respectively, and W the weight of water passing per second, then g being the acceleration of gravity. We also have the relation 7 _ Area at b_ dP V Area at a D^' Combining these equations and solving for Vj Fig. 61. — Venturi Meter. from which the cubic feet per second discharged under ideal conditions is Q' = area X velocity Owing to friction losses the discharge thus calculated is too high. To allow for this, a coefficient of discharge, C, less than unity, is introduced. Combining V 2^ and 0.7854, for convenience, the formula becomes 7)2 ^ Q = 6.3C . VIT^ in which R is the ratio of D to rf, and D is in feet. The value of C for a well designed Venturi meter is between ^ 22 FLOW METERS 109 0.95 and 0.99, and the value of R is usually 2 or 3 to 1. It is thus seen that an uncalibrated Venturi meter may be used with not more than 2 per cent of error by assuming C = 0.97. The meter is generally shaped with an annular space A, Fig. 62, from which to lead the opening transmitting pressure. Be- tween this annular space, or pressure cham- ber, and the interior of the tube are circular openings connecting the two. This arrange- ment transmits the pressure more truly than would a single opening. For measuring the difference of pressure, H-h, a mercury manometer is generally used connected as shown by Fig. 61. When the manometer is graduated in inches, the flow may be calculated or obtained from a calibration curve determined experiment- ally. The manometer is sometimes gradu- ated in quantity rates so that no curve need be used. Some forms of Venturi meter employ apparatus giving a continuous record on a time chart which, when integrated, yivjlds total quantities. One of these is illustrated by Fig. 63. Note the cam by which movement of the mercury column (pro- portional to the square of the velocity), is rectified to give uniform radial chart ordinates. (a) The Calibration at Various Rates may be made by con- trolling the rate by a stop valve in the water line and measuring the rate by discharging the water into a calibrated tank or by weighing it. A curve should be drawn between the rates and the differences of mercury level (manometer readings). Rules 3, 4 and 5, page 8, should be carefully observed. (b) The Coefficient of Discharge is determined from the formula at any rate when the values of Q, iJ-/i, and the diameters of the instrument are known. Fig. 62. no FLOW METERS 22 The head in inches of mercury should be transposed to feet of water. Referring to Fig. 61, it is seen that the column of water on the right above X balances an equal column on the left. The . (-Metal Disc for Chart — Capillary ?en Ten Arm a Pay Clock- in Metal Case •Aluminum Vise Counter Dial f late J iiuj I > i I ,u ■ Counier Dial 4Day Integrating Clock- ^ ' " " ^ ^' " " '^" ^ Aluminum Yoke -^v.-.VV~^n / \ /X" Indkahr Dial hand CamRoller "'' /) v ^ J A^fA Indicaf or dial 'Removed Support ior Indicafordiol-- ZeroUne-- — -- Cam-- — " Main Shaft Main Levari From Float/ --Case Fig. 63. — Builder's Iron Foundry Venturi Meter Recorder. column of water between X and F, however, is balanced by mercury, so that the pressure difference between sections a and b is not XF inches of mercury, but XY inches of mercury minus XY inches of water; that is (^^'^-^) XY=1,05 XY, feet of water. 23 FLOW METERS 111 Problem 22i. Given the diameter ratio 3:1; smaller diameter, 1 inch; find the constants Ki and K2 in the following equations: q^k.cVhI Lbs. per sec. =K2C\^Hi in which Hi is the difference of level in the mercury manometer in inches. Problem 222. Draw the calibration for the meter of Problem 22i, assuming that C = 1, up to a value of Hi = 6 ins. 23. Calibration of a Venturi Meter for Gas Principles. The deduction of the flow formula differs from that for water on account of the fact that gas carries intrinsic energy due to its expansive property which must be accounted for in the equation of energy. Otherwise the principle of the deduction is the same. The flow formula has been presented by Mr. E. P. Coleman in a paper to be found in the transactions of the A.S.M.E., Vol. 28, page 483. The general arrangement of the instrument is the same as for water. It has not been extensively used for gases probably because the Pitot tube (see Test 24) answers the same purpose more cheaply, is considerably smaller, and has been more developed experimentally. Never- theless, there are obtainable and in successful use recording Venturi meters in large sizes for the measurement of gases and steam. One of these is similar to Fig. 63. To convert the records into standard cubic feet, corrections for both pressure and temperature must be appHed. (a) Calibration at Various Rates may be accompHshed by using one of the methods described under Tests 25, 27, 28, or 29 for measuring the true quantity of gas; or if the Venturi meter is of small size, by using a gasometer. The rates may be obtained in cubic feet per second or minute, and plotted against difference of pressure in inches of water or mercury. Note that the tem- perature conditions must not materially vary from those in use, since a change of temperature is accompanied by a change of flow. 112 FLOW METERS 24 24. Calibration of a Pitot Meter for Water Principles, t Fig. 64 represents a Pitot meter, which is merely a curved tube placed in a stream of velocity V feet per second so that the immersed end of the tube faces the stream. The kinetic energy of a given weight of the water, W, is IFF2/2gr, in which V^/2g is called the " velocity rr^^^rir^ head '' or the head of water, H, in feet, which under ideal conditions may produce a velocity, V. In the Pitot tube, Fig. 64, the water rises until the head in the tube just balances the velocity head of the stream. Hence Fig. 64. Pitot Tube. V = V2gH, The height H thus becomes a measure of velocity and therefore quantity. If the stream is in a closed conduit, the water may be under a pressure greater than atmospheric which would cause it to rise in the Pitot tube to a height greater than that due to velocity. This may be allowed for by making a separate measurement of pressure. Thus, in Fig. 65, H2 ft. of water balances veloc- ity plus pressure, and Hi ft. in the straight tube is due to pressure only owing to the fact that the velocity is not impressed upon this tube opening. The velocity is then V = V2g{H2-Hi), The Pitot tube opening is called L T VwIE^V." III*. velocity opening and the the '' other, the ** static opening.'' They are often connected to a differential gage as shown by the dotted lines of Fig. 65.— Pitot Meter. 24 FLOW METERS 113 Fig. 65 so that the pressure is balanced, and a single reading gives the velocity head direct. The plane of the static opening should be parallel to the stream; for, if it is inclined toward it, the velocity is partially impressed; or, if away from it, suction will result. With a correct static opening there m.ay be the same effects if the stream is not parallel to the pipe direction, which may be the case at points near bends or elbows, or when the instrument itself inter- feres with the regularity of the flow. Generally two static open- ings on diameters at right angles, connected together, are used. When the Pitot tube and static opening are properly designed and applied, the actual condition of flow is the same as that represented by the formula, so that there need be no coefficient to determine as with tlie nozzle, weir, and Venturi meters. In a closed conduit, the velocity of the stream varies through the cross-section, being maximum at the center and minimum at the sides. It is therefore necessary either to find the velocity at enough points to get a fair average or to read the instrument at a point of mean velocity. The mean velocity is approximately 0.83 X velocity at center, and this rule is .. , « , ,, station Nq sometimes used for rough results. y<^^^^^"::l (a) Determination of Average Velocity /Zv^^^^^xv^"^ and of Quantity Rates by Traversing. r/u /^^^\ uTi^ . r'rrrl*''s //III In Fig. 66, the concentric circles mark \\\\^^ off equal areas so that ai = a2 = as = a4 = 05, \^^^^^/:il the area of the pipe being A = 5gi. The ^^^.^sa^^- — 10 average velocities in these areas are vi, Fig. 66. 1^2, i'3, etc., respectively, the average veloc- ity in the whole pipe section being V. Then, if Q represents the cubic feet per second, Q = AV = aiVi+a2V2+asvs+etc., = 5aiV = ai{vi+V2+vs+etc.)j and y^ vi+V2+V3+etc. ^ 5 114 FLOW METERS 24 That is, the average velocity in the pipe is the average of veloc- ities taken at points representing equal areas. The method to be pursued, then, is to take readings of the differential gage at such points for a single determination of quantity, the quantity being calculated by taking the product of the average velocity, F, and the area of the pipe. It is cus- tomary to take readings at ten points, or stations, as shown by I'ig. 66. The readings on one side of the pipe center should duplicate those on the other, and there are two readings for each area. The stations should be located at the following distances from the pipe wall, D being the diameter of the pipe, in order to represent equal areas. station No. 1, .0256D No. 6, .658D No. 2. .08171) No. 7, .7741) No. 3, .146D No. 8, .854D No. 4, .226D No. 9, .918D No. 5, .342D No. 10, .974D The calculation for V is simplified by taking the average of the square roots of the differential gage readings, and using this in the velocity formula for V//. Note that the head of the gage liquid should be converted into equivalent head of water in feet. If mercury is used as the gaging liquid, this may h done as described under Test 22 (6). If some other Hquid, ai oil, is used, its specific gravity should be taken into accoun according to the same principle. The quantity rate can b expressed as Q = a constant X 2 v^'gage reading for the simplification of numerical work. Recording Pitot meters in various forms are in considerabh use, and of these a good example is that of the General Electri( Co., appHcable also to steam and gas flow (see page 128). Thes( 24 FLOW METERS 115 instruments are calibrated with the velocity opening at a fixed position in the stream, and yield charted results in terms of pounds, gallons and cubic feet per unit of time. (b) Location of the Point of Mean Velocity. If the pipe is traversed and the average of the square roots of the gage readings obtained as under (a), then the square of this average represents the gage reading at the point of mean velocity. This point may then be located by plotting on a chart gage readings against distances from the wall of the pipe; the distance corresponding to the square of the average square root of the gage readings being then taken from the chart. The location may be found without plotting a curve by searching with the Pitot tube for the point at which is registered the gage reading as calculated above and then measuring the distance of the velocity opening from the pipe wall. If this is done, a center reading should be taken when making the traverse by which the uniformity of flow may be checked when the search- ing is done. Problem 24i. Deduce the values given in the table under (a) for the dis- tances of the stations from the pipe wall. Problem 242. Give a rough value of the quantity rate in cubic feet per minute in a 10-in. pipe (internal diameter = 10.02 in.) if the differential gage reading at the center is 26 ins. of oil the specific gravity of which is 0.9, an inverted U-tube being used. Ans.y 102 cu. ft. per min. Problem 243. Figure the constant for use in the quantity formula for an 8-in. pipe (internal diameter = 7.98 ins.), the gaging hquid being mercury. Ana.y .285, in cu. ft. per sec. for 10 stations. Problem 244. Figure the cubic feet per second in an 8-in. pipe (internal diameter = 7.98 ins.) if a traverse gives the readings, 1.02, 1.26, 1.42, 1.56, 1.69, 1.65, 1.5, 1.38, 1.25, 1.01 inches of mercury. Ans., 3.32 cu. ft. per sec. 25. Constants of a Pitot Meter for Gas Principles. The Pitot meter may be used for gas exactly the same as for water (see Test 24) except that greater precau- tions should be taken on account of the fact that gas is a much 116 FLOW METERS 25 M <- 1". more mobile fluid. The instrument should be placed at a distance of at least 12 pipe diameters from the nearest bend on the up-stream side, and four on the down-stream. A Pi tot tube of unusual proportions or design should not be used without previous calibra- tion, as it has been found by experi- ment that apparently unimportant details cause large errors in the indi- cations. The best proportions of Pitot meter for gas under general conditions have not yet been satisfactorily established, but Fig. 67 represents the form recommended by the American Society of Mechanical Engineers. Numerous experiments, how- ever, lead to the conclusion that it is sufficient to have two static openings at the wall of the pipe, instead of as shown by Fig. 67.* In the case of gas, in the formula y "^-i -0.02" Ho 1 65 '•Static Tube, ky I'ci- "'Velocity Tube. ^' Diet. Fig. 67.— Pitot Tube for Air. V = V2gH, H is the head due to velocity" expressed in feet of whatever gas is flowing, allowing for its density due to its condition of pressure and temperature. The observed head in terms of inches of the gaging liquid must therefore be translated. For this purpose the following relation may be used, Tj_h density of gaging liquid 12 density of gas in pipe ' in which h is the observed head in the U-tube connected as shown in Fig. 65, expressed in inches. The densities are generally given in pounds per cubic foot. Water is usually used for the gaging liquid, the density of which may be taken as 62.3 lbs., ♦ See work of Wm. Rawse, Vol. 35, Trans. A.S.M.E. 25 FLOW METERS 117 as it varies but little with temperature.' Kerosene is also used. Its density may be figured from its specific gravity. (a) Determination of Average Velocity and of Quantity Rate by Traversing. The experimental procedure is exactly the same as for Test 24 (a) when the gas is at room conditions of temperature and pressure, that is, approximately 70° F., and 14.7 lbs. Air, for example, under these conditions weighs .0749 lb. per cubic feet, so /IX62.3 ^=12^<:07r9 = ^^-^^^ from which V = V2g(mM) =m.7Vh, in which h is the observed head in inches of water. At other pressures and temperatures, the density varies according to the relation (for perfect gases) 144 U4:pv = p~^ = RT, w in which p = absolute pressure in pounds per square inch; ?; = specific volume in cubic feet per pound; u' = density, in pounds per cubic foot; i2 = 53.4, for air; 7 = absolute temperature, degrees F. From this relation, follows 144p Now V = V2yH = yJ2g^X 62.3 w 118 FLOW METERS 25 Substituting the value of w and simplifying, ="-^Vf^ P from which the quantity, Q, in cubic feet per second, may be figured b}^ multiplying by the area of the conduit. If the quantity rate, in pounds per second, W, is wished, the following may be used: W = wQ = '^X.7S5i^xn.l 4'- in which (i = diameter of conduit in inches. Simplifying, TF = .163d2^^|. The absolute temperature is figured by adding 460° to the tem- perature as obtained by a Fahrenheit thermometer. For the absolute pressure of the gas, p, the barometer should be read and added in the same units to the static pressure of the gas as shown by a L'-tube or other pressure gage. This gage may be con- nected to the static opening of the Pitot meter. For any other gas than air, or for any other gaging liquid than water, an equation may be deduced similar to the above by the same method. The procedure, then, for gas at temperatures and pressures materially different from room conditions is either Firstj to make a traverse from which the average of the square roots of the differential gage readings yields V^, and to get one set of readings of temperature, static pressure, and barometer. Secondy to place the Pitot tube at a point of average velocity, by which h is obtained by a single reading, other measurements the same. 26 FLOW METERS 119 (b) The Location of the Point of Mean Velocity may be found exactly the same as for water, Test 24 (6) . Problem 25i. What is the velocity, cu. ft. per second, and pounds per second of flow of illuminating gas in a 3-in. pipe (internal diameter = 3.07 ins.) if the reading of the differential gage is 1.5 ins. of oil of specific gravity 0.85? Pressure of the gas is 4 ins. of water; barometer, 29.7 ins. mercury; temperature 55° F. R, for this gas, is 60.7. Ans.y 0.276 lb. per sec. Problem 252. Figure the constant in a formula like F = 66.7V/i, to apply to Problem 25i. Take average conditions to be 14.7 lbs. absolute pressure and 60° F. Ans., 65.8. Problem 253. What is the velocity in feet per second if /i = 12 ins. of water, pressure =4 ins. of mercury, temperature = 120° F., barometer = 30.1 ins. of mercury, the gas being air. Figure answer by both approximate and accurate formulas. Ans., 231 and 226 ft. per sec. 26. Calibration of an Orifice for Water Principles. If water is caused to pass through an orifice, the pressure behind the orifice being measured, the flow may be calculated. Suppose that the velocity of the water behind the orifice is negligibly small; then the energy available is WH, W being in pounds per second, and Hj the pressure in feet of water. This pressure energy is expended in imparting velocity, or kinetic energy, to the water upon passing through the orifice, so that, neglecting friction, etc., WH = WV''^/2g, F' being the velocity in feet per second, and g the acceleration of gravity. Hence, under ideal conditions, V = \^2gH, Owing to friction losses, the actual velocity is somewhat less than this, so that if ci is a number less than one, V = ciV2gH. If we multiply this by the cross-sectional area of the stream, we shall get the quantity, Q, in cubic feet per second. Now, this area is less than that of the orifice; the stream being contracted 120 FLOW METERS 26 by virtue of the tendency of the water particles to flow in the plane of the orifice ; so that if co is a number less than one, area of stream = C2X. 7854 d^, the orifice being circular and d ft. in diameter. It follows that Q = ciC2X.7854dV2ffi/ = cX.78o4:dW2gH. ciy C2, and c are called the '^ coefficients of velocity, contraction, and discharge, '' respectively. Merriman gives average values for them as .98, .62, and .61 for the case of orifices with sharp edges, that is, orifices in thin plates beveled on the side not touched by the water, so that the water touches only one line of the orifice. The coefficients vary with the head and with the diameter of the orifice. In order that the velocity back of the orifice shall be negligible, the cross-section of the stream in the conduit should be at least one hundred times that of the orifice. If the water conduit is round, this means its diameter should be at least ten tinies that of the orifice. The pressure back of the orifice may be measured by a mercury manometer or by a Bourdon gage, or the actual height of water above the orifice may be measured direct with a gage glass, float, or hook gage (see p. 96). As with a rectangular weir, the coefficients vary considerably with both the head and the size of the opening. The average value, c = .61, should therefore be taken only for rough results. The coefficient of contraction varies with the shape of the orifice, one having edges rounded toward the inside giving markedly less contraction. (a) Determination of Quantity Rates at Various Heads may be made by discharging the water into a weighing tank, 26 FLOW METERS 121 or by measuring its volume. The quantity discharged in cubic feet per minute should be plotted against the head in the observed units. (b) Determination of Coefficients. The value of c may be calculated from the formula when the values of Q, H, and d are known. The coefficient of contraction may be found by measur- ing the diameter of the stream at the contracted section with a cahper, this section being distant from the plane of the orifice by about a half diameter. Knowing this coefficient, and the coefficient of discharge, the coefficient of velocity is readily obtained. Problem 26i. What is the coefficient of discharge, if an orifice discharges 92 lbs. of water per minute under a pressure of 3 lbs. per square inch? Diameter of the orifice is 0.6 in. Ans., 0.594. Problem 262. If the diameter of the contracted section (see Problem 24i) is 0.36 in., what are the coefficients of contraction and velocity? Arts., 0.6; 0.99. 27. Calibration of an Orifice for Gas Principles. The deduction of the flow formula differs from that for water on account of the fact that gas carries intrinsic energy due to its expansive property, which must be accounted for in the equation of energy. The theoretically correct flow formula is deduced in various works on thermodynamics. It includes necessarily a coefficient c to allow for contraction and losses, as is the case with water passing through an orifice. For gas, however, the value of c is very uncertain, especially for high pressures, there being insufficient experimental data on this quantity. When the pressure drop between the two sides of the orifice is small, the volume of the gas changes but little, and consequently only little intrinsic energy is delivered to influence the flow. Under these circumstances, the intrinsic energy may be ignored, and an equation deduced similar to that for water (Test 62, 122 FLOW METERS 27 principles), namely V = c\/2gH, the head, H^ then being the height of a column of gas to produce the pressure drop, its density being taken into account. Since the orifice generally may be designed of such size to produce a small pressure drop, it seems hardly worth while to use the accurate and much more complex formula, especially in view of the uncertainty of the v^alues of the coefficient of discharge under those conditions to which the hydraulic formula does not apply. The gas may be caused to flow into the atmosphere, in which case, the pressure drop equals the pressure of the gas above atmosphere, and may be read by a manometer. If the gas can- not be discharged in this way, the orifice may be in a plate fitting square across the gas conduit, and the drop of pressure measured with a differential gage as with the Venturi meter, Fig. 61, except that water should be used as a gaging fluid. In any case, the cross-section of the entrance to the orifice should be of such size as to reduce the entrance velocity to a negligible value. If the orifice needs to be large to secure the desired pressure drop, and the conduit is relativel}^ small, the purpose can be accomplished by making an enlarged section in the conduit. In the case of the Pitot meter. Test 25 (a), velocity is measured by measuring a static pressure caused by it. In the case of an orifice, the procedure is reversed in that a static pressure, caus- ing velocity, is measured and from it the velocity is determined. It follows that the derivation of the velocity formula is the same, and we have for an orifice after introducing the coefficient of discharge, y = c66.7V/i, for room conditions of air, V = cllA\l -T, for general conditions, 27 FLOW METERS 123 and for the rate in pounds per second, d, being the diameter of the orifice in inches the other notation being as given for the Pitot meter. The value of c has been fairly well established for orifices in thin plates, up to about 5 ins. in diameter, and to a pressure of about 6 ins. of water. An average value of 0.6 may be taken within these limits wnth less than 2 per cent of error. (a) Determination of Quantity Rates at Various Heads. The rate may be varied by varying the output or the speed of the machine handling the gas. If an air compressor or blower^ the speed may be varied. If the orifice is used for such a purpose as measuring the exhaust from a gas engine, its external load may be varied, thus changing the amount of fuel and air used. The true rate may be measured by any of the methods of Tests 25, 28, 29, or by a gasometer if the volume of gas is not too large. Readings of the pressure difference between the two sides of the orifice should be plotted in the gage units against true rates. (b) Determination of the Coefficient of Discharge. This is readily calculated from the flow formula, the calibration data of (a) being known. It is instructive to plot values of c against the pressure drop through each size of orifice, and against orifice diameters for each value of the pressure drop. Problem 27i. Write the equation of energy of air on the two sides of an orifice, neglecting kinetic energy at the entrance. Allowing a drop of pressure equal to 6 ins. of water, compare the velocity due to pressure energy with that due to intrinsic energy assuming adiabatic flow. Problem 272. Design an orifice and containing conduit to measure the air suppHed to a 12 H. P. gas engine taking about 20 cu. ft. of fuel gas per horse-power hour and about 12 cu. ft. of air to one of fuel. Drop of pressure through the orifice should not exceed 6 ins. of water. 124 FLOW METERS 28 28. Calibration of an Anemometer Principles. An anemometer is a meter of the velocity type, generally consisting of a wheel with vanes against which the cur- rent of gas impacts causing a rotary motion proportional to the velocity of the current. This motion is transmitted to a gear and counter combination which registers linear feet continuously. By counting the time, the velocity in feet per second or minute is calculable. When used to measure quantity, the anemometer is generally placed at the exit cross-section of the conduit discharging the gas. If the cross-section is rectangular it may be divided into a number of small squares defined, for convenience, by light strings or wire fastened from wall to wall of the conduit. The anemometer is placed in the middle of each of these squares and the velocity read. The average velocity through all of them may then be used with which to multiply the total area to get cubic feet per minute or second. If the conduit is round, the anemometer should be placed at points located as for a Pitot tube, Test 24 (a). Anemometers generally are not adapted for velocities higher than 100 ft. per second, and are not very reliable. The vanes are apt to becomxO deformed, causing false indications, and changes of frictional resistance of the bearings will have the same result. When the velocities exceed the capacity of the anemometer, the discharge conduit may be enlarged in cross-section at the exit. (a) Calibration against the Velocity of the Instrument in Still Air. The anemometer is mounted on one end of a horizontal arm 3 or 4 ft. long and pivoted at the other end so that the instrument may be caused to travel through the circumference of a circle. For this purpose the pivot may be supplied with a grooved wheel whereby the arm may ]je driven, through a belt, 28 FLOW METERS 125 by a motor or by hand. Knowing the revolutions per minute of the arm and its radius to the center of the anemometer, the linear velocity of the anemometer may be calculated. This is the true velocity of the air relative to the anemometer, and corresponds to the instrument reading. A number of such determinations are made at different velocities, and plotted as a calibration curve. Care should be taken that the velocity is uniform through- out each trial, and that the error of starting and stopping is made sufficiently small. A small lever is generally arranged on anemometers by which the recording mechanism may be thrown in or out of gear. This may in some cases be operated while the instrument is moving. (b) Curve of Correction Factors. Corrections may be figured as quantities in linear feet per minute to be added to or sub- tracted from the instrument indication for one minute. These should be plotted against linear velocities as shown by the instrument. Problem 28i. A blower discharges 2000 cu. ft. of air per minute through an 8-in. pipe. Design an exit conduit to reduce the velocity a proper amount so that the air may be measured with an anemometer, and show where the anemometer should be placed. Problem 282. If the encircling frame of an anemometer is the same diameter as the opening through which gas is discharged, what should be the area with which to calculate quantity? Examine an anemometer to answer this question. 29. Testing a Calorimetric Apparatus for Measuring Gas Principles. If gas flowing through a conduit is arranged to be heated or cooled by steam, water, or electric current, then, barring radiation from the conduit, the heat gained by the one medium equals that lost by the other. Thus, supposing the r^as to be cooled by water pipes, if W = weight of gas passing in a given time, TF» = weight of water passing in same time, 126 FLOW METERS 29 Ti, 72 = initial and final temperatures of the gas, h, ^2 = initial and final temperatures of the water, Cp = specific heat of the gas at constant pressure, then from which, CATi~T2) It is thus seen that with such an apparatus the air passing in a given time may be measured by weighing the water and taking the temperatures of the gas and water before and after cooling. If steam is used in the coils, being condensed by the air, it is necessary to take the temperature of the water discharged and the pressure and quality of the entering steam from which its heat content may be obtained with the steam tables. If electric current is used, the heat equivalent may be figured from voltmeter and ammeter readings. The calorimetric method is sometimes useful for measuring large quantities of air or gas. The Thomas Electric Gas Meter is an elaborate apparatus of this type, and is perhaps the most accurate device for measuring gas, especially in large quantities, on the market. Resistance thermometers are used, by which a constant temperature differ- ence is maintained; and the current necessary to maintain this difference of temperature is measured in terms of standard cubic feet of air. The meter is entirely automatic and autographic. An advantage of this type of meter is that no corrections for pressure and temperature are necessary, since the indications are proportional to weight and, therefore, to standard cubic feet. (a) Examination of Instnmients. The instruments should be sufficiently precise that the error of reading should be less than 2 per cent of the corresponding factor in the formula. The 29 FLOW METERS 127 weight of water may be measured readily with proper precision. The temperatures, however, appear as differences which may be only a few degrees. Hence, thermometers graduated to tenths may be necessary. It is sometimes useful to figure beforehand rough values of w^eights and temperature differences in order to ascertain the required precision of the instruments. It is best, when using the apparatus, to take temperatures at various points in the cross-section of the gas conduit, to search for variations. (b) Determination of Radiation Correction may be made approximately by stopping the flow of gas and maintaining the temperature within the conduit at an average value betw^een the limits in actual operation. The heat necessary to maintain this temperature may then be figured for a unit of time. This may be used as a correction if very precise results are desired. Problem 29i. What should be the least count of an ammeter to measure 600 cu. ft. of air per minute under room conditions within 3 per cent of eiror? The voltage of the hne is about 110. What should be the least count of the thermometers? Temp, rise of air to be about 20° F. Ans.y about 2 amp. 30. Calibration of a Steam Meter Principles and Types. Steam meters are built on the Pitot, Venturi, and orifice principles. The quantity of steam flowing, in pounds per unit of time, is therefore proportional to the square root of a pressure or difference in pressure. The differential pressure, varying with the flow, actuates an indicating or recording device. When arranged to give a time chart showing rates and total quantities, the recording mechanism is generally rather delicate and complicated. It should be noted that with such meters, the steam flow is proportional not to the motion of the indicator or height of the chart, but to the square root of these quantities, unless some rectifying device is employed. 128 FLOW METERS 80 Changes in density of the steam, due to difference in pressure or superheat, should be allowed for, since the meters generally indicate the quantity in terms of pounds. This may be done by applying diferent taUes, furnished by the makers, to interpret the indications, or by a hand adjustment of the recording mechanism. Variation of density due to wetness may be avoided by passing the stream through a separator just before it reaches the meter. The General Electric Co. steam flow meter operates on the Pitot principle, the static and dynamic openings being made through a '^ nozzle plug '' which is screwed into the steam main, different lengths being furnished for different diameters. The differential head is transferred through |-in. pipe filled with con- densed steam, to a cast-iron, closed mercury manometer of the cup type, the rising column of which supports a float. On this float is a vertical spindle terminating in a rack. As the float rises and falls with the variation of pressure made by the steam flow, it revolves a magnet by means of the rack and a pinion. Another magnet, outside the mercury container (which, of course is under full steam pressure), follows the motion of the inside magnet; and this outside magnet motion actuates the indicator and recording pen mechanism. The graduations of the instru- ment are in arbitrary units from 1 to 10. To interpret the indica- tions, it is necessary to.multiply by KiXKoXKsXKi determined, respectively, by the internal pipe diameter, quality and pres- sure of the steam, and the (exchangeable) size of the internal mechanism of the meter. Values of these quantities are fur- nished by the makers in the form of curves. Integration of the chart for total quantities may be accomplished Vvith a special cam-operated planimeter which corrects for the variable ordinates. The Curnon steam flow meter is a Pitot instrument, in which the differential pressure operates on a diaphragm set in a recorder case. The resulting motion of this diaphragm is communicated through an ingenious hnk-work to a pen-arm, rectifying the square 30 FLOW METERS 129 root motion so that the rise of the recorder pen is very nearly proportional to the steam flow. A feature of this instrument is that differences of density, accompanying variable steam pres- sure, are automatically corrected by a Bourdon tube. A Venturi steam meter is made by the Builder's Iron Foundry and is, in principle, identical with the water meter illustrated on page 110. The General Electric Co. also apply the Venturi, instead of the Pitot principle, with the recorder previously de- scribed, for pipe sizes of 2 ins. and less. The St. John steam meter uses the orifice principle at a constant difference of pressure and varies in orifice size to allow various amounts of steam to pass. This is accomplished by a float set in the orifice and so shaped that its motion varies the effective area of the orifice. The motion is transmitted to an indicating or recording device. In this case, the height of the diagram obtained is directly proportional to the steam flow. A Simple Orifice Meter. When steam passes through an orifice, dropping in absolute pressure from P to p, the flow increases with the drop until p = 0.58P, which is known as the '^ critical pressure. '' For lower pressures than this, there is no increase in the flow. A convenient method of orifice measurement, when the steam is discharged at a pressure low^er than 0.58P, depends upon the application of Napier's formula, namely, PA TF = 70 in which W is the w^eight in pounds per second of dry saturated steam at an absolute pressure P lbs. per square inch, behind the orifice, and A is the area of the orifice in square inches. Steam meters generally are not to be depended upon when the flow is verv variable or intermittent. This condition mav often be remedied by the location of the meter. 130 FLOW METERS 30 Integration of drum charts with uniform ordinates may be accomphshed with the usual polar planimeter; but for circular charts the methods of Test 16 (6) may be applied. (a) Calibration may be made by comparison with an accurate steam meter, or bj^ direct weighing of the steam. The latter method is the more dependable. All of the steam passed through the meter in a given time should be condensed in a surface con- denser and then weighed. A calibration curve may be made for each pressure or condition of superheat, if desired; the quan- tity of steam being varied by a valve in the steam line, between the meter and condenser. Generally it is sufficient to make the calibration at one condition of pressure, the steam being sat- urated. Throttling calorimeter readings should be made to insure the latter condition. The rate of flow should be kept as constant as possible during each of a number of runs at different rates, and the total condensate compared with the total obtained by integration of the chart, or average indications multiplied by time. Before testing, the meter should be set correct at zero according to the maker's directions. (b) Sensitiveness of recording meters may be examined by quickly stopping the flow of steam, and noting the time and character of the curve drawn when the pen returns to zero. Another useful test is to note the minimum amount of change in the valve opening regulating the flow, to produce a change in the recorder pen position. From this can be found the smallest change in the flow rate to which the meter will respond. Problem 30i. Using Napier's formula, what is the flow of steam in pounds per second through a ^-in. diameter orifice, if the gage pressure is 30 lbs.? What is the lowest pressure to which this method appUes if the steam dis- charges into the atmosphere? Ans.j 0.0314 lb. per sec; 25 lb. gage. Problem 3O2. Using a chart record from an actual steam meter, figure the average rate by taking off velocities at a number of equal time intervals. Figure the average rate from the mean height obtained by a planimeter. Compare results. 31 THERMOMETERS 131 THERMOMETRY Temperature may be defined as a measure of heat. It is purely relative and is generally dated from the freezing-point of water. The expansion of materials, when heated, is approximately proportional to the heat added. It follows that the increase of length of a material is a measure of heat intensity. Upon this principle, the mercury thermometer was devised, mercury being chosen on account of its expansive properties. The Fahrenheit scale of degrees w^as chosen in a roundabout way by its inventor, who exposed his thermometer first to freezing water and then to water at the boiling-point. He marked the stem of the instru- ment at the level of the mercury in each case, and divided the distance between the marks into 180 equal parts. He continued the scale below the freezing-point by 32 of these divisions. The freezing-point thus became 32 degrees, and the boiling-point 212 degrees. Therefore the Fahrenheit degree may be defined roughly as the increase of temperature corresponding to 1-180 of the total linear expansion of the material chosen for a ther- mometer between the freezing- and boiling-points of w^ater. The material may be liquid, solid, or gaseous. Now, no know^n material expands uniforml}^ in proportion to the heat added. The departure from uniformity, although slight, is appreciable in accurate work, especially at high temperatures. It follows that the divisions of a mercury thermometer, although absolutely equal, do not measure equal amounts of heat, and a degree of temperature is a quantity varying w^ith its location on the scale. Also different materials expand according to different laws. Consequently, two thermometers of different materials, standing the same at the freezing- and boiling-points of water, will differ at all other points. It must not be thought 132 THERMOMETERS 31 that this is because either one is inaccurate; it is simply that they are different standards. The linear expansion of a particular material, such as mercury, yields an entirely definite, though arbitrary, temperature scale, because the expansive properties of such a material, when pure, are constant. In a mercurial thermometer, however, the degree is not measured by the expansion of mercury only; the glass containing it also expands. The scale, therefore, depends upon the relative expan- sion of mercury and glass. The latter varies considerably both in manufacture and expansive properties, so that for a standard scale it must be specified with great care. Owing to the difficulty of obtaining glass of uniform quality, other materials than mercury have been preferred for accurate work. For the expansive material, air has been commonly used on account of its great expansiveness compared with that of the containing material. Nitrogen and hydrogen are now in more extensive use. Gas thermometers are of two types: constant pressure and constant volume. The former uses the expansive properties of the fluid as in the mercury thermometer, while the latter measures the temperature indirectly by the pressure, which varies directly with the temperature according to Boyle's law. The resulting scales are different, but the differences are so slight that for most engineering purposes it is not necessary to discriminate between them. The gas scales are very nearly coincident with each other and with the theoretical ^* work scale '' devised by Lord Kelvin. This latter is the ideal scale in which the degrees stand for equal amounts of heat. The simple mercury scale is lower than the others between the freez- ing- and boiling-points of water and higher above the boiling- point. The m.ercury-in-glass scale is higher than the others between the freezing- and boiling-points. The nitrogen scale is the one commonly employed in scientific work, but the standard (between the freezing- and boiling-points) t 31 THERMOMETERS 133 is that of the constant-volume hydrogen thermometer. This was defined in 1887 by the International Bureau of Weights and Measures. The standard instrument is operated at an external pressure of one standard atmosphere, or 760 mm. of mercury, and the hydrogen is maintained at a pressure, when at the freezing-point, of one meter of mercury. 31. Calibration of High-reading Thermometers and Pyrometers Principles and Types. Instruments for measuring temper- atures above 600° F., are often referred to as pyrometers, but as there is no clear distinction between various devices denoted by this term and by the term '' thermometer,'' the latter will be used in a generic sense. The writer prefers to use ^^ pyrometer '' for thermometers applicable to flame temperatures. Mercury-in-glass thermometers are made for temperatures up to 1000° F. Their use, however, is limited because of their fragility and by the fact that the sensitive bulb and graduated scale are necessarily very close together. Recording thermometers with disc charts have found much favor in power-plant work because of their convenience and accuracy. These are of the constant-volume type, working, "in reality, as a pressure gage. The helical tube of the gage is con- nected by means of a flexible tube of small internal diameter to a bulb, and the system filled with a thermometric medium. Upon heating the bulb, the pressure of the medium is raised, transmitted to the helical tube, and recorded in terms of temperature. The working medium usually is a liquid for low temperatures, a vapor for medium, and a perfect gas for high. The first and the third employ charts with uniform scales, but the graduations of vapor (as alcohol) thermometers increase with the range. These are unaffected by changes of temperature of the flexible and Bour- don tubes. Such changes cause error with the thermometers 134 THERMOMETERS 31 using liquids and gases, unless equipped with special com- pensators. Another form of expansion thermometer takes advantage of the relative expansion of two metals. As they are heated, the motion of one relative to the other is magnified by a gear combination and transmitted so as to rotate a needle over a grad- uated dial, thus indicating the temperature. The thermo-electric couple is one of the most accurate and convenient instruments for measuring temperature. It depends upon the fact that two wires of different metals having appro- priate thermo-electrical properties will generate an electromotive force when connected at their ends, which electromotive force is proportional to the temperature difference between the ends. If it is arranged that the current be measured with a sensitive galvanometer, placed at any convenient distance from the thermo-electric ^^ couple/' w^e have an indirect measure of temperature. The galvanometer may be graduated in degrees or a calibration curve may be used to translate the electrical units. In the case of thermo-couples, readings should be made of the temperature of the ^^ cold j unction, '^ that is, the ends of the couple to which the galvanometer leads are joined. This is because the temperature indicated by the galvanometer is the difference between those of the cold and hot junctions. The cold junctions are often placed in ice to keep them at a constant known temperature. If a couple has been caliL rated in this way against a standard couple, allowance should be made for the temperature of the cold junction when in ordinary use. This may be done by adding to the indications the difference between freezing temperature and the temperature of the cold junction. For temperatures up to 1200 or 1400° F., the couple is com- posed of a wire of nickel and another of nickel and chromium. For temperatures up to 3000°, the metals are platinum and platinum v.'ith 10 per cent rhodium. The latter combination may be used for the low^ temperatures, but the former is preferred 31 THERMOMETERS 135 on account of cheapness. Many other combinations have been used, but those cited above are the most usual. The electrical resistance thermometer is one of the most accurate of temperature-measuring devices. This consists of a length of wire material, capable of resisting the heat, as platinum or nickel, the resistance of which can be measured with a Wheat- stone bridge. When the temperature of the wire increases, its resistance goes up, so that the one can be measured by the other, when the coefficient of resistance is known (that is, the change of resistance per degree of temperature). This coefficient may be determined with great accuracy, and from it can be plotted a calibration curve of temperatures against resistance. Optical pyrometers are advantageous when the hot body to be measured is inaccessible to a couple or bulb. One of them, the Morse, depends upon a comparison of the brightness of the hot body with that of an electric filament which is caused to glow more or less brightl}^ by varying the current passing through it. Then, by measuring the current, an indirect m^easure of the temperature is obtained as wdth the thermo-electric couple. When used to measure furnace temperatures in boiler testing, a thin plate of iron is hung at the required point and its bright- ness is compared with that of the filament. This type of pyrometer is not very precise because it is difficult to judge exact similarity of brightness. Another optical pyrometer depends upon the thermo-electric couple principle, but the couple is acted upon by radiant heat concentrated upon it by means of lenses in the form of a tele- scope. There are other forms of pyrometers using other principles, but the ones listed above are the principal ones. There are three ways generally used to calibrate high-reading thermometers and pyrometers : first, by comparison with a stand- ard or secondary standard instrument; second, by comparison with the temperature of saturated or wet steam determined from 136 THERMOMETERS 31 its pressure; third, by comparison with temperatures as shown by the melting-points of metals or boiling-poin-ts of fluids and salts. (a) Calibration against a Standard. For this purpose, mer- cury thermometers may be used for temperatures up to 1000° F. Above, and often below^ that temperature, a favorite instrument is the thermo-electric couple, as it is one of the most accurate and easy to use. The temperature is varied in a gas or electric furnace in which the bulbs of the standard instrument and the one to be tested are placed. Care should be taken to bring the whole furnace up to a uniform temperature before recording observations, by allowing sufficient time for heating. The sensitive portions of the two instruments should be placed as close to each other as possible to avoid errors from locahzed temperatures. It is best to take a series of decreasing readings to supplement the increasing ones, allowing the furnace to cool for this purpose. If the up and down readings are different at a given temperature, as they will be w^ith certain types of instruments, they should be averaged. (See Test 2, principles.) (b) Calibration against Steam Temperatures. This method is limited by the available pressure. At 200 lbs. gage, the tem- perature is 388° F., and at 500 lbs., about 470 degrees. It is thus apparent that not very high temperatures can be reached with saturated steam. The procedure is to vary the temperature in a steam cham- ber similar to that used for testing indicator springs, Fig. 33, page £4, by controlling the pressure. The thermometer is inserted in a well set in the chamber and readings taken of it and of an accurate and sufficiently precise pressure gage at each variation of the pressure. The actual temperatures are ascer- tained by reference to the steam tables. A barometer reading is necessary to get absolute pressures. ^^hcn the steam is throttled to reduce its pressure it may Leconie superheated, in which case its temperature is not deter- 31 THERMOMETERS 137 minable. To avoid this, water may he sprayed into the steam before it enters the steam chamber, or the chamber may be water- jacketed. It is essential that there should be definite knowledge of the steam's wetness, for which purpose a throttling calorim- eter (see Test £2) may be referred to. A calibration of an instrument indicating beyond the available temperatures may be had by exterpolation. That is, after the experimental data have been plotted, the curve is continued beyond the known points. If the curve is a straight line, the result may be good, but caution should be used not to extend the exterpolation too far. (c) Calibration against Melting- and Boiling-points. This method will be found quite convenient for ranges between 200° and 800° F. Its accuracy depends upon the purity of the materials. When using the liquids and salts, they may be boiled in Florence flasks over a Bunsen burner, and the thermometer should preferably touch the liquid as well as be surrounded by the vapor. The following materials may be used : Water, boihng at 212° F. Aniline, boiling at 365° F. Naphthaline, boiling at 420° F. Diphenylamine, boiling at 590° F. Anthracine, boiling at 664° F. Zinc, melting at 786° F. Sulphur, boiling at 832° F. Antimony, melting at 1167° F. (d) Stem Corrections. If a mercury thermometer is to indicate correctly, all of the mercury, both in the stem and bulb, should be subjected to the measured temperature. In practice this is rarely the case, as part of the stem containing mercury is at or near room temperature. For accurate work it is then necessary to apply a '^ stem correction.'' 138 THERMOMETERS 31 Let *S = stem correction in degrees; fl' = height of column above actual position of mercury, if uniformly heated, inches; Z = length of one degree on the stem, inches; A^ = number of degrees on the stem exposed to room temperature; r = tem.perature, Fahrenheit, of the bulb; ^ = average temperature, Fahrenheit, of the exposed mercury and stem; C = cubical coefficient of expansion of the glass and mercury, combined by subtracting the value of one from that of the other. Then Also H = C{lXX){T-t) H -'-T Hence S = CX{T-t). The value of C for the Fahrenheit scale may be taken as 0.000088 and fcr the Centigrade scale, 0.00016. It is generally sufficiently accurate to take the actual read- ing as the value of T. If desired, the corrected temperature thus obtained may then he used as T, and a second and more nearly exact stem correction calculated. The value of t is somewhere between room temperature and that of the bulb. It is often estimated by hanging a second thermometer against the one to be corrected, vith its bulb at a middle point on the exposed mercury column. It is very doubtful that this yields a close value for t, ^^ hether or not a stem correction is necessary depends upon the purpose for which the temperature is measured. In engineer- ing work, thermometers are generally used to measure tem- perature differences, so that the percentage of error in the result 32 STEAM CALORIMETERS 139 may be based upon a much smaller quantity than the actual number of degrees read. In many cases, when the temperatures are comparatively low or when the stem is well immersed, the correction is negligible. Problem 31i. A thermometer reads 2<^° when it is immersed to the 60° graduation. If temperature of room is 80°, what is the actual measured temperature? Estimate the stem temperature as an average of room and indicated temperatures. Ans., 241.4°. Problem 3I2. What should be the least count of a pressure gage to cali- brate by steam a thermometer whose least count is 2 degrees? Whv? Ans., 1 lb. at 300°. Problem 3I3. Account for the differences between up and down readings in the calibration of a thermo-electric couple. HEAT OF STEAM— CALORIMETRY— SAMPLING The English measure of heat is the British thermal unit, or B.t.u. This is loosely defined as the amount of heat necessary to raise the temperature of 1 lb. of water 1° F. As the specific heat of water varies with the temperature, a precise definition should name the temperature range. Several ranges have been used, as 32 to 33 degrees, 39 to 40 degrees, 61 to 62 degrees, so that there are a number of values for the. B.t.u. The present tendency favors the '' mean B.t.u.'' which is the average amount of heat per degree required to raise a standard pound of water from the freezing- to the boiling- point. One advantage of this unit is that it is independent of the temperature standard (whether gas or mercury) since it is fixed by the two temperatures which are the same on all thermometric scales. This is the unit used in the Marks and Davis' steam tables, values from which will be used in the examples in this work. The heat of steam is counted from a temperature of 32° F. and is the amount of heat necessarV to convert 1 lb. of water 140 STEAM CALORIMETERS 32 at that temperature into steam under the given physical condi- tions. This includes the heat added to the liquid to bring it to the boiling-point at the given pressure, and the heat then necessary to vaporize it. If the steam is superheated, still another amount of heat is added to it to raise its temperature from that at the boiling-point, the pressure remaining the same. All of these heat quantities depend upon the pressure of the steam. It is thus seen that the physical conditions of steam determining its heat content are, first, its pressure, and second, its wetness or superheat. For example, the heat of the liquid, referred to as h, of steam at 14.7 lbs. absolute, is 180 B.t.u., being the heat necessary to raise the temperature of 1 lb. of water from 32 to 212°; 970.4 B.t.u. are then necessary to vaporize it. The heat of vaporization is referred to as L. Thus the total heat, //, necessary to make 1 lb. of dry steam at 14.7 lbs. is h+L = l\50A B.t.u. If less than the w^hole poimd of water has been evaporated so that there is 1—x lb. of water as a mixture, x being the part of a pound actually evaporated, then H = h+xL. This is the generic expression for the heat added to make 1 lb. of wet steam in which x may have any value up to unity. For superheated steam the generic expression is H = h+L+Cj,{T-ts), in which Cp is the specific heat of superheated steam, ts is the temperature of the dry or ^^ saturated '^ steam at the given pressure, and T is the temperature of superheat. The value of Cp varies with T and with the pressure. These various physical conditions are represented by Fig. 68, which shows 1 lb. of H2O in a cylinder with a movable end under a pressure P. 32 STEAM CALORIMETERS 141 It should be remembered that the datum temperature of 32'' is taken purely as a matter of convenience, and that the actual amount of heat contained by steam, or for that matter any material, is a relative quantity. The significance of heat quan- tities so counted enters when we take the difference between two of them representing two conditions of H2O. Thus the heat per pound given up by a boiler in making steam is the difference between the heat content of the H2O leaving the boiler, counting from 32°, and that of the feed-water entering, counted ein ilarly. Af Freezina Point m Boilinc^ Point- ^r:-52im -t°= Parfly Vaporized I r I rijiiii %Lb.5feoirri- '1:XLby(afer lllllj!! iflllllli Saturated ■•'Steam':' t^. Heat added- ■h "h-xL ^H*L =h*XL*CpCr-iO Fig. 68.— Heat Added to One Pound of H2O. To measure the heat of a given quantity of steam, it is neces- sary to know the amount in pounds and the heat content, i7, or heat added per pound; the one multiplied by the other gives the heat of the total quantity. The weight of steam may be obtained by a steam meter, Test 30, or by any of the methods given under engine or boiler testing. The steam tables are used to get the value of Hy since they list the heats of liquid and vaporization at different pressures. If the steam is dry, it is sufficient to take its pressure or temperature for reference in the tables. If it is superheated, its pressure should be read, and its temperature, T, The steam tables furnish values of is, and Cp, from which H may be calculated, knowing also h and L, The steam tables also contain heat contents of superheated steam, so that the calculation is not always necessary. 142 STEAM CALORIMETERS 32 If the steam is ^vet, the value of x, as well as the pressure or temperature, must be known to fix its heat content. This is the condition generally met in practice, which makes deter- minations of wetness or '' quality " important, especially for engine and boiler tests. The Heat of Steam when Mixed with Perfect Gases. If the pressure of the steam were known, its total heat could be found by reference to the steam tables as previously described. When steam is mixed with other gases, however, its pressure is less than that of the mixture. This follows from Dalton's law, which may be stated thus: In a gos mixture occvpying a given volume^ the pressure of each constituent gas is the same as though it occupied the volume alone, and the pressure of the mixture equals the sum of the pressures cf the constituent gases. For example, 1 cu. ft. of air at 60° F., and 14.7 lbs. pressure weighs 0.0764 lb. 1 cu. ft. of steam at 60° F., and 0.256 lb. pr. weighs 0.00083 lb. 1 cu. ft. of mixture has a pressure of 14.956 lbs., weighs 0.07723 lb. The figures here given for the steam apply to the saturated condition. At the temperature named, no greater weight of steam than 0.00083 lb. could exist in one cubic foot of volume, whether that volume were also occupied with another gas or not, because if there were more than this amount of H2O present, its density would be greater than that of saturated steam at 60°, and consequently some of the H2O would be in the form of water. On the other hand, at this temperature, there may be less than the nam.ed amount of steam present. In such a case, the pressure of the steam is less tl an 0.256 lb., since there is less of it, and therefore it is at a temperature higher than that due to saturation; that is, the steam is then superheated. This is the form in which humidity in the atmos- 32 STEAM CALORIMETERS 143 phere usually exists. It is also the form in which H2O appears in the products of coml:ustion of fuels. Consider now how the total heat of superheated steam in such a mixture may be determined. Let P and T stand for the absolute pressure in pounds per square foot and the absolute tem- perature in degrees Fahrenheit respectively, of the mixture. These quantities are readily measurable. Also it is possible to figure the weight of one cubic foot of the gases exclusive of the steam, and the weight of steam in one cubic foot of the mixture. Now the pressure of the gases exclusive of steam may be figured from the relation PiVi = RT, in which Pi is the desired pressure, Fi is the reciprocal of the weight of the gases per cubic foot, and R may be obtained from works on thermo- dynamics. (For air, 72 = 53.4.) Then the pressure of the steam equals Knowing the pressure of the steam, values of /i, L, and saturation temperature, tsy may be found from the steam tables; which values, together with the temperature of superheat, T, make possible the calculation for total heat, H^ according to the expres- sion previously given. (See also ^' Hygrometry,'' Appendix.) This calculation is laborious, so the following m^ethod, suf- ficiently accurate for engineering purposes, is preferable. The total heat of steam in the form of humidity in air or gases of combustion equals 1058.7+0.455 Te, in which Te is the tem- perature in degrees, Fahrenheit, of the mixture. This is an empirical relation proposed by Professor Diederichs. In the analyses of boiler, gas engine, and gas producer trials, the heat of the steam in the exhaust gases, counting from room temperature, is required. The heat in the H2O before vaporization is ^ — 32, t being the room temperature. Sub- tracting this from the expression just given, we have, roughly, 1090+0.46 Te-t. 144 STEAM CALORIMETERS 32 Steam calorimeters are instruments for measuring the quality of wet steam. Various forms are made depending upon different principles. These depend either upon a trans- fer of heat by which it can be equated to a measurable quan- tity or upon the mechanical separation of the entrained mois- ture. The first is strictly a calorim.etric process. Thus if a sample of the steam whose wetness is to be measured is con- densed in water, the heat given up to the water is readily meas- ured, and this quantity can be equated to h+xLj in which x is unknown. The equation then yields the value of x. Another method is to superheat the steam, in which form its heat con- tent is readily measured. The mechanical separation m.ethod uses an apparatus similar to the ordinary steam separator, and involves weighing both the steam and the separated water. Sampling. As usually arranged only a small sample of the total steam is tested for a quality determination. The accuracy of the result is primarily dependent upon the representativeness of the sample, so that every care should he used to secure a cor- rect one. Unfortunately, it is always uncertain that a reason- aV)ly accurate sample has been obtained, but by using the proper shape of sampling pipe, inaccuracy may ]}e reduced to a minimum. In a horizontal steam pipe, water is r.,pt to run along at the bottom, separated from the steam. If ai) cf this water is passed into the sampling pipe, an undue amount of water appears in the sample. In a \--. --/n6.DiaofMarr>->^ vertical pipe moisture runs down the BBll^^^^^^^^ 1 inside of the pipe wall. Undoubtedly \p,]:Jj^^' ^\SJi , . ify'^'ir'^ , ■■-Slots fof^cc some of this should be included m the P-pe Thread. stream. sample, but it is no easy matter, theo- Fig. 69.— Sampling Pipe. retically or practically, to secure the right proportions. Fig. 09 sho^^ s an approved form of sampling tube. 32 STEAM CALORIMETERS 145 32. The Throttling Calorimeter Principles. Fig. 70 represents the instrument diagrammatic- ally. Steam from a sampling tube enters the steam pipe from which it passes through the orifice 0, about yq in. in diameter, into the chamber C, which is open to the atmosphere. The steam is throttled upon passing through the ori- fice, and drops to a pressure only a little in excess of atmospheric. Now the heat contained b}^ 1 lb. of steam at high pressure is greater than the heat con- tained at low pressure, if superheat does not exist. Upon reaching the chamber, C, the steam therefore contains an excess of heat, and this excess goes to evapo- rate the moisture carried in wath the steam and to superheat both. In this condition, the heat content is readily measured, which makes possible a heat equation involving one unknown. Before entering the orifice, the heat of 1 lb. of the H2O is hi +xLi. (See page 140 for notation.) In the calorim- eter chamber, it is /?2+L2+Cp(r2 — fe). Neglecting radiation, ii! I Fig. 70. Throttling Calorimeter. from which, hi+xLi = h2+L2+Cp{T2-t2) h2+L2+Cp(T2-t2)-hi X The values of h and L and (2 are found from the steam tables, by reference to the pressures indicated by the pressure gage P and the manometer M, Fig. 70. A barometer should be read to reduce these pressures to absolute. The temperature T2 is obtained from the thermometer K. At atmospheric pressure Cp equals 0.47, but for rough and ready calculations it may be taken as 0.50. 146 STEAM CALORIMETERS 32 Certain approximations in the use of the above formula may be made to simplify calculations, which, in view of the uncer- tainty of sampling, give an ample degree of accuracy. Thus, the pressure in the calorimeter chamber generally is only a few inches of mercury, above atmosphere. If it is taken as 14.7 lbs. absolute, 7^2+^2 = 1150, and ^2 = 212. This obviates the use of the manometer and barometer. Then the equation may be w-ritten 1150-/U , .47(^2-212) x = Li ' Li If the pressure on the entering side fluctuates but little, say 5 or 10 lbs., constant values of Iti and Li may be applied. Now, a value of x may be calculated for 72 — 212 = 0, taking hi and Li at an average pressure. The increment of x corresponding to one degree of superheat should then be figured. It is then a simple matter to add to x (when T'2 — 212 = 0) the increment corresponding to any number of degrees of superheat. For example, w^hen the average pressure is 100 lbs. gage hi = 308 and Li = 880. With no superheat, a: = (1150-/ii)^Li = (1150-308)-^880 = 0.956. To this must be added for each degree of superheat an amount equal to 0.47 X (1°) ^880 = 0.00053. If the thermometer in the calorimeter chamber shows 222°, the superheat is 10° and the quality of the steam is 0.956 + 10 X 0.00053 = 0.961, and so on. This method of calculation is convenient for use during an engine or boiler test, since the quality is readily figured from the thermometer reading only, once the constants as oljtained above are know^n. The errors of tlie throttling calorimeter are due mainly to false thermometer readings of the superheat, and to radiation of heat from the instrument or fittino;s. It is best to set the thermometer in the calorimeter without using a well, which m.ay be readily done with a perforated plug of wood or rubber. The thermometer should be moved vertically in the calorimeter 32 STEAM CALORIMETERS 147 until the hottest part is found when the steam is passing as in regular use. To avoid radiation, all the parts should be well lagged. Not too large an orifice should be used, as this raises the back pressure in the calorimeter, and passes more steam than necessary. (a) Determination of the Radiation Correction is sometimes made for extremely accurate work. For this purpose the heat equation should be written <•- Thermometer .-■Pressure Caofe Drymcj Coil in which R is the heat radiated from the calorimeter from each pound of steam. Using an apparatus like that shown diagrammatically by Fig. 71, the entering steam may be completely dried. The value of X is then unity, and the above equation may be solved for R. The correction R may then be applied to find more accurate values of the quality when the instrument is in ordinary use. Strictly speaking, the correction applies only to the pressure, room temperature, and orifice of the test. The first two items may vary considerably without much change in the correction. A more convenient form for the ra- diation correction may be had by figuring ' 1 1 1 ^ ^^ ^^ ^ number of degrees to be added \iteam to the thermometer readings. Fig. 71. The proper amount of heat to dry the entering steam is maintained by regu- lating the current through the drying coils. This may be done by using a water, or other type, rheostat in the line. In order to be sure that the steam is dry, one or two degrees of superheat l-KW^ 148 STEAM CALORIMETERS 32 may be carried as shown by the thermometer in the drying chamber, its reading being compared with the temperature cor- responding to the pressure, as given by the steam tables. Problem 32i. Pressure of steam in the calorimeter chamber is 1.5 ins. of mercury. Barometer is 30.3 ins. of mercury. If the steam were saturated in the chamber, what would the temperature be? If the thermometer indicates 280°, how many degrees of superheat ar6 there? What is the total heat of the steam in the calorimeter at 280°? If the pressure of the incoming steam is 84 lbs. gage, what is its quality? Ans., x= .995. Problem 322. Figure the quaHty from the data given in Problem 32i, assuming the calorimeter pressure to be equal to atmospheric, 14.7 lbs. What is the percentage of error? Problem 323. Figure the quaHty of steam corresponding to superheats of 25, 45, and 65°, using the approximate method of constants for Problem 32 1. Ans.y .972, etc. Problem 324. What is the maximum degree of superheat that it is pos- sible for the steam in the calorimeter to attain if the steam pressure is 95 lbs. gage, and the calorimeter pressure 14.7 lbs. abs.? What is the maxi- mum if the steam pressure is 65 lbs. gage? Problem 325. What is the maximum percentage of moisture that can be shown by a calorimeter under the two conditions named in Problem 324? If the calorimeter pressure is reduced to 10 lbs. abs. by connection with a condenser, what then is the maximum percentage of moisture? Problem 326. If a thermometer reads 3° low on account of radiation, what is the percentage of error resulting from ignoring the radiation cor- rection? Use the data of Problem 32i. Ans., 0.17%. 33. The Separating Calorimeter Principles. If the water entrained in steam is mechanically separated, and the weights of the dry steam and separated water are then measured the percentage of water may be readily calculated. IVIechanical separation may be effected by deflect- ing the steam and water through a sharp bend; the water is then thrown out by centrifugal force. Fig. 72 shows diagrammatically the Carpenter separating calorimeter. The water collects in the calibrated chamber C and its amount is measured by the scale S placed against a 33 STEAM CALORIMETERS 149 Steam Sample gage glass. The weight of dry steam is measured by the orifice method according to Napier's rule (see p. 116), the orifice being located at 0. Since the weight of steam discharged from an orifice into the atmosphere equals a constant times the absolute pressure, an ordinary pressure gage G may be calibrated to indicate the weight of steam passing per minute. In opera- tion, a steam sample is passed through the calorimeter, and, after it is thoroughly heated, initial and final readings of the water level are made for a measured interval of time, together with a number of readings of the gage ^113) from which an average is calculated. The gage gives the pounds of dry steam passing per minute; multiplying this by the number of minutes gives the total weight of steam. This weight is then divided by the sum of the weights of water and steam to get the quality. The chief advantage of the separating over the throttling calorimeter is that it is operative no matter how low the quality. Experiments have shown that complete separation of the water may be depended upon with a properly designed separator. (a) Calibration of the Dry Steam Meter may be made as for Test 30 (a). A calibration curve for the gage should be plotted. (b) Calibration of the Water Gage. The chamber C, Fig. 72, is allowed to fill with water separated from steam passing as in usual operation. A small amount of this water is then drawn off from the pet cock P into a flask of cold water (to prevent evaporation). The weights of the flask and contents and the heights of the levels in the water gage before and after the oper- ation are carefully measured. A number of such determinations furnish the data for a calibration curve. Fig. 72. — Separating Calorimeter. 150 STEAM CALORIMETERS 33 If the water used for the calibration is cold, its weight should be corrected for the difference in density due to the different temperatures. The temperature in usual operation may be taken as that of the steam passing through the calo- rimeter. (See Appendix for density of water.) (c) Determination of Radiation Correction. Radiation from the instrument may cause a greater amount of water to be thrown down than was in the sample. In the Carpenter instrument, on account of the steam jacket arrangement (see Fig. 72), radiation occurs after the steam has left the separator; the water gage then remains correct, but the orifice measurement may be faulty since the orifice passes wet instead of dry steam. If the gage has been calibrated for the particular conditions of radiation, this calibration takes care of the radiation correction. If radiation causes an increase of water in the water gage the correction may be determined as follows: Dry steam should be supplied to the calorimeter either with an apparatus as described under Test 32 (a) or by taking the sample from another steam separator. Any water that shows at the water gage of the calorimeter is then due to radiation. If it is figured as so many pounds per minute, the correction in ordinary use is readily applied. Problem 33i. If the water gage has been calibrated using the water separated from steam at 100 lbs. gage, what percentage of error will there be when the instrument is used for steam at 50 lbs. gage, the error being due to the change in density of the water between the two temperatures? If the water in the gage glass is 150° F., due to radiation, and the water in the calorimeter chamber is 325° F., will the level in the glass be above or below the inside level? Will these errors make material error in the results of x and why? Ans., 2.4%. Problem 332. If the orifice of the separating calorimeter is used as part of a throttling calorimeter so as to allow for moisture escaping the separator, deduce a formula for the quality of the steam in terms of the weights shown by the separating calorimeter and the quality (xi) as shown by the throttling calorimeter. 34 STEAM CALORIMETERS 151 34. The Condensing Calorimeter Principles. If a sample of steam the quality of which is to be determined, is condensed either by mixing with or radiating through coils to water, the arrangement constitutes a condensing calorimeter. Let TFs = weight of condensate, including moisture in sample; h, L, x = heat of the liquid, latent heat, and quality of the steam sample; Wtc = weight of condensing water; ^M, == temperature of water before it is heated; Twj = temperature of water after it is heated; Ts = temperature of the condensate. If condensation is accomplished by mixing, Tw = Ts, otherwise they have different values. Now, if the calorimeter operates continuously, and if radiation is neglected Ws{{h+xL)-{Ts-32)} =W^,{T^-Q. That is, the heat lost by the steam equals that gained by the water. If the operation is not continuous, the material of the calo- rimeter absorbs an amount of heat v/hich must be accounted for. This quantity is called the ^^ water equivalent,'' being the weight of water that absorbs the same amount of heat for a given tem- perature rise as does the calorimeter. For non-continuous condensing calorimeters, the water equivalent should be added to Tf «,. The equation may be solved for x, the other quantities being obtained experimentally, h and L are found from the steam tables, the pressure of the steam being observed. 152 STEAM CALORIMETERS 34 A barrel of water on a platform scales makes a non-con- tinuous mixing calorim.eter. An injector may be used as a con- tinuous mixing calorimeter. A surface condenser may be arranged as a continuous non-mixing calorim.eter. (a) Determination of the Water Equivalent. The condenser should be isolated and filled with water either hotter or colder than the material of the calorimeter. The initial and final tem- peratures of the water, h and toj and the weight of water W should be observed. If Q is the water equivalent, and t is the initial temperature of the calorimeter, then W(tl-t2)=Q{t2'-t) since the heat lost by the water equals that gained b}' the calo- rimeter, or vice versa. This equation ma}' then be solved for Q. The equation neglects radiation. To avoid the consequent error, a second test may be m.ade with the temperatures of calorimeter and water so adjusted that the temperature rise up to room temperature approximately equals that above. For example, suppose that for the first test water at 110° F. cools to 80°, raising the temperature of the calorimeter from that of the room, 70°, to 80°. The rise of temperature of the calorimeter during the test is 10°. Now, if its initial temperature were 65° and its final 75°, radiation to and from the room would be balanced. Hence, for the second test, the calorimeter should be previously cooled to 65°, and then heated with water at 105° so that the 30° drop in the water temperature, noted in the first test, will bring the final temperature to the desired 75°. The variation will not, of course, be exactly equal above and below the room temperature, but by this method the effect of radiation upon the accuracy of the determination of the water equivalent is made negligil)le. The student should note the fact that radiation thus taken care of is an entirely different quantity from that which occurs 34 STEAM CALORIMETERS 153 in the usual operation of the instrument. For accurate work, the latter should be taken into account as follows. (b) Determination of the Radiation Correction. For non- continuous condensing calorimeters such as the barrel calorim- eter, radiation correction may be avoided in actual use in exactly the same way as that described for the water equivalent determination. The flow^ of steam into the calorimeter is con- tinued sufficiently long to raise the temperature of the cold condensing water as much above room temperature as it was below. For continuous calorimeters, the radiation correction must be found and applied in the equation, as follows, W^{{h + xL)-{Ts-^2)]=W^,{T^,-tJ+R = W^,{T^+t'-Q, in which R is the heat radiated from Wu, lbs. of cooling water and To find t\ the calorimeter is operated as in usual practice, except that dry steam is furnished to it either by the method of Test 32 (a) or by using a steam separator. The value of x is then 1, and the equation may be solved for t\ The correction applies only to the temperature conditions of the radiation test. If the conditions in ordinary operation are markedly different, the radiation test should be repeated to fit the new conditions. It is possible, however, to keep the initial and final temperatures of the cooling water practically the same for different conditions of the steam samples by varying the rate of cooling water. If this is done, and if the room temperature is not very variable, only a single value of the radiation correction is needed. Problem 34i. The data from a barrel calorimeter determination are as follows: Weight of water in barrel before condensing =350 lbs., temperature = 55® F. Weight after condensing = 370.6 lbs., temperature = 115°. Pressure 154 FRICTION TESTERS 35 of steam sample = 100 lbs. gage. What is the quahty, neglecting the water equivalent and radiation? Ans.y 0.901. Problem 342. A water equivalent determination for the preceding example shows that 300 lbs. of water will fall from 98.6° to 97.3° F. when placed in the barrel at 60°. What is the water equivalent, and what is the corrected value of the qualit}^? Ans.y 10 lbs.; 0.934. Problem 343. The circulating water in a surface condenser rises in tem- perature from 50° to 86° F., 275 lbs. being used to condense 10 lbs. of a steam sample at 80 lbs. gage. The temperature of the condensate is 98°. What is the quahty of the sample? Ans.y 0.856. FRICTION Friction is the force which resists the relative motion of two bodies in contact, and is due to the interference of their particles at the siu'face of contact. The laws controlling this force are different depending upon whether the rubbing materials are fluid or solid. Solid friction may be either from sliding or rolling contact, but in this work sliding friction only will be considered. There is a third case, generally of greatest impor- tance to the mechanical engineer, namely, the friction of lubri- cated solids. The controlling laws fall between those for solid and fluid friction, resembling the one or the other according to the amount of lubrication. The laws of fluid friction are well established, but this is unfortunately not true of solid friction. An understanding of the latter is important in the analyses of friction drives, belt forces, etc., and important also to our knowledge of lubricated friction since the rubbing action of solids is a limiting condition of lubricated machine parts. It has generally been assumed that the friction between two dry solids is a constant fraction of the normal force pressing the solids together, independent of the area of contact and velocity of sliding, and depending only upon the nature of the surfaces. These hypotheses have been discredited, but, thus far, experi- 35 FRICTION TESTERS 155 mentation upon this subject has not proceded enough to give us more than an idea wherein they are fallacious. It is possible that they are true for certain materials or certain conditions, but unquestionably they are not generally true. The variation of friction, in the general case, depends upon the normal force between the surfaces, the amount of contact area, the velocity of sliding, and the materials of the bodies. The following table is arranged to give a ready comparison of the several cases. It should be remembered, however, that the statements under solid and lubricated friction are not well established, and are possibly subject to exceptions. VARIATION OF FRICTION Fluid. Solid. Lubricated Solid. Contact area. Directly proportional. Independent (approx.) Directly proportional. Velocity. Directly proportional Inversely, at a Inversely for low as the square, ex- diminishing speeds, directly as cept at low speeds. ral^e. square root for high speeds. Character of Independent. Varies. Varies. surface. Normal force. Independent. Directly pro- Independent. portional. It is further known that the frictional resistance to a fluid mov- ing upon a solid is related in some way to the viscosity of the fluid, decreasing as the viscosity decreases. This property has an important bearing upon lubricated solid friction because the viscosity of lubricants varies with temperature, thus introducing another variable in this case. For solid friction, the working hypothesis is that F=^fN 156 FRICTION TESTERS 35 in which F is the force of friction, N the force normal to the rubbing surfaces, and / a number less than one called the " co- efficient of friction/' 35. Oil Testers Principles. Oil testers are instruments for determining the coefficient of friction in the case of lubricated solids. Their operation generally depends upon the balancing of the friction by a static moment which can be measured; from this and the constants of the instrument, the coefficient may be calculated. Referring to Fig. 73, aS is a revolving shaft to which is fitted a bearing carrying a pendulum. It is arranged that the bearing swing freely and bear on the shaft with a measured force, iV. The oil to be tested is fed to the bearing, and the shaft caused to revolve in a clockwise direc- tion. The force of friction then swings the pendulum to such an angle as to establish equilibrium. If the radius of the shaft is r ft., then the moment of the frictional force, fN, is fNXr, The weight W of the pendulum acts on an arm of 72 sin ^ , i? being the distance of the center of the weight to the center of the shaft ; consequently the moment of the pendulum equals WXR sin A. As this moment equals the moment of the frictional force, we have RsinA") KiG. 73. Oil Tester. and fNr = WR sin A, WR sin A f= Nr For a given set of conditions, all of the quantities on the right 35 FRICTION TESTERS 157 of the equation are constant except sin^, which thus becomes a measure of /. The Thurston oil testing machine depends upon this prin- ciple. The force N is applied and varied by means of a spring mounted on the pendulum, by tightening which the two parts of the bearing may be clamped more or less tightly together. The total force, A', equals twice the tension of the spring plus the weight of the pendulum. There are a pointer and scale on the pendulum by which the total force may be read directly. Another pointer on the pendulum moves over a stationary scale graduated to values of WR sin A-r-r. A thermometer well is provided in the upper bearing so running temperatures may be ascertained. The Riehl6 oil testing machine carries a hand screw for apply- ing the pressure, and the pressure is measured by means of a scale beam. A second scale beam measures the moment of the turning force induced by friction. By equating this moment to fNr, as in the Thurston machine, the coefficient of friction may be obtained. (a) Constants of the Instrument. In the Riehl6 machine, the only constant generally necessary to test is the value of r. If desired the indications of the beams may be tested according to the principles of Test No. 1. With the Thurston machine, it is necessary to find WRy r, and to test the spring. To find WRy the pendulum should be swung to a horizontal position and supported on a pedestal resting on a platform scales. A test is then made similar to that for the unbalanced weight of a Prony brake, Test No. 6 (a). The result should be multi- plied by the horizontal distance between the point of application of the pendulum on the pedestal and the center of motion of the pendulum. This gives the desired moment, WR. In addition to measuring the radius of the bearing, r, its length should be determined, so that the bearing pressure in pounds per square inch of projected area may be calculated. 158 FRICTION TESTERS 36 The graduations on the stationary scale may be tested with these data V.)y calculating their values at any values of the angle A. To test the indications of the spring its scale should be determined according to Test No. 2. As the spring is a heavy one, a strength testing machine is required to compress it. Problem 35i. Run a series of tests with an oil testing machine to show the relation between coefficient and load in pounds per square inch. Problem 862. Run a series to show the relation between coefficient and velocity. Problem 383. Run a series to show the relation between coefficient and temperature. 36. Belt Testers Transmissioji Front/ Brake 'Dynamomefer | — -^ ..Z— <— -- ^ Principles. When power is transmitted from one shaft to another by means of a belt run- ning on puUeySj friction is the use- ful force. Friction sets up ten- sions in the belt; on one side, a greater amount T\ , and on the other a lesser, T2 (see Fig. 74). The difference between these tensions is the net force, T. which effects a turning effort of the follower. It is shown in works on machine design that tll'lTy'^'^olloyrer^ Fig. 74.— Belt Tester. ^ = 10* T2 and T=Ti-T2 = Ti(l 107 in which A' = .0076/^; / being coefficient of friction and ^ the angle of contact of the belt in degrees. The formulas are derived on the assumption that / varies only with the normal force of contact and that centrifugal force on the belt is negligible. For belt speeds over 2500 ft. per min., centrifugal force must be 36 FRICTION TESTERS 159 considered. Its effect is to lessen the normal force between belt and pulley, thus decreasing the effective force, and -^.--('■.-^)('-ii.). in which w is the weight in pounds of a strip of belt 1 in. long and full width; v, its velocity in feet per second; and g, the accele- ration of gravity. In usual operation, there is always a certain amount of ^^ slip '' between the belt and the pulle^^s. Instead of running at the same linear velocity of points of contact, there is a relative velocity difference between the belt and each pulley rim. This fact invalidates to some extent the formula giving the relation between the belt tensions, since friction varies with the velocity of rubbing. Furthermore, so little is definitely known about solid friction, that the assumption F =fN is of doubtful accuracy. It is very likely that, in the case of belts, the coefficient of fric- tion / varies with the normal force N as well as with the velocity of slipping. As the formula depends upon an opposite assump- tion, results of the coefficient of friction obtained from it must be considered of very questionable value. On the other hand, we have no better formula, and for this reason it must be used. Belt-testing machines are instruments for testing the efficiency of transmission, for determining the slip under given conditions, and for determining the coefficient of friction. The efficiency of transmission may be found by measuring the power delivered to the belt wnth a transmission dynamom- eter and the power delivered to the follower pulley by an absorption dynamometer (see Fig. 74), suitable allowance being made for the friction of the shaft bearings. The difference between these quantities is the losses, which are due to work done by friction in moving through a distance equal to the slip and the work done in flexing the belt, windage neglected. 160 FRICTION TESTERS 36 The slip may be ascertained by counting the R.p.m. of the shafts; the difference between ^the linear velocities of the pulley rims is the total slip. The slip over either pulley may be found independently by measuring the linear velocity of the belt. This may be done by counting the number of times a chalk mark on the belt appears in a given time or by arranging a piece of metal to project from the edge of the belt so as to trip a revolution counter. Slip should be expressed in per cent of the driving pulley rim speed. Some forms of belt-testing machines have a differential gear arrangement by which the per cent cf slip may be directly read. To test for the coefficient of friction, apparatus must be pro- vided for the determination of the belt tensions, Ti and T2, so that the formula may be solved for /. This is usually done by separate measurements of the sum and difference of the belt tensions; adding these results and dividing by two gives Ti, knov.'ing which, To is readily obtained. The turning force of the belt, 7", equals the difference of the tensions. The moment of this turning force equals the torque shown by the friction brake (Fig. 74). Therefore, the difference of belt tensions may be calculated by dividing the torque sIioavti by the brake by the radius of the follower pulley. This radius should be m.rasured to the center line of the belt. To get the sum of the belt tensions, not including that due to centrifugal force, one type of machine has the driver pulley mounted freely on one arm of a bell-crank lever the other arm of which bears on a platform scales. The belt pull is then indicated on the scales in inverse proportion to the lever arms. Another t^'pe of machine has the belt arranged vertically, the follower pulley lacing freely suspended. The sum of the belt ten- sions is then equal to the weight of the follower pulley and attachments together with any additional weights used for the purpose of increasing the belt tensions. In both types, the total tension may be varied. 36 FRICTION TESTERS 161 The coefficient varies markedly with the condition of the rubbing surfaces, so every precaution should be used to keep this and other controllable conditions constant. The coefficient also varies with the humidity of the surrounding atmosphere; it is therefore well to make observations of this. (a) The Constants of the Instrument are those of the Prony brake (see Test No. 6) and of any lever arms used for getting the tensions. These are readily obtainable by direct measurement. Problem 36i. The torque as shown by the friction brake is 100 Ib.-ft. If the follower pulley is 2 ft. in diameter, w^hat is the difference between the belt tensions? If the sum of the belt tensions is 200 lbs. and the angle of contact is 190°, what is the coefficient of friction? Ans., /=0.33. Problem 36> Describe how a test should be made to show the variation of the coefficient with slip, all other conditions being constant. Problem 863. Describe how a test should be made to show the variation of the coefficient with the normal force of contact, shp and other conditions being constant. PART TWO THE ANALYSIS OF COMBUSTION THE CONSTITUENTS OF FUELS The principal commercial fuels are coals, oils, and gases in their various forms. The elemental constituents of these fuels, which for the most part are common to all of them, are carbon, hydrogen, oxygen, nitrogen, and sulphur. Of these constituents the ones depended upon to yield heat through com- bustion are carbon and hydrogen. Sulphur has a heat value, but it is an undesirable element in fuel since in coal it goes to form clinker and in gas it may combine with water to make sulphuric acid, these processes accompan}'ing the combustion of the fuel. Nitrogen and carbon in the form of CO2 are inert gases and are valueless to combustion. Carbon and hydrogen occur free or in combination with each other as hydrocarbons or in combination with oxygen. The only combustible carbon-oxygen compound is carbon monoxide, which is one of the most important of fuel gas constituents. Coal may be classified broadly as anthracite, semi-anthracite, semi-bituminous and bituminous, distinguishable by the amounts of so-called *' volatile matter '^ they contain. This is burnable material, mainly hAxIrocarbons, which may be driven from the coal without ignition. The usual percentages by weight of vola- tile matter in the '' combustible '' of the four classes of coal are given in the following table, which also shows the amounts 162 37 CONSTITUENTS OF FUELS 163 that are left of carbon (referred to as '^ fixed carbon '^) when the volatile matter is driven off. By ^' combustible '' is meant the volatile matter and fixed carbon, leaving out of consideration ash and moisture. PROXIMATE ANALYSES OF DRY COMBUSTIBLE Anthracite. Semi-anthra. Semi-bit. Bituminous. Volatile matter 3 to 7.5 5 95 7.5 to 12.5 10 90 12.5 to 25 19 81 25 to 50 Volatile matter, average . Fixed carbon 37.5 62.5 The ash from coals is the residue when the combustible parts have been burned, and consists of such materials as clay, sand, slate, etc. The ash does not vary with the class of the coal, and may be widely different in proportion and quality in each of the classes. Water is also contained in coals, the amount varying with atmospheric and storage conditions. It should be observed that anthracite coal is mainly carbon and ash, there being generally very little volatile matter. A complete chemical analysis of a coal is called its ^^ ultimate analysis.'' The following table is for representative samples of the American product, and gives percentages based on the com- bustible. ULTIMATE ANALYSES OF COALS Anthracite. Semi-anthra. Semi-bit. Bituminoiia. Carbon 95 2.0 0.8 2.0 90.5 5 '4' 87 5 1.5 4 81 Hydrogen 6 Nitrogen 1 5 Oxygen 7.5 When such an analysis is required it should be obtained from a chemist, as the methods and apparatus are remote from mechanical 164 CONSTITUENTS OF FUELS 37 experimentation. An analysis yielding the percentages of mois- ture, volatile matter, fixed carbon and ash, however, may readily be made by the skilled engineer, and often serves all the purposes in the study of combustion. This analysis is called the '^ proxi- mate analysis.'^ The kind of coal and its properties as fuel are determined roughly by the locality at which it is mined, but it should be noted that they may vary markedly in samples even from the same mine. The commercial grades of coal with relation to size are as follows, being listed in the order of the size, largest first. ANTHRACITE SIZE, INS. BITUMINOUS Broken 4 Run of mine Egg 3 Lump, various sizes Stove 2 Nut, various sizes Chestnut 1 j " Screenings, various sizes Pea I Washed sizes Buckwheat, No. 1 Ye Buckwheat, No. 2 I Buckwheat, No. 3 | Oils used for fuel are composed of different hydrocarbons of the form CnH2n-f2 or Cn-Hn, which have a wide range in such physical properties as specific gravity, volatility, burning and flash points. Gasoline and kerosene are the lighter distillates from crude oil. The percentages by weight of carbon and hydrogen in various fuel oils and their distillates from all parts of the w^orld are not very different. Carbon is generally between 83 and 87 per cent and hydrogen between 11 and 15 per cent, the rest being oxygen, nitrogen and sulphur. Gases. The principal gases used for fuel are illuminating gas, producer gas, natural gas, and blast furnace gas. The 37 CONSTITUENTS OF FUELS 165 following table gives the percentages by volume of the constituents of representative American gases. CONSTITUENTS OF GAS FUELS FOR POWER " Low " means less than 1 ner cent. Carbon monoxide, CO .... Hydrogen, H2 Methane, CH4 Ethylene, C2H4 Benzol, CeHe Heavy hydrocarbons Oxygen, O2. Sulphureted hydrogen, H2S . Sulphur dioxide, SO2 Carbon dioxide, CO2 Nitrogen, N2 Producer. Illuminatinf 25 12 2 low low low 5 55 15 45 25 1 low Natural. low 2 95 low low low low 9 Blast furnace gas is combustible mainly through CO. It contains a little hydrogen and methane, and is high in nitrogen. Analysis of these gases must be made by a chemist, with the exception, possibly, of producer gas and blast furnace gas. These may be analyzed by the Orsat apparatus (Test No. 40) if a pipette for the determination of hydrogen is provided, methane being ignored. 37. The Proximate Analysis of Coal Sampling. When an analysis of a small sample is made to represent a large amount of coal, every precaution should be taken to secure a truly representative sample. For the purposes of boiler and producer tests, this may be done as follows. As each barrowful or charge of coal is removed from the pile for firing, an amount varying between a handful and a shovelful is withdrawn and put in a closed receptacle to make up a gross sample. The quantity of coal in each of these samplings and of 166 CONSTITUENTS OF FUELS 37 the gross sample necessary for accurate results depends upon the lump size of the coal, upon its homogeneity, and to a limited extent upon the total amount used. For the smallest sizes of coal of fairly uniform ciuality, the gross sample may be no more than 100 lbs.; under other conditions, it need not exceed 250 lbs. Assuming 200 lbs., the gross sample is broken on a clean surface, preferably a piece of sheet iron, with the assistance of a tamping bar or weight, so that the largest lumps are not more than ^ in. diameter. This coal is then mixed and piled in the form of a cone. The cone should be ^' quartered '' into four heaps by passing a board through the cone axis in two planes at right angles. Tw^o diagonally opposite heaps are then dis- carded and the remaining two mixed, broken to | in., coned and again quartered. The process of quartering and discarding should he repeated until about 5 lbs. of coal lumps not larger than ^ inch are left. Half of this may be put aside in a sealed glass jar for check determinations if desired; the balance is to le run through a coffee mill or other crusher adjusted so that the lumps are reduced to about yq ^^- ^^^d less. After this has been thor- oughly mixed, a sufficient quantity of it for the proximate analysis is crushed by hand \vith mortar and pestle until all of that quan- tity is of such lump size as to pass through a sieve of 20 meshes to the inch. This last amount is used as follows. (a) Determination of Moisture, Volatile Matter, fixed Car- bon and Ash. About 5 gms. of the jt in. sample are carefully weighed before crushing in the mortar. After crushing, it is spread out on a large watch-glass, care being taken that no fine dust adheres to the mortar or pestle, and placed in a gas oven where it is kept at a temperature of 220° to 230° F. It is then placed in a desiccator to cool so that no moisture may be absorbed from the air. AMien cool enough to weigh accurately, it is covered, removed from the desiccator and weighed. It is then returned to the oven and left for a half hour, and the cooling and weigh- ing processes repeated. This is continued until the coal shows 37 CONSTITUENTS OF FUELS 167 no further decrease in weight. The difference between the first weight and the last is the weight of moisture. The percentage is figured on the basis of the weight of the sample including moisture. The gross sample may lose some of its surface moisture dur- ing the processes of quartering and crushing, by evaporation to the air. To avoid this as much as possible, reduction of the gross sample should be performed in a cool room in which the atmos- phere is neither very dry nor very moist, and it should be accom- plished as quickly as possible. To determine volatile matter, about 1 gm. of the coal is pulverized to pass through a 60-mesh sieve, having been pre- viously weighed. It is then placed in a covered crucible and put in the hottest part of the flame of a Bunsen burner which is 8 ins. in height when burning free. After seven minutes, it is removed, cooled in a desiccator, and weighed. The difference in weight of the sample before and after heating equals the sum of its moisture and volatile matter. Knowing the former, the latter may be readily calculated. In this determination, it is important to exclude air from the crucible as otherwise some of the fixed carbon may be driven off as CO2. Some experimenters prefer to wet the coal after the first weighing so that the steam generated will displace the air in the crucible before the distillation of the volatile matter. Fixed carbon is found by subjecting the residue from the last test to the heat of a blast flame, the cover of the crucible being removed. Occasional stirring with a platinum wire assists combustion. It is generally a lengthy process to consume all of the fixed carbon; it may be hastened by directing a gentle stream of oxygen from a c^dinder filled Vvith that gas into the crucible. When the carbon is all burned, its amount is ascertained by cooling the sample in the desiccator, and weighing as before. The ash is determined by weighing the residue from the last test. 168 CONSTITUENTS OF FUELS 37 Sulphur, which occurs both in the volatile matter and in the ash, is sometimes separately analyzed for in the proximate analysis. To shorten the total time necessary for the proximate analysis, it is recommended that the tests for volatile matter, fixed carbon, and ash be made during the time that a separate sample is being dried out for the moisture determination. These tests will show volatile matter and fixed carbon plus moisture; allowance for the latter may be m.ade afterwards. (b) Calculation of Hydrogen and Volatile and Total Car- bon from the Proximate Analysis. For the complete analysis of boiler and producer performance, it is necessary to know the percentage of total carbon in the fuel and of hydrogen in the volatile matter. As the proximate analysis shows only the fixed carbon, that in the volatile matter may be estim.atcd and added to the amount of fixed carbon to get the total. Professor Lionel S. IMarks provides an empirical method cf doing this and of estimating the hydrogen in the volatile m.attcr. He has pointed out a relation applying to American coals by means of curves,* and these curves have been expressed, in part, by the following equations due to Professor Diederichs: Let /?c = hydrogen, exclusive of that in moisture; Cc = carbon in the volatile matter or ^S^olatile carbon"; z'c= volatile matter: all expressed a. weight-percentages of the combustible. Then Cc =0.02vc^ or OMvc - 10) for anthracites; Cc = 0.9(rc — 14) for bituminous coals. * rawer, Dec, 1908. 37 CONSTITUENTS OF FUELS 169 As an example of the use of these formulas, take the proxi- mate analysis given on page 270, and let it be required to find the hydrogen in one pound of the coal, Ht, and the total car- bon, Ct. The combustible, being the sum of the fixed carbon and volatile matter, is .807 + .0617 =0.869 lb. per lb. of coal. Hence Vc = ' Q^f. X 100 -7.1 per cent, and hc = 7.l L^^^^^ -0m3\ =3 per cent. This is the percentage of hydrogen based on the combustible. To base it on the coal, we have Hi = yfo X0.869 = .026 lb. of hydrogen per lb. of coal. Similarly for the volatile carbon, Cc = .02X7.l2 = l per cent. Consequently in 1 lb. of coal, there is j^^X -869 =.00869 lb. of volatile carbon, and the total carbon is C, = . 8:7 + .00869 = .816 lb. Problem 37i. The proximate analysis of a coal gives moisture = 1 per cent, volatile matter =22, fixed carbon = 72, and ash =5. What are the percentages of hydrogen and carbon in the volatile matter, and what is the percentage of total carbon? Base answers on coal as analyzed, not on com- bustible. Ans., 4.6, 8.5, 80.5%. Problem 372. Give the proximate analysis in the preceding problem -^n the basis of " dry '' coal instead of coal " as received.'^ Arts., 1.01%, etc. 170 HEAT VALUE OF FUELS 38 THE HEAT VALUE OF FUELS When used for the generation of power, combustion may be defined as the rapid chemical combination of the oxygen in air with the combustiljle constituents of fuel, which combination is accompanied by the evolution of heat. It has been pointed out that the elemental combustibles in fuels are carbon, hydrogen, and to a lesser degree, sulphur. The complete combustion of carbon forms carbon dioxide, CO2, and of hydrogen, water, H2O. When a unit mass of fuel is burned completely, the heat evolved raises the temperature of the materials entering into the combination and of surrounding objects. If the products of combustion are cooled to the temperature before combustion, then the total heat given up is the *' heat ^' or ^' calorific value '^ of the fuel. Or, more briefly, the heat value of a fuel is the number of heat units that ore released by the complete combustion of a unit mass of the fuel. It should be noted that to release all of the heat generated, the products must be cooled down to room temperature. This may be done in two ways, namely, so that the H2O formed by combustion of the hydrogen remains as steam or so that the H2O is condensed. In the former case the latent heat of the steam remains in the products of combustion, the heat released is correspondingly less, and is referred to as the ^' lower heat value. ^' In the latter case the latent heat of the steam is included in the heat released which is then called the ^^ higher heat value.'' Whether the one or the other quantity should be used depends upon the character of the test for which the heat value is needed. The difference between the two values depends upon the amount of hydrogen in the fuel. For coals, it is comparatively small, but for gases and oils it may be as high as 15 per cent. The units in which heat values are expressed in the United States are as follows, corresponding French units being used to a limited extent only. L 38 HEAT VALUE OF FUELS 171 For solids, B.t.u.s per pound. For liquids, B.t.u.s per pound or per gallon. For gases, B.t.u.s per standard cubic foot. The standard cubic foot of gas is a cubic foot of gas under standard conditions of pressure and temperature. That this specification is necessary will be seen when it is considered that the mass of gas in a cubic foot depends upon these conditions, and consequently its heat value. The standard conditions of pressure and temperature are either 29.92 ins. of mercury and 32° F., or 30 ins. of mercury and 62° F. These pressures are the same and equal to 14.7 lbs. per square inch, the difference in the mercury columns being due to the temperature differences. In this work the 32 degrees standard will be used. The following gives experimentally determined heat values of the elemental combustibles and of various gases, and of fuels. HEAT VALUES IN B.T.U. PER POUND Carbon burned to CO2 14,600 Carbon burned to CO 4,400 ' Sulphur burned to SO2 4,000 XT . . XT r^ f 62,000, higher Hydrogen to H^O j^^isoo! lower HEAT VALUES IN B.T.U. PER STANDARD CUBIC FOOT (32°) Higher. Lower. Carbon monoxide, CO 342 .... Hydrogen, H2 346 294 Methane, CH4 1065 955 Ethylene, C2H4 1680 1560 Benzol, CeHg 4000 3830 HIGHER HEAT VALUES OF COMMERCIAL FUELS, B.T.U Coals 11,000 to 15,000 (per lb.) Oils 18,000 to 20,000 Illuminating gas, average 650 (per cu. ft.) Producer gas " 150 '' Natural gas " 1050 '' 172 HEAT VALUE OF FUELS 38 If it is desired to refer the heat values of the gases to the 62 "^ standard, it is only necessary to multiply by 0.943, the ratio of absolute temperatures. Instruments for determining the heat value of fuels are called ^' fuel calorimeters/^ 38. The Determination of the Heat Value of Coal Principles. This may be done by calculation from empirical formulas involving the results of the proximate or ultimate analysis of the coal, or by the use of a fuel calorimeter. The latter method is the more accurate. Results from coal calorimeters are obtained by burning a small sample of the coal in an air-tight chamber immersed in water. The heat given up to the water and calorimeter parts by the combustion of this coal is measured by the rise of tem- perature, from which the heat value of the coal may be calculated. The essential parts of a coal calorimeter are the water vessel, jacketed to prevent radiation, the combustion chamber or ^^ bomb ^' with a device for igniting the charge, and a ther- mometer or its equivalent. Ignition is accomplished either by an electric current or by dropping a bit of white hot wire through a tubeinto the bomb, a valve being arranged to allow its entrance and to prevent the exit of the gases generated. To support combustion, oxygen is charged with the coal, either in the free state from a cylinder under pressure, or in the form of a chemical rich in oxygen. One of the most convenient of these instruments is the Parr calorimeter, with which sodium peroxide is used as a source of oxygen. Sampling of the coal to be tested should he done exactly as for Test 37, except that the last crushing should be to particles that will pass through a 100-mesh sieve. The final sample should 38 HEAT VALUE OF FUELS 173 be dried in an oven at 220^ to 230° F. before it is charged in the calorimeter. (a) Determination of Heat Value by the Parr Calorimeter. Let W stand for the weight of water used in pounds, w, the water equivalent of the bomb, water vessel and parts (that is, the weight of water that would absorb the same amount of heat in the same temperature range), and T, the temperature rise brought about by the combustion of C lbs. of coal mixed with the appropriate weight of sodium peroxide. The heat given up by the com- bustion is then (W+w)T, Now, 27 per cent of this heat is due to the by-reactions of the sodium peroxide, so that there remains an amount equal to 0.73 (TF+'?^)T' generated by the coal. There- fore, the heat value of the coal is .73{W+w)T The water equivalent, v:, may be taken as 0.3. Generally 2 liters of water and | gram of coal are used. In English units, these weights are 4.41 and 0.001102 lb. Combining the con- stants, we have Heat value = •'^^^^-^|+^-^V = 31177-. The temperature T is the observed temperature minus cer- tain corrections. The hot wire adds some heat which should be allowed for by subtracting 0.022° F., from the observed tem- perature. Anthracite coal is somewhat difficult to burn com- pletely in the bomb, so an additional chemical (about 1 gm.) called ^^ accelerator '^ is used, the heat from which should be allowed for. The accelerator consists of 2 parts by weight of potassium persulphate and one of ammonium persulphate. The corrections are 0.005 degree for each per cent of ash and 0.010 for each per cent of sulphur, to be subtracted. 174 HEAT VALUE OF FUELS 38 Radiation from the calorimeter is very smalL It may be corrected for roughly by noting the fall in temperature imme- diately after the maximum temperature has been reached and during an interval of time equal to that between ignition and the occurrence of maximum temperature. The correction should be added to the observed rise. Radiation may be practically obviated by making the initial temperature of the water about 2° less than that of the room. As the observed rise in temperature is between 4 and 5° the radiation will be balanced. The procedure for the test is to add about 9 gms. of sodium peroxide to ^ gm. of coal, mix thoroughly in the bomb, ignite, and, during the period of heating, to revolve the bomb in the calorimeter so as to circulate the water. This last is accomplished by means of vanes attached to the bomb, the purpose being to quickly make the temperature of the water uniform. The temperature rise is noted from a finely graduated thermometer. Care should be taken not to allow water to touch the sodium peroxide, as they react violently. (b) Calculation of Heat Value from the Fuel Analysis. If the combustibles in coal were in the elemental form, it would be easy to calculate the heating effect from each according to its amount and thus get the heating value of the coal. This, how- ever, is not so; they are combined as hydrocarbons and other- wise. Now when combustion takes place some heat must be given up to the hydrocarbons to separate the carbon from the hydrogen so that they may recombine with oxj'gen. That is, some heat becomes latent through dissociation of the elements which lessens the heat availal^le from their combination with oxygen, ^o there is an interchange of heat in burning coal which makes its heat value dependent upon the previous com- bination of its elements. We therefore cannot calculate heat values with precision in this wa}', but certain empirical for- 38 HEAT VALUE OF FUELS 175 mulas enable us to make fair estimate?. One of them is Dulong's as below. Heat value = 14,600C+62,00cf^-g j +4000>S, the symbols C, H, 0, and S standing for the weights in pounds of carbon, hydrogen, oxygen, and sulphur in 1 lb. of the fuel, respectively. The result is in B.t.u. per pound. This formula uses the ultimate analysis of the coal, and is more applicable to anthracite than to bituminous coals. Another formula, using the proxim_ate analysis, is Goutal's.* This is Heat Yslue = K7.GXfc+KXvm, in which fc and vm are the percentages of fixed carbon and volatile matter in the fuel as received, respectively, and K has different values depending upon the amount of volatile matter, as shown in the curve, Fig. 75. 260 250 ?40 250 2Z0 2iO 200 190 180 170 160 150 140 150 120 110 kT \ V \ "^ ^^ ^^ ^^^ "'^ \ \ jr I jt 10 12 14 16 18 20 22 24 26 Z8 30 32 54 36 38 40 42 PERCENT VOLATILE MATTER IN FUEL AS RECEIVED 44 46 Fig. 75. Fig. 76 is a reproduction of IMahler's curve, from which, probably, may be had as reliable a result of heat value as any * Wisconsin Engineer, Dec, 1911. 176 HEAT VALUE OF FUELS 38 of the relations proposed for this purpose. As an example of its use assume a coal with 16.9 per cent of volatile matter and 70.8 per c^nt of fixed carbon. Then Combustible in the coal =16.9+70.8 =87.7 per cent; Fixed carbon in the combustible =70.8-^87.7 =80.6 per cent. ^^500- — ^ 65 jQ 75. 80 85 90 95 100 Per Cent of Fixed Carbgn in Combustible Fig. 76. — Mahler's Curve for Coal Heat Values. From Fig. 76, against 80.6 per cent is found the heat value of the combustible, 15,800 B.t.u. per pound. Consequently, the Heat value of the coal =15,800 X. 877 = 13,900 B.t.u. It should be emphasized that all of these relations for calcu- lating the heat value of coal are approximate, and generally give better values with the lower percentages of volatile matter; the probable error then being within 2 per cent. Problem 38i. A sample of bituminous coal is tested for heat value. Ignition by hot wire. 2.5 liters of water used. Water equivalent of calo- rimeter =0.40 lb. Sample weighs 0.6 gm. How much heat is generated and what is the heat vahie if temperature rise is 4.23° F.? Ans., 13,300 B.t.u. Problem 38> Calculate the heat value of coal giving a proximate analysis as follows: moisture, 2.75; volatile matter, 6.00; fixed carbon, 78.45. Ash, 12.8 per cent. Use Mahler's curve. What would be the heat value if the coal were drv? Ans., 12,900 and 13,300 B.t u. 39 HEAT VALUE OF FUELS 177 39. The Determination of the Heat Valle of Gases AND Oils Principles. The heat vahies of gases may be calculated readily from their chemxical analyses, but this is not true of oils on account of their complex structure. Both oils and gases may be tested for heat value by the use of a properly designed calo- rimeter. The Junker calorimeter is universally used for this purpose. This instrument is an ingenious arrangement of heating surfaces surrounded by water, by which all the heat generated by the fuel to be tested is passed to the water. The water is kept flowing through the calorimeter at a constant rate, secured by keeping it under a constant head, and enters continuously at a uniform temperature. Upon leaving the calorimeter, it m.ay be weighed, and the heat added ascertained by noting its rise of temperature. In order that all the heat be given up to the water, the products of combustion must return to the tem- perature of the fuel and air from which they came, before leaving the calorimeter. This is ascertained by a thermometer placed in the exit gas flue. The water resulting from the burning of hydrogen is condensed and collected, should it be desired to calculate the lower heat value. (See p. 170.) For gases, a Bunsen burner is used and a small gas m.eter to measure the fuel in cubic feet. For liquid fuels, a special regenerative burner is used which, together with the lamp con- taining the fuel, is attached to one arm of a beam balance so that the weight of fuel burned ma}^ be measured at any time during the test. There is no water equivalent of the calorimeter to be con- sidered since, during operation, all parts are at constant tem- peratures. Radiation is provided against by air jacketing and polished surfaces, and is neghgible. 178 HEAT VALUE OF FUELS 39 Sampling. If the sample to be tested represents a gas used in a test of several hours' duration, it is best to take a continuous sample covering the whole time of the test as described on page 193, for exhaust gas sampling. This involves rather a large gas container, however, and it is more convenient to draw the gas from the main directly into the calorimeter. For this purpose the main should be tapped at a point as near as possible to the place where the gas is used. Then, if a number of heat value determinations are made covering equal intervals of time and separated by equal intervals, their average will be the average heat value of the total gas delivered in the main. (a) Determination of Higher Heat Value. The rates of water and gas flow should be adjusted so that the temperature of the products of combustion upon leaving the calorimeter is that of the room. Then, if t and T are the temperatures of the water before and after heating, respectively, in degrees Fahrenheit, ]r, its weight in pounds, and G, the cubic feet of gas burned, we may say Higher heat value= (^-OTF-^G. In this, G is the number of cubic feet of gas under standard con- ditions (see p. 170). To convert the gas meter reading into standard cubic feet, it is necessary to use the relation that the volume of a gas varies directly as its absolute temperature and inverse!}^ as its absolute pressure. Consequently, the pressure as well as the temperature of the gas should be noted. This involves a reading of the barometer and of a manometer set in the gas main. The heat value determined in this way is not quite the higher value, for the reason that not quite all the water of combustion is condensed. This is because the air entering combustion is not saturated with water vapor (although the fuel may be), but the products of combustion are saturated. Tlie difference in the humidities is due to the water of combustion which is 39 HEAT VALUE OF FUELS 179 not condensed. To avoid this error, it may be arranged to feed the calorimeter with saturated air and gas. The determinations as made without this precaution are acceptable for most purposes. (b) Determination of Lower Heat Value. This is determined correctly by subtracting from the heat added to the water the amount which came from the vapor in condensing, or its latent heat. To get this amount correctly, we should know the weight of the vapor and its latent heat per pound. The latent heat of steam is generally determined from its pressure by reference to the steam tables. In the case of steam mixed with other gases, the pressure of the steam is only partial (see p. 142) and therefore difficult to determine. Under the conditions existing during the operation of the Junker calorimeter, it is convenient and sufficiently accurate to take the latent heat of the steam as that corresponding to the temperature of the exhaust gases, that is, room temperature. Letting L stand for this heat and w for the weight of condensation, we have Lower heat value = ^ — ^ , the other notation being as used under (a). An average value of L may be taken as 1060 for temperatures between 50° and 70° F. (c) Calculation of the Heat Value from the Fuel Analysis. This maj^ be readily and accurately done in the case of gases when the complete analysis is known. The following rule may be used: To calculate the higher or lower heat value of a fuel gas, multiply the higher or lower heat value of each of the constituent gases, in B.tM, per standard cubic foot, by its volume percentage, as shown by the fuel gas analysis, and divide by 100. Add these results together; the sum is the desired heat value. The heat values of various constituents of fuel gases are 180 PRODUCTS OF COMBUSTION 40 given on page 171. An example of the calculation is given in columns 1, 2, 6 and 7 of the table on page 294. Problem 39i. Figure the higher heat value from a calorimeter test giving data as follows. Pressure of gas = 4 ins. of water. Barometer, 29.4 ins.; temperature of gas, 70° F.; 7.24 lbs. of water raised from 60.7° to 116.3°. Volume of gas burned, 0.875 cu. ft. by meter. Ans.j 500 B.t.u. Problem 392. In the preceding problem, if there were .048 lb. of water of condensation, what would be the lower heat value? Ans., 437 B.t.u. Problem SSa. Calculate the higher and lower heat values of the producer gas, analysis of which is given in the table on page 165. Ans., 148 B.t.u. THE PRODUCTS OF COMBUSTION The products of combustion of fuels used CDmmercially are called exhaust gases. By their analysis, we learn the completeness of combustion and the directions and amounts of heat losses in the operation of boilers, internal combustion engines, and gas producers. Commercial combustion, as previously defined (p. 170) involves the chemical comljination of the oxygen in air vith the combustibles of a fuel, resulting in CO2 and H2O. Air is principally oxygen and nitrogen, the other constituents being negligible in this analysis, and the proportions may be taken as 21 of oxygen to 79 of nitrogen by volume. Now, in order to secure complete combustion, it is necessary always to furnish an excess of air over tho amount required to convert all the carbon to CO2 and hydrogen to H2O. The exhaust gases will therefore contain free oxygen and nitrogen due to this extra air, in addition to CO2 and H2O. Sometimes the combustion is incomplete, in which case the exhaust gases may contain CO, free hydrogen, and hydrocarbons. With proper operation however, these are each less than 1 per cent by volume of the total exhaust . gases, and the hydrogen and hydrocarbons are almost always negligible. The experimental determinations 40 PRODUCTS OF COMBUSTION 181 are therefore generally only for CO2, CO, O2, and N2; H2O being calculated from the fuel analysis. The analysis of the exhaust gases is found and expressed as percentages by volume. The ratio, by volume, of the air actually suppUed to the fuel to that required for '^ complete theoretical combustion," is called the '^ excess coefficient. '^ The Principles Involved in the Applications of exhaust gas analyses depend upon Avogadro's law. It is important that this law be thoroughly understood. Following is a statement of it: In a given volume of any gas, there is always the same number of molecules, regardless of the nature of the gas, provided the con- ditions of pressure and temperature are constant. We therefore know that in a vessel containing a mixture of gases, there is the same number of molecules as though only one of them or of any gas existed there alone, irrespective of the number of atoms in the molecules. Also, the number of mole- cules in 2 cu. ft., for example, is twice the number in one; that is, the number of molecules in a gas is directly proportional to its volume. It follows from Avogadro's law that, for given conditions of pressure and temperature, the volume occupied by a single molecule of any gas is a constant quantity. Since all of the determinations from exhaust gas analysis are relative, it will be convenient to conceive this volume as a cubic foot and to use the unit, ^^ molecule-foot,'^ to express it. Elemental gases are supposed to have two atoms to a molecule. For that reason they are written O2, N2, H2, etc. Carbon does not occur as a gas except in combination with other elements, but it will be convenient to consider hypothetical gaseous carbon having a single atom to the molecule. The relative weights of the elements under consideration, compared with that of hydrogen (that is, their atomic weights), rro as follows. H = l, = 16, N = 14, C = 12 ..^^iM 182 PRODUCTS OF COMBUSTION 40 V ?? oo •o Ni troofen « 19 .t?. Carbon Dioxide V oo oo V oo V oo oo V ^ oo oo •Carbon Monoxiole Fig. 77. Molecule-feet. cents of the per cent is a fcot contains The molecular weight of a gas equals the sum of the weights of the atoms in its molecule. Thus, H2 weighs 1 + 1=2, O2 weighs 16 + 16-32, CO2 weighs 12 + 16+16 = 44, and so forth. As an illustration of the way in which these principles are applied, consider a mixture of gases consisting of 10 per cent of CO2, 1 of CO, 9 of O2, and 80 of N2; all per cents being by volume. Since these gases are expressed relatively (the basis of the comparison being 100 parts, i.e., per cent) we may consider their percent- ages as cubic feet, or as molecule-feet. Fig. 77 represents the per gases considered thus, each cubic foot and each cubic a single molecule. Suppose we wish to find the ratio by weight of the oxygen in the gas to the carbon. There are 9 molecule-feet of oxygen as such, 10 molecule-feet of oxygen in the form of CO2, and one-half a molecule -foot as CO, making a total of 19.5 molecule- feet. Since the molecular weight of O2 is 32, the total weight of O2 is 19.5X32. Similarl}^ the number of molecule-feet of carbon is 10+1 = 11, having a weight of 11X12. Dividing the weight of oxygen by the weight of carbon, 19.5X32-^132, we get the desired ratio of weights, 4.72. Since this is a ratio, it may be expressed in any units of weight, for example, 4.72 lbs. f oxygen per pound of carbon. In this way we may figure the weight in pounds of any or all of the gases or of the elements composing them per pound of any of the constituents. The total carbon used in combustion may be measured when in the form of fuel. If this weight is multiplied by that of any of the products of combustion, expressed in pounds per pound of carbon, the result is the total weight of that product of com- bustion. This follows from the assumption that all of the carbon iji the fuel appears in the exhaust gas analysis. 40 PRODUCTS OF COMBUSTION 183 Theoretical Reactions of Fuels Products from Coal Combustion. In the burning of pure carbon, if complete combustion could take place with no excess of air, the reaction would be 79N2+2IO2+2IC-2ICO2+79N2 showing that the exhaust gas would consist of 21 per cent of CO2 and 79 per cent of N2. Now, if more than this amount of air is used, the sum of the free oxygen and of the CO2 in the exhaust gas will bear the same relation by volume to the nitrogen as the oxygen did in the air, since the volume of the oxygen is not increased by combination with carbon. Consequently the sum of O2 and CO2 is 21 per cent, and N2 is again 79 per cent. Ash does not vary this relation, but the effect of hydrogen, oxygen, and nitrogen in the coal is to alter it. The last two have slight effect, but the hydrogen needs oxygen from the air to burn to water, and as the water does not appear in the exhaust gas analysis, a corresponding amount of oxygen disappears. This increases the percentage of nitrogen. The formation of CO instead of CO2 has an opposite effect, since the oxygen entering the combination makes twice the volume of CO* on the other hand CO is generally low. Anthracite and semi-anthracite coals, being low in hydro- gen, will yield exhaust gas having between 79 and 80 per cent of N2. Bituminous coals will yield between 80 and 81.5 per cent. Results outside of these figures are questionable. It is obvious that the less air is used, the less will be the free oxygen in the exhaust gas, and the greater will be the CO2. It will be shown (Test No. 54) that the less the air used the more economical is the combustion, provided that there is not so little air as to cause material loss from incomplete combustion. Con- sequently high CO2 is a desirable indication. 184 PRODUCTS OF COMBUSTION 40 Fig. 78 shows the variation in the products of combustion of carbon and of sohd fuels, for ^ arious amounts of air, assum- ing complete combustion. Products of Oil Combustion. Since the proportions of the elemental coni-tituents of fuel oils a:e approximately constant for all of them, the products of their complete combustion will also be constant under the sa:::e conditions of air supply. An average analysis is C, 84, and II2, 1-i per cent by weight. The ratio of PRODUCTS OF COMBUSTION FROM FUELS E ^15 [Carbon > \Anfhracife '^Bifuminouz —— 1 lie k ^^0, ^"^?$4^^^*-— y ^ ' — «>«^ ^ / "^ 1 ^, i>- >< ■^ / Producer Gon Illuminating 5^j4— — |— 1 ^ oJ ^ y weight of the air containing it, the air required to burn 32 each pound of C is ■ lbs., or ^ 12X.23 11.6 lbs. of air to burn 1 lb. of C. Two molecules of hydrogen, weighing 4, unite with 1 of O2 to make H2O. Consequently there will be 4- -^.23 lb. of air required to burn each pound of H2, or 34.8 lbs. of air to burn 1 lb. of H2. If C and H stand for the weight of carbon and hydrogen in one pound of the fuel, and it the fuel contains no oxygen by which combustion may be supported, then the total amount of air needed per pound of fuel is 11.6C+34.8//. If the fuel con- tains Us. of oxygen per II3., a corresponding amount less of air is needed, namely ^0 = 4.35 0. In the general case, then, Air required = 11.6C+34.8^-4.3o lbs. per lb. fuel. For Gas Fuels, the air required is generally expressed in cubic feet of air per cubic foot of fuel, the conditions of temperature and pressure being the same for both. 40 PRODUCTS OF COMBUSTION 189 Letting c, /i, and g stand for the number of molecule-feet of C, H2, and O2, in 100 molecule-feet of the fuel, counted as in columns 3, 4, and 5 of the table on page 294, there will be required c molecule-feet of O2 to burn the C to CO2, and 0.5 h molecule- feet of O2 to burn the H2 to H2O. Since there are g molecule- feet of O2 contained by the fuel, only {c+0,5h — g) molecule-feet of O2 will be required from the air to burn 100 molecule-feet of the fuel. Therefore, Air required^- ' ' cu. ft. per cu. ft. fuel. xUU /\ .^ i 40. The Analysis of Exhaust Gas Principles. The gas analysis apparatus depends upon the separate absorption of the products of combustion by certain reagents. A measured volume of the gas is brought into contact with one of these reagents which removes the CO2, but does not take up any of the other constituents. The CO2 is then deter- mined by measuring the diminution in volume. In this way the volumes of CO and O2 may also be found. The residue is assumed to be N2. It is convenient to make the original volume 100 units, as cubic centimeters, in which case the differences are per cents. The Orsat apparatus in its various forms is in general use for engineering analj^ses of exhaust gas. It consists of a measuring flask, jB', called the burette (see Fig. 82), a distributing tube, T, and three so-called pipettes, DD\ 00' , and MM\ containing the reagents. The gas sample is displaced from the burette into each pipette in turn by filling the burette with water from the bottle B, The right leg of the pipette is completely filled with reagent just before the gas enters; the gas displaces it into the left leg. Rubber bags, /?, seal the left legs of the pipettes 190 PRODUCTS OF COMBUSTION 40 so that the reagents will not deteriorate through contact with the atmosphere. If desired, the apparatus may be provided with a fourth pipette for determining hydrogen. There are many other types of exhaust gas analysis apparatus, ^amplincf Tube Rubber Tube * Jm/m//////////////////^^^>r ^ Fig. 81. — Gas Sampling Bottle. To F ^ M' K M K r 1 \-~ ■ -J y\ Fig. 82. — Orsat Apparatus. the most important of which are recording instruments giving the percentage of CO2 in boiler flue gas continuously. CO2 Recorders.* These may be divided into two classes, continuous and intermittent. Of the former, a representative one is the Uehling. Its principle is shown diagrammatically by Fig. 8S. A steam aspirator draws the gas through the two orifices, A and B, between which is a special, dry absorbent of CO2. If no CO2 is present, there will be a definite pressure, below atmosphere, between the two orifices. If CO2 is present * For methods of installing and adjusting various iy\)Qs of CO2 recorders, see Bulletin 91, Bureau of Mines, on Iftslrumcnts for Recording CO2 in Flue Gases, by Barkley and Flagg. 40 PRODUCTS OF COMBUSTION 191 it is absorbed between the orifices, reducing the volume of gas in this space, and thereby decreasing its pressure. Pressure there- fore becomes a measure of CO2 removed, and is recorded by a low pressure recording gage calibrated in percentages of CO2. TO BOILER ROOM INOJCATQR TO RECOROINC CAUCE ABSORPTION CHAMBER A INDICATING COLUMN-*- FILTER WATE R ^ ■ ■ ■ 6AS INLCr Fig. 83. — Diagram of Uehling CO2 Analyzer. The instrument is provided with a regulator for automatically maintaining a uniform flow. The Simmance-Abady CO2 recorder is typical of inter- mittent instruments for this purpose. Referring to Fig. 84, the water-sealed meter tank on the left alternately draws in and discharges a definite volume of flue gas by means of the rising and falling meter bell. This gas is delivered to the absorption tank, shown at the bottom of the figure, from which it is forced 192 PRODUCTS OF COMBUSTION 40 by the downward stroke of the meter bell into the recorder tank on the right, raising the counterbalanced recorder bell to a height proportional to the final volume of the gas. The last posi- S is used to receive the sample. To start with, it is filled with water. During collection, the water is syphoned into flask R through T' and the gas flows through H into the space evacuated, branch F being closed. All the air in the tube H should be displaced before taking the sample. This may be done either by raising the flask R above the level of the sampling tube so that water will syphon into the the tube //, or by drawing a small charge of gas into flask *S in the regular manner and then discharging it through a three- way cock at the end of the branch F. The latter procedure leaves flue gas in the tube H very slightly diluted with air. The sample should be collected at a uniform rate, and, if more than one sample of the same gas or for the same test is to be analyzed, time periods during which collections are made should be equal in order to get a correct average result. The rate may be kept practically uniform by placing flask R several feet below S and 40 PRODUCTS OF COMBUSTION 195 by choking the end of the syphon at t with a sHver of wood. The change in the rate due to the decreasing distance between the water levels in the flasks may then be inconsiderable. For boiler and gas engine tests, it is well to collect the sample during half hour or hour periods, and during the collection of each sample to analyze the preceding one. This has the advan- tage of showing the uniformity of combustion as the test proceeds. It is also well to have a duplicate sampling outfit, collecting gas at a very slow rate so that the sample will cover the whole test. This may be analyzed at the convenience of the experimeter; the results should check the average of the separate analyses. (a) Determination of CO2, O9, CO and N2. The Orsat apparatus is first connected with a rubber tube to the branch F leading from the sample bottle (see Figs. 81 and 82). The reagents in the pipettes are brought to the levels a, by manipu- lation of the bottle B, the three-way cock / being closed. This being done, and the cocks, d, 0, and m, closed, the water level in the burette is raised to the point n, thus expelling the air previously contained through the three-way cock / which is open to the atmosphere for that purpose. The pinch-cock C on the samjjling bottle flue connection is now closed, and the flask R raised so as to put the sample under pressure. The cocks between the sample bottle and the burette are then opened, and the bottle B lowered so that part of the sample will flow into the burette. The gas now in the burette is diluted with air or other gas which was in the distributing tube and in the rubber tube leading to the sampling bottle. To get a purer charge, this first one is discarded through the three-way cock, /, and another one brought into the burette, in the same way as the first, which may be accepted for analysis. This charge should be somewhat greater than 100 cc. Having secured this sample by closing the three-way cock, the bottle B is raised a trifle until the water level in the burette reaches the lowest graduation which marks 100 cc. of gas. As 196 PRODUCTS OF COMBUSTION 40 the sample has been compressed by this rise in water level, the pressure should be made equal to atmospheric by opening the three-way cock for an instant, the pinch-cock p being closed so as to maintain the water level at the lowest graduation. The sample should now be worked back and forth in the KOH solution to remove the CO2. After this has been done for a few minutes, it should be returned to the burette, care being taken that the reagent is at its original level, a; the cock d should be closed; and a volume measurement of the gas made. This must be done with the sample under the same condition of pressure as wlien originally measured, that is, atmospheric. For this reason, the w\ater levels in the burette and in the bottle B should be coincident when the reading is made. Before making the reading it is well to allow the walls of the burette to drain for a minute. After the reading the gas is returned to the KOH solution and worked a few more times, then measured again. If the volume is the same the result is satisfactory, if not, the process should be repeated until all the CO2 has been removed as indicated by constant volume. The diminution of volume is the per cent CO2. Tl e O2 and CO are removed and measured in the same Avay and in the order named. The difference between the sum of the per cents of CO2, O2, and CO, and 100 may be taken as the percentage of No. Precautions in Operating. Before using the apparatus, all connecting tubes and cocks should be tested for leaks by putting air in the system under pressure or partial vacuum with the bottle B, and noting whether the volume remains constant as shown by the level in the burette. Analyses should be made at a uniform temperature of not less than 60° F. During operation, the apparatus should not be exposed to a changing temperature, or placed where drafts or sun may strike it. The corresponding changes in the volume of the sample would give false results. 40 PRODUCTS OF COMBUSTION 197 Water absorbs all of the gases to some extent. To avoid the resulting errors, it is well to use water that has been previously saturated with exhaust gas, so that it will not take up any more. To do this the exhaust gas is caused to bubble through the water, used in the sampling flask and in the burette. If a little coloring matter, such as red ink, is added to the water used in the burette, it will aid in the reading of the gradua- tions. It is well to keep a record of the volumes absorbed by each reagent so that it will be known when their absorptive capacity has been reached. The volume of reagent in a pipette is about 150 cc. (b) Calculations from Exhaust Gas Analyses. The principles upon which these depend are stated and illustrated on pages 180 to 183. They should be thoroughly understood. The results for coal combustion are generally based upon 1 lb. of dry ccal, while those for fuel gas are based on one standard cubic foot of the fuel. Therefore two different sets of formulas will be deduced for the two cases. It is convenient to apply the following rule for a number of purposes. The density of a gas, in pounds per standard cubic foot, equals the density of hydrogen times the ratio of molecular weights of the gas and hydrogen. The density of hydrogen is 0.00559 lb. per standard cubic foot; consequently the density cf gaseous carbon, for instance, is 0.00559 X 2' =0.0335. The following notation will be used for the two cases in com- mon D, ikf, 0, A", // = percentages cf carbon dioxide, monoxide, oxygen, nitrogen, and hydrogen, by volume, in the exhaust gas, respectively. Fd = volume cf dry exhaust gas in cubic feet per pound cf coal or per cubic foot of fuel gas. Tra = weight of air supplied in pounds per pound of coal, or per cubic foot of fuel gas. ja 198 PRODUCTS OF COMBUSTION 40 Tr4i = weight of dry exhaust gas in pounds per pound of coal, or per cubic foot of fuel gas. TT\ = weight of H2O in the exhaust gas, per pound of coal, or per cubic foot of fuel gas. X = excess coefficient; that is, the ratio of the amount of air supplied to that required for complete theoretical combustion. It should be borne in mind that the weights here tabulated are quantities resulting from the combustion of 1 lb. of dry coalj or from 1 standard cubic foot of fuel gas (see page 170). Formulas for Coal Combustion. In 100 molecule-feet of the exhaust gas there are D+M molecule-feet of carbon, since each per cent cf CO2 and CO contains 1 molecule-foot of carbon. Therefore, the ratio 100-^ (D+M) is the number of cubic feet of dry exhaust gas per cubic foot of gaseous carbon contained by it. This is for dry exhaust gas (that is, the volume cf the water actually contained is omitted) because the analysis does not take account of the H2O. If it is divided by the weight of a cubic foot of gaseous carbon, 0.0335 lb., the result is the number of cubic feet of dry exhaust gas per pound of carbon in it, or 2980-f-(Z)+il/). Multiplying this by the weight of carbon that is gasified from 1 lb. cf dry coal, we have the volume cf dry exhaust gas per pound of dry coal, or Co rd-2980 D+M' in w^hich Co is the weight of carbon gasified. This quantity is all of the carbon in 1 lb. of dry coal, G, except that lost through the grate and removed with the ash, C^; or Cg =^Ct — Ca assuming carbon deposited as soot to be negligible. Ct may be estimated from the proximate analysis and Ca measured from the 40 PRODUCTS OF COMBUSTION 199 total ash (Test 54 (c)). If Ct is found from the analysis in terms of percentage cf the coal as analyzed, that is, wet coal, it should be divided by 100 minus the percentage of moisture to reduce to weight per pound of dry coal. To find the weight of air supplied per pound of dry coal, we may assume that all of the nitrogen in the exhaust gas comes from the air, a very nearly correct assumption since coal con- tains but little nitrogen. Now, there are 28 N weights of N2 in the exhaust gas, and 12{D+M) weights of C; 28 and 12 being the molecular weights, respectively. Therefore, the weight of N2 supplied by the air to each pound of carbon gasified is pounds. Dividing this by the proportion of N2 in air, 0.77 by weight, gives the pounds of air supplied to a pound of the carbon in the exhaust gas. Multiplying by the weight of carbon gasified from 1 lb. of dry coal gives the weight of air supplied per pound of dry coal, or Wa 12X.77X{D+M) NCa 3.04 D+M The weight of dry exhaust gas is that of the air supplied plus that of the carbon combined with it, approximately-, or This is approximate since some of the oxygen in the air has combined with the H2 in the coal to form water which is sepa- rately counted. This, however, is comparatively small. Also other constituents than carbon from the coal are in the dry exhaust gas, oxygen and sulphur, for instance. With bituminous 200 PRODUCTS OF COMBUSTION 40 coals, the 0x3 gen may be as high as 10 per cent by weight, but this amount would figure as less than 1 per cent of the dry prod- ucts of combustion. Water vapor in the exhaust gas comes from three sources, namely from combustion of hydrogen, from moisture in the coal, and from the moisture in the air supplied. The first two only need be considered. If Ht is the weight of hydrogen in 1 lb. of dry coal, the result- ing water vapor, if all the hydrogen is burned, will be 9 //<, since the ratio of weights of H2O to the H2 in it is (2 + 16)4-2 = 9. If 771 is the weight of moisture in the coal per pound of dry coal, then the total weight of H2O in the exhaust gas, per pound of dry coal is The assumption that all the H2 is burned is sufficiently accurate under usual operating conditions. If lit and m are found from the proximate analysis (see Test 37, (a) and (6) ) as percentages of the coal as analyzed, they should be divided by 100 minus the percentage of moisture to reduce to pounds per pound of dry coal. The weight o'^ carbon incompletely burned, per pound of dry coal, may })e calculated from the CO appearing in the exhaust under the assumption that there is no incomplete combusti^^n through unl)urned hydrocarbons. The method is the same as for the determination of the weight of air. Let Wi be the desired weight. Then i 12(£>+M) D+M To find the excess coefficient, it is necessary to divide the 40 PRODUCTS OF COMBUSTION 201 value of Waj as deduced above, by the expression for the air required as given on page 189, then, neglecting O2 in the coal, X = TT,,-^(11.6Cl+34.8//,). The formulas above also apply to the combustion of oils if Ct is substituted for C^, and if m is left out of the expression for Wv. Formulas for Gas Combustion. These are deduced upon the assumption that all the carbon in the fuel appears in the exhaust gas analysis, and that none other does. Contrary to this, in the case of internal combustion engines, is the fact that some carbon is left as a deposit in the cylinder, but it is so small compared with the total carbon used as to be negligible. Also, if the lubricating oil burns, it will appear as CO2 in the exhaust, so care should be taken to avoid this condition. Hydrocarbons in the exhaust, too, will prevent the correct application of the formulas. If the CO in the exhaust is less than 1 per cent, it is very unlikely that there is any hydrogen or hydrocarbon, because CO is the least readily burned of the fuel gas constituents. The following relation will be used to get most of the for- mulas. Weight or volume of the substance sought, per cubic foot of fuel gas = weight or volume of that substance contained in 1 cu. ft. of exhaust gas X volume of exhaust gas per cubic foot of fuel gas. If an expression for the last named quantity, which is Fd, be deduced, it will remain only to find the required quantities per cubic foot of exhaust gas. The following additional notation will be used. Cjh^g =the number of molecule-feet in 100 molecule-feet of the fuel gas, of carl:on, hydrogen, and oxygen, respectively; counted as in columns 3, 4 and 5 of the table on page 294. 202 PRODUCTS OF COMBUSTION 40 R = Ratio, by volume, of air supplied to gas, that is, the numbr of cubic feet of air per cu. ft. fuel. To find Vd^ Since there are D+M molecule-feet of carbon in 100 of the exhaust gas, and c molecule-feet in 100 of the fuel gas. Cubic feet of exhaust gas per cubic foot of gaseous C in it Cubic feet of fuel gas per cubic foot of gaseous C in it = D+M 100 c By assumption, the gaseous carbon is the same in both gases. Hence, by division. Cubic feet of exhaust gas per cubic foot of fuel gas = T D+M The volumes of exhaust gas above are for dry gas. The volume of air supplied per cubic foot of fuel gas is found as follows. The oxj^gen appearing in 100 molecule-feet of the exhaust gas is D+0+.5M molecule-feet. Dividing this by .21, the proportion of oxygen in air by volume, gives the cor- responding amount of air; and the cubic feet of air which sup- plied this oxygen, per cubic foot of exhaust gas, is '- ■, ^ -^^ ' 100X.21 Multiplying by Vd^ gives the cubic feet of air per cubic foot of fuel, that came in with the oxygen that appears in the exhaust gas. But some oxygen has disappeared in the form of water. As there are h molecule-feet of hydrogen in 100 of the fuel, and as each one combines with half its volume of O2, is the 2X100 cubic feet of oxygen disappearing as water, per cubic foot of fuel. But some of the oxygen comes from the fuel itself, and we wish only that which comes from the air. Subtracting the molecule- feet of oxygen in the fuel gives {.5h — g)'^100. Dividing by 40 PRODUCTS OF COMBUSTION 203 0.21, we get the corresponding air. Then the cubic feet of air supplied per cubic foot of fuel gas is, If there is H per cent of hydrogen in the exhaust, too much oxygen has been counted. To allow for this, if the free hydrogen is known, subtract 0.5H from the quantity in the parenthesis. To find Wd' The density of CO2 in pounds per cubic foot is 44 D 0.00559 X-^ (see page 197). Multiplying this by -77^7 gives the z luu weight of the CO2 in one cubic foot of the exhaust gas. In the same way the weights of all the other constituents of the dry exhaust gas may be obtained, and there results '■^^^^{UD+32O+28M+28N)-^l00. Multiplying this by Fd, and simplifying, we have, Wa = ^{nD+80 + 7{M+N)}. To find Wv Besides the water of combustion, there is some water vapor in the exhaust due to moisture in the air and fuel gas. These will be disregarded, as they have but a sUght effect upon the heat analysis owing to the fact that latent heat is not lost to the H2O of humidity. Since there are rrrrj cu. ft. of hydrogen per cubic foot of fuel, and since the weight of the resulting H2O is 9 times the weight of the H2, we have, = . 0005/1. 204 PRODUCTS OF COMBUSTION 40 If hydrogen in the exhaust has been analyzed, W, = .0005(h-HVa) since free hydrogen would mean a corresponding decrease of H2O. The cubic feet of unburned CO per cubic foot of fuel equals Vi = MVa^ 100. If hydrogen has been found, it may be expressed similarly. To find the excess coefficient, the value of /?, as deduced above, should be divided by the expression for the air required as given on page 189, or 217? X c+ .5h — g' Problem 40i. Draw a set of curves like Fig. 78 for the semi-anthracite coal whose ultimate analysis is C = 0.80, H = 0.04, = 0.03, Ash = 0.10. Problem 4O2. How many pounds of air are required to burn 1 lb. of the coal in the last problem? In this calculation, what per cent of error is involved if the oxygen contained in the coal is ignored? Ans., 10.5 lbs. Problem 4O3. How many cubic feet of air are required to burn 1 cu. ft. of the producer gas, analysis of which is given on page 165? What is the weight of this air? Ans.y 1.07 cu. ft. Problem 4O4. Figure the density of the producer gas of the last problem by the molecular weight method, page 197. A/is., .0703 lb. Problem 4O5. Deduce an expression for W^ similar to Wa, for coal. Problem 406. An exhaust gas analysis (coal) gives CO2, 6 percent; O2, 13 per cent; CO, 1 per cent; N2, 80 per cent. What are the weight and volume of total oxygen in it per pound of carbon gasified? Why would not a calculation for the air supplied, based on this result, give the same value as one based on the N2 in the exhaust gas? Ans., 7.43 lbs.; 83.1 cu. ft. Problem 4O7. An exhaust gas analysis from the illuminating gas in the table on page 165 gives CO2, 5 per cent; O2, 10 per cent; CO, 1 per cent; N2, 84 per cent. What are the values of R, Wa, W^j Ff, and X? PART THREE THE TESTING OF POWER PLANT UNITS 41. The Determination of Cylinder Clearance Principles. Linear clearance of a piston engine may be defined as the least distance between the piston and cylinder head in a direction parallel to the center line of the cylinder, when the engine is on dead center. It may have different values at the head end and crank end of the stroke. Volumetric clearance is the cylinder volume between the piston and nearer cylinder end, which may be occupied by the working medium when the engine is on dead center. It may have different values on the two ends. The volumetric clear- ance is not only that in the bore of the cylinder, but includes the volume of the ports up to the valve face and the volume of any fittings, such as indicator piping, which may be filled with the working medium in the usual operation of the engine. The space in cylinder drain pipes open to the C34inder is sometimes considered as clearance volume; in some cases, however, this space, in usual operation, is filled with water of condensation so that it is not part of the clearance. Volumetric clearance is expressed as a part or per cent of the piston displacement. ^^ Piston displacement '^ is the volume swept through by 205 206 STEAM ENGINE TESTING 41 one stroke of the piston, that is, the area of the piston times the length of stroke. A knowledge of the clearance of engines is necessary to an analysis of their performance and losses, especially in connec- tion with indicator diagrams. See Tests 44 (a) and (6). (a) Linear and Volumetric Clearance by Linear Measurements. The most accurate way to determine linear clearance, if the engine is not too large, is to loosen the connecting rod when the piston is at the end of its stroke, and then note how far the piston rod moves when it is pushed from the dead center posi- tion to contact with the cylinder cover. If the engine is too large for this the cylinder cover may be removed, and the measurement made by compressing between it and the piston, a small quantity of putty. The putty should be stuck to the cover at the part where the distance between it and the piston, or the piston rod extension, appears to be least. The piston should first be oiled and then dusted with graphite, so that the putty will not stick to it. The putty is then compressed by bolting the cover in place. The least thickness of the putty is the linear clearance. It may be measured by the use of a piece of fine, stiff wire. The volumetric clearance may be obtained by mensuration from the drawings of the engine. This gives only an approximate result since the actual castings may differ materially from their drawings, and since the position of the piston in the cylinder may change with wear of the connecting rod bearings. If mensuration is used, it is best to make drawings of the engine clearances from the engine as it stands, as nearly as possible to scale. (b) Volimietric Clearance by Water Measurement. The engine should be put on the desired dead center by putting the crank and connecting rod in line by eye. The steam valve or valves should be made tight either by smearing its face with heavy cylinder oil or, with sHde valves, by squeezing a piece 41 STEAM ENGINE TESTING 207 of rubber gasket between the valve face and seat. The piston and cyUnder bore should be well oiled to prevent leakage. If the cylinder has holes tapped on the top for indicator piping, they may be used for the introduction of water by which the clearance volume may be completely filled. By taking the weight of the water before and after filling, the amount necessary to fill the clearance space is determined. Dividing this by the density of the water gives the clearance volume. The density may be taken as 0.0361 lb. per cubic inch at 60° F. If the tem- perature is materially different from this, it should be noted and the corresponding density used. Should there be a slight amount of leakage which cannot be prevented, it may be corrected for by determining the " leakage rate.'' This is done by measuring the amount of water necessary to keep the clearance space full for a period of one minute. Now, this is probably the maximum rate of leakage, since, dur- ing the filling, the leakage probably varied with the head of water in the cylinder. The average leakage may be taken as one- half that shown by the test. The period of time necessary for the filling should therefore be multiplied by one-half the maximum leakage rate to get the total leakage that occurred during filling. This weight subtracted from the weight used in the filling gives the weight corresponding to the actual clearance volume. It should be noted that there are several assumptions in the foregoing which make the method approximate; it should not be used when the leakage is very large. If the cylinder to be tested contains pockets in which air may be trapped during the fiUing, as is likely to be the case with internal combustion engines, these pockets should be blanked off and measured separately if possible. If this is not possible, the water method should not be used. For accurate results, several determinations should be made and none accepted unless they show fair agreement. 208 STEAM ENGINE TESTING 41 To express the clearance volume in percentage, the piston displacement must be known. The bore may be measured with inside calipers, and the stroke by measuring the distance between dead center positions of the cross-head, a mark being made on the cross-head guides at each end to indicate these positions. (c) Volumetric Clearance from the Indicator Diagram. Pro- fessor Paul Clayton proposed a method based on the fact that gases and vapors expanding or being compressed in closed cylinders follow the law that Absolute pressure X volume^ = a constant. This law is represented by a logarithmic curve. Consequently if the amounts of the pressures and volumes obeying it are plotted on logarithmic coordinating paper (the coordinates being pro- portional to the logarithms of their markings as with the scale of a slide-rule), the result is a straight line. In an indicator diagram, the volumes represented are the total volumes of the working medium behind the piston, which include that of the clearance space. In order to transfer the indicator diagram to logarithmic coordinates, then, it is necessary to know the clearance volume so that the axis of abscissas may be located. If the indicator diagram is located on logarithmic coordinates by assuming a value of the clearance volume, the resulting expansion and compression curves v;ill be concave to the origin, if the assumed value is too small, and convex if too large. This provides a method of determining the clearance volume, since it is only necessary to plot the expansion or compression curve from the indicator diagram on the logarithmic scale using a number of assumed values of tl:e clearance volume until that one is found which produces a straight line. A convenient procedure is as follows. Divide the indicator diagram with equidistant vertical lines into ten spaces, and mark the points of intersection of the verticals 41 STEAM ENGINE TESTING 209 with the expansion curve 1, 2, 3, etc. The coordinates of these points will be used to locate the logarithmic diagram. The absolute pressures corresponding to these points should be measured from the zero pressure line which is laid off 14.7 lbs. below tlje atmosphere line. After choosing a suitable scale with w^hich to represent these pressures on the logarithmic chart, their positions are indicated by placing small marks against the vertical axis of logarithmic coordinates. Now, let a value of the clearance volume, x, be assumed in per cent. Then the point, 1, corresponds to a volume of 10 j^lus x per cent; point 2, to a volume of 20 plus x per cent, and so on. Using these volumes expressed as percentages, the points are readily located on the logarithmic chart. If the resulting curve is concave to the origin, a larger value of the clearance is assumed, and so on until that value w^hich produces a straight line is found. It will be noted that there are limiting values of the assumed clearance between w^hich the straight line condition seems to be satisfied. On this account the method is recommended only where the clearance is large, as in internal combustion engines; the percentage of error then being not excessive. Problem 41i. Following are the data from a test for volumetric clear- ance by the water method. Weight of bucket and water before filling, 12 lbs. 141 ozs. Weight after filling, 10 lbs. 2h ozs. Time of fiUing, 95 seconds. To keep clearance space full for 60 seconds, 8 ozs. What is the average leakage rate in pounds per m^inute? What is the clearance in cubic inches allowing for leakage? What is the per cent of clearance if the engine is 10 ins. X 16 ins. (bore X stroke)? Ans.y 5.22%. Problem 4l£. In the preceding problem room temperature 60° F. of the water is assumed. How much percentage of error w^ould be involved if the actual temperature were 40° F.? If 80°? Arts., 0.1%, 0.3%. 210 STEAM ENGINE TESTING 42 42. Valve Setting of a Simple Slide Valve Engine Principles. It is assumed that the student is acquainted with the principles and operation of the simple slide valve and linkage and ^^ith the various quantities pertaining, such as steam lap, exhaust lap, angular advance, etc., which subjects are amply covered by various works on the steam engine. With a finished steam engine, in order to set the slide valve so as to better the distribution of steam, there are only two parts that may be adjusted without altering the design of the parts, namely, the valve stem, which may be changed in length, and the eccentric, which may be changed in its position on the shaft relative to the crank. The former adjustment affects the laps and lead of the valve; the latter, the angular advance. A study of the valve motion will show the effects of such adjust- ments upon the valve and upon the steam distribution as follows. Effect of Increasing. Angular Advance. Stem Length. On Head End. Crank End. Head End. Crank End. Outside lap Inside lap Same Same Increases Earlier Earlier Earlier Earlier Same Same Increases Earlier Earlier Earlier Earlier Increases Decreases Decreases Later Earlier Earlier Later Decreases Increases Lead Increases Admission Earlier Cut-off Later Release Later Compression Earlier The student should confirm this table by drawing the link- age as in Fig. 85 to represent the positions at the various events of the stroke, taking them first for one end of the cylinder and then the other, and observing from the drawings the effects of 42 STEAM ENGINE TESTING 211 the adjustments as tabulated. In Fig. 85 the engine is shown at crank end release. The valve stem is broken so as to show the valve on top of the cylinder, for convenience, instead of. at the side. It should be noted that the laps may be measured when the eccentric is vertical, as this position of the eccentric puts the valve practically in its mid-position. (a) Measurement of Lead. This is made by measuring the amount of port opening, the valve chest cover being removed, when the engine is on dead center, that is, w^hen the crank and connecting rod are in line. The engine should not be put on dead center by noting the extreme position of the cross-head '¥^ YdlveSfeyn Eccenrric-') f/y//A////A Fig. 85. Fig. 86. because, at the end of the stroke, there is no appreciable move- ment of the cross-head when the crank moves through several degrees. The eccentric, however, is then in a position where a few degrees of error will cause a considerable error in the position of the valve. Consequently, the dead center must be accurately located. The following method may be used. (See Fig. 86.) The crank is turned until it is about 30 degrees from the dead center position sought. A mark, 1, is then made on the cross-head against a mark, 2, on the guides. Another mark, 3, is made on the flywheel against a mark, 4, on some stationary object. Now the engine is turned through its dead center posi- tion until the cross-head mark 1 again comes into the coincidence with 2. The crank and connecting rod will then occupy the positions shown by the dotted lines and the mark 3 a\ ill be at 212 STEAM ENGINE TESTING 42 5. A new mark is now made on the flywheel opposite 4, and the distance between this and 5 on the flywheel rim is bisected by the line 6. If the flywheel is then turned until 6 is opposite 4, the engine will be on dead center. Care should be taken that the motion of the linkage, when advancing to the positions for marking, should always be in the direction of the dead center sought so as to avoid error through lost motion of the parts. If there is no place conveniently near on which to put the mark 4, a pair of trammels should be used. (b) Setting the Valve for Equal Leads. From the table given under '^ principles/' it is seen a change in the angular advance will make the leads on both ends larger or both smaller, while a change of the stem length will make the lead on one end larger and on the other smaller. It will therefore be con- venient to change the stem length to equalize the leads, and then to adjust the angular advance until they become the desired amount. The procedure is as follows. The eccentric is first put in its approximate position, that is, about 135° ahead of the crank. The leads are then meas- ured according to (a). If the lead on the head end is greater than on the crank end, the stem length must be increased to equalize them, and vice versa (see table). If the leads are then both too small, the eccentric is shifted on the shaft further away from the crank until the desired leads are obtained, and vice versa if the leads are too large. The proper amount of lead depends upon the travel of the valve, the engine speed, and the amount of compression. More lead is required for high speed engines, and less when the com- pression is high. For low speed engines, leads up to re ^^- ^re usual, and for high speeds, twice that amount. It is advisable, after setting for equal leads, to indicate the engine as a check upon the setting. The lead should be such as to give a vertical line at the admission for both head and crank ends. 42 STEAM ENGINE TESTING 213 (c) Setting for Equal Cut-offs by the Bilgram Diagram. The typical Bilgram diagram is shown by Fig. 87, the positions of the crank corresponding to the various events of the stroke being shown (for the head end only) by the radial lines. The events of the stroke for the crank end may be found by reference to the crank end lap circles with similar construction. For convenience the lower half of the diagram may be revolved through 180° so as to be superposed on the upper half. For other details and for proof, see Halsey's Valve Gears. Rad = Head End St Lap- " f>/7. " •• Cranff Posifion fbr Admission - 0/ » » » Cuf-O-ff - 0? '• •♦ Release - OZ " • »' Compression ■ 04 L Cross head J Conn. Rod. -^ 6^roke Bad. • Crank End St Lap- " • •• >' E^h. ••- Rad. 'Eccen. Fig. 87. — Bilgram Valve Diagram. To lay out the diagram for the purpose of valve setting, we must assume a cut-off, and measure the connecting rod and crank lengths and eccentricity from the engine. If the cut-off is C inches from the end of the stroke, the corresponding crank positions, 01 and 02, may be found by drawing the engine link- age to scale as in Fig. 88. The diagram may be constructed on these lines, starting by putting in the eccentric circle as shown. The values of the steam laps will depend upon the setting of the valve, but we may locate the lap circles by determining the sum of the steam laps. This equals the length of the valve 214 STEAM ENGINE TESTING 42 in the direction of its motion minus the distance between the outside edges of the ports, in the case of the D-valve taking steam outside. The steam lap circles may be constructed by first locating a point x on the eccentric circle such that the sum of its perpendicular distances from the lines 01 and 02 equals the sum of the steam laps. The lap circles may now be drawn about x as a center and tangent to the lines 01 and 02. The leads and maximum port openings are then determined as shown. If the leads are too large, a later cut-off must be assumed and the construction repeated. C. E. St Lai Bad ' Conn. Rod Lencjih Fig. 88.— Setting for Equal Cut-offs. Using the data for the lead and port opening at one end (preferably the crank end, since there they are larger) the valve may now be set for the assumed cut-offs. To do this, the crank is revolved until the valve has moved as far as it will toward the head end of the cyUnder, thus giving the maximum port opening on the crank end and making the eccentricity parallel to the engine center line. The stem length is then adjusted until the crank end port is open an amount equal to that indicated by the diagram. Next the engine is put on its crank end dead center by the method given under {a) and the lead made equal to that shown by the diagram by s\\inging the eccentric on the shaft. This completes the setting, but the lead and port opening 42 STEAM ENGINE TESTING 215 should be measured on the head end as a check, and conipared with the values given by the diagram. (d) Valve Setting by the Indicator. The ultimate test by^ which the steam distribution must be judged is by the indicator. The valve setting should be such that not only does the engine run smoothly, but that it should give the maximum power for the steam used. Valves may be set by deductions from the indicator diagrams, and the previously described methods dispensed with. The procedure may l)e more laborious and less systematic, since it is largely cut and try. Events +00 Ewrli^ Even+s foo Late Fig. 89. — Faulty Valve Setting shown by Indicator Diagrams. Fig. 89 shows indicator diagrams, superposed on ideal ones represented by dotted lines, from Vfhich may be noted the variations caused by too early and too late occurrence of the events of the stroke. If the admission is too early (that is, if there is too much lead), full boiler pressure is admitted to the cylinder before the beginning of the stroke and the admission line rises at a point other than the extreme of the diagram. If the admission is too late (too little lead), the admission line slants inward because the full boiler pressure does not reach the cylinder until the piston has advanced appreciably in its forward stroke. 216 STEAM ENGINE TESTING 42 The cut-off may be too early on either end of the cylinder only in relation to that on the other end; they should be approx- imately equal for equal division of the load. The simple slide valve engine does not cut off earlier than six-tenths of the stroke; if the cut-off on either end is much later than this, as shown by the point at which the expansion line begins on the diagram, either the valve is not well designed or its setting is imperfect. If release takes place too earty, the pressure is released from the cylinder before the end of the stroke; the result is a curtail- ing of the expansion line and a sharp drop down to the backpres- sure line. If the release is too late, expansion may take place clear to the end of the stroke, but when the piston returns there is not enough opening for the steam to exhaust through freely. The result is excessive back pressure at the beginning of the return stroke as shown by the rounded toe of the diagram in Fig. 89. The compressions on the two ends should begin at approx- imately the same percentage of the stroke. If there is too little compression, the engine will not run smoothly; if too much, the maximum power is reduced, although the economy in the use of steam may be increased. Compression tends to reduce the steam loss due to clearance. To set a slide valve by the indicator, it is necessary to have diagrams from both ends of the cylinder. Faulty steam dis- tribution may then be deter- mined in detail by the effects on the diagrams as just de- scribed. A knowledge of the effects of the adjustments of stem length and eccentric Fig. 90. position, as given in the table on page 210, then enables one to correct the steam distribution. The engine should then be indicated again, and further corrections made if necessary. 42 STEAM ENGINE TESTING 217 As an example of the reasoning involved, consider Fig. 90. It is well first to make a table showing the existing characteristics of the diagrams, as follows: Admission. Head end Early Crank end Late Cut-off. Release. Compression. Late Late Early Early Early Late By reference to the table on page 210, it is seen that to change the angular advance will aggravate some of the errors, which- Ecoentrio too far ahead. Fig. 91. — Faulty Valve Setting and Diagrams. (Reproduced from Power.) ever way it is adjusted. But if the stem length is increased, the events will tend to equalize and change to proper amounts. The stem length should therefore be increased and diagrams taken, the procedure being repeated until the cut-offs are about equal. It may then develop that all of the events are too ^^ 218 STEAM ENGINE TESTING 42 early or too late, in which case the eccentric should be adjusted until the admission lines are vertical. If the release and com- pression are then satisfactory, the setting is acceptable. Samples of indicator diagrams showing faulty valve setting, etc., are shown by Fig. 91. (e) Study of the Steam Distribution by the Bilgram or Zeuner Diagrams. This may be done before or after setting the valve in order to decide upon the best setting or how the setting may be improved, thus possibly saving a number of trial settings and of indicator trials. For this purpose, the necessary measurements are made of the valve and engine parts, from which a number of diagrams are constructed with different adjustments of eccentric and stem length assumed. Indicator diagrams may be con- structed from the data yielded by the Bilgram or Zeuner diagrams (the expansion and compression curves being drawn as rect- angular hyperbolas), by comparison of which, the best setting may be selected. The measurements to be made from the engine are of the con- necting rod and crank lengths, the eccentricity, and the lead and outside and inside lap on one end. The outside lap at either end may be readily determined by noting the distance th^ valve must move from mid-position to begin to uncover the port. The mid-position may be found by making a prick point or scratch on the valve stem and measuring to this mark. The inside lap at either end may be obtained by subtracting from the length of the valve face, the length of the port and the outside lap, the dimensions being taken from the end considered. The sum of the outside laps should also be found as described under (c), and the sum of the inside laps, found similarly, by subtracting the distance between the inside edges of the valve faces from the distance between the inside edges of the ports. The Bilgram diagram may now be laid out by drawing first the eccentric circle and the lead at the end for which it has been measured, say the head. (See Fig. 87.) Next, the head end 42 STEAM ENGINE TESTING 219 lap circle is drawn with its center at such a point, x, on the eccen- tric circle as to make the lap circle tangent to the lead line. The angular advance line is then drawn in, which locates the centers of the other lap circles. Having described these the events of the stroke, in per- centages, may be deter- mined. The Zeuner diagram may be laid out similarly, start- ing with the eccentric circle (see Fig. 92). A point X is then located at a dis- tance from the center of the eccentric circle equal to the lap plus the lead on the head end. The circle OX A is next constructed, which fixes the angular advance by the line OA. When the lap circles are put in, the events of the stroke may be determined in the usual manner. It may be noted that it is convenient to work with the sum of the outside laps and of the inside laps, since, if it is desired to reconstruct the diagram with a different lap on one end, the opposite one is readily determined by subtraction. Verify the table on page 210 by the method given in the Eccen. Fig. 92. — Zeuner Valve Diagram. Problem 42i. text following it. Problem 422. The lead on the head end of a steam engine is found to be TS in., and on the crank end A in. If the leads are to be made equal to ihb in., should the valve stem be lengthened or shortened and how much? Should the angular advance be increased or decreased? Problem 423. A D-slide valve has a face 1.5 ins. long at each end, and the distance between the faces is 2.75 ins. The ports are each H in., and the outside edges of the ports are 4.50 ins. apart. If the head end outside lap is .625 in., what are the values of the other three laps? Ans., f, 3 16) A in. 220 STEAM ENGINE TESTING 43 Problem 424. The valve in the preceding problem has an eccentricity of 1.375 ins. Find the lead and the maximum port opening on the crank end for equal cut-offs, using the Bilgram diagram. The connecting rod is 28 ins. long and the crank 5 ins. Problem 42> Find the events of the stroke in per cents, using the data of the last problem and the Bilgram diagram. Problem 426. Repeat the last problem, using the Zeuner diagram. Problem 42;. Why cannot a valve be set for equal leads and equal cut- offs at the same time? If for equal leads, which cut-off is greater? Problem 428. How could the events of the stroke be measured direct from an engine whose valve was set, by reference to the valve and measure- ments of the cross-head travel? Problem 429. Set the valve of an engine for equal cut-offs. Then measure the events of the stroke from the engine, from the indicator diagram actually obtained, and from the Bilgram diagram. Test 43. Setting a Corliss Valve Gear Principles. The action of the CorHss valve gear is explained in numerous works on the steam engine. The student should have an understanding of this action to grasp the following: The setting may be considered in two parts; first, for the proper laps and leads, and, second, for the governor regulation. Usual values of the laps and leads are as follows, the smaller ones corresponding to the smaller engine sizes. Steam lap ^ to ^ inch. Exhaust lap . . i^ to 3^ inch. Lead A to | inch. The laps are adjusted and measured when the linkage is in its mid-position, as indicated by Fig. 93. This figure also names the terms by which the various parts will be referred to, so that the following instructions may be understood. (a) Adjustment of Laps and Leads. The first step is to set the wrist plate in its center position, the hook rod being lifted to free the wrist plate. There is generally a mark on the wrist plate hub which registers with three stationary marks, as shown in 43 STEAM ENGINE TESTING 221 Fig. 93. The middle stationary mark indicates the correct center position of the wrist plate, and the outer marks, its extreme positions. If desired, the center position may be checked with a plumb line. Having located this, the hook rod length should be adjusted so that, when engaged with the wrist plate, the rocker arm stands vertical as shown by a plumb hne. The eccentric Fig. 93. rod length may now be adjusted so that the eccentric throws the wrist plate to the correct extreme positions. Now, with the wrist plate in its center position and the steam valves hooked up, the laps may be made the desired amounts by altering the lengths of the steam and exhaust links. The laps are readily measured when the exhaust bonnets are removed, as lines will be found to indicate the edges of the valves and ports. This accomplished, put the engine on head end dead center (see Test 42 (a) for method) and make the head end lead the selected value by swinging the eccentric on the shaft, thus moving the valve to the desired position for lead. Then fasten the 222 STEAM EXGIXE TESTING 43 eccentric, put the engine on the other dead center, and measure the crank end lead. If the leads are not equal, the crank end steam link may be changed in length slighth' to obtain equahty. (b) Adjustment of Governor Rods. With the governor in the lowest running plane (but not in the safety stop plane), throw the wrist plate b\' hand to the head end limit as shown by the mark on the wrist-plate hub. The crank-end knock-off cam should then trip its valve just at this extreme wrist plate position; if it does not the crank end governor rod length must be changed. This done, the head end rod is dealt with similarly. The cut-oflfs will then be latest when the governor is in its lowest running plane. The no-load action of the governor should next be checked. Block up the governor to its highest plane, in which position the steam valves should just fail to hook up. Another procedure is to set the governor rods at the highest position of the governor so as to open the valves a very small amount when the valves are tripped; and, for the lowest position the valves are not released at all. It is understood that a setting at one limit of the governor travel cannot be made without affecting that at the other. (c) Adjustment of Dash-pot Rod. Each steam valve hook engages with a '' catch-block " on an arm rigidly fastened to the valve, and this arm is connected with the dash-pot rod. By lengthening or shortening the dash-pot rod, the catch-block may be raised or lowered. When the valve hook is in its lowest position (that is, when the wrist plate is at an extreme position), the cor- responding dash-pot rod should be changed in length until there is an equal clearance above and below the catch-block, between it and the hook. (d) A Check of the Setting by Indicator should be made after the completion of all adjustments. In particular, the amount of compression should be ascertained, and the action of the dash-pots towards a sharp cut-off, together with the equahzation of cut- 44 • STEAM ENGINE TESTING 223 offs. Improvements in the setting may be made often by changing the steam and exhaust Hnks. Problem 43i. Will increasing the length of a steam link increase or decrease the lap and the lead? Why? What effect will an increase of the' angular advance have on laps and leads? Why? Problem 432. If an indicator diagram shows the compression on the head end to be too early, should the exhaust hnk length be increased or decreased, and what effect will the readjustment have on the release? 44. The Mechanical Efficiency Test of a Steam Engine Principles. The mechanical efficiency of a steam engine is equal to the useful horse-power divided by the horse-power developed by the steam in the cylinder. If a Prony brake is used to measure the useful horse-power, then (see Test 6) B.h.p. = BTFiV is the useful horse-power. Using the following notation, I.h.p. = Indicated horse-power; Pji and Pc = the mean effective pressure on the head end and crank end respectively; L = the length of the stroke in feet; a = the area of the cylinder, in square inches; a' = the area of piston rod, in square inches; iV = the number of revolutions per minute; then the cylinder horse-powder may be expressed, On the head end, I.h.p.^ = ^ =KnPhN, . . (1) On the crank end, I.h.p.c = ^'^J^ I.^'- ^ = KcPcN (2) oo, UUU Kj, and Kc are called the " engine constants." Total I.h.p. = I.h.p.ft4-I.h.p.c. 224 STEA:\I EXGIXE testing 44 ^Mechanical friction causes a loss of power so that all the work developed in the cylinder does not appear at the fl^-wheel. The friction horse-power equals F.h.p. = I.h.p.-B.h.p (3) When the brake is entirely removed from the engine, the work done in the cylinder to keep the engine running is expended to overcome friction only. The function of the engine governor is to keep the speed constant. This is done by the action of any change of speed, through centrifugal force, to alter the position of the governor weight. More or less steam is admitted into the cylinder accord- ing to the position of this weight, and therefore more or less cylinder work is done. To accommodate itself to a variable load, then, the engine 7?iust allow some change of speed to regulate the cylinder work. At no load, with the governor admitting the least steam, the speed is greatest, and at maximum load, least. Good regulation requires that the difference between these limits of speed be small. For comparative purposes the speed regulation is expressed as a percentage variation from the mean speed. If Xm and Nn are the speeds at maximum and no load, respectively, then Per cent speed regulation =^ .^.^^^ ^^.*". ' ^T xiOO. (a) The Indicated Horse-power is determined by measur- ing the quantities in formulas 1 and 2, the engine constants being calculated before the test. The mean effective pressures are found from indicator diagrams by integration with a plan- imeter. The speed is determined with a Ijand or continuous counter. The brake horse-power being the independent variable, it is first calculated what net forces should be obtained at the brake scales to produce the required horse-powers. The engine 44 STEAM ENGINE TESTING 225 is then operated at one of these horse-powers by adjusting the tension of the brake strap to give the necessary force at the scales, and to maintain it at that value. This means constant observation of the brake scales and occasional regulation of the brake-strap tension. The engine should be operated at each load for ten minutes or more so that it may adjust itself to the new conditions of load and friction. A number of indicator diagrams and measurements of the R.p.m. are then taken. It is convenient to average the readings of Pn, Pc, and N at each load and to use the averages for substitution in formulas 1 and 2. A more convenient, although approximate, formula for calculating the indicated horse-power, is as follows: Ui.p. = k{Pb+Pe)N in which k is the average of the two engine constants or L( a— — J -T- 33,000. A brief consideration will show that the more nearly is the area on the crank end equal to that on the head (that is, the smaller is the area of the piston rod relative to that of the cylinder) the less error is there in the approximate formula. Also, the less difference is there betv/een the mean effective pressures on the two sides of the piston, the less error is there. When they are equal the results from the two methods of calcu- lation are the same. The following is a rational formula by which the per cent of error ensuing from the approximate formula may be determined for any conditions. Let iR = Ratioof P^toPft; i:on which takes advantage of the law discovered by him that there is a definite relation between the amount of cylinder condensation and the exponent of expansion * See also foot-note, page 238. 45 STEAM ENGINE TESTING 231 in the equation Py'* = a constant, at all events for certain types of engines. (See Journal A.S.M.E., April, 1912.) He plots the indicator diagram on logarithmic coordinates (see Test 41 (c)) and from the slant of the expansion line gets the value of n. By using a set of curves giving the quality of the steam in the cylinder just after cut-off at various values of pressure and ??, the quality of the steam at cut-off and the cylinder condensa- tion may be calculated. These curves have not been sufficiently verified as yet to make them of general application. Further- more, the method seems to take no account of leakage of steam past the valve, which may never enter the cylinder, but is never- theless consumed by the engine. The clearance should be determined as described under Test 41. The expression for cut-off, C, may be found by divid- ing the distance of &, Fig. 32, from ae, by the length of the diagram, in inches. For the sampling of diagrams, see Test 10 (e). By Condenser. All of the steam used is passed into a surface condenser, and the condensate weighed for a counted time. This is probably the most accurate way of testing for steam consumption. Numerous time-quantity readings should be made to determine uniformity of flow. The condenser must be operated with more circulating water than is used in practice, so that the condensate will emerge cool; otherwise a large amount may escape unweighed by evaporation. The piping between the condenser and engine must be examined for tightness, and the condenser tested for leakage. The latter may be done by running the air-pump when no steam is flowing, and noting if any circulating water is drawn through, preferably when the condenser is hot. If it leaks a small amount, a leakage rate may be found and applied as a correction to the results. If the engine is to be tested '' non-condensing,'' that is, with no vacuum, the condenser must be vented in order to establish this condition. 232 STEAM ENGINE TESTING 45 By Steam Meter. One of the commercial forms of steam meter may be used in the steam pipe supplying the engine. See Test 30. By Feed-water Measurement. For this method, the engine and boiler supplying it should be isolated so that all of the steam generated by the boiler is used in the engine. Sometimes it is necessary to supph^ steam to auxiliary apparatus, such as a feed pump, from the boiler supplying the engine tested. In such a case, it is necessary to make a separate measurement of this steam, either by establishing the rate beforehand or, better, by condensing the steam used by the auxiliary during the test. It is necessary to examine the boiler and piping for tightness, the latter especially at branches stopped by valves. This is done by closing all valves in branches and the main stop valve at the engine so that the supply pipe is open from the boiler to the engine valve, but closed everywhere else. V^ith a quiet furnace fire so that there is no active evaporation, the level is then noted in the water column at a mmiber of uniform intervals of time. If the level falls, leakage is taking place, and the rate should be determined from the area of water surface calculated from the measurements of the boiler. This leakage may then l^e applied to the results of a test as a correction. The feed water may be measured by any of the methods given under Test 54. Willan's Law states that the weight of steam per unit of time used by an engine with a throttling governor varies directly as the indicated horse-power of the engine, very nearly'. The work represented by an indicator diagram in which the expan- sion follows the law that PT' = a constant (very nearly the case with steam) is mathematically proportional to the initial pressure, cut-off l)eing constant. As the pressure is proportional to the density of the steam, approximately, it follows that the weight of the steam is proportional to the work, and the indicated horse- power. The weight of steam used also varies directly with the 45 STEAM ENGINE TESTING 233 brake horse-power, since B.h.p. = I.h.p. — a constant. Experi- ment has shown that this relation applies not only to throttling engines, but to those of the cut-off type, and to steam tur- bines. The practical application of Willan's law lies in the conse- quence that if the weight of steam used per hour by an engine is plotted against its indicated or brake horse-power, the result is a straight line. This furnishes a check upon the results of a test as the test proceeds; if points so plotted do not follow a straight line, there is error. It should be noted that at over- loads, the curve is apt to deviate slightly from straightness, and lean toward the axis of steam weights. The duration of the test should depend upon the uniformity of conditions, the capacity of the engine, and the method used for measurement of the steam. During each test at a given load, weighings are made at uniform time intervals, say ten or fifteen minutes. When there are four to six of these of nearly equal amounts recorded consecutively, the run may be dis- continued, provided the error of starting and stopping is within reasonable limits. (See page 9.) This error depends upon the method of measuring the steam. If a condenser is used, the error will be relatively small, since it equals the difference in the amounts of condensate in the condenser at starting and stopping. If the boiler method is used, the test must be much longer, as there may be large error in the level of the water column, due to differences of density, ebullition, etc. With a steam meter, the test need be only long enough to get sufficient indicator diagrams for a fair average, provided the engine has been pre- viously given a settling run. Determinations of the condition of the steam supplied as to quality and pressure, and of the pressure or temperature of the exhaust, should be made and included in the statement of steam consumption per horse-power-hour. The relation between the steam consumption in pounds per 234 STEAM ENGINE TESTING 45 indicated horse-power-hour, Si, and per brake horse-power-hour, S2y is /Si = aS2 X mechanical efficiency. (b) Cylinder Condensation is often figured by subtracting the total steam used per hour, as shown by the indicator diagram, from that determined by direct measurement. The difi'erence includes not only cylinder condensation, but valve leakage in the case of engines which do not have separate valves controlling the exhaust. (c) Thermal Efficiency. There are two standards, one having a commercial, the other a scientific value. The former is the ratio of the heat equivalent of the useful work to the heat units consumed as defined under ^^ principles.^' Since there are S{H — h') heat units consumed for every horse-power-hour of useful work, and since the heat equivalent of a horse-power- hour is 2545 B.t.u., 2545 E = thermal efficiency = -^7 S{H-h f\f in which S may be based on indicated or brake horse-power. If the former, the result is the '^ cylinder efficiency ''; if the latter, it is the ^* over-all efficiency.'' H may be obtained from the pressure and quality deter- minations of the steam supplied, by use of the steam tables; h is determined similarly from readings of a pressure gage or ther- mometer in the exhaust. The scientific standard is the Clausius efficiency, which is the ratio of the heat converted into work by the actual engine to that by an ideal one working without clearance space and with non-heat-conducting cylinder walls with cut-off early enough to allow expansion clear down to the back pressure. There will then be no clearance loss and the expansion will be adiabatic. The indicator diagram representing these conditions is shown 45 STEAM ENGINE TESTING 235 by Fig. 94, and is that of the Clausius cycle although it is more frequently referred to as the Rankine cycle. The initial pres- sure and quality of the steam and the back pressure are assumed to be the same in the ideal engine as in the actual. This is a more reason- able standard for efficiency than the commercial standard since the latter charges against the engine heat that it could not use under even ideal circumstances because of the limi- tations in the operation of the work- ing medium. To figure the Clausius efficiency it is first necessary to get the heat units that are converted into useful work from 1 lb. of steam under actual conditions. This is Fig. 94. — Clausius Cycle. E{H-h'). Under the conditions of the assumed ideal engine the heat con- verted into work is the difference between the total heat H of the steam supplied and the total heat of the exha.ust Hij since there are no losses. Hi is the theoretical amount of heat left in a pound of steam after it has expanded adiabatically from the given pressure and condition as to quality to the given back pressure. It may be calculated by the use of entropy tables, but it is more convenient to get it directly from the Mollier total heat-entropy diagram which gives the heat of steam under all conditions and at various stages of adiabatic expansion. Hav- ing found Hij the Clausius efficiency is obtained from the relation Ec = E{H-h') H-Hi • Another way of figuring this efficiency is to divide the steam 236 STEAM ENGINE TESTING 45 consumption of the ideal engine, Scy in pounds per horse-power- hour, by that of the actual engine, aS. Sc^ 2545 1 S ~H-HiS' This is a useful form, since by it the cylinder or over-all efficiency may be readily obtained, depending upon the basis of S. Problem 45i. An indicator diagram shows the cut-off to be one-fifth of the stroke. The pressure at cut-off is 110 lbs. abs.; at the end of compres- sion it is 25 lbs. abs. The engine is 10 in.Xl2 in. X 100 R.p.m., single acting with 4 per cent clearance. How many pounds of steam are supphed per hour, allowing 25 per cent of that shown by the diagram for condensation? Ans., 233. Problem 45:. If the mean-effective pressure in the preceding is 25 lbs., what is the steam consumption in pounds per I. h. p. -hour? Ans.y 39.2. Problem 45.> If the steam in the supply pipe (last problem) is at 105 lbs. gage and contains 3 per cent of moisture, and if the exhaust is at 3 lbs. gage, what is the thermal efficiency? Atis.^ 6.69%. Problem 45;. What is the Clausius efficienc}' for the foregoing? Ans., 48.1%. Problem 455. Deduce from the topical form of Willan's line, the form of the curve between steam consumption in pounds per B.h.p.-hour and B.h.p. What is the value of the steam consumption when B.h.p. =0? 46. Test of a ^Multiple Expaxsiox Engine Principles. The results to be sought are in part identical to those for a simple engine; hence the principles under Tests 44 and 45 are appropriate and should be read in this connec- tion. In addition, there are other data useful to the study of multiple expansion, principally pertaining to the indicator dia- grams. The sampling of diagrams is therefore very in portant, and should be done according to Test 10 (e). Although, for brevity, a compound engine only will be con- sidered here, the methods apply equally to any multiple expan- sion. 46 STEAM ENGINE TESTING 237 (a) I.h.p., B.h.p., F.h.p., and Mechanical Efficiency may be found as for a simple engine, but in many cases the unit will be too large to brake conveniently, or a generator connection will make that procedure impossible. In the former case, the F.h.p. may be determined by run- ning the engine free and taking indicator diagrams, called under these circumstances ^' friction diagrams.'' The I.h.p. from such diagrams equals the friction horse-power. If the F.h.p. is assumed constant at all loads, this single determination of it at zero load enables the calculation of the B.h.p. at any load, since B.h.p. = I.h.p. -F.h.p. When there is a direct connected generator, the electrical load should be measured as for a steam turbine (Test 47 (a) ). If the efficiency curve of the generator is known, the B.h.p. of the engine may then be closely estimated. The I.h.p. may be obtained by figuring that for each cylinder separately, and adding them to get the total I.h.p. Or the '^ equivalent mean effective pressure '' (to be defined later) may be used in a single calculation upon one cylinder. Whenever possible, the B.h.p. should be used as the inde- pendent variable (if results from the engine alone are to be considered). (b) Steam Consumption by condenser, steam meter, or feed-water measurement. See Test 45 (a). (c) Thermal Efficiency. See Test 45 (c). (d) Equivalent and Aggregate M.e.p. The equivalei* c M.e.p. referred to any cylinder may be defined as a pressure of such value as to produce the same horse-power in the referred to as in the actual cylinder. Thus, Let Ah and Ai = net piston areas for high- and low-pressure cylinders, respectively. ► 238 STEAM ENGINE TESTING 46 Ph and Pi = the M.e.p.'s, high- and low-pressure cylinders, respectively. Then the M.e.p. of the high-pressure C3'linder, referred to the low, is and the M.e.p. of the low-pressure cylinder, referred to the high, is The combined or '^ aggregate ^' M.e.p. is one of such value that, if it prevailed in the cylinder referred to, there would be produced in that cylinder an I.h.p. equal to that actually pro- duced by all cyhnders. That is (calling the aggregate M.e.p., Referred to the H.P. cyhnder, Pm = Pn+^XPi. Referred to the L.P. cylinder, Pin = PhX-^+Pi. and similarly for three or more cylinders. (e) Steam Accounted for by Indicator Diagrams. On p. 230 is Reduced the relation that the weight of steam per hour shown by an indicator diagram equals * 60X D{W{c+C)-wc}. Now, for a single cyhnder engine, PLaN PN(DIU) I.h.p. = 33,000 33,000 * This formula is sometimes quoted with ic{c-\-k) in place of wc, c+k then standing for the volume of the steam at the beginning of the compres- sion curve 46 STEAM ENGINE TESTING 239 Dividing the one equation by the other, we have Wt. of steam per H.p.-hour = — ~ — {W{c+C) — wc)y in which P is the mean effective pressure, c and C are the clearance and cut-off volumes expressed as parts of the piston displacement, respectively; and W and w the densities of satur- ated steam at the pressures of cut-off and compression, respec- tively. This last equation is the more convenient form for the diagram water rate. The procedure then is to measure C, TF, and w on repre- sentative diagrams (c being known) from the cylinder considered. The aggregate M.e.p. referred to that cylinder (defined under (d) ) is then calculated and taken as the value of P in the water rate formula. The result is the steam accounted for by the diagram from the cylinder considered. The procedure is repeated for the other cylinders. (f) Combined Diagram. Let Dh and A = piston displacements, cu. ft., of high- and-low pressure cylinders, respectively. Vh and IV = clearance volumes, cu. ft., of high- and low-pressure cylinders, respectively. Select representative diagrams from the cylinders, as in Figs. 95 and 96, and divide them into ten or more equal spaces by vertical lines. Choose convenient scales of pressure and volume for the com- bined diagram. Fig 97, and lay them off on coordinate paper. Draw in the atmospheric pressure line. Locate the vertical line 1-2, Fig. 97, at the volume graduation corresponding to the clearance volume, Vi. Locate the vertical 3-4 at the volume graduation corresponding to Vi+Di. Make ten (or more, corresponding to Fig. 95) spaces between lines 1-2 and 3-4 with equidistant vertical lines. 240 STEAM ENGINE TESTING 46 2/ 22 > B o'lle r Pressure *. ' " LT "^TT-, 1 \ \ \ 15 16 " \ CIO <"Zero Volume ' 21 24 X--V /4.7/b. 1 1 — —^^. /2 1 \Bo'ilerPn Fig. 96.— H. P. Diagram. Tifr- >> \ i II \ \ 1 r ' ' i. \ \ 2 ^! Q 7 > l] \ \ I X i 1 i 1 V \ TS^ /4.7/d. I i , 1 "">^-TN \ \ V ■ ■ \ ;\ '< > i 1 \ 1 \| \ ,^^ " , \ \ Condenser Pressure-^ i \ \ Fig. 95.— L.P. Diagram. 1 , \\ \ A \ \ 1 ;\ \ \ 1 1 ' V \ V| \ . \ V \iA T \ \ 1 \l \ // T 1 3 \ 1 II.- 7 ' \ 1 \ » \ 2 ^: b 7\ ' \ 1 V \ N. ^ \^ \^ __U_i._i_J__. ^ 1 ^1 1 1 "r\h -^1 ' — n ' ^ T- ■ T T ■ r ■ 'i conaen:)(fr rr. •» -♦- i — — zero Pr Fig. 97. — Combined Diagrams from a Compound Engine. 46 STEAM ENGINE TESTING 241 Points 5, 6, 7, etc., on the reconstructed diagram may now be located on these verticals by scaling the pressures of the corre- sponding points of Fig. 95 from the atmospheric line. In this way the full low-pressure diagram may be reproduced on the com- bined diagram. Locate vertical 11-12, Fig. 97, to represent the clearance volume Vh] and 13-14 to represent Vn+Dn^ Draw equidistant verticals between 11-12 and 13-14, and locate points 15, 16, 17, etc., as for the low-pressure diagram. This establishes the high-pressure diagram. The combined diagram. Fig. 97, fairly represents the whole expansion of the steam on a single P-V scale. When making comparisons with assumed ideal expansion diagrams, however, it should be borne in mind that Fig. 97 does not truly represent the continuous expansion of a given weight of steam. The high- pressure expansion curve is for all of the steam in the high-pressure cylinder; but the low-pressure expansion is for a lesser quantity of steam by the amount caught in the clearance of the high- pressure cylinder. Furthermore, valve and piston leakage will affect the validity of comparisons made with the hyperbolic ex- pansion curve or the constant steam weight curves. To draw in the ideal expansion line for the given conditions (the ideal being assumed hyperbolic, or PF = a constant), the boiler pressure line should first be drawn in on both the high- pressure and combined diagrams, as indicated on Figs. 96 and 97. The compression line of the high-pressure diagram (Fig. 96) is continued on a hyperbolic curve until it intersects the boiler pressure line at point 21. The expansion curve is continued similarly, thus locating point 22. The volume corresponding to the distance between 21 and 22 is now calculated in cubic feet. This volume is assumed to be that of the steam received from the boiler per stroke, as though in an engine without clearance. Now continue line 1-2, Fig. 97, until it intercepts the boiler pressure line at 23. From 23 lay off 23-24 equal to the volume 242 STEAM ENGINE TESTING: 46 just calculated. Through 24, construct the required hyperbolic curve by one of the well-known methods, using the hne 1-2 and the condenser pressure line as zero axes. (g) The Ratio of Expansion is equal to the volume of the low- pressure cylinder, including clearance, divided by the volume of the steam in the high-pressure cy.inder, including clearance, at the point of cut-off. The last named is found as follows and is then termed the ^' commercial cut-off/' Referring to the high- pressure diagram, Fig. 96, a horizontal is drawn through the highest point on the steam admission line. The intersection of this horizontal with the prolonged expansion curve, that is point 26, is the commercial cut-off. (h) The Diagram Factor may be found by dividing the area of the combined diagram. Fig. 97, by the area of the ideal diagram, 23-24-25-4-3-1. Or it may be calculated by dividing the aggre- gate M.e.p. referred to the low-pressure cylinder by the ideal M.e.p. obtained from the following formula: Ideal M.e.p. =^(1+Iogei20-P, K in which P' = boiler pressure, lbs. per sq. in., absolute; p = condenser pressure, lbs. per. sq. in., absolute; ^, . , , ,. . . length 1-3 it = ideal ratio of expansion = , ° ^^ ^ . , ^ length 23-24 47. Economy Test of a Steam Turbine Principles. The measurements and results, in general, are the same as those for a reciprocating engine, except that there can be no indicated horse-power determination, and often no brake measurements, an electrical load being considered instead. Since it is not possible to indicate a turbine, the term ^^ internal horse-power '* is sometimes used to express the equivalent of indicated horse-power, but it is not a definite quantity. It is 47 STEAM ENGINE TESTING 243 often impracticable to apply a brake to the turbine shaft on account of the direct connection of a generator; in such a case the tur- bine and generator must be tested as a single unit. For other details, see Test 45, principles. (a) Determination of the Useful Horse-power may be made the same as for Test 44 if the turbine alone is tested with the use of a brake. Otherwise, the electrical load should be measured in kilowatts by taking either wattmeter readings or readings of amperes and volts. The horse-power equivalent to the electrical output, that is, the ^' electrical horse-power, '^ may be found from 1 Electrical horse-power (E.h.p.) =0.746 kilowatt. For alternating current generators, the code of the A.S.M.E. states that the electrical output is the kilowatts delivered to the switch- board less that required for field excitation when the field is separately excited. Under this condition, therefore, measure- ments of the field current and voltage should be made. (b) Steam Consumption. The pounds of steam consumed per hour may be measured by any of the methods described under Test 45 (a) except by indicator diagram. Dividing this by the kilowatts or horse-power gives the pounds of steam per kilowatt- or horse-power-hour. It is often desirable, for purposes of comparison, to base the steam consumption on brake horse-power or ^^ internal horse- power.'' The former quantity may be estimated, if an effi- ciency curve of the generator is available, by multiplying the steam consumption in pounds per electrical horse-power-hour at a given load by the generator efficiency at that load. The internal horse-power is difficult to estimate with any degree of accuracy. It is sometimes assumed to be the quo- tient of the brake horse-power and the mechanical efficiency of a steam engine working under the same conditions. This, of course, is a crude estimate. Using it, however, the steam con- sumption may be expressed on the basis of internal horse-power. 244 STEAM ENGINE TESTING 47 For duration of the test, see page 233. Additional Data. If there are traps arranged to catch con- densation from the turbine casing, they should be drained regu- larly and the condensate weighed in with the steam consumed. Readings should be made of the pressure in the nozzle chamber to show the drop of pressure through the governor valve. If this drop is excessive, the steam consumption will be correspond- ingly high. The predetermined conditions of pressure, quality, and back pressure or vacuum should be kept as constant as possible, and the Cjuantities carefully measured, as they have a decided influence upon the economy of a turbine. It is impor- tant that the barometer be read to get the required accuracy in the measurement of vacuum which should be expressed as an absolute pressure. This is because at low pressures the heat content of steam varies materiall}' with the pressure, and also because turbine economy is more dependent upon the predeter- mined vacuum than pressure or superheat. For the purpose of estimating the steam consumption of a turbine under a given set of conditions of steam pressure, quality and vacuum, such as are stated in the manufacturer's guarantee, the turbine being tested under somewhat different conditions, correction curves are suppHed by the manufacturer. These show the number of pounds of steam per horse-power- or kilo- watt-hour to be subtracted from the test result if the stated pressure is higher than the actual, the number to be subtracted if the stated superheat is higher, and the number to be subtracted if the stated back pressure is lower, or vice versa. Willan's line should be plotted during all trials under vari- able output. (c) The Thermal EflBciencies are obtained exactly as for Test 45 (c), the basis for the computation of useful work being the electrical, brake, or internal horse-power. (d) Separation of Losses. The losses of a turbine ma}- be considered in two groups. First, approximately constant losses 47 STEAM ENGINE TESTING 245 which include those due to friction and radiation Frictional resistance is encountered at the bearings and stuffing boxes, and between the discs and blades and the steam, and through wind- age of the external parts. Second, steam losses including leakage through clearance spaces, condensation, and faulty action of the blades and nozzles in not completely absorbing the energy of the steam. These losses may not be separately measured without an involved test. Professor Carpenter has indicated a method of separating the two groups by the use of Willan's line. When plotted against brake horse-powers, this line intercepts the axis of steam consumption at a point w^hich shows the steam con- sumed per hour to overcome the first group of losses, that is, at no load. The distance parallel to the load axis, measured in horse-power, necessary to move Willan's line so that it shall pass through the origin, equals the power given to the first group of losses. At any other load, this quantity is to be subtracted from the power that would be developed by the actual amount of steam consumed if operating on the Clausius cycle; the result is the actual brake horse-power plus the second group of losses, from which the second group may be readily obtained. Problem 47i. A turbine, tested at full load, consumes 3150 lbs. of steam in 90 minutes. The current delivered is 340 amperes and 220 volts. The generator efficiency at full load is 95 per cent and the friction losses of the turbine are 5 per cent of the power deUvered to the generator. What is the steam consumption in pounds per kilowatt-hour, per E.h.p.-hour, per B.h.p.- hour, and per internal horse-power-hour? Arts., 28.1 per Kw.-hr. Problem 472. For the test of Problem 47i, average values as follows were obtained. Steam pressure, 150 lbs. gage; superheat, 80° F.; vacuum, 20 inches mercury; barometer, 28.5 inches. What would have been the steam consumption if the following conditions held? Steam pressure, 180 lbs., abs.; superheat, 100° F.; vacuum, 28 ins.; barometer, 30 ins. Correc- tions are 0.05 lb. per kilowatt-hour for each pound difference in the steam pressure, 0.02 lb. for each degree of superheat, and 1.0 lb. for each inch of vacuum. Arts., 20.5 lbs. per Kw.-hr. Problem 473. What is the efficiency (British standard) for the results of Problem 47i? How much efficiency should be added or subtracted for each unit of steam pressure, back pressure, and superheat. (See Problem 472.) 246 STEAM ENGINE TESTING 48 48. Economy Test of a Steam Power Plant Principles. A complete test consists of measurements of the amounts of heat distributed and lost in the entire system, beginning with the energy of the fuel and ending with the energy delivered at the shaft or switchboard. For the present we shall consider only that part of the plant beyond the boiler, the subject of boiler trials being separately treated under Test 54. The most important result from power plant tests is the fuel consumption in pounds of fuel per horse-power- or kilowatt- hour. Other results are the steam and heat consumption of the engine and the auxiliaries, and the heat balance. The latter is an equation between the total heat available and the various amounts accounted for in its distribution. They may be found in heat units per hour and expressed as per cents of the total heat per hour added to the feed water entering the boiler. If tliese percentages are separately multiplied by the boiler efficiency, the items of the heat balance will then be percentages of the heat available in tie fuel. This follows from the fact that boiler efficiency is that part of the fuel energy which is added to the feed water and distributed as steam. The boiler trial, which is part of the complete test and con- ducted at the same time, gives the efficiency of the boiler and its losses, all based on the heat value of the fuel. A complete heat balance is thereby obtainable. The usual condensing power plant contains as auxiliaries a condenser, circulating pump, air pump, and feed water pump. There may also be a cooling tower and its auxiliaries, and a feed water heater using the exhaust steam from the auxiliaries, and such minor apparatus as separators, traps, etc., wliich may or may not be arranged to drain back to the boiler. The rearrangement of the apparatus and piping for the pur- pose of testing should interfere as little as possible with normal operating conditions, and any departures from them that may 48 STEAM ENGINE TESTING 247 effect the results, such as different feed water temperatures, should be allowed for by making a separate test to measure the actual working quantities that have been altered. " , Equipments of different power plants are too varied for very specific directions for the measurements of the various quan- tities. Any of the methods given under Test 45 (a) for the measurement of steam weights should be applied according to the exigencies of the particular test. Any one item of the heat balance may be omitted from the direct measurements, since one item may always be figured by subtraction. The basis of all heat measurements is the heat contained by the feed water just before it enters the boiler or economizer if there is one. Duration. If a boiler trial is included, its duration deter- mines the length of the test; if the engine and auxiliaries only are to be tested, the duration should be the same as for a test of the engine alone. See Tests 45 and 54, principles. (a) Steam and Heat Consumption of Engine and Auxiliaries per Horse-power- or Kilowatt-hour. Let w stand for weight of steam per hour; H, for its total heat per pound above 32 degrees depending upon its pressure and quality; and let h be the number of heat units per pound of the feed water above 32 degrees. Let the subscripts e, c, a, /, and b refer to the engine, circulating pump, air pump, feed pump, and boiler respectively. Then the steam consumption is (we+Wc+Wa+W/) -T-horse-power or kilowatts output. To get the heat consumption, the various values of H should be used for strict accuracy, as determined by the pressure and quality of the steam just before it is delivered to each unit, but in most cases the following form is practically correct. Heat consumed per hour = We{He — h) + {wc+Wa+Wf)(Hb — h) . Dividing this by the horse-power or kilowatts gives the required quantity. 248 STEAM ENGINE TESTING 48 The heat consumed per hour by the engine and auxiharies may also be determined by subtracting the heat lost to leakage and drips from the total heat added to the feed water (see (6) and (c) following). The values of H should be obtained from the steam tables by reference to the measurements of pressure, temperature, and quality of the steam at the point considered. For Hb this should be immediately beyond the main stop valve of the boiler; for Hej it should be just behind the main stop valve of the engine, between it and the separator if one is used, h is obtained from the temperature of the feed water just before it enters the boiler. If an injector is used, the temperature should be taken before entering the injector, since the heat added by that instrument comes from the boiler and returns to it. The heat consumed by the feed pump in this case should be figured separately and is very nearly equal to the heat equivalent of the work done in pumping. (See Test 52.) (b) Heat Added per Hour to the Feed Water. If there is only one source of supply yielding W lbs. per hour, then the heat added is W{Hi,-li), If in addition to this there is another supply such as would be obtained from traps, separators, etc., draining back to the boiler in an independent pipe carrying Wo lbs. per hour, then the heat added is Wi{Ih-li{) + W2{Hr,-h2), the subscripts 1 and 2 referring to the main and auxiliary supplies, respectively. The quantities Ih and h are measured as under («). The weight of the main supply is generally measured by a weighing system as for boiler trials (see Test 54 (6)). Auxiliary supplies 48 STEAM ENGINE TESTING 249 of feed may be metered or directly weighed during a special test made for that purpose. (c) Heat Lost to Leakage and Drains. Leakage may occur from the steam space of the boiler or from the steam pipes either to the air or to pipe branches, and it m.ay occur below the w^ater level in the boiler. Leakage wdnch cannot be prevented should be measured by a preliminary test similar to that described on page 231 for leakage correction. It is assumed that the rate of leakage thus determined remains the same through the test of the plant. Calling it wi pounds per hour, the heat lost is Wi{Hb — h) If the separators, traps, etc., do not drain back to the boiler, they may be kept closed during the test and drained at regular intervals into buckets of cold water whereby they are w^eighed. If Wd is the number of pounds of w^ater wlthdraw^n per hour, the loss is iVd{Hb — h) If this water is returned as an auxiliary supply, /i2 should be substituted for h in the above. (d) Heat Balance. All the items, having been measured as above in heat units per hour, may now be expressed as percentages of the heat added to the feed w^ater. Then the heat balance is 100% = % of heat consumed by engine + % of heat consum.ed by auxiliaries (stated sepa- rately or collectively) +% of heat lost to leakage and drains. The first item on the right-hand side may be subdivided into the per cent of heat equivalent to the useful work and the per cents representing the various engine losses. It should be noted that this method of analyzing the heat 250 STEAM PUMP TESTING 49 distribution charges against the engine and auxiUaries the losses of radiation between the condenser and the boiler. Also, if a feed water heater is used, the heat consumed by the engine figures less, although the actual performance of the engine is exactly the same as if no heater were used, because the value of hj the heat of the feed water, is higher. The only way in which the effect of the heater appears numerically is in the heat added to the feed water, but no idea of the saving due to the heater may be formed. Problem 48i. A condensing plant is arranged so that the exhaust from the auxiliaries preheats the feed water after it leaves the condenser, in a closed heater. Tell how the phmt could be tested so as to show the loss due to drop in the heat of the liquid between the engine exhaust and the heater entrance, and the gain due to the feed water heater. 49. Valve Setting of a Duplex (Steam) Pump Principles. The duplex pump consists of two reciprocating steam pumps operating side by side and arranged so that the piston rod motion of one operates the steam valve of the other. Each pump consists of a water cylinder whose piston is directly driven by the piston rod of the steam cylinder. The steam valves distribute the steam so that one pump is on its forward stroke when the other is on its return. The valves have neither laps nor lead, so that cut-off occurs simultane- ously with release. The valve stem of each pump is driven by a rocker deriving its motion from the piston rod of the other pump (see Fig. 98). As each Fig. 98.— Duplex Pump Valve-Motion, rocker moves through the whole piston rod stroke and as it is desirable that the valves throw only at the end of the stroke, a certain amount of lost motion is provided between the valve 49 STEAM PUMP TESTING 251 stem and the valve. This is shown by the distance c in the figure. The valve stem passes freely through a hole in a lug on the valve, and gives motion to the valve only when the nuts n and n come into contact with the lug. By adjusting the lost motion, the valve may have more or less throw. There are two steam and two exhaust ports for each steam cylinder, SS and EE, This is arranged as a safeguard against the piston hitting the cylinder head. If the valve should not close the exhaust port before the end of the exhaust stroke, the piston itself will close it, thus entraining steam in the clearance space which acts as a cushion. (a) Adjustment of Lost Motion of Valve. This is accom- plished by setting the valves in their mid-positions when the pistons are in their mid-positions. The pistons should be set by reference to prick marks on the piston rods. The limiting positions of stroke should be meas- ured by prying each piston rod with a bar to the extreme of its travel, pressure behind the pistons being released by opening drains or otherwise. When the piston rods are set midway between these positions, the rockers should be vertical. With the steam chest cover removed, the valves are now placed so that they completely cover the ports. The nuts n, n, Fig. 98, are then adjusted so that there is an equal amount of clearance between each one and the valve lug. With some designs, there is only one nut to be adjusted on each stem, this nut then being between two lugs. In such a case the clearances may not be changed in amount, but only equalized. In other designs there is a ^^ lost motion link '' outside of the valve chest by which the clearances may be adjusted without opening the chest. The proper amount of clearance depends upon the size and design of the pump and may be determined by trial. If the steam ports are to be opened full each stroke, then the total lost motion should be equal to the throw of the valve stem corresponding to 252 STEAM PUMP TESTING 50 normal piston stroke less twice the steam port length parallel to the stroke. (b) Readjustment after Trial. If, after the valves are set, the pump runs ^' lame,'^ that is, the strokes are unequal in length or time, it may be because the resistances of the water cylinders are different. They should then be examined for leaky water valves, tight stuffing boxes, etc. Such faults being corrected, if the pump still runs lame, the lost motion of the valves must be readjusted until the desired equality of strokes is obtained. It need only be remembered that to diminish the lost motion makes the valve throw greater, thus providing better access to the steam and release to the exhaust. Problem 49i. Explain why the ordinary duplex pump cannot use steam expansively. Problem 492. If the stroke of one piston rod of a duplex pump were curtailed at the head end, being normal in other particulars, what should be done to the valve motion to remedy it? 50. Mechanical Efficiency Test of a Reciprocating Steam Pump Principles. The mechanical efficiency of a steam pump equals the useful or water horse-power, W.h.p., divided by the indicated horse-power of the steam cylinders. If D is the total head in feet pumped against, including suction and dis- charge, and W is the number of pounds of water delivered per minute, then, ^^•^•^^• = 33;000^ If there were no leakage of water in the pump from one side of the piston to the other or through the valves, then the work done per minute would be equal to the product of the total pressure pumped against in pounds per square foot and the volume 50 STEAM PUMP TESTING 253 displaced by the piston in cubic feet per minute. If p stands for the pressure in the discharge pipe; p\ for tlie vacuum in the suction pipe, both in pounds per square inch ; and if L and A are the same as in the formula for indicated horse-power, and N is the number of working strokes per minute, then lU(p+v^)LAN '^ ^^' 33,000X144 • On account of leakage this formula is not a reliable one with which to determine the water horse-power. It may be used only by assuming a value for the leakage, and this may be very inexact. Leakage of water in a pump, of the kind referred to, is called ^^ slip.'' It is generally expressed numerically as a percentage of the piston displacement. (a) Steam End Indicated Horse-power at Various Water Horse-powers. The indicated horse-power is found exactly as for a steam engine (see Test 44 (a)), except in regard to measure- ment of the stroke length, L. With direct acting reciprocating pumps, there is no constant limit to the stroke length and in ordinary operation it may vary materially. An average value should therefore be obtained from a number of measurements throughout the test. There is on the market a continuous recording device for this purpose, but if one is not available, the average stroke may be obtained from the average lengths of the indicator diagrams, the ratio of reduction being known. Another method is to set a scale against a mark on some projecting part of the piston rod, and to note the travel of this mark at regular time intervals. The w^ater horse-power may be varied either by changing the speed of the pump or the discharge pressure. With reciprocat- ing steam pumps, the pressure is usually approximately constant, and the water load varies with the quantity of water demanded. Either the pressure or the speed may be the independent variable during test, according to the operating conditions of the pump. 254 STEAM PUMP TESTING 50 The pressure may be varied during the test for different runs, by opening the stop valve in the discharge pipe more or less. The quantity of water delivered per minute may be measured by any of the methods of determining water rates. For large pumps, weirs may be used. The head against which the water is discharged may be measured with a pressure gage set in the discharge pipe.* The suction head generally may be measured in feet, and taken as the difference in level between that of the water supplied and the center of the pressure gage used for micasuring discharge pressure. Since 1 lb. per square inch = 2.3 feet head, the total head is in which Z)' is the suction head in feet. Readings of p and D' should be taken at regular intervals during each run. These quantities determine the water horse-power according to the formula previously given. The water horse-power may be estimated, according to the second formula, if the discharge pressure and the number of strokes per minute are measured, and if a value for the percentage of slip is assumed (see (rf)). Neither of the formulas for water horse-power takes into account the kinetic energy of the water delivered. Generally the velocities of the water are low enough to make this a negligible quantity. If it is desired to calculate the horse-power due to kinetic energy, the velocity should first be figured from the cubic feet discharge per unit of time and the cross-section of the pipe. The result is then obtained ])y, W.h.p. available from kinetic energy = -^ ^33,000 in which W has the same value as before, v is the velocity in feet per second, and r/ = 32.2, nearly. * See also Test 70 (c). 60 STEAM PUMP TESTING 255 (b) Mechanical and Fluid Losses. The loss due to mechanical friction of the pump parts may be obtained b}^ indicating both the water and steam ends of the pump. The indicated horse- power of the water end is obtained in exactly the same way as ' for the steam cyhnder, the same values being used for the num- ber of strokes per minute and the average length of stroke. Then the steam end I.h.p. minus the water end I.h.p. equals the mechanical friction horse-power. The fluid losses are due to leakage, or slip, fluid friction of the water against its passage in the por!:s, eddies, etc. Slip causes loss of power through water being pumped against pres- sure from one part of the pump to another without being dis- charged into the delivery main. These losses are included in the power shown by the indicator diagram for the water end. Consequently the horse-power lost equals the I.h.p. of the water end minus the W.h.p. as calculated under (a). (c) The Gross Efficiency for each value of W.h.p. is obtained by dividing the W.h.p. by the corresponding I.h.p. of the steam end. It is sufficient, for each run, to use average values of heads, water rates, mean effective pressures, and stroke lengths and speeds with which to calculate a single value of efficiency. The indicated horse-power of the water cylinders is some- times measured. This divided by the I.h.p. of the steam cylinders is the efficiency covering mechanical losses only. (d) Slip. The piston displacement in cubic feet is "T7T" per minute. The water actually displaced, in the same units, is Tr/62.5 at ordinary temperatures. The percentage of slip is therefore, LAN W_ 144 62.5^^^^^ ^__ ^^Q^^ LAN 144 \ LAN) w -^■' 256 STEAM PUMP TESTING 50 The quantities involved have been obtained for the other determinations. (e) The Capacity of pirnips is generally expressed in gallons per twenty-four hours. Knowing the weight of water, or cubic feet, discharged per minute, the capacity is readily calculated, for which purpose the following closely approximate relations may be used. 1 gal. weighs 8.33 lbs. i cu.ft. contains 7.5 gal. Problem 50i. The follo^^-ing data are obtained from the test of a duplex pump. Discharge pressure, gage, 35 lbs.; suction lift, 4.5 ft.; water dis- charged per minute, 110 lbs.; length of stroke, 5 ins.; number of strokes per minute, both cylinders, 250; size of water cylinders, 2 ins.Xo ins. What is the W.h.p., the percentage of slip, and the capacity of the pump? An^., 0.283 H.p.; 22.6%. Problem SOo. In the preceding problem, if the internal diameter of the discharge pipe is 1.38 ins., what is the horse-power due to velocit}'? Problem 5O3. If the pressure in the discharge pipe is 12 lbs., and if the water supply is 6 feet above the gage indicating the discharge pressure, what is the total head? Am., 21.6 ft. Problem 50> Run a series of tests on a steam pump to show the rela- tion between slip and discharge pressure, and slip and speed. 51. Economy Test of a Stea:ii Pump Principles. These, in general, are the same as given for the economy test of a steam engine, Test 45, the only difference being that the useful work is measured in terms of water horse- power as defined under Test 50. In addition to the measurements listed under Test 45, another one is usually required, namely, of '^ duty/' Duty is the number of foot-pounds of useful work performed by a pump per miUion B.t.u. consumed by the engine. (a) Steam and Heat Consumption. The pounds of steam consumed per hour may be found by any of the methods under Test 45 (a). The water horse-power is determined as under 51 STEAM PUMP TESTING 257 Test 50 (a). From these two quantities the pounds of steam per W.h.p.-hour may be calculated. The heat consumed per pound of steam is H — h\ using the same notation and reasoning as given under Test 45, principles.' Pressure readings of the supply and exhaust steam, and quality determinations of the supply steam are required for these heat quantities. (b) Thermal Efficiency. This is the same as for Test 45 (c) except that the British standard only need be used in most cases. (c) Duty. The thermal efficiency (British standard), when expressed as a fraction, is the heat equivalent of the useful work done per B.t.u. consumed. The number of foot-pounds of usefui work done by each B.t.u. consumed is therefore 778 times the efficiency, 778 being the mechanical equivalent of heat. Since the duty is the number of foot-pounds per milhon B.t.u. consumed, Duty = 778,000,000 X Efficiency. It should be noted that the efficiency is here expressed not as a per cent, but as a fraction of the heat consumed. Problem 51i. The steam used for the test cited in Problem 50i was 88 lbs. per hour, and was at 85 lbs. gage pressure, quality 97 per cent. The pump exhaust steam was at 10 lbs. gage. What were the steam consump- tion in pounds per horse-power-hour, the heat consumption in B.t.u. per horse-power-hour, the thermal efficiency, and the duty? Ans,, Eff.=0.86%. Problem 5I2. A pump discharges 4750 lbs. of water against a total head of 100 ft., in a certain time. During the same time it is supplied with 100 lbs. of steam and from each pound it consumes 1000 B.t.u. What is the duty of the pump? Ans., 4,750,000. 52. Economy Test of an Injector Principles. The injector is a pump in which the heat energy of steam is directly used. Works on steam engines and steam 258 STEAM PUMP TESTING 52 Octaes^ .> Boifer or CotfoH' ^ }\Pre66ure Injector- Feed Wafer Tank--'' Fig. 99.— Injector Test. boilers describe the instrument in detail. The results from an injector test are the same as those from a steam pump test. In addition, the number of pounds of water pumped per pound of steam sup- plied is usually quoted. The methods of testing are somewhat different, inas- much as a direct measurement of the weight of steam per hour is not neces- sary, this quantity being obtained from the heat balance. Fig. 99 shows diagrammatically the arrangement of an injector for test. ' An expression for the weight of steam used per minute is deduced by equating the heat energy of the steam entering the injector, plus the mechanical and heat energy of the water entering, to the heat and mechanical energy of the water discharged. The datum of the heat measure- ments is at 32° F., and of the energy measurements is the level of the injector. Let W^ = weights, in pounds per minute; /i = heat of the liquid; L = heat of vaporization of the steam supplied; a: = quahty of the steam supplied, if wet; p = pressure of discharge, pounds per square inch; Z)',D'' = suction head, and distance between injector and gage, feet, respectively; / = temperatures, degrees F. Subscripts /, .s. d refer to feed water, steam, and discharge, respectively. Then, expressing all energies in heat units, and neglecting kinetic energy WA WfD' 778 ^Ws{hs+xL) = WJia+ Wa{2.Sp+D") 778 Radiation. 52 STEAM PUMP TESTING 259 Also, W^ boiler. The calculations from the test of an anthracite suction pro- ducer plant will first be given and then the modifications neces- sary for other types. Tables 1 and 2, pages 305 and 306, give the required test data together with the notation used in the formulas. The data are part of the full observations of a test reported in the Journal of the A.S.M.E., December, 1909, for which the ultimate as well as the proximate coal analysis and calorimetric determinations of fuel and gas were made, and the gas metered. The reader may thus compare the results by the approximate methods to be presented with the more exact results of the report.* All the items of the heat balance will l)e figured on the basis of 1 lb. of drv coal. The calorific value of the drv coal will thus * Note that these results are given for the standard gas condition of 62° F. and 30 ins. of mercury, whereas the standard here used is for 32° F. and 29.92 ins. The volume per pound of the latter is 0.943 times that of the former. Also the specific heats of the gases are different, the values here quoted being by later authorities. 62 GAS PRODUCER TESTING 305 Table 1 GIVING DATA FROM A SUCTION GAS PRODUCER TEST AND NOTATION USED IN FORMULAS Total weight of coal charged, pounds = 798 Total weight of ash and refuse, pounds = 85 Total weight of water used in vaporizer =268 Proximate Analysis of the Coal. Per Cents by Weight of the Coal AS Fired Moisture =2.75 Volatile matter = 6 . 00 Fixed carbon = 78 . 45 Ash =12.8 m, vm, /c = weights of moisture, volatile matter, and fixed carbon per pound of dry coal, respectively. Weight of carbon in 1 lb. of dry refuse, pounds= 0.388 Tj; = temperature of gas leaving producer, degrees F. = 1108 <= temperature of fire room, degrees F. =82 Ci = total weight of carbon in 1 lb. of dry coal, pounds. Ca= weight of carbon wasted in ash, per pound dry coal, pounds. Cf^ = weight of carbon gasified per pound dry coal, pounds, c, p = sums of columns 3 and 5, Table 2, respectively. F = volume of dry gas generated per pound of dry coal, standard cubic feet. 1^2?= weight of the producer gas per pound of dry coal, pounds. TTa = weight of the air furnished per pound of dry coal, pounds. 1^5 = weight of steam furnished per pound of dry coal, from the vaporizer, pounds. !:;« = weight of steam not dissociated per pound of dry coal, pounds. be the heat supplied; the sensible heat carried in by air, water, etc., being neglected. The principles upon which most of the calculations depend are given under Test 40 (6), coal combustion, and should be thoroughly understood. (a) Quantities to be Found Prior to Calculation of the Results. The proximate analysis of the coal should be based upon its dry weight. This calculation is the same as for Test 54 (c), as is that for Ctj the total carbon per pound of dry coal; since the same 306 GAS PRODUCER TESTING 62 Table 2 ANALYSIS OF GAS GENERATED DURING TEST, AND COMPUTA- TION OF QUANTITIES USED IN FIGURING RESULTS (1) Constit- uents of Gas. CO H2 CH4 C2H4 O2 CO2 Na (2) Percentage by Volume. 27.0 10.4 1.8 0.0 0.2 4.2 56.4 (3) Subscrint of CX(2) c = 33.0 (4) Molecular Wt. of (1). 27.0 28 2 1.8 16 28 32 4.2 44 .... 28 (5) (2)X(4) 756 20.8 28.8 6.4 184.8 1579.2 p = 2576.0 (0) Higher Hoat Value of (1). 342 348 1065 1680 (7) (6)X(2) 100 92.4 36.2 19.2 147.8 = higher heat value of gas fuel analysis has been assumed. The methods of finding Ca and Cg are also the same as given under Test 54 (c). For the data given by Table 1, Total weight of dry coal consumed = 798 -0.0275X798 = 776 lbs. and ^^^85X0^^Q^Q^2 lb. 776 The carbon gasified is Cg = Ct-Ca = 0.81G - 0.042 = 0.774 lb. per pound of dry coal. The volume of dry gas generated per pound of dry coal, under standard conditions of pressure and temperature, may be found from a formula derived similarly to that for Vdj page 198. For producer work D+M becomes c since carbon may 62 GAS PRODUCER TESTING .307 exist in other gases than CO2 and CO. c is found as shown in column 3 of Table 2. Then For the given data, 2980 C, ^, 2980X0.774 .^ n f+ ^u a 1 V= ^^ = 69.9 cu. ft. per lb. dry coal. The weight of dry gas per pound of dry coal may be obtained from its volum.e if the weight of a cubic foot of the gas is known. For the latter quantity, the method of finding the density of a gas described on page 197 may be used. The weight of a molecule- foot of the producer gas is p-^ 100, p being determined as in column 5, Table 2. The weight of a molecule-foot of hydrogen is 2, and its density under standard conditions is approximately 0.0056. Consequently, Density of dry producer gas = 0.0056 X^^^^ = 0.000028p. For the given data, Density of producer gas - 0.000028 X 2576 = 0.0721 lb. per cubic foot, from which the weight of the dry producer gas per pound of dry coal is TF^ = 0.0721X69.9 = 5.04 lbs. The volume of gas may also be obtained by metering it through the whole test, but the method outlined above will generally be found sufficiently accurate if reasonable care is taken in the sampling and analysis of the gas. The weight of air supplied to the producer per pound of dry coal may be found from an expression similar to that for Wa for 308 GAS PRODUCER TESTING 62 coal combustion, page 199; the quantitj^ D+M being replaced by c. The formula then is, 3MxN2XCg vY a J N2 being the per cent by volume of nitrogen in the gas as given in column 2, Table 2. For the given data, ^, 3.04X56.4X0.774 . ^. ., Wa = 23 "" ^-^^ ^^• The weight of steam supplied by the vaporizer per pound of dry coal is found by dividing the total weight of water to the vaporizer by total weight of dry coal. For the given data, TF. = ^ = 0.345 lb. Coming now to the heat balance, the first item is (b) Useful Heat in the Cool Gas. This is exclusive of sensible heat if the gas is to be used for power, and is due to its calorific value when completely burned. The higher heat value will be used. Since all items of the heat balance are based on 1 lb. of coal, the useful heat may be found by multiplj^ing the volume of gas per pound of coal, V, by the higher heat value in B.t.u. per standard cubic foot. The heat value may be figured as in column 7 of Table 2. This gives the heat values of the gas con- stituents, according to their amounts in one cubic foot, the sum of which is the required heat value. For the given data, Useful heat = 69.9X148 = 10,300 B.t.u. The heat value of the dry coal was found to be 13,040 B.t.u., so the useful heat is 10,300^13,040 = 79.0 per cent. This is the ^^ cold gas " efficiency of the producer. 62 GAS PRODUCER TESTING 309 uoo . r — r— " J T I / «5 / X / o0,30 /^ ^^ ^ ^ r^ ci ^ y ^ ^ n?c; _^ 30 (c) Sensible Heat in the Dry Gas Leaving the Producer is equal to TTpX specific heatX(T2,-0. The weight of the dry gas, Wv, has been previously figured. The specific heat of producer gas, varies greatly with the hydrogen content. Except for hydrogen the average specific heat of all the gases, exclusive of steam, may be taken as 0.26 for a temperature of 1100'' or 1200° F. The specific heat of hydrogen for these temperatures is about 3.72, so that even though its per cent by weight is always small the effect of hydrogen upon the average specific heat of pro- ducer gas is very marked and varies with the amount of hydrogen present. The curve, Fig. 104, gives the average specific heat of normal producer gas with various percentages of hydrogen. For the given data (^2 = 10.4 per cent) it is seen to be 0.288. The temperature of the gas should be taken near the outlet at the producer with a suitable pyrometer. For the given data. Sensible heat = 5.04 X 0.288 X (1108 -82) = 1490 B.t.u. or 1490^13,040 = 11.4 per cent. (d) Heat Lost by Excess of Steam to the Producer. This is estimated from the weight of steam found in the gas per pound of dry coal, and equals ID 20 Per Cent Hg Fig. 104.— Specific Heat of Producer Gas. u'sX total heat per pound of the steam above feed temperature. 310 GAS PRODUCER TESTING 62 The total heat of the steam may be taken with sufficient accuracy for this calculation as 1000+0.5 XTp. For a more exact value, the expression quoted on page 143 may be used. To find Ws several methods may be used. It may be meas- ured directly by drawing a sample of the producer gas through a tube of calcium chloride, the increase of weight of w^hich gives the moisture absorbed. The gas is syphoned into a container of known size so that its volume, and hence its weight, may be obtained. iCs may also be figured from the hydrogen content of the coal and the gas. An easier method is based upon the fact that the sum of the weights of the gasified carbon, air, and water vapor fed into the producer must equal the weight of the producer gas including moisture. Hence, Co+Wa+Ws+m+YSipor brought in with tiir — Wp = Ws* The air vapor may be neglected here, although it may be a large percentage of the total steam, since its latent heat is not added by the coal. Then, for the given data, ^., = 0.774+4.02+0.345+0.0283-5.04 = 0.137 lb., from which the heat lost to steam is 0.137X(1000+0.5Xll08)=213B.t.u. or 21 3 -^ 13,040 = 1.6 per cent. (e) Heat Transferred to Scrubber Water. Items (c) and (d) together equal the heat given to the scrubber plus the heat radiated between the scrubber and producer outlets. For purposes of comparison, or to get an estimate of the amount of ^55^^ 62 GAS PRODUCER TESTING 311 sensible and latent heat in the gas without measuring it as just described, the heat added to the scrubber water may be deter- mined. The water may be measured by a meter, and its tem- perature as for the jacket water of a gas engine. In the test quoted the total weight of scrubber water was 22,200 lbs. and its temperature rise was 45.8° F. Hence, the heat given to the scnibb9r per pound of dry coal is, ^-^^X45.8 = 1310B.tu. (f) The Heat Lost to Carbon in the Ash. Taking the heat value of carbon as 14^600 B.t.u., this loss, per pound of dry coal is 14,600 XCa. For the given data, 14,600X0.042 = 613 B.t.u. or 613 -T- 13,040 = 4.7 per cent. (g) Radiation from the Producer and other Losses. These may be grouped in one item by subtracting the previously calculated heat balance quantities from the heat supplied, or some of them may be separately determined. The loss by leakage of air in the case of a suction producer plant may be found by comparing the useful heat, as herein calculated, before and after the dilution. In a pressure producer plant, any leakage is apt to be detected; the only way to measure it is by metering the gas since leakage does not alter its composition. The loss due to tar and soot may be found by a special analysis of the gas as it leaves the producer. Grouping these losses for the given data, we have Radiation, etc. = 100- (79.0+11.4+1.6+4.7) =3.3 per cent. 312 GAS PRODUCER TESTING 62 (h) Other Efficiencies and Results. The "hot gas" efficiency is often expressed when the gas is used for heating. In this case the sensible heat is also '^ useful.'' If, then, the first three items of the heat balance in per cent are added, the result will be the hot gas efficiency. For the given data, this is 79.0+11.4+1.6 = 92.0 per cent. The " efficiency based on combustible," corresponding to the boiler efficiency so known, is the efficiency that would be obtained if there were no loss of fuel in the ash, and equals Eff . based on coal ^ ( 1 yt ) > \ vm+jcj the quantity in the parenthesis being the efficiency of the grate, or cleaning. For the given data, this efficiency equals for the cold gas. For purposes of comparison of tests with different kinds of fuel, it is useful to obtain the volume of gas per pound of com- bustible. This equals V -r- {vm +/c) . In capacity tests, the output may be measured in cubic feet per hour by multiplying F, as herein calculated, by the weight of dry coal used per hour. For pressure producers it is necessary to account for the coal used in the auxiliary boiler to make steam. This may be included in the total coal charged against the producer, and another item added to the heat balance to account for the heat lost in the steam making process. Or we may subtract from the volume of gas generated an amount equivalent to the steam supplied, which does not seem to be so logical a process. 63 TESTING REFRIGERATION MACHINERY 313 For bituminous producers, if much carbon disappears as tar, it is necessary either to meter the gas to get F, or to determine the amount of carbon going to tar from 1 lb. of dry coal, by analysis of a sample extracted from a measured volume of gas. From this result a more correct value of the carbon gasified is obtainable. The heat balance may be extended to cover the distribu- tion of heat in a gas engine supplied by the producer, by the methods indicated under Test 57 covering this subject. In this case the gas need not be metered, since the fuel quantities are measured as coal, and the heat quantities should be based upon 1 lb. of dry coal instead of 1 cu. ft. of gas. The exhaust losses as calculated under Test 57 may be readily changed to the coal basis by multiplying them by V as herein obtained. Problem 62i. Using the data of the test example, what is the percentage of heat radiated from the scrubber and immediate piping? Problem 62.2. Assuming that the engine of the example under Test 60 was operated with gas from the producer of the example of Test 62 with the same engine heat balance items, calculate these items in per cents of the heat value of the dry coal. 63. Test of a Refrigeration Plant * (Ammonia Compression System) Principles. The student, it is assumed, is informed upon the mechanical and thermal features of the ammonia refrigerating machine, descriptions of which are available in numerous treatises. Following are given definitions of the quantities usually sought in tests of refrigerating machinery. Refrigerating Effect is the amoimt of heat abstracted by the ammonia from the cooling medium, as brine, expressed in B.t.u. per unit of time (minute, hour or twenty-four-hour day). This includes the waste cooling effect due to heat transferred from * This and the two following tests are enlarged from a series by the author, in Powevy Sept. 19, Oct. 10, 1916, and April 10, 1917. 314 TESTINXt refrigeration machinery 63 bodies it is not desired to cool — a waste necessarily ensuing from imperfect insulation, manipulation, etc. The Unit of Refrigeration is a refrigerating efifect of 288,000 B.t.u. per twenty-four hours, or 200 B.t.u. per minute. To obtain this effect by ice at 32° F., it would be necessarj^ to melt 1 ton (2000 lbs.) of it in twenty-four hours, the latent heat of ice being 144 B.t.u. Units of refrigeration are therefore spoken of as tons more conmionly than as B.t.u. The Capacity of a plant equals the number of units of refriger- ation it delivers: That is, the number of tons of 32° ice it would be necessar}' to melt per twent3'-four-hour day to produce a refriger- ating effect equivalent to that of the ammonia. Hence, this quantity is often referred to as '* ice-melting capacity.'' Ice-making Capacity is sometimes considered in the case of plants devoted exclusively to the manufacture of ice. Expressed in tons per twenty-four hom's, this is equal to between one-half and eight-tenths of the ice-melting capacity" pre\'iously defined, the diminution l^eing due to the losses in the process of heat abstraction b\^ the brine, manipulations of cans, and to the fact that the water must first be cooled to 32° and after freezing, be chilled below that point. Rating m terms of ice-making capacity is therefore onl}' definite when the temperatures of water and finished ice are stated. The Coefficient of Performance is a more correct term for what is sometimes miscalled the efficiency of a refrigerating sj'stem. This quantity is the ratio of the refrigerating effect in B.t.u. per unit of time to the heat equivalent to the indicated work done by the compressor in the same time; that is, it is the useful effect divided by the power put in, and in this respect is superficiall}- an efficiency. The term efficienc}' generally has reference to the relation of an energ}', after passing through a conversion, to its value at the source. In the case of refrigerating machiner>^ the compressor energ}' is not the source of the useful effect. In reality, it is the condensing water that does the coohng, the com- 63 TESTING REFRIGERATION MACHINERY 315 pressor being merely an auxiliary in the process. As the work done upon the ammonia is the paid-for item and as the re- frigerating effect is the thing desired, it is useful to know the ratio of the two. The Ideal Coefficient of Performance is the maximum that could be obtained under a given set of operating conditions if there were no losses. It is fixed by the operating temperatures of condenser and refrigerator and is equal to 460+ Tr ' Tc-Tr' in which the numerator is the absolute temperature of the refrig- erator, Tt is its temperature in degrees Fahrenheit, and Tc is the temperature of the condenser in the same units. It should be noticed that neither refrigerator nor condenser is ever at one uniform temperature in operation. To maintain the heat flow, the brine must always be a little warmer than the ammonia it boils, and the circulating water always a little cooler than the vapor it condenses. But, assuming ideal apparatus, the ammonia vapor could be worked in the refrigerator up to the temperature of the outgoing brine (just as in a perfect steam boiler the steam might be worked up to the temperature of the outgoing flue gases), and in the condenser the vapor could be worked down to the tem- perature of the outgoing water. If these temperatures be used in the calculation, then, the resulting coefficient of performance represents ideal conditions of the whole system, including heat transmission of refrigerator and condenser. If, however, the temperatures corresponding to the vapor pressures of the am- monia are used, the resulting coefficient is that of the system, exclusive of losses in heat transmission in refrigerator and con- denser. Numerical examples of these two values of the ideal coefficient of performance will be cited later. The Efficiency of the plant may be expressed as the ratio of the actual to the ideal coefficient of performance. 316 TESTING REFRIGERATIOX AIACHIXERY 63 The Economy of compression plants is often stated in pounds of refrigerating effect (ice-melting) per pound of coal, on the assumption that a certain number of pounds of coal are con- sumed to make one indicated horse-power at the compressor. Other Results should include the expense of condensing water (under certain conditions this may be as large as the cost of the fuel) and the cost of auxiliary powder. For complete tests, enabhng a stud}^ of all the heat transfers, temperature and time-quantity determination should be made of both ammonia and cooling water. The Duration of the trial should be at least twelve hours, and preferably twenty-four, to allow for the possible error at the finish of the test due to a different amount of heat being stored in the refrigerator, condenser, etc., from that contained at the beginning. (a) Refrigerating Effect by Measurement of the Brine. Re- frigerating effect in B.t.u. per minute, equals R = W{T-t)C in which Tr = weight of brine in pounds per minute; r = temperature of brine at inlet in degrees Fahrenheit; ^ = temperature of brine at outlet in degrees Fahrenheit; C = specific heat of brine. For the determination of W the various methods of water measurement have been applied. Owing to the large quantit}' of brine circulated even in small plants, the method of direct weighing Ij}^ tanks and scales is inconvenient. A modification of this consists in running the brine through two tanks, one above the other, the upper one having in its bottom a number of orifices through which the brine flows. The rate of flow varies with the lieight of the brine level in the upper tank. One of the orifices may be i-eadily calibrated during the trial b}^ collecting, weighing 63 TESTING REFRIGERATION MACHINERY 317 and timing its discharge at various heads. The total brine flowing through all the orifices may then be found by multiplication. When meters calibrated in gallons or cubic feet are used, a separate determination of the weight of the brine per gallon or cubic foot is necessary. This may be made with a hydrometer, care being taken to test a sample withdrawn near the meter and at approximately the same temperature as it has in the pipe. Concerning temperatures T and t, as the range is only between 5 and 10°, finely graduated thermometers must be used. For not more than 2 per cent of error the graduations must be about 2 per cent of the temperature range — that is, between one-fifth and one-tenth degree. The thermometers should be inserted in wells filled with mercury or oil and should be located in the inlet and outlet pipes as near as possible to the cooler. The protruding portions of the wells should be well insulated. During the trial it is well to interchange the thermometers as a check on their accuracy. The Specific Heat of Brine varies with its concentration, con- stituents and temperature. The last-named variation is com- paratively small — about 0.05 per cent decrease of the specific heat~ for each degree decrease in temperature. As to the effect of the constituents, the presence in calcium chloride brine of manganese and sodium chloride in moderate quantities (say up to 20 per cent) does not affect the specific heat of the mixture materially. The effect of the concentration, however, is to lower the specific heat from unity (that of water) down to about 0.65 at a concentration corresponding to a specific gravity of 1.26. The following formula for pure calcium chloride brine will give results for the specific heat of commercial calcium chloride brine to within 1 or 2 per cent of error, between the limits of —4 and 40° F., and specific gravities between 1.10 and 1.26: C=1.833~0.93(?-0.0005(32-ra). 318 TESTING REFRIGERATION :\IACHINERY 63 In this formula* G is the specific gravit}', and Ta is the average temperature of the brine in degrees Fahrenheit at inlet and outlet. (b) Refrigerating Effect by Ammonia Measurements. The heat added to the ammonia in the brine cooler equals the heat lost by the brine. If the former quantity be found it is therefore a measure of the refrigerating effect, and we can put in which R is as before, A is the number of pounds of anhj^drous ammonia circulated per minute, and H = the total heat of the ammonia per pound leaving the cooler, h' = the heat of the liquid at the expansion valve. To find A, see Test 64 (h). H and h^ are to be found from tables of the properties of ammonia, t or from the ]\Iollier diagram for ammonia. To use these tables, the same data as for steam are necessary. For H the suction pressure must be read, together with the temperature, so that the heat of superheat may be calculated. The specific heat of superheated ammonia at low pressures may be taken as 0.51. For /i', the head pressure may be referred to. It is difficult to get the exact amount of superheat of the ammonia leaving the cooler, and also to maintain a uniform quantity of ammonia in the cooler to avoid the error of starting and stopping as in a boiler test. For these reasons the refrigerating effect as obtained by this method may be expected only roughly to check the result by the brine method which is therefore to be preferred. When the cooling is done by the direct expansion of ammonia, there is no choice between these methods, as brine measurements are eliminated under such conditions. An approximation of the * Deduced from the values given in Bureau of Standards Bulletin No. 135. t See Appendix for properties of saturated ammonia. 63 TESTING REFRIGERATION MACHINERY 319 refrigerating effect can be made by still another method which is also useful as a rough check of either (a) or (b) . (c) Approximate Calculation of Refrigerating Effect. Neglect- ing effects of radiation, etc., the heat added in the refrigerating plant equals the heat equivalent to the compressor work, plus the heat added to the ammonia, R. This sum equals the heat taken awa}^, or the heat imparted to circulating water. By finding the heat taken up by the condenser water and jackets and sub- tracting from this the heat equivalent to the compressor work, we thus have a rough measure of the refrigerating effect. The condenser * water may be measured as under (g). Its temperature rise should be obtained by thermometers at inlet and outlet, from which data the heat removed may be calculated. (d) Ice-melting Capacity is readily calculated from the value of the refrigerating effect R in B.t.u. per minute, by dividing by 200, the result being in tons per twenty-four hours. (e) To obtain the actual coefficient of performance, it is neces- sary to indicate the comipressor. The process here is similar to that ^or steam-engine trials and hardly needs comment other than that a special steel-lined indicator must be used with as short pipe connections as possible to avoid materially increasing the clearance space. Having obtained the indicated horse-power of the compressor, the coefficient sought is 42.4Xl.h.p.' (f) The Ideal Coffiecient of Performance may be found from the average thermometer readings at the brine and condenser water outlets, as previously defined. Or, if vapor pressures are used, the corresponding temperatures may be found from the ammonia tables. When the plant is equipped with pressure gages bearing thermometric scales, the ammonia tables may be dispensed with. 320 TESTING REFRIGERATION :MACHINERY 63 As an illustration of the difference that may exist between the values of the ideal coefficient as obtained by the two methods previously discussed, consider the following data: Suction pressure, 28-lb. gage; from tables, temperature, 15°; head pressure, 151-lb. gage; from tables, temperature, 84.5°; outgoing brine temperature, 28.9°; outgoing condenser- water temperature, 83.5°. From these figures the ideal coefficient of the whole sj^stem is 460+28.9 _ 83.5-28.9 ^-^^ and for the system, exclusive of condenser and refrigerator trans- mission losses, is 460+15 84.5-15 = 6.83. (g) Gallons of Cooling Water per Minute per Ton. The measurement of the condenser water is simpler than that of the brine, the quantity being much less. Direct weighing or the usual forms of water meter may be emploj-ed, care being taken to select one appropriate to the conditions of flow, whether pulsating or steady. The number of gallons of cooling water per minute per ton of ice-melting capacity should be figured for purposes of comparison and also in order to add the cost of this item to the other costs to obtain the total. This item should include all cooling water used, such as compressor jacket water and water to steam condenser if one is used. (h) Overall Economy. The performance of auxiliaries may be either estimated or measured. When the}^ and the com- pressor are steam driven, it is well to measure the total steam supplied to the plant b}' the boiler-feed method or b}^ a steam meter installed so as to avoid inaccuracies due to pulsating flow. The steam consumption of the compressor and of the whole plant may then be stated in pounds of steam per ton of ice-melting. ''•^ 63 TESTING REFRIGERATION MACHINERY 321 Ratings are generally based on head and suction pressures of 185 and 15.3 gage respectively, corresponding to temperatures of C6 and 0° F., respectively. Any departure from these con- ditions should be considered in making comparisons of test results'. Problem 63i. What is the tonnage (ice-melting capacity) of a plant that circulates 6000 lbs. of brine (specific heat = 0.80) per hour at an average tem- perature fall ofl5°F.? Ans. Q tons. Problem 682. What is the specific heat of a calcium chloride brine having a specific gravity of 1.2, if its temperature is 32° F.? If its temperature is 0° F.? Ans., 0.717; 0.701. Problem 683. Supposing 600 lbs. of anhydrous ammonia are circulated per hour at a head pressure of 160 lbs. gage, and a suction pressure of 20 lbs. gage, the superheat being 25°; what should be the refrigerating effect? Ans., 29,600 B.t.u. per hr. Problem 684. A refrigerating plant uses 14,220 lbs. of water per hour in the ammonia condenser, with average incoming and outgoing temperatures of 50° and 75°, respectively. The I.h.p. of the compressor is 20. Approxi- mately what is the tonnage (ice-melting capacity)? Ans. 25 A tons. Problem 685. What is the actual coefficient of performance for the data of Problem 684? Ans. 6. 64. Test of a Refrigeration Plant. (Ammonia Absorption System) Principles. In some respects the results from and methods for the test of an absorption plant are identical to those applying to the compression system, for which, see Test 63. The capacity in terms of ice-melting effect may be found in the same way, and the investigation of the condenser operation is the same. The actual coefficient of performance may not readily be obtained, since the energy imparted to the ammonia (barring the work of the ammonia pump, which is comparatively small) is in the form of heat instead of compressor work. But the ideal coefficient of performance may be determined as for a compression plant and may be useful for purposes of comparison of the two systems. The principal economy result is the steam consumption expressed in pounds of steam per hour per ton of refrigerating 322 TESTING REFRIGERATION MACHINERY 64 effect. This may be determined in toto for the plant or itemized as live steam to the pump and steam to the generator, the latter being subdivided into live and exhaust steam according to whether the one or the other or a combination is used. Under favorable circumstances the generator will use 30 lbs. of steam per hour per ton. The steam consumption of ammonia pumps is subject to wide variations due to their construction. Although the energy delivered is small compared with the heat transferred in the generator, a test of this pump should be included in economy trials because of the bearing of its performance on the steam consumption of the plant; and the pump test should preferably include a determination of the horse-power delivered. In addition to these results it is desirable to ascertain the con- dition of the aqua ammonia and, if convenient, the amount of anhydrous circulated per unit of time. The former is expressed in terms of its concentration; that is, the part of a pound of ammonia in one pound of the aqua ammonia (more frequently expressed as a percentage). The concentration results show the working of the absorber and generator and enable calculations regarding the ammonia circulation. (a) Refrigerating Effect, 2 methods. See Test 63, (a) and (b). (b) Ice-melting Capacity. See Test 63, (d). (c) Ideal Coefficient of Performance. See Test 63 (/). (d) Gallons of Cooling Water per Minute per Ton. See Test 63 {g) in so far as condenser water is concerned. All other cooling water supplied, if in separate amounts, should be included in this total, b}' similar methods of measurement. (e) The Steam Consumed by the Generator is readily ascer- tained by piping the generator-trap discharge into a weighing barrel. The barrel, to start with, should be about half full of cold water to prevent evaporation of the condensate from the trap. Quick emptying should be provided for. Weights should be recorded at uniform time intervals (to show uniformity of operation), from which data the rate in pounds per hour may be had. 64 TESTING REFRIGERATION MACHINERY 323 Quality determinations of the steam are important, unless an efficient separator is installed to remove the moisture from the incoming steam, to the consideration of the results, as also are pressure readings. If reduced hve steam is used in addition to exhaust and it is sought to measure them separately, a steam meter may be appHed to the live-steam line. The exhaust-steam quantity then equals the total trap condensate minus the meter reading. Measure- ment of the feed water, as for a boiler test, may also be resorted to, in cases where the plant may be isolated. ^ATien the generator is supplied with exhaust steam from the pumps plus reduced live steam, the hve steam may be found by subtracting from the generator trap discharge the steam con- sumed by the pumps. This last may be measured as follows: (f) Steam Used by Ammonia and Brine pumps. A separate test should be made to determine this, but if conditions are not favorable, the steam required to drive the pumps may be esti- mated from the manufactuer's figures for their water rates and from the horse-power actually delivered. These remarks of course apply to steam pimips; where power pumps are installed, the energy may be considered in the list of costs. (g) Work of the Ammonia-pump. It is preferable to find the net horse-power output rather than the indicated horse-power. From the data required for the net horse-power and from the num- ber of pump displacements, the sHp may be calculated as in ordinary pumping-engine trials. The required formula for horse-power is XT ^u 144(Pi-P2)F Net horse-power =—33^^^^-, in which Pi and P2 are the gage pressures worked against in pounds per square inch (that is, of the generator and absorber, respectively) and V is the number of cubic feet of strong aqua circulated per minute. 324 TESTING REFRIGERATION MACHINERY 64 The quantity of strong aqua V may be determined in several ways. A specially calibrated meter may be used on the discharge side of the pump; the aqua may be measured in calibrated tanks on the suction side; or it may be calculated from the amount of anhydrous circulating or from the quantity of weak aqua, the concentrations being known. For this last method (see(i)). When a receiver is installed to supply the ammonia pump, it may be readily calibrated so that the volume contained, corre- sponding to any height of the liquid in the gage-glass, is known. Now, by cutting off the flow from the absorber into this receiver for a short interval, the rate, in cubic feet per minute, at which the strong aqua is pumped out, may be ascertained. If desired, two receivers may be arranged in parallel, thereby enabling contin- uous measurement. (h) Weight of Anhydrous NH3 Circulated per Minute. Vol- ume measurements may be made in the same way as described under (g) for strong aqua. To convert the volumetric results into weights, a temperature or pressure reading also should be obtained to find the density of the liquid from the tables of prop- erties of ammonia. When closely accurate results on the anhy- drous quantity rate are desired, a favorite method is by direct weighing. Two ammonia drums, arranged in parallel, are piped in the line betw^een the condenser and expansion valve, so that they can be filled and emptied alternately. These drums are set on platform scales, the connections to them being horizontal and sufficientl}^ long to deflect about J in. under a load at the end of about I lb. The drums and contents may then be weighed with- out sensible error. The increase of accuracy of this procedure probably does not justify the elaboration of the apparatus. It is useful to find the number of pounds of anhydrous per minute per ton of refrigerating effect and to compare this with the amount theoretically required as tabulated in handbooks or calculated from heat contents under prevaiHng conditions. 64 TESTING REFRIGERATION MACHINERY 325 (i) Concentration and Specific Gravity of the Aqua. The concentration of aqua ammonia is determinable from its specific gravity. Given a definite solution of ammonia in water, its spe- V "" — r \ 40 s, N \ \ \ *>3 \ \ 623 \ ^ y 30 \ ■y^ y X 60.0 %- rV y \ ^- ,.^^ \ > r \ V^ y 25 N ,y y 57.5 \ y^ y >\ 1 /^ \ % 1 ^^ s 20 > - Ac4 *i*5 y \c S6o = 0.865+0.003(75-60)(l-0.865) -0.871. The value 0.871 is then to be referred to the chart for the cor- responding concentration. When the reverse calculation is sought (for the density deter- mination of aqua at high temperatures) this formula may be ex- pressed thus: aSgo- 0.003 (^-60) St = 1-0.003(^-60) (j) Calculation of Aqua and Anhydrous Weights per Minute from the Concentrations. This method is based upon the follow- ing rational relations. * Curves presented in Marks' Mechanical Engineers' Handbook may also be used. t See also the equation and chart given under Test 65 (a). 328 TESTING REFRIGERATION MACHINERY 64 v^s ^t x^, i-a iij — ^j yr Xw4|/7, X-^s> A. = A.S AfD) in which As^ Aic and A are the weights in pounds per minute of the strong and weak aqua and anh3'drous respectively, and C, and C^ are the concentrations of the strong and weak aqua respectively, in pounds of NH3 per pound of solution. For direct measurement of these quantities, much the same methods may be employed as for the strong aqua. (See (g).) The reader is reminded that only one of the three quantities, Ay Au,, or As, need be directly measured for a fairly accurate knowledge of the performance of the plant when the concentra- tions are known. The ammonia, whether aqua or anh3'drous, may therefore be directly metered at a point selected according to the existing layout. It should be borne in mind, however, that the results depending upon concentration figures may not be exact, because of the difficulty in getting close values of the concentra- tions. It is to be noted that, since these relations are between weights, a knowledge of densities is necessary to convert them into or from volumes. For the aqua this involves a measurement of specific gravity; for the anhjTlrous the ammonia tables may be referred to. The chart, Fig. 105, gives values of the density of aqua corre- sponding to those of specific gravity, the density scale being on the right. As an example of how these relations are to be applied, let us suppose that the concentrations of the strong and weak aqua are 38, and 2G per cent respectively (the concentrations having 65 TESTING REFRIGERATION MACHINERY 329 been found as under (z)), and that the number of pounds of anhy- drous circulated per minute is 20. Then. A,= ^-TTz — '-z-^-X20 = 123 lbs. per minute. 0.38 — 0.26 Referring to the chart, it is seen that 38 per cent aqua has a specific gravity of 0.873, if the aqua is at 60° F., and a density of 54.4 lbs. per cu. ft. For the calculation of (gf), if the temperature of the aqua at the pump is not much higher than this, then the cubic feet dis- charged per minute is 123-^54.4 = 2.26, which is the value of V to be used in the formula for horse-power. 65. Heat Balance of a Refrigeration Plant (Ammonia Absorption System) Principles. The over-all heat transfers in an absorption refrigeration plant may be summarized very briefly as follows: Energy is added to the system, first by the steam supplied to the generator, second by the work of the ammonia pump, and third by the heat added to the brine during the refrigerating process. Heat is removed from the system by circulating water, first in the ammonia condenser, second in the absorber, and lastly, in the weak-aqua cooler and the rectifier. The energy added equals the heat removed, as itemized, plus or minus radiation. A study of this over-all heat balance is useful, but before making comparisons of grand totals, it is preferable to analyze the performance of separate units. Of these it is the purpose here to deal with the generator and the absorber. To review the action of the generator, strong aqua ammonia enters at a comparatively low temperature, to which heat is added by steam pipes. Some of the ammonia is thereby boiled out of the water holding it in solution. There result from the process a quantity of superheated anhydrous ammonia, mixed with a small 330 TESTING REFRIGERATION IMACHINERY 65 percentage of steam, and a larger quantity of weak aqua, com- paratively hot, which is to be retm^ned to the absorber. The heat in the steam supplied goes to vaporize and superheat ammonia from the form of strong aqua and to raise the temperature of the entering aqua to a higher value upon leaving. Furthermore, a certain quantity of heat is required to break the bond between the hquid ammonia and the water holding it in solution, before vrpor- ization can take place. This quantity is additional to that re- quired to vaporize liquid anhydrous ammonia and is referred to as the " heat of solution.'^ Experimental values of it have been made showing that it is independent of pressure and temperature and varies only with the concentration of the solution, being about 347 B.t.u. per pound for very weak solutions (approximately to zero percentage of ammonia) and diminishing as the concentra- tion is increased to a zero value when the concentration is 60 per cent. It is convenient to base the heat calculations of the ammonia upon a single pound of the NH3 going through a complete cycle of temperature and state changes. From these results hourly quan- tities may be figured by multiplying by the number of pounds of anhydrous circulated per hour. Thus, let A represent the latter quantity and W the number of pounds of weak aqua circulated per pound of anhydrous vaporized; then the heat transfer '^d in the generator per hour = ^ X(Trxheat added to 1 lb. of the aqua+heat of solution in B.t.u. per pound of NH3 + difference in ^' heat content '^ of NH3 per pound, from tables). The quantity in the parenthesis is the heat transferred for the circulation of one pound of the anhydrous. The product, representing B.t.u. per hour, must equal the heat given up by the steam supplied to the generator, if the losses due to radiation and steam in the superheated ammonia are ignored. The Measurements Necessary to make for the determination of this heat balance are in part the same as those for an economy trial, for which see Test 64. In addition it is necessary to deter- "'^^ 65 TESTING REFRIGERATION MACHINERY 331 mine temperatures of the ingoing and outgoing aqua near the generator, the temperature of the ammonia vapor before it enters the rectifier and the head pressure — readings of which should be taken sufficiently to get fair averages. The vapor data are used to determine the ^^ heat content '^ from the tables (see Appendix), or Mollier diagram for ammonia. For the steam-heat quantities, pressure and quality must be ascertained as well as the tempera- ture of the condensate at the generator tiup. (a) To determine the number of pounds of weak aqua cir- culated per pound of anhydrous (that is, IF), it is necessary to measure the concentrations of the weak and strong aqua (referred to as Cto and C^, respectively) as described under Test 64 (z). The desired quantity may then be calculated from the rational formula, TIT ^W -I ^a Ji. L/5 i^n} A simpler procedure may be adopted through the use of the accompanying curves. Referring to Fig. 106, the lines slanting diagonally upward from left to right show values of the number of pounds of weak aqua per pound of anhydrous corresponding to various combinations of concentrations. To use these curves assume, for example, that the concentration of the strong aqua is 0.34, and of the weak, 0.24. On the chart the lines representing these values intersect between the curves marked 6.5 and 7, at about one-fifth of the distance across, so the value of W is 6.6. This chart also gives the ^' heat of solution,'^ which is plotted from the experimental values of H. Molher. As previously remarked, this depends only upon the concentration. During the driving-off process in the generator, the concentration varies from that of the strong aqua to that of the weak. It is the average concentration, then, that determines the heat of solution. This condition is met in the chart, as before, by the intersection of the lines representing the concentrations; the location of this point 332 TESTING REFRIGERATION MACHINERY 65 with relation to the ''heat Knes " (slanting downward from left to right) gives the heat of solution. For example, using the concentrations 0.34 and 0.24, the point of intersection is about four-fifths of the distance across from the 205 to the 210 B.t.u. line. Therefore the heat of solution is 209 B.t.u. Q20 02\ 022 0.23 024 025 026 027 028 029 030 0.31 052 033 0.34 0.35 0.36 037 0.38 0.39 0,40 Concentrotion of strong Aqua Fig. 106. — Heat of Solution of Aqua Ammonia (b) Heat Added to NH3 and Aqua in Generator. We no\A have means of finding the number of pounds of weak aqua pci pound of ammonia vaporized and the heat of solution per pound, Referring to the heat equation for the generator, already given, ii will be noticed that there are still to be found the heat added t' one pound of the weak aqua and the difference in ^^ heat content 'I of the NH3 before and after vaporization. The latter is readihj found from the ammonia tables or ]\Iollier diagram, being thi difference between the total heat of the NH3 vapor at the heacj pressure and outgoing temperature and the heat of the liquici NH3 at the temperature of the incoming strong aqua. 65 TESTING REFRIGERATION MACHINERY 333 Considering, now, the heat added to one pound of the aqua passing through the generator, it is to be remarked that there are no tabulated values of the heat of the liquid of mixtures of ammo- nia and water, or of the specific heats of such mixtures. It will, however, be sufficiently accurate to assume that the heat capacity 210 200 190 180 170 160 T3 C150 D £l40 ©130 Q. 3 120 +-■ «=°JI0 73 dIOO o- ':j 90 , in inches of water, into //, in feet of air, we have, 66 TESTING OF AIR MACHINERY 339 for the given data. Consequently, // = 68.5X0.5 = 34.25, and the ' velocity is 7 = 8.02VF 7 = S.02V34.25 = 47 ft. per second. If the area of the pipe is 0.33 sq. ft., the cubic feet of air per minute is 60X0.33X47 = 930. To reduce this to free air, it is multiplied by the ratio of temperatures and the inverse ratio of pressures. 525 30 2 Free air per minute = 930X37^X7^777^ = 934 cu. ft. 527 29.9 (c) Horse-power Supplied per Thousand Cubic Feet of Free Air per Minute. This quantity is obtained from the results of (a) and (b) being the quotient between each two corresponding values multiphed by 1000. (d) Air Horse-power. For the data previously given, the weight of air delivered per minute is 930X0.0758 = 70.5 lbs. The velocity head is 34.25 ft. of air, and the pressure head, 68.5X4 = 274 feet of air. Then the air horse-power is . , 70.5(34.25+274) „ ._^ A.h.p. = 33^^^^ = 0.659. (e) The Efficiency equals the air horse-power divided by the horse-power supplied. Problem 661. In the test of a blower, if gasoline, specific gravity =0.75, is used as a gaging fluid with a pitot tube, what is the velocity head in feet of air, if /i=4.5? Pressure is 6 ins. of the same fluid. Barometer is 30.3 ins. mercury. Temperature is 70° F. Ans.j 229 ft. Problem 662. In the preceding how many foot-pounds of work will be done in one minute if pipe dia. =6 in.? Ans., 58100. 340 TESTING OF AIR MACHINERY 67 Problem 663. In the operation of a blower, the volume discharged varies very nearly as the rotative speed. The pressure is due to centrifugal force. From these facts, deduce how the power will vary with the speed. 67. Test of a Reciprocating Air Compressor Principles. In the operation of an air compressor, it is the purpose to increase the pressure of the air suppHed so as to make available the energy it contains. As this energy is to be used when the air is cool, it is desirable to compress the air isothermally. If it is allowed to heat, the pressures during compression are higher and more work is required for compression. For this reason, w^ater jackets and intercoolers are used, the heat removed by them being a saving. Referring to Fig. 108, the dotted lines show an ideal air com- pressor diagram from a cylinder without clearance in w^hich the air is discharged at a pressure, 42 — 5i, equal to that in the de- 5".T — 4}\\^ Inlet Valve Opens at 1 Hvcry main. The supply is %%^55u?e ^A "^ ^^^'^^ " ^P^^""^^ " ^ drawn in at atmospheric pres- v\ - '> 0363 ' ^^^^ along the line 61 — 2i and °'*{ Fig. 110.— Hydraulic Ram. 69 TESTING OF WATER MOTORS 351 Two values for the useful work of a ram may be obtained, depending upon the level from w^hich the head pum_ped against is dated. Referred to the level of the supply water, the useful work is that corresponding to the elevation of a weight of water through the distance H, Fig. 110. Referred to the level of the ram, it is the work performed in lifting the same weight of water through the distance Ha- The one result leads to what is known as Rankine's efficiency, the other to D^Aubisson's. No confusion should arise through the existence of the two different efficiencies. Whether the one or the other should be used depends upon w^hether one is interested in pumping water from the supply level or from the level of the ram. Selection of the Independent Variable. Laboratory tests are generally conducted under a constant supply head, although this may be varied in the same way as for the test of a water turbine. If the supply head is maintained constant, either the number of strokes per minute of the waste valve or the discharge head may be made the independent variable. (a) Capacity is expressed in gallons of water pumped per tw^enty-four hours. This may be measured b}^ catching the discharge in a pail, or larger vessel if necessary, during a counted time. Instead of pumping against a static head as in regular operation, the discharge may be throttled by means of a valve in the discharge pipe which may then be short enough to collect conveniently the water delivered. The desired head is ascer- tained and regulated by the aid of a pressure gage between the ram and the throttle valve. If the number of strokes per minute of the waste valve is the independent variable, it can be varied by changing the lift of the valve, or adjusting the spring tension if it is operated by a spring. (b) Efficiencies. Let W and H stand for the weight of water flowing per minute in pounds and head in feet, respectively; and let the subscripts 5, w, and d refer to the supply, Avaste, 352 TESTING OF WATER IMOTORS 69 and discharge, respectively, as indicated by Fig. 110. According to Rankine's efficiency a weight of water Ww must fall Hs ft. in order to raise Wa lbs. of water H ft. Therefore, Rankine's efficiency = W^H, According to D'Aubisson's efficiency, the energy available to the ram is the denominator of the following expression, and this energy accomplishes Wa Ha ft-lbs. of work. D'Aubisson's efficiency = , . Wstls Since Wa was measured for the capacity determination, it is necessary only to measure the waste water to determine Ws- This may be done by allowing the waste to collect in a cahbrated tank. The head H may be found from the pressure gage read- ings, and Hs measured before the test. It is a good plan to use a float valve in the line which feeds the supply tank so that a constant level may be maintained in it automatically. (c) Curves of capacity, total amount of water supplied in gallons per twenty-four hours, and efficiency against the indepen- dent variable may be plotted from the data previously mentioned. Problem 69i. The capacity of a ram operating against 20 lbs. pressure is 1042 gals, per twenty-four hours, and its efficiency (Rankine) is 35 per cent. The supply level is 10.5 feet above the ram. How much water passes through the waste valve in gallons per twenty-four hours? Arts., 10,100 gals. Problem 69j. Using the data of the preceding problem, what is the D'Aubisson efficiency? Ans., 41%. 70. Test of a Centrifugal Pump Principles. The useful work of a centrifugal pump is the product of a weight of water delivered in a given time in pounds 70 MISCELLANEOUS TESTS 353 and the total head pumped against in feet. The total head includes the friction heads of suction and discharge pipes and the velocity head. The work supplied to the pump is that received by its shaft in the case of a belt-driven machine, or one directly connected to an electric motor. In the case when the drive is a directly connected steam engine, both the drive and the pump are gen- erally tested as a single unit as would be a reciprocating pump. Selection of the Independent Variable. The rotative speed, quantity discharged, or head pumped against may be varied independently for a test. When one is varied arbitrarily, another is kept constant, and the third becomes a dependent variable. Two series of tests are useful; one at constant speed and the other at constant head, the independent variable being head and speed, respectively. When the speed is kept constant, the head may be varied by throttling the discharge, and when the head is kept constant, the speed is varied by control of the motor driving the pump. In the latter case, each change of speed must be accom^panied by a change in the valve opening in the discharge pipe in order to maintain a constant head. (a) Capacity may be expressed in gallons per twenty-four hours or per minute. The usual methods of measuring water rates mentioned under the heads of hydraulic turbines and reciprocating pumps, may be used. (b) Horse-power Supplied. The method of measuring this item depends upon the drive. If belt-driven, a transmission dyna- mometer is applicable. If motor driven, the motor should be calibrated (Test 74). If driven by a steam engine or turbine, it is generally more convenient to find the horse-power supplied to the set rather than to the pump alone. (c) The Water Horse-power may be calculated from the relation ^•^•P- 33,000* 354 MISCELLANEOUS TESTS 70 W is the weight of the water discharged, in pounds per minute, measured as under (a). D is the total head pumped against, in feet, and may be determined as follows. Connect a pressure gage to the discharge pipe as close to the pump as possible. To the suction pipe, also close to the pump, connect a Bourdon gage or a mercury manometer. Call the indications of these instruments Pa = discharge gage reading, pounds per square inch; Psj P5 = suction gage reading, inches of mercury or pounds per square inch; /i = manometer reading, inches of mercuiy. Also let d and r/' represent the distances in feet between the gages as shown b}^ Fig. 111. Assuming the diameters of the discharge and suction pipes equal, the velocity heads in these pipes will be equal. Then, since the energy WD added by the pump to the water equals the difference in energies on the discharge and suction sides (note that Ps is a negative pressure, counting from atmosphere), WD = Wx2,3Pa+d-WXi-lA3ps), and D = 2.3P,+d+l,13ps, . . . . (i) Fig. IIL — Measure- ment of Head. which relation is to be used when the suction pipe pressure is read with a vac- uum gage. Similarly, D = 2'3P,+d' + lA3h, .... (2) which is the appropriate relation when a mercurj^ manometer is employed. 70 MISCELLANEOUS TESTS 355 If the level of the water supplied is higher than the pump, a pressure gage is used in the suction pipe instead of a vacuum gage. Then the term 1.13^5 in equation (1) changes to — 2.3Ps, Ps being in pounds per square inch. Or, if a manometer is used, the term l.lSh in Eq. (2) changes to — 1.13/i. If the diameters of discharge and suction pipes are different, the change in velocity head should be credited to the pump. If Vd and Vs stand for the velocities in feet per second on the dis- charge and suction sides, respectively, then there should be added to D (as obtained from Eq. (1) or (2) ), the following: 64.4 • The method of finding the head when testing a reciprocating pump (see p. 254), may also be used, but this does not credit the pump with the friction head in the suction pipe. (d) Hydraulic Efficiency may be calculated by dividing each value of water horse-power by the corresponding value of the horse-power supplied. (e) Curves may be plotted, from the data obtained, as follows : For constant speed tests, power supplied, capacity, and efficiency against head. For constant head tests, the same results plotted against speed. Sometimes speed or head, power supplied, and efficiency are plotted against quantity discharged. Problem 70i. How would you determine separately the work done by the various impellers of a stage centrifugal pump? Problem 7O2. Does or does not the measurement of total head by gages, outlined under (c), include the friction head of suction and discharge pipes, and why? Does it include the friction head of the water in passing through the pump, and ought this head to be included? Why? 71. Test of a ^^ Power '^ Pump Principles. By '^ power '^ pump is meant a reciprocating pump driven by a crank shaft which receives its power through a 356 MISCELLANEOUS TESTS 71 belted pulley, or gears from a motor. The general principles to be studied for testing are similar to these previously outlined under Test 50. (a) Water Horse-power. See Tests 50 (a) and 70 (c). (b) Available Horse-power. This may be found as for a centrifugal pump, Test 70 (6), when the drive is by belt or geared motor. (c) Mechanical and Fluid Losses and Efficiencies. The dif- ference between the water horse-power and the indicated horse- power equals the hydraulic losses. The difference between the indicated horse-power and item (&) equals the mechanical losses. Expressions for the corresponding efficiencies are obvious. The total efficiency is item (a) divided by item (6). (d) Slip and Capacity. See Test 50 {d) and (e). 72. Test of a Hoist Principles. A hoist is a machine by which a large weight may be lifted by the appUcation of a small force. This is accomplished usually by passing a chain, or chains, over a num- ber of w^heels geared together in such a way that a large motion of one end of the chain downward produces a small motion of the other end upward, whereby a mechanical advantage is obtained. The Ideal Mechanical Advantage is the ratio of a dis- tance moved through by the driving chain to the correspond- ing distance moved through by the following chain. Refer- ring to Fig. 112, representing a hoist diagrammatically, this ratio is D/d. If there were no friction, this would be the ratio of the weight lifted, Wy to the force applied F. As there is friction, The Actual Mechanical Advantage equals the ratio of the weight lifted to the force appUed, or W/F. i 72 MISCELLANEOUS TESTS 357 The efficiency of a hoist equals the work done in hfting the weight through any distance divided by the work done by the applied force acting through the corresponding distance. If the efficiency of a hoist is more than 50 per cent, the weight lifted will return by gravity when the hoisting force is removed unless there is a locking device. Where this is provided, it is ar- ranged to lock against the force of gravity only, and not against a force applied to the driving chain for the purpose of lowering the weight. (a) The Ideal Mechanical Advantage may be determined by actual measurement of the distances, D and d. Fig. 112. As d is generally very small compared with D, the result by this method may not have the desired degree of accuracy. A better method consists of counting the numbers of teeth of the various gears of the hoist and figuring from thedata obtained, by the principles of kinematics, the velocity ratio of driver to follower. (b) The Actual Mechanical Advantage may be determined by measuring the force applied to lift various loads. The desired results vary with the load, and may be plotted against its values. The loads may be applied by using various dead weights, suf- ficient to cover the working range of the hoist. The force required to lift these weights may be measured by applying the force through a spring balance hooked into the driving chain. Owing to the difficulty of reading a m.oving instrument, this is not a very accurate method. A better one is for the experimenter to stand on a platform scales and to apply the driving force at a uniform rate with one hand and at the same time, w^ith the other hand, to balance the scales by adjusting the jockey weight. The weight of the experimenter minus the reading of the scales then equals the force applied to the hoist. 358 MISCELLANEOUS TESTS 72 Several determinations of the force applied should be noted at each load, and their mean used to obtain the actual mechan- ical advantage at that load. It should not be attempted to make mental averages. (c) Efficiency equals (see Fig. 112) W Work done WXd F Actual mechanical advantage Work applied FXD D Ideal mechanical advantage ' "d Consequently each result under (b) may be divided by that under (a) to get the corresponding efficiency. The efficiencies should be plotted against the loads. Problem 72]. Assuming that the friction losses of a hoist are constant throughout its working range, deduce the form of, and sketch roughly, curves between force applied and load hfted and between efficiency and load lifted. Will these curves pass through the origin or not, and why? Problem 720. A differential hoist has 12 chain notches on the driving wheel and eleven on the smaller. What is its ideal mechanical advantage? Ans., 24. Problem 723. The efficiency of a hoist is 60 per cent and its ideal mechan- ical advantage is 40. What load will a force of 4 lbs. lift? Ans., 96 lbs. Problem 72 j. Prove that a hoist having an efficiency greater than 50 per cent needs a locking device. 73. Tests of Lubricating Oils Principles. The most indicative results of the relative values of lubricating oils are ol)tained from tests of viscosity, flash and chill points, and coefficient of friction. Viscosity manifests itself as internal friction of the oil, a prop- erty which opposes the motion of the particles upon themselves, resulting in a reluctance to flow. It is related to, but is not proportional to the density. Since it opposes motion, it is an undesirable property, but there is such a tiling as too little vis- 73 MISCELLANEOUS TESTS 359 cosity for good results. If the oil flows too readily, it may be squeezed out of the space between the surfaces it should lubricate, and the total amount of oil needed for proper lubrication might then become excessive. This depends largely upon the pressure between the bearing surfaces. The term ^^ body '' is also used to denote viscosity. The flash point is the temperature at which the oil will vaporize fast enough to form an explosive mixture with air. This tem- perature should be higher than the working temperature to be encountered in the service of the oil. Consequently it should be judged in connection with its service. The burning point is the temperature at which a body of the oil considered will burn w^hen a flame is placed a short distance over its surface. The chill point is the temperature at which the oil loses its fluidity. Its determination is necessary only when the tem- peratures during service are low. For more complete details concerning the requirements for and usual constants of lubricating oils, see Stillman's ^^ Engin- eering Chemistry'' or Marks' ^' Mechanical Engineer's Hand- book." (a) The Specific Gravity is of interest in connection with viscosity, since a high value of the one generally indicates a high value of the other. It may be determined by balancing a column of oil in one leg of a Li-tube against a column of water in the other leg. Then the specific gravity of the oil equals the height of the water column divided by the height of the oil column. A more convenient method is to use a hydrometer if one is available. Hydrometers are obtainable graduated to indicate specific gravity relative to the weight of water, but more usually they are graduated according to an arbitrary scale. The so-called Baume scale is largely used in the United States, although the more logical scale based on the weight of water is preferable. 360 MISCELLANEOUS TESTS 73 Hydrometers so graduated indicate Baume degrees (deg. Ee.). The relation between these degrees and specific gravity on the water basis is, for liquids heavier than water, Specific gravity = 145 -^ (145 — deg. Be.) and for liquids lighter than water, Specific gravity = 140-^ (130+deg. B6.) (b) Viscosity. This is a purely relative measurement. There are different standards for its expression, but, in general, it may be taken as the ratio of the time required by a given volume of the oil considered to flow through an orifice of a given size under a given head, or drop in head, to the time required by the same volume of another liquid, as water, to flow under the same conditions. The temperature of the oil has to do with its viscosity, so for comparative results the temperature must be kept constant during all tests. It should be remembered that the temperature during a test may be quite different from that in actual ser- vice, so the results are strictly comparative and not always indicative of the true merits of oils to be used at high tem- peratures. Apparatus for viscosity tests, or ^^ viscosimeters,'' may be readily improvised. It is desirable that the vessel containing the oil be water-jacketed to maintain a constant temperature. The orifice should be about xe in. in diameter. The head on the orifice may start at about 6 ins. and end at about 4 ins., the total volume of oil passing through the orifice being that between the levels at the start and finish. Some forms of viscosimeters are arranged so that the flow shall be under a con- stant head. (c) Flash, Burning, and Chill Points. The flash point may be foimd by placing the bulb of a mercury thermometer in a "^^ 73 MISCELLANEOUS TESTS 361 porcelain dish filled with oil to be tested, and heating the oil over a Bunsen burner until a flash may be obtained from it by passing a lighted taper over its surface. The temperature of the oil when this happens is noted as the flash point. The burn- ing point is found similarly, by carrying the heating to a point at which the flash causes a burning of the oil in the dish. The chill point may be found by chilling a small amount of the oil in the bottom of a test tube by surrounding it with a freezing mixture until it congeals. The test tube is then removed and the oil stirred with a thermometer until it has warmed sufficiently to flow^ from one end of the tube to the other. The temperature is then noted as the chill point. (d) Coeflicient of Friction. To determine this, an oil test- ing machine should be used. See Test 35. The oil to be tested should be used under the same bearing pressure and the same temperature as it will meet in service, as far as is possible. Com- parative tests of different oils should be made under uniform conditions of temperature, pressure and velocity, or else the results wall not be comparable. (e) Endurance Tests have to do with the total amount of oil necessary to secure required lubrication. An oil that is satisfactory in all other respects may be of prohibitive cost because its lack of body may necessitate a large rate of feed. An idea of the endurance of an oil may be formed by supplying the bear- ing of an oil tester with a limited amount of it and noting the time required to raise the temperature of the bearing a pre- determined amount. Another method is to note the time required to raise the coefficient of friction a predetermined amount. Still another is to measure the amount of oil during a given period of time when it is fed at a rate just sufficient to prevent a rise of temperature. Problem 73i. If the specific gravity of an oil is 0.85, what is its specific gravity in degrees Baume? If specific gravity is 1.15, what is its value in degrees Baume? Ans., 34.8°, 18.9°. 362 MISCELLANEOUS TESTS 74 74. Horse-power Test of an Electric Motor Principles. In mechanical engineering tests, it is often desirable to know the horse-power deUvered by an electric motor to the unit it drives, as, for example, a motor-driven centrifugal pump or blower. It then becomes necessar}^ to make a separate test of the motor. This can be done, of course, with a Prony brake by getting corresponding values of B.h.p. and current sup- plied. Such procedure is not always convenient, however, nor are the results as accurate as when the useful horse-power is found by the measurement of losses. Consequentl}^, the latter method will be described. The following notation will be used. V = voltage of Une ; A = armature current in amperes, motor loaded; Ao = armature current, motor running free; F = field current, amperes; /? = resistance of armature, ohms. Now the power delivered at an}- load, in watts, is 746 X B.h.p. = watts input — losses. The losses ma}' be grouped as constant and variable. The variable loss to be considered is due to the armature resistance, increasing as the armature current increases, and equals A-R, The constant losses, entering the calculation, are due, first to friction and windage, and second, to hysteresis and eddy currents (the so-called '' iron losses '')• These losses may be considered constant at all loads, provided only that the speed is approximately constant. Now, when the motor is operated with- out load, the watts input equals the losses; and, since A^R losses at no load are very small, it follows: Constant losses = V{Ao+F). 74 MISCELLANEOUS TESTS 363 The watts input, under load, obviously equals V{A+F), Substituting these values of input and losses in the equation for B.h.p., we have 746 B.h.p. = y(A+F)-A2i2-7(4o+F) = VA + VF-Am-VAQ-VF = A{V-AR)-VAq] and B.h.p. = .00134{4(F~Ai2)-7^o}. (a) Determination of Horse-power Output. In the equation last given, VAo and R are taken as constant, and may be prede- termined. Then, at any load applied to the motor, it is only necessary to measure the armature current, A, corresponding to that load, and the voltage; F, in order to calculate the B.h.p. The armature resistance, R, may be determined by the ''drop of potential'' method. The armature being stationary, connect the armature leads to the line with a resistance and ammeter in series, being careful to avoid injury to the coils with excessive current. Measure the amperes flowing, and the E.m.f. drop across the brushes with a voltmeter. Then Resistance, ohms = 72 = — t -. Amperes This should be repeated for a number of different positions of the armature, and the average resistance from the various positions taken. Repeat, also, for another value of the current. Next, the motor should be connected as in service, but with an ammeter in the armature circuit, and a voltmeter to indicate the voltage at the armature terminals. It is then run at no load for a period of fifteen to thirty minutes, in order to obtain uniform ^^^ 364 MISCELLIXEOUS TESTS 74 conditions of friction, etc. If, now, the armature current is read, this furnishes the required value of VAq. If the motor is equipped with a rheostatic control, giving it different speeds, the no load value of the armature watts. AT^o, should be determined at each different speed at which the motor is to be run, and a speed-ampere curve drawn. Then, when the motor is operating under load, it is necessar}^ not onl}- to read the armature amperes, but also the speed in order to appl}^ the corresponding value of AVo in the B.h.p. formula. (b) Efficiency. If this is required, it is only necessarj^ to obtain the total watts input. This divided into the watts out- put equals the efficiency. For a shunt wound constant speed motor, the field current, being approximately constant, ma}' be predetermined and added as a constant to the armature current to get the total amperes input. Problem 74i. At no load, a motor takes 10.5 amperes armature current at 220 volt?. What is the value of AT'o? Is this what is referred to as the "constant " loss? What is the constant loss, in watts (see Problem 743)? Afis., 2310 watts. Problem 74:. Same motor, given the armature resistance = 0.038 ohm. What is the brake horse-power, when the armature current is 150 amperes? Arts., 40 B.h.p. Problem 74^. What is the efficiency of the preceding, if the field current is 5.8 amperes. Ans., 87 per cent. APPENDIX LOGARITHMS To Find the Fractional Power of a Number Less than Unity. To avoid the use of negative characteristics, the following rule is suggested. Rule. Express the given number as a fraction whose numer- ator is unity. Find the required power of the denominator of this fraction, and then reduce to a decimal. For example, To find 0.787l•^^ Log. 1.27'-''=' = 1.33X0.1C4 = 0.138; 0.138 = log 1.37; .'. 1.271-33 = 1.37, 1 1 and .7871-33 1.271-33 1.37 = 0.73. To Find the Napierian Logarithm (Base e =2.718) of a Number. Rule. Multiply the common logarithm (base 10) by the constant 2.302, or 2.3, approximately. For example. To find log. of 315, (see page 366). Logio 315 = 2.498, .-. Log. 315 = 2.3X2.498 = 5.750. S65 366 APPENDIX COMMON LOGARITHMS No. 1 2 3 4 5 6 7 8 9 Dif. 42 0000 3010 4771 6021 6990 7782 8451 9031 9542 10 0000 0043 0086 0128 0170 {J'Z12 0253 0294 0334 0374 11 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 38 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 35 13 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 32 14 15 1461 1492 1523 1553 1584 1614 1903 1644 1931 1673 1959 1703 1US7 1732 2014 30 28 1761 1790 1818 1847 1875 16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 26 17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 25 18 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 24 19 20 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 22 21 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 20 22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 19 23 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 19 24 26 3802 3820 3838 3856 3874 3892 4065 3909 4082 3927 4099 3945 4116 3962 4133 18 17 3979 3997 4014 4031 4048 26 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 16 27 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 16 28 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 15 29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 15 14 30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 31 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 14 32 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 13 33 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 13 34 35 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 13 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 12 36 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 12 37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 12 38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 11 39 40 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 11 11 6021 6031 6042 6C53 6064 6075 6085 6096 6107 6117 41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 10 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 10 43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 10 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 10 10 45 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 9 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 9 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 9 49 50 6902 6911 6920 7007 6928 7016 6937 7024 6946 6955 6964 6972 6981 9 9 6990 6998 7033 7042 7050 7059 7067 51 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 9 52 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 8 53 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 8 54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 8 APPENDIX 367 COMMON LOGARITHMS No. 1 2 3 4 5 6 7 8 9 Dif. 8 55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 56 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 8 57 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 8 58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 7 59 SO 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 7 7 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 7 62 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 7 63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 7 64 65 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 7 7 8129 8135 8142 8149 8156 8162 8169 8176 8182 8189 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 7 67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 6 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 6 69 70 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 6 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 6 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 6 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 6 73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 6 74 75 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 6 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 6 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 6 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 6 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 6 79 80 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 5 5 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 5 82 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 5 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 5 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 5 85 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 5 86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 5 87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 5 88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 5 89 90 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 5 5 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 5 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 5 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 5 94 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 5 5 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 4 97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 4 98 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 4 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 4 368 APPENDIX DIAMETERS AND AREAS OF CIRCLES Diam. Area. Diam. Area. Diam. Area. Diam. Area. Diam. Area. A .00307 H 6.78 ~H~ 26.5 t 102. i 230. i .0123 3. 7.07 7 8 27.1 104. 1 4 234. A .0276 A 7.37 11 27.7 1 106. 3 8 237. 1 4 .0491 i 7.67 6. 28.3 3 4 108. i 240. A .0767 A 7.98 i 8 29.5 7 8 111. f 244. 1 .110 1- ■1 8.30 1 it 30.7 12. 113. f 247. A .150 A 8.62 31.9 i 115. 7 8 251. i .196 3 8 8.95 1 33.2 i 118. 18. 254. A .248 A 9.28 1 34.5 i 120. i 258. 1 .307 1 2 9.62 3 4 35.8 1 2 123. -1- 262. H .371 A 9.97 7 8 37.1 5 8 125. 1 265. 3 4 .442 5 8 10.3 7. 38.5 i 128. i 269. H .518 H 10.7 i 39.9 7 8 130. 5 8 272. 7 8 .601 3 4 11.0 1 4 41.3 13. 133. f 276. U .690 13. 16 11.4 f 42.7 1 135. 1 280. 1. .785 i 11.8 1 2 44.2 1 4 138. 19. 283. A .887 H 12.2 5 8 45.7 1 140. 1 8 287. 1 .994 4. 12.6 3 4 47.2 1 143. i 291. A 1.11 A 13.0 i 48.7 1 146. 3 8 295. , i 1.23 i 13.4 8. 50.3 1 4 148. 1 299. A 1.35 16 13.8 1 8 51.8 1 151. 1 302. f 1.48 i 14.2 4 53.5 14. 154. 3 4 306. A 1.62 A 14.6 3 8 55.1 1 8 157. 7 8 310. j 1.77 3 "8 15.0 1 56.7 1 159. 20. 314. 1.92 A 15.5 58.4 162. 1 8 318. 1 2.07 i 2 15.9 3 4 60.1 1 2 165. i 322. 16 2.24 9 16 16.3 7 "8 61.9 t 168. f 326. 3 4 2.40 5 8 16.8 9. 63.6 3 4 171. § 330. H 2.58 H 17.3 1 8 65.4 7 8 174. 5 8 334. 1 2.76 3 4 17.7 1 67.2 15. 177. 1 338. H 2.95 a 18.2 69.0 i 180. i 342. 2. 3.14 i 18.7 1 2 70.9 i 4 183. 21. 346. A 3.34 a 19.1 5 8 72.8 f 186. 1 350. i 3.55 5. 19.6 1 74.7 f 189. i 4 355. A 3.76 16 20.1 J 76.6 192. 359. i 3.98 1 20.6 10. 78.5 3 4 195. 1 363. A 4.20 A 21.1 1 80.5 7 8 198. f 367. f 4.43 1 4 21.6 i 82.5 16. 201. i 371. A 4.67 A 22.2 3 8 84.5 i 204. 7 8 376. h 4.91 3 8 22.7 1 2 86.6 1 4 207. 22. 380. A 5.16 A 23.2 1 88.7 .3 8 211. i 384. 5 8 5.41 1 2 23.8 I 90.8 1 2 214. 1 4 389. H 5.67 9 16 24.3 7 8 92.9 1 217. 1 393. 1 5.94 5 "8 24.8 11. 95.0 3 4 220. 1 2 398. H 6.21 \i 25.4 1 8 97.2 7 "8 224. 5 8 402. 7 8 6.49 3 4 26.0 i 99.4 17. 227. 1 406. APPENDIX DIAMETERS AND AREAS OF CIRCLES— Conhnwed 369 Diam. Area. Diam. Area. Diam. Area Diam. Area. Diam. Area. 1 411. 1 466. 7 8 525. i 588. 7 8 654. 23. 415. i 471. 26. 531. i 594. 29. 660. J 420. 5 8 476. i 536. i 599. 1 8 666. 1 4 425. 3 4 481. 1 4 541. 3 4 605. i 672. ^ 429. 8 485. 3 8 546. i 610. 1 677. * 434. 25. 491. i 551. 28. 616. 1 2 683. i 438. 1 8 495. f 556. J 621. 5 8 689. 3 4 443. 1 4 501. 3 4 562. 1 4 627. f 695. 7 8 448. 3 8 505. 7 8 567. 3 8 632. i 700. 24. 452. 1 2 511. 27. 573. 1 2 638. 30. 707. i 457. 5 8 515. 1 8 577. 5 8 643. i 462. i 521. i 583 f 649. WEIGHT OF ONE CUBIC FOOT OF WATER AT VARIOUS TEMPERATURES Temp., Deg. F. 1 Weight, Lbs. per Cu. Ft. Temp., Deg. F. Weight, Lbs. per Cu. Ft. 30 62.42 190 60.36 40 62.43 200 60.12 50 62.42 210 59.88 60 62.37 220 59.63 70 62.30 230 59.37 80 62.22 240 59.11 90 62.11 250 58.83 100 62.00 260 58.55 110 61.86 270 58.26 120 61.71 280 57.96 130 61.55 290 57.65 140 61.38 300 57.33 150 61.20 310 57.00 160 61.00 320 . 56.66 170 60.80 330 56.30 180 60.58 340 55.94 370 APPENDIX STEAM TABLES FOR CONDENSER CALCULATIONS Revised from Marks' Mechanical Engineers' Handbook. Vacuum in In. Temperature Deg. Fahr. of Mercury Referred to a 30-in. Bar. (Mercury at 58.4° F.) Pressure Lb. Per Sq. In. Absolute Specific Vol- ume Cu. Ft. Per Lb. Heat of the Liquid Total Heat of the Steam 50 29.637 0.1780 1702.0 18.08 1081.4 52 29.609 0.1917 1586.0 20.08 1082.3 54 29.579 0.2063 1480.0 22.08 1083.2 56 29.547 0.2219 1381.0 24.08 1084.1 58 29.513 0.2385 1291.0 26.08 1085.0 60 29.477 0.2562 1208.0 28.08 1085.9 62 29.439 0.2749 1130.0 30.08 1086.8 64 29.398 0.2949 1058.0 32.07 1087.6 66 29.354 0.3161 991.0 34.07 1088.5 68 29.308 0.3386 928.0 36.07 1089.4 70 29.259 0.3626 871.0 38.06 1090.3 72 29.208 p. 3880 817.0 40.05 1091.2 74 29.153 0.4148 767.0 42.05 1092.1 76 29.095 0.4432 720.0 44.04 1093.0 78 29.034 0.4735 677.0 46.04 1093.9 80 28.968 0.505 636.8 48.03 1094.8 82 28.899 0.539 598.7 50.03 1095.6 84 28.826 0.575 562.9 52.02 1096.5 86 28.749 0.613 529.5 54.01 1097.4 88 28.666 0.654 498.4 56.01 1098.3 90 28.580 0.696 469.3 58.00 1099.2 92 28.489 0.741 442.2 60.00 1100.1 94 28.392 0.789 417.0 61.99 1101.0 96 28.290 0.838 393.4 63.98 1101.8 98 28.183 0.891 371.4 65.98 1102.8 100 28.070 0.946 350.8 67.97 1103.6 102 27.951 1.005 331.5 69.96 1104.5 104 27 . 825 1.066 313.3 71.96 1105.3 106 27.692 1.131 296.4 73.95 1106.2 108 27.550 1.199 280.5 75.95 1107.1 110 27.404 1.271 265.5 77.94 1108.0 112 27.250 1.346 251.4 79.93 1108.8 114 27.088 1.426 238.2 81.93 1109.7 1 116 26.919 1.509 225.8 83.92 1110.6 118 26.739 1.597 214.1 85.92 1111.5 120 26.553 1.689 203. 1 87.91 1112.3 122 26.355 1.785 192.8 89.91 1113 2 124 26.149 1.886 183.1 91.90 1114.1 126 25.931 1.992 173.9 93.90 1115.0 128 25.706 2.103 165.3 95.89 1115.8 130 25.48 2.219 157.1 97.89 1116.7 135 24.84 2.53 138.7 102.9 1118.8 140 24.12 2.88 122.8 107.9 1121.0 145 23.33 3.28 109.0 112.9 1123.1 150 1 22.43 3.71 96.9 117.9 1125.3 APPENDIX 371 PROPERTIES OF SATURATED STEAM REPRODUCED FROM MARKS AND DAVIs' ^' STEAM TABLES AND DIAGRAMS (Copyright, 1909, by Longmans, Green & Co.) Pressure, Pounds Absolute. Tempera- ture Deg. F. Density Lbs. per Cu. Ft. Specific Volume Cu. Ft. per Pound 333.0 Heat of the Liquid B.t.u. h Latent Heat of Evap. B.t.u. L Total Heat of Steam B.t.u. H 1 101.83 .00300 69.8 1034.6 1104.4 2 126.15 .00576 173.5 94.0 1021.0 1115.0 3 141.52 .00845 118.5 109.4 1012.3 1121.6 4 153.01 .0111 90.5 120.9 1005.7 1126.5 5 162.28 .0136 73.33 130.1 1000.3 1130.5 6 170.06 .0162 61.89 137.9 995.8 1133.7 7 176.85 .0187 53.56 144.7 991.8 1136.5 8 182.86 .0211 47.27 150.8 988.2 1139.0 9 188.27 .0236 42.36 156.2 985.0 1141.1 10 193.22 .0261 38.38 161.1 982.0 1143.1 11 197.75 .0285 35.10 165.7 979.2 1144.9 12 201.96 .0309 32.36 169.9 976.6 1146.5 13 205.87 .0333 30.03 173.8 974.2 1148.0 14 209.55 .0357 28.02 177.5 971.9 1149.4 14.7 212 .0375 26.73 180 970.4 1150.4 15 213.0 .0381 26.27 181.0 969.7 1150.7 16 216.3 .0404 24.79 184.4 967.6 1152.0 17 219.4 .0428 23.38 187.5 965.6 1153.1 18 222.4 .0451 22.16 190.5 963.7 1154.2 19 225.2 .0475 21.07 193.4 961.8 1155.2 20 228.0 .0498 20.08 196.1 960.0 1156.2 22 233.1 .0545 18.37 201.3 956.7 1158.0 24 237.8 .0591 16.93 206.1 953.5 1159.6 26 242.2 .0636 15.72 210.6 950.6 1161.2 28 246.4 .0682 14.67 214.8 947.8 1162.6 30 250.3 .0728 13.74 218.8 945.1 1163.9 32 254.1 .0773 12.93 222.6 942.5 1165.1 34 257.6 .0818 12.22 226.2 940.1 1166.3 36 261.0 .0863 11.58 229.6 937.7 1167.3 38 264.2 .0908 11.01 232.9 935.5 1168.4 40 267.3 .0953 10.49 236.1 933.3 1169.4 42 270.2 .0998 10.02 239.1 931.2 1170.3 44 273.1 .104 9.59 242.0 929.2 1171.2 46 275.8 .109 9.20 244.8 927.2 1172.0 48 278.5 .113 8.84 247.5 925.3 1172.8 372 APPENDIX PROPERTIES OF SATURATED STEAM Pressure, Pounds Absolute. Tempera- ture Deg. F. Density Lbs. per Cu. Ft. Specific * Volume Cu. Ft. Per Pound. Heat of the Liquid B.t.u. h 1 Latent Heat of Evap. B.t.u. L Total Heat of Steam B.t.u. H 50 281.0 .117 8.51 250.1 923.5 1173.6 52 283.5 .122 8.20 252.6 921.7 1174.3 64 285.9 .126 7.91 255.1 919.9 1175.0 66 288.2 .131 7.65 257.5 918.2 1175.7 68 290.5 .135 7.40 259.8 916.5 1176.4 60 292.7 .139 7.17 262.1 914.9 1177.0 62 294.9 .144 6.95 264.3 913.3 1177.6 64 297.0 .148 6.75 266.4 911.8 1178.2 66 299.0 .152 6.56 268.5 910.2 1178.8 68 301.0 .157 6.38 270.6 908.7 1179.3 70 302.9 .161 6.20 272.6 907.2 1179.8 72 304.8 .166 6.04 274.5 905.8 1180.4 74 306.7 .170 5.89 276.5 904.4 1180.9 76 308.5 .174 5.74 278.3 903.0 1181.4 78 310.3 .179 5.60 280.2 901.7 1181.8 80 312.0 .183 5.47 282.0 900.3 1182.3 82 313.8 .187 5.34 283.8 899.0 1182.8 84 315.4 .191 5.22 285.5 897.7 1183.2 86 317.1 .196 5.10 287.2 896.4 1183.6 88 318.7 .200 5.00 288.9 895.2 1184.0 90 320.3 .204 4.89 290.5 893.9 1184.4 92 321.8 .209 4.79 292.1 892.7 1184.8 94 323.4 .213 4.69 293.7 891.5 1185.2 96 324.9 .217 4.60 295.3 890.3 1185.6 98 326.4 .221 4.51 296.8 889.2 1186.0 100 327.8 .226 4.429 298.3 888.0 1186.3 105 331.4 .236 4.230 302.0 885.2 1187.2 110 I 334.8 .247 4.047 305.5 882.5 1188.0 115 338.1 .258 3.880 309.0 879.8 1188.8 120 341.3 .268 3.726 312.3 877.2 1189.6 125 344.4 .279 3.583 315.5 874.7 1190.3 130 347.4 .290 3.452 318.6 872.3 1191.0 135 350.3 .300 3.331 321.7 869.9 1191.6 140 353 . 1 .311 3.219 324.6 867.6 1192.2 145 355.8 .321 3.112 327.4 865.4 1192.8 APPENDIX 373 PROPERTIES OF SATURATED STEAM Pressure Pounds Absolute. ! Tempera- ture Deg. F. Density Lbs. per Cu. Ft. Specific Volume Cu. Ft. per Pound. Heat of the Liquid, B.t.u. h Latent Heat of Evap., B.t.u. L Total Heat of Steam, B.t.u. H 150 358.5 .332 3.012 330.2 863.2 1193.4 155 361.0 .342 2.920 332.9 861.0 1194.0 160 363.6 .353 2.834. 335.6 858.8 1194.5 165 366.0 .363 2.753 338.2 856.8 1195.0 170 368.5 .374 2.675 340.7 854.7 1195.4 175 370.8 .384 2.602 343.2 852.7 1195.9 180 373.1 .395 2.553 345.6 850.8 1196.4 185 375.4 .405 2.468 348.0 848.8 1196.8 190 377.6 .416 2.406 350.4 846.9 1197.3 195 379.8 .426 2.346 352.7 845.0 1197.7 200 381.9 .437 2.290 354.9 843.2 1198.1 205 384.0 .447 2.237 357.1 841.4 1198.5 210 386.0 .457 2.187 359.2 839.6 1198.8 215 388.0 .468 2.138 361.4 837.9 1199.2 220 389.9 .478 2.091 363.4 836.2 1199.6 225 391.9 .489 2.046 365.5 834.4 1199.9 230 393.8 .499 2.004 367.5 832.8 1200.2 235 395.6 .509 1.964 369.4 831.1 1200.6 240 397.4 .520 1.924 371.4 829.5 1200.9 245 399.3 .530 1.887 373.3 827.9 1201.2 250 401.1 .541 1.850 375.2 826.3 1201.5 374 APPENDIX Temperciturs and l^eaf of Liquid 180 200 220 240 260 280 500 320 MO 360 380 Ldtenf Heat 640 660 880 900 920 940 960 980 025 0X)75 0.125 0.175 0225 Q275 0.325 0.375 0.425 0.475 li60 1130 n s i t y >-i<-Jofo\ HeatH 1200 D Temperature and Heofof Liquid 70 90 110 130 150 170 IPO 2|0 960 Lcitent Heat 9S0 1000 1020 1040 0.0025 0.007S 0.0125 Q0I75 0.0225 00275 00325 iiOO PowEt^ [-<-•• --D e n 5 I t 1120 1140 Total Heat-J 1130 Fig. 113. — Properties of Steam. "''^^ APPENDIX 375 CURVES OF THE PROPERTIES OF SATURATED STEAM (Reprinted from Power ^ Nov. 17, 1914) Explanation Heat quantities may be read to the nearest unit; that is, to within about one B.t.u. or degree F. for any pressure between 1 and 230 lbs. absolute. The upper part of the chart deals with pressures above atmosphere, and the lower part, pressures below atmosphere. To use the chart, find the given pressure on the left-hand scale, and follow the horizontal line at this pressure until it inter- sects the curve of the property sought; then follow vertically to the corresponding scale. If temperature is given instead of pressure, use the tempera- ture curve in place of the pressure scale. 376 APPENDIX 1350 1300 1250 1200 1150 1 100 1050 1000 950 900 850 800 - ,A ^ ^ ^/^'^ "^ ^ ^ ^ '/^ ~ <7/ e^^ g ^ ^ ^ ^ ^ ...ii!^ r^>^c^/ 2;^ ^ ^ ^ ^ ?? : ^ yy. ^^ y^ ^ ^ \'A c^ '/">* ^ c*^^ ^ ^ ^ 'yy^ g ^ y\p ^ ^C2 ^ /^ ^ ^ ^?c^ II 1.1, 1 ^ 1 h _ ^ ^ ^y-c^y^ % y^yy ^ -^^P^T-iS^ 5 ^^^^:I^^^ 1 ^^ ^ $ ^ g ^ ^ ^ ^ ^^ ^ ^ ^ ^ ^ >2j^ // ^ 5^^ ^ .^\X % ^S< ^ y^ y' P ^ ^ ^ ^<^ § s /^^ ^ '^,<^ g^ g $ ^ ^^^ ^ ^ -<<^ ^ ^ ^ S ^ /^ ^ ^y\ g ?^ g ^ ><: p^ ^5 g ^ S -^ ^ >3 >< ;>* >^ ' — ^ ^ o^ ^ ^ ^ P :^ ^ >- ^ t^ X^ ^ ^ >< >< >^ >< '^^ _,^^ r^ 6^ ^ € X >^ >< ^j" ^ ^ >< >< >< >< ^fo te^ .rit i: > X >^ >tr^ s^f ^ :^ .-"^ >^ 146 150 IM 158 1j62 1.66 1.70 MOLLIER DIAGRAM < STEAM > 174 Dd ■"I!" APPENDIX g 0i § 5i g s ^ ^ ^ ^1 S /; ^ •^ g ^••SZ' s^ S ^ 1 ^ ^ 7^ g ^ ^ ^ 3 S ^ ~r'--~- :^ ^2^ 7^ 2^ sa ^ 1 ^ ?^ ^^ :2f ^ ^ ^^^ i !^ ^ ^ ^ ^ ;2 ^ ^ ^ ;:^ ^ ^ ^ ^ ^^ s ^ p ;^ ^ g ^ g s fe ?^ ^ ^ ^ g ^ 1 s g pd S=: ;^ ^ ^.^ :^ ^ ^:j^ ^ ^ ^ S g s^ ^ ^^ ^ g ^ ^$ fe: ^ ^ ^ rr** g ;^ ^ ^ 1? ^ ^ p^ ^ *;l_ 2^ r ^ afura/-/'or? — Curve >< .^5*^ >< ^ ^ ^ ■= — . -^%; ^ ^>" n = ^ ^p^^ E ^< ><^ ^ ' _^_^ r >- :::^ • 5 -^ ^ >- 377 1350 1300 1250 1200 1150 1100 1050 1000 = 950 178 1.82 1.66 190 194 1.98 MOLLIER DIAGRAM 2j02 2D6 2J0 Key EMTROPY See page 378 for explanation. 378 APPENDIX MOLLIER DIAGRAM— EXPLANATION Total heat of steam, H, is plotted against corresponding values of entropy. The condition of the steam as regards press- ure and quaUty are denoted by diagonal lines (see key, page 377). Any two of these diagonals intersect at a point which establishes the total heat and entropy corresponding to the condition. ExA]MPLE 1. Find the total heat of steam at 100 lbs. press- ure absolute, and a quality of 95 per cent. Fu'st, determine the intersection of the 100 lb. pressure line with the .95 quality line. At the intersection, read the ordinate value, 1142 B.t.u. Ex.\MPLE 2. Find the total heat of steam at 100 lbs. pressure, absolute, and a temperature of 378°. From the steam table, p. 372, it is found that the given tem- perature is 50° higher than the temperature of saturation at 100 lbs. Referring to the ]\Iollier Diagram, find the intersection of the 100 lb. absolute line with the 50° superheat line. At this point read the ordinate value, 1215 B.t.u. Example 3. Find the condition of steam after it has ex- panded adiabatically from 100 lbs. absolute and 50° superheat to a final pressure of 15 lbs. absolute. The intersection of the 100 lb. line and the 50° superheat Une, on the chart, corresponds to an entropy of 1.636. Find where this entrop}' Hne intersects the 15 lb. curve. The corresponding quality is seen to be .916 and the total heat, 1070 B.t.u. Note that the difference between the initial and final heats, namely 1215—1070=145 B.t.u., is the heat available to do work on the Clausius cycle. This method is therefore useful to cal- culate the Clausius efficiency (see p. 235). Ex.^iPLE 4. Find the qualit}^ of steam from a throtthng calorimeter determination, data as on page 146. Take the calorimeter pressure as 15 lbs. and the absolute (high) steam pressure as 115 lbs. The superheat in the calorimeter APPENDIX 379 chamber is 10°. Find the intersection of the 15 lb. Une, on the chart, with the 10° superheat hne. The corresponding total heat is 1157 B.t.u. Find where the 1157 total heat line inter- sects the 115 lb. line (tracing horizontally to the left). This inter- section represents the condition of the steam before expanding, and the quality, from the chart, is .961. Note. When scaling the diagram and tracing constant entropy or constant total heat lines, a pair of dividers will be found convenient. '^y^ 380 APPENDIX PROPERTIES OF AMMONIA (GooDENOUGH and AIosher) T> Specific Volume Heat C ontent Temp. Deg. Fahr. Pressure, Heat Lb. per Sq. In., Abs. of Liquid Cu. Ft. per Lb. of Sat. Vapor Cu. Ft. per Lb. of Liquid. of Sat. Vapor. of Vapor- ization. -40 10.12 0.0234 25.45 -75.3 526.6 601.9 -35 11.74 0.0235 22.14 -70.2 528.2 598.3 -30 13.56 0.0236 19.35 -65.0 529.8 594.7 -25 15.61 0.0238 16.95 -59.8 531.3 591.1 -20 17.91 0.0239 14.89 -54.6 532.8 587.4 -15 20.46 0.0240 13.15 -49.4 534.3 583.6 -10 23.30 0.0241 11.63 -44.2 535.7 579.9 - 5 26.46 0.0242 10.32 -38.9 537.1 576.1 29.95 0.0244 9.19 -33.7 538.5 572.2 5 33.79 0.0245 8.20 -28.4 539.9 568.3 10 38.02 0.0246 7.34 -23.2 541.2 564.4 15 42.67 0.0248 6.583 -17.9 542.5 560.4 20 47.75 0.0249 5.920 -12.6 543.7 556 . 3 25 53.30 0.0250 5.336 - 7.3 545.0 552.2 30 59.39 0.0252 4.820 - 1.9 546.2 548.1 35 65.91 0.0253 4.364 + 3.5 547.4 543.9 40 73.03 0.0255 3.959 8.9 548.5 539.7 45 80.75 0.0256 3.599 14.3 549.7 535.3 50 89.09 0.0258 3.278 19.8 550.8 531.0 55 98.03 0.0259 2.992 25.3 551.9 526.5 60 107.7 0.0261 2.734 30.9 552.9 522.0 65 118.1 0.0263 2.503 36.5 554.0 517.5 70 129.2 0.0264 2.296 42.1 555.0 512.8 75 141.1 0.0266 2.109 47.8 . 556.0 508.1 80 153.9 0.0268 1.940 53.6 557.0 503.4 85 167.4 0.0270 1.788 59.4 557.9 498.5 90 181.8 0.0271 1.650 65.3 558.9 493.5 95 197.3 0.0273 1.524 71.3 559.8 488.5 100 213.8 0.0275 1.408 77.3 560.7 483.4 105 231.2 0.0277 1 . 305 83.4 561.6 478 . 2 110 249.6 0.0280 1.210 89.6 562.5 472.9 115 269.2 0.0282 1.122 95.9 563.3 467.4 120 289.9 0.0284 1.042 102.2 564.2 461.9 125 311.6 0.0286 0.970 108.7 565.0 456.3 APPENDIX 381 HYGROMETRY Hygrometry deals with the determination of the properties of mixtures of water vapor and air. Dalton's Law (p. 142) bears directly upon this subject and should be understood. It has been shown that a cubic foot of space at a given tempera- ture, tj can contain no more than a fixed amount of H2O vapor, regardless of the presence or absence of any other gas. This maximum amount is the weight of a cubic foot of saturated steam at the existing temperature, t. Supposing that the cubic foot of space contains air at the same time that it contains the maximum amount of H2O corre- sponding to the temperature, t. Then the air is said to be ^^ satu- rated,^' and to have 100 per cent relative humidity. If, however, there is less vapor than this present, Per cent, Relative Humidity __ Weight of water present, pounds per cubic foot ^^ Density of saturated steam at / degrees The relative humidity is determined by the " wet-and-dry bulb" thermometer, or '' psychrometer.'' This instrument con- sists of two thermometers, the bulb of one of which is kept wet by surrounding it with a wick saturated with water at room tem- perature. The evaporation from this wick lowers the tempera- ture of the wet bulb. The dryer is the room air, the lower is the wet bulb temperature; hence the difference between the indica- tions of the two thermometers is a measure of the humidity. The following table, taken from Kent's Mechanical Engineers' Pocket- book, may be used: 382 APPENDIX Relative Humidity f, Per Cent Difference between the Dry and Wet Thermometers, Deg. F. Dry Ther- 1 1 1 1 1 1 n mometer, 1 2 3 4 5 6 7 8 9 10 11 12 13 14115116117 18 19|20|21|22|23|24|26|28j3C| Deg. F. 1 1 1 1 1 Relative Humidity, Saturation being 100. (Barometer =30 ins.) 32 89 79 69 59 49 39 30 20 11 2 40 92 83 75 68 60 52 45 37 29 23 15 7 50 93 87 80 74 67 61 55 49 43 38 32 27 21 16 11 5 60 94 89 83 78 73 68 63 58 53 48 43 39 34 30 26 21 17 13 9 5 1 70 95 90 86 81 77 72 68 64 59 55 51 48 44 40 36 33 29 25 22 19 15 12 9 6 80 9u 91 87 83 79 75 72 68 64 61 57 54 50 47 44 41 38 35 32 29 26 23 20 18 12 7 90 96 92 89 85 81 78 74 71 68 65 61 58 55 52 49 47 44 41 39 36 34 31 29 26 22 17 13 100 96 93 89 86 83 80 77 73 70 68 65 62 59 56 54 51 49 46 44 41 39 37 35 33 28 24 21 110 97 93 90 87 84 81 78 75 73 70 67 65 62 60 57 55 52 50 48 46 44 42 40 38 34 30 26 120 97 94 91 88 85 82 80 77 74 72 69 67 65 62 60 58 55 53 51 49 47 45 43 41 38 34 31 140 97 95 92 89 87 84 82 79 77 75 73 70 68 66 64 62 60 58 56 54 53 51 49 47 44 41 38 For example, if the wet bulb indicates 60° and the dry bulb 70°, then the difference is 10° and the humidity is 55 per cent. Calculation of pressures and weights of air, water vapor, and mixture. The following notation will be used, all pressures in pounds per square inch absolute, and weights in pounds per cubic foot. Pmy T7m = pressure and weight of mixture; Pay TFa = partial pressure, and weight of the air; Pc, ir^^ partial pressure and weight of the vapor; Pj T^ ' = pressure and weight of saturated steam at tempera- ture, t; < = temperature, degrees F., of the mixture; //"^ relative humidity, per cent. To find partial pressures, given total pressure, temperature and humidity. Find P' from the steam tables, corresponding with t. Then P.-jqqXP', and ■* a — -1 m -* r I APPENDIX 383 The pressure of the mixture is to be found from the barometer, and the humidity as previously described. For example, if the barometer reads 29.33'', the corresponding Pm = 14: Al lbs. per square inch. Suppose the relative humidity is 55 per cent and the temperature of the mixture is 70°. From the steam tables (p. 370) saturated steam at 70° has a pressure of 0.363 lbs. ( = P0- Hence, the partial pressure of the vapor in the mixture is P. = .55X0.363 = 0.2 lb., and Pa = 14.41 -.2 = 14.21 lbs. To find weights, given partial pressures, temperature and humidity. Find TF' (density) from steam tables corresponding to t. Then \\t 100^^^ ' 144P ^''' ^ 53.4 X (^+460) ' fr««^^^=«7^; For example, using the previous data, the density of saturated steam at 70° is 0.00115( = #''). PF„ = .55X.00115 = .00063; _ 144X14.21 ^"-53.4X530 =-0^25, TF„ = .00063 + .0725 = .0731. 384 APPENDIX REPORTS OF EXGIXEERIXG TESTS A complete report should describe concisely the experimental object and how it was accomplished, and it should give numerical results and the conclusions formed from them. Whether the report is upon work perform.ed by a student in the laboratory, or by an engineer in practice, its material ma}^ be arranged to advantage under the following heads. (1) Object of the test. (2) Description and principles of apparatus tested. (3) Method of testing. (4) Sample calculations. (5) Results and curves. (6) Discussion. (7) Rough notes or condensed observations. The subjects under these sub-heads ma}^ be treated as follows. (1) Object of the Experiment. This should be a clear, complete, and concise statement, preferably in one sentence. Its purpose, in practice, is to enable the reader to decide without a full reading whether or not the contents of the report come within his scope of interest. In student work, it should be included as a matter of training. In any case, the object of the test should be stated in writing before its performance in order that the experimenter and others concerned shall have a clear view of the undertaking. (2) Description and Principles. This division should deal only with the machine, instrument, or apparatus tested. The extent of the treatment is governed by the requirements of those for whom the report is intended. A report prepared as a technical article or address kills itself if it talks over the heads APPENDIX 385 of its audience or bores them with details with which they are familiar, however much satisfaction it may give the author. This is a matter for judgment. A good rule to follow is to give complete descriptions only of new or little known appa- ratus; for others it is sufficient to give only commercial sizes and names. It should be remembered, however, that any dis- tinctive feature or any characteristic affecting the test results should be fully described. This depends upon the object of the test. For example, in the report of a mechanical efficiency test of a steam engine, it is appropriate to describe thoroughly anything affecting friction in operation such as lubrication details, balancing of valves, etc. But if the same engine were tested for its steam distribution, lubrication need not be men- tioned at all; the valve mechanism then being the important item. In this division there may be deduced any formulas used in getting results provided they are original or unusual. Otherwise, they may be quoted without deduction, with reference to the authority. (3) Method of Testing. A logical way to begin this subject is by reference to the formulas for the quantities sought. Each formula, reduced to the desired form, shows the quantities that must be directly measured. The means of measuring them may then be described. Usual instruments may be merely mentioned by name, but special apparatus (original, or applicable only to the particular test) should be described fully. Any limitations of apparatus or unusual facilities affecting the pre- cision of measurements should be mentioned to enable the reader to judge for himself the accuracy of the results. For the same reason, the duration of the test should be stated with such items as frequency of readings. In this connection it is a good plan to refer to a sample set of observations which may be included in division 7. (4) Sample Calculations. In practice, these should some- times be included to make clear the method of testing and as a 386 APPENDIX voucher of the accuracy of the calculations. They should be omitted if these points do not need amplifying. They should be brief, proceeding at once from the expression for the desired quantity, in which is substituted the test data, to the numerical result. The form under Test 56 {d) may be used as a model. Reports by students should ahva^^s contain sample calcula- tions. The student should bear in mind that sample means something representative of the whole. Therefore, if five different quantities are tested for, three times for each one in the same way, five samples are necessary and sufficient. If these tests were repeated by another method involving a different calcula- tion, ten samples are needed. If only one determination is made of each quantity, the sample must be all of the calculations to be representative. (5) Results and Curves. Numerical results should always be presented in the form of curves w^hen possible, and also as a table. This enables the busy reader to size up the report with- out fully reading it. Curves and tables should have definite titles and enough information to explain their meaning without reference to the text. Curve sheets should bear the scales of coordinates, and the axes should be scaled for ready reading. Where several curves appear on one sheet, their plotted points should be differentiated by such conventions as circles in out- line, solid, half solid, etc. The points should be clearly marked so that they will not be obliterated when the curve is drawn in. The student should take care to differentiate between results and observations. Sometimes observations are results, but this is seldom the case. Further, there may be many intermediary quantities between the two which should not be confused with results. If the object of the experiment is clearly stated, it will always show what should comprise the results; in case of doubt, it should be referred to. (6) Discussion. This should deal with the probal^le accuracy of the results as affected by the precision of the instruments and APPENDIX 387 methods used and as indicated by the concordance of the results; it should compare the results with corresponding ones from similar tests, records of which are available in hand-books or elsewhere; and it should give the conclusions to be formed relative to the performance of the apparatus tested and to the physical laws controlling the performance. The conclusions to be formed from a test are the most important part of experimentation, in fact, its very raison d^etre; so they should be fully given in the report. In practice, there w^ould be no value whatever to a test from which conclusions could not be, or were not, made. (7) Rough Notes, Observations. Complete reports should contain tables giving the observations in full so that their con- cordance and validity may be checked by the scientific investigator. When this is not considered necessary, a sample set may be sub- mitted, as for division 3. Students should include in reports the original notes taken in the laboratory, a loose-leaf note- book being used for convenience. Rough notes should be taken neatly and contain enough data not only to remind the experimenter of the noted quantities, but to enable an outsider without additional explanation to interpret them fully. Inexperienced observers, to save time, are prone to use arbitrary symbols or abbreviations in their notes, without meaning to anyone but themselves. The objec- tions to this practice are that the notes cannot be checked by others and the observer himself is apt to forget their meaning. In concluding the general subject of reports, it may be well to mention the custom of including in voluminous ones, as a sort of addendum, a synopsis of the whole work, relating briefly the results and conclusions. This enables the busy reader to get the gist of it without a full reading. In technical papers addressed to scientific societies, or published as pamphlets, such a synopsis should conclude the report. If published as an article in a technical journal, it should be at the commence- ment. 388 APPENDIX A METHOD FOR CONDUCTING STUDENT TESTS* The following method has been used with success at Syracuse Universitj\ The first laboratory work assigned is, as far as the equipment will allow, individual. After a little training in the methods of the work, the experiments are given as problems, the theory of which is taught in the classroom. In the laboratory the student is quizzed at intervals during his work, to insure that it be performed not as a matter of rote. Approximate calcula- tions from observations are exacted as the observations are obtained. It is a great mistake to allow the postponement of such calculations until after the test is completed. This point cannot be too strongly emphasized. It is far better to have an experiment only partly but intelligently done than to have a vast amount of observations leading to faulty results and a half- grasp of the principles. As the course advances, the tests, especially those upon large units, require more than one student to make all the neces- sary operations and measurements. For the successful conduct] of some, it is expedient to have four or five stations at each ofj which one observer is needed. These advanced tests are imder- taken in this way. In the classroom the students solve problems upon the principles involved and are given the special instruc- tions which they could not reasonably be expected to obtain for themselves. When they have shown a satisfactory understand- ing of the principles, they are allowed to proceed with the exper- imental work, conducted as follows: For a test requiring five * Abstracted from a paper by the present WTiter on ** The Teaching of Experimental Engineering," Educational Review, June, 1912. APPENDIX 389 stations, for instance, a squad of six men is selected. For the first fifteen minutes or so of the test, observers A and B are at station No. 1, C at No. 2, D at No. 3, E at No. 4, and F at No. 5. Then B moves to station No. 2, where he is instructed by C in its duties. As soon as B has become famiUar with them, C moves on to station No. 3 and is instructed by D concerning the work there, after which D moves to station No. 4 with E, and so on. The scheme can best be understood by the follow- ing schedule. STATION NO Time 1 2 3 4 5 10 : 00- : 15 AB C D E F : 15- : 20 A BC D E F : 20- : 25 A B CD E F : 25- : 30 A B C DE F : 30- : 35 A B C D EF : 35- : 40 FA B C D E : 40- : 45 F AB C D E Etc. The advantages of this method over shifting all the students at one time are obvious. There is absolutely no break in the accuracy of the observations or continuity of the test since only one man shifts at a time and he does not make measurements to be used before he has become somewhat familiar with the apparatus. The instructor is relieved of the small but essential details of instruction by the students themselves. Room is made for an additional man on the test without sacrificing the work of any of the others. A complete shift of every man can be made in a shorter time; in the example cited, the interval is thirty minutes. The time necessary for an observer at a station to instruct the newcomer varies, of course, with the duties of the station. In a boiler test the average time is about ten minutes, so that a complete shift of six men would be effected in sixty minutes. 390 APPENDIX If all the men shifted at once, the interval should not be less than ninety minutes, preferably two hours. The shifting is automatic. All that each student needs to know is the sequence of stations, and to remember that he is to move to the next one only when he has been relieved by, and has instructed his successor. It has been found of considerable advantage to include a station the duty at which is to maintain a ^^ General Log.'' This contains the observations from all the stations. The student in charge of it checks to some extent these observations upon recording them, and is required also to calculate roughly indicative results as the test proceeds. The log may be used for reference by all the students and enables a clearer view of the whole test. At the end of a complete shift, three of the men are replaced by three new ones, and put upon the final calculations under the instructor's supervision. When these are completed the resulting quantities are plotted on a large chart, in common use for all who have made the test. In the meantime the test is continued by the three new and the thiee old observers, the arbitrarily varied quantity of the test having been changed. At the end of the next complete shift, half the .men are again replaced, the ones remaining being the more recent ones. In this way each group of three men serves two complete shifts and makes the calculations from the observations of one. When all the results are in, their concordance is checked by the regularity of the plotted curves, and these are presented as a whole to the class for consideration. INDEX ABSORPTION DYNAMOMETERS Absorption dynamometers, 34 fan brakes, 38 hydraulic friction brakes, 36 Prony brakes, 34 rope brakes, 35 Accuracy, absolute, 1 evidence of, 4, 7 of instruments, 3 Air, blowers, 336 (see also Fan Blowers). compression, isothermal, 344 compressor efficiencies, definitions, 342 compressor losses, 340 compressor testing, 340 capacity, 342 efficiencies, 344 heat measurements, 346 indicator diagrams, 340, 343 separation of losses, 345 density, formula, 118 head, equivalent to water, 116 horse-power, definition, 336 gross, definition, 341 net, definition, 341 measurement (see Gas Meters). required for combustion, 188 steam mixtures, 383 thermometer, 132 velocity by anemometer, 124 A.L.A.M. rating of auto engines, 301 Ammonia, heat of the liauid, 333 measurements, 318, 324, 327, 331 tables, 380 aqua, concentration test, 325 heat of solution, 332 heat of the liquid, 333 specific gravity, 325 compressor, indicating, 319 pump test, 323 Analyses of coals, table, 163 Anemometer, calibration, 124 correction factors, 125 principles, 124 Angular velocity measurement, 30 Areas of circles, 368 Ash in coal, test, 167 A.S.M.E. standard of heat consumption, 229 Atomic w^eights, 181 Auto engine testing, 300 economy, 302 friction torque, 301 mechanical efficiency, 301 BRITISH THERMAL UNIT Auxiliaries of steam power plant, test, 247 condenser tests, 276 feed water heater, 281 Avogadro's law, 181 Barrel calorimeter, 152 Baume scale of specific gravity, 359 Belt dynamometers, 40 friction, formula, 158 , test for, 159 slip, allowance for, 337 test of, 157 tension, formula, 158 test for, 160 testers, 159 constants of, 161 transmission, efficiency test, 159 Bilgram diagram, 213 use in valve setting, 214, 217 Blowers, 304 (see also Fa^i Blowers). Boiler, flue gases, excess air, 183 horse-power, definition, 264 leakage, heat lost to, 232, 249 test of, 232 performance, units expressing, 263 test calculations, 270 testing, coal measurements, 267 efficiencies, 272, 275 feed-water measurements, 268 heat losses, 273 sampling flue gas, 193 starting and stopping, 265 various results, 275 Brake, constant, definition, 35 fan, 38 calibration, 38 horse-power constant, 39 Brakes, friction, 34 constants, 35 hydraulic, 36 rope, 35 unbalanced weight, test, 37 Brake horse-power, definition, 35 test, 224 Brine, measurement, 316 specific heat of, 317 pump test, 323 British standard of heat consumption, 228 steam engine efficiency, 234 British thermal unit, definition, 149 391 ^ 392 DCDEX #1 III HI ill CALORIFIC VALUE Calorific value, 170 [^s€t aho Heat Value). Calorimeters, 144, 172 {see also qualifying xcord). Calorimetric gas meter, 126 radiauon correction, 127 Calorimetr>- of steam, 139 Carbon, in coal, esumation of, 168 heat value of, 171 dioxide recorders, 190 monoxide, heat value of, 171 Carburetors, adjustment, 286 Carpenter's calorimeter, 148 Central laboratory- dj-namometer, 45 Centrifugal pump testing, 352 capacity, 353 eflficiencj-, 355 horse-power supplied, 354 independent variable, 353 Chronograph, 31 Circles, table of, 368 Clausius cycle, .235 eflBciency steam engine, 234, 378 Cla\-ton's analvsis of indicator diagrams, " 208, 230 Clearance of cylinder, testing for, 205 by indicator, 208 by mensuration, 206 by water quantity, 206 linear, definition, 205 volumetric, definition, 205 CO, analysis for, 195 reagents for, 193 CO*, analysis for, 195 reagent for, 193 significance of, 183 Coal, air required for complete combustion, 186 calorimeters, 172 carbon in, 168 classification of, 162 combustion of, 183 (see also Cotnbustion). commercial sizes, 164 constituents of, 163 heat value of, 171 {see also Heat Value). heat value calculation from analysis, 174 heat value test, 173 hydrogen in, 162, 168 proximate analysis of, 163, 166 sampling, 165 ultimate analysis of, 163 weighings for boiler test, 267 Coefficient, excess, definition. 181 effect upon products of combustion, 185 formula for (coal). 201 formula for (gas), 2Q4 of friction, of belts, formula, 158 definition. 156 test for, 159 variation of, 160 of oils, test for, 156 of performance, 314. 319 Coefficients for nozilea. test, 107 values of, 106 for orifices for gas, 122 for orifices for water, 119 DENSITY OF A GAS Coefficients for weirs, 97 Coffin planimeter, 84 Combining discordant observarions, 5 Combustible of coal, definition, 168 Combustion, of coal, 183, 198 {see also Boiler Testing) . air supplied, 199 effect of air upon, 183 flue gases from, 185, 186 incomplete, 183 vapor formed by, 200 complete theoreticaJ, definition, 188 formula for air required, 188 definition of, 179 of fuel, calculations from exhaust gas, 179 predetermination of exhaust gas, 185 of gas, 185. 201 (see also Gas Engine Test- ing) • air supplied, 203 calculations from exhaust gas analysis, 201 incomplete, 200, 204 of oU, 184 products of, 180 rate, definition, 264 Complete theoretical combustion, definition, 188 Compound engine test, 236 Condenser, leakage test of, 231 •measurement of steam, 232 surface test, 276 jet test, 280 Condensing calorimeter, 151 formula, 151 radiation correction, 153 water equivalent, 150 pyower plant, test, 246 Constants for steam engine testing, 223 Constituents of fuel, 162 of oil fuel, proportions, 184 Conventions for curves, 7 Conversion of units of gaging, liquid, 116 Cord, indicator, test, 60 Corliss valve setting. 220 Correction factor, definition, 93 Corrections for steam turbine perfcnrance, 246 stem, 137 Counter, continuous, 30 hand. 30 Couple, thermo-electric. 133 Cur.ves. conventiors for plotting, 7 Curve sheets, form of. 386 Cvlinder clearance, 200 (see alf-y Clearance). Cvlinder condensation, 230, 233 test, 233 Dalton'slaw, 142 D'Aubisson's efficiency of ram, 352 Dead center of steam engine test, 211 Density (see under required maieriaf) . of a gas, calculation from molecular weight, 197 INDEX 393 DIAGRAM Diagram (see under qualifying word). factor, 242 Discussion of test results, 387 Draft gage, 27 {see also Gage). Drying steam, apparatus for, 147 Drum motion of indicator, 57 {see also Indicator) . motion tester, Smallwood's, 61 applied to reducing wheel tests, 74 Duplex steam pump, test of valve motion, 250 Duration of time rate tests, 9 Duty of pumps, definition, 257 trials, 257 Dynamometers, absorption, 34 {see also Brakes) . allowance for friction, etc., 44, 48, 49 spring type, transmission, 46 calibration, 48 Central Laboratory, 46 Flather, 47 Van Winkle, 46 weight-arm type, transmission, 40 belt, 41, 44 calibration, 43 constants, 43 pillow block, 41 Webber, 42 Efficiency, air compressor, 342 auto engine, 300 blower, 339 boiler and furnace, 275 boiler, grate and cleaning, 275 boiler, overall, 272 centrifugal pump, 352 electric motor, 364 gas engine, mechanical, 290 gas engine, thermal, 295 hoist, 356 injector, 262 producer, cold gas, 308 producer, grate and cleaning, 312 producer, hot gas, 312 ram, 350 refrigeration machine, 315 steam engine, mechanical, 226 thermal, 234 steam pump, 252 steam turbine, 244 water turbine, 348 Electric motor, test, 362 Electrical horse-power, definition, 243 output, measurements, 244 Emerson dynamometer, 43 Endurance tests of lubricants, 362 Engine indicator, 50 {see also Indicator) . Equation, personal, 2 Equivalent evaporation, calculation, 272 definition, 264 Errors, accidental, 2 Error diagrams of indicator drum motion, 62 from reducing wheels, 75 FRICTION OF BELTS Errors of indicator diagrams, ordinates, 52 abscissas, 59 instrumental, 2 Error, number of digits for 1 per cent of, 2 Errors, personal, 2 Error, starting and stopping, 9 Evaporation, equivalent, 263, 271 factor of, 263 from and at 212°, 263 unit of, 263 Events of the stroke, measurement of, 218 Excess coefficient, calculation of, 275, 299 definition of, 181 effect upon combustion, 185 formulas, 201, 204 Exhaust gas analysis, 189 apparatus for, 189 calculations from, 201, 272, 296 reagents for, 193 samphng for, 193, 291 to be expected, formulas, 185 from boiler, calculations, 273 from different fuels, 185 from gas engines, calculations, 296 specific heat of, 273, 296 vapor, heat contained by, 143 variation with air excess, 185 Factor of evaporation, calculation of, 271 definition, 263 Fahrenheit scale, 131 Fan, brake, 38 {see also Brakes). blower testing, 336 air horse-power, 339 capacity, 338 curves for, 336 efl&ciency, 339 horse-power supplied, 337 independent variable, 336 Feed water heater test, 281 measurements, 268 of steam, 231 Fixed carbon in coal, test for, 167 Flash point of lubricants, 359 Flather dynamometer, 47 Flow of air through orifice, formula, 122 in pipes, test for average velocity, 117 of steam through orifice, 128 Flue gas analysis, 188 apparatus for, 189 calculations from, 198, 273 reagents for, 193 sampling for, 193 to be expected, formulas, 185 Flue gas, from dififerent fuels, 185 heat losses, 273 specific heat, 273 vapor, heat contained, 143 variation with air excess, 185 Forces, measurement of, 12 Francis' formula for weirs, 99 Free air, definition, 336 Friction of belts, formula, 158 test, 160 J 3W INDEX FRICTION, COEFFICIENT OF Friction, coefficient of, 156 (see also Coeffici- ent). definition, etc., 154 horse-power, definition, 223 test, 226 effect upon instruments, IS, 24, 43, 44, 49 of indicator drum, test, 60 of oil, test, 156, 360 testers, 156 (see also Oil Testers) variation of, 155 Fuel, constituents of, 162 consumption of power plant, test, 246 gas, 165 {see also Gas Fuels). oil, 164 (see also Oil Fuel). Fuels, theoretical reactions of, 183 (see also Combustion). Gage, draft, 28 calibration, 28 Kent's, 29 hook, 96, 100 pressure, 23 calibration of, 23 ** test," 24 testing apparatus, 24 constants of, 25 vacuum, 24 Gaging liquid, conversion of units, 117 specific gravity of, 28 Gas, air required for combustion, 188 analysis from assumed combustion, 185 analysis, exhaust, 189 (see also Exhaust Gas Analysis). Gases, calculation of volume ratio, 182 calculation of weight ratio, 182 Gas combustion, 185 (see also Combustion) . Gas engine, advance of ignition, 283 cycle, 282 exhaust gas, effect of excess air, 185 indicator diagrams, 282 test calculations, 292 test data, 293 testing, adjustment, 282 cylinder clearance, 205 duration, 292 eronomy, 290 efficiency, mechanical, 288 efficiency, thermal, 295 excess coefficient, 299 friction loss, 295 fuel consumption, 292 heat consumption, 294 heat lost in exhaust, 296 heat lost in incomplete combustion, 298 heat lost to jacket water, 295 heat lost to radiation, 298 sampling gases, 193 timing ignition, 285 timing by indicator, 287 timing valves, 284 volume of exhaust gas, 296 water vapor in exhaust, 297 fuels, constituents of, 162 HOIST. MECHANICAL ADVANTAGE Gas, fuels, heat value of, calculation of, lS5f 294, 306 definition, 170 table, 171 test, 178 fuel mixture, adjustment of, 285 fuel sampling, 178, 193, 291 meters, 91 (see also under foUoiring), aneniometer, 124 calorimetric, 125 gasometer, 94 orifice, 121 pitot, 115 venturi. 111 volume, 93 producer testing, 302 (see also Producer). standard cubic foot of, 171 Gasoline, constituents of, 164, 300 engine testing, 282, 300 (see Auto and Gas Engines). heat value of, 300 specific gravity, 300 Gasometer, 94 Geared pump test, 356 Goutal's formula for heat value, 177 Xlead of air, equivalent of, 116 Heat, balance, gas engine, 290 gas producer, 302 injector, 258 refrigeration plant, 329 steam boiler, 262 steam power plant, 249 consumed by a steam engine, 227 consumption of power plant auxiliaries, 249 consumption of pumps, 256 of steam in exhaust gas, 143 of steam, measurement of, 141 of steam mixed with perfect gases, 143 of steam, notation for, 140 unit, definition of, 139 value, 170 coal, calculation, 173 coal, test, 172 coals, table, 171 definitions, 170 elements, table, 171 gases, calculation, 179, 294 table, 171 test, 179 sampling for, 178, 193 oils, 171 test, 177 Heater, feed-water, test, 281 Heat transmission in condensers, 278, 280 Higher heat value, definition, IVO calculation, 189 test for, 178 Hit-and-miss gas engines, sampling gases, 291 Hoist, test of, 356 efficiency, 358 mechanical advantage, 356 INDEX 395 HOOK GAGE Hook gage, 98 zero ot, test, 100 Hooka's law, exceptions to, 19, 55 Horse-power constant of brake, 38 direct by planimeter, 84 Humidity of air, 142, 381 heat of, 143 table, 382 Hydraulic, friction brake, 36 ram testing, 350 capacity, 351 efficiencies, 351 independent variable, 351 turbine testing, 347 available horse-power, 248 best operating speed, 349 efficiency, 349 independent variable, 348 Hydrogen in coal by proxim.ate analysis, 168 density of, 197 heat value of, 170 specific heat of, 309 Hygrometry, 381 Ice melting capacity, 314 Ignition of gas engine, 283 Illuminating gas, constituents, 165 heat value, 171 (see also Heat Value). Incomplete combustion (see Combustion). Indicated horse-power, approximate for- mula, 224 error from, 225 direct by planimeter, 84, 226 gas engine, 288 steam engine, 224 pumps, 253 Indicator, applied to gas engine timing, 287 cord, testing of, 60 stresses in, 58 stresses produced by redv.cirg wheels, 68 diagrams, abnormal valve setting, 215, 287 air compressor, 340 air compressor analysis, 345 Clayton's analysis of, 208, 220 clearance from, 208 Clausius cycle, 235 combining, 239 compound engine, 240 correction of horizontal errors, 63 correction of reducing wheel errors, 74 correction of vertical errors, 55 efTect of inertia upon, 52, 57, 68, 72 errors of abscissas, 59 errors of ordinates, 52 error diagrams for, 62, 75 errors from reducing wheels, 71 factor, 242 faulty, 217 gas engine, 282 logarithmic coordinates, 208,230 mean height by polar planimeter, 76 mean height by Coffin planimeter, 85 LUBRICANTS, VISCOSITY Indicator, diagrams, sampling, 56 steam consumption Irom, 229, 238 steam engine, 51 valve setting by, 215, 222, 287 drum motion, errors of, 59, 71 effect of guide pulleys, 62 forces affecting, 57, 72 drum motion tester, Smallwood's, 61 drum motion, testing of, 61 drum spring tension, adjustment, 59 test, 59 engine, 50 reducing motions, 64 (see also Reducing), spring scale, test 53 springs, calibration of, 52 test apparatus, 54 pencil motion, test, 53 Injector, heat balance, 258 test, 257 Instruments, precision and accuracy, 3 Intercoolers, effect upon air compressor performance, 340 Internal combustion engines (see Auto and Gas Engines). Internal horse-power, steam turbine, 243 Isothermal compression of air, 343 J et condenser test, 280 Junker calorimeter, 177 Jvelvin's work scale of temperature, 132 Kent's draft gage, 29 Kerosene, constituents of, 164 heat value of, 300 specific gravity of, 300 Kilowatt equivalent of horse-power, 243 l^ap of slide-valve, measurement, 211 of Corliss valve, 220 Lead of slide-valve, measurement, 211 of Corliss valve, 220 Leakage, power plant, heat lost to, 249 Leakage test, boiler and piping, 232 condenser, 231 Lcar^ squares, method of, 20 Logarithmic coordinates, 208, 231 Logarithms, calculations, 365 tables, 366 Logs for boiler testing, 268, 269 Lost motion of duplex pump valves, 250 Lower heat value, 170 calculation, 179 test, 179 Lubricants, tests of, 358 endurance, 361 flash, burning and chill points, 360 friction, 361 specific gravity, 359 viscosity, 360 J 396 INDEX MAHLER'S CURVE Mahler's curve, 176 formula for heat value, 175 Manometer, conversion of readings, 23, 117 mercury, 106 water, 23 Mean effective pressure, aggregate, 237 correction of, 55, 63 definition, 50 equivalent, 238 gasoline engine, 301 Mean height of indicator diagrams, 76 by Coffin planimeter, 85 by polar planimeter, 76 Mechanical advantage of hoist, 357 Melting- and boiling-points, 137 Meters, flow {see under Gas^ Steam and Water). Mercury, pressure equivalent of, 23 specific gravity, 23 Method of least squares, 20, 54 of testing, reporting, 302 Mixture of gas and steam, pressure of, 142 for internal combustion engines, 285 Moisture in coal, test of, 166 in gas, test of, 310 Molecular weights, 182 Molecule-foot, definition, 181 MoUier diagram, 376 use of, 235 explanation of, 378 Motor, electric, test, 364 Napierian logarithms, 365 Ns, analysis for, 187 Natural gas, constituents of, 165 heat value of, 171 Net air horse-power, definition, 341 indicated horse-power, definition, 289 Notation, boiler test, 266 gas engine test, 293 gas producer test, 305 heat of steam, 139 Nozzles, water, 104 calibration, 106 coefficient measurement, 107 coefficient values, 105 formula, 104 O2, analysis for, 195 reagents for, 193 Object of tests, statement of, 301 Oil, air required for combustion of, 188 conibustion, 184 {see also Combustion). engine testing {see Auto and Gas Engines). fuel, constituents, 164, 183, 300 heat value of, 171, 300 heat value determination, 177 lubricants, 358 {see also Lubricants). specific gravity, 300 testers, constant of, 157 types, 156 PRODUCER, TESTING Optical indicator, 300 Optical pyrometers, 135 Orifice, flow of steam through, 128 gas, calibration, 122 coefficients, 122 water, calibration, 120 coefficients, 120 Orsat apparatus, 189 operation, 195 reagents for, 193 sampling for, 193 x^antagraph reducing motions, 64 Parr calorimeter, 172 formula, 173 Partial pressure of gases, 142, 276, 382 Pendulum reducing motions, 65 Pillow block dynamometer, 41 Piping, leakage test of, 231 Piston displacement, definition, 205 Pitot gas meter, 1, 15 best proportions, 116 formulas, 117 Pitot tube, traversing, 113 water meter, 112 mean velocity by, 115 Planimeter, Coflfin, 85 test of, 87 on circular diagrams, 90 polar, 76 adjustment, 83 equation, 77 horse-power by, 84, 226 testing, 83 zero circle, 77 radial, 88 Platform scales, 13 calibration, 14 leverage ratio, 14 sensitiveness, 14 test of rider, 15 Polar planimeter {see Planimeter), Power, measurements of, 33 units of, 33 Power plant, steam testing, 246 pump test, 356 Precision of instruments, 3 Pressure, 22 equivalents, 23 mean effective {see also Mean), partial, of gases, 142, 276, 382 standard, 171 units of, 22 Pressure gage, 23 calibration, 25 recording, 26 Producer gas, constituents, 165 density calculation, 307 heat value, 177 heat value calculation, 306 specific heat of, 309 Producer, heat balance of, 302 test calculations, 305 testing, 302 INDEX 397 PRODUCER, TESTING Producer, testing, air supplied. 307 capacity, 312 efficiencies. 308, 312 heat in cool gas, 308 heat lost to refuse, 311 heat lost to scrubber, 310 heat lost to steam, 309 necessary data, 305 notation, 305 radiation, 311 sensible heat, 309 starting and stopping, 303 steam supplied, 308 vaporizer water, 304 volume of gas, 306 weight of dry gas, 307 Products of combustion, 180 Properties, of ammonia, 380 of steam, chart, 374 explanation, 140 Mollier diagram, 376 tables, 371 Prony brake, 34 (see also Brakes). Proximate analysis of coal, 166 calculations from, 270, 305 carbon estimation, 168 heat value estimation, 175 hydrogen estimation, 168 sampling, 165 table, 163 Psychrometer, 381 Pulsometer test. 262 Pump slip, 253. 255 Pump testing (see Steam and Centrifugal Pumps, Ammonia, Brine^ " Powers'* Injector, Pulsometer, Ram). Pyrometers, 135 calibration, 136 Vuality of steam, 142 sampling for, 144 tests for, 145, 149, 151 R for air, value of, 143 Radial planimeter, 16 Radiation correction, calorimetric gas meter, 127 condensing calorimeter, 147 Parr calorimeter, 173 separating calorimeter, 148 throttling calorimeter, 149 Rankine cycle, 233 Rankine's efficiency of ram, 352 Rating of auto engines, A.L.A.M., 301 Ratio of expansion, 242 Reactions of fuels, theoretical, 183 (see also Combustion) . Reagents for exhaust gas analysis, 193 Recording instrument charts, 88 averaging, 90 Recording instruments, CO2 analyzer, 190 flow meters, 101, 110, 127 gages, 26 STEAM CALORIMETERS, SAMPLING FOR Recording instruments, tachometers, 30 thermoinetors, 133 V-notch weir, 101 Reducing motions, 64 calibration of, 66 errors of, 66 Reducing wheels, 67 effect of friction, 77 errors produced by, 71 force of acceleration of, 72 forces in operation, 68 testing, 73 Refrigerating effect, 313 Refrigeration plant tests, absorption, 321 compression, 313 heat balance, 329 Reports of engineering tests, 301 Riehle oil tester, 157 Rope brakes, 36 (see also Brakes). Rules for testing, 8 Sample calculations in reports, 303 Sampling, box, 194 coal, 165, 172 exhaust gas, 190, 291 fuel gas, 178, 193 indicator diagrams, 56 producer gas, 304 steam, 144 Separating calorimeter, 148 calibration, 149 radiation correction, 150 Simmance-Abady CO2 recorder, 192 Slide-valve setting, 210 effects of adjustments, 210 equal cut-offs, 213 equal leads, 212 by indicator, 215 lead measurement, 211 Slip of belts, 160 Slip of pumps, definition, 253 Specific gravity, Baum^ scale, 359 conversion, to Beaum6 scale, 359 Specific heat, flue gas, 273 test for, 255 of brine, 317 gas engine exhaust, 296 producer gas, 309 Speed regulation of engines, 224 Spring instruments, calibration, 18 Spring scale, test for, 19 Standard cubic foot of gas, 171 pressure and temperature, 171 Standards, primary and secondary, 3 Standard thermometric scale, 133 weight gage tester, 25 Starting and stopping boiler tests, 265 producer tests, 303 Steam boiler testing, 262 (see also Boiler). Steam calorimeters, 144 barrel, 152 condensing, 151 radiation corrections, 147, 150, 153 sampling for, 144 398 INDEX STEAM CALORIMETERS, SEPARATING Steam calorimeters, separating, 148 throttling, 145 water equivalent, 152 Steam, chart of properties, 374 consumption, 227 consumption tests, 227 injector, 257 power plant auxiliaries, 247 pumps, 256 refrigerating machines, 322, 335 steam engine, 229, 237 turbine, 244 distribution in engine, 218 Steam engine, constants, 224 indicator diagrams, 51,215, 216, 240 testing, cylinder clearance, 205 (see also Clearance). cylinder condensation, 234 dead center, 211 economy, 227 efficiency, mechanical, 223 efficiency, thermal, 234 multiple expansion, 236 valve setting, 210 (see also Slide-valve). Steam, from coal combustion, formula, 201 from gas combustion, formula, 203 heat content, 200 (see also Heat). definitions, 139 notation, 140 measurements, 141 tables, 371 meters, 127 calibration, 130 Curnon, 128 General Electric Co., 128 St. John, 129 Venturi, 129 power plant testing, 246 auxilaries, 247 engine, 247 heat balance, 249 leakage, 249 properties, chart, 374 tables, 371 MoUier diagram, 376 pump testing. capacity, 299 duty, 257 economy, 256 efficiency, mechanical, 255 efficiency, thermal, 257 losses, 255 slip, 255 valve setting, 250 quality tests, 145, 149, 151 sampling, 144 tables, 371 turbine testing, 242 corrections for pressure, etc., 245 economy, 243 horse-power output, 243 internal horse-power, 243 losses, 244 valve laps, measurement, 211 valves, 212 VARIABLES, DEFINITIONS Stem corrections, thermometers, 137 Student tests method of conducting, 388 Suction diagram, gas engine, 289 Sulphur, heat value of, 171 Surface condenser test, 276 Tachagraph, 31 Tachometer, 30 calibration, 30 recording, caUbration, 33 Temperature, definition, 131 measurement, 131 standard, 170 Testing, rules for, 8 Thermal unit, definition, 139 Thermo-electric pyrometers, 133 Thermometers, 131 calibration, 133 constant volume, 133 electric resistance, 135 gas, 132 materials of, 131 mercury-in-glass, 132 recording, 133 scales, 132 stem corrections, 137 wet-and-dry bulb, 381 Thermometry, 131 Thoma.s gas meter, 126 Throttling calorimeter, 145 formulas, 146 radiation correction, 147 Thurston oil tester, 157 Timing gas engines, ignition, 285 valves, 254 Transmission dynamometers, 40, 46 (see also Dyyiamometers) . Trapezoidal weir formula, 99 Traversing pitot tube, 113, 117 Turbine (see Steam Hydraulic). Uehling CO2 recorder, 191 Ultimate analysis, table, 163 heat value from, 175 Unbalanced weight of brake, 37 Unit of evaporation, definition, 263 U-tube, 23 (see also Manometer). Vacuum gage, 24, 277 testing apparatus, 24 Vacuums, ideal and actual, 277 Valve motion of a duplex pump, 250 setting (see Gas Engine Testing, Slide- valve and Corliss Setting, Steam Pump Testing). Van Winkle dynamometer, 45 Vapor tension, 142 tables, 370 Variables, definitions, 6 ' INDEX 399 VELOCITY, ANGULAR Velocity, angular, 30 of approach of weirs, 97 head of air, 336 measurement of gases, 111, 115, 121, 123, 125 of steam, 127, 149 of water, 96, 104, 106, 112, 115 Velocities in pipe section, 113 Venturi, gas meter. 111 calibration, 111 water meter, 107 calibration, 109 coefficients, 108 coefficients, text for, 109 formula, 108 recorder, 110 Viscosity of lubricants, 358 test, 360 V-notch weir formula, 99 recorder, 101 Volatile matter, definition, 162 test, 167 Volume, gas meters, 93 calibration, 95 correction factors, 93 measurement of gas, 93, 306 of steam, 127 of water, 92 water meters, 91 calibration, 92 correction factors, 93 Volumetric efficiency, air compressor, 342 vrater equivalent of steam calorimeter, 152 of Parr calorimeter, 173 ZEUNER DIAGRAM Water, horse-power, definition, 252 test, 253, 347, 353 meters, nozzles, 104 orifice, 119 pitot, 112 venturi, 107 volume, 92 weirs, 96 pump testing, 347 (see Steam and Centri- fugal Pumps, Injector, Pulsometer, Hydraulic Ram). turbine testing, 347 (see under Hydraulic) , weight of, 23 Webber dynamometer, 42 Weights, measurement of, 12 table of, 369 Weir calibration, 100 coefficients, 97 test for, 100 values of, 98, 99 formulas, Francis', 98 rational, 97 trapezoidal, 99 V-notch, 99 velocity of approach, 97 Willans' law, 232 Work scale of temperature, 132 i^ero circle of planimeter, 77 equation, 77 measurement of, 81 of h(;ok gage, 100 Zeuner diagram in valve setting, 218 J D. VAN NOSTRAND COMPANY are prepared to supply, either from their complete stock or at short notice, TECHNICAL BOOKS OF EVERY DESCRIPTION in addition to publishing a very large and varied number cf Scientific and Engineering Books, D. Van Nostrand Company have on hand the largest assortment in the United States of such books issued by American and foreign publishers. All inquiries are cheerfully and care-- fully answered and complete catalogs and special lists sent free on request. 25 PARK PLACE - - NEW YORK i ^ Deacidified using the Bookkeeper proc< Neutralizing agent: Magnesium Oxide Treatment Date: June 2004 PreservationTechnologif A WORLD LEADER IN PAPER PRESERVAT 1 1 1 Thomson Park Dnve Cranberry Township. PA 16066 (724)779-2111