Gornell University Library Dthaca, New York THE LIBRARY OF EMIL KUICHLING, C. E. ROCHESTER, NEW YORK THE GIFT OF SARAH L. KUICHLING 1919 Cornell University Library YJ 250.R21 A manual of the stea MI) (init 005 020 A MANUAL OF THE STEAM ENGINE, AND OTHER PRIME MOVERS. Professor Hankine’s SERIES OF PRACTICAL MANUALS oN CIVIL ENGINEERING AND MECHANICS, Crown 8vo. ee APPLIED MECHANICS; COMPRISING Provcies oF Stratics, CiIveEMATICs, AND Dynamics, AND THEORY OF STRUCTURES, MECHANISM, AND MACHINES. With numerous Illustrations, price 12s. 6d. THE STEAM ENGINE, AND OTHER PRIME MOVERS. With numerous Tables and Illustrations, price 12s. 6d. CIVIL ENGINEERING; COMPRISING Enxaiverntne Survers, EARTHWORK, FounDATIONS, Masonry, CARPENTRY, METAL- Works, Roaps, Rattwars, Canars, Rivers, WaTER-Works, Harsours, &c. With numerous Tables and Illustrations, price 16s. USEFUL RULES AND TABLES FOR ARCHITECTS, BUILDERS, CARPENTERS, ENGINEERS, FOUNDERS, MECHANICS, SHIPBUILDEBS, AND SURVEYORS. With numerous Tables and Illustrations, price 98. MACHINERY AND MILL WORK} COMPRISING GxromeTry or Macaivery, Dyxamics or Macminery, Marertars, STRENGTIC AND Construction or Macuivery. With numerous Tables and Illustrations, price 12s, 6d. A MANUAL OF THE STEAM ENGINE AND OTHER PRIME MOVERS. BY WILLIAM JOHN MACQUORN RANKINE, CIVIL ENGINEER; LL.D. TRIN. COLL. DUB.; F.R.SS. LOND. AND EDIN.; F.R.8.S.A 3 REGIUS PROFESSOR OF CIVIL ENGINEERING AND MECHANICS IN THE UNIVERSITY OF GLASGOW; . ASSOCIATE MEMBER OF COUNCIL OF THE INSTITUTION OF NAVAL ARCHITECTS, AND OF THE PHILOSOPHIC SOCIETY OF SCOTLAND; PAST-PRESIDENT OF THE INSTITUTION OF ENGINEERS AND SHIPBUILDERS IN SCOTLAND; CONSULTING ENGINEER OF THE HIGHLAND AND AGRICULTURAL SOCIETY OF SCOTLAND; MEMBER OF THE INSTITUTION OF MECHANICAL ENGINEERS}; HONORARY MEMBER OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES, OF THE ROYAL ACADEMY OF SCIENCES OF SWEDEN, OF THE LITERARY AND PHILOSOPHICAL SOCIETY OF MANCHESTER, OF THE ROYAL SOCIETY OF TASMANIA, OF THE LITERARY AND PHILOSOPHIC SOCIETY OF LIVERPOOL, OF THE HISTORIC SOCIETY OF LANCASHIRE AND CHESHIRE, OF THE SOCIETY OF NATURAL SCIENCES OF CHERBOURG, ETC. ETC. With Bunerous Engravings, AND A DIAGRAM OF THE MECHANICAL PROPERTIES OF STEAM. SIXTH EDITION, REVISED. LONDON: CHARLES GRIFFIN AND COMPANY, STATIONERS HALL COURT. 1873. [The Author reserves the right of Translation.] +" GLascow!: BELL AND BAIN, PRINTERS, MITCHELL STREET. PREFACE TO THE FIRST EDITION. THE purpose of this book is to explain the scientific principles of the action of “ Prime Movers,” or machines for obtaining motive power, and to show how those principles are to be applied to practical questions. It has been deemed advisable to prefix to the Treatise a very brief Historical Sketch, relating chiefly to the Steam Engine, the only prime mover whose history is known. The body of the work commences with an Introduction, treating of principles, and of mechanical contrivances, which are common to all prime movers, and of the laws of the strength of materials, so far as they are applicable to those machines. Some passages in the Introduction are extracted from a previous Treatise on Applied Mechanics, and abridged or amplified as may be required, in order to suit the purpose of the present Treatise. Such passages are indicated by the letters A. /., with a reference to the number of the corresponding Article in that work. The first part following the Introduction treats of the use of muscular strength to obtain motive power. The second part treats of prime movers driven by the motion of water and of air, including water-pressure engines, waterwheels, turbines, and windmills. The third and largest part treats of engines driven by the me- chanical action of heat, and especially of the steam engine. It ex- plains, in the first place, the phenomena of heat, so far as they affect, directly or indirectly, mechanical action in engines; secondly, the laws of combustion and properties of fuel, and the principles upon which economy of fuel depends; thirdly, the laws of the action of heat in producing motive power, or “ PRINCIPLES OF THERMODYNAMICS,” as applied to the various engines in which that action takes place, and especially to steam engines of all varieties ; fourthly, the nature and action of the parts of furnaces and boilers ; fifthly, the nature and action of the mechanism of steam engines. The fourth part explains the principles of the action of electro- vi PREFACE. magnetic engines; but very briefly, in consideration of their small importance as prime movers, and absence of economy; the true practical use of electro-magnetism being, not to drive machinery, but to make signals; and the subject of telegraphy being foreign to the purpose of this work. The principles of thermodynamics, or the science of the me- chanical action of heat, are explained in the third chapter of the third part more fully than would have been necessary but for the fact, that this is the first systematic treatise on that science which has ever appeared; the only previous sources of information re- garding it being detached memoirs in the transactions of learned societies, and in scientific journals.* The experimental and practical examples used to illustrate the application of the principles of that science, and of rules and tables deduced from them, are, to a considerable extent, taken from the Author’s personal observations of the performance of marine engines. At the end of the book, as well as interspersed through it, are various tables, useful in calculations respecting prime movers, especially the steam engine; and many of those tables contain results which have never before been published. The Author has endeavoured to the best of his ability and recollection to acknowledge, in the course of the book, the sources from which he has derived information. For much of that informa- tion, for opportunities of inspecting furnaces, boilers, and engines, and of making experiments, and in some cases for drawings of engines, which have been reduced to a small scale to illustrate this work, he has to return his most grateful thanks to many engineers, shipbuilders, manufacturers, and men of science. Guascow University, 22d September, 1859. W.J.M.R. The Sixth Edition has been carefully revised, and augmented by information relating to recent discoveries and inventions, W. J. MR. Guascow University, Dec., 1872, * Since the ahove was written, several treatises on Thermodynamics have appeared ; gongs which may be specified, in German, the works of Clausius and of Zeuner ; in French, those of Hirn, Saint-Robert, Cazin, and Briot; in English, those of Balfour Stewart, and of Tait—the last-mentioned book being valuable for its cle the different methods followed by the original investigators of the mabieck. Sane CONTENTS. Page HisroricaL SKETCH, RELATING CHIEFLY TO THE STEAM ENGINE, *. . XV INTRODUCTION,—OF MACHINES IN GENERAL, Sxction 1.—Of Resistance and Work. Art. Page Diction of a Machine, . S . Work, its definition and measures, . Rate of Work—Horse-power, . » Velocity, . Work in Terms of “Angular Motion, . Work in Terms of a and Volume, 3 Table of Units of Pressur 2, . Algebraical Expressions for Work, . Work against an Oblique Force, . . Summation of Quantities of Work, Reduction of Resistance to Driv amb ote AAO ONNe oma ing Point, . 7 10. Representation of Work by an Area, . 8 11. Work against varying Resistance, 9 lla. qpeesmae Computation of sat 12. van a ork anid Lost Work - 18 13. Friction, . - id 14. Ungnents, . 16 14 a. Work of ‘Acceleration—Mass— Momentum (see paye xiv.). . 18 15. Summation of Work of Accelera- tion — Moment of Inertia — Inertia reduced to Driving Point, . 21 16. Summary of various kinds of Work, . A A 7 . 24 Srcrion 2.—Of Deviating and Centri- Jugal Force. 17. Deviating Force of a Single Boum, 25 18. Centrifugal Force, 26 . . 19, Revolving Pendulum, . is 26 20. Deviating Force in Terms of Angu- lar Velocity, . - 26 21. Resultant Centrifugal Force, « Se 22. Centrifugal Rong Eau Axis, . 27 Section 3.—Of Fffort, Pits Prniee and Efficiency. 23, Effort, a ese 0) 24. Condition of Uniform Speed, - 3l 25. Energy—Potential Energy, 82 26. eu ity of Energy exerted and ae erformed, - 82 27, various Factors of "Energy, - 83 28, Energy exerted in Acceleration, . 33 Art. 29. Accelerating Effort, . - « 33 30. Work during ‘Retardation — Energy Stored and ee 35 31, Actual Energy, . . . 35 32. Reciprocating Force, . - . 36 33, Periodical Motion, . ‘ = Of 34. Starting and Stopping, ‘ . 38 35. Efficiency, . 388 36. Power and Effect —Horse-power, 40) 37. General Equation and Principle, . 40 Section 4.—OQf Dynamometers. 38. Dynamometers defined and cly ae 40 89. Friction Dynamometer, - 41 40. Traction Dynamometer, . 42 41. Kotatory Dynamometer (sec p. 80), 45 42, Integrating Dynamometers, . 46 43. Indicator—Application to the Steam Engine, . - 47 44, Indicator—Other Applications, . 52 Sxecrion 5.—Of Brakes. 45. Brakes Defined and Classed, « 82 46, Action of Brakes in gener. al, » 62 47, Block Brakes, . . » 53 48. Brakes of Carriages, . : . 54 49, Flexible Brakes, . . . do 50. Pump Brakes, . . «© « 56 51. Fan Brakes, “ ® i « 38 Section 6.—Of Fly Wheels. 52. Periodical Fluctuations of Speeds 59 53. Fly Wheels, Se 61 Section 7.—Of Regulators and Gover- nors in coe 54, Regulators, ee e162 55. Pendulum Governors, . . 63 56. Balanced Governors, . - 63 57. Fan Governors, . 5 . . 63 Sxcrion 8.—Summary of Principles of the Strength of Machines. 58. Nature and Division of the Subject, 64 59, Factors of Safety, . . . G4 60. Proof or Testing, » . 65 61. Tenacity of Bars, . . 66 62. suns Boilers and Pipes, ‘ 63. Spherical Shells, : . . 68 Thick Hollow Cylinder, . » 69 G5. Thick Hollow Sphere,. .« «~ U9 vill CONTENTS. Section 8.—Summary of Principles of the Strength of Machines—continued. Art. Page Art. 7 Page 66. BoilerStays, . . . . 69 72. Strength of Timber Posts, Struts, _ 67. Cylindrical Flues, $ F . 70 and Connecting Rods, . . 74 68. Elliptical Flues, . » « %1{| 73. Resistance to Cross Breaking, . 75 69. Shearing Force of Keys, Pins, 74, Resistance to Wrenching—Axles, 78 Bolts, and Rivets, . » 71 | 75. Twisting and Bending combined, ie 70, Resistance to direct Crushing , « 72] 76, Teeth of Wheels, 4 3 : 71. Resistance of Iron Rods and Pil- Srcrion 9.—Prime Movers Classed, a lars to Crushing by Bending, . 73 | ADpenpum—Dynamometers, . « 0 PART L—OF MUSCULAR POWER. CuapTer I,—GENERAL PRINCIPLES. 78, Nature of the Subject, * . 8 Time of Working, on Daily Work, 82 79. Daily Work—Circumstances af- 81. Influence of other circumstances— fecting it, ‘ ‘ “ ~ Bh Race, Food, Air, &., » 82 80. Influence of Load, Velocity, and 82. Transport of Loads, . P = BS CuapTer I].—Power or MEN. 83. Tables of the Performance of Men, 84 | 85. Lifting Weights by a Rope, . . 86 84. Work of a Man raising his own 86. Other modes of Exertion, . - 86 Weight, . oR a 85 | 87. Transporting Loads, . : IST Cuapter III.—Power or Horses AND OTHER Erasts. 88. Tables of the Performance of 90. HorseGin,. . . . . Horses, . - ss . 88] 91. Treadwheels for Horses and Oxen, 89. Oxen, Mules, Asses, . , . 89 —(See Appendiz,) . 2 . 89 PART IL—OF WATER POWER AND WIND POWER. CHarter I.—Or Sources oF WATER FoR PowEr. 92. Nature of Sources in general— 94, Measurement of a Source of Water Mill-site or Fall, . A ~ OL Power, . 7 ‘ i - 92 93. Power of a Fall of Water, . « 9h Cuarrer II.—Or Water Power ENGINEs IN GENERAL. 89 95. Parts and Appendages of Water and Jet Pump, . és - 98 Power Engines,—I. Head- 97. Water Power Engines with Arti- Race; II. By-Wash; III. Re- ficial sources, a r . 98 gulator ; - Engine Proper; 98. Form assumed by Energy of Fall V. Tail-Race, . 7 . 7 —Dynamic Head, . . - 98 96. Classes of Water Power Engines,— 99. Loss of Head—Available Head I. Water Bucket Engines; IT. and Power—Efficiency of the Water Pressure Engines ; III. Fall—Factors of Resistance, 100 Vertical Water Wheels; IV. 100. Action of the Water on the Turbines; V. Hydraulic Ram Engine, . A 3 is . 103 CuapTer II.—Or Water Bucker Enetes. 101. Water Bucket Hoist, ‘ . 105 | 103. Double Acting Bucket Engi 102. Loss of Head in Bucket Hoists, 106 i CHarter IV.—Or Water Pressure ENGINES. SECTION 1.— General Principles. 107 4. Pressure and Vacuum Gauges, 110 104, Parts. of a Water Pressure En- 108, Fixing Diameter of Supply Pipe, : 5 . 107 —(See also Article 140 A) . 112 gine, «te 105. Suction Pipes—Vacuum, . . 108 | 109. Effect of the Regulator, .° . 115 106. Least Atmospheric Pressure, . 109 110. Action of the Water on the Piston, 116 1u7. Expansion of Water by Heat— Comparison of Heads of Water Section 2.—Of Valves. with Pressures in other Units, 109 | 111. Valves in general, , < JAZ ‘ CONTENTS, CaarTer IV.—Or Water Pressure ENGINES—continued. 3 Page Pot-lid, or Conical 113. Giaccn Safety Valve (Relief va 112. Heme Clacks, see Article 134 a), . 119 114, Ball Clack, : » 120 115. Divided Conical Valves, . 120 116. Pee on Valve—Equili- um Valv 117. Flap Vz Valve -Butterft - 122 118. Flap and Grating oe: also Article 134 B), “ 3 119. Disc and Pivot or Throttle Valve, 123 120. Slide Valves, . . » 124 121. Piston Valves, . 6 gS. «1285 122. Cocks, - 126 123. Flexible Tube and Diaphragm Valves, . . - 126 Section 3.—Of Plungers, Pistons, and Packing of Water Pressure Engines. + 120 124. Plungers, » 127 125. Cupped Leather Collar, - - 128 126. Leather Packed Piston, 5128 127, Hempen Packing, . . » 129 Section 4.— Of Hydraulic Presses and Hoists. 128, Hydraulic Press, ; - 129 Art. Page 129, Direct Water Pressure Hoists and Purchases, ‘ « 133 180. Water Pressure Cage Hoist— Water Pressure Cranes, . . 134 Section 5.—Of Self-Acting Water Pressure Engines. 131. General Description, - «188 182, Single Acting Water Pressure’ Engine, . 140 133. Double Acting Water Pressure” Engine 134, Rotative Water Pressure Engines, 143 134. Relief Clacks, % 144 Supplement to Part IT., Chapter IV., Section 2. 134 B. Compound Clacks, . « 144 Szction 6.—Of Water Pressure Engines with Air Pistons. 135. Hungarian Machine, . . . 144 136, Tae Gece ‘ . 148 Supplement to Part It, Chapter L., Article 94. 136 a. Water Meters, . : . 148 CuapTer V.—Or-VerticaAL WATER WHEELS. Secrion 1.—General Principles. 187. Pond and Weir, . 150 138. Backwater, - 151 139. Waste sluices, . 153 140. Head-Race ard Sluices, « 153 140 a. Table of Squares and Fifth Powers, . % . 156 141. Regulating Sluice, - 4 « 156 142. Water Wheel Governors, . x 158 143. General Description of Vertical Water Wheels, . 160 Impulse of Water on Vanes, . 163 Best form of Vane to receive Jet—Poncelet’s Floats, 170 Effect of Friction during Impulse, 171 Direct Action distinguished from Reaction, 173 Efficiency of Vertical Water Wheels in General,—I. Weight and Impulse Wheels ; II. Im- ulse Wheels without and with eaction, . . 174 149. Choice of a Class of Wheels, a lit SEcTION 2.—Of Overshot and Breast Wheels. 150. Overshot and Breast ees Dis- tinguished, . « - 177 144. 145. 146. 147. 148. 151. Description of a Breast Wheel, . 178 152. Diameter of Wheel, . a . 180 153. Pinion and Cogged Rings, . 181 154. Strength of Gudgeons, . 181 155. Strengthof Arms, . 181 156. Speed and Dimensions of Shroud- i 8° ing, . Figure and Dimensions of Buc- 157. ets, « : : . . 183, 158. Guide Blades and Regulator, . 183 159. Breast—Tail-Race, . : . 184 160. Efficiency—Energy of Fall per Horse-Power, - 185 161. Overshot Wheels “at High” Speeds, SU oey 2 . 185 Section 3.—Of Undershot Wheels. 162. Description of a Poncelet Wheel, 186 163. Diameter of Wheel, . : - 186 164, Depth of Shrouding, . - . 187 165. Regulating Sluice, * - 187 166. Wheel Race, . . 187 167. Surface Velocity of Wheels, » 188 168, Vanes or Floats, - 188 Efficiency—Energy of Fall per Horse-Power, 2 @ 188 Wheel in an Open Current, « 185 169. 170. N 1.—General Principles. Art. Page Art SReriON ReDrEa EHD oe 179. Efficiency as ri by Teg, 171, Turbines generally Described and lator, Classed, « 189 aie i 172. Meleciey of Flow—Dimensions of Section 2.—Description of Various 173. Vacate of Whirl—Inclination of ees Vanes, . 180. Fontaine’s Turbine, . « 201 174, Efficiency without Friction, : "193 181. Jonval’s, or Koechlin & Co’s 175. Greatest Eeciengy without Turbine, . » « 203 Friction, . 196 | 182. Fourneyron’s Turbine - 204 176. Reaction Wheel, : 197 | 183. Various Outward Flow Tur- 177, Efficiency of Turbines, allowing bines, _. ¥ m » 205 for Friction, 184, Reaction Wheels, ‘ ‘ . 206 178. Volume of Flow and size of 185. Thomson’s Turbine or Vortex Orifices,. . « «© «© 200 Wheel, . - . 207 CuapTer VIJ.—Or Fiuip-on-Fiuip Imputse ENGINES. 186. Introductory Explanations, - 211 | 187 a. Jet Pump — Water ene 187. Hydraulic Ram, tg eed Blast Pipe. . . + 213 Cuarter VIII.—Or WInpDMILLs. 188. General Description, - 214|191. Best Speed, . . . . 218 189. General Principles, . 215 | 192, Power and Efficiency, - 218 190. Best Form and # Eropartions of 193. Tower Mill—Self-acting Cap, . 219 Sails, . . 217 | 194. Reefing, or Regulation of Suils,. 219 PART III.—OF STEAM AND OTHER HEAT ENGINES, 195. Nature and Division of the Subject, . . . . ‘ , & - 223 Cuarter I—Or ReLations aMonGst THE PHENOMENA or HEAt. 196, Heat defined and described, . 224 | 206. Pressure of Vapours—continued. Section 1.—Of Temperatures. bie pepe and Condensa- pies 197. Equal Temperatures, ¢ 225 viL "'Bhullition, » 241 198. Fixed Temperatures, + 225 VIIL. Resistance to Boiling, » 242 199. Degrees ot Temperature—Per- IX. Cloud or Nebulous Vapour, 242 si oe cat Spats ae i - 226 X. Superheated Vapour, . 242 . Different Thermometric Scales, . 227 201. Absolute Zero—Absolute Tem- F eEeneN 2 OF oe of Heat perature, 928 207. Comparison of Quantities of Heat 202. Expansion of Gases~Imperfect : ‘ ; ; 7? 7% Hollow cylinder or ring, external radius 7, internal 7’, ag Hollow cylinder or ring, insensibly thin, radius 7,...... er The square of the radius of gyration of a body rotating about an axis which does not traverse its centre of gravity, is equal to the square of its radius of gyration about a parallel axis traversing its centre of gravity, added to the square of the distance between those two axes, Il. Inertia Reduced to the Driving Point.—If by the principles of 24 INTRODUCTION. pure mechanism it is known, that in a machine, a certain moving piece whose weight is W, has a velocity always bearing the ratio n:1 to the velocity of the driving point, it is evident that when the driving point undergoes a given acceleration, the work performed in producing the corresponding acceleration in the piece in question is the same with that which would have been required if a weight ®? W had been concentrated at the driving point. Tf a similar calculation be performed for each moving piece in the machine, and the results added together, the sum gives the weight which, being concentrated at the driving point, would require the same work for a given acceleration of the driving point that the actual machine requires ; so that if , is the initial, and », the final velocity of the driving point, the work of accelera- tion of the whole machine is 2 2 Be at Wh aactvGitanacanncnccen (9.) 29 This operation may be called the reduction of the inertia to the driving point. Mr. Moseley, by whom it was first introduced into the theory of machines, calls the expression (8.) the “co-efficient of steadiness,” for reasons which will afterwards appear. In finding the reduced inertia of a machine, the mass of each rotating piece is to be treated as if concentrated at a distance from its axis equal to its radius of gyration e; so that if v represents the velocity of the driving point at any instant, and a the corresponding angular velocity of the rotating piece in question, we are to make 28) nm = Cdeeaminne da dauitetoca winnie 10,000 Fir, pine, ,, oy «Gacaundenamanaeeny 5,400 to 6,200 Teak, Indian, Sy ha ale Mislead Saeislemnwcieentadinoa 12,000 The resistance of timber to crushing, while green, is about one- half of its resistance after having been dried. 71. Besistance of Iron Rods and Pillars to Crushing by Bending (4. U., 327-335).—Pillars and struts whose lengths exceed their diameters in considerable proportions (as is almost always the case with those of timber and metal), give way, not by direct crushing, but by bending sideways and breaking across—being crushed at one side and torn asunder at the other. Let P be the crushing load of a long rod or pillar, in Ibs. ; S the sectional area of material in it, in square inches ; l, its length, h, its least external diameter, Then, approximately— S pa Sin vote reine, ecbiniasereievarersvatubdeie¥e (1.) lta \ both in the same units of measure. The following are the values of fand a, as computed from ex- periments on pillars FIXED AT BOTH ENDS, by having flat capitals and bases :— JS, Ibs. per inch. a. 4 I Wrought iron (round rods), ............. 36,000 ...... eT Cast iron (hollow pillars), ................ 80,000 ...... a A pillar or rod ROUNDED OR JOINTED AT BOTH ENDS is as flexible . aga pillar of the same diameter, fixed at both ends, and of double G4 INTRODUCTION. the length, and its strength is nearly the same. Hence, for such pilars— In the case of a pillar fixed at one end and jointed at the other, for the multiplier 4 in the denominator of the above formula, 2 16 substitute 7 : In using the formule, the ratio is generally fixed beforehand, to a degree of approximation sufficient for the purposes of the cal- culation. ConnectTine rops of double acting steam engines are to be con- sidered as in the condition of pillars rounded at both ends; Piston RODS, as in the condition of pillars fixed at one end and rounded at the other. The piston rods of single acting steam engines are exposed to tension only. In wrought iron framework and machinery, the bars which act as struts, in order that they may have sufiicient stiffness, are made of various forms in cross-section, well known as “angle iron,” “channel iron,” “'T-iron,” “ double T-iron,” &c. In each of these forms, the quantity represented by 2? in equation 1 is to be made equal to 16 times the square of the least radius of gyration of the cross-section. Wrought ton cells ave rectangular tubes (generally square) usually composed of four plate iron sides, rivetted to angle iron bars at the corners. The «ultimate resistance of a single square cell to crushing by the buckling or bending of its sides, when the thick- ness of the plates is not less than one-thirtieth of the diameter of the eell, as determined by Mr. Fairbairn and Mr. Hodgkinson, is 27,000 lbs. per square inch section of iron; but when a number of cells exist side by side, their stiffness is increased, and their ultimate resistance to a thrust may be taken at 33,000 to 36,000 Ibs. per square inch section of iron. The latter co-efficients apply also to cylindrical cells, 72. Strength of Timber Posts, Struts, and Connecting Rods.—The following formula is given on the authority of Mr. Hodgkinson’s experiments, for the ultimate resistance of posts of oak and red pine to crushing by bending :— ee TIMBER POSTS AND RODS—BIAMS. 73 S being the sectional area in square inches, /:2 the ratio of the least diameter to the length, and A = 3,000,000 Ibs. per square inch, The factor of safety for the working load of timber is 10. For square posts and struts, the formula becomes If the strength of a timber post be computed both by this for- mula and by the formula for direct crushing, viz.:— the lesser value should be adopted as the true strength. Timber connecting rods for steam engines, being in the condition of pillars jointed at both ends, are of the same strength with fixed pilars of double the length. 73. Wesistance to Cross Breaking.— The formule of this Article are applicable not only to beams for supporting weights, but to levers, cross-heads, cross-tails, axles, journals, cranks, and all pieces in machinery or framework to which forces are applied tending to break them across, The tendency of a force to bend or break a beam is called the moment of flecwre. It is the product of the magnitude of the force into its leverage—that is, into the perpendicular distance from the line of action of the force to the place where the beam will soonest give way. When the load is distributed over a finite length of the beam, the leverage of its resultant is to be taken. The place where the beam will soonest give way 1s— In a beam fixed at one end and free at the other, the boundary between the fixed and free parts ; In a beam supported at both ends and loaded at any intermedi- ate point, or supported at any intermediate point and loaded at the ends, the intermediate point; In a beam supported at both ends, with an uniformly distributed load, the middle of the beam, ; The magnitude of the load is most conveniently expressed in pounds,.and the leverage in inches; so that the moment of flecure may be said to be expressed in inch-pounds. ; In the following formule, W denotes the total load, in pounds ; c, in beams fixed at one end and free at the other, the length of the free part, in inches ; 76 INTRODUCTION. c, in beams either loaded or supported at both ends, the half span, between the extreme points of load or support and the middle, in inches ; M, the moment of flexure in inch-pounds. ( fixed at one end and loaded at the other,........ccce00e i M=¢W...... (1.) fixed at one end and uni- cw formly loaded, .............4. \ M=

= ( = TB) breadths of the lateral hollows,............ 6 bh an 1 hs IV. Hollow square, 12-1... ecccceeseeeee tenes 6 (1 aay 1 8 Win ONO wr ellipse) scsi cp ssl adciness cetiscnencansnens 102 (1 —s:). WL Hollow circle jececuitcnasectacs cacscnneieaccnen ce ee ; ; 10-2 ha J Wrought iron, plate beams, ...........ccecceeeeeeeeeeeeeeeeeee 42,000 3 gy) WATS TANG ARIES). atonteinscsmmonweene eden deur 54,000 CASE AP OR sda cavicyndsianwiarenntacimeminoenemabaren 18,750 + 23,000 = (where H is the depth of solid metal in the section of the beam, and / the extreme depth.) ASD cone isinnicdincuagauientasereebtnarciadetteaneedevaamenctins 12,000 to 14,000 BS SUNG se) va Soautenwreaenpangoidees sop ewinendwa aadancsit 4,000 to 12,300 AGAPCH vcracsteianennie ene acai aeons meelane has yastoaentmars 5,000 to 10,000 Oak, British, Russian, and American,......... 10,000 to 13,600 MD CAE cscsscice-actaglainint oe Ssiniokrains deitie Bisse ctbciein ne telseamen ne IEAT ean 14,800 The modulus of rupture is eighteen times the load required to break a bar, one inch square, supported at two points, one foot apart, by being applied in the middle of the bar. The section for cast iron beams first proposed by Mr. Hodgkin- son, in consequence of his discovery of the fact, that the resistance of cast iron to direct crushing is more than six times its resistance to tearing, consists, as in fig. 22, of a lower flange B, an upper flange A, and-a vertical web connecting them. The sectional area of the lower flange, which is subjected to tension, is nearly six 78 INTRODUCTION. times that of the upper flange, which is subjected to thrust. In order that the beam, when cast, may not be liable to crack from unequal cooling, the vertical web has a thickness at its lower side nearly equal to that of the lower flange, and at its upper side, nearly equal to that of the upper flange. The tendency of beams of this class to break by tearing of the lower flange is slightly greater than the tendency to break by crushing of the upper flange; and their modulus of rupture is equal, or nearly equal, to the direct tenacity of the iron of which they are made, being, on an average of different kinds of British iron, 16,500 Ibs. per square inch. The following formula for the moment of rupture of such beams, though not strictly exact, is in general near enough to the truth for practical purposes:—Let B be the sectional area of the lower flange, in square inches; h' the depth in inches from the centre of the upper flange to the centre of the lower flange; then MM =16900 A Bi wcsesswstnnweseeieas ox (8.) 74, Resistance to Wrenching.—For equal values of the modulus of rupture, denoted by f, the strength of a cylindrical axle to resist wrenching is double of its strength to resist breaking across. Let / denote the length, in inches, of the lever (such as a crank), at the end of which a wrenching or twisting force is applied to an axle; let the working load, in pounds, multiplied by a suitable factor of safety (usually siz) be denoted by W; then FT UP cc srecrennigesiclee ce (1.) is the wrenching moment, in inch-pounds. The following are the formule which serve to compute the dimensions of axles whose resistances to wrenching shall be equal to a given wrenching moment :— For a solid axle, let A be its diameter; then 7,3 e/R A Wy Mao ond = fo anes ed (2: For a hollow axle, let h, be the external and h, the internal diameter; then SAK) _ Fh , Ay.) ST ee =o (1-73) 5 ii / ( = 5 |, iia (3) Fig. 22. r STRENGTH OF AXLES. 7) which last formula serves to compute the diameter of a hollow axle when the ratio hy : h, of its internal and external diameter has been fixed. The values of the modulus of wrenching / are— ROT CASE IPOD godevseaceowceraeesiccedeays about 27,700 For wrought iron,............eceeeeees 99 0,000 and taking six as the factor of safety, if we put the greatest working moment of torsion for M in the formule instead of the wrenching moment, we may put instead of f— FOr Cast ION. ..cccesesvessccceceseensseesevs cies 4,500 For wrought iron,..........:.ssceeees 8,000 to 9,000 75. Twisting and Bending Combined (4. M,, 325). — One of the most important examples of this is shown in fig. 23, which represents a shaft having a crank at one end. At the centre of the crank-pin P is ap- plied the pressure of the connecting rod; and at . the centre of the bearing S acts the equal and ; opposite resistance of that bearing. Represent- ing the common magnitude of those forces by P, they form a couple whose moment is Nw M M=P-SP. Draw S$ Q bisecting the angle PSM. OnSQ let fall the perpendicular PQ. From Q let fall Fig. 23. QM perpendicular to SM. Calculate the diameter of the shaft as if to resist the bending action of P applied at M, and it will be strong enough to resist the combined bending and twisting action of P applied at the point marked P. To express this symbolically, taking the factor of safety at 6, let W=6P. Make the angle PSM =j; then Si = Ps - Tod, Q and the diameter # of the axles is to be suited to the moment of - breaking across— M=W-SM=W-SP Portes (1.) that is, 80 INTRODUCTION. 76, Teeth of Wheels—The following is Tredgold’s formula for the thickness of the cast iron teeth of wheels, which are to trans- mit the working pressure P. Let that pressure be expressed in pounds, and the thickness h of each tooth in inches; then et oes Ay Section 9.—Prime Movers Classed. 77, Prime movers are classed according to the forms in which the energy that drives them is first obtained. These are— I, Muscular Power, applied by men to machines and implements of very various kinds,—and by beasts, chiefly to overcoming resist- ance by traction and to carrying of burdens. Il. The Weight and Motion of Fluids, acting in water pressure engines, water wheels, and other hydraulic engines, and in wind- mills. III. Heat, obtained by means of chemical combination, and applied to the producing of changes in the volume and pressure of fluids, so as to drive engines, of which the steam engine is the chiet. IV. Electricity, obtained originally by means of chemical com- bination, and applied to the production and alteration of magnetic force, so as to drive certain engines. The division of the remainder of this work is founded on the above classification. AppENDUM To ARrTIcLE 41, Pace 46. Rotatory Dynamometer.—In the ‘‘Pandynamometer” of M. G. A. Hirn, the torsion of the rotating shaft which transmits power is made the means of measuring and recording, by a self-acting apparatus, the moment of the couple by which the shaft is driven. Two toothed spur-wheels, fixed on the shaft at two different points, communicate rotations of equal speed in opposite directions to two bevel wheels which gear with one intermediate bevel wheel at opposite sides of itsrim. The axis of the third wheel in- dicates by its position one-half of the angle through which the shaft is twisted between the spur-wheels, and communicates its motion to the pencil of the recording apparatus. (See Annales des Mines, 1867.) PART I. OF MUSCULAR POWER. CHAPTER I. GENERAL PRINCIPLES. 78. Natare of the Subject.—Although it has been shown, in a paper by Dr. Joule and the late Dr. Scoresby (Phil. Mag., 1846), that animals acting as prime movers have a higher efficiency than any inorganic machines, still the present state of our knowledge is in-. sufficient to enable us to frame a complete theory of their efficiency. We cannot determine with precision the whole amount of energy which a given animal developes in a given time, so as to compare that amount with the energy which can be rendered effective in the same time in overcoming mechanical resistance. All that we can do is to ascertain by experiment and observation the quantities of effective energy exerted by different animals working under dif- ferent circumstances, and to compare those quantities with each other. In the present chapter will be stated some principles which hold respecting the muscular power both of men and of beasts. The power of men will be considered specially in the second chapter, and that of beasts in the third. 79. The Daily Work of an animal is the product of three quan- tities—the resistance overcome, the velocity with which it is over- come, and the number of wnits of time per day during which work is continued. It is known that the amount of the daily work depends on various circumstances, of which the principal are— (1.) The species and race. (2.) The health, strength, activity, and disposition of the in- dividual. (3.) The abundance and quality of food and air, the climate, and other external circumstances affecting those mentioned under ‘head 2. (4.) The load, or resistance overcome. (5.) The velocity. a 82 MUSCULAR POWER. (6.) The fraction of the day employed in working. : (7.) The nature of the machine or implement used in performing the work. This cause affects men more especially, owing to the variety and complexity of the machines on which they can exert their muscular power. Beasts are made to work almost exclusively in two ways—by traction and by carrying of burdens; so that little variation in the amount of their mechanical work arises from the circumstances under the present head. (8.) The practice and training of the individual. This applies principally to men, and in a less degree to beasts. 80. Influence of Load, Velocity, and Time of Working on Daily Work.—It is known that for each individual animal there is a cer- tain set of values of the three factors of the daily work which makes their product a maximum, and is therefore the best for economy of power, and that any ‘departure from that set of values diminishes the daily work. Various attempts have been made to represent the law of that diminution by an equation, but they have succeeded imperfectly. The equation which agrees on the whole best with observation is that of Maschek, which is as fol- lows:—Let R,, V,, T,, represent respectively the resistance, velo- city, and daily time of working which give the greatest daily work, and R, V, T, any other resistance, velocity, and daily time of work- ing; then BSc VEO — be ba 8... iiinaiiiteate 1 R Vv, TT, tt) According to this equation, the maximum daily work R,V,T, is realized under the following circumstances :— R, is one-third of the resistance which the man or beast can overcome for an instant and no more. V, is one-third of the velocity which can be maintained without resistance for an instant. T, is one-third of a day. This last principle is generally ad- mitted to be true; the others are doubtful. The above formula agrees approximately with experiment for circumstances not greatly deviating from those in which the daily work is a maximum. 81. Infiuence of Other Circumstances.—The circumstances num- bered 4, 5, and 6 in Article 79 have been considered first, because for them alone has anything approaching to a mathematical prin- ciple been ascertained. The effect of the circumstance 7 will be considered in the ensuing chapters. The influence of the other circumstances, 1, 2, 3, and 8, involves questions of natural history and physiology rather than of mechanics. With respect to the eircumstance 3, it may be stated, that other things being alike, TRANSPORT OF LOADS. 83 the individual that can beneficially breathe most air and digest most food, can also perform most muscular work; and inasmuch as the capacity for the beneficial digestion of food depends in a great measure on the capacity for the beneficial breathing of air, the volume, strength, and soundness of the lungs, and the abundance and purity of the air supplied to them, are of primary importance to muscular power. _It is well known that, by a reciprocal action, muscular exertion increases the powers of respiration and digestion. 82. In the Transport of Leads, cases sometimes occur in which it is impossible exactly to determine the resistance overcome by an animal; and it is consequently impossible to calculate the absolute value of the work performed. But a quantity can be computed in each such case which bears some unknown proportion to the work performed, viz.:—the product of the load into the horizontal distance over which it is conveyed. That product is called “ transport,” and examples of its values will be given in the sequel. 84 CHAPTER ITI. POWER OF MEN. 83. Tables of the Performance of Men.—The results in the fol- lowing tables are given on the authority of Coulomb, Navier, and Poncelet, with the exception of those marked 16, which are from experiments by Lieutenant David Rankine. J. Work or a Maw acatnst Known Resistances. R Vv saa RV RVT IIRD/OR: EXERTION: Ibs. ft. p.sec| (hours a ft.-Ibs. p. day. p. day.) 1. Raising his own weight up stair or ladder, ...........0. 143 05 8 | 72:5 | 2,088,000 2. Hauling up weights with rope, and lowering the rope unloaded, .........0.06 40 0:75 6 30 648,000 8. Lifting weights by hand,. ... 44 055 | 6 | 24:2 | 522,790 4, Carrying weights up stairs, and returning unloaded, 143° 0-13 6 | 185 399,600 5. Shovelling up earth to a height of 5 ft. 3 in.,...... 6 1:3 10 v8 280,800 6. Wheeling earth in barrow up slope of 1 in 12, $ horiz. veloc. 0°9 ft. per sec., and returning unloaded,........ 132 0-075 | 10 9-9 356,400 7. Pushing or pulling horizon- tally (capstan or oar),..... 265 2-0 8 53 | 1,526,400 126 5:0 2 62:5 eee | 8. Turning a crank or winch,... {189 2°5 8 45 | 1,296,000 200 {14-4 |2mins.] 288 eo 9. Working pump, 13-2 2°5 10 33 | 1,188,000 10. Hammering,.... 2% 15 ? 82] 2 480,000 Explanation.—R, resistance; V, effective velocity = distance through which R is overcome + total time occupied, including the time of moving unloaded, if any; T", time of working, in iv seconds per day ; 3600" me time, in hours per day; RV, effective : power, in foot-pounds per second; R VT, daily work. POWER OF MEN. 85 II. PERFORMANCE oF A Man in Transportina Loaps Horizonvaty. T LV KInp oF EXERTION, 7 vy 3600 fits. con-| LVT Ibs. ft. p. Sec} (hours | veyed | lbs. conveyed p. day.) | 1 foot. 1 foot. 11. Walking unloaded, transport of own weight,.......ssce00 140 5 10 700 | 25,200,000 12. Wheeling load L in 2-whld. . barrow, return. unloaded, 224 12 10 873 | 18,428,000 13. Ditto in 1-wh. barrow, ditto, 132 14 10 220 | 7,920,000 14, Travelling with burden,...... 90 23 7 225 | 5,670,000 15. Carrying burden, returning unloaded, ....sseseeseereeeeee 140 12 6 233 | 5,032,800 4 252 0 ves 0 one 16 Cares Derleth mepedse-) tie | at | ae as LY yssaveveesvaes verse 0 93-1 me 0 Ezxplanation.—L, load ; V, effective velocity, computed as before; T", time of working, in seconds per day ; 3600" in hours per day, as before; LV, transport per second, in foot-pounds; LV T, daily transport. 84. Work of » Man Raising his Own Weight.— The average amount of this is given in line 1 of the table in Article 83, and is greater than the work which the man can perform by any other mode of exertion. The most simple method of rendering available this kind of work is that invented by a French officer of engineers, Captain Coignet, and applied to the lifting of barrows of earth from an excavation about forty feet deep. A hoist is constructed, con- sisting of a strong rope passing over a large pulley, and having suspended at each end of it a cage or enclosed platform. Each barrow of earth on being brought to the foot of the hoist is placed in the cage which has just descended to the lower level. At the same time a man with an empty barrow steps into the other cage at the upper level, and descending along with it, causes the cage con- taining the full barrow to rise to the higher level, and the barrow is then removed. The man then leaves the cage in which he has descended, and at once returns to the higher level by mount- ing a ladder. When he mounts the ladder, he stores energy to an amount equal to the product of his weight into the vertical height of ascent, which energy is expended when he descends in one cage and raises the load in the other. A party of men are employed in this operation alone, the barrows being wheeled to and from the hoist by others. There is one man whose sole duty it is to attend 8&6 MUSCULAR POWER. to the machine, and either by hand or by means of a brake to con- trol the motion when it tends to become too rapid. The velocity of vertical ascent given in the table being the effective velocity only, is found by dividing the whole height ascended in a day by the whole number of seconds occupied, whether in ascending or in descending. 85. Lifting Weights by a Rope.—The data in line 2 of the tables are obtained from the results of the exertions of men in working a ringing pile engine, in which a heavy ram moving vertically between guides is attached to a rope passing over a pulley. The other end of the rope branches out into several smaller ropes, held by a suffi- cient number of men, in the proportion of about one man for each 40 lb. weight of the ram. The men, pulling all together, lift the ram from three to four feet, and let it drop suddenly on the head of the pile. It is found that they work most effectively when, after every three or four minutes of exertion, they have an interval of rest. 86. Other Modes of Exertion.—It is scarcely necessary to state that in none of the lines of the first table except that marked 1 is the weight of the man himself included in any load which he is stated as moving. In line 6, the resistance R = 132 Ibs. is the net weight of the earth in the barrow, and excludes the weight of the barrow itself. The mean actual velocity going and returning is 1°8 feet per second ; but as the effective velocity is to be computed from the distance travelled when loaded only, it is one-half of 1°8, or 0-9 foot per second ; and as the rate of ascent of the slope is 1 in 12, the effective vertical velocity is 0-9 + 12 = 0-075 of a foot per second, as set down in the column V. It is to be observed that the work set down in this line is that due to the vertical raising of the earth only, and is by no means the whole work performed by the man; the conveying the earth horizontally also involves the overcoming of resistance and performing of work, though to what amount is only known by a rough approximation to be mentioned in the next Article. Line 7 shows that, next to raising his own weight up a ladder, the most favourable modes of exerting a man’s strength are the pushing of a capstan bar and pulling of an oar. Next in amount of daily work, as shown by line 8, is the turn- ing of a crank or winch—the ordinary mode of driving purchases, cranes, monkey pile engines, and a great variety of other machines. The result in line 9, relative to working a pump, will also apply to windlasses which are worked by levers in the position of pump handles. It applies, amongst other pumps, to those of hydraulic presses—a kind of machine which, although generally worked by POWER OF MEN. 87 men, involves hydrodynamic principles, which make it necessary to defer its consideration till Part II. of this work. In line 10, relative to swinging a 15 Ib. hammer, some of the data are wanting, and the result is doubtful. 87. Transporting Loads.—In the second table, the only line in which the weight of the man is taken into account is that marked 11, where his own weight is the only load conveyed. By comparing line 13 in the second table with line 6 in the first, it appears that the exertion of wheeling a load of earth horizontally in a one-wheeled barrow from ten to twelve feet or thereabouts, must be nearly equal to that due to the raising of the same earth one foot vertically in wheeling it up a slope. 88 CHAPTER III. POWER OF HORSES AND OTHER BEASTS. 88. Tables of the Performance of Hlorses.— The results in the following table are given on the authority of Navier and Poncelet, except the line marked 1, which is from experiments by Mr. David Rankine and the Author. Line 2 contains the mean of several results of experiments on draught horses, and may be considered the average of their ordinary performance under the most favourable circumstances as to time of working and velocity. I. Work or A Horse acainst A Known REsISTANCE. Kinp or EXeExrrTion. R Vv sam RV RV1L 1. Cantering and trotting, draw- ing a light railway car- | (min. 22} riage (thoroughbred),...... {esaaodl 142 4 | 4473 | 6,444,000 max. 50 2. Horse drawing cart or boat, walking (draught horse), 120 36 8 | 432 | 12,441,600 3. Horse drawing a gin or mill, WALKING, ...ceseveeeeseeeeces 100 3-0 8 | 300 8,640,000 4. Ditto, trotting,..........ccceeee 66 6:5 4% | 429 6,950,000 Explanation. —R, resistance, in Ibs.; V, velocity, in feet per second ; T= 3600, hours’ work per day; RV, work: per second ; RV T, work per day. II. PERFORMANCE oF A HorsE In TrRaANnsportTinG Loaps HORIZONTALLY. Kinp OF EXERTION. L Vv 3600 LV LVT 5. Walking with cart, always TBRHEU, scismisacercceonnnnnanns 1,500 3°6 10 | 5,400 .| 194,400,000 6. Trotting ditto,.....ccesceeee 750 | 72 43 |5,400 | 87,480,000 7. Walking with cart, going loaded, returning empty; V=4 mean velocity,...... 1,500 2-0 10 | 3,000 | 108,000,000 8. Carrying ee ee 270 36 10 972 | 84,992,000 9. Ditto, trotting,... sayeaitent 180 7-2 7 {1,296 | 382,659,200 | » eae © a eta HORSES—-OXEN—MULES— ASSES. 89 Lxplanation.—L, load, in lbs,; V, velocity in feet per second ; T=3600, working hours per day; LV, transport per second; LV T, transport per day. Table IT. has reference to conveyance on common roads only, and those evidently in bad order as respects the resistance to traction upon them. The average power of a draught horse, as given in line 2, Table I., being 432 foot-pounds per second, is ae = 0-785 of the conventional value assigned by Watt to the ordinary unit of the rate of work of prime movers (Article 3). 89. Oxen, Mules, Asses.— Authorities differ considerably as to the power of these animals. The following may be taken as an approximative comparison between them and draught horses :— Ox.—Load, the same as that of average draught horse ; best velocity, and work, 2 of horse. Mute.—Load, one-half of that of average draught horse ; best velocity, the same with horse ; work, one-half. Ass.—Load, one quarter of that of average draught horse ; best velocity, the same ; work, one quarter. 90, Hforse Gin.—In this machine, as is shown by line 3, a horse works less advantageously than in drawing a carriage along a straight track. In order that the best possible results may be realized with a horse gin, the diameter of the circular track in which the horse walks should not be less than about forty feet. 91. Tread Wheels for Horses and Oxen have been used, each consisting of a plane circular platform, rotating about an axis somewhat inclined to the vertical, and ribbed to prevent the feet of the animal from slipping. The animal walks continually up the slope of the platform at or near one end of the horizontal diameter, and by its weight causes the platform to rotate against a resistance. PART IL OF WATER POWER AND WIND POWER. CHAPTER I. OF SOURCES OF WATER FOR POWER. 92. Nature of Sources in General.—The original source of water power is the solar heat, which evaporates liquid water from the surface of the earth and sea. The vapour, condensing in the upper and colder regions of the atmosphere, falls as rain, and forms streams, whose waters, in descending from a high to a low level, exert energy equal to the product of the weight of water which descends into the height through which it descends. In the natural condition of a stream, the whole of the energy due to the descent of its waters is employed in wearing and carrying away the materials of its bed, and in producing heat by friction; but by proper management, a part of that energy can be made available to overcome the resistance of machines. The art of collecting and distributing, for useful purposes, the rain-fall of a district,—of planning and making reservoirs for storing part of it in seasons of flood, in order to supply its deficiency in seasons of drought, and of adapting natural lakes to answer the same purposes—the art of preserving and improving the natural channels in which it flows, and of planning and making artificial channels, constitute a great and important branch of civil engineering, and cannot be considered within the limits of the present treatise, whose object, as applied to water power, is to set forth the principles and the mode of action of those engines which render that power avail- able when a convenient source has been obtained; that is to say, a stream, discharging a given quantity of water per second, and having a given vertical descent within a convenient distance. Such a combination of circumstances makes a “MILL sITE” or “ FALL.” 93. Power of a Fall of Water—Efficiency.— Lhe gross power of a fall of water is the product of the weight of water discharged in a given unit of time (such as a second, or a minute), into the total head ; that is, the difference of vertical elevation of the upper surfuce 92. WATER POWER AND WIND POWER. of the water at the points where the fall in question begins and ends. To express this in symbols, let Q be the flow, or volume of water discharged, in cubic feet per second ; D, the weight of a cubic foot of water, in Ibs., = 62-4 lbs., nearly ; H, the total head; then is the gross power, in foot-Ibs. per second; which being divided by 550, gives the gross horse-power. There is in every case a certain loss of head arising from the waste of energy in various ways to be afterwards mentioned. That waste can usually be computed in the form of a certain fraction of the whole energy exerted; let & denote that fraction; then the effective power, in foot-lbs. per second, is (1 — &) D QE}... eeeeeeeeeeeeees (2.) and the efficiency is k #1 is called the loss of head, and (1 — k) H the effective head. 94, Measurement of a Source of Water Power.—I'wo things are to be measured about a fall of water, the head H, and the flow Q. The head is measured by the ordinary operation of levelling. The flow is measured by different methods, according to circumstances. I. In large streams, the flow can in general be only measured directly ; that is, by finding the area of cross-section of the stream, reeasuring by suitable instruments the velocities of the current, at - various points in that cross-section; taking the mean of these velocities, and multiplying it by the sectional area. The most convenient instrument for such measurements of velocity is a small light revolving fan, on whose axis there is a screw, which drives a train of wheel work, carrying indexes that record the number of revolutions made in a given time. The whole apparatus is fixed at the end of a pole, so that it can be immersed to different depths in different parts of the channel. The relation between the number of revolutions of the fan per minute, and the corresponding velocity ; of the current, should be determined experimentally, by moving the instrument with different known velocities through a piece of still water, and noting the revolutions of the fan in a given time. II. When from the want of the proper instrument, or any other cause, the velocity of the current cannot be measured at various points, the velocity of its swiftest part, which is at the middle of the surface of the stream, may be measured by observing the motions of any convenient body floating down. Let this greatest velocity in MEASUREMENT OF SOURCE OF WATER. 93 feet per second be denoted by V; then according to an empirical formula of Prony’s, the mean velocity is T71+V v=V 02s ave eeu sae aye (1.) ITT. When the stream is so small that it is practicable to make across it a temporary weir, such a weir is to be made, care being taken that it shall be perfectly water tight at every point except the outlet through which the whole flow of the stream is to pass. The site ought to be chosen with a view to the tightness and security of the weir; and the channel of the stream immediately below the weir should be straight, in order that the rapid current rushing from the outlet may not injure the banks. The outlet should be a notch or depression in the upper edge of a vertical board; hence weirs of this class are called notch boards. In tig. 24, A repre- sents a front view, and B a vertical section, of a notch board with a rec- tangular notch. The sides and bottom of the notch should be chamfered to a fine edge, with a vertical surface opposed to the water in the pond above the weir, as shown in the section B; and the better to fulfil this condition, the notch may be edged all round with thin sheet iron. The object of this is, to prevent as far as possible the friction and cohesion between the water and the edge of the notch from interfering with the result. A vertical scale, divided into feet and decimals, and having its zero at the level of the lower edge of the notch, is to be placed in the pond above the notch board, at some point where the water is either sensibly still, or has a very slow motion only; and the height at which the surface of the water stands on that scale is to be noted trom time to time. Let h be that height, in feet; let b be the breadth of the notch, also in feet, Then the flow, in cubic feet per second, is given by the formula Fig. 24. = 22-64 J Bghs Sobers hcrn ciate (1) 29 being 64:4, and ,/2gh the velocity due to the height h; while cisa fraction called the co-efficient of contraction, expressing the 94 WATER POWER AND WIND POWER. ratio which the sectional area of the most contracted part of the jet or cascade flowing from the notch bears to the area of the rectangle bh. The above formula may also be expressed as follows :-— (= DIBD- 6 Bild ceceesreseeagace: gece *(2.) It is advisable that the breadth of the notch should not be less than one-fourth of that of the weir. It may have any convenient breadth from that amount up to the entire width of the weir. The values of the co-efficient of contraction are— For a notch of 1 of the width of the weir,............. 595 For a notch of the whole width of the weir, .......... 667 and for intermediate proportions, the following empirical formula is very nearly correct :— c= 057 + —— B being the breadth of the weir. When the velocity of the current at the point where the vertical scale stands is too large to be neglected, let v denote that velocity (called the velocity of approach), and 2 h, = 57 0 a9 the height due to it. Then, according to Mr. Neville’s work on Hydraulics, the flow is the difference between that from a still pond due to the height 4 + ho, and that due to the height 4,; so that it is given by the formula Q = 5:35 cb Ah + hy) — hight veeereresseeeees (4) ‘When ~ cannot be directly measured, it can be computed approxi- mately by taking an approximate value of Q from equation 2, and dividing by the sectional area of the channel at the place where the scale stands. TABLE OF VALUES OF ¢ AND 5°35 c. I'o og 08 oF 06 OF Of Of O'25 Cy sense 667 66. 65 64 63 ‘62 “61 ‘60 ‘595 5°35 6 3°37 383 3°48 3°42 3°37 3°32 3°26 3:21 3°18 * 15 is easily computed, as follows, by the aid of an ordinary table of squares and cubes :—Look in the column of squares for the nearest square to 2; then opposite, in the column of cubes, will bé’an approximate value of he. . NOTCH BOARDS—ORIFICES. 95 IV. Besides the variations in the co-efficient of contraction already stated, which depend on the proportion between the breadths of the weir and of the notch, there are other variations which have been reduced to no general law, depending on the proportions of the dimensions of the notch to each other. To avoid this inconvenience, Professor Thomson of Bel- fast has adopted a form of notch in which the section of the issuing jet is always of a similar figure—that is to say, a triangle with the apex down- ; wards, as in fig. 25. Eig 20s Let h be the depth, in feet, of the apex of the notch below the surface of still water in the pond, 6 the breadth of the notch at the level of the surface of still water ; then the area of the triangle bounded by that level and the edges of the notch. is 40/; and theory gives for the discharge in cubic feet per second— 8e bh Q=5 a Ne gh. shenantaueeunaneaen (5.) Mr. Thomson’s experiments, made for the British Association, give for the co-efficient of contraction— os S| (6.) Wiebe ea Ye ; and consequently for the discharge— 2 (7) i ae (7. V. Instead of an open notch in the top of a weir board, there may be an orifice, or a row of orifices, wholly beneath the level of the water in the pond. In that case, on account of the variations in the co-efficient of contraction which occur when the orifice has various proportions of length to breadth, and also when the ratio of the head of water above the orifice to the breadth of the orifice varies, it is desirable to select such forms and proportions as shall give rise to the smallest variations. For that purpose the orifices should be made either square or circular ; and their size should be such that the height of the surface of still water in the pond shall not be less at any time than three times the diameter of an ori- fice. These conditions being fulfilled, let A be the area of an 96 WATER POWER AND WIND POWER. orifice, h the depth of its centre below the upper surface of still water ; then the flow through it in cubic feet per second is Q HCA JAK sercrvererecerere encase (9.) the values of ¢ being— For round orifices,............ceceecseceereesens o0'618 For square ovifices,.........cccseseeeseneeneee ees 06 and the values of ¢ J/2g = 8-025 e— For round orifices, ...........cec ce ceeeeeee ene eee 4°90 For square orifices, ............:.sscseeeseresves 4815 No very serious error will be incurred by using these co-efficients, even when the height / falls to double the diameter of the orifice. VI. When the edge of an orifice partly coincides with the bor- der of the channel by which the water is brought to it, so that the water is partially guided in a straight course towards the orifice, the case is called one of partial contraction; and in computing the discharge, instead of the co-efficient c, there is to be employed— CO 0 Getic disccroerieanvecans --(10.) n being the fraction of the edge of the orifice which coincides with the border of the channel. This formula is Mr. Neville’s, and is shown by him to be sensibly correct when m is any fraction not exceeding 3. 97 CHAPTER II. OF WATER POWER ENGINES IN GENERAL. 95. Parts and Appendages of Water Power Engines. —In every water power engine, or in connection with it, there exist the fol- lowing parts, or parts equivalent to them :— I. The cHANNEL OF SUPPLY, or HEAD RACE, whereby water is brought to the engine, and which extends from the beginning of the fall to the place where the water begins to act on the mecha- nism. It may be an open conduit, or a close pipe, or a combina- tion of both. Economy of power requires that it should be as large as possible : economy of first cost that it should be as small as possible. The right mean is a matter for the judgment of the engineer in each particular case. This channel usually commences at a head reservoir or pond, and the lower end of it is sometimes of such dimensions as to constitute a second reservoir or pentstock. The lower end of the supply channel is of various kinds and forms according to the nature of the engine. II. The wasTE CHANNEL, or BYE WASH, whereby any flow of water which is in excess of that required for the stream, and which there is not reservoir room to store, is discharged into the natural drainage channels of the country. This generally commences with a weir or overfall forming part of the boundary of a reservoir, and of such length that the greatest possible flow of waste water can escape over it without rising to a dangerous or inconvenient height. III. The recuator, being the sluice, valve, or other apparatus whereby the flow of water delivered by the head race to the engine is adjusted to the work to be performed. For reasons which will afterwards appear, economy of power requires that the regulator should be as close as possible to the engine, and therefore at the lower end of the channel of supply. The regulator is very fre- quently controlled by a govertior, usually of the revolving pendulum class (Art. 55), of which the details will be exemplified farther on. IV. The ENGINE PROPER, being the machine to which the water transmits energy. . . “V. The Tai Racg, by which the water is discharged after having driven the engine, and which terminates at the bottom of the fall. The same principles of economy of power and economy of cost apply to this as to the head ee 98 WATER POWER AND WIND POWER. 96. The Classes of Water Power Engines are :-— I. WarTER-BUCKET ENGINES, in which water, poured into sus- pended buckets, causes them to descend vertically, and so to lift loads or overcome other resistance, as in certain hydraulic hoists. II. WaTeER-PRESSURE ENGINES, in which water by its pressure drives a piston. IIT. VERTICAL WATER WHEELS, being wheels rotating in a verti- cal plane, and driven by the weight and impulse of water. These are the most common of all water power engines. ITV. Horizontal WATER WHEELS, or TURBINES, being wheels rotating in a horizontal plane, and driven by the pressure and impulse of water. V. Rams and JET Pumps, in which the impulse of one mass of fluid is used to drive another. 97. Water Power Engines with Artificial Sources.— The smooth- ness and steadiness of motion, and some other advantages of water power engines, sometimes occasion the use of machines exactly resembling them in everything, except that the flow and head of water are produced artificially—for example, by pumps worked by hand, as in the common hydraulic press, or by pumps worked by steam, as in some hydraulic hoists and cranes, and in some water wheels for driving fine manufacturing machinery, which are sup- plied by pumping steam engines. Such machines are not, properly speaking, prime movers tor obtaining energy from natural sources, but rather pieces of mecha- nism for transmitting and conveniently applying energy already obtained by means of other prime movers. The identity of their construction and action, however, with those of true water power engines, renders it advisable to consider them in the present treatise. 98. Form Assumed by Emergy of Fall (A. M,, 619-621).— Let a continuous and uniform stream, whose volume of flow is Q cubic feet per second, and weight of flow DQ lbs. per second, descend from the height or head of H feet to a given point of dis- charge. That stream is capable of performing work, by the direct ACTION OF ITS WEIGHT in descending, to the amount of DQH ft.-lbs. per second................005 (1.) Now suppose that from the original elevation H of the upper surface of the stream, down to a point whose elevation above the bottom of the fall is 2 feet, the descent of the water takes place without resistance. It will at the latter point possess the power of performing work by tts weight to the amount of D Qz ft.-Ibs. per second only;......... vesseee(2) FORMS OF ENERGY OF A FALL OF WATER. 99 but supposing the source to be a reservoir, where the velocity is ° insensible, the stream will now by its free descent through the height H —z, have acquired the velocity— 2G CB S2) Si eiewiecieraaceareanees (3.) so that, before being brought back to an insensible velocity, it is capable, by IMPULSE, of performing the additional work due to its actual energy, viz.:— DQ 29 = DQ (H-2) ft-lbs. per second,......... (4.) which being added to the quantity of work in the expression 2, reproduces D Q H, the total original power. Next, let the stream be supposed to descend, in a.close pipe so large that the velocity of current is still insensible, from the ori- ginal head H to the less elevation z above the bottom of the fall. Then, as in the last example, equation 2, the stream will at the latter point possess the power of performing DQz ft-lbs. per second only of work by its weight; but its pressure will have become, in lbs. on the square foot— and BY MEANS OF ITS PRESSURE the stream will be capable of per- forming work to the amount of pQ=DQ(H--) ft-lbs. per second,............ (6.) which being added to the quantity of work in equation 2, repre- duces the total original power D Q H, as before. It appears, then, that if it were possible for a stream to descend absolutely without resistance from the elevation H to any less elevation above the bottom of the fall, and if the pressure at the latter elevation were p lbs. on the square foot, and the velocity v feet per second, the power or energy per second at that elevation, being equal to the original power, would be expressed by e Dv? Q (p+ Det 3 2 Ones (7.) or, if the height due to the pressure be denoted by p + D— v b) — +2 )= DQE Lc eccrecsenene (8 DQ (+5 + D Q (8) In this expression, 100 WATER POWER AND WIND POWER. P\ is potential energy, or capacity for perform- ] ue (: x b) ing work by weight and pressure. (9.) DQ: actual energy, or capacity for performing work ‘24 g by impulse. The following equation :— 2 at et & = Bysecessseeceeesseen (10.) shows, that at a given elevation z, where the velocity of the stream is v, and the pressure p, there is, Besides the actual head z, A virtual head, composed of — The height due to the velocity, v? +249, And the height due to the pressure, p+ D, making together a total head, which, if the stream has descended without resistance, is equal to the original head H. Throughout this Article, and the present Part of the treatise, when not otherwise specified, presswre is used to mean, the excess of the pressure of the water above that of the atmosphere. 99, Loss of Head is the form in which the effect of waste of energy in the stream of water during its descent is most con- veniently expressed. It may be denoted in the form of a certain fraction of the total head— A= H, and then Hah =O —£) Desesccsen sasecesscsac(.) will be the available head ; DQ (H-*’) =(1-A)DQH,..... (2.) the available power, or the energy exerted per second by the fall on the engine; and , H-h 1-#= FL rceeeesseseeess (3.) the efficiency of the fall. If, in the working of the engine, there is a further waste of the fraction &' of the energy exerted on it, so that the useful effect is @=2) 0) DG Uewsiaioncacds, (4) LOSS OF HEAD—FRICTION OF CHANNELS. 101 then 1-2" is the efficiency of the mechanism, and (1—A’) (1-4) = 1-4 (as in Article 93).........(5.) the resultant efficiency of the fall and engine combined. The causes of loss of head are, the velocity of the current in the tail race, and fluid friction. I. Current in the tail race.—If v' be the velocity with which the stream is discharged along the tail race, there must be a descent of v2~2g to produce that velocity, which descent is a loss of head. Hence, as stated in Article 95, the tail race should be as large as is consistent with due economy of first cost. II. Friction of passages and channels in general.Let A be the sectional area of any passage or channel along which the stream is conveyed, then is the mean velocity of the current through it. The loss of head from friction is expressed by the following general formula :— 2 that is, the product of the height due to the velocity by a factor of resistance F', whose value depends mainly on the nature, form, and. dimensions of the passage. The friction takes effect in open channels by producing a decli-~ vity of the surface and a loss of actual head; in a close pipe it. takes effect by diminishing the pressure, and the virtual head due- to it. é A few values of the factor denoted by F have already been given in Article 50, under the head of “ Pump Brakes.” They will now be repeated in greater detail, and with several additions. IIL. Friction of an orifice in a thin plate :— IV. Friction of mouthpieces or entrances from reservoirs into pipes.—Straight cylindrical mouthpiece, perpendicular to side of reservoir :— The same mouthpiece making the angle ¢ with a perpendicular to the side of the reservoir :— F = 0:505 + 0-308 sin i -+ 0:226 sin? é.....0.., (10.) ‘ 102 WATER POWER AND WIND POWER. For 2 mouthpiece of the form of the “ contracted vein,” that is, one of such a form, that if d be its diameter on leaving the reser- voir, then at a distance d+ 2 from the side of the reservoir it con- tracts to the diameter 7854 d,—the resistance is insensible, and F nearly = 0. V. Friction at sudden enlargements.—Let A be the sectional area of a channel, in which a sluice, or slide valve, or some such object, produces a sudden contraction to the smaller area a, fol- lowed by a sudden enlargement back again to the original area A. Let v = Q=A be the velocity in the enlarged part of the channel. The effective area of the orifice a will be ca, c being a co-efficient of 2, contraction whose value may be taken at ‘618 + 1 — 618 we Let the ratio in which the channel is suddenly enlarged be denoted b . A? m=A+ca= a/ (26185 m 1618) fine (11) Then mv is the velocity in the most contracted part. It appears that all the energy due to the difference of the velocities, mv and v, is expended in fluid friction, and consequently that there is a loss of head given by the formula— v2 (m—-1)?- Iq) Lsdangve suave estore (12.) so that in this case TS Gi Pops ciecheaeinccuiasicess (12 a.) VI. Friction in pipes and conduits.—Let A be the sectional area of a channel; 6 its border, that is, the length of that part of its girth which is in contact with the water; / the length of the chan- nel; then, for the friction between the water and the sides of the channel— F=f: . Sie spiauaios muaavenaueena age (13.) in which the co-efficient f has the following values :-— For iron pipes (d = diam. in feet), = 0-005(1 +73); (14,) For open conduits, .....f = 0°00741 +- se Awsnemexd (15.) The ratio = is called the “hydraulic mean depth” of the channel, and 6 for cylindrical and square pipes running full is obviously one-fourth we FRICTION OF CHANNELS. 103 of the diameter ; and the same is its value for a semi-cylindrical open conduit, and for an open conduit whose sides are tangents to a, semi- circle of a diameter equal to twice the greatest depth of the conduit. In an open conduit, the loss of head— flb 2 A= AS a9 tee ener eee esearesesecees (16.) takes place as an actual fall in the surface of the water, producing a declivity at the rate— h_ fb wv. Tyg Sorte (17.) and by the last two formule are to be determined the fall and the rate of declivity of open head races and tail races of given dimen- sions, which are to convey a given flow. In close pipes, the loss of head takes place in the virtual head due to the pressure. VII. For bends in circular pipes, let d be the diameter of the pipe, 7 the radius of curvature of its centre line at the bend, 7 the angle through which it is bent, + two right angles ; then, according to Professor Weisbach— i aN% Fa* {ors +1847 (2)*t ee (18) VIII. For bends in rectangular pipes :— if 7 Fat { 0-124 ++ 3-104 (4)' \ Ait Soe (19.) IX. For knees, or sharp turns in pipes, let ¢ be the angle made by the two portions of the pipe at the knee ; then F = 0-946 sin? 5 + 2-05 sint 5 iene (20.) X. Summary of losses of head.—Let v' be the velocity of the current in the tail race; F’ the factor of resistance for the tail race ; » the velocity in any other part of the course of the water; F the proper factor of resistance for that part of the course; then the whole loss of head may be thus expressed :— 2 v2 = UN sad SS TAP yo sence cidienteid 21. 100. The Action of the Water on the Engine has already been distinguished, in Articles 96 and 98, as taking place in three ways i—. 104 WATER POWER AND WIND POWER. I. By weight. IL. By pressure. TIT. By impulse. Now, in all those three modes of acting, the immediate effort by which energy is exerted by the water on the engine is a pressure between a certain layer of the water and the surface of a moving piece, whether a bucket, a piston, a vane, or another fluid mass which that layer of water drives before it; and the original cause of that effort is the weight of the descending stream. The distinction set forth arises in the nature of the process whereby the weight causes the pressure. I. When the water is said to act by weight, portions of it are poured into buckets, and the pressure by which each bucket is driven is the direct effect of, and simply equal to the weight of the water contained in the bucket, and acts vertically downwards, its resultant traversing the centre of gravity of the mass of water in the bucket. Waste of energy may occur in this case through spilling of the water from the buckets during their descent, or through the remain- ing of water in the buckets during their ascent. The latter cause of waste of energy ought not to operate to any sensible amount in a well designed machine. The former ought to be reduced to as small an amount as possible. II. When the water is said to act by pressure, the pressure which drives the piston or vane acted upon is not simply the effect of the weight of a portion of water descending along with it, but is the effect of the weight of some more or less distant mass of water transmitted through an intervening mass, and altered to any ex- tent in direction and in the velocity of its action. III. When the water is said to act by impulse, its weight, either directly, or through intervening pressure, is allowed to act freely to such an extent as to produce a jet or current of a certain velocity, whose particles, coming in contact with a float board or vane, or another fluid mass, have that velocity either diminished or taken away; and during that operation they exert a pressure against the float board or vane, or the driven mass of fluid, proportional to the momentum which is taken away from them in each second. 105 CHAPTER ITI. OF WATER BUCKET ENGINES. 101. The Water Bucket Hoist, the simplest engine driven di- rectly by the weight of water, is frequently used for raising waggons of coal and other materials to an elevated platform. It consists of — I. A strong timber frame, supporting at the top one or more large pulleys. Il. A chain passing over the pulleys. III. A cage for waggons, hung to one end of the chain, and moving between vertical guides. The upper and lower platforms, between which the cage travels, should be provided with strong catches to fix the cage at the higher and lower levels when required. IV. A water bucket, hung to the other end of the chain, usually moving between vertical guides, and having a valve in the bottom, opening upwards, for discharging the water. This valve may be made self-acting, by making its spindle project downwards, below the bottom of the bucket, so that when the bucket has finished its descent, the spindle may strike upon a floor and lift the valve; but in some cases it is more convenient that the valve should be opened by hand. Rectangular wooden buckets are used; but for lightness and strength, the best material is sheet iron, and the best shape a cylindrical body with a hemispherical bottom. V_ A reservoir and spout for filling the bucket when it is at the higher level. The valve of the spout may, if required, be made self-acting, by causing it to be opened by the rising and shut by the falling of a weighted lever, which is lifted by the edge of the bucket when it reaches the top of its ascent, held up until the bucket is full, and allowed to drop when the bucket begins to descend. VI. A drain or tail race, to carry away the water discharged from the bucket at the lower level. VII. A brake, which may be applied to one of the pulleys. It is advisable, for safety’s sake, in most cases, to enclose the course of the cage and that of the bucket in light wooden casings. The weight of the unloaded cage ought to be somewhat in excess of that of the empty bucket, added to the friction of the machine when unloaded. ; The weight of the full bucket ought to be somewhat in excess of that of the loaded cage, added to the friction of the machine when loaded. 106 WATER POWER AND WIND POWER. The friction is from one-tenth to one-twentietlr of the gross load. In order that the weight of the chain may always be balanced, two pieces of chain with their lower ends lying loose on the ground are hung, the one from the bottom of the cage, and the other from the bottom of the bucket. The bucket hoist is a bulky and heavy machine, and slow in its operation ; but from its great simplicity, it is easy to make, main- tain, and manage, and very durable. Its reservoir may be sup- plied by a natural source, where one is available ; in other cases, water may be raised to it by a pump worked by a steam engine. The latter combination is a good means of economizing power when heavy loads have to be lifted during short times and at distant intervals. During the intervals when the hoist is standing idle, the steam engine is still storing energy by pumping water into the reservoir; so the work performed by the hoist during a few hours of each day may be distributed, so far as the exertion of energy by the steam engine is concerned, over the whole twenty-four hours ; and a steam engine, quite inadequate to lift the load to be raised directly, may thus be made to perform the whole work easily by the intervention of the reservoir and hoist as means of storing and restoring energy. 102. Bess of Head in Bucket Moists—The actual energy with which the water runs from the reservoir into the bucket, and from the bucket into the tail race, is wholly wasted in fluid friction. Therefore in every bucket engine, besides the fall of the tail race, there is a loss of head equal to the height of the surface of the water in the reservoir above the highest level of the surface of the water in the bucket, added to the height of the surface of the water in the bucket when at the bottom of its stroke above the surface of the water in the tail race ; that is, the depth of the bucket at least. In other words, while the total head is the elevation of the top water of the reservoir above the outfall of the tail race, the avail- able head is the height through which the bucket descends only. 103. A Double Acting Bucket Engine has sometimes been used, consisting of a balanced beam, having a pair of equal and similar buckets hung to its two ends, which rise and fall alternately. Hach bucket, on arriving at the top of its stroke, is filled with water by a spout from a reservoir, with a valve which is opened and closed by the mechanism. On arriving at the bottom of its stroke, each bucket is emptied through a self-acting valve in its bottom into the tail race. Thus, as in the bucket hoist, the buckets descend full and ascend empty; and the energy due to the descent of the water in them is employed to work pumps, or otherwise. The chief advantage of this kind of machine is its adaptation to regions where only rude workmanship can be obtained, 107 CHAPTER IV. OF WATER PRESSURE ENGINES. Section 1.—General Principles. 104. Parts of a Water Pressure Engine.— In a water pressure engine, the several principal parts mentioned in Article 95 as be- longing to water power engines in general, take forms suited to that class of engine. I. The head race consists of a supply pipe leading from a reser- voir to the working cylinder. That pipe, together with the reser- voir, constitute what is called the pressure column. Besides the regulator, to be presently mentioned, there should be a stop valve or sluice at the upper end of the supply pipe, in or close to the reservoir, so that in the event of an accident occurring to the supply pipe, the current of water may be prevented from entering it. There should also be a grating to prevent the entrance of solid bodies from the reservoir. All water contains air diffused through it, and most water con- tains sediment. If there are summits and hollows in the course of the supply pipe (which is often of great length), the air collects at the former and the sediment at the latter. There should be a cock at the upper side of each summit in the course of the pipe, for blowing off air, and at the lower side of each hollow for blowing off sediment, II. The bye wash has no peculiarities arising from the class of engines. III. The regulator is a valve of one or other of certain kinds to be afterwards mentioned, which are capable of being adjusted to any required extent of opening. : IV. The engine proper consists of a piston moving in a cylinder, together with the valves for admitting and discharging the water from the cylinder. The engine is single acting or double acting according as the water acts on one face of the piston only or on each face alternately. . The valves are sometimes worked by hand, in which case the same valve may act as the regulator and the admission valve,— sometimes by mechanism directly driven by the piston of the engine,—and sometimes by a small auxiliary water pressure engine. 108 WATER POWER AND WIND POWER. The place of the piston is sometimes supplied by a mass of air ; in which case the alterations of volume of that air require to be taken into account, V. The tal race consists of a discharge pipe, whose final outlet may be either at, below, or above the level of the cylinder. 105. Suction Pipe.—The pressure of the water at the outlet of the discharge pipe is equal to that of the atmosphere, added to that due to the depth at which the water outside the pipe stands above that outlet; so that when the outlet is below the level of the piston, the pressure within the upper end of the discharge pipe, and in the cylinder while the water is being discharged, may be less than the atmospheric pressure. In this case, the discharge pipe is called a suction pipe, and the pressure at its upper end is described by stating by how much it is below the atmospheric pressure, either in pounds on the square inch or square foot, or in feet of water, and that deficiency of pressure is conventionally called so many pounds on the inch or foot, or so many feet, “of vacuum.” Thus, if the atmospheric pressure is 14:7 lbs. on the square inch, being equi- valent to 33-9 feet of head of water, and the absolute pressure in the cylinder during the discharge is two lbs. on the square inch, being equivalent to 4°6 feet of head of water, that pressure is described as 12-7 lbs. on the square inch, or 29°3 feet, of vacuwm. This mode of expression has been adopted on account of the prac- tical convenience of reckoning pressures from that of the atmo- sphere as an arbitrary zero. The absolute pressure against the piston during the discharge is equal to the atmospheric pressure, added to the pressure required to overcome the resistance of the discharge pipe, less the pressure due to the elevation of the upper surface of the water beneath the piston above the bottom of the fall. There never acts in water, at all events in agitated water, negative pressure (that is, tension) to an amount appreciable in practice; therefore, the height of the upper surface of the water beneath the piston can never be greater than the head due to the atmospheric pressure, added to the head lost in overcoming the friction in the discharge pipe. Should the height of the piston itself above the bottom of the fall be greater than this, the water in the cylinder, on the opening of the discharge valve, will not continue in contact with the piston, but will sud- denly drop down to the level given by the principle just stated, leaving between itself and the piston what is commonly called a “vacuum” or “empty space,” being in reality a space filled with rare vapour. The height of that space is so much head lost; its existence tends to make the piston leak, and its periodical empty- ing and filling is accompanied by shocks or abrupt motions in the water, which tend to injure and wear out the machine; therefore, SUCTION PIPE—-ATMOSPHERIC PRESSURE—EXPANSION, 109 its formation ought to be avoided; and for that purpose the height of the piston above the bottom of the fall ought never to be greater than that due to the least atmospheric pressure and the resistance of the discharge pipe. Now, the water in the discharge pipe is some- times at rest, and then the resistance is nothing; so that we arrive finally at this rule:—The greatest height of the piston above the bottom of the fall ought not to exceed the head of water equivalent to the least atmospheric pressure in the locality. 106. The Least Atmospheric Pressure at the level of the sea is about 28 inches of mercury, or 13°75 lbs. on the square inch, or 31-7 feet of water. The ratio in which the least atmospheric pressure is less than the above amount at a given elevation (z) above the level of the sea, is computed with sufficient exactness for practical purposes. by the following formula, in which p, is the pressure at the level of the sea, and p, the pressure at the elevation of 2 feet :— Fe Lae log Pr Raed eh ee ee eae eons (1.) In the absence of tables of logarithms, the following formula, deduced from one proposed by Mr. Babinet, is approximately correct, for heights not exceeding 3,000 feet :— Py 52400 — 2 (2.) ar Bute Ee ee ; When the height exceeds 3,000 feet, divide it into a series of stages, each not exceeding 3,000 feet in height; calculate the ratio of the pressures at the top and bottom of each stage, and multiply together the several ratios so found for the ratio of the pressures at the top and bottom of the entire height. For moderate heights, the following rule is sufficient :—deduct from the pressure one-hundredth part of itself for each 262 feet of elevation, 107. Expansion of Water by Heat—Approximate Formula—Com- parison of Units of Pressure.—It is seldom necessary in calculations connected with water pressure engines to take into account the expansion of water by heat; but in the event of its being at any time requisite to do so, the following formula, although only a rough approximation in a scientific point of view, 1s sufficiently accurate for the practical purpose in question, and is extremely convenient, from the ease and rapidity with which its results can be computed, especially when a table of reciprocals is at hand :— Let D, = 62°425 lbs. to the cubic foot, be the maximum density 110 WATER POWER AND WIND POWER. of water; D, its density at a given temperature of T° on Fahren- heit’s scale; then 2D, D, neatly = qey ary 500 _ 500 * T°+ 461° At 212°, this formula gives too great a result by about 3§5; at lower temperatures its errors are much smaller. CompaRIsON OF Heaps oF WaTER IN FEET WITH PRESSURES IN Various Units. © One foot of water at 39°1 Fahr. = 62°425 Ibs. on the square foot. 0°4335 lbs. on the square inch. 0°0295 atmosphere. 0°8826 inch of mercury at 32°. ”? a7 o> 32 a a2 d feet of air at 32°, and 2 2 7733 1 atmosphere. One Ib. on the square foot,.......... 0'01602 foot of water. One lb. on the square inch,........ 2°307 feet of water. One atmosphere of 29922 inches ; Of MELCULY)secccenesieseeess diene 33°9 2 2 One inch of mercury at 32°,......... I°133 4 ‘ foot of air at 32°, and eis at 32°, and one | Gooregs , cas use eae ea One foot of average sea water,...... 1026 ~— foot of pure water. 107 A. Pressure Gauges— Vacuum Gauges.— Instruments for indicating the intensity of the pressure of a fluid contained in a close vessel are called “pressure gauges,” or “vacuum gauges,” according as they show how much that pressure is above or how much it is below that of the atmosphere. Frequently the same instrument answers both those purposes. Of this an example has already been given, in the Indicator (Articles 43, 44), which can be applied to water pressure engines as well as to the steam engine. The following are three examples of other kinds of gauges :— I. The mercurial pressure gauge is the most exact for scientific purposes, It consists, like a siphon barometer, of an inverted siphon, or U-shaped tube, the lower part of which contains mer- cury, and whose vertical legs have a scale attached alongside of them, divided either into inches and decimals, or divisions corre- sponding to pounds on the square inch, or other convenient units of pressure. One leg, by means of a brass nozzle, communicates with the vessel within which the fluid is contained; the other is open to the air. The mercury stands lowest in that leg in which the PRESSURE GAUGES. 111 pressure on its upper surface is most intense; and the difference of level of the mercury in the two legs indicates the difference between the pressure in the vessel, and the atmospheric pressure. To determine, if required, the absolute pressure within the vessel, the absolute pressure of the atmosphere at the time of observation may be ascertained by means of an ordinary barometer. Mercurial vacuum gauges are sometimes used, which indicate directly the absolute pressure within a vessel, by being constructed exactly like a barometer, having the leg containing the mercurial column that balances the pressure to be measured closed hermeti- cally at the top, with a Torricellian vacuum above the mercury, produced in the usual way, by inverting the tube and boiling the mercury in it. It is necessary to accurate measurement, that the scales of mer- curial pressure gauges should be exactly vertical. The relations stated in Articles 6 and 107 between inches of mercury and other units of intensity of pressure, have reference to a temperature of 32° Fahrenheit. For any other temperature, T°, on Fahrenheit’s scale, let h’ be the observed height of a mercurial column, and f the corresponding height reduced to 32°; then i! h= T + 0-0001008 (T° — 33°) wee eee eee eneee (1.) II. The air manometer consists of a long vertical glass tube, closed at the upper end, open at the lower end, containing air, provided with a scale, and immersed, along with a thermo- meter, in a transparent liquid, such as water or oil, contained in a strong cylinder of glass, which communicates with the vessel in which the pressure is to be ascertained. The scale shows the volume occupied by the air in the tube. Let % be that volume, at the temperature of 32° Fahrenheit, and mean pressure of the atmosphere p); let v, be the volume of the air, at the temperature T°, and under the absolute pressure to be measured, p,; then _ (T° + 461°) po % (2) 1 = 493° ‘i Y% ewe rn eters erence eee . III. Bourdon’s gauge is the most useful yet known for practical purposes, Its ordinary construction is represented in fig. 26. A is a cock, communicating with the vessel in which the pressure is to be measured. BB is a curved metallic tube, communicating with A at one end, and closed at the other. The cross-section of this tube is of the flattened form represented in fig. 27, and its greatest breadth is in the direction perpendicular to the plane in which the 112 WATER POWER AND WIND POWER. tube is curved. When the pressure within the tube is greater than the pressure without, the tube becomes less curved; when the pressure without is the greater, it be- eaeae comes more curved. Hig Bis The motions of the closed end of the tube are communi- cated either through the link C D, and lever D E, or by means of wheel-work, to the index EF, which points to a graduated arc. The positions of the graduations on the arc are fixed by comparison either with a mercurial gauge for moderate pressures, and an air manometer for very high pressures, or with another Bourdon’s gauge known to be correctly graduated. These gauges can be made of any required degree of sensibility, so that a some are suited to measure pressures Fig. 26. of less than one atmosphere, and others to measure pressures of several thousand lbs. on the square inch. Their mechanism is usually contained in a cylindrical brass box, and the dial plate and index are protected by a plate of glass, They can be screwed in every required position upon machines acting by the pressure of fluids. 108. Fixing Diameter of Supply Pipe.— In designing a water pressure engine, it ig often necessary to fix the diameter of the supply pipe so that it shall deliver a given number of cubic feet of water per second with a loss of head not exceeding a given limit. Let / denote the prescribed greatest loss of head, in feet. This must correspond to the greatest velocity, and therefore to the greatest flow, through the supply pipe. Let Q be the number of cubic feet of water required by the engine per second, and Q’ the greatest flow per second through the supply pipe. Then if the piston moves for a considerable period with a continuous motion in one direction (as in hydraulic hoists), if the engine is double acting, with an uniformly moving piston, or if it has a pair of single acting cylinders with pistons moving alter- nately and uniformly, Q! HQ nearly a isces wervezon cteanoveres (1.) If the engine drives a rotating crank shaft, Q’ = 157 Q nearly 3.0... eee eee (1 a.) DIAMETER OF SUPPLY PIPE. 113 if the engine has only one single acting cylinder, and Q is reckoned per second of the whole time occupied by the piston in descending as well as in rising, the water stands still in the supply pipe while the piston is descending, and, therefore, in this case, QO! = 2Q nearlyiiccscisicccseoscnwwvened (2.) It has already been stated, in Article 99, that the loss of head in a straight pipe is given by the formula bl ee ad AGE rte (3.) Z being the length, } the circumference, A the sectional area, d the diameter in feet, and 1 J = 0:005 (1 + =) sue eeiabraereetia (4.) este i . Ad In a cylindrical pipe of the diameter d, pgs and, therefore the equations 3 and 4 may be reduced to the following form :— 4Afl. v - d = Rpg ee (5.) 1 4f= 0-02 (i + i): Preerere rere rr rere) (6.) Now A = + 7854 d®; and, therefore, the velocity in the pipe has the following value :— yee es 7 = KT FRA gabe sees (7.) and the height due to the velocity, v Q? 644 = 39°73 dt Sede e nen eeocenenernaaseon (8.) which, being introduced into equation 5, gives 471 Q? | h = 39-73 @ DOO rec erre ree sece ress escens (9.) and consequently din fest = (Gf as Pd eiiet ale (10.) In this formula, the co-efficient of friction, f, depends on the diameter, d, being the quantity sought. It is, therefore, necessary to assume I 114 WATER POWER AND WIND POWER. in the first place an approximate value for 4 f. The value com- monly assumed is 0:0258, which gives, for the first approwimation to the diameter of the pipe, ION 1 d = (0000654 Q” et = 0-2304 (ea) eed (11) The approximate diameter thus found is to be substituted in equa- tion 6, to find a corrected value of 4 f, which being employed in equation 10, gives a second approximation to the diameter of the pipe; and this is almost always sufficiently accurate. To provide for untoreseen causes of increased resistance, such as the deposit of a crust in the pipe, it is customary to add oNE-SIXTH, or thereabouts, to the diameter given by the preceding formule ; but however large the pipe may be, one inch is a sufficient addi- tion for this purpose. The diameter, though computed in feet, is commonly reduced to inches when mentioned in a specification or written on a drawing. The pipe is supposed, in this Article, to have what it ought always to have, a mouthpiece at its upper end, of the form of the contracted vein, whose resistance is nearly insensible (Article 99). The formula for the friction of water in pipes, which is that of M. Darcy, is founded on the experiments recorded in his treatise, Du Mouvement del Hau dans les Tuyaun. ‘When there are several different causes of loss of head, proceed as follows :— Assume a diameter d’, from which, by equation 7, compute the velocity v’ corresponding to the required flow Q’. From that velo- city compute by the formule of Article 99 the total loss of head hf’ corresponding to the assumed diameter. If this differs from the assigned loss of head h, the required effective diameter d is to be computed by the formula— 1. (BNE UN) sss (12) and the actual diameter is to be made one-sixth greater than this effective diameter, if the latter does not exceed six inches; but if it does exceed six inches, then the actual diameter is to be. one inch greater, hi. i arias: Cal Sa 5: If = is a ratio differing little from unity, then EFFECT OF REGULATOR. 115 d=a-{1+5 (F-1) } neaty os (12 4.) 109. Effect of the Regulator.—Let A be the sectional area of the supply pipe; a the area of the opening of the regulator, when par- tially closed ; ¢ the co-efficient of contraction of that opening, as to whose values for different openings, see Article 99. Then by comparing equations 12. and 13 of Article 99 together, it appears that for equal velocities of flow in the same supply pipe, the resistance is increased by the partial closing of the regulator in the proportion— w 32 fr a7) 1+ io) S adh) fol 2 Ata = (for a cylindrical pipe) 1 + a i 1. Let this be expressed, for brevity’s sake, by ltas:l This increased resistance may take effect either in increasing the loss of head, or in diminishing the flow, or in both ways at once ; but in any case, if Q, represents the flow and h, the loss of head, with the pipe uninterrupted, and Q, the flow and h, the loss of head, with the regulator partially closed; then hy h 1:1 igs ood gee bee cca ceneaenee tees 2. tah @) The same principle may also be expressed in the following way :— let %, %, be the effective mean speed of the piston of the engine corresponding to the discharges Q,, Q, ; then iene i aeisiuidlee sakes wea (3.) Uy Uy It is better for economy of power that the contraction of the regu- lator should take effect by diminishing the speed of the engine than by increasing the loss of head; for the volume of water whose passage is prevented by a diminution of speed can be stored in the reservoir for future use; but an increased loss of head gives rise to an irretrievable waste of energy. 116 WATER POWER AND WIND POWER. 110. Action of the Water on the Piston.—In a single acting en- gine, let H, denote the height of the top of the fall above the mean level of the face of the piston, the action of the water on which is under consideration ; h,, the loss of head, by the friction of the water in the supply pipe, regulator, valve ports, and cylinder ; Q, the mean flow, in cubic feet per second ; D, the weight of one cubic foot of water ; A, the area of the piston, in square feet ; 1, the mean intensity of the effort exerted by the water on the piston during the forward stroke, in lbs. on the square foot; w, the mean velocity of the piston, in feet per second ; k', the co-efficient of friction of the piston and mechanism, so that (1— 2") p, is the intensity of the useful load; then Dj =D. (Hy Rp secesiietesev det euccca. (1.) Ap, = D(H, -A,) A = total effort of the water on the PUSCOD Gs... ccaweecsieeanesesvancnas (2.) 2 Um 7 jreseee Cede eve nee cree snaanes (38.) energy is exerted by the water on the piston during the forward stroke, at the mean rate of wAp, = 2D Q(H,—A,) ft-lb. per second;....... (4.) and useful work performed, at the rate of 2(1-#)wAp, = 2(1-k) DQ (H,—A,).........(5.) The value of x’, from experiments of the Messrs. More and the Author, is about 2. for ordinary packing. 10 Further, let H, be the mean height of the face of the piston above the bot- tom of the fall (not exceeding 31-7 feet).—If the bottom of the fall is above the mean level of the piston face, H, is to be made ne- gative ; hg, the loss of head in the discharge pipe and valves ; P», the mean intensity of the effort exerted on the piston during the back stroke; then HEDGE. aces eau) Ap, =D (Gah) Aa wiscsccccsenit) ACTION OF WATER ON PISTON—VALVES. 117 If H, is less than hg, or negative, these expressions become nega- tive, and represent resistance exerted by the water against the piston. During the return stroke energy is exerted on the piston at the mean rate of uA py, = 2D Q(H,— he). ft.-lb. per second......... (8.) If this expression is negative, it represents work lost in forcing the water out of the cylinder. Finally, taking the mean of the expressions 4 and 8, we find for the whole energy exerted by the water on the piston, per second— wA PEP: _ DQ A, + Hy - hy ~ he) EGE SG aeaetaupain: (9.) H =H, + H, being the total fall, and h=h, +h, the total loss of head; while the useful work per second is (1=2") D Q (LAD) cesses rte eeee (10.) and the combined efficiency of the fall and engine— (1—2")(H-A) OS tetrttteeteeeeesenees (11.) This varies, in different cases, from about 0:67 to about 0:8. Section 2.—Of Valves. . 111. Vatves in General, considered with reference to the means by which they are moved, may be divided into three principal classes :—Valves, sometimes called clacks, which are opened and shut by the pressure of the fluid that traverses their openings, and are usually intended for the purpose of permitting the passage of the fluid in one direction only, and stopping its return ;—valves moved by hand ;—and valves moved by mechanism. When a pis- ton drives a fluid, as in ordinary pumps, the valves are usually moved by the fluid: when the fluid drives the piston, it is in general necessary that the valves should be moved by hand or by mechanism. In water pressure engines that work occasionally and at irregular intervals, such as hydraulic hoists and cranes, the valves are usually opened and shut by hand; in those which work periodically and continuously, they are moved by mechanism con- nected with the engine. 118 WATER POWER AND WIND POWER. Safety valves for permitting a fluid to escape from a vessel when the pressure tends to rise above the limit of safety, belong to the class that are moved by the fluid. Regulating valves are adjusted either by hand, or by means of a governor. The seat of a valve is the fixed surface on which it rests, or against which it presses. The Face of a valve is that part of its surface which comes in contact with the seat. When a valve occurs in the course of a pipe or passage, the valve box or chamber, being that part of the passage in which the valve works, should always be of such a shape as to allow a free passage for the fluid when the valve is open, so that the fluid may pass the valve with as little contraction of the stream as possible; and if necessary for that purpose, the valve chamber may be made of larger diameter than the rest of the passage. The usual materials for valves and their seats are iron, bronze, brass, hardwood, leather, india rubber, and gutta, percha. When a valve and its seat are both of metal, they should be of the same metal; for when they are of different metals, a galvanic action takes place, which causes one or other of them to be cor- roded. In water pressure engines and pumps, the best material for the seats of metal valves is some hard wood, such as elm or lignum vite, the fibres being set endways, and constantly wet. India rubber and gutta percha being dissolved or softened by oils, whether fatty or bituminous, are unsuitable materials ior valves to which those fluids have access. 112. The tonnet Valve or Conical Valve is a flat or slightly arched circular plate of metal, whose face, being formed by its rim, is sometimes a frustum of a cone, and some- times a zone of a sphere, the latter figure being the best. Its seat, being the rim of the circular orifice which the valve closes, is of the same Fie. 98 figure with the face or rim of the valve, and ar the valve face and its seat are turned and ground to fit each other exactly, so that when the valve is closed no fiuid can pass. The thickness of a valve of this form is usually from a fifth to a tenth of its diameter, and the mean inclination of its rim about 45° : To insure that the valve shall rise and fall vertically and always return to its seat in closing, it is sometimes provided with a spindle, as shown in fig. 28, being a slender round rod perpendicular to the valve at its centre, and moving through a ring or cylindrical socket. A knob on the end of the spindle prevents the valve from rising too high. When the valve is to be moved by hand or by mechanism, BONNET VALVE—SAFETY VALVE. 119 the spindle may be continued through a stuffing box, and connected with a handle or a lever, so as to be the means of transmitting motion to the valve. When the valve seat is at the upper end of a, cylindrical passage, as in ordinary safety valves, the place of the spindle is often sup- plied by means of a ¢azl, which will be described in the next Article. 113. The Common Safety Valve used for steam boilers as well as for water pressure engines, is a bonnet valve loaded with a weight equal to the greatest excess of the pressure upon each area equal to that of the valve within the vessel on which the valve is fitted, above the pressure of the atmosphere, to which it is safe to subject that vessel during its ordinary use. Sometimes the valve has a vertical spindle rising from it, moving in guides, and loaded directly with cylindrical weights which rest on a collar that surrounds the spindle. Sometimes the load is applied by means of a lever, as in fig. 29, which represents a section of the valve seat and valve, and an ele- vation of the lever. A is the valve, D a stud or knob in the centre of its upper side, C B a lever jointed to a fixed fulcrum at C, B the weight, which can be shifted to different positions on the lever, so as to vary the load on the valve. ; The intensity of the effective pressure p per square inch neces- sary to open the valve is given as follows :—Let B denote the weight applied to the lever, L that of the lever itself, @ C the dis- tance of the centre of gravity of the lever from the joint G, W the weight of the valve, A its area in square inches; then B-BC+L-GC pa {BBC ee ewh es 120 WATER POWER AND WIND POWER. Fig. 30 is an elevation of the valve, showing the tail (already referred to in the last Article), by which it is guided so as to move vertically, and to return always to its seat. Fig. 31 is a horizontal section of the tail, which consists of three vertical ribs or “feathers,” radiating at angles of 120°. Their outer surfaces or edges are small portions of a vertical cylinder, turned to fit the cylindrical tube on which the valve is placed easily but not too o loosely. vv Modifications of the safety valve, spe- = cially suited to steam engines, will be de- : -. a, scribed under the head of that class of Fig. 30. Fig. 31. : rime movers. . 114. The Ball Clack (fig. 32) is a valve of the form of an accu- rately turned sphere. When of large size, it is in general hollow, in order to reduce its weight. Its face is its entire surface: its seat is a spherical zone, as in the case of some bonnet valves already referred to. As the ball clack fits its seat alike in every position, it needs neither spindle nor tail; but either the chamber in which it works must be of such a shape and size as to insure its always fall- ing into its seat, or the same object must be effected by means of wire guards enclosing it, as shown in the figure. The latter plan is the better, as it is the more likely to insure that there shall always be a free passage for the fluid round the valve when open. 115. Divided Conical Valve.—Bonnet valves of large size, when working under high pressures, often require an inconveniently great amount of work to open them, and shut with such violence ag to cause injurious shocks to the machine. To obviate this evil, a valve has sometimes been used, composed of a series of concentric rings. The largest ring may be considered as a bonnet valve, in which there is a circular orifice, forming a seat for a smaller bonnet valve, in which there is a smaller circular orifice, forming a seat for a still smaller bonnet valve, and so on, This arrangement enables a large opening for the passage of water to be formed with a moderate upward motion of each division of the valve ; and conse- quently with a moderate expenditure of work to open it, and a moderate shock when it shuts. 116. The Double-Beat Valve (an invention of Messrs. Harvey and West) is the best contrivance yet known for enabling a large passage for a fluid to be opened and shut easily under a high pres- sure. Fig. 33 represents a section of the valve, with its seats and chamber, and fig. 34 a plan of the valve alone. DOUBLE-BEAT VALVE. 121 The valve shown in the figure is for the purpose of opening and shutting the communication between the pipes A and B. The pipe B is vertical, and its upper rim carries one of the two valve seats, which are of the form of the frustum of a cone, and each marked a. A frame C, composed of radiating partitions, fixed to and resting on the upper end of the pipe B, carries a fixed circular disc, whose rim forms the other conical valve seat. The valve D is of the form of a turban, and has two annular conical faces, which, when it is shut, rest at once on and fit equally close to the two seats a, a. When the valve is raised, the fluid passes at once through the cylindrical opening between the lower edge of the valve and the upper edge of the pipe B, and through the similar opening between the upper edge of the valve and the rim of the circular disc. The greatest possible opening of the valve is when its lower edge is midway between the disc and the rim of the pipe B, and is given by the following formula :— Let d, be the diameter of the pipe B; d,, that of the disc; h, the clear height from the pipe to the disc, less the thickness of the valve ; A, the greatest area of opening of the valve; then 122 WATER POWER AND WIND POWER. dt dy | 2 A = 31416 Rieter Gy and in order that this may be at least equal to the area of the pipe B, viz., ‘7854 dj, we should have ad} . hat least — 2(d,+4,) piece eee ra ee eeeee nes (2.) which, if as is usual, d, = d,, gives h at least = a Soetvea yuauede eeaide 2d (2 a.) but / is in general considerably greater than the limit fixed by this rule. If the upper and lower seats are of equal diameter, the valve is little affected by any excess of pressure either in A or in B; anda force a little exceeding its own weight is sufficient to open it. It is then called an EQUILIBRIUM VALVE. If the diameter of the upper seat is the less, an excess of pres- sure in A over B tends to keep it shut, and an excess of pressure in B over A to open it. If the diameter of the upper seat is the greater, an excess of pressure in A over B tends to open the valve, and an excess of pressure in B over A to keep it shut. This arrangement is seldom used. In each case, the force arising from difference of intensity of pressure, and tending to open or shut the valve, as the case may be, is nearly equal to that difference multiplied by the difference between the area of the pipe B and that of the circular disc. The equilibrium valve is the kind of double-beat valve most commonly used in steam engines. In water pressure engines, . pumps, and hydraulic apparatus generally, the lower valve seat is generally made a little larger than the upper. 117. A Flap Valve, illustrated by fig. 35, is a lid which opens and shuts by turning on a hinge. The hinge may either be a metal joint, or may be provided by the flexibility of the material of the valve itself, when that is leather or india rubber. The face may be of leather, india rubber, or metal; in the last case the face and seat Fig. 35. should be carefully scraped to true planes. In hydraulic machines, the most common material for flap valves is leather, which should, as far as possible, be kept constantly wet. A large leather flap may be stiffened in the middle by a plate of wood or metal. e FLAP VALVES—THROTILE VALVES. 123 A pair of flap valves placed hinge to hinge (usually made of one piece of leather fastened down in the middle) constitute a “BUTTER- FLY CLACK.” The chamber of a flap valve should be of considerably greater diameter than the valve. 118. A Blap and Grating Valve consists of a round disc of water- proof canvas or of india rubber, resting on a flat horizontal grating, or on a plate perforated with holes, to which it is fastened down at the centre, being left loose at the edges. To prevent the valve from rising too high, it is usually provided with a guard, which is a thin metal cup formed like a segment of a sphere, grated or per- forated like the valve seat, to which it is bolted at the centre, serving also to fasten the valve down at that point. The cup should have a metal shoulder at its base, a little less in depth than the thickness of the flap, to press directly against the seat, so that the tension of the bolt may not be brought to bear on the flap, which would be unable to sustain it. When the valve is raised by _a current from below, it applies itself to the bottom of the cup. When the current is reversed, the fluid from above, pressing on the valve through the holes in the cup, drives it down to its seat again. According to Mr. Bourne, valves of this class, when made of india rubber, may be about six inches in diameter and five-eighths of an inch thick. They are adapted to large pumps by making them sufficiently numerous. They are now much used for the air pumps of steam engines, in which the pressure they have to sus- tain is less than one atmosphere. It is probable that they are not capable of bearing very high pressures. 119. The Dise and Pivot Valve, or Throttle Valve, consists of a thin flat metal plate or disc, which, when shut, fits closely the opening of a pipe or passage, generally circular in section, but sometimes rectangular. The valve turns upon two pivots or journals, placed at the extremities of a diameter traversing its centre of gravity, so that the pressure of the fluid against it is balanced about its axis of rotation, and the valve can be turned into any angular position by a force sufficient to overcome its friction. When the valve is turned so as to lie edgeways along the pas- sage, the current of fluid passes with very little obstruction: when it is turned transversely, the current is stopped, or nearly stopped. By placing the valve at various angles, various openings can be made. If the valve, when shut, is perpendicular to the axis of the pipe, the opening for any given inclination of the valve to that axis is proportional to the coversed-sine of the inclination. If the valve is oblique when shut, the opening at a given inclination is proportional to the difference between the sine of that inclination and the sine of the inclination when shut. 124 WATER POWER AND WIND POWER. The face of this valve is its rim; its seat is that part of the internal surface of the passage which the rim touches when the valve is shut; and those surfaces ought to be made to fit very accurately, without being so tight as to cause any difficulty in opening the valve. One of the journals of the valve usually passes through a bush or a stuffing box in the pipe, so as to afford the means of commu- nicating motion to the valve from the outside. It is difficult to make valves of this class perfectly water-tight or steam-tight without too much impeding their motion. They are, therefore, not so well suited for stop valves as for regulating valves, and for the latter purpose they are much used, both in water pressure engines and in steam engines. Their form will be illustrated in the figures of engines of which they form part. 120. Slide Walves.—The seat of a slide valve consists of a plane metal surface, very accurately formed, part of which is a rim sur- rounding the orifice or port, which the valve is to close, and from ri to 30 of the breadth of that orifice, while the remainder extends to a distance from the orifice equal to the diameter of the valve, in order that the valve, when in such a position as to leave the port completely open, shall still have every part of its face in contact with the seat. The valve is of such dimensions as to cover the port together with that portion of the seat which forms a rim surrounding the port. The face of the valve must be a true plane, so as to slide smoothly on the seat; and in large slide valves consists of a rim surrounding that central part of the valve which directly closes the orifice, and which is more or less concave, to enable it the better to resist the pressure which acts on the back of the valve when it is closed. Very large slide valves, such as those in the course of the main water pipes of large towns, are strengthened at the back by flanges or ribs. ' The valve and its seat are contained within an oblong box or case, large enough to permit the easy motion of the valve within it, and usually forming an enlargement in the course of a pipe. The valve rod, by means of which the valve is opened and shut, passes out through a stuffing box; or instead of such a rod, a valve of moderate size often has a nut fixed to it, within which works a screw on the end of an axle, which passes out through a bush, and has shoulders within and without to prevent it from moving longitudinally, and a square on the outer end on which the key fits that is used in turning it. SLIDE VALVES—PISTON VALVES. 125 The total pressure between the face and seat of a slide valve is equal to the total area of the valve, multiplied by the excess of ene of the pressure behind it above the pressure in front of it. That total pressure being multiplied by the co-efficient of friction between the face and seat, which may be as much as 0-2 (see Article 13), gives the resistance of the valve to being opened, which is almost always considerable. For the double purpose of enabling that resistance to be overcome by a moderate effort, and of preventing the shocks which would arise from suddenly closing the valve when there is a rapid current passing, it is necessary that the valve should move slowly as compared with the driving point of the apparatus by means of which it is moved. In mode- rate sized valves, this is usually provided for by causing them to be opened and shut by turning a screw, as already described, or by moving the valve rod by a rack and pinion of suitable dimen- sions. Large slide valves are sometimes moved by attaching the valve rod to a piston contained in a cylinder, which has a pair of supply pipes, one for each end, bringing water from the main pipe behind the valve, and a pair of discharge pipes, one for each end, leading to the main pipe in front of the valve. These four pipes are pro- vided with suitable cocks or valves to be opened and shut by hand; and thus is formed a small water pressure engine, by means of which the slide valve can be moved either way when required. ; : : The opening and shutting of a very large slide valve is sometimes facilitated by making it in two divisions—a larger and a smaller. The smaller division is opened first and closed last: the effect of which is, that it alone has to be moved against the resistance arising from the greatest difference of pressure before and behind the valve; and that the larger division has only to be moved against the resistance arising from the pressure corresponding to the loss of head caused by the contraction and subsequent enlarge- ment of the stream in passing through the smaller division of the orifice ; as to which see Article 99. : : Rotating slide valves are sometimes used, in which the valve and its seat are a pair of circular plates, having one or more equal and similar orifices in them. The passage is opened by turning the valve about its centre until its openings are opposite to those of the seat, and shut by turning it so that its openings are opposite solid portions of the seat. : . . Various forms of slide valve peculiar to the steam engine will be described under the head of that class of prime movers. : 121. A Piston Valve is a piston moving to and fro in a cylinder, 126 WATER POWER AND WIND POWER. whose internal surface is the valve seat. The port is formed by a ring or zone of openings in the cylinder, communicating with a passage which surrounds it; and by moving the piston to either side of these openings, that passage is put in communication with the opposite end of the valve cylinder. Details and particular forms of the piston valve will be illustrated farther on. 122. Cocks.—This term is sometimes applied to all valves which are opened and shut by hand, but its proper application is to those valves which are of the form of a frustum of a cone, or conoid, turning in a seat of the same figure. In the most common form of cock, the seat is a hollow cone of slight taper, having its axis at right angles to the pipe in whose course it occurs. The valve is a cone fitting the seat accurately, and having a transverse passage through it of the same figure and size with the bore of the pipe, so that in one position it forms simply a continuation of the pipe, and offers no obstruction to the current, while by turning it into different angular positions, the opening may be closed either partially or wholly. A screw and washer at the smaller end of the cock serve to tighten it in its seat. “ Schiele’s curve” (Article 14) is sometimes used for cocks. In a form of cock much used for fire plugs, a short vertical pipe rising from a water main terminates in a hollow conical frustum, tapering slightly upwards, and having an orifice in its side leading into a lateral pipe. Inside the hollow cone is the valve, being another cone, also hollow, open at the base, closed at the top, and having an orifice in its side of the same size and figure with that in the outer cone. This inner cone is pressed upwards into the outer cone by the water within and below it, which thus tends to keep the joint between the cones water-tight; and by turning the inner cone into various angular positions, the lateral orifice can be fully opened, or partially or wholly closed. 123. Blexible Tube and Diaphragm Walves.— A class of valves has lately been introduced, in which an india rubber or gutta percha pipe, which when fully open is cylindrical, can be wholly or par- tially closed by pinching it as if in a vice, by means of a screw. In another class of valves, the mouth of a cylindrical pipe, from which a current of water is discharged, has opposite to it a flexible circular diaphragm of india rubber, of larger diameter than the pipe, fixed at the edges at such a distance from the pipe as to leave a sufficient passage for the fluid between the edge of the pipe and the face of the diaphragm. Behind the diaphragm is a round, slightly convex stopper or plug, which, when pushed forward by means of a screw, presses the diaphragm tightly against the mouth of the pipe, and so closes the passage. PLUNGER—ITS LOAD. 127 Section 3.—Plungers, Pistons, and Packing of Water Pressure Engines. 124. a Plunger is a metal cylinder, closed at the ends, and accu- rately turned on the cylindrical surface, which, in a single acting pump or water pressure engine, acts at once as piston and as piston rod, by having a reciprocating motion in a cylinder. The internal diameter of the cylinder is larger than that of the plunger by an amount sufficient to prevent their touching. Round the circular aperture through which the plunger works is a water-tight “cupped leather collar,” to be described in the next Article. A section of a cylinder showing a plunger working in it is given in fig. 37, a few pages farther on. The area of the transverse section of the plunger, and not that of the cylinder in which it works, is to be used in computing the effort exerted by the pressure of the water upon it. The weight of a plunger is often made considerable, and some- times a load also is placed upon it, in order that energy may be stored in lifting it, and restored when it descends. To exemplify the mode of adjusting the weight and load of the plunger for that purpose, let W denote the gross weight of the plunger and load of a single acting water pressure engine, which is to be adjusted in such a manner that the useful resistance overcome during the ascent and descent of the plunger shall be equal. Let R, denote that useful resistance. Let P, be the effective effort of the water on the plunger during the up stroke; P,, if positive, the excess of the effort of the atmo- sphere above the resistance from back pressure of the water during the down stroke. If the latter quantity is the greater, P, becomes negative, and its sign must be reversed in the following equations (see Article 110) :-— Let R, be the friction during the up stroke, and R, during the down stroke. (As to the friction of the collar, see the next Article.) Then, during the up stroke, when W is a resistance, then subtracting (1) from (2), and dividing by 2, we find, We pes es Ea een eB) 128 WATER POWER AND WIND POWER. 125. The cupped Leather Collar through which a plunger works is shown in section on a small scale in fig. 37, farther on, and on a larger scale in fig. 38. It resembles in shape an inverted annular channel; and is lodged in an annular recess surrounding the plunger. Its hollow channel is turned towards the inside of the cylinder; and the water, tending to enlarge that channel, presses its outer side against the recess, and its inner side against the plunger, and so keeps a water-tight joint. The friction between a plunger and its leather collar is given approximately by the following formula: let d be the diameter of the plunger, in inches; 7, the pressure, in lbs. on the square inch; R’, the friction, in lbs., then R=fp d. According to Mr. William More’s experiments, f= about 1:2 x the depth of bearing surface of the collar; and the friction is, roughly, one-tenth of the load in ordinary cases; according to Mr. John Hick’s experiments, f ranges from ‘05 to -03. 126, Leather Packed Piston. A piston is distinguished from a plunger by accurately fitting the cylinder in which it works, so as to be water-tight, and by being of no greater thickness than is necessary to make it water-tight. It is attached to a rod, strong enough to transmit the effort that acts on it to the mechanism which it drives (see Articles 61,71), The water acts on one face of the piston, or on both, according as the engine is single acting or double acting. When the water acts on that side of the piston from which the rod extends, the cylinder cover has a stuffing box in its centre, through which the rod works; and the opening is made water-tight by a leather collar, as already described, or by hempen packing. In computing the effort exerted by the water on that side of the piston from which the rod extends, the sectional area of the rod is to be deducted from the area of the piston; in other words, the effective area of the piston on that side is less than the total area in the ratio d? 1- il; where d’ is the diameter of the rod, and d that of the piston. ‘When the piston is to be packed by means of leather, its disc, which fits the cylinder easily (and to which the rod is firmly attached by a screw, or a screw and nut, ora key), is made slightly concave on the upper and under faces; then on each of those faces is placed a leather ring, shaped somewhat like a saucer with a hole in the centre, and having its edge turned up all round so as to press PACKING—-HYDRAULIC PRESS. 129 flat against the inside of the cylinder for a breadth of an inch, or an inch and a-half, or thereabouts. ‘The edges of those leather rings are thus turned opposite ways, that of the upper ring upwards, and that of the lower ring downwards. Each of the rings is held in its place by a round saucer-shaped guard or piston cover, bolted or screwed to the body of the piston. The friction of such pistons, like that of plungers, is found to be about one-tenth of the effort of the water. A piston, like a plunger, may be loaded for the purpose of storing energy, and according to the same principles. 127. Wempen Packing.—The body of a piston which is to be packed with hemp is from two to four inches less in diameter than the cylinder in which it is to work; and its depth is about one-sixth of the diameter of the cylinder. It bulges a little at the middle of its depth. Round its base there projects a horizontal flange, whose rim fits the cylinder easily. Above that flange and round the body of the piston is wrapped the packing, consisting either of loose hemp, or of a soft loosely spun hempen rope, called “gasket,” soaked with grease. Above the packing is a ring of the same size and figure with the flange, for pressing the packing down, and causing it to fit tightly in the cylinder. This “junk-ring” is held down and can be moved towards the flange so as to compress the packing when required, by means of screws. The stuffing box of a piston rod is packed with hemp in a similar manner, the hemp being pressed down and made to fit tightly round the piston rod by means of the stuffing box cover and its bolts or Screws, Section 4.—Of Hydraulic Presses and Hoists. 128. The Hydraulic Press is supplied with water from an arti- ficial source, as stated in Article 97, and is therefore not a prime mover, but a piece of mechanism for conveniently applying the energy of the muscular power, or steam power, by which its supply pumps are worked. It is described here first on account of its exemplifying in a simple form various parts which enter into water pressure engines generally. : Fig. 36 is an elevation of a hydraulic press supplied by a hand forcing pump; fig. 37 is a vertical section of the cylinder and pump; and fig. 38 represents the plunger collar: these figures have already been referred to in Articles 124, 125. Fig. 39 is the safety valve, differing from that previously shown in Article 113 only in being so small that the spindle is of as great diameter as the valve. ; A is the press cylinder, made thick enough to resist the pressure, according to the principles of Article 64, The bottom should be K 130 WATER POWER AND WIND POWER. segmental or hemispherical, not flat. Bis the plunger; Q its collar (see Articles 124, 125); C a plate carried on the head of the 14 D On ll if a TT gin if (Dp arora SS G tcl et | =e S HAL INS& S \ oo \ = i Zi) aa eo a AVS CAB NI. Vig 36. Fig. 39, plunger; D the upper plate of the press; E standards guiding the motion of the plate C, and strong enough to resist a working ten- sion equal to the force to be exerted by the plunger. F is the HYDRAULIC PRESS. 131 pump cylinder, [ its plunger, and K a guide for the plunger rod. Gis the pump handle; H and H’ are two alternative centres, about either of which it can be made to work, so as to give a greater or a less leverage as required. L is the supply pipe of the press cylinder, through which water is forced into it by the pump. It contains a self-acting clack, N, opening towards the press cylinder, to prevent the return of water towards the pump. M is the supply valve or suction valve of the pump, being a clack opening upwards; O is the safety valve, P its weight; R the escape valve or discharge valve, being a conical plug worked by means of a screw, kept shut while the plunger is being raised, and opened, so as to let the water escape from the press cylinder, when the plunger is to be allowed to descend by its weight. The discharge pipe, leading from this valve to a tank from which the pump draws its water, is the tail race of the machine. The following formule relate to the efficiency of the hydraulic press, and show how to compute the force and the energy required to work it. Let R be the useful resistance to be overcome by the plunger in rising, and v the velocity with which it is to rise in feet per second. Then the useful work per second is Piicnoe Ferenc te (1.) Let W be the weight of the plunger; then R + W is the gross load of the plunger. To this has to be added, for friction, a quantity estimated by the formula of Article 125, so that the effort of the water on the plunger is nearly P=(R+W)( ees (2) A being the area, and d the diameter of the plunger. Then the intensity of the effective pressure of the water in the press cylinder ought to be 2 d p=g FMA ean (3.) in pounds on the square foot or square inch, according as A is in square feet or square inches. Let a’ be the sectional area of the supply pipe L; then ae J is the velocity with which the water flows through that pipe; and 2 AD IE the height due to that velocity. 132 ; WATER POWER AND WIND POWER. Let 2+ F be the sum of the various factors of resistance due to the length and diameter of that pipe, and the several bends, knees, contractions, enlargements, and other causes of resistance which occur in its course, computed according to the principles of Article 99. The head due to the velocity of the current in the pipe is lost owing to the sudden enlargement of the channel in entering the cylinder. Hence the loss of head in the pipe is v? A? Ga es! aaa Scere ener rceensaseeees (4.) Let p' = Dh be the pressure equivalent to this loss of head. Then is the pressure in the pump; and if a be the area of the pump plunger, : é ‘ oo A is the effort to be exerted by it on the water, with a velocity ae “ so that the energy exerted per second by the pump plunger on the water is OA ADAE DP) eiswsdnvsderdoncuatesdenges (7.) To this has to be added an allowance for the friction of the pump, which, as it includes not only the friction of the plunger collar, but that of the mechanism and valves, may be estimated at about one-fifth of the effort on the water; giving for the whole energy expended per second, ERG iacontiecasties (8) Comparing this with the expression (1) for the useful work, it appears that the efficiency of the machine is fp 5 Ep egy (9.) Let be the ratio of the velocity of the pump handle to that of the pump plunger; then HYDRAULIC PRESS—HOISTS—PURCHASES. 133 is the effective velocity of the pump handle, reckoning down strokes only, and 6a(p +p) | RTT tttteateneensenssens dl.) is the effort required there. The effort which would have been required, had there been no friction and no loss of head, and no load except the useful load, would have been Sp srrsisiai ameareansanenaiee (12.) being less than the actual effort (11) in the same proportion in which the efficiency (9) is less than unity. In order to produce a continuous current of water into the press cylinder, there are sometimes a pair of pumps having their plungers connected to the opposite arms of a lever with two arms of equal length, so as to perform their down strokes alternately. At the end of each arm of the lever is a cross bar for the workmen to lay hold of. When the pumps are worked by a steam engine, it is usual to have a set of three, with their plungers respectively connected with three cranks on one shaft, making angles of 120° with each other. Let s be the length of stroke of one of them, @ the area of its plunger, T the number of revolutions made by the shaft in a second ; then, as the quantity of water required per second is v A, we must have The hydraulic press may be worked by water from a natural | source; in which case the waste of energy owing to the friction of the pump disappears, and the efficiency becomes simply R . A@ Eph the flow and total head required to drive the machine being respectively 129. Water Pressnre lists and Parchases.—The simplest water pressure hoist is a hydraulic press, having on the top of its press plunger a cross-head, from the ends of which hang chains for lifting a load. Such was the apparatus used in raising the girders of the Britannia Bridge. 134 WATER POWER AND WIND POWER. For this machine, R, in the equations of the preceding Article, represents the load to be lifted, and W the weight of the plunger, cross-head, and chains. : To a similar class belongs the water pressure hoist or purchase invented by Mr. Miller for dragging ships up the inclined plane of ‘‘ Morton’s slip.” In this machine the press cylinder is placed at the upper end of the inclined plane, and at an inclination equal to that of the plane; and the tractive force is exerted upon the chain. which drags the vessel either by a plunger with a cross-head, or by a piston with a piston rod passing through a stuffing box in the bot- tom of the cylinder; the effective area of piston A in the latter case being the total area less than the sectional area of the piston rod. Let 7 denote the angle of inclination of the slip ; J, 2 co-efficient of friction, whose value is about zr; W,, the weight of the ship; R,, her total resistance to being dragged up the slip; then Ry = W, (sin t+ f COS 2)..ccecceseceseeees (1.) and if v be the velocity with which she is to be dragged, the useful work per second is Let W, be the weight of the cradle, chains, piston or plunger, and every additional weight which moves along with them; then the resistance R, + R, = (W, + W,) (sin ¢ +f 08 2)......... (3.) is to be substituted for R + W in equations 2, 3, and 9, of Article 128, when the formule of that Article will all become applicable to the machine now in question. . 130. Water Pressure Cage Moist. — A water pressure hoist for raising and lowering a cage containing mineral wagons, or other heavy bodies, consists essentially of the following parts :— I. IL. TfL A frame, carrying pulleys, a chain passing over the pulleys, and a cage hung to one end of the chain, as already described for a bucket hoist in Article 101. IV. A vertical or nearly vertical hoist cylinder, firmly fixed to one side of the frame, and having a leather packed piston (Article 126) with a piston rod passing upwards through a stuffing box in the cylinder cover. The upper end of the piston rod carries a pulley, usually about thirty or thirty-six inches in diameter. The chain is carried under this pulley, and its end made fast to the top of the frame ; the effect of which is, that the velocity of the piston is one-half of that of the cage; and the length of stroke of the piston is one-half of the lift. WATER PRESSURE HOIST. 135 V. The supply pipe of the hoist cylinder; having, near the hoist - cylinder, its regulator, which is a screw slide valve, opened and shut by hand. VI. The discharge pipe of the hoist cylinder, having also its screw slide valve. As to relief clacks, see Article 134 a. ‘ VII. The store cylinder, from which the supply pipe of the hoist cylinder comes, resembles a hydraulic press, with its collared plunger. It is destined to contain a reserve of water to supply the hoist when it is occasionally worked so rapidly as to expend water faster than the source can supply it. The store cylinder is re- plenished with water from the source in the intervals when the hoist is standing idle. The plunger of the store cylinder is loaded with a weight corresponding to the pressure required. The same store cylinder, if large enough, may answer for several hoists. The store cylinder may also be made like a hydraulic press inverted, the plunger being fixed, and standing on a firm founda- tion, with the supply and discharge pipes traversing it; and the cylinder being moveable, with its collared end downwards, and its closed end upwards, and a sufficient weight placed upon it. VIII. The supply pipe of the store cylinder. TX. The source, which may be an elevated reservoir, or a water work main giving a sufficient flow and pressure, but which is much more frequently artificial, being a set of forcing pumps worked by a steam engine, as described in Article 128. The following are the formule applicable to machines of this kind. Let R, be the useful load to be lifted, s, the height to which it is to be lifted in the time ¢ with the velocity v, = s, + ¢; then the useful work per second is An ordinary value of v, is one foot per second. For a first rough estimate of the power required to produce this effect, the efficiency of the whole machine may be taken approxi- mately at 3 ; so that the energy expended per second will be 3 DQH= E Ry My, NEGrly. ..ceeeereeerece eee (2) The object of making this rough estimate is to fix the size of the hoist cylinder. If the source is a reservoir or a water work pipe, the total head H is in general fixed; if the source is artificial, there are in most cases reasons which fix a limit to H ; it is seldom, for example, desirable to exceed 500 or 600 feet. The value of H. having been fixed approximately, we have for the flow of water per second while the cage is being lifted— 136 WATER POWER AND WIND POWER. ey oe (3,) and for the flow per stroke of the hoist, which is the effective volume of the hoist cylinder— Gp (4.) DH 9 eee A, being the effective area of the piston; that is, the excess of the area of the piston above that of the piston rod; and s,-+ 2 its length of stroke, so that ae 2Q¢ 3R, 1 3s DH When H is limited to 500 feet, the piston rod may be made one- fiftieth of the area, or about one-seventh of the diameter, of the piston; so that we shall have in that case— . Re 50:A, _,, — Diameter of piston = 1 x<7854 = 114 ,/A,...(6.) Let W, be the weight of the cage ; then Ris Wa sxccncanece biedaontetaecaiety (7.) is the working tension on the chain; and six times this should be the ultimate strength of the chain. Let W, be the weight of the chain and pulleys ; then eet 10 will be very nearly the friction of the mechanism. Inasmuch as by the tackle used, the velocity of the piston is half that of the chain, we shall have for the tension on the piston v0od— 2(Ray AP Ro) jeswsvs excunserersericanna a (9.) to which adding one-tenth for the friction of the piston and rod, we find for the efort p A, and intensity of pressure p, exerted by the water on the piston— pA=i (+R) | ee (10.) p= To ie The loss of head by the resistance of the supply pipe, and the corresponding pressure, are found as in equation 4 of Article 128, Ww. — 30 cba fecake ap acaean (8.) HYDRAULIC HOIST. 137 with due attention to the formule of Article 99. ct py’ be the pressure so found. Then is the pressure in the store cylinder when its plunger is falling. Let A, be the area of the plunger of the store cylinder, to be fixed in a manner which will be afterwards explained; and d, its diameter. Then, adding the friction of the collar, we have— (pp Ag EF Gc nnn (12.) for the gross load of the store cylinder plunger, including its own. weight. The pressure in the store cylinder when its plunger is rising is (1 +58) i a svhclvesectsaanese (13.) and not only the store cylinder but the hoist cylinder and supply pipe ought to have their strength adapted to this working pressure, by making their bursting pressure six-fold, and using the rules of Article 64. i Let p" be the pressure due to the resistance of the supply pipe leading from the source to the store cylinder ; then d, 1 2 mt DH, =p,=(+ 42) (pty) + pl vee (14) is the pressure corresponding to the total head required at the source, natural or artificial. Should the head H, calculated by this “ formula prove greater than the head H originally assumed, the supply pipes should be made larger, so as to diminish their resist- ance until H, does not exceed H. As to this, see Article 108. Then the energy expended by the water for each second that the hoist works is , Pp Q— DQ Ac escerdinage dion (15.) and the efficiency of the fall of water is Ry, % et a cascnsacuvescereusenes yeast 16. no (16.) If the source is artificial, the work lost in overcoming the fric- tion of the pumps or other mechanism used in producing it is to be added to p, Q in estimating the whole energy expended per second of working of the hoist and the resultant efficiency of the entire machine. A single store cylinder and a single source or set of pumps may supply either one hoist or several, To find the rate of flow from 138 WATER POWER AND WIND POWER. the pumps or other source into the store cylinder, ascertain the length of the interval during which the hoists usually stand idle, and add to it the length of the following interval during which they are at work. Let T be the number of geconds in the whole period so found; and of these seconds let T, be the number of seconds during which any hoist is rising, and Q the quantity of water it requires per second while rising. Then summing the quantities for all the hoists— is the quantity of water required in each period of T seconds; so that the uniform rate of flow from the source into the store cylinder should be giving for the uniform power of the fall, in foot-pounds per second, D Q, H,. The capacity absolutely necessary for the store cylinder is fig Sg ST SS Tyo cssusanciscnes (19.) (s, being its length of stroke); but it is in general advisable to make In the preceding description, the chain tackle is supposed to be so arranged that the velocity of the hoist cylinder piston is one- half of that of the cage; but any required velocity-ratio can be given by suitably arranged fixed and moving pulleys. This com- bination in mechanism of chain-and-pulley tackle, with hydraulic connection, was first introduced by Sir William Armstrong, who has applied it not only to hoists but to cranes and various other machines. (See Z'rans. of the Inst. of Mechanical Engineers, Aug., 1858.) , Suction 5.—Of Self-Acting Water Pressure Engines. 131. General Deseription— When a “ water pressure engine” is spoken of without qualification, it is generally a self- “acting water pressure engine that is meant; that is, an engine which differs from a mere press, hoist, or crane, in having distributing valves for regulating the supply and discharge of the water, which are moved, directly or indirectly, by the engine itself; so that it isa machine having a periodical motion, which motion having once been made to commence, goes on of itself until it is stopped, either by shutting WATER PRESSURE ENGINES, 139 the throttle valve and so stopping the supply of water, or by dis- engaging or otherwise stopping the valve motion. The distributing valves are in general of the piston valve kind (Article 121), and worked by a small auxiliary water pressure engine. Inasmuch as the friction of water in passages varies as the square of the velocity, and the work performed in overcoming it as the cube of the velocity (other things being equal),—and inasmuch as the velocity for a given flow of water varies inversely as the area of the passage :—it is favourable to the efficiency of a water pressure engine, which is to perform useful work at a given rate, that its dimensions should be made as large and its movement as slow as is consistent with due economy of first cost in each particular case. It is also favourable to efficiency that the stroke of the piston should be long, for the reversal of its motion is seldom unaccom- panied by shock; and at each such reversal the position of the valves has to be altered; both of which cause loss of work. The most advantageous use, therefore, to which a water pressure engine can be applied is the pumping of water, to which slow motion and a long stroke are well adapted, because they are favourable to efficiency, not only in the engine but in the pump which it works. Nevertheless, in situations where a large supply of water at a high pressure can easily and cheaply be obtained, water pressure engines have been used with advantage where considerable speed is requisite, as in driving rotating machinery. Various engines of this kind have been designed and executed by Sir William Armstrong. The whole of the mathematical principles which apply to water pressure engines have been explained in the preceding sections of this chapter. Their resultant efficiency, as ascertained by practical experience, ig stated by different authorities at values ranging from 0-66 to 0-8. The variations probably arise chiefly from differences in the resistance of the passages traversed by the water, and perhaps also to some extent from errors in the mode of calculating the quantity of water used. In estimating the probable efficiency of any proposed water pressure engine, the lowest value of the efficiency, viz, 0-66, is of course the safest to assume as a rough estimate; but a closer approximation may be obtained by making a calculation according to the method already exemplified in detail in Articles 128 and 130; that is, commencing with the resistance of the useful work and the velocity of the piston, and computing in their order all the 140 WATER POWER AND WIND POWER. different prejudicial resistances to be overcome, and the quantities . of work to be performed in oyercoming them. 132. Single Acting Water Pressure Engine. — The example chosen to illustrate this kind of water pressure engine is a mine pumping engine, designed by M. Junker, as described by Mr. Delaunay. It resembles in many respects the pumping engines of Mr. Darlington. Fig. 40 is a complete vertical section of the engine, during the induction, or admission of the water to the cylinder. SINGLE ACTING WATER PRESSURE ENGINE. 141 Fig. 41 is a vertical section of the valve ports and passages during the eduction, or discharge of water from the cylinder. Both figures are lettered alike. A is the main piston, which lifts the an) QPP pump plunger rod by means of a rod tra- f mE versing the bottom of the main cylitider d BB. C is the supply pipe, and U its throttle valve. D is the valve port, consisting of a pipe connecting the bottom of the cylinder with an annular passage surrounding the valve cylinder, as already described in Article 121. E is the piston valve. G the discharge pipe, and V its throttle valve. When E is below D, as in fig. 40, D communicates with C, and water is ad- mitted into the cylinder to raise the main piston. When E is above D, as in fig. 41, D communicates with G, and the water is discharged from the cylinder during the descent of the main piston. The piston valve E is notched at the edges, in the manner shown in the figure, in order that the opening and closing of the port may take place oy degrees—the water flow- ing partially through the notches for a short time before and after the edge of the piston arrives at the edge of the ports. The valve cylinder consists of two parts of unequal diameter, the upper being the larger. In the lower, or smaller part, the piston valve E works. In the upper, or larger part, wholly above the supply pipe, works the counter-piston F ; this being larger than E, and fixed to the same rod, the pressure of the water between E and F tends to raise them both. The upper side of F is provided, if necessary, with a rod, or a “érunk” (that is, a hollow piston rod), passing through a stuffing box in the top of the valve cylinder.’ The use of this is to diminish the effective area of the upper side of F, so that it shall not be more than is requisite to enable the pressure of the water, when admitted through the port I into the " space above F, to overcome the friction of the piston valve and its appendages, together with the excess of the pressure on the lower Fig. 41. 142 WATER POWER AND WIND POWER. side of F above the effective pressure on E. The sectional area of this rod or trunk, therefore, should be about as much less than the area of E as the area of E is less than the whole area of F. H is the supply pipe and M the discharge pipe of the part of the valve cylinder above the counter-piston, which, with its cylinder, forms an auxiliary enginé to work the valve of the principal engine. K is the piston valve of this auxiliary engine, which regulates the admission and discharge of the water through the port I, exactly as the main piston valve E regulates the admission and discharge of the water through the port D of the main cylinder. L is a plunger of the same size with K, and fixed to the same rod, in order that the pressure of the water in the space between K and L may not tend to move the piston valve K either upwards or downwards. The auxiliary valve rod to which K and L are fixed is connected by means of a train of levers and linkwork marked OQRST, with a lever carrying on its end a “crutch,” P. N is a vertical “tappet rod,” carried by the main piston A, from which project the tappets X and Y for moving the crutch P. The engine works in the following manner :— Suppose, asin fig. 41, that the main piston valve E is raised, the water escaping by the route DG from the main cylinder, and the main piston falling. When the main piston approaches the bottom of its stroke, the upper tappet Y strikes the lower hook of the crutch P, and depresses it, together with the auxiliary piston valve K. This admits water from the main supply pipe C, by the route HI, to the annular space above the counter-piston F, so as to depress it, together with the main piston valve EH, into the position shown in fig. 40. Then the water from the main supply pipe passes through D into the main cylinder BB, and lifts the main piston A. When the main piston approaches the top of its stroke, the lower tappet X strikes the upper hook of the crutch P, and raises it, together with the auxiliary piston valve K. This allows the water to be discharged from the annular space above the counter-piston F, by the route I M ; so that the pressure of the water between F and the main piston valve E upon the excess of the area of F above that of E, raises F and E together back to the position shown in fig. 41, cuts off the supply of water to the main cylinder, and opens the passage for the discharge of water from the main cylinder through D into G. The main piston then descends, thus completing a double stroke, and the entire cycle of operations recommences. The process may be summed up by saying, that of the two engines, the main and the auxiliary, _ each works the valve of the other. WATER PRESSURE ENGINES. 143 The frequency of the strokes of the engine depends on the speed with which the valve mechanism works ; and this can be controlled by means of regulating cocks on H and M, the supply and dis- charge pipes of the auxiliary engine. 133. A Double Acting Water Pressure Engine has a main cylinder, whose ends are both closed, the main piston rod passing out through a stuffing box in one of them, and each end being pro- vided with a port like D in figs. 40 and 41, communicating with one valve cylinder, both of whose ends communicate with the dis- charge pipe. The supply pipe enters the valve cylinder at ‘the middle of its length. On one rod are carried a pair of equal and similar piston valves, one for each port, which rise and fall to- gether: the distance between them is so adjusted, that when they are raised, and the upper piston valve leaves the upper port in communication with the supply pipe, the lower piston valve at the same time leaves the lower port in communication with the dis- charge pipe through the lower end of the valve cylinder—and that when they are depressed, and the lower piston valve leaves the lower port in communication with the supply pipe, the upper pis- ton valve at the same time leaves the upper port in communication with the discharge pipe through the upper end of the valve cylinder. The valve piston rod may be moved either directly by tappets, or indirectly by a small auxiliary engine. 134, Botative Water Pressuré Engines.—In this class of engine, ‘ the cylinders are either double or single acting, and the piston rods, by means of connecting rods and cranks, drive a shaft. In order to diminish as much as possible the variations of the effort upon the crank shaft, it is usual to have two, three, or four cylinders acting in succession; but a single cylinder would answer, if the fly wheel were made of sufficient inertia. : The inertia of the fly wheel for a rotative water pressure engine is to be determined by the same rule as for a non-expansive steam engine. (See Articles 52, 53.) : The frequency of the strokes is greater in this than in other kinds of water pressure engines; and therefore, to avoid great re- sistance, the supply and discharge pipes, and the valve ports, must be larger as compared with the piston than in other water pressure engines. The best rule is to make, if practicable, every passage of such an area, that the velocity of the water in it shall not exceed the maximum velocity of the pistons. The best valves appear to be double piston valves. Engines of this kind are very useful and convenient for driving sma!l machines in towns where there is a copious supply of water at a high pressure; and also in mines, where steam engines might be inconvenient or unsafe. In the 144 WATER POWER AND WIND POWER. latter situation they may be driven by a portion of the watcr which is pumped up by the draining engine of the mine. The most successful in practice of rotative water pressure en- gines are those of Sir William Armstrong, as to which, and as to hydraulic cranes and hoists, detailed information may be found in the Transactions of the Institution of Mechanical Engineers, ne 1858. Their efficiency is roughly estimated at from -66 to *77. 134 4, Relief Clacks form an important part of the engines of Sir William Armstrong. Their object is to prevent the shocks which would otherwise occur within the cylinder on the closing of the port, and consequent sudden stopping of the motion of the water. A set of relief clacks for a single acting cylinder consists of two, one opening upwards, in a passage leading from the cylinder port into the supply pipe, and the other opening upwards, in a passage leading from the discharge pipe into the cylinder port. The effect is, that the pressure in the cylinder cannot rise above that in the supply pipe, nor fall below that in the exhaust pipe. For a double acting cylinder, four clacks are required, two for each port. Supplement to Part I[., Chapter IV., Section 2. 134 B. Compound Clacks for large pumps are now much used, in which the general form of the compound seat is like a cone with its vertex upwards, and an inclination of from 45° to 75°; but the sides do not slope, being formed into a series of flat circular steps. Each of those flat steps is pierced with a ring of openings, and forms the seat of a clack or set of clacks, prevented from rising too high by a projecting.or overhanging portion of the step next above. ‘When there is a single clack to each step, it is a ring of metal or india rubber; when a set of clacks, they are leather flaps or india rubber balls. (See a paper by Mr. John Hosking, 7rans. Inst. of Mech. Engineers, August, 1858,) Section 6.—Of Water Pressure Engines with Air Pistons. 135. The Hungarian Machine is the name given to an engine first used for pumping mines at Schemnitz, in Hungary, in which the duty of a piston is performed by a mass of confined air, trans- mitting pressure and motion from a stream of water whose fall constitutes the source of power, to another mass of water, whose elevation to a given height is the useful work to be performed. Its principle is identical with that of a piece of apparatus known as “ Hero’s Fountain,” from having been described in the Pneu- HUNGARIAN MACHINE. 145 matics of Hero of Alexandria, a philosopher who flourished in the second century B.C. The flow of the fall must ex- ceed the quantity of water to be raised in a given time, and the head must exceed the height to which that water is to be raised, in proportions whose approxi- mate values will afterwards be pointed out. The principal parts of the machine are indicated in fig. 42. A, a tank or well at the bot- tom of a shaft, for collecting the water to be raised. B, an air-tight receiver, of sufficient strength to resist the greatest internal pressure that acts in the apparatus, wholly im- mersed in the water of the well. This may be called the pump barrel. The bottom of the re- ceiver must not touch the bottom of the well, for there must be space enough between to admit R the access of the water of the well to C, a clack opening inwards, in the bottom of the receiver B. _. D,a delivery pipe, rising from near the bottom of B to the drain at the top of the shaft which carries away the water raised. It is desirable, though not abso- lutely necessary, to have at the = BHF, bottom of D a clack opening up- = wards. E, an air-tight receiver, at | least as strong as B, which cor- j responds to the cylinder of a Wig 22 common water pressure engine, eee and is placed tr any ae the top of the shaft which is convenient for discharging the water of the driving source after it has done its work. This may be called the working barrel. — F, the air pipe, connecting the top of the pump barrel B with the top of the working barrel E. "e | bu 146 WATER POWER AND WIND POWER. G, the waste air cock, at the top of E. H, the discharge valve, at the bottom of H, for discharging ihe water which has performed its work in the working barrel. I, a reservoir, at the top of the fall. K, the supply pipe, connecting that reservoir with the bottom of the working barrel E. L, the admission valve, near the bottom of the supply pipe. The valves H and L may be opened and shut by floats in the working barrel, or by a small auxiliary water pressure engine, or by a small wheel driven by the water discharged. The sketch shows them as spindle valves; but a single piston valve might be made to do the duty of both. The machine is set to work by opening the air waste cock G, L at the same time being shut. The water from the well A opens the clack C, enters and fills the working barrel B, and drives out the air through G, so that E and F only remain filled with air. Then G is shut, and remains shut while the machine is working; H is shut and L opened, and the working proceeds as follows :— The driving water from I descends through K and L into EH, and compresses the air contained in EH and F. The pressure so exerted on that air is transmitted to the water in B, and causes it to rise in the delivery pipe D. When the pressure has become equal to that of the column of water in D added to its resistance, " the lifted water issues from D into the drain, and continues to do so until E is filled with water. Then by the valve gearing, L is shut and H opened; and the water in E is made to flow out, partly by its own weight, and partly by the pressure of the expand- ing air. As soon as the air has fallen to its original pressure, more water from the well flows through C into B, and drives all the air back into F and E. Then H is shut and L opened, and the cycle of operations recommences. In the following investigation of the efficiency of this engine, the fluctuations of level of the water in the pumping and working barrels, B and H, are neglected in comparison with the height of lift, and the head of fall. Let h, denote the head of water which is equivalent to one atmosphere, or 33:9 feet on an average. Let h, be the height of the outlet of the delivery pipe D above the surface of the water in A; D, the weight of a cubic foot of water, or 62:4 Ibs.; Q,, the number of cubic feet per second to be raised ; then DQ hijscisscceveee vieteeeeeeseeeens (1.) is the useful work per second. Let hy be the head lost by the resistance in the pipe D, com- puted by the principles of Article 99; then HUNGARIAN MACHINE. 147 Rigs hy b hagen escewcasesvacs seceeeseens(Qs) is the head of water equivalent to the pressure to which the air must be compressed in E, F, and B, before the water will issue from the outlet of D. That pressure, in atmospheres, may be expressed thus— h, +h. n=1thth, Setar eae evista 0 and the working pressure which the barrels and air pipe must be adapted to bear is n —1 atmospheres. The volume of air which must pass per second from E into B, while the water is being forced out of B, is Q, cubic feet at the pressure of m atmospheres, When air is compressed or dilated so suddenly that it has not time to lose or gain heat by communication with adjoining bodies, its density varies much more slowly than its pressure; but when there is time for all the heat produced by compression to be con- ducted away, and for all the heat which disappears during expan- sion to be replaced from neighbouring bodies, the density varies very nearly as the pressure simply. It is probable that the latter supposition is very near the truth in the present case, especially as the air is charged with moisture, which facilitates the communica- tion of heat. Therefore, as the original pressure of the air, before being com- pressed by the descent of the water from I into H, is one atmo- sphere, the volume of the mass of air which descends per second, at the original pressure, is O29 Oona ee: (4,) and this algo is the volume of water which must descend from the source per second, in order to perform the work. Let B and E be taken respectively to represent the capacities of those portions of the pump barrel and working barrel which are ulternately filled and emptied of water at each stroke, and let F denote the capacity of the air pipe; then we must evidently have Be Tn qaemassamae (5) BoP = ee Let h, be the loss of head by the resistance of the supply pipe, valves, dsc. Then the total head required for the fall is HL = hy H hig H hg jeneesenreereerseeveneee(6s) so that the total energy expended per second is 148 WATER POWER AND WIND POWER. DQH=2DQ, (hy thet hz) h, th, +he : = FATS DO Gy tha the)j saieiseece (7.) 0 and comparing this with the useful work in formula 1, it appears that the efficiency of the engine is Qik, h, = hy hy QH 7 nh, hy thy) (hy Fh, Thy) (hy Fg hy)” 1. The diminution of efficiency represented by the factor ae the 3) above expression, and corresponding to a loss of head to the amount of n arises from the loss of the energy exerted in compressing the air, and in agitating the water in E and K during the time of that compression, when the head is more than sufficient to produce the entrance of the water with the proper velocity. The energy exerted in compressing the air is restored during its expansion ; but being wholly employed in forcing the water out of the discharge valve H, it is lost in the end. The chief recommendation of the Hungarian machine appears to be its simplicity. | 136. Am Air Vessel is a sufficiently strong air-tight receiver, generally cylindrical, with a hemispherical top, the upper part of which contains some imprisoned air, while the lower part contains water, and communicates with the cylinder or. the supply pipe of a water pressure engine, or any other vessel or passage in which changes of the velocity of a mass of water occur. The compressi- bility and expansibility of the air, admitting of the alternate flow of a portion of water into and out of the air vessel, enable such changes of velocity to be made by degrees. Rotative water engines were formerly made with an air vessel in connection with each end of the cylinder; but relief valves (Article 134 a) are now considered preferable. Supplement to Part II., Chapter I., Article 94. 136 A. Water Meters are instruments for measuring and record- ing the flow of water through pipes. Detailed descriptions of several kinds may be found in the Z’ransactions of the Institution of Mechanical Engineers for 1856. The meters now in ordinary use may be divided into two classes: piston meters and wheel meters. . WATER METERS. 149 As an example of a piston meter may be taken Mr. Kennedy’s, which is a small double acting water pressure engine, driven by the flow of water to be measured. As it-has been found, in other piston meters, that the recording merely the nwmber of strokes made by the piston leads to errors in computing the flow, this meter is so constructed that, by means of a rack on the piston rod driving pinions, the distance traversed by the piston is recorded by a train of wheelwork, with dial plates and indexes. An example of a wheel meter is that of Mr. Siemens, being a small reaction turbine or “ Barker’s mill,” driven by the flow. The revolutions are recorded by a train of wheelwork, with dial plates and indexes. Another example of a wheel meter is that of Mr. Gorman, being a small fan turbine or vortex wheel driven by the flow, and driving the indexes of dial plates. All those three meters are found to answer well in practice, and can be placed in the course of a pipe under any pressure. The ordinary errors of a good water meter are from 3 to 1 per cent. ; in extreme cases of variation of pressure and speed, errors may occur of 24 per cent. The value of the revolutions of a wheel meter should be ascer- tained experimentally, by finding the number of revolutions made during the filling of a tank of known capacity. 150 CHAPTER V. OF VERTICAL WATER WHEELS, Srction 1.—General Principles. 137. Pond and Weir.—The head race or supply channel of a vertical water wheel commences either at a large store reservoir, being a natural or artificial lake in which the rainfall of a district is collected, or at a smaller reservoir or pond, being an enlargement in the course of a river, formed by building a weir or dam across it. The object of that weir is not-merely to store a surplus flow of water at one time, and employ it to supply deficiency of flow at another, but to prolong a high top water level from its natural situation at a place some distance up the stream, to a place as near as possible to the bottom of the fall, where the tail race joins the natural channel, and thus to diminish as far as possible the loss of head arising from friction in the head race and tail race. The weir, throughout either the whole or a part of its length, acts asa waste weir or overfall, discharging over its crest the surplus flow of floods, beyond what the wheel can use. I. Level of Pond—Weir not Drowned.—In order to find how high the water in the pond will stand above the crest of the weir, a formula is to be used founded on equation 2 of Article 94, with this difference, that whereas for a sharp edged notch the co-efficient of discharge ¢ is from 0-595 xo 0°667, it is considerably smaller for the flat or slightly rounded crest of a weir. Its values under various circumstances have been determined by the experiments of Mr. Blackwell. For the purpose at present in view, it is sufficiently accurate to take the following average value :— For waste weirs, CSOD MEATY. «co iacitedousnsessthascrse (1.) This gives for the flow over the weir, in cubic feet per second, Q = 5°35 6b WF = 2-67 DRE 5. sseeesseneeeee(2) so that the greatest height A, in feet, at which the water in the pond near the weir stands above the crest of the weir is given by the following formula :— h= \/ = NOU 3 sees connrwewsewent (3.) POND AND WEIR—BACKWATER. 151 Q being the greatest flow in cubic feet per second, and 6 the breadth in feet of the outlet over the weir crest. II. Weir Drowned.—A. weir is said to be “ drowned” when the water in the channel below it is higher than its crest. Let h, h', be the heights of the water above the weir crest, in the pond and in the waste channel respectively ; then the flow per second is Qaseby/ {2g@—m). (u+4) re wa(4.) when Q and /' are given, the exact determination of h requires the solution of a cubic equation, but the following approximate solution is in general sufficient :— first approximation, hy =h'+ / > ide drdinaee asses (5.) This always gives too great a result. Second approximation. An amended value h, of h, is given by the formula 5 h’ — — / —- oe hg =h, -—h ( fh ees Closer approximations may be obtained by repeating the process. 138. Backwater is the effect produced by the elevation of the water level in the pond close behind the weir, upon the surface of the stream at places still farther up its channel. For a channel of uniform breadth and declivity, the following is an approximate method of determining the figure which a given elevation of the water close behind a weir will cause the surface of the stream farther up to assume. Let ¢ denote the rate of inclination of the bottom of the stream, which is also the rate of inclination of its surface before being altered by the weir. Let 4, be the natural depth of the stream, before the erection of the weir. Let 3, be the depth as altered, close behind the weir. Let 6, be any other depth in the altered part of the stream. It is required to find x, the distance from the weir in a direction up the stream at which the altered depth 4, will be found. Denote the ratio in which the depth is altered at any point by 3 yy; =T; 8 And let ¢ denote the following function of that ratio :— 152 WATER POWER AND WIND POWER. fics {ae = 5 BYP. log. {1 Gres =e} is + a tan. = a | A convenient approximate formula for ee @? is as follows :— 1 5 _ + 87 eee ceenecccrrace (2.) Compute the values, 9, and 9%, of this function, corresponding to the ratios Q nearly = s 772 +=; 3, i i, 1 and 7? = i Then pee ae ~~ 264). (¢, — %) Ryesronee(B,) The following table gives some values of 9 :— r G r Q T!O: seecawan vores © US. catwarievsewss 166 TAT spestuxee strane 680 TQ- caeessaen season 147 B29 secceshrmessnauis 480 210: sas deeseemrewaisiers 132 D3) inmes neta siete 376 D2 wessauuiddaerice 107 MA, tectare Uetopepacerenisis 304 DAS) wsadinstodeces 089 Ter apsduasuumecen ee 255 BAO: eswwauenresaves 076 TO cscesnacccesscns 218 BAS). | wieupewcnsavawe 065 TZ: . ssiaceweeiatncdy ‘189 SO! awnateaceueeancs 056 The first term in the right hand side of the formula 3 is obviously the distance back from the weir at which the depth 5, would be found if the surface of the water were level. The second term is the additional distance arising from the declivity of that surface towards the weir. The constant 264 is an approximation to 2+/, J being the co-efficient of friction. For a natural declivity of 1 in 264, the second term vanishes. For a steeper declivity, it becomes negative, indicating that the surface of the water rises towards the weir; but although that rise really takes place in such cases, the agreement of its true amount with that given by the formula is somewhat uncertain, inasmuch as the formula involves assumptions which are less exact for steep than for moderate natural declivities. It is best, therefore, in cases of natural declivities steeper than 1 in 264, to compute the extent of backwater simply from the first term of the formula. WASTE SLUICES—HEAD RACE—SLUICES, 153 139. Waste Stuices in a wall forming part of the weir are used to enable the surplus water of floods to be discharged with a lower elevation of the surface of the pond, and a less extent of backwater than would be practicable if all the surplus flow had to pass over the weir-crest, A. self-acting waste sluice invented by a French engineer, M. Chaubart, _ A is shown in fg. 43, which is a ver == tical section. It has been found to answer well where it is required to maintain the surface of the water in a pond or canal very accurately at a certain level. AB is the sluice or valve plate, re- a shut, its upper edge A 5 kK eing at the proper water level. TD Lyi The dite ie Pinned pair of m7 A cast iron sectors, resting on horizontal Hig ae: platforms. E is one of those sectors; F G its platform. The edge of each sector has a groove, in which lies a chain, fixed at F to the platform, and at H to the sector. This pair of chains resists the tendency of the water to press the sluice forward. When the water is at the level of A, the resultant of its pressure acts at a depth AO which is two-thirds of the whole depth A B of the sluice. Through C draw C D perpendicular to A B, cutting the centre line of the chain FH in D. Then the sectors and plat- forms must be so formed and placed, that when the sluice is shut, the point of contact of each sector with its platform shall be vertically below D ; and then the combined resistance of the chains and platforms will be directly opposed to the pressure of the water, and will balance it. When the water rises above A, and begins to overflow, the centre of pressure rises above C, so that the pressure and the resistance are no longer directly opposed. The sluice then rolls upon its sectors into a new position of equilibrium, and in so doing, it not only depresses the edge A, so as to make the overflow more rapid, but raises the edge B, so as to make an outlet at the bottom of the passage B K, through which the surplus water escapes much more rapidly than it could do by merely overflowing. 140. Head Race and Sluices.—To protect the conduit, which is the head race, from the surplus water of floods, it is advisable that between it and the natural stream there should be a wall or an embankment rising a sufficient height (say from two to three feet) above the highest level of floods; and also that a similar wall or embankment should extend across the upper end of the conduit, 154 | WATER POWER AND WIND POWER. where it leaves the pond. In the latter situation a wall is the more suitable. It is traversed by a passage for admitting water from the pond to the conduit, capable of being closed or opened to a greater or less extent, by means of one or more slwices, which are slide valves moving vertically in guides, made of timber or iron, and moved by means of a screw, or of a rack and pinion. It is advis- able not to make sluices broader than about four or five feet. Ifa greater width of opening is required, the passage from the pond into the conduit should be divided by walls or piers into a sufficient number of parallel passages, each furnished with a sluice. The loss of head at a sluice is to be found by the principles of Article 99, Division V. The channel of the head race is to be made as large as is con- sistent with proper economy in first cost. Supposing its flow Q in cubic feet per second, and its figure and dimensions, to be fixed beforehand, the declivity which it requires is to be computed by the principles of Article 99, Division VI., equations 13, 15, 16, 17. Supposing the flow Q, and the rate of declivity 7 = h +7 (h being the fall), to be given, the figure and transverse dimensions of the channel are to be fixed in the following manner :— The form of least resistance for the cross-section of an open channel of a given area A, is obviously a semicircle; its border 6 being the shortest which can enclose the given area. Its hydraulic mean depth is one-half of its radius; that is, r being its radius, and also the maximum depth of water in it, and m the hydraulic mean depth, Mr. Neville has shown, that if it is necessary that the cross- section of a channel should be bounded by straight lines, the form of least resistance, for given directions of those lines, is one in which all the straight lines are tangents to one semicircle, having for its radius the greatest depth of water in the channel; and in such forms, the hydraulic mean depth is still one-half of the radius of the semicircle, as in equa- tion 1. For example, let it be required to draw the best figure for a channel with a flat bottom, and sides of a given slope. In fig. 44, let C A D represent the surface Fig. 44. of the water, and AB=r its greatest depth. With the radius A B describe a semicircle ; draw a horizontal tangent to it, EBF, for the bottom of the CHANNEL OF HEAD RACE. 155 channel, and a pair of tangents EG, F D, at the given inclination, for the sides. The border is6—=CEFD, and the area A —dr=vr. In such channels, the length of each of the slopes, CE, FD, is equal to the half-breadth C A. If the channel is to be built of brick, stone, or concrete, with cement or hydraulic mortar, either the semicircular form may be employed, or a rectangular form with a flat bottom and vertical sides, the breadth being double of the depth; or a semi-hexagon, consisting of a flat bottom whose breadth is equal to half the breadth at the surface of the water, and a pair of slopes inclined at 60° to the horizon. The second and third are figures which fall under Mr. Neville’s rule; and the third has the least resistance of all figures whose borders consist of a bottom and two slopes. If the channel is to be made of clay with rubble stone pitching, Mr. Neville’s form is to be used, with slopes of at least 14 to one. The figure having been selected, it is obvious that the sectional areas of all similar figures will be proportional to the squares of their hydraulic mean depths; so that we may put n being a factor depending on the figure. For a semicircle, ga 2 CD89 2 i ences neem eenenseree (3.) For a half-square, n=8 pee ee cence res vee er eeeener eneees (4.) For a half-hexagon, n=4 j= C928 aechncengiad ean (5.) For Mr. Neville’s figure, with a flat bottom, and slopes inclined at any angle 4 to the horizon, 8 n=4 (cosee 6+ tan 3) scope eaaabeataveeawe (6.) The velocity of flow is VQ MM. .ecseccrcecereceeeesenes (7.) Making, therefore, the proper substitutions in equation 17 of Article 99, we find fe he (8) m 2gremi 2gn? me’ from which is deduced the following value of the required hydraulic mean depth :— : m= a) a leet (9.) 29 n? 4 156 WATER POWER AND WIND POWER. The value of f is given in Article 99, equation 15, and contains a small term varying inversely as the velocity. Assuming as an approximate average value f= 0°007565j..ccsecssetsescseseees (10.) we find 2 Q2 z a= sears) Pee (11.) and having computed the required hydraulic mean depth, all the other dimensions of the channel can be deduced from it. The head race should have a waste weir and sluice of its own, near its lower end, to prevent the risk of the water overflowing its banks; and if it is of great length, it may be advisable to have several waste weirs along its course. 140 A. Table of Squares and Fifth Powers.—The preceding for- mula is exactly similar to equation 11 of Article 108, except that in the present case the diameter of the pipe d is replaced by the hydraulic mean depth of the channel m, and the multiplier 0-23 by (8512 n2)- 5, Considering that for pipes and channels of similar figures, the fifth powers of the corresponding transverse dimensions are propor- tional to the squares of the volumes of flow, it appears that a table of squares and fifth powers, such as is here given, is useful in com- paring pipes and channels of different dimensions. Suppose, for example, that for two similar channels of the same declivity, the volumes of flow are in a given proportion, look, in the column of fifth powers, for two numbers as nearly as possible in that propor- tion ; and opposite them, in the column of squares, will be found two numbers nearly proportional to the corresponding transverse dimensions of the channels. 141. The Regulating StImice should be placed as close as possible to the wheel. It delivers the supply of water either above its upper edge, like a weir or notch board, or between its lower edge and the lower edge or si// of the opening in which it slides. The delivery above the sluice is the best suited for wheels on which the water acts chiefly by its weight. The discharge in cubic feet per second for a given depression of the upper edge of the sluice below the surface of the water in the head race may be cal- culated by the formule of Article 94, Division III. The delivery between the lower edge of the sluice and the sill is the best suited to wheels on which the water acts chiefly by impulse. In both these cases, the co-efficient of discharge for a vertical sluice may be taken on an average as C= OF sssvevs avlurnaacenswersan +e(1.) TABLE OF SQUARES AND FIFTH POWERS. 15 > ‘ Square. Fifth Power. Square. Fifth Power. to I 00 I 00000 55 30 25 5032 84375 11 I 21 I 61051 56 31 36 5507 31776 12 I44 2 48832 57 32 49 6016 92057 13 1 69 371293 58 | 33 64 6563 56768 14 I 96 5 37824 59 34 81 4149 24299 15 225 7 59375 60 36 00 4776 00000 16 256 10 48576 61 37 21 8445 96301 17 289 14 19857 62 38 44 g161 32832 18 324 18 89568 63 | 3969 9924 36543 19 3 61 24 76099 64 | 4096 | 10737 41824 20 4.00 32 00000 65 42 25 11602 90625 21 441 40 84101 66 43 56 12523 32576 22 484 5I 53632 67 44 89 13501 25107 23 529 64 36343 68 | 4624 | 14539 33568 24 5 76 79 62624 69 | 4761 | 1564031349 25 6 25 97 65625 79° 4900 |. 16807 00000 26 6 76 118 81376 41 50 41 18042 29351 27 7 29 143 48907 72 | 5184 | 19349 17632 28 7 84 172 10368 73 53 29 20730 71593 29 8 41 205 T1149 94 5476 22190 06624 30 9 00 243 00000 95 50 25 23730 46875 31 9 61 286 29151 76 57 76 25355 25370 32 | 1024 335 54432 77 | 5929 | 27067 84157 33 | 1089 391 35393 78 | 6084 | 28871 74368 34 | 1156 45435424 || 79 | 6241 | 3077056399 35 1225 525 21875 80 64 00 32768 00000 36 12 96 604 66176 81 65 61 34867 84401 37 | 13 69 693 43957 82 | 6724 | 37073 98439 38 | 1444 792 35108 83 | 6889 | 39390 40643 39 I5 21 902 24199 84 40 56 41821 19424 40 16 00 1024 00000 85 9225 44370 53125 41 16 81 1158 56201 86 43 96 47042 70176 42 | 1764 | 1306 91232 87 | 7569 | 49842 09207 43 | 1849 | 147008443 88 | 7744 | 52773 19168 44 | 1936 | 1649 16224 89 | 7920 | 5584059449 45 20 25 1845 28125 go 81 00 59049 00000 46 21 16 2059 62976 gI 82 81 62403 21451 4] 22 09 2293 45007 92 84 64 65908 15232 48 | 2304 | 2548 03968 93 | 8649 | 69568 83693 49 | 2401 | 282475249 94 | 8836 | 73390 40224 5o 25 00 3125 00000 95 90 25 447378 09375 51 26 OL 3450 25251 96 92 16 81537 26976 52 | 2704 | 380204032 97 | 9409 | 85873 40257 53 | 2809 | 4181 95403 98 | 9604 | 90392 07968 54 | 2916 | 4591 65024 99 _i 9801 | 95099 00499 158 WATER POWER AND WIND POWER. because the contraction is partial ; but the sluice is .ery often inclined ; and then, for an inclination of 60° to the horizon, or thereabouts, e=0-74 Sree e neces eneeneacecersetccees (2. ) and for an inclination of 45°, or less, C0 Sivccweey, sbastenmsueesnre swat (3.) The regulating sluice is moved by mechanism suitable for adjust- ing its position with nicety, such as a rack and pinion, or a screw. 142. Water Wheel Governors are all much alike in principle, though varied in details. The single example here chosen to illustrate them is by Mr. Hewes. Figs. 45 and 46 are elevations of this appara- tus viewed along and across a horizontal shaft, to be afterwards men- tioned ; fig. 47 is a hori- zontal section, below the level of the pair of re- volving pendulums, which are shown in theelevation as forming the uppermost part of the apparatus, and. are carried by a vertical : spindle, driven by the Hig, 47. water wheel. As to revolving pendulums in general, see Articles 19, 55. WATER WHEEL GOVERNORS. 159 From the rods of the revolving pendulums two links suspend a square slider, which rotates, rises and falls with the balls of. the pendulum, and from which projects a cam A. From a vertical shaft D, there projects a horizontal fork B, whose prongs are at opposite sides of the pendulum spindle. The end of the right-hand prong is above, and the left-hand prong below, the level of the cam A, when it is at the elevation corresponding to the proper speed of the wheel, so that the cam revolves without touch- ing either prong; but the slider, immediately above and. below the cam, is of such dimensions, as to bring the fork to its middle position if it has deviated from it. [In many water wheel governors, the fork corresponding to B is four-pronged, having one pair of prongs at the middle elevation of the cam, and wide enough apart to allow the cam to revolve freely between them when the fork is in its middle position. The other two prongs are closer to the spindle, and one is above, and the other below, the middle elevation of the cam, like the two prongs of the fork shown in the figures. | The lower end of the pendulum-spindle carries a horizontal bevel wheel, which drives two vertical bevel wheels, turning loosely on a horizontal shaft, which by suitable mechanism is connected with the regulating sluice. The vertical bevel wheels obviously rotate in opposite directions. E is a double clutch, which in its middle position is free of both the vertical bevel wheels; but which, by being moved to one side or to the other, can be made to lay hold of either of those wheels, so as to make that wheel communicate its rotation to the horizontal shaft. ' C is a second fork, projecting from the vertical shaft D, and clasping the clutch, so as to regulate its position. When the water wheel goes faster than its proper speed, the pendulums rise, lifting along with them the revolving cam A, which strikes the upper and right-hand prong of the fork B, and drives it towards the right, together with the second fork C, which shifts the clutch so as to lay hold of one of the vertical bevel wheels, and thus causes the horizontal shaft to rotate in such a direction as to close by degrees the regulating sluice; and this closing goes on until the water wheel has resumed its proper speed, when the pen- dulums fall to their middle position, and lower the cam so that it no longer strikes either prong of the fork. The clutch is then disengaged from both wheels, and the sluice remains in the position to which it has been brought. When the water wheel goes slower than its proper speed the pendulums sink, lowering at the same time the cam A, which strikes the lower and left-hand prong of the fork B, and drives it 160 WATER POWER AND WIND POWER. towards the left, together with the second fork C, which shifts the clutch so as to make it lay hold of the other vertical bevel wheel, and thus causes the horizontal shaft to rotate in such a direction as to open by degrees the regulating sluice ; and this opening goes on until the water wheel has resumed its proper speed, when the pen- dulums rise to their middle position, and lift the cam A so that it no longer strikes either prong of the fork. The clutch is then dis- engaged from both wheels, and the sluice remains in the position to which it has been brought. 143. A General Description of Vertical Water Wheels will now be given, and illustrated by figures of those forms of the different classes of wheels which were most common before the latest im- provements, these being reserved for the more detailed descriptions in the ensuing sections. Vertical water wheels may be classed as follows :—I. Overshot wheels and breast wheels, being vertical wheels, on which the water acts partly by its weight, or by potential energy, and partly by its impulse, or by actual energy. II. Undershot wheels, being ver- tical wheels, on which the water acts by its impulse. The follow- ing are the essential parts common to all vertical water wheels :— 1. The avis or shaft, and its gudgeons or journals. 2. The radiating parts on which the water acts; which in overshot and breast wheels are buckets or cells ; in undershot wheels, floats or vanes. 3. The arms or spokes and other framework by which the buckets or floats are connected with the shaft. The channel or chamber in which the wheel works is called the wheel race or wheel trough. Water wheels are protected from frost, and from other causes of stoppage and injury, by being enclosed in a wheel house. I. Overshot and Breast Wheels.—The water is supplied to this class of wheels at or below the summit, and act’ wholly, or chiefly, by its weight. The periphery of an overshot wheel con- sists of the sole plate, a cylindrical drum, and the crowns, being two thin vertical rings, connected with the shaft by arms and braces, and having the space between them divided into cells by curved or angular trough-shaped partitions called buckets. The water pours from the pentstock through the regulating sluice, some- times guided by a spout, into the openings at the outer edges of the circle of buckets, filling them in succession. Formerly the buckets used to be closed at their inner sides, which are parts of the sole plate, but now they are made with openings for the escape and re-entrance of air. While the buckets are descending, part of the water overflows and escapes, and this is a cause of waste of energy : as each bucket arrives at the lowest point of its revolution, it discharges all its water into the tail race, and ascends empty. A breast wheel differs from an overshot wheel chiefly in having VERTICAL WATER WHEELS. 161 the water poured into the buckets at a somewhat lower elevation as compared with the summit of the wheel, and in being provided with a casing or trough, called a breast, of the form of an arc of a cylinder, extending from the regulating sluice to the commencement of the tail race, and nearly fitting the periphery of the wheel, which revolves within it. The effect of the breast is to prevent the over- flow of water from the lips of the buckets until they are over the tail race. The usual velocity of the periphery of overshot and high breast wheels is from three to six feet per second ; and their avail- able efficiency, when well designed and constructed, is from 0-7 to 0-8. The diameter of an overshot wheel must be little less than the height of the fall of water, and that of a high breast wheel somewhat greater ; and they are, consequently, sometimes of enor- mous size. A few exist exceeding seventy feet in diameter. Wheels of this class are the best where there are large supplies of water and falls that are not too low. II. Undershot and Low Breast Wheels.—Wheels of this class are driven chiefly by the impulse of water, discharged from an opening at the bottom of the reservoir with the velocity produced by the fall, against floats or vanes. Every such wheel has a certain velocity of maximum efficiency, being the velocity of the wheel which gives the least possible velocity to the discharged water, and bearing a ratio to the supply-velocity of the water which depends on the form of the floats, but does not in any case differ much from 3. In undershot wheels of the old construction, the floats are flat boards in the direction of radii of the wheel, and the maximum theoretical efficiency is 4. The available efficiency is much less, seldom ex- ceeding 4. An undershot wheel, provided with a breast or casing extending as before described from the sluice to the commencement of the tail race, becomes a low breast wheel, in which the water acts partly by weight, though chiefly by impulse. This class of wheels was much improved by Poncelet, who curved the floats with a concavity backwards, adjusting their position and figure so that the water should be supplied to them without shock, and should drop from them ixto the tail race without any horizontal velocity. The maximum theoretical efficiency of such wheels is as great as that of overshot wheels, but their available efficiency has not been found to exceed 0:6. They are well adapted to low falls with large supplies of water. Fig. 48 is a general view of an overshot wheel of the old con- struction. A, spout; B, shaft and gudgeons; C, spokes ; D, crowns, one having a toothed ring, for driving a pinion, and so giving motion to machinery ; E, sole plate; F, buckets; G, tail race, in which the water runs in the direction opposite to that of the motion of the adjoining part of the wheel. M 162 WATER POWER AND WIND POWER. Figs. 49, 50, and 51, are vertical sections of part of the rim of an overshot wheel ; figs. 49 and 50 showing wooden buckets, and fig. Fig. 49. Fig. 50. Fig. 51. 31 iron buckets. In each of these figures, D denotes the crown, E the sole plate, F the buckets. Two methods were formerly em- ployed of preventing the air in the buckets from impeding the entrance of the water; one was to make a few small holes in the sole plate, and the other, to make the wheel broader than the spout, so that the air could escape at the ends of the buckets while the water en- tered in the middle. The method now used will be de- scribed in the sequel. Fig. 52 is a wooden breast wheel of the old construction, with flat floats. A, reservoir ; B, sluice, worked by a rack and pinion; C, breast and wheel trough ; D, wheel; E, ef tail race, in which the water wt #4 moves along with the wheel. NE S| The water acts on this wheel ee ANN Lg partly by impulse and partly \ i by weight. Fig. 53 is an undershot wheel of the old construction. A, reservoir; B, sluice; C, wheel trough ; D, wheel; E, tail race, in which the water IMPULSE OF WATER ON VANES. 163 Se with the wheel. The water acts on this wheel wholly 144, Impulse of Water on Vanes (partl : y extracted from 4. i. 648, 649).—The action of water “by impulse” against & solid Fig. 56. surface, is that pressure which is exerted by the water against the surface in consequence of the velocity and direction of the motion of the water being changed by contact with the surface. The direction and amount of the pressure exerted by a jet or stream of water against the solid surface are determined by the following principles, which are the expression of the second law of motion (already cited in Articles 14, 29, 30),as applied to this case :— I. The direction of that pressure is opposite to the direction of the change produced in the motion of the stream during its contact with the surface. ‘II. The magnitude of that pressure bears to the weight of water flowing along the stream in a second, the same ratio which the velocity per second of the change in the motion of the stream bears to the velocity generated by gravity in a second (viz., g = 32-2 feet per second). . It only remains to be shown, how the direction and velocity of the change of motion of the stream are to be determined. In what follows, the effect of friction between the stream and the vane is supposed to be insensible. 164 WATER POWER AND WIND POWER. In each of the figs. 54, 55, 56, 57, A represents the stream or jet, and B the vane. Fig. 54 represents the case in which the vane guides the stream in one definite direction E F ; and the solution of this case leads to, or comprehends, the solution of the others. Figs. 55 and 57 represent cases in which the vane has a plane sur- face, and the stream glances off it in various directions. In fig. 55 the vane is perpendicular, and in fig. 57 oblique, to the direction of the stream. Fig. 56 represents a concave cup-shaped vane, turning the stream backwards. Corresponding lines on the different figures are marked with the same letters. A jet of fluid A, striking a smooth surface, is deflected so as to glide along the surface, and at length glances off at the edge E, in a direction tangent to the surface. As the particles of fluid in contact with the surface move along it, and the only sensible force exerted between them and the surface is perpendicular to their direction of motion, that force cannot accelerate or retard the motion of the particles, relatively to the surface, but can only deviate it, When the surface has a motion of translation in any direction with the velocity u, let BD represent that direction and velocity, and BO the direction and original velocity v of the jet. Then D C represents the direction and velocity of the original motion of the jet relatively to the surface. Draw E F = DC tangent to the surface at E, where the jet glances off ; this represents the relative velocity and direction with which the jet leaves the surface. Draw FG || and = BD, and join EG; this last line represents the direction and velocity relatively to the earth, with which the jet leaves the surface, being the resultant of E F and FG. I. General Problem.—Draw D H parallel to the tangent EF, and equal to D ©; then will the base C H of the isosceles triangle CDH represent the direction and velocity of the change of motion undergone by the jet during its contact with the vane; so that, according to the first of the principles already laid down, HC is the direction of the pressure exerted by the jet against the vane ; and, according to the second of those principles, the magnitude of that pressure is ae. g 2 oe stare Gh when D Q is the weight of the flow of water in a second. But the whole magnitude of that pressure is of less importance than the magnitude of that component of it which is an efforé as respects the vane; that is, which acts along the direction BD of IMPULSE OF WATER ON VANES. 165 the vane’s motion. To find that effort, HC in equation | is to be replaced by its projection on BD, viz, LM; H Land CM being perpendiculars let fall on BD from the two ends of HC. There- fore, let P denote the effort required ; then P=DQ-2%,.... eee (2) - and the energy per second exerted by the jet on the vane is Puspo le BD. oo ous (3.) g [In fig. 55, the line corresponding to LM is simply DO, the difference between the velocities of the jet and vane. | To express these principles algebraically, let v, = BOC denote the original velocity of the jet ; u= BD, the velocity of the vane ; a= DBC, the angle between the directions of those veloci- ties ; y¥=—MDH= supplement —EFG, the angle which a tangent to the vane at the edge where the jet leaves it, makes with the direction of motion of the vane ; then, BM=2, cosa; DM=», cosa —u; DH=DC=,/fi+u?- 2 uv, cos a}. DL=— DH cos y (in which it is to be observed, that cosines of obtuse angles are negative) ; and, consequently, LM =», cos # —u—cosy*/ fri tu2—2 uv cos #f ...(4.) P=DQ*4{ 0, cose —u— cosy: J foi tu? — 2w 2, cos «} 1 Pu=D i fue cosa —u2—u‘cosy’ ge .a(6.) J foi + u? — 2 wv, cos «} If the final velocity of the water, EG = BH, be denoted by ., its value is v= /{BD?+DH?+2BD-D H «cos 7} icy = J ju} 2u(rcose—u)+2ucosy af (vi-bu? — 2uv, cose) 166 WATER POWER AND WIND POWER. From which it is evident that equation 6 is equivalent to the following :— wo U5 PT a is excinaiougicaa (8.) that is, the energy exerted by the water on the vane is equal to the actual energy lost by the water, a consequence of the assumption that the friction is insensible. The EFFICIENCY of the action of the jet on the vane is the ratio of the energy exerted on the vane in a second to the actual energy of the flow in a second; that is, its value is ipo toe -= : v v DQ:=+ I _ 29 (9.) w we ue wb = 2—-cose#——- —'cosy’ 1+— —2 —cose v VY % vy VY J It is obvious that there are two cases in which the efficiency is nothing ; first, when the vane stands still, or w= 0; and, secondly, when the vane moves at such a speed that P=0; that is, when w+ vy = Cos & + sin & COtAD yo... eeeeee eee (10.) For each particular pair of angles # and y, there is an inter- mediate value of the ratio w+ v,, which makes the efficiency a maximum. The determination of that ratio in the most general case involves the solution of an equaticn of the fourth order, and is not useful in proportion to the trouble of obtaining it. The ratio, therefore, will be determined in those particular cases only which are most useful. IL. Case in which HC || B D.—In this case, the pressure exerted by the jet on the vane is wholly an effort, being parallel to the direction of motion of the vane. In order that it may be so, the angles C D M, H D M= y, made respectively by the original and final motion of the jet relatively to the vane, with the direction of motion of the vane, must be equal, so that DLIL=DM=», cos2—w; and equations 4, 5, 6, 7, and 9, become LM=2(v, cose —w);..... ciutggicons (il.) 2D Q(v, cos @ — wu) | a PS g IMPULSE OF WATER ON VANES. 167 _ 2DQu(v, cos « — u) SS Pu QS tetetieeenees (13.) Ug = J fo? — 4 (v1 COS & — U)E j.ceeeeceseees (14.) ahs Ey Se) les D Ga Vv VY 29 _In this it is evident, that the efficiency is nothing when u is either = 0, or = v, cos «, and that the speed of greatest efficiency is for which the effort, the energy exerted per second, and the final velocity of the water, have the values Paris, ae (17,) D Q v3 cos? « Pu= Bg ie Rae naueeaegeaies (18.) Vg, Vy SIO jeecosccascccnscccsseoners (19.) and the greatest efficiency itself is LE COS? iss vecsvaarseeesaecdewsns (20.) IIL. Case of a Flat Vane, normal to the Jet, and moving in the same direction (fig. 55).—In this case the water glances off from the edge of the vane in all directions; cos#=1; cosy =0; and equations 5, 6, 7, and 9, become P=DQ:4—; So Pisusesseeas (21) Bie ee rare (22,) g =f 2 we? Paareens (23.) _ 2uv —u) DR a sssssessssetenees (24.) The greatest efficiency evidently takes place when and in that case 168 WATER POWER AND WIND POWER. DQ» Pi anaes (26.) 2 as aaa Ae (27.) v. 53 Semen ceeee secre esccccaenes (28.) 1 Sh aera eau: (29.) so that at least one-half of the energy of the jet is lost. IV. Case of a Cup Vane (fig. 56).—Let the motion of this vane be in the same direction with that of the jet, so that’ cos «=1; and to avoid the inconvenience of using negative quantities, let B= y7—90° be the acute angle made by the edge of the cup, all round which the water glances off, with the axis of the cup; so that — cos y =-+ cos 8. Then equations 4, 5, 6, 7, and 9, become LM = (v, —u) (1 + 008 6) 5..-eeceeeeeee (30.) P=DQ-A~ -(1 + e088); i seaaiaie (31.) Py ri @ g aooe cm, (32.) 0 = J foi—2 w(x, —u) + (1 + cos p)}.......(33.) ee ee The speed of greatest efficiency is obviously, as in case IIL, wes Ddvadaensubsevsehwetineeys (35.) and then P=DQ- 51 -(1+e0s 8); auaercn (36.) v a ae wri al) Diiebeadenes (37.) nay A/(1 ~ A) ar (38.) __ 1+ cos 6 Da esas Data (39.) INPULSE OF WATER ON VANES. 169 The form of greatest. efficiency for the vane is a hemisphere, for which cos 8 = 1; and then, when the speed of greatest efticiency is maintained, we find D 2 P= a8 SnslaacsdeseicCan staal (40.) D 2 By scecettentena wsdl) Pi Seance ed: (42) ys Coreen (43.) being perfect efficiency. V. Case of a Flat Vane, oblique to the Jet (fig. 57).—In this case, the easiest method of solution is the following :— Let v =D C be the velocity of the jet relatively to the vane, found as in the general case. Let the angle C D K which it makes with a normal to the vane be denoted by 4 Regolve v' = C D into two components, viz. :— D K normal to the vane = v’ : cos 6; K C along the vane = v'’ sin 0; - Then according to the supposition that friction is insensible, K C is not affected in magnitude by the vane; but D K is entirely taken away; so that D K, in fig. 57, corresponds to HC in fig. 54, and represents the direction and velocity of the entire change of motion produced by the action of the vane on the water. Hence the whole pressure exerted by the water on the vane is in a direc- tion normal to the vane, and its magnitude is v' + cos 4 seseabueiaaeecaael (45.) Now let w be the velocity with which the vane moves, in a direc- tion making the angle 6 with the normal to its surface; then the effort of the water on the vane is v' cos 6 cos 3 P=P cst =DQ°: 9° peeeeeesons (46.) and the energy exerted, ‘ Pu=DQ oo cae which being divided by DQ vj + 2g, as in former cases, gives the efficiency. se : ‘Another mode of arriving at the same result is as follows :— 170 WATER POWER AND WIND POWER. Let ¢ be the angle which the original direction of the jet makes with the normal to the vane. Then V' COS 6 = VY, COS C — U COB G5... .sceeesenees (48.) from which we obtain v, cos ¢ cos 8 — wu cos? 3 P=Dq-3 Se (49.) Pu=DQ EE EO TE CO pO) 2 1b = 25+ cos ¢ cos 8 27 - eos? 9 baile (51.) The speed of greatest efliciency is , x TS seoseneeeeeeeeeeessenee (522) giving the following results :— P=DQ: oe, Peiiemeage (53.) Pu=DQ- Ges, agai: (54.) 1-ka SES, Peano ieee (55,) which is independent of 6. 145. west form of Wane to receive Jet.—In all water wheels, whether the water acts chiefly by weight or chiefly by impulse, it is desirable, in order to reduce to as small an amount as possible the loss of energy by agitation of the water, that the jet, on first coming in contact with the vane, float, or bucket lip, should not strike it, but glide along it. That object is attained in the following manner :— In fig. 58, OBE is a vane, float, or bucket, moving in the direction BD with the velocity u=BD. A is a jet, moving in the direction BC with the velocity v,=B OC, and first touching the vane at and near the point B. Join DO: then that line will represent the direction and velocity of the motion of the water relatively to the vane; and of what shape soever the vane may be elsewhere, its surface at and near B, where it first receives the jet, should be parallel to D C. PONCELET’S FLOATS—FRICTION. jl Poncexer’s Froats.—This improvement in the form of vanes or floats was introduced by Poncelet, and applied to his undershot wheels, which will be further described in the sequel. The prin- ciple is applicable to all wheels whatsoever. The following consequences of the principle are applicable to the case No. II. of Article 144, in which the angle y=N DH, made by the edge of the vane where the water glances off, with the direction of motion of the vane, is supplementary to the angle which is made with that direction by the original relative motion of the jet. This condition is fulfilled in Poncelet’s wheels ; for the water, after running up towards O, to the vertical height due to its relative velocity D C, returns, and glances off at the edge E near B; so that D H, equal and opposite to D C, represents the direction and velocity of its final motion relatively to the vane, and BH the direction and velocity of that motion relatively to the earth. It has been shown, in the division of Article 144 just referred to, that the speed of greatest efficiency, neglecting friction, is _ 1 COS & rae 4 (where e=. > that velocity may vary between the limits 0°3 (v, cos #) and 0°7 (v, cos @) without any important waste of energy. If the average efficiency of overshot and breast wheeis, designed and constructed in the best manner, be estimated at 0-75, it follows that the energy of the available fall, from the penstock to the tail race, to give one effective horse-power, is on an average, 33,000 0-75 161. Overshot Wheels at Bligh Speeds (A. M, 634).—In a few cases of not very ordinary occurrence, it is necessary to give the = 44,000 foot-lbs. per nuinute. -. wheel so great a speed that the centrifugal force causes a sensible proportion of the water to be spilt from the buckets during their descent. In fig. 64, let C represent the axis of the wheel, A and B a bucket. Let a denote the angular velocity of the wheel, whose value is Take C A vertically upwards from the axis, to re- present, as given by the equation az gn" _g g CAS Tr =p =Teage Fig. 64. where 7 is the number of revolutions per second. ' Then the surface of the water in the bucket is perpendicular to A b, 186 WATER POWER AND WIND POWER. The height of A above C is independent of every circumstance except the time of revolution; being, in fact, the height of a revolving pendulum which revolves in the same time with the wheel (see Article 19). The point A is the same for all buckets carried by the same wheel with the same angular velocity, and for- all points in the surface of the water in the same bucket, whether nearer to or farther from the axis C ; so that the upper surface of the water in each bucket is part of a cylinder described about an axis traversing A, and parallel to the axis of the wheel. By drawing a vertical section of the circle of buckets to a scale, finding the point A, and describing arcs about it to represent the surface of the water in each bucket, the waste of water and of energy by centrifugal force may be determined. If A is in the cir- cumference of the wheel, no water can enter the buckets. Section 3.—Of Undershot Wheels. 162. Weseription of a Poncelet Wheel—The wheel represented in fig. 65 is one erected in England by Mr. Fairbairn, and is of the Fig. 65. best design in every respect except one, viz., that the bottom of the wheel race is straight, instead of being curved in a manner which will be described in Article 166. A is the reservoir; B, the wheel race; OC, the regulating sluice, held against the pressure of the water by jointed links, balanced by a counterpoise, and moved by a rack and pinion; D, the wheel, having a pair of crowns, no sole plate, and a series of curved vanes ; E, the tail race, with a drop ittto it from the end of the wheel race, as for a breast wheel. 163. Diameter of Wheel.— When not fixed by other considera- UNDERSHOT WHEEL. 187 tions, it is usual to make the diameter of the wheel about double the fall. 164. The mepth >£ Shrouding ought to be sufficient to prevent the water which glides up the vanes from overflowing their upper edges ; because in order to produce the best efficiency, the water should all glide down again, and glance off at the lower edges of the vanes. The best velocity of the water relatively to the vanes is about 0:4 of the velocity of supply v, ; but to provide for the contingency of that velocity amounting to 0-7 ¥,, it is advisable to give the shrouding the depth due to 0-7 v,; that is to say, about half the depth from the topwater level in the penstock to the outlet of the sluice. 165. The Regulating Sinice is placed as close ag possible to the wheel, and is consequently inclined. The co-efficient of contraction c of its outlet (as already stated, Article 140), is from 0°74 to 0°8 ; therefore, the depth of its opening is from four-thirds to five-fourths of the depth of the stream which issues from it. The greatest depth of that stream should not exceed about one- fifth of the depth of the shrouding ; therefore, the depth of opening of the sluice for the maximum flow should be about one-fourth of the depth of the shrouding, or one-eighth of the depth of the centre of the orifice below the topwater level. Let Q be the greatest flow to be used, in cubic feet per second ; i’, the depth of the middle of the orifice below topwater ; d, the depth of the orifice ; 1, the length of the orifice, or breadth of the opening of the sluice ; then cdv, ed J2gh'’ all dimensions being in feet. 166, The Wheel Race is designed as follows (see fig. 66) :— Draw H F G a tangent to the wheel, with a declivity of one in ten. This declivity is to preserve the velocity of supply v, undiminished. At the height ¢ d (Article 165) above H F G, draw £ K L to represent the upper surface of the stream, meet- ing the circumference of the whecl at the point L. Then make the section of the bot- tom of the wheel race from G to F an arc of a circle, equal to G L, and of the same radius; that is, the radius of the wheel. ’ 188 WATER POWER AND WIND POWER. From G to E the wheel race is formed so as to clear the wheel by about 0-4 inch. 167. The Surface Vetocity of the wheel for the greatest efficiency has already been stated, in Article 146, to be =D COR toes swevensiweawnayesanssonan (1.) In this expression « is to be held to represent the mean angle which the stream makes with a tangent to the wheel, which is very nearly l . ed #5 are. versin. —......, Pana wanses (2.) 168. Vanes or Floats—As to the number of vanes, from two to three in the length of the are L G are in general enough. The determination of the proper form for those vanes, near their outer edges, has already been explained in Articles 145, 146. They are usually curved in a circular arc, so that their inner ends are tangents to radii of the wheel. 169. The Eaiciency has been stated, in Article 148, to be about 0-6 when the wheel is not drowned, and 0-48 when it is drowned. At these rates, the energy of the available fall from the penstock to the tail race, for each effective horse-power, is Foot-Ibs. per minute. For the undrowned wheel, ...........:.ee00 eS we 55,000 For the drowned wheel,.........:...ceeeeeeees ae = 68,750 170. Wheel in an Open Current.—Wheels of this class are carried by boats moored ina rapid current. Their floats are usually plane and radial, and fixed at distances apart equal to their length in the direction of a radius. According to the experiments of Poncelet, the following is the useful work per second of such a wheel; v, being the velocity of the current ; u, that of the centre of a float; A, the area of a float in square feet ; and D, the weight of a cubic foot of water :— DA », (v,-U) uw ——— According to this formula, the velocity of the centres of the floats for the greatest efficiency is half the velocity of the current; and the efficiency at that speed is 0-4, if A v, be taken to represent the volume of water acting on the wheel in a second. Ru=08 189 CHAPTER V1, OF TURBINES. Secrion 1.—General Principles. 171. Turbines Generally Described and Classed.—A_ turbine is a water wheel with a vertical axis, receiving and discharging water in various directions round its circumference. The wheel consists of a drum or annular passage, containing a set of suitably formed vanes, which are curved backwards in such a manner, that the water, after glancing off them, is left behind with as little energy as possible. Turbines have the advantage of being of small bulk for their power, and equally efficient for the highest and the lowest falls. The supply of water takes place either directly. from a reservoir, in which case the wheel is placed close to a suitable opening at the bottom of the reservoir, or through a supply pipe and wheel case. The former method is the best suited to moderate falls, the latter to very high falls. The opening through which the water is delivered to the wheel is in most cases furnished with guide blades, to make the water arrive at the wheel in the direction best suited to drive it efficiently. Turbines may be divided into three classes, according to the direction in which the water moves before reaching the guide blades, and after leaving the wheel, viz. :— I. Parallel Flow Turbines, in which the water is supplied and discharged in a current parallel to the axis. II. Outward Flow Turbines, in which the water is supplied and discharged in currents radiating from the axis. III. Inward Flow Turbines, in which the water is supplied and discharged in currents converging radially towards the axis. -Those three classes of turbines differ in certain details; but there are general principles which are applicable to them all, and general equations which are adapted to any one of them merely by assigning suitable values to certain symbols in them. The diagrams which will now be given show the general arrangement of the principal parts of each, the details of their construction being reserved until Jater. Fig. 67 represents a parallel flow turbine. A is the supply; 190 WATER POWER AND WIND POWER, chamber, being an annular passage through the bottom of the reservoir, which contains the guide blades; these are vertical at Fig. 67. Fig. 68, Fig. 70. Fig. 71. their upper edges: the form and position of their lower edges, as shown by dotted lines, are such as to direct the water in several small streams or jets obliquely against all parts of the circum- ference of the wheel B. The wheel B consists also of an annular passage between two cylindrical drums, containing a series of vanes, resembling the guide blades in shape, "put turned with their lower edges pointing backwards. Fig. 68 shows a vertical section of a few of the guide blades C, and vanes D. Fig. 69 is a horizontal section of part of an outward flow turbine ; A is the supply chamber, being a vertical cylinder with a ring of openings round its lower end ; C are the guide blades for directing the water obliquely forwards as it rushes out of these openings ; B is the wheel surrounding the ring of openings, and consisting of a pair of crowns, or flat rings, with a series of curved vanes D between them ; these vanes are radial at their inner edges, and directed obliquely backwards at their outer edges. Fig. 70 represents a plan of one form of the reaction wheel—a kind of outward flow turbine without guide blades. The water is conducted by a vertical supply pipe A into the centre of a rotating TURBINES—VELOCITY OF FLOW. 191 hollow disc, provided with two or three hollow arms, which dis- charge the water through orifices directed backwards. In the figure, the hollow disc, and its two arms B B, are shown of such a form as to leave the largest possible space for the motion of the water from the centre of the disc towards the circumference, in order to avoid friction, and for other reasons which will afterwards appear. OC, C, are the orifices. The circumferences of the arms B,.B, here perform the functions of vanes. Fig. 71 is a horizontal section of an inward flow turbine. A is the supply chamber ; ©, one of the guide blades, directing the water obliquely forwards against the wheel ; B is the wheel, occupying a central space surrounded by the supply chamber, and discharging the water through openings in its centre; it consists of a pair of crowns with a.set of curved vanes D between them: these vanes are radial at their outer ends, and are directed obliquely backwards at their inner ends. In treating of the theory of the efficiency of turbines, it will be assumed that they are constructed of the forms and proportions, and worked in the manner most favourable to efficiency, according to rules which will presently be explained. The waste of power caused by deviations from those rules can afterwards be allowed for by means of empirically-found multipliers. 172. By Velocity of Flow is to be understood the velocity of that component of the motion of the water by which it is carried towards, through, and away from the wheel; that is, the com- ponent, whether parallel to the axis or radial, which is at right angles to the motion of the vanes. Let A denote the total effective sectional area in square feet of the orifices through which the water passes, whether in the wheel, or amongst the guide blades, as measured upon a surface perpen- dicular to the direction of the flow; that is, ina parallel flow tur- bine, on a plane perpendicular to the axis, and in an outward or inward radial flow turbine, on a cylindrical surface described about the axis. Let Q be the volume of water used in cubic feet per second, Then Q) = Aviceaccecsaaeerereeeasecieseads (1.) is the velocity of flow. Inasmuch as sudden changes in the velocity of a stream are accompanied with waste of energy, it is desirable that the velocity of flow should either be constant, or change slowly during the passage of the water through the wheel. : In parallel flow turbines, such as fig. 67, the velocity of flow would be made constant, if the vanes were insensibly thin, by making the drum, or annular case containing the vanes, simply 192 WATER POWER AND WIND POWER. cylindrical; but owing to the obliquity of the vanes at their lower edges, they occupy more of the passage there than at their upper edges; so that the drum has to be made to spread a little at its lower end, as will be shown afterwards in the detailed figure. In radial flow turbines, the a! uniformity of the velocity of flow may be insured by making the or vertical section of the drum of a dl a the wheel of the shape shown in fig, 72; that is to say, let OX Q be the axis; O Ra radius at the middle of the depth of the wheel ; the vertical sections MN, PQ, La of the rings or crowns between Fig 72. which the vanes are carried are to be portions of hyperbolas having O X and O R for asymptotes; or in other words, the depths of the inside and outside circum- ferences of the wheel, M P, N Q, are to be inversely as their respec- tive radii. Out of the available head fA, in the supply chamber, there will be expended to produce the velocity of flow, when that changes gradually or not at all, Q . 2 og. pero ornsneneenennnrcennnen (2.) where A, denotes the sectional area of the stream where it leaves the wheel. 173. Velocity of Whirl—Let v denote the whirling or tangential component of the velocity with which the water issues from between the guide blades and arrives upon the wheel. This is the velocity which would be computed by dividing Q by the sum of the effective areas of the openings between the guide blades, as measured upon the planes marked E F in fig. 68, It is evident that the velocity of flow has the following value in terms of this initial velo- city of whirl :-— e——FGE being the inclination of the guide blades to the direction of the whirling motion. The ordinary values of 2 range from 22° to 35° in different examples; and about 30° may be taken as an average value. In order that the water may work to the best advantage, it should enter the wheel without shock, and leave it without whirl- ing motion; for which purpose, the velocity of whirl, on first TURBINES—EFFICIENCY—ANGULAR MOMENTUM. 193 entering the wheel, should be equal to that of the first circum- ference of the wheel, and the velocity of whirl relatively to the wheel, on leaving the wheel, should be equal and contrary to that of the second circumference of the wheel. Consequently, the ratio of the latter of these velocities (w) to the former (v) should be that of the radius of the discharging side of the wheel to the radius of the receiving side. Let » denote that ratio; then w= v; in which, for a parallel flow turbine, n= 1; for an outward flow turbine, n => 1; }.. (2.) for an inward flow turbine, » —1; } and if the drum is made of that figure which causes the velocity of flow to be uniform, the angle & = —— H K Lin fig. 68, which the hinder edges of the vanes make with a tangent to the wheel, should have the value given by the equation H tan « + B ——— 3 Perera rere rere rrr 3. an aL = (3.) and as H L=2-: EG, this formula is equivalent to the follow- ing :— fe es Bi ws ee aevennennnne (3 a.) 174. Efiiciency without Friction.—The following investigation has reference to the case in which the supply of water is sufficient to fill the orifices and channels. Reference will be made in it to the principle of the equality of angular impulse and angular momen- tum—a consequence of the second law of motion, which will now be explained (A. Jf, 560, 561, 562). . Let a body whose weight is W move with a velocity V in a given direction relatively to a point C; let r denote the length of a per- pendicular let fall from C upon a tangent to the path of the body ‘W’s motion. Then the angular momentum of W relatively to C means the guantity WVr g Let M denote the moment of a couple of equal and opposite, but not directly opposed, forces ; that is, the product of their common magnitude into their am or lever, which is the perpendicular dis- tance between the lines along which they act. : The angular impulse of such a couple means, the product of its Oo 194 WATER POWER AND WIND POWER. moment into the time during which it acts. To produce a given change in the angular momentum of a body, an equal angular impulse is required—a principle expressed by the equation To apply this to the action of water on a turbine, the weight of water acting in a second (DQ) is to be ascertained; when the moment of the couple exerted between it and the wheel will be measured simply by the change which its angular momentum undergoes in passing through the wheel. The product of that couple into the angular velocity of the whecl a is the energy exerted by the water on the wheel in a second (Article 5). I. Computation of the Energy Exerted by the Water on the Wheel. —Let r be the radius of the wheel where it receives the water. (For parallel flow turbines, the mean radius may be taken.) Then nr is its radius where it discharges the water, and a 7, and nar, are its two surface velocities. Then, the velocity of whirl of the water when it enters the wheel being », its initial angular momentum per second is DQovr. g 2 and as the velocity of whirl of the water when it leaves the wheel, as determined by the conditions of Article 173, is nar—w=n(ar—?), its final angular momentum per second is DQr(ar—-v)r. g 2 the difference between these quantities, being the moment of the couple exerted between the water and the wheel, is n\vr— nar? mM-pq- Gt 5 suiisver senses and the energy exerted per second by the water on the wheel is Ma=DQq-CPuesr man wuladee: (3.) The factor by which DQ is multiplied in equation 3 is the effective head, neglecting friction. EFFICIENCY OF TURBINE WITHOUT FRICTION. 195 II. Computation of the Energy Expended.—This calculation is best made by finding the head required to produce the various velocities that are given to the water. To produce the final velocity of flow nv tan &, there is required the head nv tan? 6+ 29. To produce the initial velocity of whirl v, there is required the head vs 2g. To produce the reversed relative velocity ot whirl with which the water leaves the wheel, w = 7 v, there is required the head nv 2g; and to balance centrifugal force, the head . a r? (1 —n?) + 2g, negative outward flow which is < nothing ;for< parallel flow > turbines. positive f inward flow Putting these quantities of head together, we find for the head in the supply chamber, h,= = { (1 +n? + n? tan? 8) v? + (1 — 0?) a? r? \ jee(4.) g for the energy expended at the wheel, per second, DQ hy sersiversencensscceses sesseeeee(5.) and for the EFFICIENCY (neglecting friction), Ma _ 21+ nr) avr — Qn? ar? (6) DQh, (L4+n?-+ ni? tan? g) v? + (1 —n?) ate?" The above are general expressions for all turbines with guide blades. For parallel flow turbines, they become 1 legge P) Os iausnonioneeesaea seed (7.) Ma | 4avr—2ar (8) Doh a Claes oe ; By the aid of equation 4, v can be expressed in terms of h, and ar,so as to transform equations 6 and 8, as follows :— s 196 WATER POWER AND WIND POWER. ps of Fi EN RO cess veaces (5 Jitn?+n? tan? 6 ar Let Sigh, = #, then, Ma 20 +n 2° /1 — 22+ 2 2 = — 2 n? 2?;...(10. DQA, J 1l+n?+ n? tan? 6 a at which, when 7 = 1, becomes Ma 42 a 11. D Qh, J 2+ tan? 3 as) The efficiency of the reaction wheel is a special case, which will be considered in Article 176. 175. The Greatest Efficiency without Friction is attained, as has been stated in Article 173, when Substituting this value of v in equation 4 of the last Article, we find 2 m2 hy = (2-+ 72 tan? 8) et spdebinnaeae tus (2.) and, consequently, the surface velocity of the wheel, where it re- ceives the water, should be - 2gh, ar=a/ ea) Baas w..(3:) So that in equations 10 and 11, 1 sa fd +n? tan? 3 The efficiency corresponding to this speed is Ma 2 pee ep 28 DQ, sows sdgaes iniawaineen er (4) showing that the only energy lost is that due to the final velocity of flow, nv tan 8 = nar tan 6. The following table shows some values of the best speed as com- pared with the speed due to the whole available head, and of the greatest efficiency, neglecting friction, for a few values of the obliquity @ of the vanes, and on different suppositions as to the value of 2 :— LFFICIENCY OF TURBINE—REACTION WHEEL. 197 4 bee - for its or or 1 a tan B, 2 ——— = 222 wi 2 n=1 n= > D Q hy 14°3 20° 36° "364 "685 "93 18° 25° 43° "466 672 "90 224 30° 49° ‘577,055 ‘86 26°5 35 543 "700 634 "So The proportion x = ,/ 2 is usual in outward flow turbines, such as Fourneyron’s; 2 =5 is usual in inward flow turbines, such as Thomson’s vortex wheel. The case of n = 1, 6 = 30°, is very nearly that of Fontaine’s parallel flow turbines. Theory gives, as the above table shows, for the best velocity of the wheel, at the middle of the ring of vanes, CP S098 gf 2G Wg satisiedennacansseceeed (5.) The experiments of General Morin give ar= 645 J2gh,; and the agreement is as close as can be expected. 176, The Reaction Wheel is equivalent to an outward flow tur- bine in which 8 = 0, 7 = 0, = 0; while for nr is to be substituted 9", the radius from the axis to the centres of the orifices ; for nv is to be put w, its original symbol ; for nz is to be substituted any N2gh? Then for the velocity of outflow of the water from the orifices, we have ga w= f2gh, terra Jite? J 2ghjue.(L) and for the efficiency, neglecting friction, Ma 22 DQh, #+f1+# eee weecenee cas sseas(2.) This expression increases towards the limit 1, or perfect efficiency, as 2’ increases without limit; so that if there were no friction, the efficiency of a reaction wheel would have no maximum, but would increase towards unity as the velocity increased without limit. 177. Efficiency of Tarbines, Allowing for Friction.—I. Parallel Flow Turbines.—The fact stated in Article 175, that the best 198 WATER POWER AND WIND POWER. actual speed of these turbines is the same with that calculated in the supposition that there is no friction, shows that the loss of energy by friction may be allowed for by multiplying by a constant factor, less than unity. From the experiments of General Morin and others, it appears that the value of that factor is nearly the same as for the best over- shot and undershot wheels ; that is to say, (1—4")=from ‘75 to ‘8, with an average value of about ‘78. If we multiply the efficiencies in the table of Article 175, corre- sponding ton = 1, 6= 25°, and 30°, we find the following results, which agree well with experiment :— 1 ah ke B ae? "15 78 ‘8 25° *90 675 “702 72 | resultant 30° 36 645 O71 688 f efficiency. Il. Inward Flow Turbines.—In these turbines, the co-efficient (1 — &'') appears to be about the same as for parallel flow turbines ; which, for 6 = 36°, 2 = ? gives, as the average resultant efficiency, about ‘73—a conclusion confirmed by practical experience. Til. Outward Flow Turbines, which generally work drowned, lose in overcoming fluid friction a quantity of work per second, which has been shown by Poncelet, and by General Morin, to be proportional to the volume of flow, and to the height due to the velocity of the outer circumference of the wheel. That velocity being denoted by nar=n2,/2gh,, the loss of work per second by friction is n? a? 7? 29 being the fraction / n? =* of the energy expended. J is a co-efficient of friction, whose value, as deduced from experi- ments by General Morin, is nearly fa 025. SDQ =F DQ Pe? Tig te eee ener ae (3) This cause of loss of work not only diminishes the efficiency of the turbine, but diminishes very considerably the speed of greatest efficiency. Subtracting fn? 2? from equation 10 of Article 174, we find for the actual efficiency of an outward flow turbine, at any given velocity ar =z ,/ 2g h, of its inner periphery, the value EIFICIENCY OF TURBINES WITIL FRICTION. 199 Ma _2(w2+1):2: /l+@?-)2 DQAy J 1+ ni? «sec? 6 The following are the results of investigating the conditions which make this quantity a maximum :— Let a, r = 2 ,/ 2g h, be the best speed. For brevity’s sake, let nt — AJ (ebsre AieNtD | =4/ (Seee} ae (3.) and the greatest efficiency is given by the formula _ O+f/e-U 04- eos! (4) _ O+/) n? 2? (2.) Then J a 8 DQh, Asa numerical example and verification of these formule, the case may be taken of a Fourneyron’s turbine, for which n = 2 nearly; f= 0°25; 1 n? tan? B = 5 nearly. Using these data, we find U = 3-16, and, consequently, a= J 215 = 464; | Efficiency, U x ='68; results which exactly agree with those of experiment. IV. Reaction Wheel.—If we assume that this wheel is resisted in the same manner with an outward flow turbine, and denote, as in Article 176, the ratio of the speed of the ortfice to that due to the available head by 2’, and the best value of that ratio by 2’,, we find, for the efficiency in general, ; Ma 22 ie af’ Sees cseeeneee (1.) DQh f+ JI +2? which being made a maximum, gives { 2+f—- JC ‘ z= 3 JO+FPoL Sie “soe (2) 200 WATER POWER AND WIND POWER. My Barf EIS icine C85 DQh, 2 From experiments by Professor Weisbach, it appears, that the greatest efficiency of a good reaction wheel is which value being substituted in equation 3, gives for the co-efficient of friction and for the ratio of the best speed of the orifices to that due to the available fall, Bi SUB OAs csc secwateamseaaenens (6.) This result is confirmed by general experience of the working of these wheels, from which it appears that the best velocity for the orifices is very nearly equal to that due to the available fall, and the greatest efficiency about 2. 178. Volume of Flow and Size of Orifices. —In Article 174, equation 9, an expression is given for the whirling or tangential component of the velocity of flow through the openings between the guide blades ; from which are deduced the following expressions for the total velocities, through the openings between the guide blades, and through the openings between the vanes of the wheel respec- tively; in which, Q being as before the volume of flow per second, the joint area of the contracted stream in the former set of openings is denoted by O,, and that in the latter set by O, :— san NI +(—1)2 =v sec & = sec a* 29h te Ts Nal Jltnisec®s 7 (1) Mal LA Ma Wee J 1+ n?+ sec? 6 a) 0; Q . : 6, =P sec B= sec B J 2ghy 2 For reaction wheels, o w= (igh (TEE Seesesas Sawcute (2 a.) The formule ee ee ee, eee” Ope OL Fae eee Peeeeccee -(3.) serve to determine the effective areas of inlet and outlet required to employ to the best advantage a given flow of water in a given TURBINES—EFFICIENCY—FONTAINE'S. 201 wheel, with a given available fall and speed, the speed being that of greatest efficiency, computed as in Articles 175 and 177. The co-efficient of contraction for the inlets and outlets of turbines ranges from ‘85 to ‘95, and is about ‘9 on an average; so that the actual openings are to be made one-ninth larger than those given by the equations. 179. Efficiency as affected by Regulator. — The flow of water through a turbine is controlled by a regulating valve, of which different kinds will afterwards be described. In parallel flow and outward flow turbines, the regulator usually consists of a set of slide valves applied to the orifices of supply between the guide blades. In the best form of reaction wheel, known as Whitelaw and Stirrat’s, the regulator consists of slide valves applied to the orifices at the ends of the arms. In Thomson’s inward flow turbine, the regulator consists of the guide blades themselves, which turn about axes near their inner ends, so as to be set at any required angle « to the circumference of the wheel. The preceding investigations and statements of efficiency have reference to the case in which the passages of supply are uninter- rupted, or nearly so. Their partial closing by slide valves causcs loss of energy through sudden contractions and expansions of the stream. The following are average values of the reductions of efficiency produced by partial closing of the supply passages by slide valves :— Ratio of the actual opening) 1 2 1 to the full opening,.......f5 5 9 Ratio of the diminished efi-) 1 9 5 ciency to the maximum e 3 eR CFFCIENCY, «2... scree ee eeeeen ‘ Such diminutions of efficiency do not occur where the flow is regulated by varying the orifices of discharge, or by varying the inclination of the guide blades. Section 2.—Description of Various Turbines. 180, Fontaine's Turbine, a parallel flow turbine, the invention of M. Fontaine-Baron, is illustrated by fig. 73, which is a vertical diametral section, and by fig. 74, which is a vertical section by a cylindrical surface traversing the guide blades and vanes, like that given in an elementary form in fig. 68. ett : A is the tank or reservoir, in the bottom of which is the ring- 202 WATER POWER AND WIND POWER. shaped cast iron passage B, containing the guide blades c, and regu- lating sluice valves d. There are as many sluices as guide blades, Vig. 78. each guide blade having a sluice sliding vertically behind it. The backs of the sluices are rounded, so as to make the contraction and deflection of the stream gradual. Each sluice is hung by a rod b from the iron ring a, which is raised and lowered by means of three rods marked ¢, so as to raise, lower, or close, the whole of the sluices at once. C is the drum or annular passage of the wheel, containing the vanes f, E is a disc, by which the drum is carried. The disc, drum, and vanes, may all be cast in one piece. FF is the hollow vertical shaft of the wheel, at the top of which TURBINES—FONTAINE S—JONVAL’S, OR KOECHLIN’S. 203 is the pivot, supported upon the top of the fixed vertical spindle G, which rises from the bottom of the tail race within the hollow shaft. The object of this is to facilitate the oiling of the pivot. The dimensions and proportions of turbines of this class may be varied to suit different circumstances ; nevertheless the followin x a5 given as being usual in practice, on the authority of General orin :— 2, obliquity of the guide blades, ............22° to 25°. 8, obliquity of the vanes,..........s008 seeeeee20° tO 30° Breadth of ring-shaped passages— = from yy to ry of mean diameter of wheel. Least depths of openings between guide blades, and betwcen vanes, from 23 inches to 6 inches. Depth of drum of wheel = depth of openings x 2. As to the work, efficiency, best speed, and volume of flow, see Articles 172, 173, 174, 175, 177, Division I., 178. The speed may deviate from the best speed to the extent of one quarter, without materially diminishing the effi- ciency. As to the effect of the sluices, see Article 179. To avoid the diminution of efficiency by the lowering of the sluices, double turbines have been used, consisting of a pair of concentric wheels made in one piece, supplied with water by a similar pair of concentric annular supply pas- sages. Each of those passages has its own set of sluices, hung from an indepen- dent ring; so that either division of the double wheel can have its supply of water cut off at pleasure. Thus the power of the turbine can be varied in a proportion exceeding that of two to one, without the necessity for employing very contracted orifices, and conso- quently wasting energy. 181. Sonval’s, or Koechlin’s Turbine, the invention of M. Jonval, and made by Messrs. Koechlin & Co., resembles Fontaine’s turbine, with the wheel working in a vertical suction pipe (Article 103) in which the pressure is below that of the atmosphere. This cnables the wheel to be placed at any convenient elevation not exceeding the head equivalent to one atmosphere, above the level Fig. 74. 204 WATER POWER AND WIND POWER. of the surface of the tail race, without incurring (as would be the case in the absence of the suction pipe) a loss of head equal to the drop from the bottom of the wheel to the water level of the tail race. 182, Fourneyron’s Turbine, one of the earliest and best known of turbines with guide blades, is an outward flow turbine. The average ratio of the outer to the inner radius of the wheel is n=,/ 2, and the depth of the wheel is about equal to, or a little greater than the breadth of the crowns. An example is represented in figs. 75, 76, of which fig. 75 is a vertical section, and fig. 76 a sectional plan of the wheel and supply cylinder, showing the form and arrangement of the guide blades and vanes. A i HEY AE AE A is the tank or penstocx ; B, the supply cylinder. This is the arrangement for moderate falls; for very high falls, the water may be brought down from a reservoir to the supply cylinder by a pipe, whose resistance must be allowed for in determining the available fall. TURBINES—FOURNEYRON’S, &c. 205 The cylinder B consists of two concentric tubes: the upper isfixed : the lower slides within it like the inner tube of a telescope, and is raised and lowered by means of the rods 6. Near the upper edge of the inner tube is a leather collar, to make the joint between it and the outer tube water-tight. The lower part a of the inner tube acts as a regulating sluice for all the orifices at once. It has fixed to its internal surface wooden blocks, so shaped as to round off the turns in the course of the water towards the orifices. The bottom of the supply cylinder is formed by a fixed disc C, which is — supported by hanging at the lower Fig. 76. end of a fixed vertical tube enclosing the shaft. This disc carries the guide blades. D are the vanes of the wheel. In the example shown, the passages between the vanes are divided into three sets, or horizontal layers, by two intermediate crowns or horizontal ring-shaped parti- tions. The object of this is to secure that the passages shall be filled by the stream at three different elevations of the sluice, and so to diminish the loss of efficiency which occurs when the opening of the sluice is small. E is the disc of the wheel; F, its shaft ; G, the tail race. The pivot at the lower end of the shaft is supplied with oil through a small tube seen in the figure, which is laid down one side and along the bottom of the tail race, and rises directly below the pivot. K H is a lever which supports the step of the pivot, and is itself supported by fixed bearings at K, and by a rod, L, which can be raised or lowered by a screw, so as to adjust the wheel to the proper level. . 183. Various Outward Flow Turbines——An improvement in the regulating apparatus of Fourneyron’s turbine, introduced by Mr. Redtenbacher, is to vary the supply openings when required, by raising or lowering the disc C which carries the guide blades, by means of a screw at the top of the tube to which it is fixed. This dispenses with the necessity for an internal sliding cylinder within the fixed supply cylinder. Another modification of the regulating apparatus of Fourneyron’s turbine, by M. Callon, is to make the sliding vertical tubular sluice in several segments, which can be opened or shut separately. To prevent the drowning of Fourneyron’s turbine, M. Girard 206 WATER POWER AND WIND POWER. added to it a bell, or fixed vertical cylinder with the mouth down- wards, which dips into the tail race, and within which the wheel works. ~- reduction of the art of designing windmills to general principles _ is almost wholly due to an experimental investigation by Smeaton, communicated to the Royal Society in 1759, and re- published in Tredgold’s Practs on Hydraulics, The general principles esta- blished by Smeaton are to a certain extent capable of being expressed by a proper adapta- tion of the formule of Article 144, Case V., equations 49 to 15—a term being subtracted to represent loss of energy by fric- tion between the air and the sail, as follows :— Let D denote the weight of a cubic foot of air ; Q, the volume of air which acts on the sail, or part of a sail, under consideration, in cubic feet per second ; v, the velocity of the wind, in feet per second. It s be taken to represent the sectional area of the cylinder, or annular cylinder of wind © i through which the sail, or part oo of a sail, in question sweeps in CIEE Oe: the course of its revolution, we may put ‘ i, where ¢ is a co-efficient to be found empirically. As it is difficult, if not impossible, in the present state of our knowledge, to distinguish between that factor in the power of a windmill which depends on the quantity of wind that acts upon it, 216 WATER POWER AND WIND POWER. and that factor which expresses the diminution of efficiency by the friction of the shaft, itis best to make the co-efficient c, in the above equation, comprehend the allowance for that friction: and this. being understood, it appears from experimental data by Smeaton, to be afterwards referred to, that for a windmill with four sails proportioned in the best manner, if s be taken for the sectional area of the whole cylinder of wind in which the wheel rotates, 6010 MC ya siiswie seeitarmns os eae ven (2.) The friction of the air will be separately allowed for. Let € denote the weather of the yail ; then because the direction of motion of each point in the sail is perpendicular to that of the wind, we must make, in the formule of Article 144, 6 = 90° — Z, and cos 6 = sin & Consider a narrow band of a sail at a given distance from the axis, and let w be its velocity. The whole velocity of the wind relatively to this band is ,/ v?-++ u?; and as it is probable that the energy lost through the friction of the air is proportional to the square of that velocity, we may pub for that lost cnergy, per pound of the acting stream of wind, Jf being a co-efficient of friction, to be found empirically. From data by Smeaton, to be afterwards referred to, it appears that the probable value of this co-efficient for the best sails is Then modifying the symbols in equation 50, as already described, and deducting the loss of energy by aerial friction, we find for the useful work per second done by the action of the wind on the band, or bands of sail, that sweep through the stream of air whose sec- tional area is s, RuseDsv-yo | 2uv- cos sing —u2(2 sin’ f+ /)—feo} 29 =eDev-y fuvssin2 u? (1 2 Pye - 5 2-22 (1 cos 2¢+f)—fo" | (4) Dsv Dividing this by 2g , the whole energy per second of the EFFICIENCY AND PROPORTIONS OF WINDMILL. 217 stream of wind, we find for the efficiency of the uction of that stream w. u2 A a {fsin 2 c—% (1—cos 2 c+s)-s} (5) The ratio of the speed of greatest efficiency for a given weather ¢, to the speed of the wind, is Uy sin 2 ” 2 —cos20+f) eA eats (6.) The efficiency corresponding to that speed is ‘laacemsap—t fi guhiSwarssonwise (7.) and the useful work corresponding to that efficiency 8 sin? 2¢ R,w=ceDs Wiiiamh—} seneees (8.) The following are some examples of the results of these formulx, taking, as already stated, f= 0-016, ¢ = 0°75 :— ‘i Ry é axl D ys v s Iq tae 2°63 0°24 13" 1°86 O20 Pusisseemms ane’ (9.) 19° I'4I o'31 It will afterwards be shown within what limits these formule are applicable. 190. The Best Form and Proportions of Sails, as determined experimentally by Smeaton, are as follows :— : In fig. 85, A is the wind shaft; AC, the whip of one sail; BD ECO, the main or following division of the sail, which is rectangular; B F C, the leading division of the sail, which is trian- ir The following are the best proportions :— The following are the best values for the angle of weather at different distances from the axis :—- 218 WATER POWER AND WIND POWER. Distance in siaths | : i be Be of A Bb, we eveneee (first bay) (tip) (2) Weather, f.....+. 18° rg? x8° 16° ras 7° c 3 191. The Best Speed for the tips of the sails, weathered as above, was found by Smeaton to be about 2°6 times the velocity of the wind; that is, for C= 7°, Uy = 26 Ve. eeeneee (1.) Tt is from this experimental result that the value of the co-efficient of friction employed in Article 189 -has been deduced, viz., f= 0-016. The result computed in the same Article, that for = 19°, -! = 1-41, indicates that 19° is the E proper angle of weather for a point about the middle of the sail; which is confirmed by experi- A ment. Vie. 85. The application of the formule of that Article to i all parts of the sail would give it a slightly convex surface ; but Smeaton found a slightly concave surface (as indicated by Table 2, Article 190) to be somewhat more efficient ; upon which he observes, “that when the wind falls upon a concave sur- face, it is an advantage to the power of the whole, though every part, taken separately, should not be disposed to the best advantage.” It further appears, that the formule should not be applied between the middle and the inner end of the sail, it being better to preserve nearly the same angle of weather throughout that part of it. 192. Power and Efficiency.—The effective power of a windmill, as Smeaton ascertained by experiment, and as equations 4 and § cf Article 189 indicate, varies as s, the sectional area of the acting stream of wind, that is, for similar wheels, as the squares of the radit. The value 0°75, assigned to the multiplier ¢ in Article 189, is founded on the fact ascertained by Smeaton, that the effective power of a windmill with sails of the best form, and about 154 feet radius, with a breeze of 13 feet per second, is about one horse-power. In the computations founded on that fact, the mean angle of weather ¢ is made = 13°, and f= ‘016 as before. Then making the radius A B-=71, and the area of the cylinder of wind, sar, equation 8 of Article 189 becomes as follows :— 3 R, m= 029-55. CT oh iach eoowanteets (1.) TOWER WINDMILL. 219 being the effective power at the best speed, when the tips of the sails move at 2-6 times the speed of the wind. To find the effective power at any speed, equation 4 is referred to, which, when ¢= 13°, becomes— Dv Rw=075 Zoe { 0-438 00— 0-117 ut— 0016 ¢ \ (2.) The value of D,—the weight of a cubic foot of air,—may be found exactly by means of Tables IL. and III. at the end of this volume ; but taking it on an average at 0-075 Jb., the above formule become,— Be Biythy = 0022 57 a tBiessssssceeeseeee (14) Ru=0056 + a 02 { 0-438 wv —O-117 u2 - 0-016 v2 \ (24.) g From equation 1 it appears that a windmill of the best form and proportions, with the tips of the sails moving at 2°6 times the speed of the breeze, has an effective power equal to ¥% of the actual energy of the cylinder of wind which passes it in a second. 193. Tower Mill._Self-Acting Cap.—Fig. 86 is a vertical section, and fig. 87 a horizontal section, of the top of a tower mill, with its self-acting cap. A A A is the tower; BBB the cap, whose lower edge is an iron ring, resting on a circle of rollers which rest on another iron ring on the top of the tower, and are kept at their proper distance apart by an intermediate ring R, in which their axes have bearings. a, a, a, a are blocks with horizontal guide rollers. C is a circular rack fixed to the top of the tower. S is the wind shaft, carrying a bevel wheel D, which drives a bevel wheel on the upright shaft N, through which motion is given to the machinery of the mill. From the back of the cap projects the frame L L, carrying the fan M, which through a train of wheelwork marked 6 and cc, drives the pinion f, which works in the rack c, already mentioned. When the wind wheel faces the wind, the fan is turned edgewise towards the wind, and remains at rest. So soon as the wind changes its direction, it makes the fan rotate in one direction or ‘another, and so drives the pinion /, which makes the cap turn until the wind wheel again faces the wind. _ The bevel wheel D on the wind shaft is often used also asa brake-wheel, its rim being encircled by a flexible brake (Article 49). 194. Reefing, or Regulation of Sails—The old method of cover- ing a windmill sail was with a sheet of canvas, of which a greater or less extent could be spread according to the strength of the wind. 220 WATER POWER AND WIND POWER. Various methods have been invented for varying the surface exposed to the wind while the mill is in motion, such as rollers, upon which a greater or less extent of the canvas can be rolled up; Fig. 87. boards furling by sliding behind each other like the sticks of a fan; and boards turning on axes into different positions, like the bars of a Venetian blind. The last method, the invention of Sir William Cubitt, is illustrated in figs. 88 and 89. Fig. 88 is a side view, REGULATION OF WINDMILL SAILS. 221. fig. 89, a front view. A is the wind shaft, which is hollow; BC, a rod passing through it; OC, a swivel, to enable the foremost end of the rod to rotate with the shaft; CD, the hinder end of the rod, which is a toothed rack, ; working with the pinion E; F,a ¢ drum on the axis of that pinion ; G, a cord wound on it, from which hangs a weight W; I, a guide roller for the rack. K is the licad of the rod BC, connected by links L with the levers M, which turn on bearers carried by the project- ing brackets IY. P is a rack; V, a guide roller ; Q, a pinion ; R, a lever ; 8, a rod, connected with all the levers for moving the valves, or transverse boards, which, when shut, or turned flatwise to the wind, fill the spaces between the bars of the sail, and make a continuous flat surface; when opened, or turned edgewise to the wind, allow it to pass through with little action on the sail; and when turned into intermediate positions, give the same effect with a greater or less surface of sail. Tach sail has similar apparatus. The axes on which the valves turn are placed nearer to one edge than to the other, so that the pressure of the wind tends to open them. It is opposed by the weight W, which tends to close them. The valves adjust their own obliquity, so that the pressure of the wind balances the weight W; and thus the effort of the wind on the sails is maintained nearly constant through all variations of its speed. PART IIL OF STEAM AND OTHER HEAT ENGINES. 195. Nature and Division of the Subject.—It is believed to have been first remarked by George Stephenson, that the original source of the power of heat engines is the sun, whose beams furnish the energy that enables vegetables to decompose carbonic acid, and so to form a store of carbon and of its combustible compounds, afterwards used as fuel. The combination of that fuel with oxygen in furnaces produces the state of heat, which being com- municated to some fluid, such as water, causes it to exert an augmented pressure, and occupy an increased volume; and those changes are made available for the driving of mechanism. According to a speculation originated by Mr. Waterston, and modified and developed by Prof. Sir William Thomson, the heat of the sun is produced by the fall of a shower of matter into it; so that the original source of the power of heat is gravitation. In the present treatise we are concerned with those operations only in the obtaining of mechanical energy by means of heat, which are performed after the fuel has been procured in a state fit for use. The present part of this treatise consists of two main divisions; the first treating of those laws of the relations amongst the pheno- mena of chemical combination, heat and mechanical energy, upon which the work and efficiency of heat engines depend : the second, of the structure and operation of those engines. The former of those main divisions consists of three subdivisions, the first treating of relations amongst the phenomena of heat them- selves; the second, of combustion, or the production of heat by. chemical action; and the third, of the relations between heat and mechanical energy, whose principles form the science of THERMO- DYNAMICS. Lead The latter of the two main divisions consists of two subdivisions, the first relating to the apparatus by which heat is obtained from burning fuel, and communicated to a fluid, which apparatus, In the steam engine, comprehends the furnace and boiler; the second, relating to the apparatus by which the heated fluid is made to per- form work by driving mechanism, being the “ engine ” proper, as distinguished from the furnace and boiley. CHAPTER I. OF RELATIONS AMONGST THE PHENOMENA OF IEAT. 196, Mieat Defined and Described—The word “HEAT” is used in two senses— I. A certain class of sensations. IL That condition of bodies which consists in the capacity for producing such sensations. It is in the second of those senses that the word will be employed in this treatise. The condition called heat has other properties besides that by which it has been defined. Of these the principal are as follows :— I. Heat is transferrible from one body to another ; that is, one body can heat another by becoming less hot itself; and the ten- dencies to effect that transfer are capable of being compared together by means of a scale of quantities on which they depend, called temperatures. II. The transfer of the condition of heat between two bodies tends to bring them to a state called that of uniform temperature, at which the transfer ceases. III. The quantities called temperatures are accompanied in each body by certain conditions as to the relations between density and elasticity ; the general law being, that the hotter a body is, the less is its elasticity of figure, or tendency to preserve a definite form and arrangement of parts, and the greater its elasticity of volume, that is, its tendency, if solid or liquid, to preserve a definite volume, and if gaseous, to éxpand indefinitely. IV. The condition of heat is a condition of ENERGY; that is, of capacity to effect changes. One of those changes has already been mentioned under the head I., viz, the change in the condition of heat of bodies which are unequally hot, tending to bring them to uniformity of temperature. Amongst other of those changes are changes of density, changes of elasticity, chemical, electrical, and magnetic changes. V. The condition of heat, considered as a kind of energy, is capable of being indirectly measured, so as to be expressed as a quantity, by means of one or other of the directly measurable effects which it produces. VI. When the condition of heat is thus expressed as a quantity, TEMPERATURES. 225 it is found to be subject, like other forms of energy (mechanical energy, for example,) to a law of conservation; that is, if in any system of bodies, no heat is expended or produced through changes other than changes of temperature, then the total quantity of heat in the system cannot be changed by the mutual actions of the bodies; but what one body loses, another gains; and if there are changes other than changes of temperature, then if by those changes the total heat of the system is changed in amount, that change is compensated exactly by an opposite change in some other form of energy. Although the present chapter treats specially of relations amongst the phenomena of heat, yet it is impossible to explain these relations without occasionally referring to relations between phenomena of heat, and other classes of phenomena, as has already been done in the preceding general description of heat. » The remainder of this chapter is divided into three sections. The first relates to the measurement of temperature, and to the phenomena with which particular temperatures are accompanied. The second relates to the measurement and comparison of guan- tities of heat, whether such as are lost by one body and gained by another during changes of temperature, or such as appear and disappear during changes of other kinds. The third relates to the rapidity with which the transfer of heat takes place under various circumstances. Section 1.—Of Temperatures, and Phenomena depending on them. 197. Equal Temperatures.—Two bodies are said to be at equal temperatures, or at the same temperature, when there is no tendency to the transfer of heat from either to the other. 198, Hixed Temperatmres, or standard temperatures, are tempera- tures identified by means of certain phenomena which occur at them. The most important and useful of fixed temperatures is that of the MELTING OF ICE under the average atmospheric pressure. This pressure is specified for the sake of precision; for although the variation of the temperature of melting ice with variations of pres- sure is exceedingly small, it is still appreciable. Next in importance and utility is the BOILING POINT OF PURE WATER UNDER THE AVERAGE ATMOSPHERIC PRESSURE of 147 Ibs. on the square inch, or -2116°3 Ibs. on the square foot, or 29°922 inches, or 760 millimétres of a vertical column of mercury, at the temperature of melting ice, or 10,333 kilogrammes on sy square métre, 226 STEAM AND OTHER HEAT ENGINES. There are many other phenomena besides the melting of ice and boiling of water under the mean atmospheric pressure, which serve to identify fixed temperatures; but the two phenomena which have been specified are chosen, because of the precision with which they can be observed, for the purpose of fixing the standard tem- peratures on the scales of THERMOMETERS, or instruments for measuring temperature. 199. Degrees of Temperature—Perfect Gas Thermometer.— The two standard points of thé scale of temperatures having been found, it is next requisite to express all other temperatures by means of a scale of degrees, and fractions of a degree; which scale is to be graduated according to the magnitude of some directly measurable quantity depending on temperature. The quantity chosen for that purpose is the product of the pres- sure and volume of a given mass of a perfect gas. ; A PERFECT GAS is a substance in such a condition, that the total pressure exerted by any number of portions of it, at a given tem- perature, against the sides of a vessél in which they are enclosed, is the sum of the pressures which each such portion would exert if enclosed in the vessel separately at the same temperature; in other words, a substance in which the tendency to expand of each appre- ciable mass, how small soever, that is diffused through a given space, is a property independent of the presence of other masses within the same space. Absolutely perfect gases are not found in nature; every gas approximates more closely to the condition of a perfect gas the more it is heated and rarefied; and air is sufficiently near to the condition of aperfect gas for thermometric purposes. Let v denote the volume of a given weight of any perfect gas under a pressure of the intensity y, at the temperature of melting ice, and 7% % the product of those factors ;—a quantity whose value in foot-pounds, for one pound avoirdupois of air and other gases, is given in Table II., at the end of this volume. Let p, v, be the corresponding product for the temperature of water boiling under the pressure of one atmosphere. Then it is known from the experiments of M. Regnault and Mr. Rudberg, that these two products bear to each other the fol- lowing proportion :— Sr Geman (1) Po Yo Now let T,, T,, denote respectively the temperatures of melting ice and boiling water under the pressure of one atmosphere, in de- grees of the scale of a perfect gas thermometer, the intervals upon which scale correspond with the intervals between the values of the ratio p v + pp %. THERMOMETRIC SCALES. 227 Let T be any third temperature, and p v the corresponding pro- duct of the pressure and volume of the gas. Then because the interval T, — Ty corresponds to the difference Bh 0-365, it is clear that the interval T—T,, corre- Po %o eek ads : Pp V— Po VY 3 ponding to the difference Saas must have the following value :— Ae m _ T—Ty pv—rr%, T—T, OES mae See (2.) and this equation expresses the relation between intervals of tem- perature, and differences of the product p v. 200. Different Thermometric Seales——The number of degrees T,—T, into which the interval between the two standard tem- peratures is divided, and the number of degrees, T,, between the zero of the scale and the temperature of melting ice, are arbitrary. On Réawmur’s scale, the zero is the temperature of melting ice, and T, — T, = 80°; therefore, Tt, = 0°; T= 80"; eo, (80? PP—Po% _ 9490.9 PVP—Po% T—Th= 7365 * a ae = 219°:3 a wa (li) On the Centigrade scale, used in France, and over most of the continent of Europe, the zero is the temperature of melting ice, and T, — Ty) = 100°; therefore, TS = 0°; Ty =— 100°; 100° pvu—pm % Pp V— Py % Ty eee (2. = 0°365 Po an Po Y% oo) On Fahrenheit’s scale, used in Britain and America, the zero is an arbitrary point, 32° below the temperature of melting ice; T, — T, = 180°; and therefore, es 95. Tt a1" — 180° pv—p% _ 29 P®—Po% (3 T—T, — 0°365. * py % _ 493 ad i Po V% —...( -) In the present treatise, Fahrenheit’s scale is used when no other is specified. On all thermometric scales, temperatures below zero are reckoned downwards, and distinguished by having the negative sign pre- fixed. 228 STEAM AND OTHER HEAT ENGINES. 201. Absolute Zero—Absolute Wem perature.— There is a tempera- ture which is fixed by reasoning, although no opportunity ever occurs of observing it; and that is, the temperature corresponding to the disappearance of gaseous elasticity, at which p v—0. This is called the aBsoLUTE ZERO of the perfect gas thermometer. By reckoning temperatures from it, the laws of all the phenomena which depend on temperature are found to be expressed more simply than by reckoning from any ordinary zero. It is therefore the most suitable zero for purposes of scientific reasoning. For the purpose of recording observations, the ordinary zeros are more con- venient, because of the remoteness of the absolute zero from any temperature which is ever observed. Temperatures reckoned from the absolute zero are called azso- LUTE TEMPERATURES. In this treatise, they will be denoted by the symbol +. Let 7 be the absolute temperature of melting ice; and 7, that of boiling water, under the pressure of one atmosphere. Let 7 be any third absolute temperature. Then T,—T = = 3053 ae ec ene econ neces cess eeeeeenee (1.) y= 1:365 Tj tee ce cee e ee ewe ert eneceones (2.) = 744 ae T= 70 Gia, Pe ee ee (3.) These formule become— for Réwumur’s scale, % = 219°2; 2, = 299°2; 2 = 91972 2? )} = T+ 219°2; for the Centigrade scale, for Fahrenheit’s scale, 5) a= 49802; 2, = 67392; r= 493°-9 P® 0 2 ; Po % ...(6.) = T+ 461°2; f and the positions of the absolute zero on the ordinary scales are, on Réaumw’s scale, — 219°:2, | on the Centigrade scale, — 2740, on Fahrenheit’s scale, — 461°-2. EXPANSION AND ELASTICITY OF GASES, 229 Table ITT, at the end of the volume, shows a series of ordinary temperatures on the Centigrade and Fahrenheit’s scales, with the corresponding absolute temperatures, and the corresponding values of p v + Mo U% 202. Expansion and Elasticity of Gases.— A. gas sensibly perfect has the law of its expansion and elasticity expressed as follows :— DV 8 1 a5 ee ee (1) and the results of this formula are given in Table IIL, already referred to. The co-efficient of expansion of a perfect gas, being the increase of volume under constant pressure, for one degree of rise of tempera- ture, of so much of the gas as fills unity of space at the temperature of melting ice, is the reciprocal of the absolute temperature of melting ice, or, 1 + 493-2 = 0-0020276 per degree of Fahrenheit; 1 + 274 =0-00365 per degree Centigrade. This is a theoretical limit to which the co-efficients of expansion of gases approximate as their densities diminish and temperatures in- crease. Their actual co-efficients of expansion exceed that limit by small quantities depending on the nature, density, and temperature of the gas. A hypothesis called that of “ molecular vortices,’ referred to in the historical sketch prefixed to this work, led to the conclusion, in the case of imperfect gases, that the law of their expansion and elasticity would be found to be expressed approximately by an equa- tion of the form, OE ai ae ee (2.) = 3 Po % 7 t & Ao, Aj, &c., being functions of the density = , to be determined empirically. This conclusion was verified by a comparison with the experiments of M. Regnault. (Memoirs of the Academy of Sciences, 1847; Trans. Roy. Soc. Edin., 1850; Phil. Mag., Dec., 1851; Proc. Roy. Soc. Edin., 1855; Phil. Mag., March, 1858.) The formula for cARBONIC ACID Gas is as follows :— pv r 342 ww, (3.) Po% 4932 7 Oy? in which p, = 2116-4lbs. on the square foot; v = 815725 cubic feet to the lb. ; p % = 17264 foot-pounds. 230 STEAM AND OTHER HEAT ENGINES. It is probable that a formula of this class will at some future period be found to express the relation between the temperature, pressure, and density of steam; but at present it is impossible to find such a formula, for want of experimental data. The difficulty of ascertaining exactly how much of the water or other fluid within a given space is in the liquid state, and how much in the state of vapour, constitutes a serious obstacle in the way of obtaining such data. The principal causes of that difficulty are, first, that a vapour near the point of liquefaction has the power of retaining suspended in it a portion of its liquid in the state of clowd or mist; and, secondly, that if in experiments on the density and expansion of steam, glass vessels are used, in order to show when the steam is free from cloud, a new cause of uncertainty is introduced by the fact, that the attraction between glass and water is sufficient to retain in the liquid state, and in contact with the glass, a film of water at a temperature at which, but for the attraction of the glass, it would be in the state of steam. The ideal density of perfectly gaseous steam, given in Table IL, is deduced from its chemical composition. One cubic foot of hydrogen, and half a cubic foot of oxygen, combine together, and collapse into one cubic foot of steam. Hence the ideal weight of a cubic foot of steam at 32°, and under one atmosphere (being a quantity to be used in calculation only, inasmuch as steam cannot exist at that pressure and temperature), is computed as follows :— Lbs. One cubic foot of hydrogen, ................. 0'005592 Half a cubic foot of oxygen, ................ 0'°044628 One cubic foot of ideal steam, D,,......... = 0°'050220 From this result are calculated the following, ideal also :— Volume of one Ib. steam at 32° and one atmosphere, 1 ; Y= a 19-913 cubic feet ; feahet (4.) Dy % = 19-9124 XK 2116-3 = 42141 foot-lbs. | If from these quantities are computed the corresponding quan- tities for one atmosphere of pressure and 212°, the following results are obtained :— v, = 1:365 vw = 27°18 cubic feet ; D, = 0°03679 Ibs; be, (5.) Dy Vy =1'365 po vy = 57522 foot-lbs. ; DENSITY OF STEAM. 231 The volumes and densities of steam given in Tables IV. and VI. are computed by a method which will afterwards be explained. From 32° to 104° they agree very well with the assumption of the perfectly gaseous condition, with the following values of » and Po %, Which are somewhat smaller than those deduced from chemical composition :— Vy (ideal, for 32° and one atmosphere) 19-699 cubic feet ; Dy = 0-05076 Ibs. ; (6.) Dy Cy = 41690 foot-lbs. If atmospheric steam were perfectly gaseous at 212°, the follow- ing would be the results of the above formule :— v, = 1365 v = 26°89 cubic feet ; D,=0-03719 Ibs; Fee eeeteeees (7.). Py V1 = 1365 py vy = 56907 foot-lbs. It is proved, however, by such experimental data as exist, that the actual density of steam, at pressures of one atmosphere and upwards, exceeds that computed on the assumption of the perfectly gaseous condition, and that the excess is greater, the greater the pressure; although there is no direct experimental determination of the exact amount or law of that excess. By the indirect method to be afterwards explained, the amount of that excess is found at any given temperature; but the general law which it follows is unknown. The tables give, for one atmosphere and 212°, v, = 26°36 cubic feet per Ib. 3 D,=008797; be. (8.) Py V, = 55783 foot-lbs. ; differing by about onefiftieth part from the results given in the for- mula (7); and the proportional difference at higher pressures is greater. The data from which the densities and volumes in these tables were calculated, were the experiments of M. Regnault on the heat transferred from a boiler to a condenser, by sending from the former to the latter known weights of steam under different pressures ; and it is certain, that whatsoever may prove to be the law connecting the density, pressure, and temperature of steam under other cir- cumstances, the densities and volumes in these tables cannot err, to an extent appreciable in practice for steam obtained under 232 STEAM AND OTHER HEAT ENGINES. circumstances similar to those of M. Regnault’s experiments, which circumstances are, in all important points, similar to those under which steam is obtained in ordinary steam engines. Table IV., in which the density of steam is computed by theory, was published in 1855. The results of the experiments of Messrs. Fairbairn and Tate were published in 1859, and were found to agree very closely with the results of theory. (See Phil. Trans., 1860: also Trans. of the Royal Society of Edinburgh, 1862, p. 153.) It is often convenient for practical purposes to calculate the density of the volume of steam directly from the pressure of satura- tion without reference to the temperature. (See Article 206, page 236.) The following is an empirical formula for that purpose, first published in the Phil. Trans., 1859, page 188, and applicable for pressures not exceeding 120 lbs. on the square inch; in which p denotes the absolute pressure, and v the volume of steam; p, the mean atmospheric pressure of 14-7 Ibs. on the square inch, and v, the volume of 1 1b, of atmospheric steam, or 26:36 cubic feet, os (2)\¥. eee (9.) vy yp See the engraved Diagram at the end of the volume.) n Table V., the densities of the vapour of ether are computed as for a perfect gas from its chemical composition; because in the only case in which data exist for computing its density otherwise, the results of the two modes of computation agree exactly, as will afterwards be shown. The quantities in the column headed E in Table II., being the expansions of unity of volume at 32° im rising to 212°, are 180 times the co-efficients of expansion per degree of Fahrenheit. 203. Expansion ef Liquids—Mercurial Thermometer.—The ratc of expansion of every liquid increases as the temperature becomes higher, and diminishes as the temperature becomes lower. In the case of water, there is a temperature at which the rate of expansion disappears, and the volume of a given weight reaches aminimum. That temperature, according to the most trustworthy experiments, is 39°-] Fahrenheit...........:seescesscees (1.) Between that temperature and 32°, the volume of a given weight of water increases by cold. It is possible that a similar phenomenon may take place in other liquids; but it has not yet been observed in any liquid except water. The above temperature of the maximum density of water, being the temperature at which the specific gravity of water can be most accurately ascertained, is used in France as the standard tempera EXPANSION OF LIQUIDS—MERCURIAL THERMOMETERS. 233 ture, at which the weight of an unit of volume of water is taken for an unit of weight, and of specific gravity. The standard tem- perature for the British standards of weight and measure is 62° Fahrenheit. The following empirical formula for the expansion of water between 32° and 77° Fahrenheit, deduced from the experiments of Stampffer, Despretz, and Kopp, is extracted from Professor W. H. Miller’s paper on the Standard Pound, in the Philosophical Trans- actions for 1856, and reduced so as to be suited to Fahrenheit’s scale instead of the Centigrade scale, for which it was originally computed :— v _ 10-1 (T — 39-1)? — 0-0369 (T — 39:-1)8 log ae 10,000,000 ween(2,) % denotes the volume of a given weight of water at 39°-1 Fah- renheit, and under one atmosphere of pressure, which for one pound of water, has the value 1 GF LHF = OOLGOL ID joo sssseereseen (3.) = GF-49: log = 22046414. v denotes the volume of the same weight of water at any other temperature T on Fahrenheit’s scale. . For rough calculations of the density of water, a simple approxi- mate formula, suited for most practical purposes, has already been given in Article 107, p. 110. The greater convenience of thermometers filled with liquid, as compared with those filled with air, causes the former to be em- ployed for all purposes except certain special scientific researches ; and the liquid commonly employed is mercury. A mercurial thermometer consists of a bulb and stem of glass. The stem should be as nearly as possible of uniform bore; and the inequalities in the bore should be ascertained by passing a small quantity of mercury along the stem, and marking the lengths that it occupies in different positions; and in the graduation of the scale those inequalities should be allowed for, so that each degree of the scale shall correspond to an equal portion of the capacity of the stem. A sufficient quantity of mercury having been introduced, it is boiled, to expel air and moisture, and the tube is hermetically sealed. The standard points are ascertained by immersing the thermometer in melting ice, and in the steam of water boiling under the pressure of 14:7 Ibs. on the square inch, and marking the positions of the top of the column; the interval between those points is divided into the proper number of degrees (100 for the Centigrade scale, 180 for Fahrenheit’s scale), and similar degrees 234 STEAM AND OTHER HEAT ENGINES. are marked above and below those points if necessary, the ascer- tained inequalities in the bore of the stem being allowed for. The rate of expansion of mercury with rise of temperature in- creases as the temperature becomes higher ; from which it follows, that if a thermometer showing the dilatation of mercury simpl were made to agree with au air thermometer at 32° and 212°, the mercurial thermometer would show lower temperatures than the air thermometer between those standard points, and higher tem- peratures beyond them. For example, according to M. Regnault (Mem. Acad. Se, 1847), when tke air thermometer marked 350° C. (= 662° F.), the mercurial thermometer would mark 362°-16 ©. (= 683°°89 F.), the error of the latter being in excess, 12°16 CO. (= 21°89 F.) Actual mercurial thermometers indicate intervals of temperature proportional to the apparent expansion of mercury contained in a glass vessel,—that is, the difference between the expansion of mer- cury and that of glass. The inequalities in the rate of expansion of the glass (which arc very different for different kinds of glass) correct, to a greater or less extent, the errors arising from the inequalities in the rate of expansion of the mercury. For practical purposes connected with heat engines, the mercurial thermometer made of common glass may be considered as sensibly coinciding with the air thermometer at all temperatures not ex- ceeding 500° Fahr. For full information on the comparative indications of thermo- meters, reference may be made to M. Regnault’s papers in the Memoirs of the Academy of Sciences for 1847, entitled respectively “De la Mesure des Temperatures,” and “ De la Dilatation Absolue du Mercure.” Spirit thermometers are used to measure temperatures at and below the freezing point of mercury. Their deviations from the air thermometer are greater than those of the mercurial thermo- meter. 204, Expansion of Solids.—The numbers which it is customary to give in tables of the expansion of solids are the rates of expansion of one dimension, and are therefore respectively one-third of the corresponding rates of expansion in volume. Solid thermometers are sometimes used, which indicate tempera- tures by showing the difference between the expansions of a pair of bars of two substances whose rates of expansion are different. When such thermometers are used to indicate temperatures higher than the boiling point of mercury under one atmosphere (about 676° Fahr.), they are called Pyrometers. In this case the exact value of their degrees ig somewhat uncertain. ‘ MELTING POINT—EVAPORATION, 235 205. Melting Point.—One melting point has already been men- tioned as a fixed temperature,—that of ice. It is lowered by pressure to the extent of 0°-014 for each additional atmosphere of pressure,—a fact predicted by Prof. James Thomson, and ascer- tained experimentally by Sir William Thomson. The following are the melting points of a few of the more important substances. Those marked ? have been measured by the pyrometer :— IMGreUrys ie ceanineiaoes ues — 38° | Bismuth, .......000000000. 493° TCE, veirasracroewdd gneeen decries a B29) | TOA secesecninricca van te nck 630° Alloy—Tin 38, Lead 5, LUNG Serer aoc hi reps ests 400° % Bismuth 8, about,...... BLO" |) UVP: wesc sae eeaaccey ees 280° 2 SUT PHU, Scieacine ade saecins fa 228° | Brass,...ceeecceesseesseeeeee 1869? 4 Alloy—Tin 4, Bismuth 5, COPPER sas cehcrcny easercee as 2548° 2 Vea V ssucevenvesotvacics B46? |) GOldsecscccueuscewscancenecuel 2590° 2 Alloy—Tin 1, Bismuth 1, 286° | Cast iron, ........ ee 3479° 2 Alloy—Tin 3, Lead 2,... 334° | Wrought iron, higher, but Alloy—Tin 2, Bismuth 1, 334° uncertain. UPN ss 2th aie da tenidrenassion snes 426° Ice, cast iron, bismuth, and antimony, and, according to Mr. Nasmyth, many other substances, are more bulky when in the solid state, near the melting point, than they are when in the liquid state;as is shown by the solid material floating in the melted material. é For ice, the excess of volume in the solid state above the volume in the liquid state is very great, and has been ascertained, with the following results :— Volume of 1 Ib. Weight of cubic feet. 1 cub. ft. in Ibs. Water, at: 32° svscsersnessne tien cenwee 001602 62°425 Tee," abr9 2 vacvawsaesioveesmen tee oO'oI74 575 206. Pressure of Vaponr—Evaporation—Boiling—The tempera- ture at which a given fluid boils under a given pressure, is a fixed temperature. In order to explain this phenomenon, and the laws which it follows, it is necessary in the first place to describe the distinctions between the liquid and gaseous conditions, and the mode in which substances pass from the one to the other. I. The Liquid state is that condition of each internal part of a body, which consists in tending to preserve a definite volume, and resisting change of volume, and in offering no resistance to change of figure. It is known that most substances, and believed that all substances, are capable of assuming the liquid condition under suit- able circumstances. The property of offering no resistance to 236 STEAM AND OTHER HEAT ENGINES. change of figure, is common to the condition of ligwid and gas, and constitutes the fluid condition. The liquid condition is distin- guished from the gaseous by the property of tending to preserve a definite volume : a body in the gaseous condition tends to expand indefinitely. Rise of temperature increases the resistance of liquids to compression, and diminishes their cohesion. It is known of most liquids, and believed of all, that for each temperature of a given substance, there is a certain minimum pressure on its external sur- face, which is necessary to its existence in the liquid state, and under which the communication of additional heat to the liquid mass, makes it boil, or emit bubbles of vapour from its interior. There is also reason to believe, that all liquids under all circum- stances emit vapour from their surfaces, and are surrounded by an atmosphere of their own vapour. II. Vapour is any substance in the gaseous condition, at the maximum of density consistent with that condition. This is the strict and proper meaning of the word “ Vapour.” It is sometimes used in an extended sense, identical with that of “ gas,” in speaking of substances whose ordinary condition is the liquid or solid. It is certain that most substances are volatile, that is to say, that they can and do exist in the state of vapour, at all attainable tempera- tures. Many vapours, whose existence cannot be proved by mechanical or chemical processes, are obvious to the sense of smell; for example, those of iron, copper, lead, and tin. Whether all sub- stances are volatile at all temperatures is yet uncertain. If there be cases of exception, it is to be understood that the laws stated in the sequel of this Article do not apply to them. TIT. Pressure and Density of Vapours.—For each volatile sub- stance at each temperature, there is a certain pressure which is at once the least pressure under which the substance can exist in the liquid or solid state, and the greatest pressure which it can sustain in the gaseous state at the given temperature. That pressure is called the pressure of saturation, or the pressure of vapour of the given substance at the given temperature; it is a function of the temperature; and the density of the vapour is a function of the pressure and the temperature. The relation between the pressure of vapour and the temperature, for various substances, has been the subject of many series of experiments, of which the latest and best are those of M. Regnault on steam (Memoirs de Academie des Sciences, 1847), and on various other vapours (Comptes Rendus, 1854). The best sources of information as to the pressures of vapours are the tables computed by M. Regnault from those experi- ments; but such pressures may also be computed in most cases with great accuracy by the aid of a formula, which, with the constants applicable to vapours, as deduced from M, Regnault’s experiments, Biliteneinn> PRESSURES OF VAPOURS. 237 was first given in the Hdinburgh Philosophical Journal for July, 1849, and afterwards, with revised constants, in the Philosophical Magazine, Dec., 1854. The following is the formula for calculating the pressure p of vapour from the absolute temperature 7 =T + 461°-2 Fahy. of the boiling point :— B Cc log p= A — ee The following is the inverse formula for calculating the absolute temperature of the boiling point from the pressure :— rats [a / (A=G8? + im)—soh 2) The following are the values of the constants in the formula, for temperatures in degrees of Fahrenheit, and pressures in pounds on the square foot :— FLvip. . 1 eB log c. ‘i, op. 3 A 0s B 5 9 Cc 4 ce Waiter,..... 8-2591 ... 3°43642...5°59873...0°003441...0°00001184 Alcohol, ... 7°9707 ... 3°31233---5°75323---0°001812...0°000003282 Aither,..... 4*B432 ... 3°31492...5°21700...0°006264...0°00003924 ae e 43438 ... 3°30728...5'21839...0°006136...0°00003765 Mercury,... 7°9691 ... 3°72284 For inches of mercury at 32°, subiract from A,......... 18496 » lb. on the square inch, 5 Aivecoaencas 2°1584 For the Centigrade scale, subtract from log B.......... 025527 5 log C,......... O°51054 multiply = by 15 RB ” 42 by 3°24 From the preceding formula and constants were calculcated the pressures in Tables IV. and VI. for steam, and Table V. for xther, at the end of this volume. (See Diagram facing page 468.) The general result of such formule and tables is, that the pressure of vapour increases with the temperature at a rate which itself increases rapidly with the temperature. If any vapour were a per- fect gas, its density D,, at any temperature T,, might easily be computed, when its density D,, at some other temperature T,, had been ascertained by experiment, by means of the formula, 238 STEAM AND OTHER HEAT ENGINES. D, (Ty + 461°2 Fabr) _ D,(T,-+461°2 Fahr) | 4) Pa = Ps in which p, and p, are the pressures of the vapour at the tempera- tures T, and T, respectively ; but no vapour is an absolutely per- fect gas; and the density of every vapour increases more rapidly with increase of pressurc than that which would be given by the above formula. That formula, however, is sufficiently near the truth for practical purposes when the density of the vapour is below certain limits, as is the case with the vapours of most substances at the temperatures which usually occur in the atmosphere. The experimental determination of the densities of vapours, to a certain rough degree of approximation, sufficient to enable the formula (1 a) to be applied, is easy, and is assisted by a knowledge of their chemi- cal composition, in consequence of the well established laws, jirst, that perfect gases combine by volumes in simple numerical ratios only; and, secondly, that the volume of a given weight of a compound perfect gas always bears simple numerical ratios to the volumes which its constituents would occupy separately. Examples of the application of these laws are given in the case of steam, in Art. 202, equations 4, 5, and in some parts of Table IL, marked thus,*. The direct experimental determination of the densities of vapours, to a degree of accuracy sufficient to show the exact amount of their deviation from the perfectly gaseous condition, has not yet been accomplished. A method of computing the probable value of such densities theoretically, from the heat which disappears in evaporating a given quantity of the substance, will be explained in Chapter ITI. IV. Atmospheres of Vapour—Spheroidal State—From what has been stated, it appears that every solid or liquid substance in a state of molecular equilibrium, wherever it is not enveloped by another solid or liquid substance, is enveloped by an atmosphere of its own vapour, of a density and pressure depending on the tempera- ture (provided the substance is volatile at that temperature). It has been suggested as a hypothesis, that the density of a very thin layer of this atmosphere, immediately adjoining the surface of such liquid or solid, may, owing to the attraction of the liquid or solid, be much greater than the density at considerable distances, and that the elasticity of an atmosphere of vapour so constituted may be the cause of that resistance to being brought into absolute contact, which is displayed by the surfaces of solid and liquid bodies in general (¢. g., when raindrops roll on the surface of a river), and which is so great at high temperatures as to produce what is called the “spheroidal state” of masses of liquid, in which they remain suspended over hot solid surfaces with a visible interval between. The only substance on the earth’s surface which is sufficiently MIXTURES OF VAPOURS AND GASES. 239 abundant to pervade the whole of the earth’s atmosphere at all times with vapour to an amount appreciable by mechanical and chemical processes, is water. : V. Mixtures of Vapours and Gases.—It has already been ex- plained, in Article 199, that the pressure exerted against the interior of a vessel by a given quantity of a perfect gas enclosed in it, is the sum of the pressures which any number of parts into which such quantity might be divided would exert separately, if each were enclosed in a vessel of the same bulk alone, at the same tempera- ture; and that, although this law is not exactly true for any actual gas, it is very nearly true for many. Thus, if 0:080728 Ib. of air, at 32°, being enclosed in a vessel of one cubic foot of capacity, exerts a pressure of one atmosphere, or 14-7 Ibs., on each square inch of the interior of the vessel, then will each additional 0-080728 lb. of air which is enclosed, at 32°, in the same vessel, produce very nearly an additional atmosphere of pressure. It has now further to be explained, that the same law is applicable to mixtures of gases of dif- Jerent kinds. For example, 012344 Ib. of carbonic acid gas, at 32°, being enclosed in a vessel of one cubic foot in capacity, exerts a pressure of one atmosphere; consequently, if 0080728 lb. of air and 0°12344 Ib. of carbonic acid, mixed, be enclosed at the tem- perature of 32° in a vessel of one cubic foot of capacity, the mixture will exert a pressure of two atmospheres. As a second example: let 0-0807 28 lb. of air, at 212°, be enclosed in a vessel of one cubic foot, it will exert a pressure of 212° + 461°-2 ys 39° 4 46172 = 1-365 atmosphere. Let 0:03797 lb. of steam, at 212°, be enclosed in a vessel of one cubic foot: it will exert a pressure of one atmosphere. Con- sequently, if 0-080728 Ib. of air and 0-03797 Ib. of steam be mixed and enclosed together, at 212°, in a vessel of one cubic foot, the mixture will exert a pressure of 2:365 atmospheres. It is a common but erroneous practice, in elementary books on physics, to describe this law as constituting a difference between mixed and homogeneous gases; whereas it is obvious, that for mixed and ho- mogeneous gases the law of pressure is exactly the same,—viz., that the pressure of the whole of w gaseous mass is the sum of the pressures of all its parts. This is one of the laws of mixtures of gases and vapours. A second law is, that the presence of a foreign gaseous substance in contact with the surface of a solid or liqued, does not affect the density of the vapour of that solid or liquid, unless (as M. Regnault has recently shown) there is a tendency to chemical combination between the two substances, in which case the density of the vapour 240 STEAM AND OTHER HEAT ENGINES. is slightly increased. For example: let there be a mass of liquid water in a receiver, at the temperature of 212°, and above the sur- face of the liquid water let there be a space of one cubic foot; it is necessary to molecular equilibrium at the given temperature of 212°, that that space of one cubic foot should contain 0:03797 Ib. of steam, whether the space be void of all other substances, or filled with any quantity of air, or of any other gaseous substance which does not exert an appreciable chemical attraction on the water. To illus- trate the law further, let the temperature of the water be 50°; then it is necessary to molecular equilibrium that the space of one cubic foot above the water should contain 0:00058 Ib. of watery vapour, whether and to what amount soever air, or any other gaseous sub- stance not chemically attracting the water, is contained in the same space. This and the preceding law of mixtures of gases and vapours (discovered by Dalton and Gay-Lussac), enable the following ques- tion to be solved :—Problem. Given the total pressure P, of a mix- ture of a gas and of a given vapour, in a space saturated with the vapour at the temperature T; required the pressure and density of the gas separately.—Solution. Find, from a table of experiments, or from a formula, the pressure of saturation of the vapour for the given temperature T; let it be denoted by »; then the pressure of the gas is P—; and its density is less than the density which it would have had under the pressure P, if no vapour had been pre- sent, in the ratio Pa P Example. A space contains mixed air and steam, being saturated with steam at 50°, and the total pressure is 14-7 lbs. on the square inch; what is the pressure of the air separately, and what weight of air is contained in each cubic foot of the space ?—Answer. Either from M. Regnault’s experiments, or from the formula already cited, it appears that the pressure of the steam is 0°173 lb. per square inch; consequently, the pressure of the air separately is 14:7 — 0-173 = 14:527 Ibs. per square inch. Also, the weight of air ina cubic foot, at 14-7 Ibs. per square inch and 50°, had there been no - steam present, would have been 493°:2 0-080728 xX 50° + 461°) — 0:077885 Ib. ; consequently the weight of air actually present along with the steam, in a cubic foot, is ‘5 0-077885 x el = 0:07698 lb. EVAPORATION—-CONDENSATION——-EBULLITION, 241 A second problem is, to find the density of the mixture of gas and vapour; which is solved by adding to the density of the gas already found, the density of the vapour as computed by the methods for- merly referred to. Thus, in the case last given, it appears, by com- puting from the latent heat of evaporation, that the weight of steam in a cubic foot is 0-00058 lb. ; consequently, the weight of a cubic foot of the mixture of air and steam is 0:07698 + 0:00058 — 0-07756 lb. With respect to the amount of the deviations from the foregoing laws, which occur when the ingredients of the gaseous mixture have a chemical affinity for each other, the reader is referred to the later researches of M. Regnault already mentioned, Comptes Rendus, 1854. VI. Evaporation and Condensation.—When the density of the vaporous atmosphere of a solid or liquid is diminished, either by the enlargement of the space in which the substance is contained, or by the removal of part of the vapour, whether by mechanical displacement (as when it is blown away by a current of air) or by condensation in an adjoining space, the solid or liquid evaporates until equilibrium is restored, by the restoration of the vapour to the density corresponding to the existing temperature. The same thing takes place when the molecular equilibrium is disturbed by commu- nicating heat to the solid or liquid. When the density of the vaporous atmosphere is increased, either by the contraction of the space in which the substance is contained, or by the addition of vapour from another source, part of the vapour condenses until equilibrium is restored as before. The same thing takes place when the molecular equilibrium is disturbed by abstracting heat from the vapour. Evaporation is accompanied by the disappearance of heat, called the Latent Heat of Evaporation, and condensation by the re-appearance of heat, according to laws to be stated in Section 2 of this Chapter. When the space above the solid or liquid is void of foreign substances, the restoration of equilibrium is sensibly instan- taneous; when that space contains foreign gaseous substances, the restoration of equilibrium is more or less retarded, although the conditions of equilibrium (as stated in Division V. of this Article) are not changed. It is the retardation of the diffusion of watery vapour by the presence of air which prevents every part of the earth’s atmosphere from being always saturated with moisture. VII. Lbullition—When the communication of heat to a liquid mass and the removal of the vapour are carried on continuously, so that the pressure throughout the mass of liquid is not greater than that of saturation for its temperature, evaporation takes place, not merely from the exposed surface of the liquid, but also from its interior: it gives out bubbles of vapour, and is said to boil. The ascertaining by experiment of the temperatures of ebullition, or BR 243 STEAM AND OTHER HEAT ENGINES. boiling points, of a liquid under various pressures, is the most accu- rate method of determining the relation between the temperature and pressure of saturation of its vapour. Conversely, when that relation is known for a given fluid, and expressed by formule or tables, the boiling point of the fluid may be made the means of measuring the pressure on it. On this principle is founded the method invented by Wollaston, and since perfected by Dr. J. D. Forbes, of deducing the atmospheric pressure, and thence the eleva- tion of the place of observation, from the boiling point of water in an open vessel, as measured by a very delicate thermometer. (See Edinburgh Transactions, vols. xv. and xxi.)—When the term boiling point of a fluid is used without qualification, it means the boiling point under the average atmospheric pressure of 14:7 Ibs. on the square inch. VIII. Resistance to Boiling—Brine.—The presence in a liquid of a substance dissolved in it (as salt in water), resists ebullition, and raises the temperature at which the liquid boils, under a given pressure ; but unless the dissolved substance enters into the compo- sition of the vapour, the relation between the temperature and pressure of saturation of the latter remains unchanged. A resist- ance to ebullition is also offered by a vessel of a material which attracts the liquid (as when water boils in a glass vessel), and the boiling takes place by starts. To avoid the errors which causes of this kind produce in the measurement of boiling points, it is advis- able to place the thermometer not in the liquid, but in the vapour, which shows the true boiling point, freed from the disturbing effect of the attractive nature of the vessel. The boiling point of satur- ated brine under one atmosphere is 226° Fahr., and that of weaker brine is higher than the boiling point of pure water by 1°-2 Fahr. for each vy of salt that the water contains. Average sea water contains zz; and the brine in marine boilers is not suffered to con- tain more than from sz to 3%. IX. Nebulous or Vesicular Vapour is a condition of fluids, also called Cloud, Mist, or Fog, in which the liquid floats in the air, or in its own vapour, in the form of innumerable small globules. The condition of cloud is one into which fluids pass from the state of vapour on being condensed by mingling with cold air. By heat, the globules of cloud are made to evaporate and disappear; by cold they are made to coalesce into drops, which fall to the ground, or adhere to neighbouring solid bodies. X. Superheated Vapour means vapour which has been brought to a temperature higher than the boiling point corresponding to its pressure, so as to be in the condition of a permanent gas, (See Articles 295 to 299, pages 428 to 443.) QUANTITIES OF HEAT. 243 Section 2.—Of Quantities of Heat. 207. Comparison of Quantities of Heat—The condition of heat is measured as a quantity, and its amounts in different bodies and under different circumstances compared, by means of the changes in some measurable phenomenon produced by its transfer or dis- appearance. Amongst the changes used for this purpose, changes of temperature will be first considered. Heat employed in produc- ing elevation of temperature is called sensible heat. In so using changes of temperature, it is not to be taken for granted that equal differences of temperature in the same body correspond to equal quantities of heat. This is the case, indeed, for perfectly gaseous bodies; but that is a fact only known by experi- ment. In bodies in other conditions, equal differences of tempera- ture do not exactly correspond to equal quantities of heat. To ascertain, therefore, by an experiment on the changes of temperature of any given substance, what proportion two quantities of heat bear to each other, the only method which is of itself sufficient in the absence of all other experimental data, is the comparison of the weights of that substance which are raised from one and the same lower temperature, to one and the same higher fixed temperature, by the transfer to them of the two quantities of heat respectively. For example, the double of the quantity of heat which raises the temperature of one pound of water from 32° to 32° + 30° = 62°, is not exactly the quantity of heat which raises the temperature of one pound of water from 32° to 32° + 60° = 92°; but it is exactly the quantity of heat which raises the temperature of two pounds of water from 32° to 62°. The most usual experiments on quantities of heat are those in which the equality of two quantities of heat is ascertained. For example, m pounds of a substance A, at a temperature T,, and n pounds of a substance B at a lower temperature T,, are brought into close contact, and either they are guarded against the transfer of heat to or from third bodies, or if such transfer is unavoidable, its amount is ascertained and allowed for. After a sufficient time has elapsed, equilibrium of temperature takes place, by both bodies acquiring the same temperature T,, intermediate between T, and T,. Then a certain amount of the condition called heat has been transferred from A to B; and the effects of that transfer are— . I. The lowering of the temperature of m pounds of A from T, toT, ; II. The raising of the temperature of n pounds of B from T, to T, ; from which we conclude, that the quantities of heat corresponding to those two effects are equal. A further inference from the same experiment is the following proportion :— 244 STEAM AND OTHER HEAT ENGINES. Quantity of heat corresponding to the interval of temperature between T, and T, in the substance A, : Quantity of heat corresponding to the interval of temperature between T, and T, in the substance B 225m. The same mode of experimenting may be applied to two portions of the same substance, so as to compare the quantities of heat corresponding to intervals of temperature in different parts of the thermometric scale. 207 A. A Calorimeter, or instrument for measuring quantities of heat, consists essentially of a vessel containing a known weight of some convenient liquid, such as water or mercury—a thermometer for indicating the temperature of that liquid,—and if necessary, an agitator, or fan, for making the liquid circulate, in order that all its parts may be at an uniform temperature at the same instant. Experiments of the kind mentioned in Article 207 are performed by immersing in the liquid, or mixing with it, a known weight of the substance to be experimented on, at a known temperature, different from the temperature of the liquid, and noting the com- mon temperature of the liquid and of the immersed substance when equilibrium of temperature is restored; taking care at the same time that all losses of heat, and other causes of error, are ascertained and allowed for. In the mercurial calorimeter of MM. Favre and Silbermann, there is no independent thermometer; the instrument being simply a mercurial thermometer with a bulb so large, that the body to be experimented upon can be enclosed in a small chamber in the centre of the bulb, so as to insure that all the heat which that body loses shall be transferred to the mercury. This calorimeter has no agitator. For examples of the construction and use of the water calori- meter, see M. Regnault’s papers in the Memoirs of the Academy of Sciences for 1847. . 208. Umit of Meat—For the purpose of expressing and compar- ing quantities of heat, it is convenient to adopt as an UNIT OF HEAT or THERMAL UNIT, that quantity of heat which corresponds to some definite interval of temperature in a definite weight of a particular substance. ‘Yhe thermal unit employed in Britain is— The quantity of heat which corresponds to an interval of one degree of Lahrenheit’s scale in the temperature of one pound of pure liquid water, at and near its temperature of greatest density (39°-1 Fahren-- heit). The reason for the limitation to that part of the scale of tem- THERMAL UNITS—SPECIFIC HEAT. 245 perature which is near the temperature of the greatest density of water is, that the quantity of heat corresponding to an interval of one degree in a given weight of water is not exactly the same in different parts of the scale of temperatures, but increases as the temperature rises, according to a law which will be stated in the next Article. For temperatures not higher than 80° Fahrenheit, that quantity is sensibly constant. The thermal unit employed in France (called Calorie) is the quantity of heat which corresponds to an interval of one Centigrade degree in the temperature of one kilogramme of pure liquid water, at and near its temperature of greatest density. The following statement shows the mutual ratios of the British and French units of weight, temperature, and heat, with the logarithms of those ratios :— Ratios. Logarithms. Pounds avoirdupois in a kilogramme,.........2'20462 0°3433340 Kilogramme in a Ib. avoirdupois,............64 0°453593 1'6566660 Fahrenheit degrees in a Centigrade degree, 1°8 0°2552725 Centigrade degree ina Fahrenheit degree,...0°555 174447275 British thermal units in a French thermal UN byrecrsacscasedoas ascieteeweeiicnctecitete Seiad 3°90832 0°5986065 French thermal unit in a British thermal Eatin gseeesiunsamcoaneteecaiae ome \ 0°251996 14013935 Other units in which quantities of heat can be expressed will be afterwards explained. 209. Specific Heat of Liquids and Solids—The specific heat of a substance means the quantity of heat, expressed in thermal units, which must be transferred to or from an unit of weight (such as a pound) of a given substance, in order to raise or lower its tempera- ture by one degree. é According to the definition of a thermal unit given in Article 208, the specific heat of liquid water at and near its temperature of maximum density is unity; and the specific heat of any other substance, or of water itself at another part of the scale of tem- peratures, is the ratio of the weight of water at or near 39° 1 Fahrenheit, which has its temperature altered one degree by the transfer of a given quantity of heat, to the weight of the other sub- stance under consideration, which has its temperature altered one degree by the transfer of an equal quantity of heat: the equality of quantities of heat being ascertained in the manner explained in Article 207. The specific heat of a substance is sometimes called its “ capacity . for heat.” 246 STEAM AND OTHER HEAT ENGINES. The specific heats of the substances to which reference will after- wards have to be made in this treatise, as expressed in ordinary thermal units, are given in the columns headed C in Table IL, at the end of the volume. So far as those tables relate to liquids and solids, those quantities are to be regarded as merely approximate average values, near enough to the truth for practical purposes at the temperatures which usually occur; for the specific heat of every substance in the liquid or solid state is variable, becoming greater as the temperature rises; and that to an extent which is in general greater, the more expansible the substance is. The only substance for which the exact law of that variation has been ascertained is water, on whose specific heat a series of precise experiments was made by M. Regnault, and published in the Memoirs of the Academy of Sciences tor 1847. The following empirical formule, first published in the Z'rans- actions of the Royal Society of Edinburgh for 1851, represent very closely the results of those experiments. Let T be the temperature of the water, reckoned from the ordinary zero of Fahrenheit’s scale. Then the specific heat of water at that temperature is ¢ = 1 +.0-000000309 (T — 39° 1)25.....ssscseeee(L.) the number of units of heat required to raise one pound of water from any temperature T, to any other temperature T, is as follows :— Tp 5 a= | ed T=, ~T, +0:000000103 {(T,~39°1)° -(T,- 39°-1)3} aes suet a ustnyes veteieay (2.) and the mean specific heat between any given pair of temperatures, T, and T,, is h oO 7-77 1 + 0:000000108 { (T, — 39°-1)2 +(T,—39°1) (T, —39°°1) + (T, — 39°11)" sieneesw’ (3.) To adapt these formule to the Centigrade scale, the following alterations are to be made :— for 0:000000309 is to be put 0-000001 ; for 0:000000103 55 0-00000033 ; for T — 39-1, - T— 40, The exact equivalent of 39°-1 Fahrenheit is 3°-94 Centigrade; but 4° is sufficiently near the truth for the present purpose. SPECIFIC HEAT, : 247 In calculations respecting the quantities of heat required by masses composed of various materials to produce given alterations of temperature, it is convenient to substitute for the weight of each material an equivalent weight of water, and then to calculate for the whole mass as if it were composed of water. The equivalent weight of water is found in each case by multiplying the weight of the material in question by its specific heat. Suppose, for example, that a calorimeter contains m pounds of water, and that the vessel and the agitator are made of copper, and weigh g pounds. The solid part of the apparatus accompanies the water in its changes of temperature; and the heat required to pro- ‘duce these changes must be taken into account. This is con- veniently done by supposing that for the g pounds of copper there are substituted 0951 g pounds of water (0951 being the specific heat of copper); and then computing the results of experiments made with the calorimeter as if it consisted solely of m+ ‘0951 g pounds of water. The following are the specific heats of a few liquids and solids, in addition to those given in Table II. at the end of the volume. Some are given on the authority of M. Regnault; some on that of Lavoisier and Laplace, some on that of Dalton, and the specific heat of ice on that of M. Person. ~ NGG esa ca ui csineg vdetematnad soewa sone 0'504 SulphUtsc0 ss scseaens. cheeeeneeeeseeey 0°20259 Charcoal,......... tekeeus vevaxneneeone 0°2415 Coal and coke average,............ o°201 Alumina (Corundum), ..........06 0'19762 Do. (Sapphire), ..........-.-+ 0°21732 Silica, ...... sehinebenieuisaeavslonmr bones O19 32 (Brick, being composed of silica and alumina, has probably a specific heat of about 0-2). Flint glass,........cscecsecceseeseeeeee o'l9 Carbonate of lime,......ceeeeeseeees 02085 Quicklime; i es. scnssaecussasese ves oe 0'2169 Magnesian limestone,..........+0-+- 021743 (Stones, being composed chiefly of silica, alumina, and carbo- nates of lime and magnesia, have probably specific heats not differing greatly from 0-2 or 0°22). Olive Oil, .....sscecssececserreesseones .0°3096. From some of the above data may be deduced the useful prac- £48 STEAM AND OTHER HEAT ENGINES. tical conclusion, that the average specific heat of the non-metallic materials and contents of a furnace, whether bricks, stones, or fuel, does not greatly differ from one-fifth of that of water. It was discovered by Dulong and Petit, and has been verified by MM. Regnault, Newmann, and Avogadro, that most known substances may be arranged according to the analogies of their chemical constitution in groups; and that in any one given group the specific heats of the substances are with few exceptions inversely as their chemical equivalents ; or, in other words, that the product of the specific heat of a substance by its chemical equivalent is a constant for most of the substances in one group. For most of the metals, for example, that constant product is,— According to the French scale of chemical equivalents,...37°5 ; According to the English scale, ........c0sscssceseeeeneeenerees 6° 210. Specific Meat of Gases— Although the exact value of the specific heat of air was predicted by an indirect calculation in 1850, neither it, nor that of any other gas, was determined accu- rately by direct experiment until M. Regnault made his experi- ments on that subject, the results of which were published in the Comptes Rendus of the Academy of Sciences for 1853. The specific heat of a, gas which is nearly in the perfectly gaseous state does not sensibly vary with density or with temperature; so that for such a gas, equal intervals of temperature correspond to equal quantities of heat on all parts of the thermometric scales. Hence it has been inferred as probable, that the absolute zero of the perfect gas thermometer (Article 201) coincides either exactly, or very nearly, with the absolute zero of heat, or temperature at which bodies are wholly destitute of the condition called heat. This inference is corroborated by facts to be mentioned in Chapter ITI. of this Part. It was shown by Laplace and Poisson, that the specific heat of a gas is different, according as it is maintained at a constant volume, or at a constant presswre, during the operation of changing its tem- perature, and that the ratio which these two specific heats bear to each other is connected with the velocity with which sound is trans- mitted through the gas, in the following manner :— When a pound of a given gas is enclosed in a vessel of tnvariable volume, let ¢, denote the number of units of heat required in order to raise its temperature one degree. When the same weight of the same gas is contained in a space capable of enlargement, and subjected to a constant pressure, and when its temperature is raised by one degree, it not only becomes hotter to the same extent as before, but also expands by 0-0020276 of its volume at 32°; and it is known, that to raise its temperature SPECIFIC HEAT OF GASES, 249 one degree, and expand its volume by that fraction, requires a quantity of heat ¢,, which is greater in a certain proportion than that required merely to raise its temperature one degree without expanding it (¢,). Let the ratio * = y. Then it can be shown, that when the density of the gas D is made to vary without any transfer of heat to or from the gas, the pressure varies proportionally to that power of the density whose index is the ratio ; that is— ‘The velocity with which sound is transmitted through any sub- stance is the same with that which a heavy body would acquire in falling through one-half of the height which, being multiplied by a small variation of the density of the substance, gives the corre- sponding small variation of the pressure. That is, let « denote the velocity of sound ; then w=a/ oe? )... es (2.) According to equation 1, for a gas, d ¢ aD =p =7PPH TK; “acacauause (3.) and consequently, o : BN go US wal (97mm. Z)ir= Se, ciewaraiy (4.) so that when the velocity of sound at a given absolute temperature t has been ascertained in a gas for which p, v is known, the ratio y can be calculated. The value of that ratio for atmospheric air, as deduced from the experiments of MM. Bravais and Martins, and MM. Moll and Van Beek, on the velocity of sound, is Y = 14085... cccsecrscecrreeneeererees (5.) and the same value agrees very nearly also with the experiments of Dulong on the velocity of sound in oxygen, hydrogen, and carbonic oxide. For the denser and more complex gases, its value appears to be smaller (see Edin. Trans., 1853, vol. xx., page 589.) Owing to the difficulty of experimenting on the specific heats of gases at constant volume, their specific heats under constant pres- 250 STEAM AND OTHER HEAT ENGINES. sure have alone been found by direct experiment with the calorime- ter. Examples of both kinds of specific heat are given in Table II. 211. natent Heat means, a quantity of heat which has disap- peared; having been employed to produce some change other than elevation of temperature. By exactly reversing that change, the quantity of heat which had disappeared is reproduced. When a body is said to possess or contain so much latent heat, what is meant is this,—that the body is in a condition into which it was brought from a former different condition by transferring to it a quantity of heat which did not raise its temperature, the change of condition having been different from change of temperature; and that by restoring the body to its original condition in such a man- ner as exactly to reverse all the steps of the former process, the quantity of heat formerly expeuded can be reproduced in the body and transferred to other bodies. The principles according to which such disappearance and pro- duction of heat take place belong to the Second and Third Chapters of this Part; at present the facts are merely to be stated as they are okserved. The effects other than rise of temperature, produced by quanti- ties of heat which disappear, can be used to measure and compare those quantities. 212. Latent Weat of Expansion Heat which disappears in caus- ing the volume of a body to increase under a given pressure, has already been illustrated in the case of gases. For example, to raise the temperature of a pound of air one degree of Fahrenheit, and at the same time to increase its volume by 0:0020276 of its volume at 32°, requires c, = 0°238 of a thermal unit; while the mere rise of temperature, without expansion, requires only ¢, = 0-169; and it is evident that the difference between those quanti- ties, or c, —c, = 0°069 of a thermal unit, is the heat which disap- pears in producing the before-mentioned expansion ; or, in other words, the latent heat of expansion of the air, for an expansion of 0-0020276 of its volume under the same pressure at 32°. The fact already mentioned, that the increase of the specific heat of solids and liquids as the temperature rises is greatest for those which are most expansible by heat, and in particular, the instance of that fact which takes place for water, whose least specific heat corresponds to its greatest density, makes it probable that the variable part of the specific heat of solids and liquids is latent heat of expansion; and that the real specific heat of every substance, or the heat which produces changes of temperature alone, is constant for all temperatures. 213, Latent Heat of Fusion— When a body passes from the solid to the liquid state, its temperature remains stationary, or LATENT HEAT OF FUSION. 251 nearly stationary, at a certain melting point (Art. 205) during the whole operation of melting; and in order to make that operation go on, a quantity of heat must be transferred to the substance melted, having a certain amount for each unit of weight of the substance. That heat does not raise the temperature of the sub- stance, but disappears in causing its condition to change from the solid to the liquid state; and it is called the latent heat of fusion. ‘When a body passes from the liquid to the solid state, its tem- perature remains stationary or nearly stationary during the whole operation of freezing; a quantity of heat equal to the latent heat of fusion is produced in the body; and in order that the opera- tion of freezing may go on, that heat must be transferred from the body to some other boy. The following are examples in British thermal units per lb. :— Latent heat Substances. Melting points. of fusion, Ice (according to Peclet),............. BOP asitisielas civsinas 135 », (according to Person),............ BOE, adasciaseute 142°65 Spermaceti,...... 2. ..ccccseeessenseseees BO: zgecsvemscnssts 148 Bees! Waxsug ace vai Seseesnessceraresaseac’ TAO seieilecns es ave 175 Phosphorus, ......6...:seeeeeseeeeeeeees V7]! Boasacuswes 9°06 Sulphur, seissenacesaascnasateaseesseasens AOR savevneesveviens 16°86 Til; iecosasenes sia hans wins sa eees es saad ABO worecveasnasies 500 M. Person, in a paper published in the Annales de Chimie et de Physique, for November, 1849, gives the following law as the result of his experiments on the latent heat of fusion of non-metallic substances :— ‘ Let ¢ be the specific heat of the substance in the solid state ; c’, its specific heat in the liquid state ; T, its temperature of fusion in Fahrenheit’s ordinary scale; then the latent heat of fusion of one pound, in British thermal units, is b= (cl — oe) (T + 256°)... eee ceecseeee ee (1.) In the case of ice, for example, c= 0-504; c¢ =1; T = 32°, and 1, by calculation, ...........:00. = 496 X 288 = 142°86 i, by experiment, a¢cording to M. Person,........ = 142°65 Difference,...... o'21 M. Person also gives a general formula for the latent heat of fusion of metals, as to which it is sufficient here to refer the reader to the original paper cited. The fusion of solids is sometimes used for the measurement of 252 STEAM AND OTHER HEAT ENGINES. quantities of heat. For example, an ice calorimeter consists essen- tually of a block of ice; in which a cavity has been made, with a stopper of ice for closing it. Ifa piece of some substance at a given temperature, higher than 32°, is enclosed in that cavity until its temperature falls to 32°, the quantity of heat transferred from it to the ice is indicated by the weight of ice melted, being at the rate of 142 British thermal units for each pound of ice melted. The lowering of the melting point of ice by pressure, discovered by Mr. Thomson, will be described in Chapter ITT. 214, Latent Heat of Evaporation.— W hen a body passes from the solid or liquid to the gaseous state, its temperature during the whole operation remains stationary at a certain boiling point (Article 206) depending on the pressure of the vapour produced; and in order to make the evaporation go on, a quantity of heat must be transferred to the substance evaporated, whose amount, for each unit of weight of the substance evaporated, depends on the temperature. That heat does not raise the temperature of the substance, but disappears in causing it to assume the gaseous state; and it is called the latent heat of evaporation. ‘When a body passes from the gaseous state to the liquid or solid state, its temperature remains stationary, during that operation, at the boiling point corresponding to the pressure of the: vapour; a quantity of heat equal to the latent heat of evaporation at that temperature is produced in the body; and in order that the opera- tion of condensation may go on, that heat must be transferred from the body condensed to some other body. The relations which exist between the latent heat of evaporation, and the pressure and volume of the vapour, will be explained in Chapter ITT. The following are examples of the latent heat of evaporation in British thermal units, of one pound of certain substances, when the presstire of the vapour is one atmosphere of 14:7 lbs. on the square inch :— Boiling point Latent heat in Substance, under one atm. Brith Authority. Fahr. ritish units. Water; .ccsasaseave 21270 aes 906'1 e's Regnault. | Alcohol,.......0.0+ 172°2 wg 364°3 vas Andrews. Lltheyr, .....0000++ 950 i 162°8 wo do. Bisulphuret of ; es Gato «can ; 114'8 seis 156° es do. The latent heat of evaporation of water at a series of boiling points extending from a few degrees below its freezing point up to about 375° Fahrenheit has been determined experimentally by M. Regnault (Memoirs of the Academy of Sciences, 1847). The follow- LATENT AND TOTAL HEAT OF EVAPORATION, 253 ing empirical formula represents the results of those experiments with great precision, in British thermal units :— 2 = 1091-7 — 0-695 (T — 32°) — 0:000000103 (T — 39°-1)8....(1.) This formula is not exactly the same with that given by M. Regnault himself, but is slightly modified for reasons explained in 2 paper on the specific heat of liquid water, in the Transactions of the Royal Society of Edinburgh, vol. xx. For the Centigrade scale, in French units, it becomes : L = 6065 — 0-695 T — 0-00000033 (T — 4°)8......(2.) In most of the cases which occur in practice, it is sufficient to calculate the latent heat of evaporation of water by the following approximate formula :— Inearly = 1092 — 0-7 (T — 82°) = 966 — 0-7 (T — 212°)...(3.) The latent heats of evaporation of other substances at pressures different from one atmosphere have not yet been ascertained. 215. Wotal Heat of Evaporation, or total heat of vapour, is a con- ventional phrase used to denote the sum of the heat which disappears in evaporating one pound of a given substance at a given tempera- ture (or latent heat of evaporation), and of the heat required to raise its temperature, before evaporation, from some fixed temperature up to the temperature of evaporation. The latter part of the total heat is called the sensible heat. To express this by symbols, let T, be the temperature at which the substance is originally obtained, T, that at which it is evapor- ated, ¢ its mean specific heat between those temperatures, and J, its latent heat of evaporation at the temperature T,; then its total heat of evaporation, from T., at T,, is thus expressed— Tg SG SY cinsenonoiiac (1.) In formule and tables relating to the total heat of evaporation, it is usual to take for the original temperature T,, that of melting ice. In the case of water, the experiments of M. Regnault, already referred to, led him to the discovery of the very simple law, that the total heat of steam from the temperature of melting ice increases at an uniform rate as the temperature of evaporation rises. The following is the formula by which that law is expressed, for Fah- renheit’s scale and British units :— = 1091-7 + 0:305 (T — 32°) j....ccseeeenees (2.) which, for the Centigrade scale and French units, becomes h = 606-5 4-0°305 Tose eeeeeeee eens (2 A.) 254 STEAM AND OTHER HEAT ENGINES, It is by subtracting from this expression the quantity of heat required to raise unity of weight of water from the temperature of melting ice to the temperature of evaporation T, as given in Article 209, that the formule 1 and 2 of Article 214 are obtained. Let @,. be the mean specific heat of water between the tempera- ture of melting ice and the temperature T, of the “feed water” supplied to a boiler; then we have, for the total heat expended per pound of water evaporated from T, at T,, the following formula (in British units) :-— Tiny = LOOT? 4 0-305 (7, — 32°) — oi, (Ty — 38%3..:(3)) the last term showing the diminution of the expenditure of the heat consequent upon thé temperature of the feed water being T, — 32° higher than that of melting ice. In most of the cases which occur in practice, small fractions may be neglected, and the specific heat of liquid water may be treated as constant, and = 1; so that the following approximate formule are in such cases sufficient :— h = 1092 + 03 (T — 32°) = 1146+ 0:3 (T — 212°);...(4.) fig = 1009 0-9 (Ty 999) — OT = BP elt) 215 A. Measurement of Heat by Evaporation —The heat pro- duced by the combustion of a given weight of fuel (of which examples will be given in Chapter II.) is usually ascertained by finding what weight of water it evaporates. In such experiments, it is essential to the obtaining of accurate results that the tempera- ture of the feed water and the temperature of evaporation should both be ascertained, and the total heat per pound of water com- puted; for which purpose the approximate formula 5 is sufficient. That total heat being divided by 966, the latent heat of evaporation of a pound of water at 212°, gives a multiplier, by which the weight of water actually evaporated by each pound of fuel is to be multi- plied, to reduce it to the equivalent evaporation from and at 212°; that is, the weight of water which would have been evaporated by each pound of fuel, had the water been both supplied and evaporated at the boiling point corresponding to the mean atmospheric pressure. The weight of water so calculated is called the evaporative power of the fuel. To state it is, in fact, to employ a peculiar thermal unit,—viz., the latent heat of evaporation of one pound of water at 212°, which is 966 times greater than the ordinary British thermal unit. To exemplify the reduction above described, let the water be supplied to the boiler at 104° Fahr., and evaporated at 230°. Then by equation 5 of Article 15, the total heat of evaporation in com- mon British units per pound of steam is (neglecting fractions), or a EVAPORATIVE POWER—GASEFICATION—STEAM- GAS, 2 hyyy = 1092+ 3. 198—72 = 1079; and the multiplier by which the weight of water actually evaporated Te be multiplied to find the equivalent evaporation from and at ere ail’, 1s 1079 f 066 = 1117. The following is a convenient form of the expression for that multiplier, or factor of evaporation :— , 03 (T= 212°) + (212° — 7) 966 The table on the next page gives the factor of evaporation as calculated by the above formula, for various temperatures of feed water and of boiling point. 216 otal Meat of Gasefication—It is demonstrated by rea- soning to be explained in Chapter IIT. that the total heat required to convert a given substance from a state of great density at a given temperature T,, to the perfectly gaseous state at a given temperature T,, the operation being completed under any constant pressure, is given by the equation hod (yp — Tove pss (Ly where a is a constant, and ¢’ is the specific heat of the substance in the perfectly gaseous state, under constant pressure. For steam in. the perfectly gaseous state, or steam-gas, as it may be called, for which po % = 42141 foot-lbs., the best existing data give ayant le é = 0-475. For example, to convert one pound of water at 32° into steam-gas at 212°, requires 1 1092 + 475 x 180 = 1177 units of heat; being more than the quantity required to make saturated steam at the same temperature, in the ratio 1177 1146 » Equation i was first demonstrated for certain cases in 1849, in a paper published in the Transactions of the Royal Society of Edinburgh, vol. xx.; and was afterwards more generally demonstrated in a paper read to that Society in 1855, but not yet published. = 1-028. STEAM AND OTHER HEAT ENGINES. 256 Lo.t | 60.1 1n1 | err | biz | ora | guar | og | ez | ber | der gzr go.1 | gor | or | ez2 | br.1 | ora | gtx | og | ez. | €%.r | Ger ov 90.1 Lo. 60.1 ILI €1i S11 Lut 61.1 1.1 €z.1 Fz.1 ZOE Go.1 Lo. 60.1 11.1 €1.1 S11 4.1 gL I o@.1 2z.1 Fz.1 VLE Fo. 90.1 go. OLLI Z1.1 FL. g1.1 QI. oZ.I Zo. €z.1 gGE Fo.1 90.1 go.1 OL. ZI.1 Fi. Su. L1.1 61.1 IZ. €z.1 gee €o0.1 Go.1 ho.t 60.1 ILI 1.1 Sit Lit 61.1 12.1 Zz.1 oz€é €o.1 Go.1 Lo. 60.1 ILI Zi. | F1.1 Q1.I | QI.I | O@.1 ZZ. zof zO.I Fo. go. go.1 O1.I Z1.1 VII QI. QI. 0Z.1 12.1 gz zor | For | 90.1 lot | 60.1 rr | Sr.r | Grr | Qiu | O11 | 12.1 992 10.1 £0.1 Go.1 Lo. 60.1 ILI €1.1 FI gL. gL. oz.1 ghz Io.r | zor | vor go.1 go.r | O11 ZI.t | VIL QgI.r | Ql. Oz.1 o€z oor | zor | For | gor | gor | or | rt | 1. | Gra | fra | 611 owls obIG of GI oD AL o8ST OFT obGL oFOL 098 089 00G 06S qe ‘By ayVAL paay JO oInyeradway, [eNIUT FL ‘Suiog Samog ‘NOILVUOdVAW FO SUOLOV JO TTAV TRANSFER OF HEAT—RADIATION—CONDUCTION. 257 Section 3.—Of the Transfer of Heat. 217. Transfer of Heat in General.—It has already been explained (Articles 196, 197), that equality of temperature between two bodies consists in the absence of any tendency to transfer of heat between them ; and that when their temperatures differ, there is a tendency to equalize their temperatures, by the transfer of heat from the hotter to the colder. That tendency is the greater, tlic greater the difference between those temperatures. The rate at which the transfer of heat takes place between two bodies, at unequal temperatures, depends— : first, on the tendency to transfer heat, increasing as some func- tion of the two temperatures and their difference. Secondly, on the areas of those parts of the surfaces of the bodies through which the transfer of heat takes place. In most of the cases which occur in practice, those areas are equal, and then the rate of transfer of heat is directly proportional to their common extent. Thirdly, on the nature of the material of each of the bodies, and the condition of their surfaces. Fourthly, on the nature and thickness of the intervening sub- stances, if any. Increase of that thickness diminishes the rate of transfer of heat. The transfer of heat takes place by three processes, called respec- tively, radiation, conduction, and convection. 218. Radiation of heat takes place between bodies at all distances apart, in the same manner and according to the same laws with the radiation of light. Its phenomena have been studied, and its laws ascertained, by many scientific inquirers; but for purposes con- nected with prime movers driven by means of heat, the exact and complete statement of those laws is unnecessary. It is sufficient to state, that the rate of radiation of heat by the hotter of a pair of bodies, and of its absorption by the colder, are increased by dark- ness and roughness of the surfaces of the bodies, and diminished by smoothness and polish. 219. Conduction is the transfer of heat-between two bodies or parts of a body, which touch each other. It is distinguished into internal and external conduction, according as it takes place between the parts of one continuous body, or through the surface of contact of a pair of distinct bodies. The rate at which conduction, whether internal or external, goes on, being proportional to the area of the section or surface through which it takes place, may be expressed in the form of so many thermal units per square foot of area, per hour. The rate of internal conduction through a given substance, thus expressed, is proportional— 8 258 STEAM AND OTHER HEAT ENGINES. I. To the rate at which the temperature varies along a line per- pendicular to the section through which the heat is transferred. IL. To a co-efficient called the internal conductivity of the sub- stance, which depends on the nature of the substance. It also depends to a small extent on the temperature at the section under consideration, being in general somewhat greater at higher than at lower temperatures; but the law of its increase with temperature has not yet been accurately ascertained in any case; and it is usually treated as approximately constant. Those laws are expressed mathematically as follows :— Let dx denote the distance, in a direction perpendicular to a sectional plane through which heat is transferred, between a pair of points in a mass of a given substance ; dT, the difference between the temperatures of the mass of those points ; Then the rate of conduction through the given sectional plane may be represented by dT =h Lag Deena (1.) & being the co-efficient of conductivity. Now in cases where k without sensible error may be treated as constant, the above equa- tion leads to the conclusion, that the rate of conduction through a flat layer, of any uniform thickness, is simply proportional, directly to the difference between the temperatures of the two faces of the layer, and inversely to its thickness; a principle expressed as follows :— =e where T’ and T are the temperatures at the two faces of the layer, and « its thickness. For reasons which will afterwards appear, it is convenient, in cases of this kind, instead of the conductivity itself, to use its reciprocal, which may be called the internal thermal resistance of the substance, and may be represented as follows :— 1 GZ dereeeeteencenteeneerseeseasens (3.) so as to transform equation 2 into the following form :— T—T I= ae A a ee (4.) The following are some values of the co-efficient of thermal resistance ¢, for different substances, when q is expressed in thermal CONDUCTION OF HEAT. 259 units per hour per square foot of area, and x in inches, as computed from a table of conductivities deduced by M. Peclet from experi- ments by M. Despretz :— Gold, platinum, silver, ........ccesesscseeeeee Sas COPPER, s teveevceeawasiuien ie inuseedteids yetias dees 00018 TPOM ese eacazuetiegu nce wgsvesiieavay dee eseadasy vied 0°0043 LMG wave teecctcusteasion cs castyeneaenee’ dvoatepieieel 0'0045 MSGAG, 0520 seckva pe daagooseaavedentes vid coseesnes 00090 MATblG ss iacz cad sess woecenesugesnsaboseiaune seers 0°07 16 Bile sis scene ecnenebatan aeuedssenenesnce cast eney o'T500 The total internal thermal resistance of a plate consisting of layers of different substances may be found by adding together the resistances of the several layers. Thus, let x denote the thickness of any one of those layers; e, the co-efficient of thermal resistance of the substance of which it consists : let 2, as usual, denote the summation of a set of quantities, so that Z- x, for example, is the total thickness of the compound plate ; then Sy wea, is the total thermal resistance of that plate, and T—T the rate of conduction through it per square foot per hour, when T’ and T are the temperatures of its hotter and cooler faces respec- tively. The rate of external conduction through the bounding surface between a solid body and a fluid is approximately proportional to the difference of temperature, when that is small; but when that difference is considerable, the rate of conduction increases faster than in the simple ratio of that difference, as will afterwards be shown more in detail. ' The rate of external conduction may be expressed by dividing the difference of temperature by a co-efficient of external thermal gesistance, depending on the nature of the substances, and also on their temperatures. Let the values of that co-efficient, for the two surfaces of a given plate, be denoted by o', «, respectively; let x be the thickness of the plate in inches, as before, and ¢ its co-efficient of internal thermal resistance; then the total thermal resistance of the plate and of its two external surfaces is a - ot ex; and the rate of conduction through it is 260 STEAM AND OTHER HEAT ENGINES. argc ace miele opoTee Where T’, T, are now the temperatures, not of the two surfaces of the plate, but of the two fluids which are respectively in contact with its two faces. The external thermal resistance of the metal plates of boiler flues and tubes, and other apparatus used for heating and cooling fluids, is so much greater than the internal thermal resistance, that the latter is inappreciable in comparison; and, consequently, the nature and thickness of those plates has no appreciable effect on the rate of conduction through them. The combined external thermal resistances of both surfaces of a plate, when one is in contact with a liquid and the other with air, have, according to M. Peclet, values capable of being expressed by the following formula :— ota’ f = Afl+B(—T)} PP eran ees eesseee 7.) in which the constants depend chiefly on the condition of the surface of the body, and have the following values :— B for polished metallic surfaces,.......:sssesseceeeeeeseesees 0°0028 B for rough metallic surfaces, and non-metallic surfaces, 00037 A for polished metals, about .......::scsesseceseeeneeeeeecees! 0°90 A for glassy and varnished surfaces, ..........c:sereeereeees 1°34 A for dull metallic surfaces,..............+ siavextictan anneal 1°58 A for lamp black, ........cecseseeccseceteseeeneseeeeeereneneees 178 When a metal plate has a liquid at each side of it, it appears from experiments by M. Peclet, that the constants in equation 7 take the following values :— B=0-058; A=88. It will be shown in a subsequent Article, that the results of experiments on the evaporative power of boilers agree very well with the following approximate formula for the thermal resistance of boiler plates and tubes :— desma errr ere rrr eee eee (8.) which gives for the rate of conduction, per square foot of surface per hour, , CONVECTION OF HEAT. 261 This formula is not proposed as being more thar a rough approxi- mation, but its simplicity makes it very convenient, and it will be shown that it is near enough to the truth for its purpose. The value of a lies between 160 and 200. 220. Convection or Carrying of heat means the transfer and diffusion of the state of heat in a fluid mass by means of the motion of the particles of that mass. : The conduction, properly so called, of heat through a stagnant mass of fluid, is very slow in liquids, and almost, if not wholly, inappreciable in gases. It is only by the continual circulation and mixture of the particles of the fluid that uniformity of temperature can be maintained in the fluid mass, or heat transferred between the fluid mass and a solid body. The laws of the cooling of thermometer bulbs by convection, when placed in receivers filled with different gases in different states as to pressure, were ascertained by Dulong and Petit; but the circumstances of the experiments were too unlike those which occur in boilers and furnaces to enable those laws to be used in the solution of questions connected with heat engines. The free circulation of each of the fluids which touch the sides of a solid plate is a necessary condition of the correctness of the for- mulz for the conduction of heat through that plate, which have been given in Article 219; and in each of those formule it is implied, that the circulation of each of the fluids by currents and eddies is such as to prevent any considerable difference of tempera- ture between the fluid particles in contact with one side of the: solid plate and those at considerable distances from it. It is to promote that circulation, and so to insure uniformity of temperature in the fluid mass, that an agitator is employed in the- water calorimeter, as already stated in Article 207 a. For a. similar purpose, large boiler flues are sometimes provided with “bafiers;” that is, projecting partitions which compel the hot. gases to take a circuitous course, in order that eddies may be formed, so as to bring as many different particles as possible suc-. cessively in contact with the heating surface. Those bafflers, how- ever, have also another object, which is to promote that thorough mixture of air with the inflammable gas from the fuel, which is. necessary to complete combustion. The most rapid convection of heat is that which is effected by means of cloudy vapour, which combines the mobility of a gas with the comparatively greater conducting power of a liquid; as when steam communicates heat to a solid body by condensing on its. surface. Some data as to the rate at which this process goes on will be given in Article 222. When heat is to be transferred by convection from one fluid to 262 STEAM AND OTHER HEAT ENGINES. another through an intervening layer of metal, the motions of the two fluid masses should if possible be in opposite directions, in order that the hottest particles of each fluid may be in communication with the hottest particles of the other, and that the minimum difference of temperature between the adjacent particles of the two fluids may be the greatest possible. ‘Thus in the surface condensation of steam, by passing it through metal tubes immersed in a current of cold water or air, the cooling fluid should be made to move in the opposite direction to the con- densing steam. In a steam boiler, it is favourable to economy of fuel that the motion of the water and steam should on the whole be opposite to that of the flame and hot gas for the furnace. Thus, if there is a “feed-water heater,” consisting of a set of ‘tubes through which the water passes to be heated before entering ‘the boiler, that apparatus should be placed in or near the foot of the chimney, so as to be heated by gas that has left the boiler, and thus to employ heat that would otherwise be wasted. The coolest, that is, the lowest portions of the water in the boiler, should, if practicable and convenient, be contiguous to the coolest parts of the furnacé and heating surface; and if there is apparatus for super- heating the steam, or raising its temperature above the boiling point corresponding to its pressure, that apparatus will be most efficient if placed in the hottest part of the furnace, like that, for example, of Messrs. Parsons and Pilgrim. 221. Eficiency of Heating Surface— When a layer of metal, lying between two flowing masses of fluid, serves as the means of transmitting heat from the hotter to the cooler of those masses, the proportion borne by the quantity of heat so transmitted to the whole quantity of heat which the hotter mass must lose in order to reduce it to the temperature of the colder mass, may be called the efficiency of the heating surface of that layer of metal. In most of the cases that occur in practice, the layer of metal consists of the flues, tubes, and other portions of the solid material of a boiler which are exposed to heat ; the cooler fluid is the water in the boiler, which is introduced by degrees in the liquid state at a low temperature, raised to a higher temperature, and evaporated ; the hotter fluid is the stream of air and hot gases which comes from thefurnace, flows along the heating surface, and finally escapes by the chimney. ‘Let W denote the weight of gas given out by the furnace in an hour; cits specific heat at constant pressure; T — ¢, the excess of its temperature above that of the water in the boiler when it is in contact with some given portion of the heating surface, the area of which portion is ds; let g denote the rate of conduction per EFFICIENCY OF HEATING SURFACE. 263 square foot of surface per hour, corresponding to the difference of temperature T —¢; then qds is the heat transmitted by the portion ds of the heating surface trom the hot gas to the water, and gds _ ow is the lowering of the temperature of the gas by passing over the portion of heating surface ds. It arrives at the next elementary portion of heating surface with a diminished temperature, and the rate of conduction is therefore diminished ; so that each successive equal portion of the heating surface transmits a less and a, legs quantity of heat, until the hot air at last leaves the heating surface and escapes up the chimney, with a certain remaining excess of temperature above that of the water in the boiler, the heat corre- sponding to which excess is wasted. Let T, denote the temperature of the hot gas when it first comes in contact with the heating surface; T, its temperature when it finally leaves the heating surface; then i re ioe as eesteceshee (1) the whole heat expended per hour is c\ W (T, — 4); \ (2.) the heat wasted per hour éW (T,—4); the efficiency of the heating surface, T,—T,, Pe t Doeeeeereereenreressenseccenn (3.) and all those quantities are connected together by the equation 1, - or by either of the following equations, which are different ways of expressing its integral :— ew Ws] gumucniees (4,) S phd ° azole ait sae (5.) in which last equation, S denotes the whole heating surface. To represent these principles graphically, draw A D, fig. 90, to represent the whole heating surface 8; and let any portion of that line, such as A X, represent s, a part of that surface. Let the ordinate A B=4q,, the rate of conduction for the initial tempera- ture T;. In DA produced, take 264 STEAM AND OTHER HEAT ENGINES. eee ‘ —t xo, sitdgeatecetetadited (6) 1 then the rectangle OA + AB will represent the whole heat ex- pended per hour. c LB Let the ordinate X Y = g represent the rate of conduction corresponding to the temperature which the hot gas has after having passed over the portion A X =s of the heating surface, and let ~~ B Y E be a curve drawn through the = summits of a series of such ordinates; 6s = J, then the area of any part of that curve, Fig. 90. such as A BY X, represents the heat transferred per hour through the part s of the heating surface; the area A BED represents the heat transferred per hour through the whole heating surface 8; and when the curve B Y E is produced indefinitely, the area contained between it and its asymptote A D approximates indefinitely to that of the rectangle O A - AB, The definite results of these principles depend on the relation between g and T. Case 1,—If we assume Peclet’s formula (Article 219, equation 7) for the thermal resistance of the plates, we find q=A(T—Af1 + B(T dhs. seecceee (7.) and this value being introduced into equation 5, gives for the integral of that equation S 1 t eu) OP Geman Be gp ide (os awa VPM 7 TB eo and for the efficiency of the heating surface, AS OW + as T,—T, ( 1) M+BQ—8 (0.) T= AS as ew 饗1)B(—#) The values of the constants A and B under different circum- stances have been given in Article 219. AS The value of e is easily found by the help of a table of hyper- , bolic logarithms, being the number whose hyperbolic logarithm is AS+¢c¢W. HEATING SURFACE—COOLING SURFACE. 265 Cas 2.—The above formula being too complex for ready use in practice, and the values of A and B being uncertain in furnaces at high temperatures, the supposition expressed in equations 8 and 9 of Article 219, viz, that the rate of conduction is nearly propor- tional to the square of the difference of temperature, has been tried, and found to agree well with experiment, as will afterwards be shown. That supposition gives as the integral of equation 5, 8 p 1 1 aye (qa em ecnccsesee (10.) from which is easily deduced the following value of the efficiency of the heating surface :— T,— Ty _ 8 (T, —?) 1 <8 “eth jpae wee (11.) This may be put into another form, as follows :—Let H denote the expenditure of heat in an hour, in raising the temperature of the hot gas above that of the water; then H es or Ds Th ras Satie pinata (12.) and making this substitution in equation 11, we find for the effi- ciency of the surface, This result is represented graphically by taking, in fig. 90, —— actWw? Oo= H 2 and making B Y E a hyperbola of the second order, with O D and O C for its asymptotes. The values to be assigned to the constants in equation 13, will be investigated in Chapter IT. 222, Cooling Surface—Surface Condensation.—The formule of the preceding Article, case 1, equations 8 and 9, are made appli- cable to cooling surfaces as follows :—Let t denote the temperature of a film of liquid, at one side of a metal plate; 8, the extent of cooling surface, as before ; let heat be communicated to the liquid at the temperature ¢ by some such process as the condensation of steam, and let that be abstracted by the flow of a current of air, 266 STEAM AND OTHER HEAT ENGINES. water, or other fluid, in contact with the metal plate; the weight of fluid which flows past per second being W, its specific heat ¢, its initial temperature T,, being lower than ¢, and its final tempera- ture T,, still lower than ¢, but higher than T,. Then in all the ee t— T, is to be substituted for T, — ¢, and ¢ — T, for | An obstacle to the use of the formule as thus modified is, that the constants A and B have not yet been ascertained for the “surface condensation” of steam. It is only known that the convection of heat by a vapour in the act of condensing is more rapid than by substances in other conditions; and that in certain particular experiments on the surface condensation of steam, certain results have been obtained, of which the following are examples :— : Steam con- Its initial tem- Material of densed per Cooling fluid. perature T, plates or square foot Authority. Fahr. tubes. per hour. Lbs. Air, 59° Cast iron. 0°36 Peclet. 3 55 Sheet iron, 0°36 * 3) 27 Glass, 0°35 72 35 4 Copper, 028 35 3 _ Tin plate, o2I ss) Water, 68° to 77° Copper, 21°5 g. sf 1 “i 1000 Joule, In these experiments, each pound of steam may be estimated on an average as corresponding in round numbers to about 1,000 British thermal units. The rapidity of the condensation depends mainly on that of the circulation of the cooling fluid at the other side of the plate. 267 CHAPTER II OF COMBUSTION AND FUEL. 223. Total Heat of Combustion of Elements.— Every chemical combination is accompanied by a production of heat: every decom- position, by a disappearance of heat, equal in amount to that which is produced by the combination of the elements which are separated. ‘When a complex chemical action takes place, in which various combinations and decompositions occur simultaneously, the heat obtained is the excess of the heat produced by the combinations a ove the heat which disappears in consequence of the decomposi- tions. Sometimes also, the heat produced is subject to a further deduction, on account of heat which disappears in melting or evaporating some of the substances which combine, either before or during the act of combination. Combustion or burning is a rapid chemical combination. The only kind of combustion which is used to produce heat for driving heat engines, is the combination of fuel of different kinds with oxygen. In the ordinary sense of the word combustible, it means, capable of combining rapidly with oxygen so as to produce heat rapidly. By an elementary or simple substance is meant one which has never been decomposed. _ The chief elementary combustible constituents of ordinary fuel are carbon and hydrogen. Sulphur is another combustible consti- tuent of ordinary fuel; but its quantity and its heat-producing power are so small, that its presence is of no appreciable value. Substances combine chemically in certain proportions only. To cach of the substances known in chemistry a certain number can be assigned called its “chemical equivalent,” having these properties— I. That the proportions by weight in which substances combine chemically can all be expressed by their chemical equivalents, or by simple multiples of their chemical equivalents. IJ. That the chemical equivalent of a compound is the sum of the chemical equivalents of its constituents. ; Chemical equivalents are sometimes called atomic weights, or atoms, in accordance with the hypothesis that they are proportional to the weights of the supposed atoms of bodies, or smadlest similar parts into which bodies are assumed to be divisible by known forces. The term atom is convenient from its shortness, and can be used to 268 STEAM AND OTHER HEAT ENGINES. mean “chemical equivalent,” without necessarily affirming or denying the hypothesis trom which it is derived, and which, how probable soever it may be, is, like other molecular hypotheses, meapable of absolute proof. The chemical equivalents of substances in the perfectly gaseous state are known to be either exactly or very nearly proportional to their densities at the same pressure and temperature, or simple multiples or submultiples of those densities. In other words, perfect gases at a given pressure and temperature combine, either exactly or very nearly, in simple numerical proportions by volume. The volume of the compound also, if perfectly gaseous, bears always, either exactly or very nearly, some simple numerical ratio to the volumes of the constituents, at the same pressure and tem- perature. These principles have already been illustrated in the case of the composition of steam, in Article 202. The following are the chemical equivalents, according to the British scale, of the principal elementary constituents of fuel, and of the atmospheric air from which the oxygen required for com-. bustion is derived, together with the symbols used in chemical writings to denote them, and their chemical equivalents by volume in the perfectly gaseous state :— Chemical Chemical Name. Symbol. equivalent by equivalent by weight. volume. ORY PCN sevcccazsnnscess Ol sepacicuiasen 8: gecgiauwetes 3 Nitrogen,..........0.. ANY cseticie sets TA. . gaieconawinena Tt Hydrogen, ............ TA snipe a. To) Se foaeeehaes t Carbon,..........0eeeee Cr adaaanartecan OB Cas dicainietstsind a Sulphwy,...... 20.20... DD csauii dasa TG. secascocaozs q These numbers are given neglecting fractions too small to be of consequence for the purposes of the present treatise. The composition of a compound substance is indicated in chemi- cal writings, by affixing to the symbol of each element the num- ber of its equivalents which enter into one equivalent of the compound. The following table shows the composition of those compounds of the above elements which are of importance to the purposes of the present treatise, either as furnishing oxygen for combustion, as entering into the composition of ordinary fuel, or as being produced by the combustion of ordinary fuel :— HEAT OF COMBUSTION OF ELEMENTS. 269 Symbol of — Proportions Chemical Proportions Chemical Name. chemical ofelements equivalent of elements equivalent composition. by weight. by weight. by volume. by volume. AAP ese ucebiads N,O N28+08 36 Ne+0O} 2h Water... HO H1r+08 9. H1+04 1 Ammonia, ....... NH, H3+Nry 17 Carbonic oxide, CO C6+08 m4 C%+0O2 1 Carbonic acid,... C O. C6+016 22 Ci+01 I eo C,H, Ciz+He 14 C?+He 1 arsh gas, or fredamp et CH, C6+He 8 OI+Hr 1 The last two substances are the chief ingredients of coal gas. [There are numerous other compounds of hydrogen and carbon, known generally as “hydro-carbons,” and comprising, amongst other substances, various fusible and volatile ingredients of coal ; but it is unnecessary to give their chemical composition in detail. ] Sulphurous acid,........... 80, $16+0 16 32 Sulphuretted hydrogen,.. SH Si6+H1 17 I Bisulphuret of carbon,... 5S, 0 S327C6 38 I The French scale of equivalents differs from the British, princi- pally in making the equivalents of oxygen and sulphur by weight double, as compared with the equivalents of most other elements, and in taking 100 to represent the equivalent of oxygen. Thus the symbol for water, according to the French system, is H, O; _and its equivalent (6-25 x 2) + 100 = 112°5. The following table shows the total heat of combustion with oxygen of one pound of each of the elementary substances named in it, in British thermal units, and also in lbs. of water evaporated from 212°. It also shows the weight of oxygen required to com- bine with each pound of the combustible element, and the weight of air necessary in order to supply that oxygen. The quantities of heat are given on the authority of experiments made by MM. Favre and Silbermann (See Annales de Chimie, 1852-53, vols. 34, 36, 37). Lb. oxygen Evaporative Combustible. per Ib. of aie ge sowie : combustible. from 212°. Hydrogen gas, ......ccecceees 8 36 62,032 64°2 Carbon, imperfectly burned so as to make carbonic ; 14 6 4,400 4°05 OX1dG ives ose setesceesesseess so as to make carbonic 12 14,500 150 Carbon, completely burned, \ 25 BCU scr creaetsaioneicians ‘idan ose 270 STEAM AND OTHER HEAT ENGINES. Tt is to be observed, that the imperfect combustion of carbon, making carbonic oxide, produces less than one-third of the heat ° which is yielded by the complete combustion. ; 224, Wotal leat of Combustion of Compounds.—The following 1s a similar table, on the same authority, for the more important compound ingredients of fuel :— Total heat Evaporative Combustible. Lb. oxygen. Lb. air. British units. eis Olefiant gas, 1 Ib.,......... 3r 157 21,344 22°1 Various liquid hydrocar- {from 21,,00 from 22} bots) L Mb. ieveosentvens \ to 19,000 to 20 Carbonic oxide, as much | as is made by the im- | perfect combustion of $ 1% 6 10,100 10°45 1 Ib. of carbon, =| With regard to the quantities stated in this and the preceding Article as being the total heat of combustion respectively of carbon completely burned, carbon imperfectly burned, and carbonic oxide, the following explanation has to be made :— The burning of carbon is always complete at first; that is to say, one pound of carbon combines with 22 lbs. of oxygen, and makeg 3§ Ibs. of carbonic acid; and although the carbon is solid imme- diately before the combustion, it passes during the combustion into the gaseous state, and the carbonic acid is gaseous. This terminates the process when the layer of carbon is not so thick, and the supply of air not so small, but that oxygen in sufficient quantity can get direct access to all the solid carbon. The quantity of heat produced is 14,500 thermal units per lb. of carbon, as already stated. But in other cases part of the solid carbon is not supplied directly with oxygen, butis first heated, and then dissolved into the gaseous state, by the hot carbonic acid gas from the other parts of the furnace. The 32 Ibs. of carbonic acid gas from 1 Jb. of carbon, are capable of dissolving an additional Ib. of carbon, making 43 Ibs. of carbonic oxide gas; and the volume of this gas is double of that of the carbonic acid gas which produces it. In this case, the heat produced, instead of being that due to the complete combustion of L Ibi of carbon; OP siiscinscancecenes seureences scarecsangiers aa oiees 14,500 talls to the amount due to the imperfect combustion of 2 Ibs. of carbon, OF.......cceeeeees descents sednGes 2X 4,400 = 8,800 Showing a loss of heat to the amount Of......c0es.sseeseeee eee 700 which disappears in volatilizing the second pound of carbon. Should HEAT OF COMBUSTION OF COMPOUNDS. 271 the process stop here, as it does in furnaces ill supplied with air, the waste of fuel is very great. But when the 43 lbs. of carbonic oxide gas, containing 2 lbs. of carbon, is mixed with a sufficient supply of fresh air, it burns with a blue flame, combining with an additional 22 lbs. of oxygen, making 7} lbs. of carbonic acid gas, and giving additional heat of double the amount due to the com- bustion of 14 Ib. of carbonic oxide ; that is to say, 10,100 X 2 = 20,200 to which being added the heat produced by the imperfect combustion of 2 Ibs. of carbon, OF .........ceescee scene eeeees 8,800 there is obtained the heat due to the complete combustion of 2 Ibs. of carbon, OY..........ceeceeeseeeeeeeeee 2 X 14,500 = 29,000 Tf the total heat of combustion of olefiant gas be compared with that of its constituents taken separately, the result is as follows :— 6 6 7 Ib. carbon; 14,500 x Terence ate = 12,430 * Ih, hydrogen; 62,032 x ; suctesniudangcs dbtnetena tere = 8,862 Total heat of combustion of 1 Ib. of olefiant gas as computed by adding together the quantities of heat produced by the combustion of its consti- mee tuents separately jcvecicacesaesvwans sncsn vce seonees dee ass ; As found by direct experiment, ...........ccceceseeene ones 21,344 Difference,.......cccsescnseeecesecee 52 Similar comparisons, for other hydrocarbons, give the same re- sult nearly, though not exactly. From these facts it is concluded, that the total heat of combustion of any compound of hydrogen and carbon is nearly the sum of the quantities of heat which the hydrogen and carbon contained in tt would produce separately by their com- bustion. (Marsh-gas is an exception. In computing by this rule the total heat of combustion of a com- pound, it is convenient to substitute for the hydrogen a quantity of carbon which would give the same quantity of heat; and this is done by multiplying the weight of hydrogen by It appears from experiments by Dulong, by Despretz, and by others, that in computing the total heat of combustion of com- pounds containing oxygen as well as hydrogen and carbon, the 272 STEAM AND OTHER HEAT ENGINES. following principle is to be observed :—When hydrogen and oxygen east in a compound in the proper proportion to form water (that is, by weight, very nearly, one part of hydrogen to eight of oxygen), these constituents have no effect on the total heat of combustion. It follows, that if hydrogen exists in a greater proportion than is necessary in order to form water with the oxygen, only the surplus of hydrogen above that which is required by the oxygen is to be taken into account. From the preceding principles is deduced the following general formula for the total heat of combustion of any compound of which the principal constituents are carbon, hydrogen, and oxygen:— Let C, H, and O, be the fractions of one pound of the compound which consist respectively of carbon, hydrogen, and oxygen; the remainder being nitrogen, ash, and other impurities. Let h be the total heat of combustion of one pound of the com- pound, in British thermal units. Then i = 14,500 \ C+ 4:28 (x = \ aioe ae (1.) Let E denote the theoretical evaporative power of one pound of the compound, in pounds of water evaporated from and at 212°. Then h O : B= 15{0+428("-$)} ee (2) Tt has already been stated, that the values adopted in this treatise for the total heat of combustion of carbon and of hydrogen are taken from the experiments of MM. Favre and Silbermann. In the case of hydrogen, the results of these experiments agree very closely with those of the experiments of Dulong (Comptes Rendus, vol. vii.), the total heat of combustion of one pound of hydrogen being, According to Favre and Silbermann,...... 62,032 British units. According to the mean of Dulong’s ex- periments 62,536» a edaleaeeueeaeuteals Sb sftiouiatd awaits In the case of carbon, the agreement amongst different experi- menters is less close. The following is a comparison of some of the results given by them :— Dulong (mean), ......sscseceeeeseeeeecee ees ++.12,906 Despretz;oeccvccaiessdsseased senesvsecenenssiva se 14,040 Favre and Silbermann,............ Jindgcdinseee 44500 The result arrived at by MM. Favre and Silbermann is adopted FUEL. 273 in this treatise, because of the great delicacy and precision of the instruments and processes by which it was obtained, and because amongst a number of different results as to total heat of com- bustion, the highest is on the whole the most likely to be correct. - most of the errors being caused by losses of heat. 225, Winds and Ingredients of Fuel.—The ingredients of every kind of fuel commonly used may be thus classed :— (L) Fixed or free carbon, which is left in the form of charcoal or coke after the volatile ingredients of the fuel have been distilled away. This ingredient burns either wholly in the solid state, or part in the solid state and part in the gaseous state, the latter part being first dissolved by previously formed carbonic acid, as already explained. (IL) Hydrocarbons, such as olefiant gas, pitch, tar, naphtha, &c., all of which must pass into the gaseous state before being burned. If mixed on their first issuing from amongst the burning carbon with a large quantity of air, these inflammable gases are completely burned with a transparent blue flame, producing carbonic acid and steam. When raised to a red heat, or thereabouts, before being mixed with a sufficient quantity of air for perfect combustion, they disengage carbon in fine powder, and pass to the condition partly of marsh gas, and partly of free hydrogen; and the higher the temperature, the greater is the proportion of carbon thus disen- gaged. _ df the disengaged carbon is cooled below the temperature of ignition before coming in contact with oxygen, it constitutes, while floating in the gas, SMOKE, and when deposited on solid bodies, soot. But if the disengaged carbon is maintained at the temperature of ignition, and supplied with oxygen sufficient for its combustion, it burns while floating in the inflammable gas, and forms RED, YELLOW, or WHITE FLAME. The flame from fuel is the larger, the more slowly its combustion is effected. _. (IIL) Oxygen and hydrogen either actually forming water, or existing in combination with the other constituents in the propor- tions which form water. According to a principle already stated, such quantities of oxygen and hydrogen are to be left out of account in determining the heat generated by the combustion. If the quantity of water actually or virtually present in each pound of fuel is so great as to make its latent heat of evaporation worth considering, that heat is to be deducted from the total heat of com- bustion of the fuel. The presence of water, or its constituents, in fuel, promotes the formation of smoke, or of the carbonaceous flame, which is ignited smoke, as the case may be, probably by mechanically sweeping along fine particles of carbon. T 274 STEAM AND OTHER HEAT ENGINES. (IV.) Nitrogen, either free or in combination with other consti- tuents. This substance is simply inert. ; . (V.) Sulphuret of tron, which exists in coal, and is detrimental, as tending to cause spontaneous combustion. . (VL) Other mineral compounds of various kinds, which are also inert, and form the asu left after complete combustion of the fuel, and also the clinker, or glassy material produced by fusion of the ash, which tends to choke the grate. 226, Minds of Fuel.—The kinds of fuel in common use may be thus classed :—I. Charcoal; II. Coke; III. Coal; IV. Peat; V. Wood. I. Charcoal is made by evaporating the volatile constituents of wood and peat, either by a partial combustion of a conical heap of the material to be charred, covered with a layer of earth, or by the combustion of a separate portion of fuel in a furnace, in which are placed retorts containing the material to be charred. According to Peclet, 100 parts by weight of wood when charred in a heap, yield from 17 to 22 parts by weight of charcoal, and when charred in a retort, from 28 to 30 parts. This has reference to the ordinary condition of the wood used in charcoal making, in which 25 parts in 100 consist of moisture. Of the remaining 75 parts, the carbon amounts to one-half, or 373 per cent. of the gross weight of the wood. Hence it appears that on an average nearly half of the carbon in the wood is lost during the partial combustion in a heap, and about one quarter during the distillation in a retort. To char 100 parts by weight of wood in a retort, 12} parts of wood must be burned in the furnace. Hence in this process, the whole expenditure of wood to produce from 28 to 30 parts of char- coal, is 1123 parts; so that if the weight of charcoal obtained is compared with the whole weight’ of wood expended, its amount is from 25 to 27 per cent. ; and the proportion of carbon lost is on an average 114 + 374 = 0°3 nearly. According to Peclet, good wood charcoal contains about 0:07 of its weight of ash. The proportion of ash in peat charcoal is very variable, and is estimated on an average at about 0:18. II. Coke is the solid material left after evaporating the volatile ingredients of coal, either by means of partial combustion in acai called coke ovens, or by distillation in the retorts of gas- works, Coke made in ovens is preferred to gas coke as fuel. It is of a oo grey colour, with slightly metallic lustre, porous, brittle, and hard. The proportion of coke yielded by a given weight of coal is very ditferent for different kinds of coal, ranging from 0-9 to 0°35. COKE—COAL. 275 Coke contains from 0:06 to 0-18 of its weight of ash, the re- mainder being carbon. Being of a porous texture, it readily attracts and retains water from the atmosphere; and sometimes, if it is kept without proper shelter, from 0-15 to 0:20 of its gross weight consists of moisture. III. Coal.—The extreme differences in the chemical composition and properties of different kinds of coal are very great; but the number of those kinds is very great, and the gradations of their differences are small. The proportion of free carbon in coal ranges from 30 to 93 per eent.; that of hydrocarbons of various kinds from 5 to 58 per cent.; that of water, or oxygen and hydrogen in the proportions which form water, from an inappreciably small quantity to 27 per cent.; that of ash, from 14 to 26 per cent. The numerous varieties of coal may be divided into principal classes as follows :— 1. Anthracite or blind coal. 2. Dry bituminous coal. 3. Caking coal. 4, Long flaming or cannel coal. 5. Lignite or brown coal. (1.) Anthracite or blind coal consists almost entirely of free carbon. It has a colour intermediate between jet black and the greyish-black of plumbago, and a lustre approaching to metallic. Its specific gravity is from 1-4 to 1-6, that of water being 1. It burns without sthoke, and, when dry, without flame also; but the presence of moisture in it produces small yellowish flames, in the manner explained in Article 225. It requires a high temperature, and in general a blast produced by mechanism, for its combustion. If suddenly heated, it splits into small pieces, which are liable to fall through the grate bars of the furnace and be lost. In furnaces where it is used, therefore, each fresh portion should be gradually heated before being ignited. (2.) Dry bituminous coal contains on an average from 70 to 80 per cent. of free carbon, about 5 per cent. of hydrogen, and 4 per cent. of oxygen; so that 42 per cent. of hydrogen is available to produce heat. This hydrogen exists in combination with part of the carbon. Such coal burns with a moderate amount of flame, and little or no smoke. Its average specific gravity is about 1:3. (3.) Bituminous caking coal contains on an average from 50 to 60 per cent. of free carbon, and about equal weights of hydrogen and oxygen, amounting to from 10 to 12 per cent. of its weight. It softens when exposed to heat, and pieces of it adhere together. It produces more flame than dry bituminous coal, and also produces 276 STEAM AND OTHER HEAT ENGINES. smoke, unless that is prevented by special means. Its average specific gravity is about 1:25. ; ire (4.) Long flaming coal differs from the last variety chiefly in con- taining more oxygen. In some examples it softens and cakes in the fire; in others not. It requires special means for the preven- tion of smoke. (5.) Brown coal, or lignite, is found in more recent strata than any of the preceding kinds. It is intermediate in appearance and properties between them and peat. It contains on an average from 27 to 50 per cent. of free carbon, about 5 per cent. of hydrogen, and 20 per cent. of oxygen. Its specific gravity is from 1:20 to 1-25, With respect to the different kinds of coal, M. Peclet makes a remark to the effect, that the caking bituminous coals pass to the dry coals and to anthracite by diminution of their oxygen and hydrogen, and to the long flaming coals and lignites by the augmentation of their oxygen. From the specific gravities already stated, it appears that a cubic foot of solid coal weighs from 70 to 90 Ibs.; but coal in pieces, such as are commonly used for feeding furnaces, including the spaces between the pieces, occupies from 175 to 17 times the spdce that the same coal fills in a continuous mass; so that the average weight of coals, including the space between the pieces, is about 52 Ibs. per cubic foot. In a few examples it is as high as 56 or 60 lbs. to the cubic foot. IV. Peat, or turf, as usually dried in the air, contains from 25 to 30 per cent. of water, which must be allowed for in estimating its heat of combustion. This water having been evaporated, the analysis of M. Regnault gives, in 100 parts of perfectly dry peat of ‘the best quality— Carbon; sscscnssssnssxsnsincaarenssesen 58 Hydrogen, ssiscsssseriesccssvaveesens 6 OXYGEN, ver eseascns savers sacreortels 31 ABD, acceusesspegnoveasaie dreieseeetareeer 5 100 In some other examples of peat, the quantity of ash is greater, amounting to 7 and sometimes to 11 per cent. The specific gravity of peat in its ordinary state is abont 0:4 or 0-5. It can be compressed by machinery to a much greater density. V. Wood, when newly felled, contains a proportion of moisture which varies very much in different kinds and in different speci- mens, ranging between 30 and 50 per cent., and being on an average about 40 per cent. After eight or twelve months’ ordinary drying in the air, the proportion of moisture is from 20 to 25 per WOOD—TOTAL HEAT OF COMBUSTION. 277 cent. This degree of dryness, or almost perfect dryness if required, can be produced by a few days’ drying in an oven supplied with air at about 240° Fahrenheit. When coal or coke is used as the fuel for that oven, 1 Ib. of fuel suffices to expel about 3 Ibs. of moisture from the wood. This is the result of experiments on a large scale by Mr. J. R. Napier. If air-dried wood were used as fuel for the oven, from 2 to 24 Ibs. of wood would probably be required to produce the same effect. oon specific gravity of different kinds of wood ranges from 0:3 to 12. Perfectly dry wood contains about 50 per cent. of carbon, the remainder consisting almost entirely of oxygen and hydrogen in the proportions which form water. The coniferous family contain a small quantity of turpentine, which is a hydrocarbon. The pro- portion of ash in wood is from 1 to 5 per cent. The total heat of combustion of all kinds of wood, when dry, is almost exactly the same, and is that due to the 50 per cent. of carbon. 227. The Total Heat of Combustion of fuel is computed from its chemical composition, according to the principles explained in Articles 223, 224, and 225. The following table gives the results of such computations, founded chiefly on the analyses of M. Reg- nault, Dr. Playfair, and Professor Richardson. The numerous kinds of fuel of which analyses have appeared have been classed in groups, and the average chemical composition of each group com- puted. By this process have been obtained the proportions of carbon, hydrogen, and oxygen, given in the columns headed C, H, and O, respectively. 7 The column headed OC’ shows the weight of pure carbon whose total heat of combustion would be the same with that of the fuel, as given by the formula C=C 44-28 (a =) E = 15 C’is the theoretical evaporative power in pounds of water supplied and evaporated at 212° by one pound of fuel. h= 14500 C'is the total heat of combustion in pounds of water raised one degree of Fahrenheit. Each kind of fuel is supposed to be perfectly dry, unless otherwise specified. With respect to the examples of coal given in the following table, it is to be observed that they are all of good quality, as it has never been the practice to submit bad coals to chemists for analysis. It may be estimated that the total heat of combustion of the worst coal in a given coal field is about two-thirds of that of the best, the differ- ence arising chiefly from the proportion of earthy matter. 278 STEAM AND OTHER HEAT ENGINES. Taste or tHe Toran Heat or Compustion oF FUEL. FuEt. C. H. 0. C. E, A. a a aoe \ 0°93 0793 | 14 | 13500 », from peat, o80 | 12 11600 IT. Coxze—good,...) 0°94 0°94 | 14 13620 » middling, | 0:88 0°88 | 13°2 | 12760 99 Da es sven 082 o'82 | 12°3 | T1890 III. Coat— 1, Anthracite,...) 0°915 | 0°035 | 0'026] top | 15°75] 15225 2. Dry bitu- , : . ’ : ac eaal 0790 | o704 | 002 | 1°06 | 15°9 | 15370 Oe 3% 5 087 | 0104 | 0°03 | 1'025)| 15°4 | 14860 4, ,, $5 080 | 0054] o016|] r'o2 | 15°3 | 14790 On 35 8 077 | 0705 | 0706 | 095 | 14°25] 13775 6. Caking,......0.. 0°88 | 0052] 0054] 1075] 16:0 | 15837 Te 5 Vise uGubaeds o81r | 0052] o'04 | ror | 15°15} 14645 8. Cannel,......... 0°84 | 0°056| o'o8 | ro4 | 15°6 | 15080 =“ ee O77 | 0°052| O15 | ogt | 13°65] 131905 10. Lignite,........ o'7o | 0705 | 0-20 | o'81r | 12°55] 11745 IV. Pzat—dry,...) 0°58 | 0°06 | 0°31 | 0°66 | too 9660 » contain- ing 25 per c. 4*281 7000 moisture, ... V. Woop—dzy,...] 0°50 0°50 78 7245 » contain- ing 20 per c. 58 5600 moisture, ... VI. MinerarOi— from......... o84 | o'16 | o 1°52 | 22°7 | 21930 WO isccapincweieer 085 | o15 | 0 1°49 | 22°38 | 214735 (See Journal of the United Service Institution, vol. xi., 1867.) 228. Radiation from Fuel. —The proportion which the heat radiated from incandescent fuel bears to the total heat of combus- tion has been determined for some kinds of fuel by the experiments of M. Peclet, with the following results :— From W00d,.....sseseessssseereeseeeeeO°2Q From charcoal and peat,.............0°5 RADIATION FROM FUEL. 279 From coal and coke M. Peclet considers that the radiation must be greater-than from charcoal, although he has not ascertained it precisely, The practical conclusion to be drawn from thig fact is, that the radiation from the fuel in the furnace of a heat engine ought to be carefully intercepted in every direction, in such a manner that the heat diffused by it may be communicated either directly or indi- rectly to the substance to be heated. The means used for effecting this are various. One of the simplest is to have the furnace wholly contained in a flue or fire box inside the boiler. Another is, to surround all those parts of the furnace whose radiation is not directly intercepted by the boiler, with brickwork so thick as not to admit of any material loss of heat by conduction. The resistance to conduction is greatly increased by having two, or three, successive layers of brickwork with air spaces between, such spaces being completely closed, in order ‘that the air in them may not circulate. Two such layers of fire-brick, the inner 9 inches thick, the outer 44, with an air space 3 inches-thick between them, have been found to answer in practice. The great resistance of this coating to the transmission of heat causes the inner surface of the inner layer, which directly receives the radiation of the fire, to rise to a white heat, or nearly so, and almost the whole of the heat which it receives is, because of that high temperature and the rapid circula- tion of the furnace gases over it, carried off by those gases, and made available for communication to the boiler. The heat which is radiated down between the grate bars is intercepted by the sides and floor of the ash pit, and carried back to the furnace by the air which enters through the ash pit. To prevent loss by radiation and conduction through the furnace door, the simplest plan is that used by Mr. Williams and others, of making it of two layers of cast iron plates, with an air space between. The plates are usually perforated with small holes for the admission of air to burn the gaseous ingredients of fuel, and care is to be taken to place no two of those holes opposite each other. Thus the heat which is radiated through the holes in the inner plate is intercepted by the outer plate. The greater part of the heat thus received by the plates is carried back into the furnace by the entering stream of air. To intercept the heat and give it out to the entering air more completely, a series of sheets of wire gauze have sometimes been interposed between the outer and inner surfaces of a perforated furnace door. , The most complete apparatus for intercepting the heat radiated to the furnace door is that of Mr. Prideaux, which consists of three gratings, each made of a, series of thin iron plates set edgeways, with narrow passages between them for the entering stream of air. The 280 STEAM AND OTHER HEAT ENGINES. radiant heat is completely intercepted: by placing two of those sets of plates with opposite obliquities, and the third parallel to the sides of the furnace mouth-piece. 229. Air required for Combustion and Dilation —The number of pounds of air required in order to supply the oxygen necessary for the combustion of one pound of any sort-of fuel whose chemical composition is known, may be computed by the aid of the data given in Article 223, at the foot of page 269. To express that weight symbolically, let it be denoted by A; then, C, H, and O, having the same meanings as before, A =12 0+ 36 (1-9) ahisydedenesseeciess (1.) The following are a few of the results :— FuEL. C. H. O. A. I. Caarcoat—from wood,...| 0°93 1116 38 from peat,.....| o'80 96 TT. CokE—good,....-..cscceceee o'94 11'28 III Coat—anthracite,.........) o-g15 | 0°035 | 0026 | 12°13 » dry bituminous, | 0°87 0°05 0°04 12°06 5 CARING ci cecvicvicas 0°85 0°05 0°06 1173 os jj: J eeaeontaes ee os 0°05 0°05 10°58 35 cannel,.......s.006. 084 o'06 008 11°88 » ary long flaming, | 0°77 0°05 Ors 10°32 93 Hignibe; wouecesex. 070 0°05 0'20 9°30 IV. PEat—dry,........0..0cceee 0°58 0°06 oO'31 7°68 V. Woop—dry,.......cecseenee 0°50 6:00 VI. Mivyerat OIL, ............ 0°85 O15 ° 15°68 It is unnecessary for practical purposes to compute the air required for the combustion of fuel to a great degree of exactness; and no material error is produced if the air required for the com- bustion of every kind of coal and coke used for furnaces is estimated at twelve pounds per pound of fuel. Besides the air required to furnish the oxygen necessary for the complete combustion of the fuel, it is also necessary to furnish an additional quantity of air for the dilution of the gaseous products of combustion, which would otherwise prevent the free access of air to the fuel. The more minute the division, and the greater the velocity with which the air rushes amongst the fuel, the smaller is the additional quantity of air required for dilution. From various experiments, especially those made for the SUPPLY OF AIR TO FUEL. 281 American government by Mr. Johnson, it appears that in ordinary boiler furnaces, where the draught is produced by means of a chimney, the weight of air required for dilution is equal to that required for combustion; so that if A’ denotes the total weight of air to be supplied to the furnace per Ib. of fuel, A’=2 A = 294 Ibs, nearly........... seseeeas(2.) But in furnaces where the draught is produced by means of a blast pipe, like those of locomotive engines, or by means of a fan, the quantity of air required for dilution, although it has not yet been exactly ascertained, is certainly much less than that which is required in furnaces with chimney draughts; and there is reason to believe that on an average it may be estimated at about one-half of the air required for combustion; so that in this case, 3 A’= 5 AL= 18 Ibs. nearly ssecscisesnncceext (3.) This estimate is roughly made; but it is the nearest approxima- tion at present attainable. It is probable that the supply of air required for dilution varies considerably in different arrangements of furnace, and for different kinds of fuel; and it is possible, that by blowing the air for combustion into a furnace in small enough jets, and with sufficient force, air for dilution might be rendered unnecessary, so that A’ would be = A. An insufficient supply of air causes imperfect combustion of the fuel, which in bituminous coal is indicated by the production of smoke, and in coke and blind coal by the discharge of carbonic oxide gas from the chimney. That gas is transparent and in- visible; but its presence may be detected by the blue or purple flame with which it burns when ignited in contact with fresh air. An excessive supply of air causes waste of heat to the amount corresponding to the weight of air in excess of that which is necessary, and to the elevation of the temperature at which it is discharged from the chimney above that of the external air. 230. Distribution of Fuel and Air—In burning charcoal, coke, and coals which contain a small proportion only of hydrocarbons, a supply of air sufficient for complete combustion will enter from the ash pit through the bars of the grate, provided there is a suffi- cient draught, and that care is taken to distribute the fresh fuel evenly over the fire, and in moderate quantities at a time, so that the thickness of the layer of burning fuel shall never differ much from ten or twelve inches. To insure the complete combustion of highly bituminous coal, other means have to be adopted. That invented by Watt was the 282 STEAM AND OTHER HEAT ENGINES. use of a dead plate; that is, a horizontal or slightly inclined plate at the mouth of the furnace, without perforations, on which each fresh charge of coal is laid, until the hydrocarbons are volatilized and expelled by the radiant heat of the fire. The layer of burning fuel on the grate being thin at the time when a fresh charge is needed, more air passes through it from the ash pit than is neces- sary for its own combustion, and the surplus serves to burn the inflammable gas as it passes above the grate. When the coal on the dead plate has been reduced to coke, it is pushed inwards and spread over the fire. The success of this: process depends wholly on the care and skill of the fireman. It is useful not only to pro- mote complete combustion, but to prevent the clogging of the bars by caking coal. In burning anthracite, a dead plate is useful for a different purpose, viz., to heat the fuel gradually; because sudden heating makes it fly into small pieces, which drop through the bars into the ash pit, and are partly wasted. In the double furnace with alternate firing, introduced by Mr. Fairbairn, the gas distilled from the fresh fuel in one of a pair of furnaces is burned by the excess of air which passes through the red coke on the grate of the other furnace. Another mode of insuring the complete combustion of the volatile parts of the coal is one of which various forms have been invented by Mr. C. W. Williams, Mr. Prideaux, Mr. Clark, and others, and consists in admitting air above the fuel to burn the gas, and below it to burn the coke. Mr. Williams admits air at a constant rate through perforations in a double door and double front. In the latest practical examples, the total area of these perforations is z's of the area of the grate, when 25 lbs. of coal are burned per hour on the square foot of grate; that is, when the area of the grate in square feet is zs of the number of ths. of coal burned per hour, the joint area of the air holes is st> of the same number. Mr. Prideaux uses a self-acting apparatus for the admission of air, like a Venetian blind, which is opened when fresh coal is supplied, and which gradually closes as the gas of the fresh fuel becomes exhausted. The object of this is to supply enough of air at the time when it is needed, and to prevent an excessive supply at other times. Mr. D. K. Clark, by steam jets, blows in jets of air through holes immediately above the fuel. According to a method which seems to have been first used in America, a fan blower blows air through two sets of nozzles, one opening into the ash pit, which is closed in front, and the other into the furnace, immediately above the fuel. Mr. Gorman opens and closes the front of the ash pit, and the DISTRIBUTION OF AIR—-TEMPERATURE OF FIRE. 283 air holes in the front of the furnaces, alternately, so that the com- bustion of the gas from the fresh fuel, and of the coke left after its expulsion, take place alternately. Dr. Marsh supplies the whole of the air for burning the coke as well as the gas, by jets directed downwards on the fuel from above. Incomplete combustion of fuel is often caused by the chilling and extinguishing of flame through contact with the surface of the boiler, before the combustion is completed. This is in some furnaces prevented by completing the combustion in fire-brick chambers or passages. For example, in the furnaces introduced by Messrs. Charles Tennant & Company, the combustion is com- pleted in an arched brick oven or reverberatory furnace, before the hot gas comes in contact with any part of the boiler. The sides and roof of that oven consist of two layers of fire-brick with a closed air space between, as already described in Article 228. In many furnaces the principles of the various contrivances beforementioned are combined; thus double furnaces are used with air holes in the front, and with fire-brick combustion cham- bers. The coal burning locomotive furnaces of various inventors are of this class. Various furnaces have been used, such as Juckes’s, in which the fuel is supplied at an uniform rate by mechanism. In the apparatus known by the name of the “Systéme Beau- fumé,” a partial combustion of the fuel is effected in a furnace surrounded by a water chamber, and supplied by a fan with just enough of air to form carbonic oxide with the whole of the free carbon, and volatilize the whole of the hydrocarbons, so that the whole of the fuel is gasefied except the ash. The mixture of car- bonic oxide and hydrocarbon gases thus produced is conducted by a pipe to a combustion chamber, where, by the introduction of jets of air of sufficient volume, it is completely burned. If smoke is mixed with carbonic acid gas at a red heat, the solid carbonaceous particles are dissolved in the gas, and carbonic oxide is produced. This is the mode of operation of contrivances for destroying smoke by keeping it at a high temperature, without providing a sufficient supply of air; and the result is a waste, instead of a saving of fuel. The details of the construction of various furnaces will be further considered in a subsequent chapter. 231. Temperature of Fire—By the temperature of the jire is here understood the temperature of the products of combustion, and the air with which they are mixed, at the instant that the combustion is complete. The elevation of that temperature above the tempera- ture at which the air and fuel are supplied to the furnace may be: computed, by dividing the total heat of combustion of one Ib. of 284 STEAM AND OTHER HEAT ENGINES. fuel by the weight and by the specific heat of the whole products of its combustion, and of the air employed for their dilution, under constant pressure. The specific heat, under constant pressure, Of carbonic acid gas is........ digits se 0'217 Of steam joc .c.xs cia renuaversion seacweuces 0°475 Of nitrogen (probably),.............0664. 0°245 Of alt eccessaenascetornecsmeny sssbaawesearets 0'238 Of ashes, probably about............... 0°200 By using these data, the following results are obtained for the two extreme cases of pure carbon and olefiant gas, burned respce- tively in air :*— Piel cise eciaess AW seis Ue tidaatiUanlenaceeieeaeatecd Carpon. OLrriant Gas. Total heat of combustion per lb.,......... 14,500 21,300 Weight of products of combustion in : : air, undiluted, ...... sageamemsmensyat: 4 \ 13 lbs. 16-43 Ibs. Their mean specific heat,..............6006 0'237 0'257 Specific heat x weight,.........c0ccesee 3°08 4°22 Elevation of temperature if undiluted, 4580° 5050° Lf diluted with air = - air for combustion— 2 Weight per Ib. of fuel,.......... eee 19 24°2 Mean specific heat,...............ceeeeeeeeee > 0°237 0°25, Specific heat x weight, ..........cseee eee 4°51 6:06 Elevation of temperature,..............0065 3215° 3515° Tf diluted with air = atr for combustion— Weight per Ib. of fuel,.........00... ccc. 25 31°86 Mean specific heat,...........cceeseeseeeeeo 0'238 0'248 Specific heat x weight, ..........sccceeeee 5°94 79 Elevation of temperature, ..............066 2440° 2710° Tt appears from these calculations that the mean specific heat of the products of combustion of furnaces differs very little from that of air when they are undiluted, and still less when they are diluted with air. 232. Rate of Combustion—The weight of fuel which can be burned in a given time in a given furnace depends on the draught, or quantity of air, which is made to pass through that furnace in a given time, and may be computed by dividing the weight of that * These calculations are made according to the same principles with those of Mr. Frideaux in his treatise on Economy of Fuel, Section V1.; but there are some differences in the data, especially as to the specific heat of steam, which lead to differences (though not great ones) in the numerical results, RATE OF COMBUSTION—DRAUGHT. 285 air by the proportion which that weight bears to the weight of fuel tes it can completely burn, according to the principles of Article The rate of combustion of coal in a furnace is usually stated in pounds per hour, burned on each square foot of grate. The follow- ing are examples :— I. Wits Cuimyey Dravucut. Lbs. per square foot per hour. 1. The slowest rate of combustion in Cornish boilers, 4 2. Ordinary rate in these boilers, ........... csssseeseeee Io 3. Ordinary rates in factory boilers, ........... aeorniaas 12 to 16 4, Ordinary rates in marine boilers,.........sseeeeeeeee 16 to 24 5. Quickest rates of complete combustion of dry coal, the supply of air coming through the > 20 to 23 grate ONLY, .....ssceeeeseeceeeeceeceers Peeisvigaianie’ pats 6. ing coal, with air holes above the fuel to the Quickest rates of complete combustion of cak- 24 to 27 extent of gs area Of grate,...ccecceeseeseeeeees Il. Wire Draveut Propucep py Buast Pirk or Fan. Te, MiGCOTHOUIVES; 5 s5is ce vslecscnniinicn cactee cea edenbaen ctneeseiee 40 to 120 233. Dranght of Furnaces. — The draught of a furnace, or quantity of mixed gas which it discharges in a given time, may be estimated either by weight or by volume; or it may be expressed by means of the velocity of the current at some particular point ; or by the pressure required to produce that current. / When either the whole or part of the oxygen in a given weight of air, at a given temperature, combines with carbon so as to form carbonic acid, the volume of the mixed gas produced is the same with the original volume of the air; and the density is increased simply in the ratio of the sum of the weights of the air and of the carbon to the weight of the air. When the whole or part of the oxygen of a given weight of air combines with hydrogen so as to form steam, the volume of the mixed gas produced is greater than the original volume of the air by an amount equal to one-half of the volume of the hydrogen taken up. But the hydrogen in ordinary fuel bears so small a proportion to the whole weight, that in calculations for practical purposes, the volume at any given temperature of the gas which a furnace dis- charges may be treated without sensible error as being equal to the volume at the same temperature of the air with which it is supplied. 286 STEAM AND OTHER HEAT ENGINES. The variations of density produced by deviations of the pressure of the furnace gas from the mean atmospheric pressure may also be neglected in practice; so that its volwme at 32° Fahrenheit may be estimated approximately at 123 cubic feet for each Ib. of air supplied to the furnace; or, if the supply of air be ek pomace, t $od_) Volumeat 32° per Ib. of fuel. ="V5 12 Ibs..per Ib. of fuel,.....seeeeeees 150 cubic feet. 18 5 Sir. cedigereibieSlerreanieins 225 33 24 5 Seo) aeeea RAR Say 300 *9 The volume at any other temperature T is , V = volume at 32° x —— = Vo = anneot la) ies Fe x. O12" = y9a2* 4 %% Qo The following are some of the results :— Te. 52° o Supply of air in Ibs. per Ib. of fuel. 12 I 24 Temperature. Volume of gases per Ib. of fuel in cubic fect. 4640° I551 3275° 1136 1704 2500° 906 1359 1812 1832° 697 1046 3395 1472° 588 882 1176 T1r2° 479 7318 957 752° 369 553 738 572° 314 471 628 392° 259 389 519 212° 205 307 409 104° 172 258 344 68° 161 241 322 32° 150 225 300 Let w denote the weight of fuel burned in a given furnace per second ; Vo, the volume at 32° of the air supplied per Ib. of fuel ; 71, the absolute temperature of the gas discharged by the chimney ; A, the sectional area of the chimney; then the velocity of the current in the chimney in feet per second is wy t, =A.w wv, b, a u=—1; a ais a sletelaesecewentinexsies (2.) A % and the density of that current, in Ibs, to the cubic foot, is very nearly DRAUGHT OF FURNACE. 287 bea” 2 (0.0807 + x) cial eases (3.) that is to say, from 0:084 to 0-087 X 7) + 7. Let 7 denote the whole length of the chimney, and of the flue leading to it, in feet; “ m, its “ hydraulic’ mean depth,” that is, its area divided by its perimeter (see Article 99); which, for a square or round flue and chimney, is one quarter of the diameter ; 3 J, a co-efficient of friction, whose value for currents of gas moving over sooty surfaces is estimated by Peclet at 0:012; G, a factor of resistance for the passage of the air through the grate and the layer of fuel above it, whose value, according to the experiments of Peclet on furnaces burning from 20 to 24 lbs. of coal per square foot of grate, is 12. Then, according to a formula of Peclet, confirmed by practical experience, the “head” required to produce the draught in question is given by the equation which, with the values assigned by Peclet to the constants, becomes — = (1st eee Sears (44) It appears that in using this formula, a conical or pyramidal chimney may, without sensible error, be treated as if it were cylindrical or prismatic, with an uniform sectional area equal to that of the opening at the top. The same formula enables the velocity wu to be computed when the head / is given; and then, by means of the equation uA tr Wee? sence ete tnncewerecnceanenes (6.) w= the weight of fuel which the furnace is capable of completely burn- ‘ing per hour can be computed. The head h is expressed in feet in height of a column of the hot gas in the chimney. It may be converted into an equivalent pressure in pounds on the square foot, by multiplying as follows by the density of that gas as given by equation 3 :— pha “a (0 0807 ts) josseesesen (6.) 288 STEAM AND OTHER HEAT ENGINES. and this again may be converted into any other convenient unit of pressure, by multiplying by a suitabie factor, such as those in Article 107, page 110. An unit of head very commonly employed is an inch of water ; siphon water gauges, graduated into inches and decimals, being used to indicate the difference of pressure within and without a flue. For this unit the multiplier is a a iad 0-192; that is to say, Headl in inches of water = 0192 p = 0-192 h = (0-0807 +5,-).(7.) 1 0 The head may be produced in three ways— I. By the draught of a chimney. II. By a blast pipe. III. By a fan or other blowing machine. I. The head produced by the draught of a chimney is equivalent to the excess of the weight of a vertical column of cool air outside the chimney, and of the same height, above that of a vertical column of equal base, of the hot gas within the chimney; and when expressed in feet of hot gas, it is found by computing the weight of a column of the cool external air as high as the top of the chimney is above the grate and one foot square in the base, dividing by the weight of a cubic foot of the hot gas for the height of an equivalent column of hot gas, and subtracting the former height from the latter. Thus, let H denote the height of the chimney, and 7, the absolute temperature of the external air (= T, + 461°-2), then H - ~2 (0-:0807) # fis se (096 HB os 1) 5 one(8.) 5 5 TT, deed ae SS 7%) X =) gi = =! (o0807-+5- whe~ Vo = 300 esl wy ir ie ! Coa Unt gigas da wae HSB (0962 3) co ccccmaesnen (9.) 72 Equation 9 serves to calculate the height of the chimney required in order to produce a given draught. For a given external temperature, there is a certain temperature within the chimney which produces the most effective draught; that is, the maximum weight of hot gas discharged per second. That temperature is found as follows :— The velocity of the gas in the chimney is proportional to / 1; and therefore to ,/ (0:96 +, — 7%). CHIMNEY-DRAUGHT—BLAST PIPE, 289 The density of that gas is proportional to = The weight discharged per second is proportional to velocity x density, and, therefore, to gO ti 3 Which expression be- comes a maximum when ie therefore, the best chimney-draught takes place when the absolute temperature of the gas in the chimney is to that of the external air as 25 to 12. ‘When this condition is fulfilled, we have evidently that is, the head for the best chimney-draught, expressed in hot gas, ts equal to the height of the chimney; and it is also obvious, that the density of the hot gas is one-half of that of the external air. Suppose, for example, that the temperature of the external air on the ordinary scale is.............cccceeeceeceeeeeenceteecens 50° Fahr. then its absolute temperature is...........02.0.:eceeeee eee 512 the absolute temperature within the chimney, to give the best draught, is 2.0.0... ee 2tz X §1l'2 = 10650: corresponding on the ordinary scale to...............4.. 6038 being a little below the temperature of melting lead. It may be laid down as a practical rule, that to insure the best possible draught through a given chimney, the temperature of the hot gas in the chimney should be nearly, but not quite, sufficient to melt lead. As the proper allowance of air for a chimney-draught is 24 Ibs. _to each Ib. of fuel, the volume, at that temperature, of the hot gas discharged by the chimney, is about 650 cubic feet per lb. of fuel, or 26 cubic feet per Ib. of the hot gas itself. When the temperature in a chimney is found to be above this limit, it is to be reduced, not by admitting cold air to dilute the hot gas, but by employing the surplus heat for some useful purpose, such as heating or evaporating water. So long as the draught in a chimney is sufficient to burn the requisite quantity of fuel in the furnace, the temperature in the _chimney may often be reduced with advantage considerably below that corresponding to the most effective draught, provided the heat abstracted from the hot gas is usefully employed; but it is never advantageous to raise the temperature in the chimney above that _ Limit. : II. The head produced by a blast pipe is equivalent to that part U 290 STEAM AND OTHER HEAT ENGINES, of the atmospheric pressure which is balanced by means of the impact of the jet of steam against the column of gas in the chimney. Its amount and effect will be considered in a subsequent chapter. III. The work which a fan or other blowing machine must per- form in a given time in blowing air into a furnace so as to produce a given head, is found by multiplying the pressure equivalent to that head, in pounds on the square foot (p, equation 6), into the number of cubic feet of air blown in, taken at the temperature at which it quits the blowing machine. Let 7; be that temperature on the absolute scale (being equal to, or higher than 7,, that of the external air, as the case may be); then the net or useful work of the blowing machine per second is 2 Vo% _ 8 (0: +) p ee a pa ances (12.) The gross power or energy required to drive a blowing fan is greater than the useful work in a proportion which varies much in different machines, and is very uncertain. In some recent experiments, as nearly as it could be ascertained, the indicated power exerted by two steam engines driving fans through long trains of shafting, pulleys, and belts, appeared in each case to be about double of the useful effect. 234, Available Hleat of Combustion—Efficiency of Furnace.— The available heat of combustion of one pound of a given sort of fuel, is that part of the total heat of combustion which is com- municated to the body to heat which the fuel is burned; for example, to the water in a steam boiler; and the efficiency of a given furnace, for a given sort of fuel, is the proportion which the available heat bears to the total heat, when the given sort of fuel is burned in the given furnace. The word “furnace” is here to be understood to- comprehend, not merely the chamber in which the combustion takes place, but the whole apparatus for burning the fuel and transferring heat to the body to be heated, including ash pit, air holes, flame chamber, flues, tubes, and heating surface of every kind, and chimney. The same kind of furnace may be more efficient for one sort of fuel than for another; and it may also be more or less efficient for the same sort of fuel, according to the way in which the combustion is managed, The available heat falls short of the total heat from several causes, of which the principal are the following :— I. Waste of Unburnt Fuel in the Solid State-—This generally arises from brittleness of the fuel, combined with want of: care in the stoker, by which causes the fuel is made to fall into small pieces, which escape between the grate bars into the ash pit. EFFICIENCY OF FURNACE. 291 Many of the most valuable kinds of coal, such as the dry steam coals, are brittle. The waste of such coals in the solid state is to be prevented by the following means :—(1.) They are to be thrown evenly and uniformly over the fire with the shovel, so that there shall be no occasion to disturb them after they are first thrown in. (2.) The fire is not to be stirred from above; and the grate bars are to be cleared when required, by a hook or slice from below. (3.) The ashes are to be riddled from time to time, and the om coal or cinders contained amongst them thrown upon the res, It is impossible to estimate the greatest amount-of this kind of waste which may arise from careless firing ; but the amount which is unavoidable with good firing has in some cases been ascertained by experiment, and found to range from nothing, up to about 24 per cent. Il. The Waste of Unburnt Fuel in the Gaseous and Smoky States, and the means of preventing that waste, by a sufficient supply and proper distribution of air, have been stated in the preceding Articles. The greatest probable amount of that waste, when the absence of any provision for introducing air to burn the inflammable gases is combined with bad firing, may be estimated by taking the propor- tion in which the total heat of combustion of the coke or fixed carbon contained in one pound of the coal is less than the total heat of combustion of all the constituents of one pound of the coal. ‘When the firing is conducted with care, but the supply of air insufficient, the waste may be estimated by treating the hydrogen as ineffective; that is, by taking the proportion in which the heat due to the whole of the carbon in the coal is less than the heat due to the carbon and to the hydrogen in excess of that required to form water with the oxygen in the coal. This method of calcula- tion proceeds on the supposition, that the whole of the hydrocarbons are decomposed into carbon and hydrogen by the heat, that the carbon is completely burnt, and that the hydrogen escapes unburnt. That supposition appears to represent with an approach to accuracy the state of things in good ordinary steam boiler furnaces which have no special provision for distributing air amongst the inflam- mable gases; for the result of experience with such furnaces is, that the relative values of coals consumed in them are nearly propor- tional to the quantities of carbon contained in those coals. It appears, then, that there are two. degrees of waste from imper- fect combustion of the gas and smoke from one pound of bituminous coal, which, as reduced to equivalent weights of carbon, may be expressed as follows :— 292 STEAM AND OTHER HEAT ENGINES. Waste reduced to carbon, (1.) Insufficient air, but good firing, the sur- \ H-¢) plus hydrogen wasted, .........02::seseeeeseeees Hse : (2.) Very insufficient air, and bad firing; all } the hydrocarbons wasted. If the hydrogen | and carbon in these are combined in the same proportion as in marsh gas (H, C); + then for every lb. of hydrogen wasted, 3 lbs. of carbon are wasted also; giving as the total waste reduced to carbon, erates | If the hydrogen and carbon are combined in the same proportion as in olefiant oe 0 (H, ©,), then for every lb. of hydrogen | 10°28 H-<); wasted, 6 Ibs. of carbon are wasted also; | giving as the total waste reduced to carbon, J and for intermediate proportions, intermediate quantities are wasted. Ill. Waste by External Radiation and Conduction—The waste by direct radiation from burning coal through an open fire door may be approximately estimated according to the principles of Article 228, by assuming, in the first place, the heat directly radiated from the fuel to be one-half of the total heat of combustion; next, con- ceiving the surface of the burning mass to be divided into several small equal parts, from each of which an equal share of the heat radiates; then, finding what fraction of the surface of a sphere de- scribed about one of those parts is subtended by the opening through which the radiation takes place, and multiplying the share of heat radiated from the part of the fuel in question by that fraction; and, lastly, adding together the products so found for the several parts of the burning fuel. The loss by conduction through the solid boundaries of the furnace might be estimated from their area, their material, their thickness, their thermal resistance, and the difference of the temperatures within and without the furnace, by the principles of Article 219. In well planned and well constructed furnaces, however, those losses of heat should: be practically inappreciable; and the general nature of the means of making them so has been stated in Article 228. IV. Waste or Loss of Heat in the Hot Gas which Escapes by the Chimney.—Considering that the temperature of the fire, in a fur- nace with a draught produced by a chimney, and supplied with 24 Ibs. of air per Ib. of fuel, is about 2400° Fahr. above the tempera- ture of the external air, ’and that the temperature of the hot gas in EFFICIENCY OF FURNACE. 293 the chimney, in order to produce the best possible draught, should be about 600° above the temperature of the external air, it appears, that under no circumstances can it be necessary to expend more than one-fourth of the total heat of combustion for the purpose of producing a draught by means of a chimney. By making the chimney of large enough dimensions as compared with the grate, a much less expenditure of heat than this may be made to produce a draught sufficient for the rate of combustion in the furnace. When the draught is produced by means of a blast pipe, or of a blowing machine, no elevation of temperature above that of the , external air is necessary in the chimney; therefore, furnaces in which the draught is so produced are capable of greater economy than those in which the draught is produced by means of a chimney. It appears further, as has already been stated, that with a forced draught there is less air required for dilution, consequently a higher temperature of the fire, consequently a more rapid conduction of heat through the heating surface, consequently a better economy of heat than there is with a chimney-draught. The proportion of the whole heat which is lost with the gas discharged by the chimney depends mainly on the efficiency of the heating surface, which has already been considered in Article 221. ja.265~ Referring to equation 13, in case 2 of that Article, let E denote the theoretical evaporative power, and E’ the available evaporative power, of one lb. of a given sort of fuel, in a boiler furnace in which the area of heating surface is 8. Then E’ 8 p= 2 —Wew Cea et aw eec cee ereanes (1.) S+ Where B is a fractional multiplier, to allow for miscellaneous losses of heat, whose value is to be found by experiment. Now c¢? W? is proportional nearly to F? Vj, where F is the number of lbs. of fuel burnt in the furnace in a given time, and V>, as ina former Article, the volume at 32° of the air supplied per lb. of fuel. Also, H « F x a constant. Hence it may be expected, that the efficiency of a furnace will be expressed to an approximate degree of accuracy, by the follow- ing formula :— Ba SB ee can wimeasl (2.) B™Staneut in which A ig a constant, which is to be found empirically, and is * This formula, and most of the examples which follow it, were first published in a paper read to the Institution of Engineers in Scotland, on the 20th of April, 1859. 294 STEAM AND OTHER HEAT ENGINES. probably proportional approximately to the square of the quantity of air supplied per Ib. of fuel. It is customary and convenient to refer various dimensions and quantities relating to a furnace to the square foot of grate; there- fore S may be taken to represent the number of square feet of heating surface, and F the number of lbs. of fuel burnt per hour, per square foot of grate. The following are the values of the constants B and A which have been found to agree best with experiment, so far as the practical performance of boilers has hitherto been compared with the formula :— Boiler Class I. The convection taking place in the best manner (see Article 220), either by introduc- ing the water at the coolest part of the boiler, and making it travel gradually to the hottest (as in Lord Dundonald’s boiler), or by heating the feed- water in a set of tubes in the uptake; the draught B A produced by a chimney,................ ccc ceeeeeeeeeeeee I O95 Boiler Class II. Ordinary convection, and chimney AraUShbcscsatsesaniaesnssanawsmmaceeasswaons se steanwneten tk O05 Boiler Class IIJ. Best convection, and forceddraught, 1 03 Boiler Class IV. Ordinary convection, and forced OTRUBHE a sansensengrewamieisaderoauates amcauenanonemeeeasinncs 3 Jo + 073 eT When there is a feed-water heater, its surface should be included in computing §; and the surface of tubes surrounded by water is to be measured outside. The formula is of course not intended to supersede experiments and practical trials, nor to give results as accurate and satisfactory as such experiments and trials, but to furnish a convenient means of estimating approximately the evaporative power of fuel in pro- posed. boilers, and the comparative efficiency of different boilers. The formula is framed on the supposition that the admission of air and the management of the fire are such, that no appreciable loss occurs, either from imperfect combustion or from excess of air, the construetion and proportions of the furnace, and the mode of using it, being the best possible for each kind of coal. If desired, the effect of imperfect combustion and bad firimg may be estimated in the manner described in Division IIT. of this Article, and that of an excess of air by increasing A in proportion to the square of the quantity of air supplied. . The following are examples of efficiency calculated Ly means of the formula :-— EFFICIENCY OF FURNACE. 295 E E 5 For class of boiler Yr I. II. III. IV. o'r o'16 O15 0'25 0°22 0°25 0°33 o'gt 0°45 0°43 o'5 0°50 | 0°46 0°62 0°59 o75 0°60 0°55 o"t 0°68 I'o 0°66 o'61 O77 073 1°25 o“vt 0°65 o81 o”“7 15 O75 0°69 0°83 O79 20 080 073 087 0°83 2°5 0°83 076 o'89 0°85 '3'0 086 o'79 oor 0°86 6:0 o'92 084 0°95 0°90 9'0 0°95 0°87 0°97 0'92 The following are particular cases :— I. North country coal— E=155; sa as; F= 25; boiler with feed-water heater, and chimney-draught; or Class L— H=155 x 0:8 = 1244, This agrees closely with the results of the experiments at New- castle on fresh coal, both by the Newcastle committee, and by the Admiralty reporters. II. Same coal, same boiler without heater— pia2 ae Gar 22 Boiler Class II.— E’=155 x 0:66 = 10:23. This nearly agrees with an experiment made by the Admiralty reporters at Newcastle, in which the result was 10:54. ITI. Same coal— S=25; F=25; no heater. Boiler Class II.— EH’ =15°5 x 0°61 =9°5. 296 STEAM AND OTHER HEAT ENGINES. This applies to several ordinary marine boilers, IV. Locomotive boiler, Class IV.— Coke, E= say 14:1; S= 60; F=56. H = 14-1 « -74 = 10-43 from 212°; Equivalent evaporation from 62° at 329°, 10-43 = 8:69. The above proportions of 8 and F are computed from a formula of Mr. D. K. Clark, as being suitable to insure an evaporative power of 9, from 62° at 329°. The difference is only zy. V. Locomotive boiler, Class IV. (mean of Mr. D. K. Clark’s experiments, Nos. 38, 39, 40, 41, 42)— E=say 14:1; S= 83; F= 652; E'= 14:1 x ‘77 = 10°86 from 212° ; Equivalent evaporation from 62° at 329°, 10-86 Mean result of experiments, ............ 8-72 Difference,.........se000s 0:33 VI. Locomotive boiler, Class IV. (mean of Mr. D. K. Clark’s experiments, Nos. 48, 49, 50, 51, 53)— E= say 14:1; S= 66-4; F= 56-2; EH =141 x (76 = 10-72 from 212° ; Equivalent evaporation from 62° at 329°, 10:72 Mean result of experiments,............ 875 Difference,..........600.. 0-18 VII. Locomotive boiler, Class IV. (Mr. D. K. Clark’s experi- ment, No, 55; mean of 10 trips}— E=say 14:1; 8S=57; F= 44; E’= 14-1 x 77 = 10-86 from 212°, EFFICIENCY OF FURNACE. 297 Equivalent evaporation from 62° at 329°, 10-86 = Ta = 9-05 Result of experiments, ............00c00 9-00 Difference,............06 0:05 VIII. Locomotive boiler, Class IV. (Mr. D. K. Clark’s experi- ment, No. 61, mean of 8 trips)— E=say 141; S=60; F=87; E’ = 14:1 x 66 = 9-3 from 212°; Equivalent evaporation from 62° at 329°, ia 775 Result of experimentt,.........cceeeese 7-2 Difference,..........s0005 0:55 The only principle followed in selecting experiments from Mr. Clark’s table is that of giving the preference to those cases in which a mean can be obtained from the results of a large number of experiments under similar or nearly similar circumstances. The general conclusion to be drawn from the preceding compari- sons is, that the formula agrees closely with the results of experiment. up to a rate of consumption of about 60 lbs. per square foot of grate; and that above that rate of consumption, although there is still an approximate agreement, the results of experiment fall somewhat short of those given by the formula. It is probable, however, that for those high rates of consumption, the combustion is not so complete as at lower rates, and that some heat is conse- quently wasted. Example TX.—Boiler Class II.— E= about 154; S= 60, nearly; F = 6-4; Result of experiment,.......sccesssssseseees 13:56 Difference,............sce00e 0:08 The above is the result of an experiment of the Author's. 298 STEAM AND OTHER HEAT ENGINES. Example X.—The Earl of Dundonald’s boiler. This boiler is considered as belonging to Class I., because of the feed-water being introduced at the part where the gas from the furnace is coolést— E = about 16? (for hand-picked Llangennech coal) ; S = 335; F=1017; EH’ = 16 x 0°87 = 13°92 Mean result of two experiments with the feed-water ath 14-20 50°, 12°14 x factor of evaporation 1°17, ......:sseeceereeres Difference, ......sssssesseresesveee sgentun devateanwacueeee 0-28 ADDENDUM To ARTICLE 254, page 324, and Article 317, page 465. Outflow of Stenm.—Let p be the absolute pressure inside a vessel, such as a boiler, and py the absolute pressure outside. Let U denote the work done by an unit of weight of steam, if admitted into a cylinder at the pressure p;, expanded till the pressure falls to yo, and expelled at the latter pressure. Then the velocity with which the steam will escape from an outlet in the vessel will be given by the follow- ing formula, in which g denotes gravity :— Ve CG Dnsuen aur) Let z be the volume occupied by unity of weight of the steam at the instant when its expansion is complete ; then the weight of steam which escapes per second through each unit of effective area of outlet is expressed as follows :— Vit = 7 (2G UG) 2 th aissesiacccmersesseumvice (2.) The following are the rules to be used for finding U and u in different cases :— Case I. For the escape through a non-conducting nozzle; u, Article 281, equation (3), page 384; or equation (3), page 885; U, Article 284, equation (1), or (1 a), page 387. Cask II. For the escape through a nozzle which communicates to the steam just heat enough to prevent liquefaction ; «(= vg), Article 287, equation (1 a), page 398; or the table headed “Steam by the Pound,” pages 564 to 567; U (= . vod p), 2 Article 287, equation (2), page 398; or the before-mentioned table; or the diagrams ‘at the end of the volume; or the following approximate formule :— 16 1 U=Ug =? (Pins Usp e017 j1— (“hats sadsameesy (3.) 2 PY Casr III. For steam-gas, the formule of Article 254, page 324. The effective area of outlet is the sectional area of the escaping jet at the point where the absolute pressure is pp. For conoidal converging nozzles, and with po not less than $ pj, the effective area may be taken as equal to the actual area at the outer end of the nozzle. The above-mentioned value of the external pressure, p, = 3p, or thereabouts, gives 1 maximum value to the weight of outflow, V+w; and the experiments of Mr. R. D, Napier have shown that probably, when po < 2 py, the effective area of outlet becomes greater than that of the nozzle in such a proportion that the weight of outflow remains constant for a given internal pressure. For a rough approximation, let g be the weight of outflow per unit area per second; then, when po=or < 2p), g=pi—70 nearly; and when pe > 3 p13 g = (po + 42) “WV (pi — pe) + 3P2.) (See The Engineer for September, October, November, and December, 1869.) oe CHAPTER IIT PRINCIPLES OF THERMODYNAMICS, Section 1.—Of the Two Laws of Thermodynamics. 235. Thermodynamics Defined. —It is a matter of ordinary observation, that heat, by expanding bodies, is a source of me- chanical energy; and conversely, that mechanical energy, being expended either in compressing bodies, or in friction, is a source of heat. Such phenomena have already been incidentally referred to, in Article 13, under the head of Friction; in Article 195, where the relations between heat and mechanical energy are mentioned ; in Article 196, under the head of the Properties of the Condition of Heat, numbered IV., V., and VI.; and in Articles 211 to 216, under the head of Latent Heat, which disappears in producing mechanical changes, and can be reproduced by reversing those changes. The reduction of the laws according to which such phenomena take place, to a physical theory, or connected system of principles, constitutes what is called the scIENCE OF THERMODYNAMICS. 236. Wirst Law of Thermodynamics. — [Heat and mechanical energy are mutually convertible; and heat requires for its production, and produces by its disappearance, mechanical energy in the propor- tion of 772 foot-pounds for each British unit of heat: the said unit being the amount of heat required to raise the temperature of one pound of liquid water by one degree of Fahrenheit, near the temperature of the maximum density of water. This law may be considered as a particular case of the application of two more general laws, viz. :—1. All forms of energy are convertible. 2. The total energy of any substance or system cannot be altered by the mutual actions of its parts. The quantity above stated, 772 foot-pounds for each British thermal unit, is commonly called “ Joule’s equivalent,” and denoted by the symbol J, in honour of Mr. Joule, who was the first to determine its value exactly. His first approximate determination of this quantity was published in 1843, a little after that of Mayer; his best set of experiments, from which the accepted value 772 is deduced, may be consulted in the Philosophical Transactions for 1850, 300 STEAM AND OTHER HEAT ENGINES, In these experiments, the heat produced by mutual friction of the particles of a diguid was compared with the mechanical energy expended in producing that friction. The advantage of this kind of experiment is, that the liquid, and all the parts of the apparatus, are left exactly in the same condition at the end of the experiment as they were at the beginning; so that it is certain, that no per- manent effect whatsoever has been produced by the mechanical energy expended, except a certain quantity of heat, which is accurately measured; and, therefore, that the heat so produced is the exact equivalent of the mechanical energy expended. In all other cases in which heat is produced by the expenditure of mechanical energy, or mechanical energy by the expenditure of heat, some other change is produced besides that which is princi- pally considered; and this prevents the heat and the mechanical energy from being exactly equivalent. The following are the values of Joule’s equivalent for different thermometric scales, and in French and British units :— J. One British thermal unit, or degree of Fahrenheit in a lb. of water, pene 772 foot-lbs. One Centigrade degree in a lb. of water, 1389°6 _,, (or very nearly 1390). One French thermal unit, or Centi- \ grade degree in a kilogramme of /- 423°55 kilogrammétres. WAGED was aees semarekiwnanen seciuwns teats f The production of heat by friction is distinguished from its pro- duction by other mechanical means, such as the compression of gases, in being irreversible; that is to say, it is impossible to make heat produce mechanical energy by any such means as reversing the process of friction. 237. Dynamical expression of Quantities of Heat.— All quantities of heat, such as the specific heat of any substance, or the latent heat corresponding to any physical effect, or any other of the quantities of heat treated of in Chapters I. and II., may be expressed dynami- cally, that is, in units of work, by multiplying their values in ordinary units of heat by Joule’s equivalent. Several examples of this mode of expressing quantities of heat, which is by far the most convenient in treating of thermodynamical questions, are given in the tables at the end of this volume. The following are additional examples :— ; Foot-lbs. Latent heat of evaporation of 1 lb. of water, ie n4g,8t2 arid at ONO? sc racawmantusants secueeneoenniunals ee ecenees Total heat of combustion of 1 Ib. of carbon,.......... 11,194,000 FIRST LAW OF THERMODYNAMICS. 301 238. Graphic Representation of the First Law.—In fig. 91, let abscisse, measured along, or parallel to, the axis O X, represent the volumes successively assumed by a given mass of an elastic substance, by whose alter- nate expansion and contraction heat is made to produce mechanical energy; O V, and OV, being the least and greatest volumes which the substance is made to assume, and O V any intermediate volume. For brevity’s 3 Yr sake, these quantities will be denoted by »v,, B %, and v, respectively. Then v, —v, may re- present the space traversed by the piston of ¢ i ab VA. "a an engine during a single stroke. : Let ordinates, measured parallel to the Fig. 91. ’ axis O Y, and at right angles to O X, denote the expansive pressures successively exerted by the substance at the volumes denoted by the abscisse. During the increase of volume from », to %, the pressure, in order that motive power may be produced, must be, on the whole, greater than during the diminution of volume from », to v,; so that, for instance, the ordinates V P, and V P., or the symbols p, and p,, may represent the pressures corresponding to a given volume v, during the expansion and contraction of the sub- stance respectively. Then, as in Article 43, and fig. 17, the area of the curvilinear figure, or indicator-diagram, A P, B P, A, will represent the energy exerted by the elastic substance on the piston during a complete stroke, or cycle of changes of volume of the elastic substance. The algebraical expression for that areu 1s Ud | (ai-p) ae; and this, in virtue of the first law of thermodynamics, represents also, in units of work, the mechanical equivalent of the heat which disappears during a complete forward and back stroke of. the piston; that is to say, if A, represents the quantity of heat, in common thermal units, received by the elastic substance during one part of the process (such, for example, as the heat communicated to a certain weight of water in a boiler in order to produce steam), and h, the’ quantity of heat rejected by the same substance during another part of the process (such, for example, as the heat abstracted trom the same quantity of water in the condenser of a condensing engine, or by the air, in a non-condensing engine); and if H, and H, are the same quantities of heat expressed in foot-pounds, then, by the first law, 302 STEAM AND OTHER HEAT ENGINES. J (hy - hy) = H, -H, =| (p.-P2) oaciaahy 239. Thermal Limes—A line drawn on a diagram of energy, such that its ordinates represent the pressures of a substance cor- responding to various volumes, while the absolute temperature is maintained at a constant value, denoted, for example, by 7, may be called the isothermal line of x for the given substance (see fig. 92). Suppose, for instance, that the co-ordinates of the point A, v, and Pay Vepresent respectively a volume and a pressure of a given sub- stance, at which the absolute temperature is 7 ; and the co-ordinates of the point B, viz., v, and »», another volume and pressure at which the absolute temperature is the same ; then are the points A and B situated on the same isothermal line TT. On the other hand, let the sub- stance be allowed to expand from TN the volume and pressure v,, p,, With- out receiving or emitting heat; and when it reaches a certain volume, v, let the pressure be represented by p., which is less than the pres- ae sure would have been had the tem- perature been maintained constant, “ls because, by expansion, heat is made a ee 2x to disappear. Then C will be a j point on a certain curve N N pass- ing through A, which may be called a curve of no transmission, or adiabatic curve. It is to be understood that, during the process last described, the mechanical energy exerted during the expansion, and which is represented by the area A C Vy V,, is entirely communicated to an external body, such as a piston; for if any part of it were expended in agitating the particles of the expanding substance, a portion of heat would be reproduced by friction. If 0 00 be a curve whose ordinates represent the pressures corre- sponding to various volumes when the substance is absolutely destitute of heat, then this curve, which may be called the line of absolute cold, is at once an isothermal curve and an adiabatic curve. So far as we yet know, the line of absolute cold, for all sub- stances for which it has been ascertained, is an asymptote to all the other isothermal curves and curves of no transmission, which approach it and each other indefinitely as the volume of the substance increases without limit; and it coincides sensibly with the straight line O X; that is to say, a substance wholly destitute of heat exerts no expansive pressure. Xo hm Ww Fig. 92. THEOREM AS TO ADIABATIC CURVES. 303 The following property of adiabatic curves, in connection with the first law of thermodynamics, is the foundation of many useful propositions. (It was first demonstrated in the Philosophical Transactions for 1854.) _THEorem. The mechanical equivalent of the heat absorbed or given out by a substance in passing from one given state as to pres- sure and volume to another given state, through a series of states represented by the co-ordinates of a given curve on a diagram of energy, is represented by the arew included between the given curve and two curves of no transmission of heat drawn from its extremities, ane indefinitely prolonged in the direction representing increase of volume. (Demonstration) (see fig. 93). Let the co-ordinates of any two points, A and B, represent respectively the volumes and pressures of the substance in any two conditions; and let a curve of any figure, ACB, represent by the co-ordinates of its points, an arbitrary succession D! of volumes and pressures N through which the sub- ¢ pM. stance is made to pass, ‘s Yo in changing from the con- Fie. 93. dition A to the condition . B. From the points A and B respectively, let two adiabatic curves AM, BN, extend indefinitely towards X; then the area referred to in the enunciation is that contained between the given arbitrary curve A C B and the two indefinitely prolonged adiabatic curves; areas above the curve A M being considered as represent- ing heat absorbed by the substance, and those below, heat given out, To fix the ideas, let us in the first place suppose the area MACBN to be situated above AM. After the substance has reached the state B, let it be expanded according to the adiabatic curve BN, until its volume and pressure are represented by the co-ordinates of the point D'. Next, let the volume vp be maintained. constant, while heat is abstracted until the pressure falls so as to be represented by the ordinate of the point D, situated on the curve of no transmission AM. Finally, let the substance be compressed, according to this curve of no transmission, until it recovers its primitive condition A. Then the area A CBD'D A, which re- presents the whole energy exerted by the substance on a piston during one cycle of operations, represents also the heat which dis- appears; that is, the difference between the heat absorbed by the x 4 304 STEAM AND OTHER HEAT ENGINES. substance during the change from A to B, and the heat emitted during the change from D’ to D; for if this were not so, the cycle of operations would alter the amount of energy in the universe, which is impossible. The further the ordinate V, D D’ is removed in the direction of X, the smaller does the heat emitted during the change from D' to D become; and consequently, the more nearly does the area ACBD'DA approximate to the equivalent of the heat absorbed during the change from A to B; to which, therefore, the area of the indefinitely proloaged diagram M ACB N is exactly equal. —QED. It is easy to see how a similar demonstration could have been applied, mutatis mutandis, had the area lain below the curve A M. Ié is evident also, that when this area lies, part above and part below the line A M, the difference between those two parts repre- sents the difference between the heat absorbed and the heat emitted during different parts of the operation. CoroLttaRy.—The difference between the whole heat absorbed, and the whole expansive energy exerted, during the operation represented by any curve, such as ACB, on a diagram of energy, depends on the initial and final conditions of the substance alone, and not on the intermediate process. (Demonstration.) In fig. 93, draw the ordinates AV,, B Vy, parallel to O Y. Then the area V, A CB Vy represents the energy exerted in a piston during the operation A CB; and it is evident that the difference between this area and the indefinitely prolonged area M A CBN, which represents the heat received by the substance, depends simply on the positions of the points A and B, which denote the initial and final conditions of the substance as co volume and pressure, and not on the form of the curve A CB, which represents the intermediate process.—Q.E.D. To express this result symbolically, it is to be considered, that che excess of the heat or actual energy received by the substance above the expansive power or potential energy given out and exerted on an external body, such as a piston, in passing from the condition ‘A to the condition B, is equal to the whole energy stored up in the substance during this operation, which consists of two parts, viz.— Actual energy; being the increase of the actual or sensible heat of the substance in passing from the condition A to the condition B, which may be represented by this expression, 4°Q=Q;- Q,. Potential energy; being the power which is stored up in producing changes of molecular arrangement during this process; and which, TOTAL ACTUAL HEAT, 305 it appears from the theorem just proved, must be represented, like the actual energy, by the difference between a function of the volume and pressure corresponding to A, and the analogous func- tion of the volume and pressure corresponding to B; that is to say, by an expression of the form AB Bg — Gye ceesessesseeeseseee(L.) Let H,s=areaMACBN represent the heat received by the substance during the operation A CB, and f° pdv area V,ACBYV, Va the power or potential energy exerted on a piston. _ Then the theorem of this Article is expressed as follows :— Hy. s= * pdv=Qs—Qut S.-S,=AQHAS.....(2) being a form of the general equation of the expansive action of heat, in which the potential of molecular action, 8, remains to be determined. 240, Total Actual Heat.—Let a substance, by the expenditure of energy in friction, be brought from a condition of total privation of heat to any particular condition as to heat. Then, if from the total energy so expended, there is subtracted—first, the mechanical work performed by the action of the substance on external bodies, through changes of its volume and figure, during such heating; secondly, the mechanical work due to mutual actions between the particles of the substance itself during such heating; the remainder will represent the energy which is employed in making the substance hot, and which might be made to reappear as ordinary mechanical energy, if it were possible to reduce the substance to a state of total privation of heat. This remainder is the quantity called the total actual heat of the substance; being the total energy, or capacity for performing work, which the substance possesses in virtue of being hot. It is not directly measurable; but its value may be computed from known quantities, by means to be after- wards explained. When a homogeneous substance *: uniformly hot, every particle of it is equally hot; and every particle is hot in virtue of a condition of its own, and independently of forces exerted between it and other particles. These are facts known by experi- ence; and they lead to the following consequence :—that when the total actual heat of a homogeneous and uniformly hot substance is xr a 306 STEAM AND OTHER HEAT ENGINES. considered as a quantity made up of any number of equal parts, all those equal parts are similarly circumstanced ; and hence follows— 241, Whe Second Law of ‘Thermedynamics.—Jf the total actual heat of a homogeneous and uniformly hot substance be concewed to.be divided into any number of equal parts, the effects of those parts in causing work to be performed are equal.—This law may be con- sidered as a particular case of a general law applicable to every kind of actual energy; that is, capacity for performing work, con- stituted by a certain condition of each particle of a substance, how small soever, independently of the presence of other particles (such as the energy of motion), The symbolical expression of the second law of thermodynamics is as follows:—Let unity of weight of a homogeneous substance, possessing the actual heat Q, undergo any indefinitely small change, so as to perform the indefinitely small amount of work dU. It is required to find how much of this work is performed by the disappearance of heat. Conceive Q to be divided into an indefinite number of indefinitely small equal parts, . each of which is$Q. Each of those paris will cause to be per- formed the quantity of work represented by d BO g0 7 Ue consequently the quantity of work performed by the disappearance of heat will be d 2°76 which quantity is known when Q, and the law of variation of dU ° with Q, are known. 242. Absolute Temperature—Specific Heat, Beal and Apparent. —Temperature is a function depending on the tendency of bodies to communicate the condition of heat to each other. Two bodies are at equal temperatures, when the tendencies of each to make the other hotter are equal. All substances absolutely devoid of heat are at the same temperature. Let this be called the absolute zero of heat; and let the scale of temperature be so graduated, that for a given homogeneous substance, each degree shall correspond to an equal increment of actual heat.* This mode of graduation neces- Wl merce (1.) * The mode of graduation above described leads to a dynamical scale of absolute temperatures. In Article 201, a scale of absolute temperatures is described, founded upon the elasticity of a perfect gas. It was anticipated some years ago, by certain theoretical ac2 hypothetical investigations, that the scale of the perfect gas thermo- meter would be foun2 to agree with the dynamical absolute thermometric scale, as to the length of its degrees; and also that the zeros of those scales would be found to be near each other, if not coincident. Throughout many of the papers referyed to, the formule were so framed as to contain unknown terms, suited to provide for the possi- ABSOLUTE TEMPERATURE—SPECIFIC HEAT. 307 sarily leads to the same scale of temperature for all substances. For if two substances A and B be at equal temperatures when the possess respectively two certain quantities of actual heat Q, and Qa, then if each of those quantities of actual heat be divided into the same number of equal parts n, the tendency of the substance A to communicate heat to B, arising from any one of the nth parts of Q,, must, from the property of actual heat already mentioned, be equal to the tendency of B to communicate heat to A, arising from any one of the nth parts of Q,; from which it follows, that so long as the quantities of actual heat possessed by the two substances are In the ratio Q,: Qs, their temperatures are equal, independently of the absolute amounts of those quantities. The amount of actual heat, expressed in units of work, which corresponds, in a given substance, to one degree of absolute temperature, is the real dynamical specific heat of that substance, and is a constant quantity for all temperatures. The total quantity of mechanical energy required to raise the temperature of unity of weight of a substance by one degree, generally includes, besides the real specific heat, work performed in overcoming molecular forces and external pressures. This is the apparent dynamical specific heat; and may be constant or variable. Joule’s equivalent is the apparent dynamical specific heat of liquid water at and near its maximum density; and it is probably equal sensibly to the real specific heat of that substance. The real specific heat of each substance is constant at all densities, so long as the substance retains the same condition, solid, liquid, or gaseous; but a change of real specific heat, sometimes considerable, often accompanies the change between any two of those conditions. From the mutual proportionality of actual heat and absolute tem- perature, there follows— 243, The Second Law of Thermodynamics, expressed: with refer- ence to ABSOLUTE TEMPERATURE. If the absolute temperature of any uniformly hot substance be divided into any number of equal parts, the effects of those parts in causing work to be performed are equal. This law is expressed algebraically as follows:—from the relation between absolute temperature (7), and actual heat (Q), it follows that e d "in aq consequently the expression 1, for the work performed by the dis- appearance of heat, is transformed into bility of a sensible difference between those zeros. But as, according to the latest and best experiments, no such appreciable difference has been found; the zero and scale of the perfect gas thermometer may be treated as sensibly, if not exactly, coin- cident with the dynamical absolute zero and absolute thermometric scale, 308 STEAM AND OTHER HEAT ENGINES. ae ro aU. won wesvsseecscoeerossved(]s) This expression is applicable, not merely to homogeneous sub- stances, but to heterogeneous aggregates. When the expressions 1 of Articles 241 and 243 are negative, they represent heat which appears in consequence of the ex- penditure of mechanical work in altering the condition of a substance. The first and second laws virtually comprise the whole theory of thermodynamics. 244, Second Law, Represented Graphically—THEOREM. Jn Sig. 94, let A, A, M, B, BLN, be any two adiabatic curves, indefinitely extended in the direction of X, intersected in the points Ax, By, Ag, B,, by two isothermal curves, Q, A, B, Q,, Q, Ay By, Q,, which corre- - spond to two absolute temperatures, 7, and r., differing by the quantity 1-1) > At ’ Then. the quadrilateral area, A, B, B, Ay, bears to the whole indefinitely prolonged area M A, B, N, the same proportion which the difference of temperature A bears to the whole absolute tempera- ture 3 or area A, B, B, Ay _4r area M A, BLN SD eetteteee terete (1.) (Demonstration.) Draw the ordinates A, Va, Ay Vax, By Vu, B, Vz, Suppose, in the first place, that a 7 is an aliquot part of 7, obtained by dividing the ep Se latter quantity by an in- < teger n, which we are at liberty to increase without y limit. The entire indefinitely N prolonged area M A, B, N represents a quantity of heat which is converted Wee “sa Ya? into mechanical energy ig. 94. during the expansion of the substance from V,, to Vz, in consequence of the continued presence of the absolute tem- . perature zr, Mutatis mutandis, a similar statement may be made respecting the area M A,B, N. (By increasing without limit the number n, and diminishing 4 7, we may make the expansion from Vaz to Vy, as nearly as we please an identical phenomenon with the expansion from V,, to Vy.) The quadrilateral A, B, B, A, represents the diminution of conversion of heat to mechanical LATENT HEAT OF EXPANSION—THERMODYNAMIC FUNCTIONS. 309 energy, which results from the abstraction of any one whatsoever of the equal parts 47 into which the absolute temperature is supposed to be divided, and it therefore represents the effect, in conversion of heat to mechanical energy, of the presence of any one of’ those parts. And as all those parts a+r are similar and similarly circumstanced, the effect of the presence of the whole absolute temperature r, in causing conversion of heat to mechanical energy, will be simply the sum of the effects of all its parts, and will bear the same ratio to the effect.of one of those parts which the whole absolute temperature bears to the part. Thus, by virtue of the general law enunciated below, the theorem is proved when ar is an aliquot part of 7,; but a7 is either an aliquot part, or a sum of aliquot parts, or may be indefinitely approximated to by a series of aliquot parts; so that the theorem is universally true.—Q. E. D. A symbolical expression of this theorem is as follows:—When the absolute temperature z,, at any given volume, is varied by the indefinitely small quantity 37, let the pressure vary by the indefi- nitely small quantity i 47; then the area of the quadrilateral A, B, B, A, will be represented by Rol ee ae oT | é ee dv > and consequently, that of the whole figure M A, B,N, or the LATENT HEAT OF EXPANSION from V,,, to Vg,,, at 7, by v Sh, =H, = nf gee cons sees a result substantially identical with that expressed in equation 1 of Article 243, when p dv is put for d U. The demonstration of this theorem is an example of a special application of the following GENERAL LAW OF THE TRANSFORMATION OF ENERGY. The effect of the presence in w substance, of a quantity of actual energy, in causing transformation of energy, is the sum of the effects of all tts parts ; a law first enunciated in a paper read to the Philosophical Society of Glasgow on the 5th of January, 1853. 245. Of Heat Potentials and Thermodynamic Functions —The second law of thermodynamics may also be expressed in the follow- ing form :—The work performed by the disappearance of heat during 310 STEAM AND OTHER HEAT ENGINES. any indefinitely small variation in the state of a substance, is expressed by the product of the absolute temperature into the variation of a cer- tain function, which function is the rate of variation of the effective work performed with temperature; that is to say, make dt then the work performed by the disappearance of heat is id Bese covevaciuevecssaseseeiss (1.) This function F has been called the heat potential of the given substance for the kind of work under consideration. Now let the substance both perform work and undergo a varia- tion of absolute temperature d 7, and let k denote its real dynamical specific heat. The whole heat which it must receive from an external source of heat, to produce those two effects simultaneously, is Jdh=dH=kdrtrdF= 7d Qj.......(2) in which LU @ aoe hyp log + oe ssseseee eaeeies (3.) @ is called the thermodynamic function of the substance for the kind of work in question; and in some papers, the heat-factor. The equation (2) is the GENERAL EQUATION OF THERMODYNAMICS, which we shall proceed, in the sequel, to apply, by determining the thermodynamic function for each particular case. In determining that function, it is to be observed, that the func- tion U, representing the work performed by the kind of change under contemplation, is first to be investigated as if the temperature were constant, and then the law of its variation with absolute tem- perature found. The property of an adiabatic curve is expressed by d-H =0; from which it is evident, that for such a curve, d 9 = 0; ‘that is to say, for a given adiabatic curve, the thermodynamic function has a constant value, proper to that curve. In fig. 94, Article 244, the indefinitely extended area between the isothermal curve Q,, Q,, and the two adiabatic curves A, M, B, N, is the product of the absolute temperature proper to the isothermal curve into the difference between the thermodynamic functions proper to the adiabatic curves. Section 2.—Hapansive Action of Heat in Fluids. 246. General Laws as Applied to Fluids. — In representing EXPANSIVE ACTION OF HEAT IN FLUIDS. 311 graphically the general laws of thermodynamics, the illustrations already employed in Articles 238, 239, and 244, have been taken from the changes of pressure and volume of fluids as affected by heat. It is to be borne in mind, however, that the general laws are applicable to the relations which heat bears to the energy of all kinds of elastic forces, as well as to the simple expansive pressure exerted by fluids. In the expression for work performed against some external resistance, dU=pdy», dv, instead of an elementary increase of the volume of a substance, solid or fluid, may represent an elementary part of the motion which takes place amongst its particles, as it returns to its original figure after having been distorted, and y, the force with which it tends to recover its original figure; in which case, v may still be represented by the abscissa, and p by the ordinate of a diagram of energy, and pdv by an elementary portion of the area of that diagram. Inasmuch, however, as all known heat engines perform work by means of the changes of pressure and volume of fluids alone, it is unnecessary in this treatise to do more than to refer in general terms to the special application of the laws of thermodynamics to the elasticity of solids. In the present section will be considered the more important of their special applications to the elasticity of fluids. Let v denote the volume in cubic feet occupied by a given mass of any fluid, whether liquid or gaseous, enclosed in a vessel of variable capacity (such as a cylinder with a piston); p the pressure, or effort to expand, which the fluid exerts against the interior of the vessel, in pounds per square foot; then, as in Articles 6, 43, &e., will pdv denote the external work in foot-pounds performed by the fluid during an indefinitely small expansion dv, and | pdv the external work performed during any finite expansion, the relation between p and v being fixed by the circumstances of the case. To find the thermodynamic function for the expansion of a fluid, the pressure p is to be expressed in the form of a function of the volume v, and absolute temperature 7, and the general value of the integral U=| pd», found on the supposition that + is constant; then the thermody- namic function will be e =k hyplog = + fS2ae biotic evn) 312 STEAM AND OTHER HEAT ENGINES. The second term of this expression is represented graphically, as in fig. 94, by the limiting ratio of the area of the band A, B, B, A, to the difference between the absolute temperatures corresponding to the upper and lower edges of that band. botnet Applying the thermodynamic function to the determination, in foot-pounds, of the whole quantity of heat dH, which must be communicated to one pound of the fluid in order to produce simultaneously the indefinitely small variation of temperature d ¢, and the indefinitely small variation of volume dv, we find, dO dg dW =r (Glar+ fav) v dp ap =(t++ [° F¥-de)ast+r Paw; saeineneens (2.) which is the general equation of the expansive action of heat in a fluid. If this expression be analyzed, it is found to consist of the fol- lowing parts :— I. The variation of the actual heat of unity of weight of the fluid kd-. II. The heat which disappears in producing work by mutual molecular actions depending on change of temperature and not on change of volume, 8 ae T | - Tat od T The lower limit of this integral is made to correspond to the state of indefinite rarefaction; that is, of perfect gas, in which those actions are null. Let D = - be the density, or weight of unity of volume of the fluid; then we have, as a more convenient form of the integral, 2 poe e oF dv=— | a (3.) a 0 pF III. The latent heat of expansion,—that is, heat which dis- appears in performing work, partly by the forcible enlargement of the vessel containing the fluid, partly by mutual molecular actions depending on expansion, T ae dv. The heat, expressed in units of work, which must be communi- cated to unity of weight of a fluid to produce any given {finite INTRINSIC ENERGY OF A FLUID. 313 changes of temperature and volume, is found by integrating the expression 2. Now that expression is not the exact differential of any function of the temperature and volume; .consequently its integral does not depend solely on the initial and final condition of the fluid as to temperature and volume, but also upon the mode of intermediate variation of those quantities. The graphic represen- ee 2 that integral is the indefinitely prolonged area MA CBN in fig. 93, 247, Xntrinsic Energy of 2 Fluid— Another mode of analyzing the expression 2 of Article 246 is as follows :— ‘ I. The variation of actual heat, as before, & d 7. II. The external work performed, p dv, represented by an ele- mentary vertical band of the area V4 A C B Vj, fig. 93. III. The internal work performed in overcoming molecular forces, V1Z. -— : v 2 d tf gage det (792 -p) dv. Now this last quantity is the exact differential of a function of the temperature and volume, viz. :— A given value of § expresses the work required to overcome molec- cular forces, in expanding unity of weight of a fluid from a given state, to that of perfect gas; and the excess of the actual heat of the fluid above this quantity, or is the intrinsic energy of the fluid, or the energy which it is capable of exerting against a piston, in changing from a given state as to temperature and volume, to a state of total privation of heat and indefinite expansion. In fig. 93, the values of the intrinsic energy of the fluid in the conditions A and B are represented respectively by the indefinitely prolonged areas X V, AM, X Vg BN. The quantity above denoted by 8 is the same with that denoted by the same symbol in Article 238. Let the suffixes a, b, denote the states of the fluid at the beginning and end of any given series of changes of temperature and volume, and H, ,, the supply of heat from an external source necessary to produce those changes, ex- pressed in foot-pounds; then Hy — [ pdo=(kr-S)— (r= Sas vere (2.) that is to say, the excess of the heat absorbed above the external work 314 STEAM AND OTHER HEAT ENGINES. performed is equal to the increase of the intrinsic energy ; so that this excess depends on the initial and final states only, as already shown in Article 238. 248, Expression of the Thermodynamic Function iu Terms of the Temperature and Pressure.—The volume of unity of weight of a fluid v, its expansive pressure p, and its absolute temperature r, form a system of three quantities, of which, when any two are given, the third is determined. In the preceding Articles, the volume and temperature are taken as independent variables, and the pressure is expressed as a function of them. In some investi- gations it is convenient to take the pressure and temperature as in- dependent variables, the volume being expressed as their function. The following expression of the thermodynamic function in terms of this pair of independent variables is taken from an unpublished paper, which has been in the hands of the Royal Society of Edin- burgh since 1855 (see their Proceedings for 1855, p. 287). Let zo, as before, be the absolute temperature of melting ice; po vp, the pro- duct of the pressure and volume of unity of weight of the fluid, in the perfectly gaseous state, at that temperature (of which quantity examples are given in Table IT., at the end of the volume); then _ (x. Poo wen (Pee, a= (i+ 7 ) hyp log = bee ADs esssee(L) By the aid of the above equation, and of the following well known theorem :— vi Pa [Redes [Pode + rm Pere Suaissiaanes (2.) all the equations of the preceding sections are easily transformed. The graphic representation of the quantity denoted by the second term of equation 1 is of the fol- “< ‘ lowing kind (see fig. 95) :—Let \ abscisse measured along O X P 4 represent volumes occupied by ~ ay) one pound of the substance. Let wy, ordinates parallel to O Y repre- ‘ sent pressures exerted by it. It is required to find the second o Way x term of the thermodynamic func- Fig. 95 tion for the condition of the i substance corresponding to the point A, on the diagram, whose co-ordinates are O V, =v, and OP=V, A, =p; the absolute temperature being z Let A, T, be the isothermal curve of +. Then the indefinitely extended area X OP A, T, is what is represented by THERMODYNAMIC FUNCTION—APPLICATIONS. 315 [i rae. Let A, T, be the isothermal curve corresponding to the absolute temperature 7— Az, and cutting A, P||OX in A, Then the symbol pPadv [ya.4? represents the limit towards which the quotient area T, A, A, T, Az approximates, when A 7 is indefinitely diminished. By using the form of the thermodynamic function explained in this Article, the general equation of the expansive action of heat in a fluid is made to take the following form :— _ ae _ (x. Po% _ | p d®v s Tdh=dH=-de=(h+ M0 _, r Sadp) ds a form which is convenient in cases where the pressure and its mode of variation are amongst the primary data of the problem. It will be shown in a subsequent Article, that the constant part i + 20% 7 of the co-efficient of dr, is the dynamical specific heat of the fluid, in the state of perfect gas, under a constant pressure. - 249, Principal Applications of the Laws of the Expansive Action of Heat.—The relation between the temperature, pressure, and volume of one pound of any particular substance being known by experiment, the principles of the preceding Articles serve to com- pute the quantity of heat which will be absorbed or rejected by one pound of that substance under given circumstances; and conversely, in some cases when the quantities of heat absorbed or rejected under given circumstances are known by experiment, the same principles serve to determine relations between the temperature, pressure, and density of the substance. The chief subjects to which the principles of the expansive action of heat are applicable, are the following :—Real and apparent specific heat; the heating and cooling of gases and vapours by compression and expansion; the 316 STEAM AND OTHER HEAT ENGINES. velocity of sound in gases; the free expansion of gases; the flow of gases through orifices and pipes; the latent and total heat of eva- poration of fluids; the latent heat of fusion; the efficiency of thermodynamic engines. The last of those subjects is that to which this treatise specially relates; but in order to make it intelligible, it is necessary In the first place to give a summary of the principles of the subjects enumerated before it. 250. Beal and Apparent Specific Hieat.—These terms have been explained in a previous Article. The symbolical expression for the apparent specific heat of a given substance, stated in units of work per degree of temperature in unity of weight, is as follows :— dv OOP ie hcis a dH d-9 OF siavs UG ie age oe gig an ae In which the term k is the real specific heat, or that which actually makes the substance hotter, being a constant quantity; while the other term represents the heat which disappears in performing work, internal and external, for each degree of rise of temperature. d'@ d- dU es The co-efficients ae and dz, represent respectively the dt complete rates of variation with temperature of the thermodyna- mic function and heat-potential, under the circumstances of the particular case. With respect to liquids and solids, it is impossible to regulate artificially the mode of variation of the thermodynamic function to an extent appreciable in practice. For substances in these states, the apparent specific heat increases with rise of tem- perature at a rate which is slow, but which appears, as theory would lead us to expect, to be connected with the rate of expan- sion. For gases, the mode of variation of the thermodynamic function with temperature may be regulated artificially in an arbi- trary manner, so as to vary the apparent specific heat in an inde-: finite number of ways. It is customary, however, to restrict the term “Specific heat” in speaking of gases, to two particular cases; that in which the volume is maintained constant during the varia- tion of temperature, and that in which the pressure is maintained constant, as formerly explained in Article 210. The specific heat at constant volume, is expressed as follows, in units of work per degree, being deduced from the expression for the thermodynamic function in Article 246, equation 1 :— 2 Jq=Kj=h47[" OE easel) a REAL AND APPARENT SPECIFIC HEAT OF GASES. 317 For a theoretically perfect gas, Ki Mise cavneaets eeeadatsiesuasduad (2.4.) The specific heat under constant pressure, deduced from the expres- sion for the thermodynamic function in Article 248, equation 1, is as follows :— 7 Pv p dv 16=Kskto = 1 8 + EP v000.0(3.) For a perfect gas, a Po %o K, =k+ re Teen eae «(3.) being simply the real specific heat increased by the work performed by unity of weight of the gas in undergoing, at any constant pres- sure, the expansion corresponding to one degree of rise of tempera- ture ; a quantity of work which is constant for a given perfect gas 2 2 a £ and ant represent- ing the deviation of the laws of the elasticity of actual gases from those of the ideal condition of perfect gas, are so small, that their effects on apparent specific heat, though calculable, fall within. the probable limits of errors of observation in the direct experi- ments hitherto made on the specific heat of the more common gases, such as air and carbonic acid. Referring, therefore, to the detailed papers already cited in the Trans. of the Royal Society of Edinburgh, vol. xx., for computations of the effects of such devia- tions, it will be sufficient for practical purposes to consider the specific heats of gases as represented by the formule 24 and 3a. The specific heats of gases, as expressed in the customary way, by their ratios to that of water, are found by dividing the quantities in these formule by Joule’s equivalent (J), and may be thus ex- pressed :— under all circumstances. The quantities iG K Cy = zy? Cp = zz" oeceeeecenere aiginie Wiser (4.) Examples of specific heat, stated in both ways, are given in Table IL., at the end of the volume. Before the period of M. Regnault’s experiments on a great variety of gases and vapours, published in the Comptes Rendus for 1853, no trustworthy direct experimental determination of the specific heat of any gas or vapour existed, ex- cept an approximate determination by Mr. Joule, made in 1852, of the specific heat of air; for the results formerly relied upon have been shown to be erroneous. In one of the papers referred to in the preceding Article, however (Edinburgh Transuctians, 1850), the 318 STEAM AND OTHER HEAT ENGINES. dynamical specific heats of air had been computed from the follow- ing data :— Po %, from M. Regnault’s experiments 26214 foot-pounds. 7 = 493°-2 Fahrenheit. K,— K, =P% = 53-15 foot-pounds per degree of Fahren- 0 heit ; being the energy exerted by one pound of air in undergoing, at a constant pressure, the expansion corresponding to one degree of rise of temperature, and the mechanical equivalent of the latent heat of expansion of the air under those circumstances, which (as stated in Article 212) is 0:069 of a British thermal unit, = 53-15 772° Y= 2 , as deduced from the velocity of sound in air, assumed in the paper referred to as approximately = 1:4; but a more exact value is 1-408. Consequently, K 20% 1 _ 53:15 1 6 Y—1~~=«(0-408 of Fahrenhett. = 180°3 foot-pounds per degree _Po% YY _ pe, TS08 han: ae = {Ra K, = Zz Sa 53°15 x 0-408 = 180°3-+ 53-15 = 183-45 foot-pounds per degree of Fahrenheit. Hence is deduced the fol- lowing ratio of the specific heat of air under constant pressure to that of water, , oR a 8 ae e, according to M. Regnault’s experiments, published) _ OT irae DOI cosy esate acd paesasnieee caesecuma ieee esas one Diflerences, oscey seacge: sinest cetanveswncas saree 0-0002 * In the calculation published in 1850, y was assumed = 1-4, and cp was com- puted as = 0-24; but the calculation just given being founded on a more accurate value of y, is of course to be preferred as a test of the dynamical theory of heat. Mr. Joule’s approximate determination in 1852 was 0°28. According to the dynamical theory of heat, the apparent specific heat of a gas under constant pressure is sensibly the same at all pressures and temperatures, if the gas is nearly perfect. According to the hypothesis of substantial caloric, that specific heat diminishes as the pressure increases, according to a law which is stated in many treatises on physics, even of the most recent dates (in some, indeed, as confidently as if it were an observed fact). The experiments of M. Regnault, by which the specific heat of air under constant pressure was determined at various temperatures from—22° Fahr. up to 437° Fahr., and at various pressures of from one to ten atmospheres, and found to be sensibly the same under all these circumstances, constitute “experimenta crucis ” conclusive against HEATING AND COOLING BY CHANGE OF VOLUME. 319 ‘951. Meating and Cooling of Gases and Vapours by Compression and Expansion.—If a substance wholly or partially in the state of gas or vapour be enclosed in a vessel which does not conduct any appreciable amount of heat to or from the substance, then the com- pression and expansion of the substance through variations of the volume of the vessel will produce respectively heating and cooling, according to a law expressed by the condition, that the thermo- dynamic function ts constant. The following equations contain two modes of expressing this condition, deduced from the expressions in Articles 246 and 248 respectively :-— k hyp log + + r cp dv = constant, ......... (1.) oc 0 (+ me) hyp log 7 — ip ee dp = constant,...(2.) and each of those is the equation of an adiubatic curve. For a perfect gas, we have 2p _ Po, dv po, (3.) Gar er and eae eee eee es hence let p, v, correspond to one given absolute temperature 7, and p, Vv, to another given absolute temperature 7, ; then for a per- fect gay, or a gas sensibly perfect, log 22 =(y — 1) log 4 = 2—*. tog 22 ; 1 Vg Pi (4.) = 9 aes: or, PDs ye ZL = Pe nae Ty %e Py These equations give, for the law of expansion of a perfect gas, without receiving or emitting heat, the following relation between the pressure and the volume, pe ene a sigvb oueenineaa uals ee (5.) and this is the simplest form of the equation of an adiabatic curve for a perfect gas. The values of the several exponents in equations 4 and 5 for atR are, that “idolon fori,” the hypothesis of caloric. Those experiments also afford evidence of the fact, that the scale of the air thermometer sensibly agrees with that of absolute temperatures. 320 STEAM AND OTHER HEAT ENGINES. = 1°408 x | y—l1 — 0'408 ot 2°451 sy = 348 x = O71 ya" = 0°29 For straw in the perfectly gaseous state, taking (as in Article 202, equation 4), p) v = 42141, and according to M. Regnault’s experiments, K, = 772 x 0-48 = 371, we find, = 0°23. In the experiments of MM. Hirn and Cazin, the value of y + y —1 ranged from 4:23 to 4-47, (Annales de Chimie, 1867, vol. x.) These values, however, are not so certain as those of the corre- sponding quantities for air. From equation 1 is easily deduced the law of the variation of the pressure with the volume of any fluid, whether perfectly gaseous or not, enclosed in a non-conducting vessel, viz. :—the rate of variation of the pressure with the volume when the fluid is enclosed in a non-conducting vessel, exceeds the rate of variation when the temperature is constant, in the ratio of the apparent specitic heat of the fluid at constant pressure to its apparent specific heat at constant volume :—a law expressed symbolically as follows :— dp d‘p dz aig = = y* do seeeee Por eeerceeeneres (6.) dz VELOCITY OF SOUND IN GASES, 321 For a perfect gas this becomes, P dp : Zell? as equation 5 also shows. The cooling of air ly expansion has been applied to practical purposes by Dr. Gorrie, Professor Piazzi Smyth, Mr. Kirk, and other inventors. 252, Velocity of Sound in Gases.*—The velocity of sound in any fluid is well known to be equal to that acquired by a heavy body in falling through one-half of the height which represents the varia- tion of the pressure of the fluid with its’ density during a sudden change of density. That is to say, let a be the velocity of sound in feet per second, g the accelerating force of gravity in a second = 32:2 feet per second, D the weight of one cubic foot of the fluid : 1 ‘ 2 é in pounds = »? and p its elastic pressure in pounds per square foot, then a=a/g. Sade (1.) During the transmission of a wave of sound, the compression and expansion of the particles of a fluid take place so rapidly, that there is not time for any appreciable transmission of heat between dif- terent particles,t and the variations of the pressure and density are related to each other as they would be in a non-conducting vessel ; consequently, if 4 represents the rate of variation of pressure with density at a constant temperature, then it follows from the principle of equation 6, Art. 251, that oe = yh, and This equation was proved long ago by Laplace and Poisson, for perfect gases, for which h =pv= ee . ‘ia pevew evens quate seeinas (Oz) 7 but it is true, as we have seen, for all fluids whatsoever. Applying the formula to air, considered as a sensibly perfect gas, with the following data:— * In this Article the sounds are supposed to be of moderate intensity, so that there is no sensible acceleration of the sound due to the cause investigated by Mr. Harnshaw: as to which see Proc. Roy. Soc., 1859. { Proved by Prof. G. G. Stokes. Y 4 322 STEAM AND OTHER HEAT ENGINES. y = 1-408 5 po Uy = 26214; r=75 Feet The following is found to be the velocity of sound in per second. pure dry air at the temperature of melting ice, ....... 10g0°2 The velocity by experiment is— According to MM. Bravais and Martins, .............. 10g0"5 According to MM. Moll and Van Beek, .............. TOgo'L Experiments on the velocity of sound serve to determine the ratio v of the specific heats of a gas at constant pressure and at constant volume. For oxygen, hydrogen, and carbonic oxide, it is sen- sibly the same as for air; for carbonic acid, considerably less, — (Edinburgh Transactions, vol. xx.) 253. Free Expansion of Gases and Vaponrs.— When the expan- sion of a gas takes effect, not by enlarging the vessel in which it is contained, and so performing work on external bodies, but by propelling the gas itself from a space in which it is at a higher pressure p, into a space in which it is at a lower pressure po, a portion of energy represented by | P21 vdp P2 is employed wholly in agitating the particles of the gas; and when the agitation so produced has entirely subsided through the mutual friction of those particles, an equivalent quantity of heat is developed, which neutralizes the previous cooling, wholly if the gas is perfect, partially if it is imperfect. The equation representing the result of this process is the following :— [erao= POO ohana ee (1.) $1 Pa In this equation, let the thermodynamic function be expressed in terms of the temperature and pressure, as in Article 248, and let K, be put for its own value, according to Article 250, equation 3; then we have [2K -¢e=|” (42 — \ ap ae (2.) ca) P2 de This quantity represents the amount whereby the heat reproduced by friction falls short of that which disappears during the expan- sion, and for a perfect gas is null. The phenomenon here in ques- tion was first employed by Mr. Joule, and Professor William Thom- son, jointly, to determine experimentally the relation between the absolute scale of temperature, and that of the air thermometer, which had previously been,to a considerable extent a matter of FREE EXPANSION OF GASES—CARNOT’S FUNCTION. 323 conjecture and hypothesis. In such experiments the variation of temperature which takes place is very small, hence we may put approximately d P K, ar=(-#_1) CT nes (3.) v P2 where + is the mean of =, and ,, and Acg= | % is the final cooling effect. Let T represent temperature measured by the air thermometer on the ordinary scale, and & the dynamical specific heat of the gas under constant pressure as referred to this scale, which is formed by multiplying the specific heat as given by M. Regnault, by Joule’s equivalent. Let the absolute tempera- ture + be regarded as a function of T, +=f(T) whose form is to be ascertained. Then for equation 3 we may put bat= (FE) gp —1) [Reap ae (4.) Each experiment, on cooling by free expansion, gives a value of the cooling effect a T, corresponding to a particular pair of pressures Py P> The relations between p, v, and T, are given by formule, founded on M. Regnault’s experiments on the elasticity of gases, and already exemplified in Article 202, equations 2 and 3. Conse- quently from each experiment on free expansion, there can be cal- culated the value of one d ae for a particular tempe- rature T on the air thermometer. This function, when multiplied by Joule’s equivalent, is called “ Carnot’s Function,” being a function of which Carnot pointed out the existence, but failed, from reasons stated in the historical sketch, to discover the form. Those experi- ments on free expansion, so far as they have yet been carried (having been made on air anc carbonic acid), indicate, that the absolute zero of heat does not appreciably differ from that of gaseous tension, and that the scale of absolute temperature sen- sibly coincides with that of the perfect gas thermometer. (Phil. Trans., 1854.) This fact having been established, experiments on free expansion become an easy and accurate means of ascertaining the relations between the pressures, temperatures, and densities of varjous elastic fluids. Experiments on the free expansion of steam B24 STEAM AND OTHER HEAT ENGINES, have been made by Mr. C. W. Siemens, and show (as theory leads us to expect), that steam, after having been freely expanded, is superheated, or above the temperature of saturation corresponding to its pressure. 254, Blow of Gases.—The principles of the flow of a perfect gas through an orifice, as deduced from the laws of thermodynamics, were investigated in 1856 by Messrs. Thomson and Joule (see Proc. Roy. Soc., May, 1856), and by Professor Julius Weisbach (Ciwilin- gemieur, 1856). The demonstration of those principles is given in A Manual of Applied Mechanics, Articles 637, 637 a. For the purposes of the present treatise, it is unnecessary to give more than the results. Let the pressure, density, and absolute temperature of a gas within a vessel be p,, —, 71, and without the vessel, p., —, 7; v “9 Let O be the area of an orifice through which the gas escapes from the vessel ; kh, a co-efficient of contraction, or of efflux, so that the effective area -of the orifice is £ O; V, the maximum velocity which the particles of the gas acquire in escaping, when there is no friction; W, the weight of the gas which escapes in a second; then, 297 Po? ‘Pa\7— Wis fe Lo “0 "3 ‘(i- ve) 7 yi 1 / y-1 7 Yat . (*) , 1 w= fOV 2 Lov: “oP. . (23), oe (2) v, Pot Py The value of the co-efficient of efflux & has been found experi- mentally by Professor Weisbach, for air with various forms of outlet, with the following results :— Conoidal mouthpieces, of the form of the vom i tracted vein, with effective pressures of from 097 to 0'99 23 to 1:1 atmosphere, ............ ce cceseseee tees Circular orifices in thin plates,.........eccecceceeeeeeee 0°55 to 0°79 Short cylindrical mouthpieces,.......... Seis teaiersesiss 0°73 to 0°84 The same, rounded at the inner end, ................. 0°92 to 0°93 Conical converging mouthpieces, the angle of : convergence about 7° 9,....see.s000. goncaceeauats \ 0°90 to 0°99 For values of y, &c., see page 320. As to the outflow of saturated steam, see page 298. The principles of the flow of liquids may be applied without sensible error, to gases made to flow by small differences of pres- sure, as in the case of the draught of chimneys, Article 233, LATENT HEAT OF EVAPORATION. 325 255. Latent Heat of Evaporation.—It is known by experiment, that the pressure under which a fluid boils at a given temperature (being the least pressure under which it can exist in the liquid state, and the greatest under which it can exist in the gaseous state, at the given temperature), is a function of the temperature only (see Article 206, Division IIL. page 237, and Tables IV., V., and VL, at the end of the volume). Let v’ be the volume occupied by one pound of a fluid, when in the liquid state, at the absolute temperature 7, and under the corresponding pressure of ebullition p, and v the volume of the same weight when in the state of saturated vapour at the same pressure and temperature. Then on applying equation 2, of Article 246, to this case, we find that because the temperature is constant, the first term is = 0; and because the dp pressure is constant, the factor 7 7 Tt of the second term is constant ; so that the integral is d r H= 72 SHO gsieagtrceahenaina a) which is the value in units of work of the heat which disappears in evaporating one pound of the fluid at the given temperature. Now suppose the weight of fluid evaporated to be . : ye that is to say, so much of the fluid, that its increase of bulk in the act of evapor- ating is one cubic foot; then L= H dp =r 2 pe v = d pO Ry SG RE CRS aR eRe n ees (2.) will be the latent heat of evaporation in foot-lbs. per cubic foot of space. This law enables us to compute the quantity of heat expended in propelling a piston through a given space, by means of a given vapour at full presswre and at any temperature, simply from the relation between the temperature and the pressure of ebullition, and without knowing the density of the vapour. The rate of increase of the pressure of ebullition with the temperature, ap, may be computed either from a table of such pressures for the fluid in question (such as those given by M. Regnault in the Memoires and Comptes Rendus of the Academy of Sciences), or from formulz of the following form, deduced from that given in Article 206, Division III. :-— L=-92=p(2 + 25) hyp log 10,.....++0.-.(3.) Bo) (hyp log 10 = 23026 nearly). 326 STEAM AND OTHER HEAT ENGINES. For the values of B and C for certain fluids, see the table in page 237. pis of course to be computed in lbs. on the square foot. This was the formula employed in computing the numbers in the columns headed L in Tables IV. and V. at the end of the volume. 256. Computation of the Density of Vapour from the Latent Heat, —As has been stated in Article 202, and in Article 206, Division TIL., the densities of vapours are but imperfectly known by direct experiment. The density of a vapour at saturation at a given temperature may be computed indirectly in the following man- ner :—Let L be, as above, the latent heat per cubic foot, and H the latent heat per pound of the fluid, ascertained by experiments (such as those of M. Regnault on water, and of Dr. Andrews on other fluids). Then is the increase of volume of one pound of the fluid in evaporating, from which the density of the vapour is easily calculated. The densities, thus computed, of the vapours of zether and sulphuret of carbon, at their boiling points under the mean atmospheric pressure (2116-3 Ib. per square foot) agree almost exactly with those com- puted from the chemical composition of those vapours, supposing them to be perfectly gaseous. The densities of the vapours of water and alcohol as computed from their latent heats of evaporation, are greater than those corresponding to the perfectly gaseous state. For steam at low pressures the difference is trifling, but increases rapidly as the pressure increases. (Proc. Roy. Soc. Hdin., 1855.) ELxample.— p = 2116-3 (one atmosphere). Ether. Bisulph. of Carbon. Water. Boiling points (ordinary scale), 95° 114°8 212° Weight of one cubic foot of vapour— Calculated from latent heat,... 0°1853 lb. o-1829 Ib. 0°03790 Ib, Calculated as perfect gasfrom | _, : eBin chemical composition,...... i Differences,............ 00003 0'0001 O‘OOIII The quantities, in the column headed D, in Table IV., are the values of — as calculated by this method. They agree so : 1 nearly with the values of ? that the difference, though capable of being computed, is unimportant in practice. In Table VI., the TOTAL HEAT OF EVAPORATION—OF GASEFICATION. 327 values of v are given in the column headed V. (See the remarks on those tables at the foot of page 231, and top of page 232.) 257, Total Meat of Evaporation.—The total heat of evaporation of unity of weight of a fluid, from one temperature, at another tempe- rature, is the quantity of heat required to raise the temperature of unity of weight of the fluid from the first temperature to the second, and then to evaporate it at the second temperature. Some fixed temperature, such as that of melting ice, is usually taken for the first temperature. It is deducible from equation 3, of Art. 248, that the total heat of evaporation of one pound of a fluid, whose vapour is sensibly a perfect gas, and very bulky as compared with the liquid, from +, at +, is sensibly equal to aie halon es aotae (1.) In which Hy, is latent heat of evaporation, in foot-pounds, of the fluid at the temperature 7), and K, is the dynamical specific heat of its gas under constant pressure. This equation is demonstrated by a different process in the Edinburgh Transactions for 1850, vol. xx. The demonstration of a principle which includes it will be given in the next Article. Steam is nota perfect gas; and its total heat of evaporation, as ascertained by experiment, is expressed in foot-pounds, by multiplying equation 2 of Article 215, by Joule’s equivalent, as follows :— Ge) ener ei ced in which @ is a certain constant, less than the specific heat under constant pressure, K,. According to M. Regnault’s experiments, let +) be the absolute temperature of melting ice; then H, = 842872 pounds. a z= 235 foot-pounds per degree of Fahrenheit.* It is by means of equation 2, that the quantities in the column headed H, in Table VI., at the end of the volume, were com- uted. : 258. Wotal Heat of Gasefication—The law of the total heat of gasefication has been already stated in Article 215 B (or 216, as it ought to have been numbered). It may be demonstrated, either by the aid of the form of the thermodynamic function given in Article 248, or by a direct process. The first method of demonstration is as follows :— * The form of equation 2 was hypothetically anticipated by the late Sir John Lubbock in 1840. 328 STEAM AND OTHER HEAT ENGINES. Let K,=% + be the dynamical specific heat under constant T, 0 pressure, of a given substance in the state of perfect gas. Let T, be a temperature so low, that the saturated vapour of the substance is sensibly a perfect gas at that temperature. (This, for example, is the case for water at 32° Fahr.) Let p, be a constant pressure to which the substance is sub- jected ; : Let T, be a temperature so high, that at that temperature, and under the pressure p,, the substance is sensibly a perfect gas ; Let the substance, by communicating heat to it, be brought from a condition of great density, whether in the liquid or solid state, at T,, to the perfectly gaseous condition at T, ; under the constant pressure 7; The volume in the denser condition must be supposed to be inap- preciable, when compared with that in the gaseous condition. The thermodynamic function, as given in Article 248, in terms of the absolute temperature and the pressure as independent variables, is pd o = Ky hyp log r— | Sadie hawaacinne (1) o as The heat absorbed by the substance, during any indefinitely small change of temperature d + and of pressure dp, is dQ do j dH = do=-(70de+7) dp see eeeeae ees (2.) In the present case, the pressure is constant; and therefore the term in which d p is a factor, vanishes; and the integration to be performed is as follows :— Ra [etom [0 ee 70 c d2 = Ky(1—=)— [ ae Frag ADA tivstcnryee (Bh) Tv) 0 t Now, because the substance, when at the higher limit of tempera- . . 2 ture 7,, is sensibly a perfect gas, the covefticient % at that tempe- T rature is sensibly =0. Therefore the value of the second term of the above formula does not sensibly vary with the higher tempera- ture 7,, and is sensibly the same as if +, were = ry Now in that case we should have TOTAL HEAT OF GASEFICATION. 329 H, = Hy, Hy being the latent heat of evaporation (in foot-pounds), of one pound of the substance at the temperature 7); so that, for equa- tion 3, may be substituted the following :— Jh, =H, = Hy + Ke (n - %) iT dtd Glia Tiras) which is the law formerly stated, when applied to quantities of heat expressed in foot-pounds. The second method of demonstration is as follows :— In fig. 96, as usual, let ab- ,. Ty scisse parallel to O X repre- sent the volumes in cubic feet a 2 assumed by one pound of the substance in question, when in the gaseous state (its vo- D c Ty lumes in the liquid state being neglected as inappreciable when compared with its vo- ° E ee lumes in the gaseous state), ae and ordinates, parallel to O Y, its pressures in pounds on the square foot. Let TT be the tsothermal curve for the vapour at a given absolute temperature +,, which, as the vapour is perfectly gaseous, is a common hyperbola, the rectangles of its co-ordinates, such as ABX BE, DC x CF, being equal for every point, and represented symbolically by 4 t pv=p' v =po% ‘— = constant F, 0 wherep=BE; v= AB; yp =CF; J =DC. Let H, H' denote the values of the total heat of gasefication under the pressures p, p’ respectively, for the same limits of tem- perature, 7), 7. Then, First, The total heat of gasefication is independent of the pressure: that is, H’ = H. This is proved as follows. Let the substance undergo the fol- lowing cycle of operations :— I. Gasefication from +, to +,, under the pressure p. In this case, The heat absorbed is ..............0068 seeemenenete aevesabh The energy exerted by the fluid on a piston........p v II. Expansion at the constant temperature 7,, from the volume 330 STEAM AND OTHER HEAT ENGINES. v to the volume v’. In this case, as the substance is perfectly gaseous, the heat absorbed and the energy exerted on a piston are each of them represented by the area ¥ av EBC F=ABCD= i, pdy= fc odp. v Pp IIT. Condensation from ,, and cooling to 79, under the pressure In this case, The heat given OUt i8....csecseeecescesccecneeeaeeeeeetes H The energy exerted by the piston on the fluid....... pv. # Pp. Hence, the heat which disappears during the cycle of operations, is H+ | pdv—H The resultant or effective energy exerted by the gas on the piston, =area ABOD=/vdp= [pde. And by the First Law of Thermodynamics, those quantities are equal ; therefore, EE 05 OP ah Scat cadecasenesessgcoamncwss —Q. E. D. Srconpiy, Let H, be the latent heat of evaporation at a tem- perature Ty, at which the saturated vapour is sensibly a perfect gas, and H, the total heat of gasefication at any higher temperature T, under any constant pressure. Suppose the gas to be first produced. by evaporation at Ty, and then raised under a constant pressure to T,; the expenditure of heat, in foot-pounds, per pound of gas, will be independent of the pressure, and will be H, =H) + Ky (T, —T)), as before proved.—Q. E. D. Taking for T, the temperature of melting ice, we have, for steam in the perfectly gaseous condition, or StEam-Gas, Hy, = 842872 foot-pounds, Kp= 0-48 x 772 = 371 foot-pounds per degree of 5 Fahrenheit above 329, 0 sa (5.) H = 842872 + 371 (T — 32°), From this formula have been calculated the numbers in the STEAM-GAS—-LATENT HEAT OF FUSION. 331 column headed H, in a Zable of the Elasticity and Total Heat of One Pound of Steam-Gas, which will be given in a subsequent Article. 258 A. Latent Heat of Eusion.—When freezing and melting are accompanied by a change of volume, the latent heat of fusion is sub- ject to a law analogous to that given in Article 255 for the latent heat of evaporation, viz., let » be the volume of unity of weight of the substance in the liquid state, v’ the volume in the solid state, dp dt rate at which that temperature varies with the external pressure under which fusion takes place ; then the latent heat of fusion, in units of work, is z the absolute temperature of fusion, and the reciprocal of the When the latent heat and temperature of fusion, and the alteration of volume v—v’, are known by experiment for a given substance, the alteration of the temperature of fusion by pressure may be com- puted by the following formula :— dz _ +(v—v) Tp ee (2.) ‘When the bulk of the substance in the solid state exceeds that in the liquid state (as is the case for water, antimony, cast iron, and dt according to Mr. Nasmyth, for many other substances), then aP is negative: that is, the temperature of fusion is lowered by pressure ; a principle first pointed out by Mr. James Thomson, as a conse- quence of Carnot’s theory (Edinburgh Tramsactions, vol. xvi.) For water we have the following data :— » = 0-016 cubic foot per pound, vo = 00174 53 53 x = 493°-2 Fahr. H= 142 X 772 = 109624 foot-pounds ; = 0-0000063 Fahrenheit, being the amount by which the melting point of ice is lowered for each pound of pres- sure on the square foot. An atmosphere of pressure being 2,116 lbs. per square foot, we have, for the lowering of the melting point per atmosphere of pressure, consequently, — 332 STEAM AND OTHER HEAT ENGINES. 116 x (— s) = 0°-0133 Fahrenheit, a result verified by the experiments of Professor William Thomson, Section 3.—H ficiency of the Fluid in Heat Engines in general. 259. Analysis of the Efficiency of Heat Engines.—If the number of British thermal units produced by the combustion of one pound of a given kind of fuel, be multiplied by Joule’s equivalent, 772 foot-pounds, the result is the total heat of combustion of the fuel in question, expressed in foot-pounds. For different kinds of fuel, as may be deduced from the data in Article 227, this quantity, in round numbers, ranges between 5,000,000 and 12,000,000 foot- pounds. This total heat is expended, in any given engine, in pro- ducing the following effects, whose sum is equal to the heat so expended :— 1. The waste heat of the furnace, being from 0:1 to 0°6 of the total heat, according to the construction of the furnace, and the skill with which the combustion is regulated. See Article 234. 2. The necessarily-rejected heat of the engine, being the excess of the whole heat communicated to the working fluid by each pound of fuel burned, above the portion of that heat which permanently disappears, being replaced by mechanical energy. 3. The heat wasted by the engine, whether by conduction or by non-fulfilment of the conditions of maximum efficiency. 4, The useless work of the engine, employed in overcoming fric- tion and other prejudicial resistances. 5. The useful work. The efficiency of a heat engine is improved by diminishing as far as possible the first four of those effects, so as to increase the fifth. It appears then that the efficiency of a heat engine is the pro- duct of three factors; viz.:—I. The efficiency of the furnace, being the ratio which the heat transferred to the working fluid bears to the total heat of combustion ; II. The efficiency of the fluid, being the fraction of the heat received by it which is transformed into mechanical energy; and, IIT., The efficiency of the mechanism, being the fraction of that energy which is available for driving machines. The first of those factors,—the efficiency of the furnace,—has been considered in Chapter IT., and especially in Article 234: the second,—the efficiency of the’ fluid,—is the special subject of the present section; the third will be considered in a subsequent section. 260. Action of the Cylinder and Piston—Indicated Power.—The part of a heat engine in which the fluid performs work consists CYLINDER AND PISTON—INDICATED POWER. 333 essentially of an enclosed space whose volume is capable of being alternately enlarged and contracted, by the motion of one of its boundaries. The enclosed space is of a cylindrical form, in all engines that are extensively used in practice; and it is called the CYLINDER, even in those exceptional engines in which it has some other figure. Its moveable boundary is called the Pisron, and is usually a cylindrical disc fitting the cylinder, in which it moves to and fro in a straight line. In some exceptional engines the piston has other forms, but its action always is to increase and diminish alternately the volume of a certain enclosed space. The steam or other working fluid, while it is entering the cylin- der and expanding, drives the piston before it, and exerts on the piston an amount of energy equal to the product of the volume swept through by the piston into the mean intensity of the pressure of the fluid. This operation is the forward stroke. During the return, or backward stroke, the piston drives the fluid before it, and either expels it from the cylinder, or compresses it, or expels part and compresses part; and in so doing the piston exerts energy upon the fluid to an amount equal to the product of the volume swept through by the piston into the mean intensity of the pressure of the fluid, which is now called back pressure. The excess of the energy exerted by the fluid on the piston dur- ing the forward stroke above the energy exerted by the piston on the fluid during the return stroke, is the effective energy exerted by the fluid on the piston during one complete stroke, or revolution, consisting of a forward stroke and a return stroke, and is equal to the work performed by the piston in overcoming resistance other than the back pressure of the fluid; and the amount of that work in some definite time, as a second, a minute, or an hour, is the INDICATED POWER of the engine. The method of computing that power from the diagram drawn by the indicator of a working engine has been explained in Article 43. It is to be borne in mind in such calculations (as has been ex- plained in Article 6), that the spaces swept through by the piston, and the intensities of the pressure, must be stated in such units that the product of a space into the intensity of a pressure shall give a quantity of work in foot-pounds. Thus, for quantities of work in Joot-pounds— UNIT OF PRESSURE. UNIT OF SPACE. One lb. on the square foot. One cubic foot. . One Ib. on the square inch. A prism a foot long and an inch square, = ee cubic foot ; 334 STEAM AND OTHER HEAT ENGINES, and for quantitics of work in hilogrammetres— UNIT OF PRESSURE. UNIT OF SPACE, One kilogramme on the square MELE). scerevevsscecseeer seeeneess One kilogramme on the square COntIMetLle,....escceeseevereceees i One cubic metre. cubic metre = D litre, 1 1 3 One kilogramme on the square | | ~~~. cubic metre = --—_. millimetre, .......-.seeseeeeneeee Set 1,000 The method of computing the power of a double-acting engine, by finding separately the quantities of effective energy exerted on the two sides of the piston, and adding them together, has been sufficiently explained and illustrated in Article 43, pages 50, 51. 261. Double Cylinder Engines—Combination of Diagrams —In a double cylinder engine, the steam or other fluid performs its work in two cylinders, a smaller and a larger, which at certain periods communicate with each other. In some cases the functions of two cylinders are performed by the two ends of one cylinder. The details of such engines will be explained in a future chapter; the object of the present Article being to show how the indicator-dia- grams of work obtained from a double cylinder engine are to be combined, so as to produce the diagram that would have been obtained had the fluid performed the same work by going through the same series of changes of pressure and volume in one cylinder. Ff — \ 10,000 BC D ¥ K G EH Na, BR — L Ss P Oo Wr Q Fig. 97. To fix the ideas, the fluid will be spoken of as steam; although the principles are applicable to any fluid. The steam, then, is first admitted from the boiler into the smaller cylinder, until it fills a certain volume, represented by B C in fig. 97 ; the absolute pressure is represented by the height of B C above the zero line POQ. The admission of the steam is then cut off, and it expands in the smaller cylinder with a pressure gradually diminishing, as shown by the ordinates of the curve CD. DWN being let fall perpen- dicular to O Q, ON represents the whole space swept through by DOUBLE-CYLINDER DIAGRAMS. 335 the piston of the smaller cylinder during its forward stroke. At the end of that stroke, a communication is opened between the smaller and the larger cylinder; and the forward stroke of the piston of the larger cylinder takes place at the same time with the return stroke of the piston of the smaller cylinder. During this process, the steam is driven before the piston of the smaller cylinder, and drives the piston of the larger cylinder; it exerts more energy on the latter piston than it receives from the former, because the piston of the larger cylinder sweeps through the greater space; and the difference between those quantities of energy is added to the energy formerly exerted by the steam on the piston of the smaller cylinder. This part of the action of the steam is represented by the curves DA and EF: the ordinates of D A representing the backward pressures exerted by the steam in the smaller cylinder, and the ordinates of E F, the forward pressures exerted by it at the same time in the larger cylinder. OP represents the space swept through by the piston of the larger cylinder, on the same scale with that according to which ON represents the correspond- ing space for the smaller cylinder. The next operation is to shut the communication between the two cylinders, and open the exhaust port of the larger cylinder, and the admission port of the smaller. Then takes place the return stroke of the larger cylinder, during which the steam is expelled, exerting a back pressure represented by the ordinates of FA; while at the same time a new portion of steam is admitted into the smaller cylinder, and expanded as before, during a new forward stroke of that cylinder. Thus are produced the two indicator diagrams, B C D A B for the smaller cylinder, and EF A E for the larger, and the sum of their areas represents the energy exerted on the piston by the quantity of steam which is expended at one stroke. When two such diagrams are taken by an indicator, for the sole purpose of computing the power of an actual engine, they may be drawn on the same or on different scales, and the quantities of work indicated by them may be computed independently, and then added together. _ Of this a detailed example has already been given in Article 43, e 51. ao if the diagrams are to be used for the purpose of examining into the thermodynamic relations between heat expended and work performed, or for other scientific purposes, it is best to combine them into one diagram, in the following manner :— Draw any straight line K GH parallel to P O Q, and intersect- ing both diagrams. Produce that line, and lay off upon it HL=-kG 336 STEAM AND OTHER HEAT ENGINES. Then GL = GH + K G represents the total volume occupied by the steam, partly in the smaller and partly in the larger cylinder, when its absolute pressure is represented by OG; and L is a point in the indicator diagram which would have been described had the whole action of the steam taken place in the larger cylinder only. By drawing a sufficient number of parallel lines, such as K L, and laying off the proper distances on them, as above, any number of points such as L may be found, so as to complete the combined diagram BCD LM AB, whose length O Q = O P represents the volume swept through by the piston of the larger cylinder; and this diagram may be reasoned about as if it represented the action of the steam in the larger cylinder alone. It is to be observed, then, as a general principle, that the energy exerted by a given portion of a fluid during a given series of changes of pressure and volume, depends on that series of changes, and not on the number and arrangement of the cylinders in which those changes are undergone. 262. Fluid Acting as a Cushion.—To determine geometrically the efficiency of a heat engine, it is necessary to know its true indicator diagram; that is to say, the curve whose co-ordinates represent the successive volumes and pressures which the fluid working the engine assumes during a complete revolution. This true indicator diagram is not necessarily identical in figure with the diagram described by the engine on the indicator card; for the abscisse representing volumes in the latter diagram, include not only the volumes assumed by that portion of the fluid, which really performs the work by alternately receiving heat while ex- panding, and emitting heat while contracting, in such a manner as permanently to transform heat into mechanical energy, but also - the volumes assumed by that portion of the fluid, if any, which acts merely as a cushion for transmitting pressure to the piston, under- “ going, during each revolu- tion, a series of changes of a pressure and volume, and =e then the same series in an eas Z order exactly the reverse Coe of the former order, so as as to transform no heat per- G c ¢ : : manently to mechanical energy. In fig. 98, let aded be xx the apparent indicator dia- Fig, 98. gram. Parallel to OX draw Ha and Le, touching this diagram in a and c respectively; E A rn ACTION OF FLUID ON PISTON, 337 then those lines will be the lines of maximum and minimum pres- sure. Let H E and LG be the volumes occupied by the cushion at the maximum and minimum pressures respectively: draw the curve EG, such that its co-ordinates shall represent the changes of volume and pressure undergone by the cushion during a revolution of the engine. Let K Fdb be any straight line of equal pressure, inter- secting this curve and the apparent indicator diagram; so that K, Kd shall represent the two volumes assumed by the whole elastic body at the pressure OK, and KF the volume of the cushion at the same pressure. On ‘this line take bb=adD=KE; then it is evident that B and D will be two points in the true indicator diagram; and in the same manner may any number of points be found. The area of the true diagram A BC D is obviously equal to that of the apparent diagram a bc d. 263, Formulx for Energy exerted by Fluid on Piston. — In fig. 99, let ABCDEA repre- sent the indicator diagramof P| 8 c a heat engine, O V as usual ( \ being the line of no pressure, H and O P that of no volume. we The area of that diagram, ql IV on representing the effective %/— ir AO energy exerted by a certain Ke —) quantity of the fluid, may be LA Ly [a 8 computed and expressed by .|_} : es either of two methods. ® "Vig. is = First Method.—Let the dot- ted lines Bb, Ee, be tangents to the diagram, parallel to OP, so that Oc =r; 0b=0'; are respectively the greatest and the least volumes occupied by the quantity of fluid in question. Let F G= v represent any small portion of the change of volume undergone by the fluid. Draw F LH, GM K, perpendi- cular to OV; and let e = mean of F H and GK, and p' =mean of FL and GM, represent the mean intensities of the pressures of the fluid when the ‘portion of the change of volume represented by F 'G=av takes Zz 338 STEAM AND OTHER HEAT ENGINES. place, during the forward stroke, and during the return stroke respectively, so that ; P—P is the effective pressure corresponding to F G. Then, (p—p’) sv =area LH KM nearly ; and by dividing the whole diagram into a number of bands, such as LH K M, and adding their areas together, we get as an approxi- mation to the whole area of the diagram, U=3 §(p—p’) av} nearly; being the value already given in Article 43. The exact value of that area is the limit towards which that sum approximates, as the bands into which the diagram is divided become more numerous and more narrow. That limit, or integral, is represented by the symbol, v9 oe U= [7 @—p) do aii eainaciee oe Second Method.—Let p, represent the greatest, and p, the least intensity of the pressure of the fluid during its action. Let N Q = 4 > represent any small portion of the change of pres- sure undergone by the fluid. Draw NTR, Q WS, perpendicular to OP, and let v =mean of N Rand QS, and vo = mean of NT and QW, represent the mean volumes occupied by the fluid when the portion of the change of pressure represented by N Q = 4 p takes place, during the forward stroke and during the return stroke respectively. Then, : (v—v') Ap=area WS RT nearly; and by dividing the whole diagram into a number of bands, such as WS RT, and adding their areas together, we get as an approxima- tion to the whole area of the diagram, U=2{(v—v) 4p} nearly. The exact value of that area is the limit towards which that sum approximates, as the bands into which the diagram is divided become more numerous and more narrow. That limit, or integral, is represented by the symbol EFFECTIVE PRESSURE—INDICATED POWER. 339 U= [P (V—V) Od Djrercceee seeedeateets (2.) being a result equal to that given by equation 1, but obtained by a different process. The first method is the best for measuring the work indicated by the diagrams of actual engines. The second is the most convenient in some theoretical inquiries. It is always most convenient to consider the quantity of fluid to which the equations 1 and 2 refer, as being ONE POUND; so that they give the energy exerted per pound of fluid, and the values of v are simply the various volumes occupied by one pound at dif- ferent periods of the revolution of the engine. To express the energy exerted per unit of space swept through by the piston (or in a double cylinder engine, by the piston of the larger cylinder), it is to be observed, that the space so swept through per pound of fluid employed, is the difference between the greatest and least volumes occupied by one pound; that is to say, V_— P55 so that, THE ENERGY EXERTED PER UNIT OF VOLUME SWEPT THROUGH U _[e-r)de_fo-») ame (3.) Vg— V,— Vy V_— Vy If the unit of volume is a cubic foot, this formula gives the mean effective presswre in pounds on the square foot; if the unit of volume is a prism a foot long and an inch square, the formula gives the mean effective pressure in pounds on the square inch. The ENERGY EXERTED IN A GIVEN TIME (such as a minute, or an hour), that is, the INDICATED POWER, is given by the expression, in which w is the weight of fluid employed in the given time ; or otherwise, as in Article 43, equation 4, by the expression, NAsU Se ee co 5. moe (5.) in which A is the area, and s the length of stroke of the piston (or of the piston of the larger cylinder, in a double cylinder engine) ; so that A sis the volume swept through per stroke; and N is the number of strokes in the given time; which number, in a double acting engine, is to be doubled, as has been explained in Article 43, unless the quantities of energy exerted on the two sides of the piston are computed separately, and added together. 340 STEAM AND OTHER HEAT ENGINES. Inasmuch as we have NAs w= 0, See eee e eee ceeeeneeeesseee (6.) it follows that the weight of fluid employed per stroke is w As N = V = vy Cee ee neem neem rece neeee (7.) If the diagram in fig. 99 is held to represent the energy exerted by one pound of the fluid, then the abscisse parallel to OV represent simply values of v, the volume of one pound. If the diagram is held to represent the energy exerted per unit of volume swept through, then the line 6 ¢ represents that unit, and the abscisse parallel to O V represent values of If the diagram is held to represent the energy exerted during one stroke, then the line be represents the volume A s, and the abscisse parallel to O V represent values of vAs sia aiaceanmaicaapeemariycaunest (9.) Vg — Vy The quantity spoken of as the “weight of fluid employed” in every cage means, the weight of fluid employed once; and if a given weight of fluid (as often happens) is made to act again and again, it is to be held to be equivalent to the same weight multi- plied by the number of times that it is envployed. 264. Equation of Energy and Work.— The principle of the equality of energy and work (Articles 26, 33) when applied to the action of the fluid in a heat engine, takes the following form :— When the engine is moving with an uniform periodical motion (that is, when each stroke occupies an equal interval of time, and when the velocity of each part of the machine is the same after any number of complete strokes), the energy exerted by the fluid on the piston during any number of complete strokes is equal to the work performed by the piston in overcoming resistance in the same period. The most convenient method of expressing this principle by a formula is as follows:— As in Articles 9 and 24, let all the resistances, useful and pre- judicial, which the engine has to overcome, be reduced to the piston as a driving point. For example, suppose that while the piston performs a stroke, of the length s, a given part of the mechanism a EQUATION OF ENERGY AND WORK. 341 moves through the distance s’, against the resistance R’. Then tbe equivalent resistance, directly applied to the piston, is 8 ? and the total resistance reduced to the piston, obtained by adding together all such quantities as the above, may be denoted as tollows :— g 8 Now if N be taken, as in the last Article, to denote the number of strokes in a given time, such as a minute, the work performed by the piston in that time is NS Ris NPS Rss ic cctte eetienjeae ss (2.) and this being equated to the energy exerted by the fluid on the piston in the same time, as given in Article 263, formule 4 and 5, gives for the equation of energy and work, the following :— NAsU Vg — Vy BS SS Pie cmuenennntia (1.) NsR=wt= Another form of expression for the same principle is obtained by dividing both sides of the above equation by N s A, as follows :— RU Now the first side of this equation is the total resistance per unit of area of piston; and the second side is the mean effective pressure of the fluid; so that the principle expressed by it may be stated as follows :— In a heat engine moving with an uniform periodical motion, the mean effective pressure of the fluid is equal to the total resistance per unit of area of piston. The proper mode of applying this principle to the steam engine was first pointed out by tie Count de Pambour in his works On Locomotives, and on the Theory of the Steam Engine. It may be summed up as follows, leaving the details to be explained further on :— The resistance is in general determined by the nature of the work performed by the engine; so that in most cases, R is known from data independent of the action of the fluid. The resistance being a fixed quantity, fixes the mean effective -- pressure according to equation 4; in other words, the action of the 342 STEAM AND OTHER HEAT ENGINES, fluid adjusts itself until the mean effective pressure balances the resistance. The process by which that adjustment takes place may be stated generally thus :—if the mean effective pressure is at first greater than the resistance, the motion of the engine is accelerated ; that is, the number of strokes in a given time is increased; the quantity of heat expended per stroke is diminished; and the mean effective pressure is diminished; and this goes on until the mean effective pressure exactly balances the resistance. If the mean effective pressure is at first less than the resistance, the motion of the engine is retarded until the same adjustment is effected by a process precisely the converse of that above described. The mean effective pressure being thus determined, the quantities U, v,—v4, and the various values of p and v, at different parts of the stroke, can be deduced from it by principles to be afterwards explained, depending on the nature of the fluid, and the manner in which its action is regulated in the particular engine. Then from equation 6 of Article 263, it appears that the number of strokes in a given time can be computed by the formula 265. Wfficiency of the Fluid im an Elementary Meat Engine—An elementary heat engine ig one in which the reception of heat by the fluid takes place wholly at ove absolute temperature 7,, and its rejection wholly at another absolute temperature +. Consequently, in such an engine, the change between those two hmiting tempera- tures must be made entirely by compression and expansion of the fluid. In fig. 100, let AB be part of the iso- 1 thermal line of -,, DC part of that of c.; and let a ADM, BCN, bea pair of adiabatic lines, cor- responding respectively to any two thermodyna- . mic functions @,, 9, and produced indefinitely Ne towards X. Then will ABCD be the diagram . of an elementary heat engine receiving heat at os x the absolute temperature ¢,, and rejecting heat wd bo «att, The action of such an engine, during one Fig. 100. stroke, consists of four operations, represented . by the four sides of the figure ABCD, as follows :— A B, expansion of the fluid at the higher limit of temperature +, ; BO, further expansion, without reception or emission of heat, till the temperature falls to cy ; CD, compression of the iluid, at the lower limit of tempera- ture 79; EFFICIENCY OF THE FLUID IN GENERAL. 343 D A, further compression, without reception or emission of heat, till the temperature rises again to +. The heat received by the fluid from the furnace, at each stroke, during the process A B, is 7, (Q,—@,) = H,, and is represented by the indefinitely produced area MABN. The heat rejected at each stroke, during the process C D, and abstracted by some refri- gerating substance (such as the jet of cold water in the condenser of a steam engine) is r, (?, — ®,) = H,, and is represented by the indefinitely-produced area MD CN. The heat permanently trans- formed into mechanical energy at each stroke is represented by the area ABCD =H,-H,=(+, = 7») (5 — Qa) seaeeeees eesece (1.) Consequently the efficiency of the engine is H,-Hy -% T,-T, i, - ta ee (2, The last equation expresses the law of the efficiency of elementary thermodynamic engines, viz. :—that the heat transformed into mecha- nical energy is to the whole heat received by the fluid as the range of temperature is to the absolute temperature at which heat is received. 266. Mfficiency of the Fluid in Heat Engines in General.— Let the closed line Aad Bed A be the diagram of any thermodynamic engine. Draw a pair of adiabatic lines AM, BN, touching the closed line in A B, respectively, and indefinitely , produced in the direction of OX. Then through- out the process represented by the part A a 6 B of the diagram, the fluid is receiving heat, and throughout the process is represented by the part | BedA, rejecting heat. Cut an indefinitely nar- row band from the diagram by any pair of indefi- nitely-close adiabatic lines a dm, 6 cm, correspond- ing to the thermodynamic functions 9, 9+d 9, respectively ; and let the absolute temperatures corresponding to the elements a6, c d, be 7, 7, respectively. Then, treating the band abcd as the dia- gram of an elementary engine, we find (expressing quantities of heat in foot-pounds), A RSsz Fig. 101. Heat received during the process a b = indefinitely-produced area mabn=dH,=7,d9; Heat rejected during the process ¢ d = indefinitely-produced area mdcn=adH,—ad 9; Heat transformed into mechanical energy = areaabcd = dH, —d Hy = (",-%) d¢. 344 STEAM AND OTHER HEAT ENGINES. Consequently, whole heat received by the fluid, =area MA ab BN=H,= : Cd Di coiinsteaenene (L) A Whole heat rejected, =area MAdcBN=H,= fig Ls Disaisnceeseutsnan vacen'ed (2.) aA Heat transformed into mechanical energy, =U=area Aab Bed A=H,-H, i; ‘ os = [(@ -p)do= | ~-o)dp= [* ee. ee (3.) Efficiency of the engine 267. Micat Engine of Maximum Efficiency.— Between given limits of temperature, the efficiency of a thermodynamic engine is the greatest possible, when the whole reception of heat takes place at the higher limit, and the whole rejection of heat at the lower; that is to say, when the engine is an elementary engine; and the effi- ciency of the fluid in such an engine is independent of the nature of the fluid employed. 268, leat Economizer, or Regenerator.—To fulfil strictly the above condition of maximum efficiency between given limits of temperature, the elevation of the temperature of the fluid must be performed wholly by compression, and the depression of its tem- perature wholly by expansion; operations which are in many cases impracticable, from the great bulk of cylinders which their per- formance would require. This difficulty is almost entirely avoided by the following process for producing alternate elevation and depression of temperature with a small expenditure of heat, invented about the year 1816 by the Rev. Dr. Robert Stirling, and subsequently improved and. modified by Mr. James Stirling, Captain Ericsson, Mr. Siemens, and others. The fluid whose temperature is to be lowered is passed through the interstices of an apparatus called an economizer or regenerator, formed by a number of thin plates of metal or other solid conduct- ing substance, or by a network of wires, exposing a great surface REGENERATOR—ISODIABATIC LINES—AIR ENGINES. 345 within a small space. The material of the economizer becomes heated by the cooling of the fluid) When the temperature of the fluid is again to be raised, it is passed through the interstices of the economizer in the contrary direction, and the heat which it had previously given out is in part restored to it. It is impossible to perform this process absolutely without waste of heat. In some experiments by Mr. Siemens, on air, the waste of heat at each stroke appears to have been about one-twentieth part of the heat alternately abstracted from and restored to the es in the air engines of the ship “ Ericsson,” about one- tenth, 269. Usodiabatic Lines.—One condition of the economical work- ing of the economizer is, that the quantity of heat given out by the fluid during any given stage of the lowering of its temperature shall be equal to the quantity received by it during the corresponding stage of the raising of its temperature. This condition is realized in the following manner :— Let EF be an arbitrary line representing the mode of variation of the pressure and volume of the fluid during the lowering of its temperature. Tie 18d Let G H be the corresponding line for the raising Sree of the temperature of the fluid. Let KL, MN, be any pair of isothermal lines, intersecting GH in A and D, and EF in B and C, respectively. Let 94, ¢n, 0, ?p, be the thermodynamic functions tor these four points. Then if, for every possible pair of isothermal lines, Y fs — fa = Fo — $d, the lines E F and GH have the required property, and are said to be isodiabatic with respect to each other. Section 4.—Of the Efficiency of Air Engines. 270. Thermal Lines for Air.—The ease with which air is obtained in any quantity, and its safety from explosion at high temperatures, have induced many inventors to devise engines in which it is the working fluid. Very few, however, of those engines have been brought into practical operation, owing chiefly to the difficulty of obtaining a sufficiently rapid convection of heat to and from the mass of air employed, and to the necessity for using a more bulky cylinder than is required for a steam engine of the same power, and with the same maximum pressure. The efficiency of air engines is here treated of before that of 346 STEAM AND OTHER HEAT ENGINES, steam engines, because of the greater simplicity of its mathematical principles. In such investigations as the present, air may without sensible error be treated as a perfect gas. Each isothermal line for a perfect gas is a common rectangular hyperbola, whose asymptotes are O X, O Y, its equations being PV=PMy%- - sebagehdmedataduraacoawades (1.) For air, Py % = cy = OS 15 foot-pounds per degree of Fahrenheit. Hach adiabatic line for a perfect gas is a curve of the hyperbolic kind, having O X, O Y, for asymptotes, its equation being 9 por = ek = comstants...ccccccccccceeeeeees (2.) y for air = 1-408. Sce Article 251. Each pati of isodiabatic lines for a perfect gas are so related to cach other, that if v, v', be the abscisse of the points of intersection of these two lines respectively, with one and the same isothermal line, the ratio v: v' is a constant quantity for all isothermal lines. The same is the case with the ratio p: p’. It follows from this, that all straight lines of constant volume, parallel to O Y, are mutually isodiabatic (which is equivalent to saying that the specific heat at constant volume is constant), and also that all straight lines of constant pressure, parallel to O X, are mutually isodiabatic (which is equivalent to saying that the specific heat under constant pres- sure is constant). See Article 250. 271. Thermodynamic Functions for Air—When the two forms of the thermodynamic function, given respectively in Article 246, and in Article 248, viz., o=k hyp loge + f $2 ao; and o= (e+ 2%) hyp log »— f S2ap; 70 d¢ are applied to a perfect gas, it is to be observed (as already stated. in Article 251), that for a substance in that condition, Por. 1, = B *y Vv Tv dp_p PERFECT AIR ENGINE. 347 dv Y __ Mo% 1, dz" > Pp and also, as has been shown in Article 250, that : ko K,= foto; 4 2K = 7 Po%. GT PT HEAD These values being introduced under the signs of integration, give the following results :— g— Po (pies = + hyp log ») + constant...... (1.) % yo = eos -_ + hyp log P) + constant......(2.) . o i In these formule, the value assigned to the arbitrary constant introduced by integration is immaterial; because the differences between thermodynamic functions have alone to be considered in any problem; and from them the arbitrary constant disappears. The values of the co-efficients in the above formule, for air, though they have already been given in Article 251, may here, for the sake of convenience, be repeated. : = 2451; —2, = 3-451; oe eae (3) Poto __ 53-15 foot-lbs. per degree of Fahrenheit. } 70 In using the formule 1 and 2 with tables of common, instead of hyperbolic logarithms, it is to be observed that hyp log n = com log n x hyp log 10; hyp log 10 = 2:3026 nearly ; Po 0 yx hyp log 10 = 53-15 x 2°3026 = 122-38 79 foot-lbs. per degree of Fahrenheit, J 272. Perfect Air Engine, without Regenerator.— Fig. 100 (Article 265) may be taken to represent the diagram of the energy exerted by one pound of air during one stroke of an engine of this class. Let 7, and 7, be the absolute temperatures of receiving and rejecting heat respectively. Then A B is part of a common hyperbola, the isothermal curve of +,; and its equation is ates 348 STEAM AND OTHER HEAT ENGINES. Pp vat + ges WILD hp deausssnmivoentinans: (1.) C D is part of a common hyperbola, the isothermal curve of 7; and its equation is pov = aay = BOAUB pacts cteen cts (2) BC and D A are portions of adiabatic curves, whose equations are of the form given in Article 270, equation 2. Let Par Pos Po Par Vay Voy Vey Var denote respectively the pressures in lbs. on the square foot, and the volumes in cubic feet, of one lb. of air, corresponding to the four angles of the diagram, A, B, C, D. Then the proportions of those quantities are regulated by the following formule :— Pa_% Pa _% oo D Supshiespanumenace (3.) ¢. 4 oe, \ 3451 Pa _ Po _ (2) =(2) Water aid anata sets. (4) Pa Pe a5 og 1 2°451 v v, T. ——; % #%_(4)71= (4%) cence ec teeneee (5.) Vg Up T,? “2 In equation 3, 7 denotes the ratio of expansion and compression of the air at constant temperature, which is arbitrary, and is to be fixed by considerations of convenience. Ifa certain quantity of air is confined within the engine, ard used over and over again to drive the piston, the absolute values of the pressures and volumes whose ratios are given in equations 3, 4, and 5, are arbitrary also. But if the air is wholly or partly dis- charged at each stroke, and a fresh supply of air taken in from the atmosphere, the minimum pressure p,, maximum volume », of one Ib. of air, and temperature of rejection of heat ¢, = p,v, + 53°15, are fixed, being those of the external air. If the temperature 7, of receiving heat is also fixed, then the pressure and volume ~, %, are fixed by the formule 7, \ 3461 eo, \ 2451 p=p-(3) 5 =0,(2) S weatedaxs (6.) 1 so that nothing remains arbitrary except the ratio r, of expansion and compression at constant temperature, which having been fixed PERFECT AIR ENGINE. 249 according to convenience, fixes the other limits of pressure and volume, viz., %% Pa=T Po5 Pa = Pej Ya 5 Ca verereees (7.) Let 9,, @, be the thermodynamic functions proper to the curves AD, BC, respectively. Then according to Article 271, equations 1, 3, and 4, the difference of those functions is a a (hyp log v, — hyp log v,) | 70 = 53-15 hyp log x \ = 122°38 com log r | being a function of the ratio of expansion at constant temperature alone. Introducing this value into the general equations of Article 265, we find the following results :— Whole expenditure of heat in foot-pounds of energy, per pound of air per stroke— Hy = (¢,—¢%.) =53'15 +, * hyp log 7 = 122:38 «, - com log r;...(9.) Heat rejected and abstracted by refrigerating apparatus— Hy = 7, (%—%.) = 53°15 75 ‘hyp log r = 122°38 +, + com log r;...(10.) Mechanical energy exerted on piston— U=H, — Hy = (% — %5) (Q— %) = 53°15 (=, — 79) hyp log r = 122°38 (¢,— 79) com log 1......eeee sees (11.) Efficiency of fluid (as in the general case)— If it were possible to perform the whole cycle of operations on the air in one cylinder, the space to be swept through by the piston, per pound of air per stroke, would be the difference between the greatest and least volumes of a pound of air; that is to say, 1 Tr? 2-451 u-4=0 {1-5 (2) le Sore er rar (13.) 350 STEAM AND OTHER HEAT ENGINES. and the mean effective pressure would be U Pe ac —1) hyp logr 0.—v D4bL er ee wenceves (14.) 2 Ua wees 2 (3 i) sa There may, on the other hand, be a compressing pump as well as a working cylinder, the air being supplied to the pump at the pressure and volume p,, v,; compressed at the constant absolute temperature 7, to the pressure and volume p,, v,; compressed with elevation of temperature to p,, v,; then transferred to the working cylinder, and expanded at the constant absolute temperature +,, to the pressure and volume p,, v,; then expanded with depression of temperature back again to p,, v,; and then discharged. In this case the compressing pump and working cylinder must be of equal size; and the piston of each of them must sweep simply through the maximum volume Ui scivenssseneeincntiacersencanased (15.) per pound of air per stroke, giving for the mean effective pressure . = p, (1° 1) hyp log t.....seeeeeees € B65 ¢ i, When the engine takes its periodical supply from the external air, p, is the atmospheric pressure. It is often convenient to express the expenditure of heat in foot- pounds per cubic foot swept through; that is, to state a pressure in pounds on the square foot, which, acting on the piston, would exert energy equivalent to the heat expended. This is given by the formula as the case may be. The following is a numerical example :— Data. Ratio of expansion, r= 2 = 2116-4 Ibs. on the square foot. Temperatures on the ordinary scale, T, = 650° F. T, = 150° F Absolute temperatures,.......... vee 4 = 11112 0 ey = 611-2. FERFECT AIR ENGINE. 351 REsvrts. oy \ 3451 2-451 7 7, 1 1 =78 2) = 0-931 = ——. (2) ts zy nen 4:33 53°15 7, e : v, = ; “2 = 15:35 cubic feet per Ib. Then by equation 8— Thermodynamic function %, — 9, = 122:38 x -30103 = 36-84. ‘By the formula (6)— py = 16656; », = 3-546. By the formula (7)— py = 2 ps B3812 oh = 3 = 1773; Pa = 2p, = 4232'8; vy = 3 = 7675; By equations 9, 10, 11— Toot-Ibs. H, = heat expended per Ib. air 1111-2 - : Der SHOKE, secede cove sdacdises See RE = es H, = heat rejected,................. . 611-2 x% 36°84 = 22,517 U = energy exerted on piston,.... 500 x 36°84 = 18,420 By equation 12— Efficiency of fluid.............0000868= = mas = O45 For one cylinder acting as compressing pump and working cylinder, by formule 13, 14— Space swept through per Ib. air per stroke— UV, — V_ = 13°58 cubic feet. Heat expended per cubic foot swept through— 40937 358 7 3014 Ibs. on the square foot. Mean effective pressure— 18420 . 1358 7 1356 Ibs. on the square foot = 9°42 Ibs, on the square inch, For separate compressing pump and working cylinder, by for- mule 15, 16— 352 STEAM AND OTHER HEAT ENGINES. Space swept through by each piston per Ib. air per stroke— v, = 15°35 cubic feet. Heat expended per cubic foot swept through— 40937 gn, T5385 = 2666 Ibs. on the square foot. Mean effective pressure— 18420 _, ‘ 535 7 1200 lbs. on the square foot = 8°33 lbs. on the square inch. This last result illustrates one of the practical difficulties attend- ing the use of air engines in which the changes of temperature are to be effected by means of changes of volume, viz., the smallness of the mean effec'ive pressure compared with the maximum pressure, and the cnsequ2nt great bulk and strength required for an engine of a given power. In the supposed example, the excess of the maximum piessure, p,, above that of the atmosphere, is 33312 — 2116 = 31196 lbs. on the square foot = 216°6 Ibs. on the square inch; and the strength of the cylinder, and of other parts of the engine, must be adapted to sustain this great pressure, of which the mean effective pressure is only about one twenty-sixth part. The better to illustrate the bulk required for the engine, on the supposition of there being a separate compressing pump and work- ing cylinder, it may be observed, that the volume to be swept ' through by the piston in its effective strokes per minute, to give one indicated horse-power, would be 33000 1200 973. Perfect Air Engines with Begenerators, in General.—_F. ig. 102, Article 269, may be taken to represent the general case of the diagram of an engine of this class. AB, D C, are portions of two isothermal lines, being common hyperbolas; A D, BC, are portions of a pair of isodiabatic lines, of any figure whatsoever, but con- nected together by the condition explained in Article 270. The structure of a regenerator, or heat economizer, has already been explained in Article 268. The operations undergone by the working mass of air are represented in the diagram as follows:— = 273 cubic feet. AIR ENGINE WITH REGENERATOR. 353 CD represents the compression of the air, at the lower limit of absolute temperature <,, the heat produced by the compression being abstracted by a refrigerating apparatus of some kind. DA represents the series of changes of pressure and volume undergone by the air in passing through the grating or network of the regenerator; which having been previously heated, gives out enough of heat to the air to raise it to the higher limit of absolute temperature ¢,. A B represents the expansion of the air at the absolute tempera- ture ¢,. BC represents the series of changes of pressure and volume undergone by the air in passing back again through the grating or network of the regenerator, to the material of which apparatus it gives out so much heat as to lower its own absolute temperature back to 7,; and that heat remains stored in the regenerator until employed to raise the temperature of the air at the next stroke. By thus storing and restoring a certain quantity of heat, the alternate lowering and raising of the temperature of the air is effected without the expenditure for that purpose of any heat from the furnace, except such as is required to supply the waste of heat that occurs in the regenerator; that waste, according to experi- ment, being from one-tenth to one-twentieth of the whole quantity of heat required to raise the temperature of the air at each stroke; which quantity of heat, yer pound of air, has the following value én foot-pounds :— in which [ pdv denotes the area between one of the isodiabatic lines (as A D), and the ordinates let fall from its ends perpendicular to OX; and that area is to be | pies \ according as | p} subtracted is the farther from O Y. (For an adiabatic line, the expression 1 becomes = 0). In the air engines which have been used in practice, the weight of material in the regenerator appears to have been about forty tumes the weight of the air passed through it at one stroke. The formule for the relations amongst the pressures, volumes, and temperatures, for the expenditure of heat in expanding the air, the energy exerted per Ib. of air per stroke, and the efficiency, are the same with those in the last Article, except that the ratio, Ei oh A oD a hs SO a a eed) Pa Po v2 Va vt Up a which in an engine without a regenerator is fixed by equation 4 of 2A 354 STEAM AND OTHER HEAT ENGINES. Article 272, becomes arbitrary in an engine with a regenerator. Hence all the equations of Article 272 hold in the present case, except 4 and its consequences, viz., 5, 6, 13, and 14; instead of which we have simply the relations given in the formula 2 of the present Article. The volume swept through by the piston per pound of air at each stroke cannot be less than the difference between the greatest and least volumes of the air, and may be greater to an extent depending on the structure and mode of working of the particular engine. Particular cases of that structure and mode of working will be considered in subsequent Articles; meanwhile the diagrams of energy of two of the more important cases are presented at one view in fig. 103. In that figure, AB A'B' is the isothermal line of the higher limit of temperature, and D’C'D C that of the lower. A D, BC, Fy Fig. 108. are a pair of adiabatic curves, so that A BC D is a diagram for the case already considered in Article 272. D A’, CB, are a pair of straight lines, each corresponding to a constant pressure; so that A'B'CD is the diagram of an engine in which the changes of temperature take place at constant pressures. A D’, BO’, are a pair of straight lines, each corresponding to a constant volume; su that A B C' D’ is the diagram of an engine in which the changes of temperature take place at constant volumes. 274. Temperature Changed at Constant Pressure — Ericsson’s Engine.—To illustrate the structure of engines whose diagrams approximate more or less closely to A' B’ CO D im fig. 103, a sketch of the principal parts of Captain Ericsson’s air engine (as used about the year 1852) is given in fig. 104, which is a vertical section of a single acting land engine of that kind. B is the working cylinder, placed over the furnace H. This ERICSSON’S AIR ENGINE. 355 cylinder consists of two parts; the upper part, accurately turned, in which the piston works, and the lower part, less accurately made, and of somewhat larger diameter, in which the air re- ceives heat from the furnace. A is the piston of that cylin- der, consisting of two parts. The upper part is accurately fitted, and provided with metallic pack- ing, so as to work air-tight in the upper part of the cylinder. The lower part is made of the same shape with the lower part of the cylinder, but of less dimensions, so as nearly to fit the cylinder, but without touching it. This lower part is hollow, and is filled with brick dust, fragments of fire clay, or some such slow conductor of heat. The object of this is to resist the transmission of heat to the upper parts of the cylinder and piston, and especially to the packing, in order that the bearing surfaces of the cylinder and packing may be kept cool. The cover of the cylinder B has holes in it marked a, to admit the external air to the space above the piston. D is the compressing pump, being a cylinder standing on the cover of the working cylinder. C is the piston of the compressing pump, connected with the piston A by three or by four piston rods, of which two are shown, and marked d. The space below the piston D, and above the piston A, forms one continuous cavity, communicating freely with the external air through the holes a. Eis the upper piston rod, by which the pistons C and A are con- nected with the mechanism. That rod traverses a stuffing box in the cover of the compressing pump. The compression of the air takes place in the upper part of the compressing pump. The air enters through the admission clack ¢, is next compressed, and is then forced through the discharge clacke into a receiver or magazine of compressed air, F. G is the regenerator, being a box containing several layers of wire gauze, which are traversed by the air when it enters and leaves the working cylinder. ; ; b is the induction valve, and f the eduction valve, both worked by the mechanism of the engine. When 6 is opened, air is admit- ted from the receiver F through the regenerator into the cylinder, and lifts the piston A. After a portion of the stroke has been per- Fig. 104. 356 STEAM AND OTHER HEAT ENGINES. formed, 5 is shut, and the admission of air cut off; the remainder of the stroke of the piston A is performed by the expansion of the air. During the return stroke, the eduction valve fis kept open, and the air driven out through the regenerator, and through the exhaust pipe g, into the atmosphere. The ratio of the sizes of the compressing pump, and of the work- ing cylinder, ought to be that of the absolute temperatures of receiving and rejecting heat; that is, compressing pump _ 7» (1.) wag eindes ge : As the lengths of their strokes are the same, the above ratio is that of the areas of their pistons. Referring back to fig. 103 in the last Article, the diagram ' A’ B’C D may be taken to represent the action of one lb. of air during one stroke in this engine, when the conditions of maximum efficiency between given limits of temperature are fulfilled. Pro- duce A’D to E,and B’Cto F. Then EDCF is the diagram of the compressing pump, and E A’ B' F the diagram of the working cylinder. FC represents the admission of the air from the atmo- sphere into the compressing pump at the atmospheric pressure p,; C D its compression in that pump at the constant absolute tem- perature =, until its pressure is raised to p,, the heat produced bv the compression being dissipated by conduction, or taken away by some refrigerating apparatus. Owing to the elevation of tempera- ture required in order to cause this heat to be given out as rapidly as it is produced, +, is always higher than the temperature of the external air, but to what extent is uncertain. DE represents the expulsion of the air from the compressing pump into the receiver. E A’, the admission of the air into the working cylinder, when, by its passage through the regenerator, its absolute temperature is raised to 7, and its volume increased from v, to 0,. In order that the operations represented by D E and E A’ may be performed without any sensible falling off in the pressure, the engine ought to be ¢raple, or still better, quadruple (like that which was tried in the steamer “ Ericsson’ ) consisting, in the latter case, of a set of four cylinders, each with its own compressing pump, all driving the same shaft, and communicating with the same receiver, and making their strokes in succession at intervals of a quarter of a revolution. This arrangement is desirable also in order to obtain steady motion. A’ B’ represents the expansion of the air in the working cylinder after its admission is cut off, at the constant absolute temperature z,, until the pressure returns to the atmospheric pressure. The heat ERICSSON’S AIR ENGINE, 357 required for this expansion is supplied by the furnace through the bottom of the cylinder. BF represents the final expulsion of the air, in the course of which it traverses the regenerator in the reverse direction, and transfers to the wire gauze a quantity of heat. which is used at the next stroke to raise the temperature of the next mass of air. The following are the formule appropriate to this class of engines :— Dara. 4, temperature at which heat is received by the air from the furnace, and the air expanded. >), temperature at which the air is compressed, and heat ab- stracted. p. atmospheric pressure, if the engine draws its air directly from, and discharges its air directly into the atmosphere, as in the engine just described. 7, ratio of expansion at constant temperature. REsvts, all of which have reference to one stroke of one pound of air, pres- sures in pounds on the square foot, and volumes in cubic feet— Pressures, Ps = Pe \ (2) Pa = Pa = % Po 53-15 ¢ Volumes, v,= 2; Pe pe Sige ONES. We Senate (3) 72 Pe Vv v 7 = 5 As Thermodynamic function, as in Article 272— ®, — 0, = 53-15 hyp log r = 122:38 com log 1......(4.) Expenditure of heat in expanding the air, as in Article 272— H, = 122:38 +, com log 7.........e0000s (5) Heat rejected during the compression of the air— H, = 122°38 <, com log 1........:-sseneeeee (6.) Mechanical energy, as in Article 272— U = 122-38 (7, — 7) com log tssssesssreenee(e) 358 STEAM AND OTHER HEAT ENGINES. Efficiency, supposing no heat wasted, as in Article 272— U Fi 28 . i Sg ee eet: (8) Heat stored and restored by regenerator, in foot-lbs.— Ky, (71 — 7%) = 183-45 (71 — ay)eseeeeccereetes (9.) Tf, according to Mr. Siemens’s experiments, one-twentieth of this quantity of heat is wasted, the efficiency will be diminished to U Hy, + 9°17 (+, — 29) But from experiments made by Professor Norton on the ship “ Kricsson,” it seems probable that the waste in the regenerator was more nearly one-tenth than one-twentieth of the heat stored ; and in that case we have for the diminished efficiency eee! ee foes EPO? eee) Volume swept through by the piston A, per pound of air per stroke— SS VUor er vevvcccceccercreese Donevere (1 1.) Mean effective pressure, per unit of area of the piston A— U =p, 1— 8 hyp loge = 23026 p, - oS “2 com log r... (12.) YW wy Heat expended per cubic foot swept through, not including waste— a = p, hyp log r = 2°3026 p, com log 7.,...... (13.) b The same, with the addition of the supposed waste from the regenerator— H, + mK, (7, — 79) % = p, (2026 com log r+ 3-451 m a=) eis 1 m is the fraction which is wasted of the whole heat stored by the regenerator, being from one-tenth to one-twentieth. In the following numerical example, the proportion of the working cylinder to the compressing pump, % : v,, and the ratio of expansion, %, :v,= 7, are those of the air engines of the “Ericsson ;” AIR ENGINES OF SHIP ‘ ERICSSON.” 359 but the temperatures of receiving and rejecting heat, and the atmospheric pressure, are merely assumed as probable. The waste of heat in the regenerator is assumed at one-tenth, Data. Ty = 122°; +, = 583°2; T, = 413°6; +, = 874°8; Po = 2116-4; 7 = 154; 2-15, *2 RESULTS. Pressures— Dy = 2116-4; pg = py = 3259°3. Volumes— v, = 14:65; w (greatest volume) = 21-97; = 951; v, = 14:27. Thermodynamic function— Gy — Og = 122-38 X 01875 = 22-95. Foot-lbs. Latent heat of expansion, ...1.... H, = 874:8 x 22:95 = 20077 Heat wasted by regenerator, ........00 ee ore = 5349 Whole heat expended per Ib. of air per stroke,......... 25426 Feat rejected s..ceccscesesseeeaseeceee H, = 583'2 x 22:95 13385 Mechanical energy per lb. air per stroke— U = 291°6 x 22-95 6692 Efficiency of fluad, supposing no heat wasted, +. Efficiency of fluid, estimating heat wasted as above— 6692 35496 = 0:263. A Mean effective pressure— 6692 5107 = 305 Ibs. on the square foot = 2:12 lbs. on the square inch, 360 STEAM AND OTHER HEAT ENGINES. The air engines of the “ Ericsson” had four working cylinders, each of 14 feet in diameter, so that the joint area of their pistons was 154 x 4 = 616 square feet. The length of stroke was 6 feet; the number of revolutions per minute 9; hence, according to the above computation of the mean effective pressure, the energy exerted by the fluid on the piston was 305 x 616 x 6 x 9 = 10,145,520 foot-lbs. per minute ; or 307 indicated horse-power. In Professor Norton’s report, the indicated horse-power 300 of those engines is stated to have been.................. I Difference,........ssesceeeeeeee Volume to be swept through by the working pistons per indicated horse-power— 33000 307 by the compressing pistons, 72 cubic feet per minute. These results show the excessive bulk of the air engines of the “ Ericsson” in proportion to their power; being the chief obstacle to their use for marine propulsion. According to Professor Norton, the quantity of fuel (anthracite) consumed in those engines per indicated horse-power per hour, was = 108 eubic feet per minute ; 1:87 Ib. This gives, for the duty of one lb. of anthracite, 1,980,000 gy 1,059,000 foot-Ibs. A probable estimate of the theoretical evaporative power of the anthracite used is 14 lbs. of water evaporated from and at 212°, which gives for the mechanical equivalent of the total heat of com- bustion of 1 Ib. of the fuel 10,440,000 foot-lbs. _ Hence the resultant efficiency of the furnace and fluid appears to have been 1,059,000 10,440,000 The probable efficiency of the fluid has already been computed to have been 0:263; hence the probable efficiency of the furnace was = 071014. AIR ENGINES OF SHIP “ERICSSON.” 361 0:1014 0:263 being about equal to the lowest efficiency of steam boiler furnaces. The heating surface in the engines of the “ Ericsson ” consisted simply of the bottoms of the cylinders, and amounted in round numbers to about 700 square feet. The consumption of fuel per hour was 560 lbs. Employing these data in equation 2 of Article 234, and making B = }3, A = 0:5 (or taking, in the table of page 295, the efficiency corresponding to S + F = 1-25), we find for the efficiency of a steam boiler furnace having the same area of heating surface, and burning fuel at the same rate, 0-71. The difference between this and 0-4 must be ascribed to the. great inferiority of air to boiling water, as a medium for the con- vection of heat. : It appears from the preceding calculations, that notwithstanding the low efficiency of the furnace in Ericsson’s air engine, the effi- ciency of the fluid was so great as to give a resultant efficiency superior to that of almost all steam engines at the time of the experiments referred to. The difficulty arising from the great bulk of the engine compared with its power, might be, and probably has been already, obviated to a certain extent, by making the engine draw its supply of air from, and deliver the air from the eduction valve f into, a second receiver containing compressed air at a lower pressure than that of the air in the receiver F. In this case, », =p, would denote the pressure of the air in the second receiver, exceeding the atmo- spheric pressure in an arbitrary ratio; py = p,=7 PD, a8 before, would denote the pressure in the first receiver F; and the mean effective pressure would be increased, and the space to be swept through by the piston per horse-power per minute, and conse- quently the bulk of the engine, would be diminished, in the ratio of p, to the atmospheric pressure. The engine, as thus altered, would require to be provided with a small compressing feed pump, to draw from the atmosphere and force into the second receiver enough of air to supply the loss by leakage. A refrigerator, consisting of tubes with a current of cold water forced through them, or other suitable apparatus, would be needed, in order to abstract from the air passing from the regenerator to the second receiver, the heat which the regenerator fails to abstract from it, by reason of the imperfection of its action; being in fact, the waste heat of the regenerator already referred to. = 0°4 nearly; 362 STEAM AND OTHER HEAT ENGINES. It might also be necessary to surround the compressing pump D with a casing containing a current of cold water, to abstract the heat produced by the compression of the air; because, owing to the diminished size of that cylinder, the abstraction of the heat by acs of its contact with the external air might not be sufficiently rapid. Some means would have to be adopted to augment the heating’ surface exposed to the furnace by the working cylinder, without inconveniently increasing the space occupied by the engine. A contrivance proposed for that purpose will be described at the end of the next Article. 275. Temperature Changed at Constant Volume—Stirling’s Engine —Napier and Rankine’s Air Heater.—In fig. 103, Article 273, ABC'D' represents the diagram of a perfect engine of the class now under consideration. A B represents the expansion of the air at the constant absolute temperature +,; BO’, the lower- ing temperature of the air by transmission through a regenerator, at the constant volume », = ¥,; C' D’, the compression of the air, at the constant absolute tempera- ture 7,; D’ A, the raising the temperature of the air, at the constant volume vz = v, %, 9% This mode of regulating the operations undergone by the air is suitable for an engine in which the same individual mass of air is kept constantly confined within an enclosed space of variable volume: an arrangement favourable to compactness, as the air can be used at any pressure consistent with safety. To show the general nature of the apparatus by means of which the air is so treated, fig. 105 is a vertical section of the principal parts of the air engine invented by Dr. Robert Stirling, and improved by Mr. James Stirling DCABACD is the air receiver, or heating and cooling vessel; Gis the cylinder, with its piston H. . The receiver and cylinder communicate freely through the nozzle F, which is at all times open while the engine works. Within the receiver is an inner receiver or lining of a similar figure, so far as it extends, viz., from B to CC. The hemispherical bottom of this lining is pierced with many small holes, and the space between it and the bottom of the outer receiver is vacant. From A A up to CC, the annular space between the outer receiver and its lining contains the regenerator; being a grating composed of a series of thin vertical oblong strips of metal or glass, with Fig. 108. Q STIRLING’S AIR ENGINE. 363 narrow passages between them. The inner surface of the cylin- drical part of the lining, from A A up to CC, is turned, and the. plunger E moves vertically up and down within it, fitting easily, so as to leave the least space possible without causing perceptible friction. This plunger is hollow, and filled with brick dust, or some such slow conductor of heat. The space from CC to DD between the barrel of the receiver and the concave part of its cover, and above the upper edge of the lining, contains the “refrigerator,” which consists of a horizontal coil of fine copper tube, through which a current of cold water is forced by a pump, not shown in the figure. There is an air compressing pump, not shown, which forces in the nozzle F enough of air to supply the loss by leakage. The hemispherical bottom A B A of the receiver forms the heat- ing surface which is exposed to the furnace. The effect of the alternate motion of the plunger E up and down is to transfer a certain mass of air, which may be called the working air, alternately to the upper and lower end of the receiver, by making it pass up and down through the regenerator between A A and CC. The perforated hemispherical lining of the bottom of the receiver causes a diffusion and rapid circulation of the air as it passes into the lower end.of the receiver, and thus facilitates the convection of heat to it, for the purpose of enabling it to undergo the expansion represented by AB in fig. 103; during which expansion it lifts the piston H. The descent of the plunger causes the air to return through the regenerator to the upper end of the receiver. It leaves the greater part of the heat corresponding to the range of temperature +, — 7, stored in the plates of the regen- erator. The remainder of that heat (being the heat wasted by the imperfect action of the regenerator) is abstracted by the refrigerator, . which also abstracts the heat produced by the compression of the air when the piston H descends. The heat stored in the regenera- tor serves to raise the temperature of the air, when, by the lifting of the plunger E, it is sent back to the lower end of the receiver. The: mechanism for moving the plunger E is so adjusted, that the up stroke of that plunger takes place when the piston H is at or near the beginning of its forward stroke, and the down stroke of the plunger when the piston H is at or near the beginning of its back stroke. The diagram represents a single acting engine. In a double acting engine, the other end of the cylinder G is connected with another air receiver similar to that shown, and the plungers of the two receivers are made to move in opposite directions to each other. Besides the working air, there is obviously a mass of air which does not pass up and down through the regenerator, but merely 364 STEAM AND OTHER HEAT ENGINES, passes into and out of the cylinder G and nozzle F. This mass of air remains always nearly at the lower absolute temperature -,, and is not the means of transforming heat to mechanical energy, but merely of transmitting pressure and motion between the work- ing air and the piston. The piston and cylinder being always cool, can be lubricated with oil without the risk of decomposing it; and the’ piston rod can be made to work through a leather collar. (For details respecting this engine, see Proceedings of the Institution of Civil Engineers, 1854.) The general theory of the action of a mass of elastic fluid in a heat engine as a cushion between the working fluid and the piston, has already been given in Article 262. The application of that theory to the present case is shown in fig. 106. Let A BCD be the real diagram ¥ of one lb. of the working mass of air, so that P B= QC=v,=12,re- presents its greatest volume in cubic feet per lb. This represents the 2 mai i Pr = RLS BIN Aa space below the plunger of the re- Q 4, ceiver when it is at the top of its - ie S x stroke. Add a space equal to the ; volume of the air contained in the Hig 106: port F, in the clearance below the piston H, in the spaces between the coils of the refrigerating tube, and in those of the upper half of the regenerator; the sum will be the whole space filled with air when the piston H is at the end of its back stroke and beginning of its forward stroke. Through A draw N J parallel to OX to represent that space; then A I repre- sents the volume of the cushion air when it is under the greatest pressure. Make NE=A JI, and make EF HG an isothermal curve; that is, a common hyperbola, the product of whose rectan- gular co-ordinates ON x N E, OP x PF, &., is constant. Draw PBF, RDH, QCG, parallel to OX, and make BK =P FE, DM=RH, CL=QG; then K, L, M, and the point I formerly found, will be the corners of the actual diagram of the cylinder; and any number of intermediate points in that diagram can be found in a similar manner. The volume to be swept through by the piston per pound of air per stroke is represented by QL-NI The ratio of the weight of the cushion air to the weight of the working air, being that of the volumes of those masses of air at the same temperature, is QG+QC ree STIRLING’S AIR ENGINE. 365 The algebraical expression of these principles will be given after the formule relating to the efficiency of the fluid. The actual indicator diagram described by Stirling’s air engine was an oval, resembling the figure I K LM with the corners rounded off. This must be ascribed partly to the fact, that the operations actually performed on the working air, are only approxi- mately represented by the figure A BC D, the heating and cooling not taking place exactly at constant volumes, nor the expansion and compression exactly at constant temperatures, and partly to. the inertia of the piston and other moving parts of the indicator. The following are the formule appropriate to the class of engine now under consideration :— Data, z,, absolute temperature of receiving heat, and expanding the working air. ), absolute temperature of compressing the working air, and rejecting heat. Pa greatest pressure. r, ratio of expansion. q, ratio of volume of clearance and passages to greatest volume of working air. NI In fig. 106, OC =l1+4¢. REsutts, per lb. of working air per stroke— Pressures— Dy = Pe 5 ] | ian w(1.) rae. af Pa=Pa* 2 | Volumes of one lb. of working air— page 7h Sy, =U, HP Ugeernseracseen (2.) Pa Thermodynamic function— ¢, — %q = 53°15 hyp log r = 122-38 com log 7...... (3.) Expenditure of heat in expanding the air— Hy, = 122°38 =, com 10g Po. .seeeeeeseeeeeeens (4.) 366 STEAM AND OTHER HEAT ENGINES. Waste heat of regenerator— (m = from v5 to 2? K, = 130-3). Heat rejected during the-compression of the air— Hy 122°38 “7, * com Jog tics sceuecer verse (6.) Mechanical energy— U = 12238 (+, — 79) com log 1... sesseseeeeee (7.) Efficiency, if m = vo nearly— The following formule have reference to the volume of the cushion air, and of the whole air, working air and cushion air together, per 1b. of working air; and the small letters affixed to the letter v refer to the points marked with the corresponding capital letters in fig. 106 :— Least total volume of air— Volumes of cushion air— 0,=U;-%= 4 (1 +49) r—lh; pe wooo (10.) yar teas AIt+gr—-l. 212 X= Total volumes— Vy, MH} Um = Vat 3 = MT % (11) =a{(1tq)r3-241f. Ratio of cushion air to working air— BLU tg) PAT f ecnesennen (12) Uz Volume swept through by the poston per lb. of air per stroke— STIRLING’S AIR ENGINE. 367 m= (»-1) = +a(r3 - 1) \ skeee (13.) Ifean effective pressure— The quantities taken as data in the preceding set of formule are those which would probably be given for a proposed engine. In the case of an existing engine, and sometimes in the case of a pro- posed engine also, the ratio of expansion 7 may at first be unknown ; and instead of it these may be given, the proportion of the space swept through by the piston to the space swept through by the plunger, viz., 0, — 2; Ue” In this case, the following formula, deduced from equation 13, serves to determine the ratio of expansion :— rare eS ta) 4145 Resales (15.) which having been found, all the formule can be used as already given. In the following numerical example, the data are taken from the account by Mr. James Stirling, in the Proceedings of the Institution of Civil Engineers, for 1845, of an air engine which worked for several years at the Dundee foundry :— Dara. T, = 650°; ~; = 111172. T, = 150°; + = 611-2. Pa = 240 x 144 = 34,560. q, roughly estimated at 0-05. %-y 1 v», 2 ReEsvtrts. 1 . r= ppp {0% (05+005) +1} = 124, ps = 27870; p, = 15330; py = 19000. 368 STEAM AND OTHER HEAT ENGINES. Vq = Ug = 1:709; vy, = v, = 2-119. 0, — % = 122°38 x 0-09517 = 11-647. Latent heat of expansion, ....... H, = 11°647 x 1111-2 = 12942 Waste heat of regenerator, .........esccsseeeeees 13x 500= 6500 Whole heat expended per lb. of air per stroke,........ 19442 Rejected heat, ..........sucsseeeeee H, = 11-647 x 611-2 7119 Mechanical energy per lb. air per stroke— U =11°647 x 500 = 5823 5823 — 03, 19443 Volume swept by piston per Ib. of air per stroke— v,—0; = 2119 + 2 = 1-06 cubic feet. Mean effective pressure— _U___ 5823 _ %—u 106 — = 37°75 lbs. on the square inch. L ficiency of fluid— 5437 Ibs. on the square foot The engine to which these calculations refer was double acting, with a cylinder of 16 inches diameter, and 4 feet length of stroke, making 28 revolutions per minute. Hence, area of piston == 200 square inches; and Energy exerted by air on piston per minute, as found by calcula- tion— = 87:75 x 200 x 4 x 28 x 2 = 1,691,200 foot-lbs. The work actually performed against a friction brake dynamometer per minute was,.............. 1,500,000 And the work performed against the friction of the engine when unloaded, having been found to be one-ninth of the useful work, or.......... 005 166,667 The energy exerted by the air on the piston per minute is found from the experiments to have DOCH iis seeing tees eeowsudantastugieccindovanceaacaan nes 1,666,667 The difference between theory and experiment,.... 24,533 is practically unimportant. STIRLING’S AIR ENGINE. 369 The work expended on the friction of the engine is estimated at one-tenth of the whole energy exerted by the air; because it was found that when the receivers were charged with air at about one- tenth of the ordinary working density, the power of the engine was just sufficient to enable it to move unloaded. The following is a comparison between theory and experiment, as to the quantity of heat abstracted by the refrigerating appara- tus — By theory, the efficiency of the fluid in the engine is found to have been 0:3; that is, three-tenths of the whole heat received by the fluid were converted into mechanical energy, leaving seven- tenths to be abstracted by the refrigerator. Therefore, the heat abstracted by the refrigerator exceeded the heat converted into mechanical energy in the ratio of 7 to 3. The mechanical energy exerted by the fluid was 1,691,200 foot-lbs. per minute. Therefore the heat abstracted by the refrigerator per minute was 1,091,200 x ta 3,946,000 foot-lbs, Mr. Stirling states, that the quantity of water passed through the refrigerator was 4 cubic feet; that is, 250 lbs. per minute, and that its temperature was raised from 16° to 18° by the heat which it abstracted. Take 17° as the average elevation of its temperature; then, as the - dynamical specific heat of water is 772 foot-lbs., we have, for the heat abstracted by this quantity of water, 250 x 17 x 722 ==3,281,000 =z Differences: sacwesar ences snes 665,000 or about one-sixth of the greater quantity. This difference may be partly accounted for by the fact, that part of the heat abstracted from the working air must have been con- ducted through the covers and the upper portions of the sides of the receivers to the external air, without affecting the water in the coils of tube. It is possible, also, that the waste of heat through imperfect action of the regenerator may have been over-estimated in the theoretical calculation. The energy exerted by the fluid in an hour was 1,666,667 x 60 = 100,000,000 foot-Ibs, The fuel consumed in 12 hours was 1000 Ibs., or 83:3 lbs, per hour, so that the indicated duty of one lb. of coal was 2B 370. STEAM AND OTHER HEAT ENGINES, 100,000,000 1, pg 1,200,000 foot-lbs. Mr. Stirling considers the coal employed to have been of about three-fourths of the evaporative power of Newcastle coal. Assum- ing, therefore, the total heat of combustion of one lb. of the coal to have been 9,000,000 foot-lbs., we find for the resultant efficiency of the furnace and fluid, 1,200,000 9,000,000 The efficiency of the fluid having been 0°3, it appears that the efficiency of the furnace was = 0-133. -The heating surface was about 75 square feet. In a steam boiler furnace, burning the same quantity of fuel, this would have given an efficiency of about 0°61. In Stirling’s engine, therefore, the efficiency of the furnace approached more nearly to that of a steam boiler furnace, than in Ericsson’s engine, owing pro- bably to the greater density of the air, and its more rapid cir- culation over the bottom of the receiver. With a view to increasing the efficiency of air engines by ob- taining an extensive heating surface, without inconveniently enlarging their bulk, Mr. James R. Napier, and the Author of this work, have proposed the heating apparatus shown in fig. 107. That figure represents the bottom of a cylindrical air ~ receiver, consisting of a flat ‘ a Ay tube-plate, from which several WINN \\ Ss tubes, open at the upper end, Fig. 107, and closed at the lower end, descend into a flame chamber. P is the lower end of a plunger, NAPIER AND RANKINE’S HEATER—JOULE’S AIR ENGINE, 371 corresponding to that marked E in fig. 105. In fig. 107, the regenerator occupies a cylindrical hole in the centre of that plunger; but it might, if convenient, occupy an annular space surrounding the plunger, as in fig. 105. S is a second, or lower plunger, consisting of a perforated plate, from which cylindrical rods descend into the tubes, and nearly fit them. When the lower plunger is depressed, the rods nearly fill the tubes, and the heat transmitted from the furnace accumulates in the metal of the tubes and rods. When the lower plunger is raised, part of the air descends into the tubes, and is heated by contact with them and with the rods, and part remains in the large cylindrical part of the receiver, and is heated by contact with the upper ends of the rods, This apparatus has been found to heat the air rapidly; but its efficiency has not yet been ascertained by any exact experiment. 276. Hleat Received and Rejected at Constant Pressnres—Joule’s Enginue.—In a paper by Mr. Joule, with a supplement by Professor William Thomson, in the Philosophical Transactions for 1851, it is proposed to use an air engine in which the regenerator and refri- gerator are dispensed with; so that the air shall receive and reject heat, not at a pair of constant temperatures, but at a pair of con- stant pressures. This proposed engine would consist essentially of three parts—a compressing pump, a heating vessel (being a set of tubes traversing a furnace), and a working cylinder. The compressing pump and working cylinder would be clothed with non-conducting materials. The compressing pump would draw air from the atmosphere, compress it in a certain proportion, and force it into one end of the heating vessel, at a temperature elevated above the atmospheric temperature to an extent corresponding to the compression. In the heating vessel, the air would have its temperature further raised, and its volume expanded, at constant pressure, by the heat received from the furnace. From the farther end of the heating vessel, the air would pass through an induction valve into the working cylinder, driving the piston through a certain part of a stroke. The valve being closed, and the admission of air cut off, the piston would be driven through the remainder of its stroke by the expansion of the air down to the atmospheric pressure; and during that expansion, the temperature would fall to a certain extent. The air would then be discharged into the atmosphere at a temperature exceeding the atmospheric temperature, the heat due to the excess of temperature being rejected along with the air. In fig. 108, A BC D A represents the diagram of energy of such 372 STEAM AND OTHER HEAT ENGINES. an engine, being found by taking away EA DFE, the diagram of the compressing pump, from EBCFE, the diagram of the working cylinder. The straight line F D represents the volume ¥, of one Ib. of air, drawn from the atmosphere, at the atmospheric pressure p,, and absolute temperature 7, D A, a portion of an adiabatic ‘ae curve, represents the compres- AB sion of that air, until it attains Ea the pressure, volume, and tem- Bp ~ q perature, Pay Vay Tar qe ON The straight line EA repre- sents the volume v, of the com- Fig. 108, pressed air, as forced into the ' heating vessel. The straight line EB represents the volume », of that air after it has traversed the heating vessel, and as it enters the working cylinder under the constant pressure p,, and at the highest absolute temperature 7,. BC, a portion of an adiabatic curve, meeting the straight line F DC in ©, represents the expansion of the air to the volume »,, at which it returns to the atmospheric pressure p, = pq, and falls to a certain temperature r,. CF represents v, the volume of the air when finally expelled into the atmosphere. The heat received by each pound of air is represented by the area between A B, and the indefinitely prolonged adiabatic curves ADM,BCN. — The heat rejected with each pound of the air when discharged is represented by the area between D C and the curves D M, CN. The energy exerted by each pound of air is represented by the area A BC D. The volume swept through by the piston of the working cylinder per pound of air is FC=»,: the volume swept through by the piston of the pump is F D = The following are the formule proper to this kind of engine :— ° K Data. Atmospheric pressure and absolute temperature, p,, 7 Ratio of compression and expansion, 7. Highest absolute temperature, ~,, JOULE’S AIR ENGINE. 373 REsvtts, per pound of air. Absolute temperatures— 7 T T= Ty 77 Lo 7, oO; 7 = oats Pie w sista eeest's (1) Pressures— aa —— eee A 14408 . eas ¢ Pa = Po = Pat? == Pat? 5 P= Pare evrvees (2) Volumes— 5 53-15 Ta te Pa — Va . Sets. . 7 ‘les . Th . Rae) Vy = Vg sien 7, res? teeeeeens(Os) . 7 VU, P UY = Vu - pres Heat received— Hy, = 183-45 (=,—+,) = 183-45 (ay — 74 79)....0006(4,) Heat rejected— Hy = 183-45 (+, ~ 24) = 183-45 (7% “s) ee pas Energy exerted— U => H, - 4H, = 183-45 { "5 (1 _ a ais (rou 1) \ 1 = ty, (1 = sis) Jeter cere nen eet een ne eee (6 ) Efficiency of flluid— U Tq? Te, 1 Ha 7, : a =1- ae tet t es eeweee (7.) Afean effective pressure—- ‘ 5 3-451 pa (ree 1) (a -4 - st) ee (8) 0 % The following is a numerical example, which, however, is ima- ginary, as no experiments have been made on engines of the kind now considered :— 374 STEAM AND OTHER HEAT ENGINES. Data. pa= 2116-4; Ty = 50°.*. ey = 511°; r= 2; Ty 5612... 102274, RESULTS. 1 - 1 0408 _. 7.897. a ie be, Re - oe = 13827 5 cme = 07537; — = 5. *b ad vq 6783 0°. Ty = 2171; +, = 7706 .- T,= 309%4. Dg = Pp =e 2-654 x 2116-3 = 5617; p, = py = 2116°3. Vg == 12°84; v, = 6-42; v, = 9°68; v, = 19°35; H, = 183-45 ~ 344°-1 = 63128 Hy = 183-45 x 259-4 = 47583 U = 183-45 « 847 15545 15545 SEES (29) 63128 Dee ‘TEefficiency of fluid, Mean effective pressure— 15545 19°35 If an engine of this class were made to work up to a high tem- perature, it would be necessary to keep the packing of the piston cool by some such means as making the lower part of the piston, as in Ericsson’s engine, hang considerably below the packing ring, its interior being hollow, and filled with a slowly conducting material. 277. Burnace-Gas Engines — Cayley’s — Gordon’s— Avenier de la Gree’s—The greater part of the waste of heat from the furnace might be prevented if it were practicable to drive the piston of an engine directly by means of the hot gaseous products of combus- tion. An engine of this kind was made and worked experimentally by Sir George Cayley. It consists essentially of the same parts with the air engine described in the preceding Article, except that in the furnace gas engine, the heating vessel and the furnace are one; that is to say, the compressing pump draws air from the atmosphere, compresses it, and forces it into a strong air-tight 802 lbs. on the square foot = 5-57 Ibs. on the square inch. FURNACE-GAS ENGINES—STEAM ENGINES, 375 furnace, where its oxygen combines with the fuel; then the mixed hot gas produced by the combustion is admitted into the working cylinder, where it drives the piston through part of its stroke at full pressure, and through the remainder by expansion, until it falls to the atmospheric pressure, and is discharged. The furnace is fed through a double valve, which is so constructed, that fuel can be introduced through it without permitting the escape of more than a very small quantity of the compressed air. The theoretical diagram of such an engine, and the formule applicable to it, are exactly similar to those given in Article 276, except that the furnace gas is somewhat denser than air. This difference may be allowed for by conceiving, that all the formule, instead of having reference to one pound of the gas, have reference to so much of the gas as is produced by supplying one pound of air to the furnace. The cylinder, piston, and valves of this engine, were found to be so rapidly destroyed by the intense heat, and the dust from the fuel, that no attempt was made to bring it into general practical use. An engine on nearly the same principle was invented by Mr. Alexander Gordon. Dr. Avenier de la Grée has proposed a kind of furnace-gas engine in which, so far as it can be judged of by mere description, without experiment, the difficulties arismg from the dust and heat may very probably be overcome; and the only objection will be that common to all air engines which draw a cylinderful of air from the atmosphere at each stroke, viz., the greatness of their bulk in proportion to their power. Ag to engines in which the air is heated by the explosion of coul-gas, see page 448, Section 5.—Of the Efficiency of the Fluid in Steam Engines. 278. Theoretical Diagrams of Steam Engines in General.—The sketches which have already been given in fig. 17, page 48, and in fig. 99, page 337, illustrate the general character of the diagrams which indicate the energy exerted by the steam in the cylinders of steam engines. The curves actually described on the indicator cards of these engines present so many differences as to the mode in which the pressure ‘and volume of the steam vary during its action on the piston, that their figures cannot be expressed exactly by any general system of mathematical formule; especially because in the present state of our knowledge, it is impossible accurately to separate those irregularities in diagrams which arise from real fluctuations in the pressure of the steam, from those which arise from the friction and 376 STEAM AND OTHER HEAT ENGINES. inertia of the moving parts of the indicator. Some of those irregu- larities will be more particularly described in a subsequent Article. In order that it may be possible to compute from theoretical principles the power and efficiency of the fluid in steam engines, a figure is asswmed for the diagram, approximating to the real figure, but more simple (see fig. 109). In that figure, A B repre- sents the volume of a certain mass of steam, when admitted into the cylinder, so as to drive the piston through a space equal to that volume. The first assumption by which the diagram is simplified is, that the pressure of the steam remains constant during its admission, so that A B is a straight x line parallel to O X, and the constant B pressure is represented by OA = GB. The curve BC represents the ex- pansion of the steam after its admis- sion is cut off. In actual diagrams, this curve presents a great variety of figures, depending upon the com- O Ge tz. munication of heat to and from the Fig. 109 steam, and other causes, and almost Se always contains undulations, which probably arise partly from vibrations in the mass of steam itself, and partly from oscillations due to the inertia of the indicator piston. The second assumption consists in assigning to the curve BC one or other of two definite figures, according to the following suppositions :— I. When the cylinder is either exposed, or simply cased in slowly conducting materials, such as felt and wood, the steam is assumed to expand without receiving or giving out heat; so that BC is an adiabatic curve, whose form will be explained in Article 281. II. When between the slow conducting casing and the cylinder, there is an iron casing or outer cylinder called the “steam jacket,” supplied with steam from the boiler, it is assumed, that the heat communicated by means of that jacket to the steam expanding in the cylinder, is just sufficient to prevent any practically appreciable part of it from becoming liquid; so that BC is part of a curve whose co-ordinates represent the pressures and the volumes of a given weight of steam of saturation. These two suppositions have reference to engines in which the steam is not “superheated ;” that is, raised to a temperature above the boiling point corresponding to its pressure. The action of superheated steam will be considered in the next section. A 4 4 ENERGY EXERTED BY STEAM ON PISTON. 377 The third assumption is, that the steam is exhausted, or dis- charged from the cylinder during the return stroke, at a constant pressure; so that the lower side EF of the diagram is a straight line parallel to OX; and the constant bach pressure is represented by OF = HE, which may be equal to, or less than the pressure at the end of the expansion HC. (It would be possible, also, to make the back pressure greater than the pressure at the end of the expansion; but this never occurs in engines that are well con- structed and worked.) The third assumption involves also the’ assumption, that the fall of pressure, if any, at the end of the stroke (represented by C E), takes place suddenly. The value taken for the assumed constant back pressure ought of course to be equal to the mean value of the actual variable back pressure, so far as it can be accurately ascertained. What that mean value is in different cases will be considered in a special Article. The fourth assumption consists in neglecting the volume of the liquid water as compared with that of the steam, so that the side FDA of the diagram is a straight line coinciding with OY, instead of being a curve having ordinates parallel to O X, represent- ing the successive volumes of the water as it sustains a gradually increasing pressure in the feed pump, and corresponding (though of much smaller magnitude) to the ordinates parallel to OX of the curves marked D A in figs. 104, Article 274, and 108, Article 277. This assumption gives rise to no error appreciable in practice. Thus is obtained a diagram for purposes of calculation, of the kind of form represented by ABCEFD A, of which the side BC alone is curved. Experience proves, that although in a dia- gram of this kind, in which the smaller fluctuations of the pressure are neglected, the pressures corresponding to particular positions of the piston sometimes differ considerably from the actual pressures, yet the differences, being in opposite directions at different points of the diagram, neutralize each other in such a manner, that the agreement between calculation and experiment is very close as regards the energy ewerted, and the mean effective pressure; being the quantities which are of the greatest importance in practice. For the present, the quantity of steam acting as a cushion (Article 262) is supposed either to be inappreciably small, or to have had its successive volumes calculated and deducted, so that the diagram in fig. 109 is freed from its effects. The effect of “ cushioning” steam will be considered farther on. 279. Forms of Expression for Energy.—The following notation will be employed in formule relating to the efficiency of steam :— 3878 STEAM AND OTHER HEAT ENGINES. Represented in the Quantity. Symbol. diagram by Absolute pressures of steam— During the admission, .............. py OA=CB Atany time during theexpansion, yp ordinate of BC At the end of the expansion,...... Pa HC =OD During the return stroke,......... Ds HE=OF = Absolute temperatures— Of the steam when admitted,...... Ty Of the steam at any time dur- ” ing the expansion, ............ Of the steam at the end of the ONPANSLON xcs crchiswiccansncieiediers *2 Of the feed water supplied to the boiler. a csesnnensmnsscianene - Temperatures on ordinary scale,..... T,, &e. Volumes of one lb. of steam— When admitted,...........cccceecees vy Atanytime during the expansion, v At the end of the expansion,...... Denstiy of steam in lbs. per cubic Sost— When admitted,.........:::csceeeree Dy Volume occupied by the mass of steam, or of sieam and liquid water, under consideration— | | When admitted,..........cccccceeeee ay AB=OG Atany time during theexpansion, uw abscissa of BC At the end of the expansion,...... Uy =P Uy DC=O0OH Ratio of expansion, .........cccceeeeeees = 2 DC+AB ‘1 Energy exerted by one lb. of steam,... U Linergy exerted by the mass of steam) u. ; under CONSIAETALLON, cesceeieeceees i = area ABCEF A UF Jean effective PVESSUTE, eee a =Pm — Ds an = the reciprocal of the ratio of expansion, is called the admission, and sometimes the cut off, being the fraction of the stroke at which the admission of steam is cut off. The reason for having the symbol uw, distinct from v,, to denote the volume of the:mass of steam when admitted, is that it is in EXPRESSIONS FOR ACTION OF STEAM. 379 some cases more convenient to consider the action of a pound of steam (in which case uw, = %,), while in other cases it is more con- venient to consider the action of so much steam as occupies a cubic foot when first admitted (in which case w= 1); or rather, to speak strictly, so much steam as occupies, when first admitted, one cubic foot more than it did in the liquid state; but the difference between these two definitions of the mass of steam under con- sideration is neglected. The relations between + (= T + 461°-2 Fahrenheit) p, v, and D, are given by the formule of Article 206, equations 1 and 2 (page 237), and of Article 256, equation 1 (page 326), and by Tables IV. and VI. (As to the interpolation of quantities in these tables, see Article 279 a, immediately following the present Article.) There are two modes of expressing and calculating the energy represented. by the area of the diagram. The first, which corre- sponds to that expressed for diagrams in general by equation 2 of Article 263, is the best suited for purposes of exact calculation, and of reasoning about principles; the second, which corresponds to the expression in equation 1 of the same Article, is the besé suited to a certain approximate method of calculation, which is expeditious and convenient in practice. Metrxop I.— To the area ABCD)... eee cee Dh dp Pz Add the rectangle DF x OD,.........0. +b Ug (Py—-Ps) Then the area ABCEFA= “3 U= i udp + Us (Pops) (1.) 1 P: The integral in this expression, as will afterwards be shown, is calculable by the aid of certain functions of the absolute tempera- tures 71, To Mertuop II.— To the rectangle OA x A Byuweeseee Py Uy Add the area GBOH,...ccuseecces +[°odu uw And subtract the rectangle OF x FE — Pz Us Then the area ABCEFA =; Usp, uy, +[ 7) pdu — Py Ug..(2.) According to this form of expression, the mean effective pressure has the value 380 STEAM AND OTHER HEAT ENGINES, Pa me we 9g = iy — ig ever.) in which the symbol p,, denotes the mean gross pressure, or mean forward pressure, which is represented in the diagram by the mean height of the line A B C above O X. The convenience of this second method arises from the fact, that within the limits of pressure and volume which usually occur in practice, the curve B C approximates to a curve of the hyperbolic class; that is, a curve in which the ordinate is inversely propor- tional to some power of the abscissa, as expressed by the equation < being an index which is different according to the circumstances of the case, and is to be found by trial. When i= 1, the curve is a common hyperbola, and the area O A BC H is U: ryt fp du=piry (1+ hyp 10g 9) 3. ocean (5.) but in the cases which occur in the working of saturated steam, ¢ is fractional, and greater than 1; and then we have Py y+ | Us pdu=py ry 5. Pte uy (ee z i emaiti : =H Gel tad. | = Py P Uy jerereven (6.) from which is obtained the following expression for the mean for- ward or gross pressure :— tr—t—r—? Pn =P ° Rea Peewee deen conse ee encene 7.) Formule of this kind, and tables computed by means of them, such as Tables VII. and VIII. at the end of the volume, are con- venient in approximate calculations for practical purposes, especially as they do not involve the temperature. 279 A. Interpolation of Quantities im the Tables. —When in using Table IV. or Table VI. for steam, or Table V. for ether, it is required to find some quantity intermediate between those given in the table, that quantity can be found with accuracy sufficient for ordinary purposes by the aid of first differences. It is to facilitate such interpolation that the logarithms of the pressures, densities, volumes, and quantities denoted by L, are given, together with the INTERPOLATION IN TABLES—BACK PRESSURE. 381 successive differences of those logarithms (denoted by 4); because the differences of the logarithms vary much less than those of the numbers to which they belong. Suppose, for example, that it is required to find from Table VI. the volume V’ corresponding to a pressure P’ which lies between two, of the pressures given in the table. Let P be the neat less pressure to P’ which is found in the table, and V the correspond- ing volume; then, approximately, . ; —Alog V log V’ = log V — (log P’— log P) - Tige and similar methods may be applied to other quantities. The sign — immediately prefixed to 4 log V is merely the algebraical mode of indicating that V diminishes when P increases. For example, let it be required to find the volume of a pound of steam in cubic feet when its absolute pressure is ¢wo atmospheres, or 29-4 lbs. upon the square inch, or 4232°8 lbs. on the square foot =f". The next less pressure in the table is 4152. Then log P' = 3-6266; log P = 36183; log V = 1-1461; slog P = 0:0678; — 4 log V = 0:0637; and therefore, 637 log V = 1:1461 — 0-0083 78 = 1:1383; and V = 13°75 cubic feet per lb. 280. Back Pressure—If the steam working in steam engines were unmixed with air, and if it could escape without resistance and in an inappreciably short time from the cylinder after having completed the forward stroke, the back pressure would be simply, in non-condensing engines (conventionally called “high pressure engines”), the atmospheric pressure for the time; and in condensing engines, the pressure corresponding to the temperature in the con- denser. This may be called the pressure of condensation. The mean back pressure, however, always exceeds the pressure of condensation, and sometimes in a considerable proportion. One cause of this, which operates in condensing engines only, is the presence of air mixed with the steam, which causes the pressure in the condenser, and consequently the back pressure also, to be greater than the pressure of condensation of the steam. For example, an ordinary temperature in a condenser when working properly, is about 104° Fahrenheit, to which the corresponding pressure of steam is 152-6 lbs. on the square foot, or 1:06 lbs. on the square inch. But the absolute pressure in the best condensers is scarcely 382 STEAM AND OTHER HEAT ENGINES, ever less than 2 lbs. on the square inch, or nearly double of the pressure of condensation. The principal cause, however, of increased back pressure, is resistance to the escape of the steam from the cylinder, by which, in condensing engines, the mean back pressure is caused to be from 1 to 3 lbs. on the square inch greater than the pressure in the condenser. There is as yet no satisfactory theory of that resistance, so that it cannot be computed for any proposed engine by means of a general formula. The back pressure, therefore, in proposed condensing engines, can for the present only be estimated roughly from the results of experience in particular cases. The following is a summary of some such results :— Mran Back Pressure, p,- Lbs. on the Lbs. on the square foot. square inch. Ratio of expansion from 1} to 3,... 720 5 from 4 to 7,.... 648 to 504 4% to 33 from 8 to 15,... 504 to 432 3% to 3 a 77 32 ” There is a deficiency of precise experimental data on this sub- ject, because of the frequent omission to observe the atmospheric barometer at the time when the indicator diagrams of steam engines are taken. The consequence of that omission is, that the diagrams show only the effective pressures of the steam, and not the absolute pressures, which are left to be roughly estimated by guessing the probable atmospheric pressure. _It is certain, that if sufficient experimental data existed, the back pressure would be found to vary with the speed of the engine, being greater at higher speeds, and also with the density of the steam at the commencement of the exhaust, and with the size of: the exhaust port through which it escapes from the cylinder. In non-condensing locomotive engines, a great number of oxperi- menial data as to back pressure have been collected and arranged, and to a certain extent reduced to a system of laws, in Mr. D. K. Clark’s work On Railway Machinery. That author finds, that the excess of the back pressure above the atmospheric pressure varies nearly— As the square of the speed ; As the pressure of the steam at the instant of release; that is, of the commencement of the exhaust ; Inversely as the square of the area of the orifice of the blast pipe, through which the steam is blown into the chimney to pro- duce a draught. Mr. Clark also finds, that the excess of back pressure is less, the greater the ratio of expansion; that it is less, the longer the time BACK PRESSURE—THERMODYNAMIC FUNCTION. 383 during which the eduction of the steam lasts; and that it is in- creased by the presence of liquid water amongst the steam, being in certain cases greater in unprotected than in protected cylinders in the ratio of 1:72 to 1. As an example of specific results obtained by Mr. Clark, it may be stated, that “with a mean of 16 per cent. of release,’—that is, with the exhaust port opened when the piston had performed 0-84 of its forward stroke—“with an admission of half stroke,”—that is, with the ratio of expansion 2, nearly, “and with a speed of piston of 600 feet per minute;” the excess of the back pressure above the atmospheric pressure, in protected cylinders, was about 0:163 of the excess of the pressure of the steam at the instant of release above the atmospheric pressure. It is probable, that the general results arrived at by Mr. Clark may be safely applied to all engines, whether condensing or non- condensing, to the following extent :— That in the same engine, going at the same speed, the excess of the mean back pressure above the pressure of condensation, varies nearly as the density of the steam at the end of the expansion ; And that in the same engine, with the same density of steam at the end of the forward stroke, that excess of back pressure varies nearly as the square of the speed. 281. Thermodynamic Function, and Adiabatic Curve, for Wixed Water and Steam.— When, as in the present investigation, the volume of a pound of water, and its variations, are treated as. insensibly small, the value of the thermodynamic function consists. simply of the first term of the expression in Article 246, equation 1; that is to say, J hyp log 7; J denoting, as usual, Joule’s equivalent, or the dynamical value of the specific heat of water. Suppose the pound of water to be raised from a fixed temperature to any given absolute temperature z, and then to be either wholly or partially evaporated; and let wu be the volume of the steam produced, which for total evaporation is equal to v, the volume of one pound of saturated steam at the given boiling point, and for partial evaporation, may have any value less than v. Then from Article 255, equation 1, it is evident, that to complete the thermodynamic function for the aggregate of water and steam, we must add to the expression already found for the water in the liquid state, the following quantity :— dp. ua giving for the complete thermodynamic function for one lb. of water and steam— 384 STEAM AND OTHER HEAT ENGINES. d o== J hyp log + -bu 5? senlgieniaaes (1.) [The same expression may be made applicable to any other fluid hy putting instead of J, J c, the dynamical specitic heat of the fluid in question in the liquid state. ] The equation of an adiabatic curve is % = constant. This enables us to find the equation of the form of the curve BC in the diagram, fig. 109, Article 278, when that curve is adiabatic ; that is, when the steam expands without receiving or giving out heat. Attending to the notation of Article 279, we have, in the present case, for the point B in the curve, Uy = V5 and for any other point, J hyp log + +4 $2 = 5 hyp log ate ge bose (2.) from which is easily deduced the following expression for the volume w occupied by one lb. of water and steam at any pressure pr = 1 : ae ets), tema (5 hyp log Te Scream ania (3.) dt When common instead of hiyperbolic logarithms are used in the calculation, for J = 772 is to be substituted, J hyp log 10 = 772 % 2°3026 = 1777-6. According to Article 255, equation 8, a B 2c oP ( Si ~~) hyp log 10j..seesseee-ee(4) by means of which formula, with the aid of equation 1 of Article 206, and the constants given in page 237, ae can be computed. The use of the equation 3 for computing the value of wu may be much facilitated, by employing the values of L, the latent heat per cubic foot, which are given for steam in Table IV. (and for ether in Table V.); for according to Article 255, equation 2 (neglecting the volume of the liquid water), ts we an STEAM WORKING EXPANSIVELY. dp_U, dz 7’ so that equation 3 of this Article becomes u=t (5 hyp Io ga + ls =). sitsaite OD A convenient modification of equations 3 and 5 is the follow- ing :— , 1 Let the weight of steam under consideration be D, = a so that its initial volume w, is one cubic foot. Then, instead of fr may be put r (= Z), the ratio in which the steam is expanded; so that we have for the value of that ratio, r= (sD, hyp log 24 + $?1) vy dt T T. L = { (JD, hyp log 2 +) aeeeeas (6.) 282. Approximate Formula for Adiabatic Curve—From the re- sults of numerical calculations of the co-ordinates of adiabatic curves for steam, it has been deduced by trial, that for such pres- sures as usually occur in the working of steam engines, the relation between those co-ordinates is approximately expressed by the following statement :—the pressure varies nearly as the reciprocal of the tenth power of the ninth root of the space occupied; that is to say, in symbols 10 RAE F MOAN Ys is caddsiveceeevienniles (1.) This formula belongs to the class already explained in Article 279, Method IT.; the value of the exponents and co-efficients being 10 3 Ld See tags telags ay H 95 oy = 10 @) The preceding equation 1, and those deduced from it, are most expeditiously employed by the aid of a table of logarithms. In the absence of a table of logarithms, the ninth root of any ratio can be found by extracting the cube root of the cube root, either by the aid of a table of cube roots, or by ordinary arithmetic, 283. Liquefaction of Steam Working Expansively.— The volume 2¢ 386 STEAM AND OTHER HEAT ENGINES. of one pound of saturated steam (neglecting the volume of the liquid water), according to Article 256, equation 1, is H' H' Co ae — ape Peer re ereneereeeeeee (1.) dt HY’ being the latent heat of evaporation of one pound. It appears by computation, that the volume w given by equation 3 or equation 5 of Article 282 is less than v in all cases which occur in practice ; from which it follows, that when steam expands in driving a piston, and receives no heat from without, a portion is liquefied. To find under what conditions, and to what extent this conden- sation by expansive working will take place, we have for the pro- portion borne by the condensed steam to the whole mass of steam and water, the following expression :— V—U eee Pie % om) p li - ee (5 hyp log ~ i. setunaiaee (2.) The value of H’ is given approximately in foot-lbs. per pound of steam by the formula H’ = a—bs = 1109550 — 540-4 e000 (3.) For any other fluid, J ¢ would have to be put instead of J, and for wand 6 their proper values, supposing them to have been ascer- tained. It may be shown by an investigation, which it is unnecessary here to give in detail, that the expression (2) is always positive so long as a Jc The principle just stated, as to the liquefaction of vapours by expansive working, was arrived at contemporaneously and indepen- dently, by Professor Clausius and the Author of this work in 1849. Its accuracy was subsequently called in question, chiefly on the ground of experiments which show that steam, after being expanded by being “wire-drawn,” that is to say, by being allowed to escape | through a narrow orifice, is super-heated, or at a higher tempera- ture than that of liquefaction at the reduced pressure. Soon afterwards, however, Professor William Thomson proved that those experiments are not relevant against the conclusion in question, by showing the difference between the free expansion of an elastic fluid, in which all the energy due to the expansion is expended in agitating the particles of the fluid, and is reconverted into heat, vy is Tess than f& (= 1437°2 for steam = 461°2 +976"). EFFICIENCY OF STEAM IN A NON-CONDUCTING CYLINDER. 387 and the expansion of the same fluid wnder a pressure equal to its own elasticity, when the energy developed is all communicated to external bodies, such, for example, as the piston of an engine. 284. Efficiency of S ina N ducting Cylinder.—In the present Article, the cylinder is supposed to be sufficiently protected against any appreciable loss of heat by conduction; and the steam is assumed to expand without receiving or emitting heat, so that BC in fig. 109, Article 278, is an adiabatic curve. The area A BC D, contained between that curve and the straight lines A B and C D, corresponding to the pressures p, and p, at the beginning and end of the expansion, has the following value, when the mass of steam under consideration is one pound : — _ fp fa, 1 a a Ps) ABOD= ["udp= [Pap a (Snyp log 1 +94 yi dc = T {4-1 + hyp log *1) ba ("1 —%) % ee 2 1 In fluids other than water, Jc is to be put instead of J. Inasmuch as the latent heat of evaporation of one pound of steam at 7, is 1% a = H’ = a-b =, = 1109550 — 540-4 +, nearly, we may transform the expression | into F{ aoe (1-+hypeg 2!) } + SSM. 4 1 It is often convenient to consider the action, not of one pound of steam, but so much steam as fills one cubic foot when first admitted into the cylinder at the pressure p,. In this case, we have A B= 4, =1 cubic foot; DC=u,=7 ratio of expansion ; and the area A BCD is found by multiplying the expression (1) * In using the formule 1 and 1 a, and those deduced from them, the following approximations are convenient :— a 27, —72) 7, e hyp log + 72 1 nearly. y—%, (1 + hyp log =} Foe Gite nearly, 1 +7 388 STEAM AND OTHER HEAT ENGINES. by D, = us the weight of one cubic foot of saturated steam at the 1 pressure of admission. Observing further, that PP i day roe 7’ we find, per cubic foot of steam admitted, ABCD= ID, {a~* (1 + hyp log *) \ of oe se) in which D, and L, can be found from Table IV. From the above equation 2, and the properties of the adiabatic curve already explained in Article 281, are deduced the following formule, most of which have reference to the action of one cubic foot of steam admitted; pressures being expressed in lbs. on the square foot :-— Data. py, absolute pressure of admission ; Ps absolute pressure at end of ex pansion ; pz, mean absolute back pressure ; t, (= T,+461°2 Fahrenheit), absolute temperature of feed water ; T,, ordivary temperature of condensation ; T,, ordinary temperature of atmosphere. REsvutts. Temperatures corresponding to the several pressures to be found by equation 2, Article 206, or by Table IV. Ratio of expansion— DC Soe L o> i ¢ 72 D, hyp log = + = Energy per cubic foot of steam admitted— -7F, UD, =ID,{ a~e(1 + hyp leg 2) \ ok a. “Ly SEP pigs ) Saas wawexasnuenrcesen cee eve (4.) Mean effective pressure, or energy per cudic foot swept through by prston— UD De Dn ~ Py ees veneer ec anesaetnn ees (5.) UNJACKETED STEAM ENGINE. 389 For Ibs, on the square inch, divide this by 144. Heat expended per cubic foot of steam admitted — Hy Dy =F Dy (4) — &) P Ly jeeeeeeeenees (6.) Heat expended per cubic foot swept through by piston, or pressure equivalent to heat expended— H, Dy TT Setter cee neteenenenenes (7.) a U Lificiency of steam, as duliav vsuuienuanedeneeons (8) Hy, Net feed water per cubic foot of steam admitted— DSi Lop heoaete en (9.) Net feed water per cubic foot swept through by piston— D ie Si diybonisweecavgasamansss (10.) Heat rejected per cubic foot of steam admitted— Ay Dj = Cy U) Digiceaccccee ase can (11.) Heat rejected per cubic foot swept through by piston— eee (12.) Lbs. of water to be injected into the condenser (if any) to abstract that heat— HAD, FU ny eee Cubic feet to be swept through by the piston per minute, for each indicated horse-power— 33000 — 330007 pert renee ene cov ene 14. Dn Ps U D, ? ( ) Available heat expended per indicated horse-power per hour— 1980000 a agesaeiaes: ead) The following is a numerical example :— STEAM AND OTHER HEAT ENGINES. 390 Data. Pressures. Lbs. per square inch. Lbs. per ae foot. Initial, p,. 33°71 4854 Final, ,. 10°16 1463 Back pressure, py 5700 420 Temperatures. Ordinary, T. Absolute, 7. Of feed water (4.) 95° 550'2 Of condensation (5.) 104 ’ Of atmosphere (6.) 59 Resvxtrs. Quantities found by Table IV. Ts T. L. i Corresponding top, = 257 “18:2 59720 008285 3) 53. Hos 194 655'2 20280 0'02685 Ratio of expansion— 718-2 a) = 2-875. 655-2 = 30280 (772 X 0°08285 x hyp log g555 T 718-9 Linergy per cubic foot of steam adnitted— UD, =772 x 0-08285 { 718-2 — 655-2 (1 i teniad i =) \ 63 9. +a 7183 x 59720 + 2 ‘875 x 743 = 182+ 5239 + 2136 = 7557 foot-lbs. Mean effective pressure— 557 oP a aar5 2629 lbs. on the square foot = 18-25 lbs. on the square inch. Heat expended per cubie foot of steam admitted— H, D,=772 x 0:08285 (718-2 — 556-2) + 59720 = 10362 + 59720 = 70082 foot-lbs. Heat expended per cubic foot swept through by piston, or pressure equivalent to heat expended— H,D, 70082 - Lol. 5-875 = = 24376 Ibs. on the square foot = 169°3 lbs. on the square inch. UNJACKETED STEAM ENGINE. 391 LE ficiency of steam— U _ 7559 _ 2629 18:95 H, 70082 24376° 169°3 Net feed water per cubic foot swept through by piston— D, _0:08285 r 2-875 Heat rejected per cubic foot of steam admitted— H, D, = 70082 — 7557 = 62525 foot-lbs. Heat rejected per cubic foot swept through by piston— 62525 2875 Injection water required to condense the steam, per cubic foot swept through by piston— 21747 1. 772 x (104 — 59) 0-626 Ib. = 100 cubic foot nearly. Cubie feet to be swept through by the piston per minute, for each indicated horse-power— =0:1077. = 0-0288 Ib. = 0-00046 cubic foot nearly. = 24376 — 2629 = 21747. 33000 2629 (or 12:55 x 60 =753 cubic feet per hour). Available heat expended per indicated horse-power per hour— 1,980,000 efficiency = 0:1077 To show how this expenditure of available heat is connected with the consumption of coal, let the coal be of such a quality, that the total heat of combustion of one Ib. of it is - 10,000,000 foot-lbs. (corresponding to a theoretical evaporative power of about 13-4). Let the efficiency of the furnace be 0:54; so that the available heat of combustion of one Ib. of coal is 5,400,000 foot-lbs. Then the consumption of coal in the engine now under considera- tion, per indicated horse-power per hour, is = 12:55 = 18,384,400 foot-lbs. 392 STEAM AND OTHER HEAT ENGINES, 18384400 5400000 The following are some deductions from the previous calcula- tions :— Net feed water per indicated horse-power per hour— 0:0288 x 753 = 21-7 lbs. = 0°347 cubic foot. Injection water per indicated horse-power per hour— 0626 x 753 = 471-4 Ibs, = 7°54 cubic feet.* 285, Approximate Formule for Non-conducting Cylinders.—The formule in the preceding Article which give the mean effective pressure, and the work of a given quantity of steam, are incon- venient in practice from the length of the calculations which their use involves, and from the circumstance, that although they serve to compute directly the ratio of expansion when the initial and final pressures are given, they cannot be so employed when the initial pressure and ratio of expansion, but not the final pressure, are given, except by the aid of a tedious process of trial and error. For practical use in ordinary cases, therefore, it is desirable to have a set of formule in which the computations are less tedious, and which can be used directly when the ratio of expansion is one of the data. When the initial pressure is not less than one atmo- sphere, nor more than twelve atmospheres, such a set of formule, sufficiently accurate in all ordinary cases, are deduced from the fact, already stated in Article 282, that during the expansive working of steam represented by an adiabatic line, = 3-405 Ibs. —10 nearly. peu The following are the formule thus obtained :— Data, 1, absolute pressure of admission ; 7, ratio of expansion ; Pz, mean absolute back pressure ; z,, absolute temperature of feed water— (=T,+461°-2); T., temperature of condensation ; T,, temperature of atmosphere. * The fundamental formuls of Article 284 were first published in a paper sent to the Royal Society in December, 1853, and published in the Philosophical Transac- tions for 1854, The same formule were also discovered independently by Professor Clausius about 1855, and published by him in Poggendorff’s Annalen for 1856. NON-CONDUCTING CYLINDER. 393 REsvtrs. Ww Final pressure, pPo=Pi tT 3 Posmucesewccenansesens (1) Mean total pressure— 10 ase be OFS aeislenen (2.) Mean effective pressure— Sy De = Pm — Px = Pr (10r-!—9 D) — Parevereeees (3.) The three preceding formule are applicable to pressures expressed in any kind of units. Energy per cubic foot of steam admitted— 1 T Dy =T (Pmn— Ps) = Pi (10—9r-5) Tf Pa jeeenee (4) in which the pressures are in lbs. on the square foot. To facilitate the use of these formule, the values of the ratios 10 £8 fr = 8 eve yea 1 and 78 _10,— 9 2-5; Pi and their reciprocals, are given in Table VII. at the end of the ea al : volume, for values of the “ admission” or “ cut off; ;? increasing at first by differences of 0-025, and afterwards by differences of 0-05. Intermediate values of the above ratios can easily be computed, when required, from those given in the table, by interpolation. Where the approximate formule of the present Article are used for calculating the energy exerted, and the mean effective pressure, the expenditure of heat, the feed water, injection water, &., may easily be computed by the formule already given in the preceding Article. But in cases where special accuracy is not required, the expenditure of heat may be computed approximately with less trouble by the following approximate formule :— Heat expended in foot-lbs. per cubic foot of steam admitted— H, D,= 133 p, + 4000 nearly,......0......000 (5.) p, being in lbs, on the square foot ; Heat expended per cubic foot swept through by piston, or pressure equivalent to heat expended— HD, 133 p, + 4000 Ibs. per square foot | oe z Faieea (6.) 394 STEAM AND OTHER HEAT ENGINES. Equivalent pressure in| _ 135 7, + 27-7 Ibs. per square inch lbs. per square inch r (6 4.) In the following numerical example, the preceding approximate formulz are applied to the case already calculated in the preceding Article, the ratio of expansion being supposed to be given. Data, Initial pressure, p,=33°71 Ibs, per square inch ; Ratio of expansion, r= 2°87E, so that Admission, : = 0348; Mean back pressure— pz=5 lbs. per square inch. REsULTs. Computation of the ratio Pe from Table VII.— Pi i Ae? zs Pn Ped Pm r r Pi Pi 3 639 05 058 = 3° : x 1:16 nearly 35 697 Therefore, for a= 348 = 35 — -002, = = 697 — 002 x 1:16=°695 nearly; 1 Mean total pressure— Pm= 93'T1 x +695 = 23°43 Ibs. on the square inch, Mean effective pressure— Po = Pm — Pz = 23°43 — 5:00 = 18:43 Ibs. on the square inch; The same as computed a 18-95 the exact formula ....... 2 » Difference,...... + 0:18 3 Pd or about it USE OF JACKET. 395 Pressure equivalent to heat expended— 134 x 33-71 + 97-7 2875 = 166 lbs. on the square inch; The same as computed 169-3 by the exact formula, » ” Difference,...... — 33 9 a5 or about +0. L ficiency of the steam, oe =0:1110 The same as computed by 07 the exact formule,...... \ Ome Difference,......... + 0:0033 or about 35. The errors arising from the use of the approximate formule, of which examples have just been given, are in most cases practically unimportant.* 286. Use of the Steam Jacket, and Hot Air Jacket.t—The con- clusion theoretically demonstrated in Article 283, that when steam or other saturated vapour in expanding performs work by driving a piston, and receives no heat from without during that expansion, a portion of it must be liquefied, is confirmed by experience in actual steam engines; for it has been ascertained, that the greater part of the liquid water which collects in unjacketed cylinders, and which was once supposed to be wholly carried over in the liquid state from the boiler (a phenomenon called “ priming”) is produced by liquefaction of part of the steam during its expansion; and also that the principal effect of the “jacket,” or annular casing envelop- ing the cylinder, filled with hot steam from the boiler, which was one of the inventions of Waitt, is to prevent that liquefaction of the steam in the cylinder. That liquefaction does not, when it first takes place, directly constitute a waste of heat or of energy; for it is accompanied by a corresponding performance of work. It does, however, afterwards, by an indirect process, diminish the efficiency of the engine; for the water which becomes liquid in the cylinder, probably in the form of mist and spray, acts as a distributer of heat, and equalizer * These approximate formule were first published in A Manual of Applied Mechanics, 1858, Article 656. ¢ Articles 286, 287, 288, and 289, are to a great extent extracted and abridged from a parer read to the Royal Society in January, 1859. 396 STEAM AND OTHER HEAT ENGINES, of temperature, abstracting heat from the hot and dense steam during its admission into the cylinder, and communicating that heat to the cool and rarefied steam which is on the point of being discharged, and thus lowering the initial pressure and increasing the final pressure of the steam, but lowering the initial pressure much more than the final pressure is increased; and so producing a loss of energy which cannot be estimated theoretically. Accord- ingly, in all cases in which steam is expanded to more than three or four times its initial volume, it has in practice been found advantageous to envelop the cylinder in a steam jacket. The liquefaction which would otherwise have taken place in tbe cylinder, takes place in the jacket instead, where the presence of the liquid water produces no bad effect; and that water is returned to the boiler. In double cylinder engines, where the expansion of the steam begins in a smaller cylinder, and finishes in a larger, the usual practice is to have steam jackets round both cylinders; but in a few examples in which the smaller cylinder alone is jacketed, the liquefaction is found to be prevented, showing that the steam during its passage from the small into the large cylinder, receives sufficient heat either directly from the small cylinder, or indirectly by conduction from the small to the large cylinder (which is in close contact with the small cylinder), to prevent any appreciable portion of it from condensing. Tt is desirable that a small quantity of the steam, not appreciable in calculating the efficiency of the engine, should be liquefied, in order to lubricate the packing of the piston. This generally does take place in jacketed engines, and is probably the effect of attrac- tion between the particles of water and the metal. The effect of a steam jacket in preventing condensation may be produced by a hot air jacket; that is, by a flue round the cylinder; or by enclosing the cylinder in the smoke box, as is done in many locomotive engines. The advantages of this are well shown in Mr. D. K. Clark’s work on Razhwoay Machinery. With this apparatus, however, there is not the same security against over dryness of the packing that there is with the steam jacket. 287, Efficiency of Dry Saturated Steam.—In the following inves- tigation, it is assumed that the steam in the cylinder, while expanding, receives just enough of heat from the steam in the jacket to prevent any appreciable part of it from condensing, with- out superheating it. This assumption is founded on the fact, that dry steam is a bad conductor of heat as compared with liquid water, or with cloudy steam, and that after cloudy steam has received enough of heat to make it dry, or nearly dry, it will receive addi- tional heat very slowly. DRY SATURATED STEAM. 307 The assumption is justified by the fact, that its results are con- firmed by experiment. The symbol v is used to denote the volume of one pound of steam én cubic feet, and the symbol p to denote pressure in pounds on the square foot, so that pressure in pounds on the square inch is denoted P YY Tae In fig. 110, let BC K be the curve whose co-ordinates represent the volumes and pressures of dry saturated steam. Vv A ZB D Cc EF iE L Kx T x G LL ™ Sc Fig. 110. Let OA =p, and A B=vy,, represent the pressure and volume of admission, and 7, the corresponding absolute temperature ; Let OD=p,, and D C=», represent the pressure and volume at the end of the expansion, and 7, the corresponding absolute temperature; then ae : ? o =r is the ratio of expansion, and v, 1 ia ; ose the admission, or effective cut-o7- 2 Let O F = p, be the pressure of exhaustion ; Let =, be the absolute temperature of the feed water. The energy exerted by one pound of steam is represented by the area of the diagram, consisting of the area ABCD= ["vdp, and 3 the area E F D C=, (p, — Ps) while the expenditure of heat per pound of steam consists of the following parts :— The sensible heat J (tr, — 7,); the latent heat of evaporation 398 STEAM AND OTHER HEAT ENGINES. at 7,; and the latent heat of expansion, which is communicated from the steam in the jacket to that in the cylinder. The work of one pound of dry saturated steam exceeds that of one pound of steam which expands from the same initial pressure to the same final pressure without receiving heat, to an amount represented by the excess of the area A BC EF A above the cor- responding area for an unjacketed cylinder, while the expenditure of heat is greater by the quantity which the steam in the cylinder receives during the expansion represented by the curve B C. The latent heat of evaporation of one pound of steam at the absolute temperature +, may be expressed with accuracy sufficient for the purposes of the present investigation, by the formula where a=1109550 foot-lbs. ; b= 540-4 foot-lbs. per degree of Fahrenheit. To find the area A BCD A, which represents part of the energy corresponding to any value of p, the value of v is to be expressed in terms of -H’, the corresponding latent heat of evaporation, according to the principle of Article 256, giving dp dz f,, the initial and final temperatures of the expanding steam, we obtain for the area A BC D A— je ee 71 =a‘ hyp. log. — — 6 (a1 —t2)5.ccececeeccenes (2.) 72 to which, adding the rectangle D C E F, the energy exerted on the piston by one pound of steam is found to be 1 Pi U = [Podp+y, (P2—Ps) which, being multiplied by dz, and integrated between ¢, and 7 =a hyp. log. = — 6 (t1 — 42) + % (Po— pg) j-++0+e(3.) in which a = 1109550 foot-lbs.; 6 = 540-4 foot-lbs, per degree of Fah. DRY SATURATED STEAM. 399 The MEAN EFFECTIVE PRESSURE, or work per unit of volume tra- versed by the piston, is Do resaes eee (4) 2 The heat expended per pound of steam, by a different mode of division from that previously given, is computed as follows :— Part of the sensible heat for raising one pound of water from the temperature of the feed to the final temperature of the expansion,— J (72 — 4); latent heat of evaporation at the temperature 7.,— H,=a-6%; heat transformed into mechanical energy between the temperatures 7 and 7— ABCDA= ["'vdp, as in equation 2. The addition of these quantities gives for the whole expenditure of heat in foot-pounds of energy per pound of steam,— =F (u—m)4a-day+ | vdp pe =I (n-a)+a(1+hyp Jog 2) —B cyeeneeneee(B.) (J = 772 foot-pounds per degree of Fahrenheit). The heat expended per unit of space traversed by the piston is equivalent to a pressure whose intensity is ij 20S, ee ener aaa (6.) of the energy exerted by the steam on the piston to the heat ex- pended on the steam; and that ratio having been determined, the available heat of a pound of fuel may be computed from the indi- cated work per pound of fuel, or vice versa, by means of the equa- tion,— available heat — J 8 jndicated work — U ee ee weal -) 400 STEAM AND OTHER HEAT ENGINES. In the practical use of equations 3, 4, 5, 6,7, and 8, the usual data are,— the initial pressure p, the ratio of expansion r, the back pressure Ps, and the absolute temperature of the feed-water t, = T, + 461°2. From p,, by the aid of known formule or of Table VLI., are to be found 7, and. Then TV, = 93 and from v», by the aid of the same formule or of Table VI, are to be found 7, and p,, and thus are completed the data for the use of equations 3 and 5, Let O L= p represent the pressure, and LK =v the volume, of a pound of steam at some standard temperature, such as that of melting ice (t) = 32° + 461°-2 = 493°2 Fahrenheit), and let Tt a= B (= — 2) e000... (9.) vf vdp=a'byp loz bo 0 be the area contained between LK and ancther parallel ordinate of the curve BC K corresponding to the absolute temperature -. Then by the aid of values of the function U, as given or inter- polated in Table VI., the equations 3 and 5 can be put in the following form :— U's Uh — Uy es ey — ee (10) f=, — Uy (2) a — 8 teases (11.) US Ue He ah hicientarenanande (12.) in which last expression for the heat expended, H, denotes the total heat of evaporation, from 7, at t,and h, the heat saved in consequence of the temperature of the feed-water being T,, instead of that of melting ice,—both quantities as given or interpolated in the columns respectively headed H and / in Table VI. The following statement then gives at one view the formule applicable to engines worked by sensibly dry saturated steam :— ' Data. Py 7) Pz Ty a8 already explained. DRY SATURATED STEAM ENGINES. 401 REsvLts. v,, volume of one lb. of steam hen admitted, to be found or in- terpolated in the column headed V, Table VI. Volume at end of expansion, — Final pressure, p, and temperature T,, to be found or interpo- lated in the columns headed P and T; Table VI. U', energy exerted by, and h, heat expended on, one Ib. of steam, to be found by equations 10 and 12, with Table VL, or by equations 3 and 5, without the Table. Mean effective pressure,— t De Da —— Dig Shas ns da ateins Sanat (14.) + i Pressure equivalent to expenditure of available heat,— a= 2; bene n weer emcee ee oenecaeeees (15.) LE ficiency of steam,— Pe Pu—P,__U'” 16 DSB tne (16.) Net feed water per cubic foot swept through by piston,— Heat rejected per 1b. of steam,— H— U' = Hy — hy — 04 (Dg — pig) jeveeeeeeeee(18.) Heat rejected per cubic foot swept through by piston,— Tea rv, Dy Pasissossaya tediansstanesis (19.) Injection water required per 1b. of steam— (T,, temperature of condensation, T,, temperature of atmosphere). i. 773 (1,1) iacaseven 2D 402 STEAM AND OTHER HEAT ENGINES. Injection water required per cubic foot swept through by piston— Pr— Pe 5 Mik Tp yaaaeats (21.) Cubic feet swept through by piston per minute for each indicated horse-power— Pe Available heat expended per hour in foot-lbs. per indicated horse- power— 1,980,000 1,980,000 », 23 iisacaes = i eee (23.) In applying these formule to an engine actually working, whose speed has been ascertained, let A. be the area of the piston ; s the distance through which it moves at each forward stroke if single acting, or during a double stroke if double acting; N the number of revolutions per minute ; R the total resistance reduced to the piston; then, as in Article 263, formula 5, and Article 264, formula 3, the energy exerted per minute is INS RSENS AS iecsenedstectiges (24.) and the indicated horse-power— NsAp e. 5 33000 Setters (25.) also, the available heat expended per minute is NGA Qipia vesseseusens wegen waeneed (26.) 288. Approximate Formulz for Dry Saturated Steam.— As the formule of the preceding Article require in their use a considerable amount of calculation, it is desirable to have, for the purpose of solving ordinary practical problems, approximate formule of a more simple kind. Those which will now be explained have been arrived at by a process of trial, and their agreement with the exact formule, and with experiment, has been tested for initial pressures ranging from 30 to 120 pounds on the square inch, and for ratios of expansion varying from 4 to 16. They may therefore be applied with confidence to engines working within these limits, and pro- bably somewhat above them; but for, pressures much exceeding 120 Ibs. on the inch, and ratios of expansion much exceeding 16, it is advisable for the present to use the exact formule. DRY SATURATED STEAM ENGINES. 403 The foundation of the approximate formule is the fact, that for pressures not exceeding 120 lbs. on the inch, or 17,280 Ibs. on the square foot, the equation of the curve BC K, fig. 110, is very nearly 7 PO Fi paaes saseesacteanimaceevatees (1.) This equation is very convenient in calculation, because the sixteenth root can be extracted with great rapidity to a degree of accuracy sufficient for practical purposes, by the aid of a table of squares alone; and, by a little additional labour, without any tables whatsoever. Let 7, as before, be the ratio of expansion; then we have evidently, the final pressure— Pg OF ese sawsaspiavgesensnyeeiay (2.) the energy exerted on the piston by one pound of steam =area ABC FA ‘; P =U= pg EP + (Ba — Ps) % 7 = {p, (17r-'— 167 - ) — pf ; Sie urs rao vs (3.) the mean total pressure, = To Mat owevsasmsementnneiaccruns sss (4.) 2 7 Spe rem aiben ear (5.) the mean effective presswre, or energy exerted per cubic foot— U ‘ elt Pa Pa Pama =P (arr — 16776) — py... (6.) It is evident, that if the pressure of exhaustion p, be given, and any two out of the three following quantities—the initial pressure py, the mean effective pressure p,, — pg, the ratio of expansion r— the fourth quantity can be calculated directly, if it is one or other of the pressures 7), Ym — P33; and if itis the expansion 7, it can be found by approximation. The approximate formula for the expenditure of heat per Ib. of steam, which has been found by trial to agree very closely with the exact formula within the limits already specified, and when the feed water is supplied at a temperature of from 100° to 120° Fahrenheit, is as follows :— d 154 p, v. = 15} py y= 5 ee eae) 404 STEAM AND OTHER HEAT ENGINES. so that the heat expended per cubic foot, or the pressure per square foot of piston to which the expenditure of heat is equivalent, is Pr= h _1gp, 8 laa vaineneeeteueeeceecs «o(8.) This gives for the efficiency 1 Pe_ Pm — Ps U'_17—16rG T De ee ek sseneeseen (9, to pe 5 153 153 Py me by means of which, when the work of a pound of coal is known, its available heat can be computed, and vice versa, as with the exact formula. To facilitate the use of these approximate formule, Table VIIL, at the end of the volume, gives the ratios p 17 <"=17 r-!— 16 r7 ie, and P1 1 PART = 16 ay, 2 and their reciprocals, for a series of values of 1+; and the right- hand division of the diagram opposite page 568 shows the values of Py +p; for various values of 1+ r by inspection. For a geo- metrical approximation to that ratio, see the Appendix, page 552. 288 A. Examples of the Action of Dry Saturated Steam.—The fol- lowing examples, being taken from the performance of actual engines, are intended at once to illustrate the use of the formule in Articles 287 and 288, and to compare their results with those of experiment. In comparing the results of formule for the expansive working of steam with those of the indicator diagrams of engines, it is not to be expected that the indicated pressures corresponding to parti- cular volumes, during or at the end of the expansion, will closely agree with those given by calculation; because considerable devia- tions, alternately upwards and downwards, arise from the friction of the indicator, the elastic vibrations of the indicator spring, and the pulsations of the particles of the steam itself. In the course of a complete stroke, however, those deviations neutralize each other, so that the indicated mean effective pressure ought to agree with that given by theory, if the theory is sound. About half a pound on the square inch, or 72 Ibs. on the square foot, may be considered as an ordinary limit of error in indicator diagrams. DRY SATURATED STEAM ENGINES—EXAMPLES, 405 Two examples of the application of the formule to actual engines, and of the comparison of their results with those of experiment, are annexed. Lxample I.—Double-cylinder engines of 744 indicated horse- power, calculated by exact formule :—* Data— Bottom of Top of cylinders. cylinders. Pressure of admission, p, + 144,........66 33°7 343 Back pressure, pz + 144,........ssesesessees 470 4'0 Ratio of expansion, 7,............cseeeeeee ees 44 61 Ordinary temperature of feed water p,=about 104° Fahren- heit. CaLcuLATED RESULTS— Bottom. Top. Final volume of 1 lb. of steam, vy, =7,, 50°375 94'4 Final pressure, py + 144,..........csceeeeees 7°367 4°867 Work of 1 1b. of steam, U’,............60.- 109552 117338 Mean effective pres- , an sure in pounds on = =P? I5‘1 10°95 the inch,............ { % Mean of both results,.........ccccsseeeseeeee 13°03 Mean effective pressure as observed, being the mean result of a series 13°10 Of Aiagramms,......sesccereeseeeceeeeceeees Difference, «i. cesasassvasssnceaiss —0'07 being within the limits of errors of observation. Bottom. Top. ded i Foot-lbs. Foot-lbs. Available heat expended per pound Of steam, Yy......ceecsesececeecsceneeeees ge00e0 925678 Pressure in pounds per square inch ; equivalent to heat, p,+144,......... i oe = seg lsveaitedeenue ceueueee ee manbe 1057 Efficiency, & EE Sea ONAN RTE o'l2r o'1e7 Pr Mean, 13:03 + 105°7, ........cecceceeee: 0'123 * These are the engines made by Messrs. Randolph, Elder, & Co., for the steamer “ Admiral,” built by Mr. James R. Napier. 406 STEAM AND OTHER HEAT ENGINES. Net feed water per cubic foot swept through by pistons— D. Bottom. Top, - INI POUNIS) cossgsrsvevase dereadsedededson o'0199 0°0134 MCAT os dc secsssisnndeecsen’s ourunatoeny se 0°0167 Heat rejected in foot- d d cg rgesedinfoot-pounds P= POW or gay 808,340 Per cubic foot swept through by pistons, 15,830 10,865 Mean, seaiougialee ute anieiegaoinueieueuuan axes 13,347 Injection water required in pounds per ] cubic foot swept through by pistons, 0'384 T, — Ty being supposed = 45°, ...... Available heat ‘expended per hour in foot-pounds per indicated horse-power— 1,980,000 _ 1,980,000 Efficiency 0123 PBS 08: ‘The actual consumption of coal was 2-97 lbs. per indicated horse power per hour; hence the available heat of combustion of 1 Ib. ot the coal was oo = 5,420,000 foot-lbs. ; which, if the total heat of combustion of 1 lb. of the coal be esti- mated at 10,000,000 foot-lbs., gives for the efficiency of the furnace and boiler, 0549 Example II., the same engines calculated by approximate for- mule :— Data— Lbs. per inch. Mean pressure of admission, iid Nan aueae ata sieeearcieneees = 34 Mean back pressure, ft sawee Dubwaaiteay nucleases idl see 4 Mean cut off, 1.9 le Font = 02 ReEsuLTs— Mean gross pressure, -——— i i 7 = 34 86 20 0D 4 snecireenstcnres 1717 Mean effective pressure, oe rv i 8, calculated, .......... 13°17 observed, ........0066 13°10 Difference, ... 00. .cceceeseeeeeeeneeeerees +007 Pressure equivalent to expenditure of heat, p, + 144, 10574 Efficiency, = aes = 0-125. i ry NEARLY-DRY STEAM. 407 289, Rules for nearly-dry Steam.—The rules of Articles 287 and 288 are accurate for one mode of expansive working only. The first five rules of the present Article are applicable to all modes of expansive working, provided only that the cylinder is supplied with heat enough to prevent any large quantity of liquid water from accumulating in it; so that the steam may be said to be nearly dry; and the last six rules give results for proposed engines, that are accurate enough for most practical purposes. In fig. 110a let A FG BH K A represent the indicator diagram of any steam engine, F being the point of admission, G that of cut-off, B the point of release, where the exhaust port is opened, H the end of the forward stroke, and K the point where “cushioning” (if any) begins (see page 420.) Let the horizontal line through C be the zero line of absolute pressures, so that heights above that line represent absolute pressures of the steam; B C, for example, being the absolute pressure at the instant of release. Through B draw B A parallel to the zero line; and, if necessary, set back the point A, so as to allow for clearance (see page 418), in order that the length A B may represent the whole volume of steam. contained in the cylinder and ports at the instant of release. From A let fall the perpendicular A O upon the zero line. Then horizontal distances on the diagram from the line O A F represent volumes occupied by the steam in the cylinder. Then if we calculate in a series of particular cases by equation 5 of Article 287, page 399, a quantity which may be called the heat of release, consisting of the total heat, sensible and latent, of the volume of steam A B at the absolute pressure C B, together with the quantity of heat which that steam would carry off from the cylinder and valve ports, supposing it to expand down to the back pressure without liquefaction, that quantity is found to be given approximately to the accuracy of about 1 per cent. by the following rule :— I. Multiply the product of the absolute pressure and volume of the steam at the point of release by 16 for a condensing engine, or by 15 for a non-condensing engine. The result will be the mechanical equivalent of the heat of release, nearly. To represent the preceding rule graphically, in fig. 110a produce AB to D, making A D=16 A’B for a condensing engine, or 15 AB for a non-condensing engine; complete the rectangle A DEO; then the area of that rectangle (= 16 or 15 AB- BC) represents the heat of release, in units of work. The area, A BH K, of that part of the steam diagram which lies below the pressure of release represents a portion of heat saved out of the heat of release, by conversion into mechanical work; and the area, A F G B, of that part of the steam diagram which lies 408 STEAM AND OTHER HEAT ENGINES, above the pressure of release represents an additional expenditure of heat, all of which is converted into work. Hence the following rules :— II. Whole heat expended on the steam = area A D EO- area AFGB. III. Heat converted into mechanical work = area AF GBH K. IV. Heat rejected with the exhaust steam = area A D E O — area A BH K, V. Efficiency of the steam = aS EoOPE area A DEO+ areaAFGB In applying the same principles to proposed engines, the same assumption may be made as in Article 278, pages 375 to 377; that is, AB may be treated as representing the whole capacity of the m S Al B. D Nee ar K °o COI ge Orel ox ene) Fig. 1104, cylinder; and K A F, FG, BH, and HK, as straight lines. Also, the expansion curve G B may, without material error, be treated as a common hyperbola. To produce such a curve, the steam must contain a little liquid water on its admission, or immediately after- wards; and that water must be evaporated during the expansion by means of heat communicated to it from the cylinder, which must receive heat either by jacketing or by superheating. Then the following approximate rules are applicable :— VI. To calculate the absolute pressure of release; divide the initial absolute pressure by the rate of expansion; that is to say, make = Dy = veteeeeeeeenereteearece renee: (1.) VII. To calculate the ratio of the mean absolute pressure to the initial absolute pressure; make Pm _ 1 + hyp logr, Poo? 7 denoting the rate of expansion. For values of this ratio and its reciprocal, see Table XI., page 443, NEARLY-DRY STEAM, 409 VIII. To calculate the mean effective pressure; trom the mean absolute pressure subtract the mean back pressure, estimated as in Article 280, page 382; that is to say, as before; Mean effective pressure, 2, = Pm — Dgccsssseeeeeeees (3.) IX. To find a pressure equivalent to the rate of expenditure of available heat: to the mean absolute pressure add 15 times the pressure of release in a condensing engine, or 14 times that pressure In @ non-condensing engine; that is to say, make, in condensing engines ; Pr = Dig TD DoF sec seesvasisennserdecee (4.) or in non-condensing engines, DiS Beg FUE Davies cgageescssies setes (4a.) X. The efficiency of the steam, as before, is Eire 2s apnea 5, Pr Pr mo XI. The mechanical equivalent of the rejected heat is found by multiplying the space swept through by the piston by 15 py + pg in condensing engines}............++ (6.) or 14 p, +p, in non-condensing engines......... (6a.) Exaupte.—Data—Condensing engine, absolute initial pressure p, = 34 lbs. on the square inch. Rate of expansion, 7 = 5. Mean back pressure, p, = 4 lbs. on the square inch. Results-—(1.) Pressure of release, p, = p, + 5 = 6°8 Ibs. on the square inch. . (a) Se es 05a, Pi 2 5 Therefore, mean absolute pressure, p,, = 34 x 0522 = 17°75 lbs. on the square inch. (3.) Mean effective pressure, p,, — p= 18°75 Ibs. on the square inch. (4.) Pressure equivalent to rate of expenditure of available heat, px, = 1775 +(15 x 68) = 119-75 Ibs. on the square inch. 13-75 O-11S 119-75 — i (6.) Mechanical equivalent of rejected heat = space swept through by piston x 106 lbs. on the square inch.* *The rules of this Article first appeared in the Engineer of the 5th January, 1866, where examples are given in greater detail. (5.) Efficiency of steam = STEAM AND OTHER HEAT ENGINES. 410 16.9 68.4 Zgo. Glo. oSS1 soba 0.96 9.€6 00.9 S6.F 190. tlo. ober 266 0.94 FL 11.9 zo.G 090. Elo. of6 rrh 0.9 9.+S z£.9 Sug go. tho. 0z9 g6F 0.96 0.$€ tol 19.9 zGo. Gzgo. org ghz 0.91 G.Gr- oI g.0 66.€ z60. of6 0.98 £0.% 160. rel 0.89 * Lo.¥ 060. gas 0.0$ 61.4 980. zLleé 0.2€ 63.4 SLo. 9gt o.FI 9.0 GS.¢ €or. GLL 0.08 65.€ col. oz9 z.€9 19.€ col. 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Condensing High Pressure Engines.—This term may be applied to engines such as Mr. Beattie’s locomotives, in which, although the steam is discharged from the cylinder at, or a little above, the atmospheric pressure, a portion of it is condensed for the purpose of heating the feed water, the remainder being used to make a blast in the chimney. This is effected by conducting steam through a branch from the exhaust pipe into a close vessel, through which there falls a shower of water from the water tank. From the bottom of that vessel water is drawn by the feed pump, and forced into the boiler, its temperature being usually about 200° Fahrenheit. In applying the exact formule to this case, T, is to be made = 200° Fahrenheit, or whatever other temperature the feed water may have. In applying the approximate formule, the results of the follow- ing calculation will in general be found sufficiently accurate. The approximate expression already given for the expenditure 1 of heat per unit of volume swept through by the piston, viz., we Py was obtained upcn the supposition of the temperature of the feed water being 104°, or thereabouts. Referring to Article 215 a, and to the Table in page 256, let f denote the “factor of evapora- tion” for the boiling point of the water in the boiler, and for the temperature of feed water 104°; and let /" be the factor of evapora- tion for the same boiling point, and for the temperature of feed water 200°; then the expenditure of heat will be reduced very nearly in the proportion J so that the approximate formula for the expenditure of heat per unit of volume swept through by the piston will now be Hf em (1.) ra ge Tet eteeeeeeeaneeeaes : For example, let the boiling point be 320° Fahrenheit, which corresponds to a pressure of 89-86 lbs. on the square inch in all, or 75 lbs, above the atmosphere nearly; then J’ =1:04; f=1:15; and a = oP MCAT YVencnis sicecesseacstecnses (2.) The pipe for conducting steam from the exhaust pipe to the condenser has a cock or valve, by means of which its opening is adjusted until it transmits the greatest quantity of steam com- HIGH PRESSURE CONDENSER—WIRE-DRAWN STEAM. 413 patible with complete, or nearly complete, condensation. According to experiments on Mr. Beattie’s engines described by Mr. Patrick Stirling, about one-fourth of the whole exhaust steam is required for this purpose; and the remaining three-fourths are adequate to produce a sufficient blast in the chimney. 290. Difference between Pressure in Boiler, and Initial Pressure in Cylinder.—Wire-Drawn Steam.—The fall which the pressure of the steam undergoes during its passage from the boiler to the cylinder, is due to the following causes :— 1. The resistance of the steam pipe through which the steam passes from the boiler to the valve box. 2. The resistance of the regulator, or throttle valve, by which the steam pipe is partially closed, in the same manner with the supply pipe of the water pressure engine, fig. 40, Article 132, page 140. 3. The resistance of the “ports,” or steam passages through which the steam is admitted from the valve box into the cylinder, and which are at times partially closed by the valves, so as to have their resistance increased. 4. The disappearance of actual energy when the steam passes from the ports into the cylinder, exchanging its previous rapid motion for the comparatively slow motion of the piston. It is impossible, in the present state of our knowledge of the properties of steam, to calculate separately the losses of pressure due to these four causes; and even were it possible, the complexity of the resulting formula would be out cf proportion to its practical. utility. All that can for the present be done is to use the theory of the discharge of gases through orifices, as explained in Article 254, in order to find the probable form of an approximate formula for the whole loss of pressure, and to determine a constant co-effi- cient in that formula empirically from experiments on existing engines. The best collection of experimental data on this subject is con- tained in Mr. D. K. Clark’s work on Railway Machinery. These data are taken partly from the experiments of Messrs. Gouin and Lechatelier, and partly from Mr. Clark’s own experiments; and are to a certain extent reduced to general laws. Amongst other general results, Mr. Clark finds that the effect of the resistance in the steam pipe is inappreciable, when the sectional area of that pipe is not less than y5 of the area of the piston for steam in an ordinary state as to dryness, and not less than 7s for steam in a very dry state; the mean speed of the piston not exceeding 600 feet per minute, or 10 feet per second. It follows, that in a well constructed engine, the steam pipe should be so proportioned, that supposing the density of the steam to be 414 STEAM AND OTHER HEAT ENGINES. the same in it and in the cylinder, the velocity of the steam through the steam pipe shall not exceed about 100 feet per second, and then the resistance in the pipe may be neglected. This result is corroborated by the known effect in practice of the ordinary rule, that where the velocity of the piston is from 200 to 240 feet per minute, the area of the steam pipe should be about zs of that of the piston, The resistance of the regulator in a properly proportioned steam pipe is inappreciable when it is wide open; and when it is partially closed, the investigation of mathematical relations between the resistance and the opening is practically unimportant, because the extent of opening of the regulator required to produce any given reduction of pressure in any existing engine can easily be found by trial. There remain to be considered, the resistance of the cylinder ports, and the loss of head on entering the cylinder. In Article 254, equation 1, is given an expression for the velocity of a gas rushing through an orifice, from a space in which the pressure is p,, into a space in which the pressure is p,. To prevent confusion, and to adapt the equation to the notation of the present section, Put p, to stand for the pressure in the boiler and valve chest, instead of p, ; And p,, the initial pressure in the cylinder, instead of po; Also put V instead of « to denote the greatest velocity of flow. Square both sides of the equation; divide by 2g; and for Sta ED y—l = head due to the maximum velocity V— v2 ( vy—1 zg ys} s substitute its equivalent, K,; then we have for the which for steam, treated as a perfect gas, becomes 0'233 5 = 366-7 7, { 1— (2) \ griuevenseell) Po From analogy with the flow of liquids and of air, it is probable that when besides producing a current of steam of a certain velocity, the difference of pressure has also to overcome the friction of a, passage, the left-hand side of the preceding equation should be multiplied by 1+ F, F being a “factor of resistance” (as in Article 99). Ihe quantity V2, being the mean square of the velocity with LOSS OF PRESSURE AT PORTS, 415 which the steam enters the cylinder, may be treated as the product of three factors, viz. :— ;: =~ of the mean velocity of the piston (let this be denoted y 3 The square of the ratio in which the area of the piston exceeds AZ the area of the port (=); - factor depending on the figure and manner of motion of the valve. For simplicity’s sake, take the product of this last factor, and of the factor 1 + F, which may be denoted by one symbol, B. Then the formula for the “loss of head” sustained by the steam becomes BV2 A2 0-233 “yar = 8067», {1 — (2) \, ies (2: Po giving the following formula for computing the ratio in which the absolute pressure of the steam falls :— { BV2 A2 429 —spxseT aa} Py Po The co-efficient, B, is to be determined empirically. As a basis for this determination in the case of dry steam may be taken one of the general conclusions arrived at by Mr. Clark, viz., that when A. 15, and V’ = 10 feet per second, Pr. 0-84 nearly; the pres- b sure in the valve chest, p;, being on an average 90 lbs. on the square inch or thereabouts, and consequently the absolute temperature 7, = 320° + 461°2 = 781°-2 nearly. These data give B = 32-4, and consequently B 82-4 1 29 X 366-7 ~ 23615°5 ~ 726’ so that equation 3 becomes ra _ Vea? Ve a 1 i Hae hee (4) In all cases in which the difference between p, and p, is small, the following formula is a sufficiently close approximation — 416 STEAM AND OTHER HEAT ENGINES. The following example is a case to which the approximate for- mula does not apply. The data are such as are sometimes met with in Cornish single acting engines :— V' = 23 feet per second ; A= 120; 7, = 745'2; whence p 4-29 41—0-8336 = 0-458; Po so that if p, = 52°52 lbs. per square inch, p, = 24 lbs. on the square inch. In the next example, the approximate formula is applicable; and the data are such as are very commonly met with in double acting expansive engines, = 25; V' = 4 feet per second; 7, == 266°-+ 461°-2 = 727°-2; whence, by equation 5, Hey. SS DB :130896 so that if p, = 39:2 Ibs, on the square inch, p, = 36:2 Ibs. on the square inch, the loss of pressure being 3 lbs. on the square inch. It appears further, from the experiments of Mr. Clark, that the loss of pressure of misty steam in traversing passages exceeds that of dry steam in a proportion which cannot be computed with any approach to precision, but which ranges from 11 to 23 and sometimes even to 3. The loss of head which occurs during the passage of steam from the boiler to the cylinder, does not wholly represent wasted energy ; for being expended in friction, it produces heat; so that steam which has had its pressure lowered by the resistance of passages, or as itis called, has been WIRE-DRAWN, is superheated (that is, is at a temperature higher than the boiling point corresponding to its pressure, although lower than the temperature in the boiler), as has already been stated in Article 253. Even supposing, however, that no energy is directly wasted when steam is wire-drawn, there is still an indirect waste of energy from the lowering of its pres- sure, which, by diminishing the forward pressure upon the piston as compared with the back pressure, and by diminishing the extent of expansive working of which the steam is capable, lowers its efficiency. -When an engine, therefore, has to work against a diminished 1 — 0-0764 = 0-9236; WIRE-DRAWING AT CUT-OFF, 417 resistance, it is better to diminish the mean effective pressure by cutting off the admission earlier, and so working with a greater ratio of expansion, than by contracting the opening of the regulator, and so lowering the initial pressure by wire-drawing. el former method makes the engine more economical, the latter ess. 291. Effects of Disturbing Causes on Diagrams.—Some of the deviations of the diagram of energy ¥ of a steam engine from the ideal form have already been ‘ considered _inci- \ dentally in the - preceding Articles ‘ of this section. In 4 the present Article ‘ the more impor- iS tant and usual of these deviations are to be classed and considered more in detail. These causes may be thus classed,— Causes which affect the power of the engine, as well as the figure of the diagram :— Nn A” mo Go I. Wire-drawing at cut-off. II. Clearance. III. Compression, or cushioning. IV. Release. V. Conduction of heat. VI. Liquid water in the cylinder. Causes which affect the figure of the diagram only :— VII. Undulations. VIIL. Friction of the indicator. IX. Position of the indicator, I. Wire-drawing at Cut-off—The valve by which the steam is admitted into one end of the cylinder, closes, in order to cut off the admission of steam, not instantaneously, but by degrees, especially when it is a slide valve. In consequence of this, the loss of pressure by the steam in passing from the valve chest into the cylinder gradually increases, and the pressure of the steam in the cylinder begins gradually to diminish, before the complete closing of the valve; so that ~~ top of the diagram, which is a 418 STEAM AND OTHER HEAT ENGINES. drawn during the admission of the steam, instead of presenting a straight line, AB (fig. 111), parallel to O X, presents a drooping curve, convex upwards, such as A HG. The point of the stroke where the complete closing of the valve, or actual cut-off, takes place, is usually marked on the diagram by a point of contrary flexure, G, where the curve convex. upwards, H G, produced by wire-drawing, touches the curve of expansion, G C, which is concave upwards. ‘The steam begins to a certain extent to work expansively before the valve is completely closed, and the energy exerted is nearly the same as if the valve closed instan- taneously at a somewhat earlier point of the stroke, which may be called the virtual, or effective cut-of: To find approximately that point, produce the expansion curve, C G, upwards, and draw the straight line, A B, to meet it; then the point B marks the effective cut-off, and determines the effective ratio of expansion to be used in computing the efficiency. II. Clearance is a term used to include, not merely the clearance proper, which is the space between the piston and the end of the cylinder to which it is nearest at the end or beginning of a stroke, but also the volume of the ports, and generally the whole minimum space between the piston and the valves. It is evident that this space, as well as the space through which the piston sweeps, has to be filled with steam, The clearance, for purposes of calculation, is expressed in the form of a fraction of the space swept through by the piston during a single stroke. Let A be the area of the piston, s the length of its stroke; then : volume of clearance Cece cte nae seen ecnnee le ee ¢ (1.) is the fraction in question, and volume of clearance = CA S...c0cceccceeeeees (2.) The length of cylinder equivalent to the clearance is Sone OT 55 cr (3) The value of the fraction ¢ ranges from 4 to 2y, and sometimes less, in different engines, being greatest in the smallest engines. The equivalent length of cylinder ¢ s varies less, being usually from one to two inches, ' The clearance affects the ratio of expansion in the following manner :— In fig. 111, let EF =As represent the whole space swept CLEARANCE. 419 through by the piston per stroke; and let LK =NA=cAs represent the clearance. The steam being cut off at B, AB in the diagram A BCEF A appears to represent the volume of steam in the cylinder at the instant of cut-off, and are the apparent cut-off and ratio of expansion. But the real volume of steami in the cylinder at the instant of cut-off is N B, and it expands to the volume LI; so that the real cut-off and ratio of expansion are fp ee ee ae po Bl Lee NB i ~ T+ e+ ge Lf the steam is completely exhausted from the cylinder during each. return stroke, the clearance produces the following effect on the expenditure of steam and of heat. The apparent volume of steam admitted per stroke being A B, and the real volume N B, the. expenditure of steam, and consequently of heat, is increased by reason of the clearance in the ratio On the same supposition, that the steam is completely exhausted during each return stroke, the mean absolute pressure is diminished nearly, but not quite, to the extent expressed by the following formula, in which 7’,, is the actual mean absolute pressure, and p,, what that pressure would be with the real expansion, r, if there were no clearance :— Dn Dm — © (Py — Dm) vevveveeeeneceaneens (6.) The diminution of mean pressure is not quite to the above extent ; because the energy with which the steam rushes in to fill the clearance is expended partly in impulse against the piston, and partly in producing heat by friction amongst the particles of steam, and that heat superheats the steam, and makes a less quantity suffice to fill a given space at a given pressure ; but it is unneces« sary to consider this in the calculation. . ; The efficiency of the steam is diminished nearly in the following proportion :— 420 STEAM AND OTHER HEAT ENGINES. cea (7) (pera. a III. Compression, or cushioning, is effected by closing the educ- tion valve before the end of the return stroke; for example, at the point corresponding to M on the diagram. This confines a certain quantity of steam in the cylinder, which is compressed by the piston during the remainder of the return stroke, the rise of its pressure being represented by some such curve as M A. In the figure, that curve is made to terminate at A, in order to represent the most advantageous adjustment of the compression, which takes place when the quantity of steam confined or “cushioned” is just suffi- cient to fill the clearance at the initial pressure py. An approximate formula for adjusting the compression is as follows :— The effect of this adjustment is to save all the additional expen- diture of steam per stroke denoted by cr’ in equation 5, and to save also the loss of energy per pound of steam expressed by the formula 6; so that the efficiency of the steam remains undiminished. The mean effective pressure, however, is diminished in the proportion rir; and the pressure equivalent to the heat expended in the same propor- tion; so that if p, and p, respectively represent those quantities, calculated, as in previous Articles, on the supposition of there being no clearance, they are altered respectively to 1 __ TDe a Peers and py, = Ga Streeter eee (9.) while the space to be swept through by the piston per minute, per indicated horse-power, is at the same time increased in the ratio rT, and becomes a in cubic feet,........--. (10.) when the pressures are expressed in pounds on the square foot. In the case which has now been considered of adjusted cushion- 2 of a whole cylinderfal of steam (clearance a : r ing, the fraction (eer RELEASE—CONDUCTION—WATER IN CYLINDER. 421 included), performs the part of a cushion according to the principles laid down for heat engines in general in Article 262, while the fraction performs the effective work. I l+er IV. Release means opening the exhaust port for the escape of the steam before the forward stroke is finished, in order to diminish the back pressure. In an engine in which there is no release (the exhaust port opening exactly at the end of the forward stroke), the diagram during the return stroke is usually a curve more or less resembling the dotted line C M K; the lower side of the ideal dia- gram used in calculation being a straight line E F, so placed that its constant ordinate p, is equal to the mean ordinate of the curve. LK TJ isastraight line, whose ordinate O L represents the pressure in the condenser (or in non-condensing engines, the atmospheric pressure). By making the release occur early enough, for example, at the point corresponding to P in the diagram, the entire fall of pressure may be made to take place towards the end of the forward stroke, so as to make the back pressure coincide sensibly with that corresponding to the ordinate of K I; and then the end of the diagram will assume a figure represented by the dotted line PI, which is usually more or less concave upwards. Energy will be saved to the amount represented by the rectangle K F x K I, and energy lost to the amount represented by the area of the figure PCIP; and on the whole, energy will be saved or lost according as the former or the latter of those areas is the larger. The greatest saving of energy is insured by making the release take place at a point Q such, that about one-half of the fall of pressure shall take place atthe end of the forward stroke, and the other half at the commencement of the return stroke, as indicated by the dotted curve Q RS. V. Conduction of heat to and from the metal of the cylinder, or VI. Zo and from liquid water contained in the cylinder, has the effect of lowering the pressure at the beginning, and raising it at the end of the stroke, in the manner already mentioned incidentally in Article 286, the lowering effect being on the whole greater than the raising effect. The general nature of the change thus produced in the diagram is shown by the dotted line GHIC F in fig. 112. The bad effect of liquid water is augmented by the increased resistance which it produces to the flow of the steam through the ports (see Article 280). The remedy for these evils, by heating the cylinder externally, has already been mentioned in Article 290, In some experiments the quantity of steam wasted through alternate liquefaction and evaporation in the cylinder has been found to be greater than the quantity which performed the work. 422 STEAM AND OTHER HEAT ENGINES. VII. Undulations, such as those sketched in fig. 113, are caused by the inertia of the indicator piston, and the elasticity of its spring. Fig. 112. Fig. 113. To diminish their extent, the spring of the indicator should be stiff, and its mechanism light. "When large, they make it extremely dif- ficult to determine the mean effective pressure from the diagram. In attempting to find that pressure, by sketching a diagram freed from undulations, it is more accurate to draw a line, such as the dotted line in the figure, midway between the crests and hollows of the waves, than to draw a line enclosing the same area with the wavy line. VIII. The friction of the indicator, by directly opposing the motion of its piston and pencil, tends to make the indicated for- ward pressure less, and the indicated back pressure greater, than the real forward and back pressure respectively, and so to make the indicated energy less than the real energy exerted by the steam on the piston; but to what extent is very uncertain. According to some experiments by Mr. Hirn (Bulletin de Mulhouse, vols. xxvii., xxviii.), the diminution of the indicated energy by the friction of the indicator agrees nearly with the work performed in overcoming the friction of the steam engine; so that the indicator shows, not the whole energy exerted by the steam on the piston, but very nearly the useful work of the steam engine; but it is doubtful how far this principle is generally applicable; and other experiments, especially those on screw steamers, are at variance with it. IX. Position of Indicator.—Experiments by Messrs. Randolph, Elder, & Co., have proved what might have been expected from the laws of fluid motion, that when a rapid current of steam blows across the orifice of the nozzle of an indicator, the indicated pres- sure is less than the real pressure. Every indicator, therefore, should be fixed, if possible, in a position where it is not exposed to this cause of error. 292. Mesistance of Engine — Efficiency of Mechanism. — The energy lost through the resistance of the engine comprehends that EFFICIENCY OF MECHANISM. 493 expended in overcoming the friction of the mechanism, in working the feed pump, in working the air pump and cold water pump of condensing engines, and generally, in overcoming all resistances arising within the engine itself, except the back pressure of the steam. Our knowledge of the amount of energy so lost is still very vague and indefinite. The formula (originally proposed by the Count de Pambour); by which it is calculated approximately, is of the follow- ing kind :— Let R, represent the useful load of the engine, reduced by the principle of virtual velocities to the piston as the driving point, as in Article 264. Then the prejudicial resistance, reduced to the piston also, probably consists of a constant part, which is the resis- tance of the engine when unloaded, and of a part increasing in proportion to the useful load; so that the total resistance, reduced to the piston, may be expressed in the following form :— Real Shi8, + Biteemanows (1.) R, being the resistance unloaded, and f the co-efficient for the variable part of the resistance. Let A be the area of the piston; then the total resistance, per unit of area of piston, which is equal to the mean effective pressure, may be thus expressed :— BR P= Pa-Po= =P) ETS Fe eames (2: The efficiency of the mechanism is given by the formula, Bea =— wae caseeearcens (3.) m — Pa Leta and this, being multiplied by the efficiency of the steam, and by the efficiency of the furnace, gives the resultant efficiency of the whole steam engine. ‘ The unloaded resistance is known by experiment to range from 4 Ib. to about 14 lb. per square inch of piston, including resistance of air pump (as to which, see p. 509), and to be on an average 1 Ib, per square inch ; hence we may put, approximately, - = 1 Ib. on the square inch = 144 lbs. on the square foot...(4.) The value of fin well-made engines in the best order is estimated 424 STEAM AND OTHER HEAT ENGINES. by the Count de Pambour at - = 0-143; and that estimate is cor- roborated by general experience, in cases in which there is no special cause for increased friction. In such cases, then, we may put for the gross resistance, in pounds, R= 1+ R, + A in square inches)....... veereee(5.) and for the efficiency of the mechanism, a : aree wexewineivne(O.) R ~ A (Pn — 23) 1143+ A se 1 In most cases which occur in practice, a result nearly agreeing with that of the preceding formula is. obtained by supposing the whole of the prejudicial resistance to be proportional to the usetul load; that is, by making ROAR Gneiiceopnacnvas (7.) the value of 7’ being somewhere between 0:2 and 0-25. In marine steam engines, a further loss of work takes place in impressing backward and lateral motion on the water; the result being to make 1+/'=from 1-6 to 167 in ordinary cases. (See Rules and Tables, page 274.) 293. Action of Steam against a known HResistamce—Pambour’s Problem.—The nature of the problem now to be considered with special reference to the action of saturated steam, has already been stated in general terms in Article 264. It was first solved by the Count de Pambour. In that author's solution, however, the weight of steam produced in the boiler in a given time was treated as a known constant quantity; while in this treatise, it is the available heat of the furnace in a given time that will be treated as a known constant quantity ; the problem being, when that quantity, and the useful resistance to be overcome by the engine, and the back pressure, and also the ratio of expansion are given, to find the mean velocity with which the piston will move. Let R, be the useful resistance, reduced to the piston. Then the total resistance, as explained in Article 292, is R= (L-Ef) By-b Rosecsessssssssescsvoes (1) Divide this by the area of the piston or pistons, in a single cylinder engine, or by the area of the larger piston or pistons, in a double cylinder engine; then PAMBOUR’S PROBLEM. 425 is the mean effective pressure, Let 7’ be the apparent ratio of expansion, c the clearance, then, as in Article 291, Division IT., we have for the real ratio of expan- sion, r+er r= TLE ay beeen e eee cee nee cnseaeeres (3.) Let the cushioning be adjusted as it ought to be so as to prevent appreciable loss of efficiency by clearance; then, as in Article 291, Division III., we have for the mean effective pressure in an ideal diagram, freed from the effect of the cushioning, PT. Bin? | | Pn=Pe + ps. J and From the real ratio of expansion r find, by the approximate for- mule of Article 285, or Table VIL., if the cylinder is unjacketed, or by the approximate formule of Article 288, or Table VIIL, if the cylinder is jacketed, the ratio fi, ? Pn then the initial pressure of the steam will be mat. Case Gao (5.) and the speed of the engine will adjust itself so as to maintain this pressure. From the initial pressure, by the proper exact formule of Article 284 or 287, or approximate formule of Article 285 or 288, as the case may be, compute the pressure equivalent to the expenditure of heat, _ Pi ‘ Ee rv, efficiency of steam 7 °°"""""" (6:) Let W be the number of Ibs. of coal burned per minute; h the available heat of combustion of one Ib. of coal in foot-lbs.; then the volume which the piston will sweep through effectively per minute will be 426 STEAM AND OTHER HEAT ENGINES. s being the length of stroke, A the area of piston, and N the number of revolutions per minute, or the double of that number, according as the engine is single or double-acting. This volume being divided by A gives the distance moved through effectively by the piston per minute (the back strokes not being reckoned in a single acting-engine), viz., Se ictetasttensicnee ERS being the solution of the problem. The indicated power, in foot-lbs. per minute, is ot N Aspe Ne Bpceceienin (9.) and the effective power NAs{*Pr_ zo} a A Dey and these quantities are reduced to horse-power, by dividing by 33,000. When the effect of clearance is inappreciable (as is often the case in practice), the preceding formule are simplified by making c= 0. This is the case in the double-acting engine from which the following example is taken; being the same engine which has already been referred to in Example I. of Article 288 a. Data. Resistance overcome at circumference of wheels, making one turn per 12900 Ibs. double stroke,.......ccceeseceeeeseeee ees Circumference, ......c6c..cceeeeeneoneeseneeees 64:4 feet. Length of stroke of piston,..........0s000-- s= 4:25 ,, Joint area of large pistons, A = 9192 square inches; f estimated 1 Ry : =x 1 Ib. per square inch, Back pressure, p; = 4 lbs. on the square inch. Weight of coal burned per minute,....... ‘W = 36'8 lbs. Ae Cot neeevessrsseniernssuey #5400000 footIhs EXAMPLE OF COMPUTATION OF SPEED. 427 REsULTs. Circumference of wheels i 64-4 Doatiashota R, = 12900 x Le = 97736 Ibs, R v 7 = _ = 10°63 Ibs. per square inch. Pm — By = 14 x 10°63 + 1 = 13-15 Ibs. per square inch. Pu = 13°15 + 4:00 = 17-15 lbs. per square inch. Ps by Table VILL (fort = 0-2) 1-98 Pm ° Tnitial pressure p, = 17-15 x 1-98 = 33-96 lbs. per square inch, 154 x 33-96 5 A p, = 105-3 x 9192 = 967,918 lbs. hW = 5,400,000 x 36-8 = 198,720,000 foot-lbs. p, by approximate formula = = 105°3. Mean velocity of pistons— hW _ 198,720,000 Ap, 967,918 the actual mean velocity of the pistons was 204 feet per minute. Indicated horse-power, from calculated speed of piston— = 205°3 feet per minute; 33,000 in The indicated horse-power as observed,.......:-++eseeeeeee 744, Effective horse-power from calculated speed of piston— 205°3 x 97736 a0 608, . Effective horse-power from observed speed— 204 x 97736 33000 = 604. 294. Customary Mode of Stating Pressures. — The customary mode of stating pressures, already described in Article 105, as 428 STEAM AND OTIIER HEAT ENGINES, applied to pressures of water, is also applied to pressures of steam; that is to say, the pressure is stated, as it is shown by a gauge or indicator, in pounds per square inch above or below the atmospheric pressure; a pressure lower than the atmospheric pressure being treated as negative, and called “vacuum.” Pressures stated in this customary manner are reduced to real or absolute pressures by adding them to the atmospheric pressure if positive, and subtract- ing them from the atmospheric pressure if negative. During experiments on steam engines intended to serve as a basis for exact calculations of efficiency, the atmospheric pressure ought to be observed from time to time by means of a barometer. When it has not been so observed, it may be guessed at 14:7 Ibs. on the square inch, at the level of the sea. As to its diminution at higher levels, see Article 106. To illustrate this by an example, suppose that the atmospheric pressure, during a given experiment, is actually 14-7 lbs. on the square inch; and that the pressure in the boiler, the initial pres- sure and mean back pressure in the cylinder, and the pressure in the condenser, are shown by the indicator and gauges, and described in customary language, as follows :— Pressure in boiler, ..........s00c008 23 Ibs. on the square inch. Initial pressure in cylinder,...... 19 3 #5 Mean vacuum in cylinder,........ 10:7 35 Fs Vacuum in condenser,............. 12:7 a 6's Then the real or absolute values of these pressures are— Pressure in boiler, p, = 14°7 + 23 = 37-7 lbs. on the square inch. Initial pressure ee __ 99, ‘in cylinder,... \ p= 17 119 = 387 mm ” Mean back pres- | pale = Te : ; SUPE; scien cciecs ; a in con- \ 14-7 19-7 —2 7 “ eNSeY, ......-. The vacuum in the condenser being often measured by a mer- curial gauge, is sometimes stated in inches of mercury. As to the reduction of inches of mercury to lbs. on the square inch, see Article 107. Srcrion 6.—On the Action of Superheated Steanr. 295. Objects and Methods of Superheating Steam.—The principal objects of heating steam to a temperature above the boiling point corresponding to its pressure are the following :— I. To raise the temperature at which the fluid receives heat, and SUPERHEATED STEAM. 429 so to increase the efficiency of the fluid (according to the principle of Article 265); and that without producing a dangerous pressure. II. To diminish the density of the steam employed to overcome a given resistance, and so to lessen the back pressure, according to oue of the principles stated in Article 280; in customary phrase, “to improve the vacuum.” III. To prevent condensation of the steam during its expansion, without the aid of a jacket. Those three effects all tend to increase the efficiency of the fluid, and economize fuel. The principal methods of superheating steam are the following :-— I. Wire-drawing, as explained in Article 290, which occasions superheating when the pressure in the cylinder is much less than that in the boiler; but seldom to an extent whose effects can be made the subject of calculation. Superheating in this way takes place more by accident than design, and does not secure all the advantages just ascribed to superheating; for although the steam in the cylinder is at a temperature higher than the boiling point corresponding to its pressure, the steam in the boiler is at a higher temperature still, and at the pressure of saturation corresponding to that higher temperature. II. Superheating by the steam jacket, which takes place when the steam jacket communicates more heat to the expanding steam in the cylinder than is necessary merely to prevent any of it from condensing. It does not appear that this kind of superheating produces an effect that can be made the subject of a definite calcu- lation. Its extent is limited, as in Method I., by the temperature in the boiler. III. Superheating in the steam chest, or upper part of the boiler, by means of flues traversing or surrounding it. By this method, the steam may be raised to a temperature somewhat, but not very much exceeding the boiling point corresponding to the pressure in the boiler. This is practised in many marine engines, and in some cases with the effect of preventing condensation in unjacketed cylinders. : IV. Superheating in tubes or passages which the steam traverses on its way from the boiler to the cylinder. By this method almost any required temperature can he given to steam of any pressure. It is difficult, if not impossible, to specify any one as the first inventor of this process. Mr. Frost was at all events one of the first to recommend it and cause it to be put in practice. It was used many years ago in the engines'of the American mail steamer “ Arctic” with good effect, and has since been used by many makers in many engines, chiefly marine, with a great variety of torms of apparatus, some of which will be described in Chap. IV. 430 STEAM AND OTHER HEAT ENGINES. V. Superheating by mixture, where a portion only of the steam is passed through superheating tubes, and raised to a very high tem- perature, and then injected amongst the remainder of the steam at or near the cylinder ports, so as to bring the whole mass of steam to a temperature intermediate between the boiling point cor- responding to its pressure, and the temperature in the super- heating tubes. The mixture thus made is called by the Hon. John Wethered, who invented the process, “combined steam.” VI. Superheating in the cylinder, by means of a fiue or of a furnace, as in Mr. Siemens’s steam engine. . 296. Limitation of the Theory to Steam-Gas-—The investigations, rules, and tables which follow are confined to the case of steam which is superheated to such an extent that it may without material error in practice be treated as perfectly gaseous. Steam in that condition may be called steam-gas. The experiments of Hirn, of Sainte-Claire Deville and Troost, of Siemens, and others, have shown that steam attains a con- dition which is sensibly that of perfect gas, by means of a very moderate extent of superheating; and it may be inferred that the formule: for the relations between heat and work which are accurate for steam-gas are not materially erroneous for actual superheated steam ; while they possess the practical advantage of great simplicity. The product of the pressure of steam-gas in pounds on the square Foot, p, and the volume of one pound of it in cubie feet, v, at any given absolute temperature, «= T° +- 461°-2 Fahrenheit, is given by the following formula :— T T+ 461°2 pv=42140-— = 42140- —79355-° = 85-447 ;...(1.) 0 a and the results of that formula, for every eighteenth degree of Fahrenheit’s scale, from T= 32° to T= 572°, are given in the column headed p v in Table IX., at the end of this section. (See Addendum, page 448.) In the column of the same Table headed H are given the values for the same series of temperatures, of the total heat of gasefication in foot-pounds required to raise one pound of water from the liquid state at 32°, to the state of perfect gas at a given temperature, under any constant pressure compatible with the perfectly gaseous state at the latter temperature. It is assumed that saturated steam at 32° is perfectly gaseous, so that the total heat of gasefica- tion for that temperature, Hp, is simply the latent heat of evapora- tion, or Hy = 842872 foot-pounds ; PROVISIONAL THEORY OF STEAM-GAS. 431 and then, according to the principles explained in Article 258, we have for the total heat of gasefication of one pound of steam-gas at any other temperature in foot-pounds— H =H, +K, (T—32°) = 842872 + 371 (T —32°)....(2.) The following are some equivalent expressions for the same quantity :— H = 659895 + 371 + = 659895 + 44-p vnearly....(2 a.) The column h gives the quantity of heat in foot-pounds required to raise one pound of liquid water from 32° to a given temperature ; the increase of the specific heat of liquid water with temperature being taken into account; but in most practical cases it is suffi- ciently accurate to use the formula, WG 2B ecsessesey ricusiogr ed (3.) 297. Efficiency of Steam-Gas Expanding without Gain or Loss of Weat.—In fig. 114, let A B represent v,, the volume occupied by one pound of steam-gas when first admitted into the cylinder of an engine at the pressure , B py = OA. Let BOC, being an “adiabatic” curve for steam gas, represent by its co-ordinates the ; fall of pressure and increase of D c volume of that fluid as it ex- | bs pands. Let DC =xyn=rv, represent the volume, and OD §& re = Po, the pressure, at the end of Fig. 114. the expansion, which is assumed not to be carried so far as to cause any appreciable liquefaction of the steam. Let O F= p, represent the mean back pressure. The probable value of this in a proposed superheated steam engine may be estimated as follows:—Let the ordinary back pressure in a dry saturated steam engine working at the same speed with the same ratio of expansion be denoted by P+ p; yp’ being the pressure of condensation, and p" the additional pres- sure, Let 7, be the absolute boiling point corresponding to the initial pressure p,, and 7’, the actual absolute temperature of the steam admitted. Then the steam-gas employed is less dense than 432 STEAM AND OTHER HEAT ENGINES. saturated steam of the same pressure in a proportion which may be expressed accurately enough for the present purpose by 3 3 so that 1 according to a principle stated in Article 280, the probable back pressure in the superheated steam engine will be , S ” Pg= pit a Diswuitontiaen wubuedeal iets (1.) 1 In most cases which occur in practice, we may put p'=1 Ib. on the square inch, and p" = 3 lbs. on the square inch; so that P3=1+8 7 in pounds on the square inch, } C stl By T or 144 + 432 = in pounds on the square foot. J The equation of the expansion curve BC may be assumed as analogous to that of the corresponding curve for air, viz. :— in which y and other indices and co-efficients depending on it fur steam-gas have the values given them in Article 251, viz. — y=13;7—1=03; | bi ge || Po eye ae eeteve ia (3.) | +077; 7 a8. | Hence, by an investigation similar to that in Article 279, Method IT, 1s found the following expression for the energy exerted on the piston by one pound of steam-gas :— Area ABCEFA=U =(p,,—p,) rx, =P, 0, (AE — 8h 7) — pg 0 Oy eerececceen ees (4) To facilitate the use of this equation, a series of values of the two following ratios and their reciprocals are given in Table X. at the end of this section :— TDn f a dd Bp cs sees ce (5.) SUPERHEATED STEAM ENGINES. 433 0 He = Akg Pi in which Table intermediate values of any ratio can be interpolated as in Tavles VII. and VIIL., already explained. The following, then, is the set of formule to be employed in computing approxi- mately the probable power and efficiency of superheated steam engines, according to the provisional theory here adopted :— Bae eee lene (5 4.) Data. Initial pressure, p,. Initial absolute temperature, z', = T', + £61°-2 Fahrenheit. Ratio of expansion, vr. Mean back pressure, ps, known directly by experiment, or estimated by the formula 1 a; the absolute boiling point, +, being found by known formule or tables. Absolute temperature of feed water, +,=T,+461°2. Temperature of condensation, T, Temperature of atmosphere, T,, RESULTS. ‘ p, % found from T’,, by equation 1 of Article 296, or by Table IX.; being the gross energy exerted by the steam on the piston during its admission. Initial and final volumes of one pound of stewam— Di Py Uy SDF Ce PO evoked oancdiadeteicicn (6.) oa and in, found by the equations 5, 5 a, or by Table X. Bnergy seriell per pound of steam; found by equation 4, or by the formula— Cs Py HPD Ui pv eeeimatienneains (7.) Pr Mean effective pressure— Ui? = — Po — =" Pa arvcvveenascerees 8. Pe = Pm P3 rv, pr Pi P3 ( ) Heat expended per pound of steam, in foot-pounds— = 842872 + 371 (T',— 32°) — 772 (T, — 32°),...(9.) or h =H, —Ay;......5 aabnonasuoaete te (9 4.) H, and fy being found by mapas es Table IX. 434 STEAM AND OTHER HEAT ENGINES. Pressure equivalent to heat expended— Pat ceeceetsnecenentntn (10.) Efficiency of steam— De a) ee Gea (11) Pr Pr Net feed water per cubic foot swept through by piston— 1 pene tim (12.) Wi Uirccssudsoccsaeds eintaen (13.) Heat rejected per cubic foot swept through by piston— y—U Fig ee eon (14.) Net condensation water— heat rejected 2 AT ttt tte cen een nnenterees Lo. 772 (T, —T,) ca) Available heat expended per indicated horse-power per hour— 5 1980000 TE ences (16.) In the following example (which is ideal), the engines are sup- posed to be the same with those already employed as Example I. in Article 288 4; and the principal question to be solved by the calculation is, what would be the probable increase of efficiency and saving of fuel if the steam, being admitted at the same mean pressure of 34 lbs. on the square inch, and cut off at the same mean effective fraction of its final volume, 0-2, were superheated so as to be admitted at the temperature T', = 428°, instead of its present mean temperature of admission, which is about 2573° Dara. p, = 84 X 144 = 4896; a, = 428 + 461-2 = 889-2. SUPERHEATED STEAM ENGINES, 435 r=5, 719 889 (or 3°43 Ibs. on the square inch). T,=104. pg= 144 +432 -—— =493 lbs. on the square foot, REsutts. p,%, by Table IX., 75976 foot-pounds 0, <8 + 4896 tg=70,=5 x 15:52=77°6 cubic feet. = 15-52 cubic feet. By TableX.— 72m_9.98, Pm _-456, 1 Pr Energy per pound of steam— U =2:28 x 75976 — 493 x 77-6 = 173225 — 38257 = 134968 foot-pounds. Mean effective pressure— Du — Ps = 456 X 4896 —493 = 1740 lbs, on the square foot, = 12-08 Ibs. on the square inch. Heat expended per pound of steam— § = 989788 — 55612 = 934176. Pressure equivalent to heat expended— Pr = ee Ps 12038 lbs. on the square foot. = 83-6 lbs. on the square inch. Efficiency of steam— 134968 1740 12:08 934176 12038 ~ 83-6 being superior to the efficiency with dry saturated steam, as com- puted in Article 289, Example L, in the ratio 145 oe 118: 1. 436 STEAM AND OTHER HEAT ENGINES. The available heat expended per indicated horse-power per hour would be 1980000 =1365 s : 0145 = 13655000 foot-pounds ; and supposing, as in some previous examples, the available heat of combustion of one pound of the coal employed to be 5400000 foot-pounds, the consumption of coal per indicated horse-power per hour would be 13655000 Be ah 4 BA00000 =~ 33 lbs.; which, being subtracted from the actual consumption, 2:97, shows a saving of 0-44 Ib., or about 15 per cent. This is less than the saving which has usually been found by experiment to result from superheating ; the reason probably being, that in the preceding calculation no account is taken of the in- creased efficiency of the furnace, owing to the superheating apparatus taking up heat which would otherwise have been wasted. To estimate the probable effect of this cause in giving increased economy, let us make the supposition (which appears to have been nearly realized in some cases), that the whole of the superheating is effected by heat which would otherwise have been wasted. Foot-Ibs. Then the heat required to produce | Ib. of saturated steam at 34 lbs. on the square inch, from water at LOS? Wel Srawvensiseets scews soctanssanineiatorntannserareeang 840,000 and the heat required to produce 1 lb. of superheated steam at 428° Fahrenheit, from water at 104° being, as computed before, ..........e. ssc eeenecweeeee 934,176 the difference,..............:0000 94,176 is to be considered, according to the supposition made, as heat saved by the superheating apparatus; so that the efficiency of the furnace is increased in the ratio 934176 840000 and the available heat of combustion of the coal, instead of 5,400,000, becomes, = 1:11 nearly; SUPERHEATED STEAM ENGINES. 437 5,400,000 x 1-11 = 6,000,000 foot-Lbs. giving as the probable consumption of coal per indicated horse- power per hour, 13655000 eee SF ae BD 6000000 = 72S Ibs. which, being subtracted from....... 2-97 Shows a saving Of......ss.seceeeeeees 0°69 Ib. or about 23 per cent. This agrees very nearly with the general results of practice. 298. Efficiency of Steam-Gas Expanding at Constant Tempera- tre.—If the temperature of steam-gas be maintained constant during its expansion, by means of a flue round the cylinder, or otherwise, its action is represented approximately by making the curve B G, fig. 114, a common hyperbola, so that a LoS In this case, the principal formule are the following :— Energy exerted by 1 lb. of steam =area ABCEFA =U =(p,,— ps) 7, =P, 0, (1 + hyp log 7) — py 7 v,...(1.) ae SE hyp log ie iecieseeeens (2.) 1 Pm Ut+thyp logr a a A series of values of these ratios, and of their reciprocals, is given in Table XI. at the end of this section. The heat expended per pound of steam consists of the total heat of gasefication, from T,, the temperature of the feed water, to T’,, the temperature of the steam-gas, as already computed in Articles 296 and 297, and given by the aid of Table IX., and of the latent heat of expansion which the steam receives to maintain its temperature constant in the cylinder, and whose value is Pp, %, hyp log v = 85-44 7 hyp logr = p, 2, ° (72 - Hae) 1 438 STEAM AND OTHER HEAT ENGINES, heuce, denoting the whole expenditure of heat per Ib. of steam by §, §=H,-ytpyy ("2s 1) = 842872 + 371(T', — 92°) —772 (T, — 32°) + 85-44 hyp log r (T’; + 461°-2) To illustrate this mode of employing steam-gas, let the data taken be the same as in the example of Article 297; that is, let p, = 34 x 144 = 4896 ; 2', = 889: 2= 428° + 461-2 25 r=d; Pe = 493; h= = 104° REsuLts. py 0, = 75970; v,=15'52; rv, = 776; as before. By Table XI, "?" — 9-61; 2 — 529, Py P1 Energy per lb. of steam— U =2-61 x 75976 — 493 x 77-6 = 198297 — 38257 = 160040 foot-lbs. Mean effective pressure— Pm — Pz = 522 x 4896 — 493 = 2063 Ibs. on the square foot == 14°38 Ibs. on the square inch. LTeat expended per Ib. of steam— YW = 989788 — 55612 + 75976 x 1°61 = 934176 + 122321 = 1056497 foot-lbs. Pressure equivalent to that heat— P= ue a = 13615 lbs. on the square foot = 94-5 Ibs. on the square inch. SUPERHEATED STEAM ENGINES. 439 Lficiency of steam— TO0EG 2068 2 9? 62 0.159; 1056497 ~~ 13615 ~ 94:5 being superior to the efficiency with dry saturated steam in the ratio 0-152 0-123 The available heat expended, per indicated horse-power per hour, would be in this case 1980000 0152 If the efficiency of the furnace, as in the second mode of treating the example in Article 297, be supposed to be such that the avail- able heat of combustion of 1 Ib. of coal is 6,000,000 foot-lbs., = 1-236: 1 nearly. = 13,000,000 foot-lbs. the probable consumption of coal in the engine now under con- sideration, per indicated horse-power per hour, is found to be 13000000 6000000. which being subtracted from the ] actual consumption with dry ~ 2:97 saturated steam, ......-....s.0e8- J = 2:17 lbs. ShOWS @ SAVING Of.........cecseeeeee oes 0°80 Ib. or 27 per cent. 299. Waficiency of Steam-Gas with Regenerator—Siemens’s Engine. —tThe “regenerative steam engine” of Mr. C. W. Siemens, is one which so far agrees with the description in the last Article, that superheated steam works expansively in it at a temperature main- tained nearly constant by placing the cylinder over a furnace; but the steam on its way to and from the space below thé plunger of that cylinder, traverses a “regenerator” nearly resembling that of Stirling’s air engine (see Article 275), the effect of which is, that the whole, or nearly the whole, of the heat employed to raise the temperature of the steam above the boiling point corresponding to its pressure, is obtained at each stroke from the regenerator, in which that heat has previously been stored by steam leaving the hot cnd of the cylinder. 440 STEAM AND OTHER HEAT ENGINES, The whole of the formule of the Article 298 are made applicable to this case, by simply taking for the value of H,, the total heat of evaporation of 1 lb. of steam at the boiling point t,, corresponding to its pressure, as given by Table VI. at the end of the volume, instead of the total heat of gasefication at the working temperature z',. Suppose, for example, that the data are the same as in the last Article. Then the total heat of evaporation of steam at 34 Ibs. on the square inch, the feed water being at 104°, as computed from: Lable: VI... i8secssssvevesaveseicvens Hy, — hy = 840000 foot-lbs., the latent heat of expan- TDi sion, as in Article 298... bo, a (“Pe 1) = 122321 and the heat expended per Ib. of steam f...... == 962321 foot-lbs. Pa the energy exerted by 1 lb. of steam, being, as in Article d U = 160040 foot-lbs., the efficiency of the steam is Tepe 160040 geasai = 01083 consequently, the available heat expended per indicated horsc- power per hour is 1980000 O16 = 11,930,000 foot- Ibs, nearly. Taking the same estimate of the available heat of combustion of 1 Ib. of coal, as in Article 298, this would give for the consumption of coal per indicated horse-power per hour 11,930,000 6,000,000 The efficiency of this engine is capable of being greatly increased by working ata high temperature; for while the energy exerted by the steam increases nearly as the absolute temperature, it is only the latent heat of expansion which increases in the same pro- portion: the total heat of evaporation remaining constant if the pressure is constant. Mr. Siemens states, that in some of his experiments with this engine, the consumption of fuel was only 1-5 Ib. per indicated horse-power per hour. The heating apparatus described at the end of Article 279, might probably be applied to this engine with advantage. == 1-99 Ib. STEAM-GAS BY THE POUND. 44] IX. Taste or Enasticrry anp Toran Heat or One Pounp oF STEAM-GAS, T pv H h BOO. scwsticuamcd AQTAO ven ccezcens ¢ 842872 sercorceee rf ° 50 43678 849550 13896 68 45216 856228 27792 86 46754 862906 41702 104 48292 869584 55012 T22) sees eee vevs 49836 vosiecsanean 876262 occ 69522 140 51368 882940 83459 158 52906 889618 97411 176 54444 896296 111363 194 55982 902974 125357 212 ssanevseaees B75 20 viwiessmores 909652 we.ceceeeee -139363 230 59058 916330 248 60596 923008 266 62134 929686 284 63672 936364 BOD LeaisetanetentO 2] Ocsamanensins 943042 320 66748 949720 338 68286 956398 356 69824 963076 374 71362 969754 BOS ssioxaectsuies's P2000} + ieisnine sie 976432 410 74438 983110 428 75976 989788 446 T7514 996466 464 79052 1003144 AO? isveweeesees 80590... .. 200000. 1009822 500 82128 1016500 518 83666 1023178 536 85204 1029856 554 86742 1036534 ID] Zi iesiegiaunietee'e 88280....0008- ++ 1043212 EXPLANATION, T, temperature on Fahrenheit’s scale. v, product of the pressure in pounds on the square foot, and volume in cubic feet, of one pound of steam in the perfectly gaseous condition, or “ steam-gas.” : H, total heat, in foot-pounds of energy, required to convert one pound of water at 32° into steam-gas at T°, under any constant pressure. h, heat, in foot-pounds of energy, required to raise the temperature of one pound of water from 32° to T°. 449 STEAM AND OTHER HEAT ENGINES. x. TABLE oF ApproximaTE Ratios ror Steam-Gas WORKING EXPANSIVELY IN A Non-ConpuctTinG CYLINDER. “ 7 7 Pm Aan: eb Pm 3 Pr T Pm Pm Pr 20 "05 2°07 "336 6-72 "149 13h °075 2°80 357 4°76 ‘210 10 oT 2°06 376 3°76 +266 8 "125 2°55 "393 3°14 318 3 "15 2°45 “409 2°73 "307 5 2 2°28 "439 2°20 "450 4 25 213 “469 1°87 534 33 = 2°01 "4907 1°66 603 25 35 1°90 526 I'50 665 22 “4 180 555 1°39 720 25 “45 171 585 1°30 "770 2 5 1°63 O15 1'23 313 Ir 55 155 646 I'l7 S51 1% 6 T'47 679 1°13 884 Iqv 65 1°40 712 I'lo ‘913 17 a 1°34 747 1:07 ‘937 1% "15 1°28 784 104 ‘O57 Ig 8 122 S22 T'03 973 iy 85 116 863 T'O15 985 Ip 9 to “906 1‘OL 993 EXPLANATION. 7, ratio of expansion. 1 =, real cut-off. r Pz, absolute pressure of admission. Pm Mean absolute pressure. T Pm Py during admission. aa TP, 2 ™m , ratio of whole gross work of steam on piston to gross work ratio of gross work during admission to whole gross work. GASES WORKING EXPANSIVELY. 443 XI. Taste or Approximate Ratios ror Perrect GASES WORKING EXPANSIVELY aT Constant TEMPERATURE: ALSO FOR NEARLY~ DRY STEAM. r = "Pm PL Pu Pn re wi TP Pm PY 20 "O05 4°00 "250 5'00 "200 135 075, 3°59 279 3°72 “209 to a 3°30 "393 3°93 *33° 8 125 3°08 "325 2°60 "385 63 “15 2°90 345 2°30 "435 5 2 2°61 383 1'92 ‘522 4 5 2°39 "419 1°68 "596 2 *3 2°20 “£5 I‘51 O61 27 39 2°05 "488 1°39 717 oh “4 Ig "523 1°31 705 22 "45 180 550 I'24 “B09 2 5 1°69 "59t 118 846 Ty, °55 160 "626 I'l4 878 12 6 151 662 I'lo “906 1s 65 1°43 “699 oor D2) mY 13600737 Og *950 a "15 1'29 Tat 1'O4 "965 IL 8 1°22 818 1°02 978 1 85 116 ‘860 I'ol "989 12 9 Ilr "905 ror 995 EXPLANATION. r, ratio of expansion. 1 2 real cut-off. Pp, absolute pressure of admission. Dy; Mean absolute pressure. r : ; a ratio of whole gross work of gas on piston to gross work Pr during admission. P1_ ratio of gross work during admission to whole gross work. r Pu 444 STEAM AND OTHER HEAT ENGINES. Section 7.—Of Binary Vapour Engines. ‘300. General Description of the Binary Vapour Engine.—This, engine, the invention of M. Prospére-Vincent du Trembley, is driven by the combined action of two different fluids, a less and a more volatile, in two separate cylinders. The less volatile'fluid is evaporated in a boiler, and drives the piston of its cylinder, in the usual way. On being discharged, it is passed vertically down- wards through a set of small tubes, contained within a cylindrical vessel: the less volatile fluid, passing downwards through the tubes, is liquefied, and gives out its heat to the more volatile fluid, which ascends in the space surrounding the tubes, and reaches the top of the vessel in the state of vapour. This vapour drives the piston of a second cylinder, during the return stroke of which it is expelled into a second surface condenser, consisting also of a number of small vertical tubes; the vapour passes downwards through these tubes, which are surrounded by a copious stream of cold water; this abstracts heat from the vapour, and causes it to be condensed, and the liquid thus produced is pumped back into the evaporating vessel to perform its work over again. The less volatile fluid is always water; for the more volatile, wther is usually employed. Full details of the construction and mode of working of these engines are given in M. du Trembley’s work, entitled, Manuel du Conducteur des Machines & Vapeurs combinées ou Machines Binaires (Lyons, 1850-51); and accounts of their performance are contained in a report by Mr. George Rennie, published in 1852; in a litho- graphed report by M. E. Gouin, on the experimental trip of the ship “ Brésil,” in 1855; and in a paper by Mr. James W. Jamieson, read to the Institution of Civil Engineers in February, 1859. 301. Theory of the Steam-and-Zther Engine.—In fig. 115, let A BCEF A represent the diagram of the steam cylinder, and KLM PQ K that of the ether cylinder. B Fig. 115. Let p, = O A be the absolute pressure of the steam at its admis- sion ; STEAM-AND-ETHER ENGINE, 445 v, = AB, the volunie of one lb. of it when admitted ; rv, = DO, the volume to which it expands; Let H, denote the available heat expended, in foot-lbs, per Ib. of steam; U = area A BC EF A, the energy exerted on the piston by one Ib. of steam. Then the heat rejected by each Ib. of steam, and given out through the tubes to the ether, is given by the equation and several examples of the mode of computing this quantity of leat have been given in the preceding sections. To find what volume will be filled with «ther vapour by means of this heat, in the first place must be computed the expenditure of heat per cubic foot of ether vapour, produced at the pressure under which the ether is evaporated, which is supposed to be given and represented by p'; = O K, and is necessarily a pressure correspond- ing toa boiling point lower than the temperature at which the steam is condensed. That expenditure of heat is dF a TS oe (2.) where L’= 7 - is the latent heat of evaporation of one cubic foot of ether vapour under the given pressure, calculated by a formula of the kind given in Article 255, or by the aid of 'I'able V. ; J c = 399°1 foot-lbs. per degree of Fahrenheit, is the specific heat of liquid ether; D'is the weight of one cubic foot of ether vapour, found by the formule of Article 256, or by the aid of Table V.; T’ is the temperature at which the ether is evaporated, and T” that at which it is condensed, and returned to the evaporating apparatus. Then the initial volume, represented by K L in the figure, of the zether evaporated per lb. of steam condensed, is found by means of the equation , H, vo Riba eDpim 1 Let p" = ON denote the intended final pressure of the ether vapour, at the end of its expansion, and p" its mean back pressure, which appears to be about 5 lbs. on the square inch. Then from the data, p, p", p”, T", by means of the formule of Articles 281 and 284, substituting only the constants which apply to ether for those which apply to steam, and using Table V. instead of Table IV., may be computed— The ratio of expansion 7”, and thence the final volume M N =r’ u of the zther evaporated per lb. of steam ; 446 STEAM AND OTHER HEAT ENGINES. The energy exerted by that ether, represented by the area KLMQK=U. The ratio MN + DOS FP Oy eececceceereeeeee (4.) is that of the volume of the ether cylinder to the volume of the steam cylinder. In practice, those cylinders are either of equal size, or the ether cylinder is somewhat the larger. The heat per Ib. of steam to be abstracted by the cold water which circulates in the ether condenser is given by the expression Ai hate ects ahs (5.) The mean effective pressures in the steam cylinder and ether cylinder respectively, are U = ry and UW + 9. eee (6.) The same amount of additional energy, which is obtained by the addition of the ether engine to the steam engine, might also be obtained by continuing the expansion of the steam sufficiently far, as represented by the line C H G, provided a sufficiently low back pressure could be insured; but this might require in some cases a cylinder so large as to be more costly than the binary engine. 302. Example of Results of Experiments.— The following quan- tities are means, computed from a long series of experimental results given in M. Gouin’s report, already mentioned, on the performance of the steam and ether engines of the “ Brésil:”— PRESSURES IN LBS. ON TIE SQUARE INCH, In boiler or Back Mean evaporator. pressure, effective, Steam, .o.......cceeseeee 43°2- 46 I1'6 PRAT sccicss sclus chane ane 312 53 get Total mean effective pressure reduced to the area of one piston, the areas and strokes of the steam and. ether pistons having been in this case the SOTNGS scr otters psibitalu'seree’siuleithlun eidavetonss'a ate daar baMasedes ines 18-7 It thus appears that the proportions of the indicated power of the engine obtained in the steam and ether cylinders respectively, were as follows:—Steam, 11°6 + 18-7 =-62; ether, 7-71 + 18-7 = 38. The gain of power, however, by the addition of the ether engine, is not quite so great as this calculation shows; because, had the steam cylinder been used alone, the back pressure would have been in all probability about 3 lbs. on the square inch less; that is, about 4°6 instead of 7:6; so that the mean effective pressure in the STEAM-AND-&:THER ENGINE——GAS-ENGINE, 447 steam cylinder would have been 14°6 instead of 11-6; and the pro- portion borne by the power of the steam engine alone to that of the binary engine would have been 14:6 + 187 = 77, leaving 100 — 77 = :23 of the whole power of the binary engine, as the real gain due to the sether engine. The consumption of fuel, according to M. Gouin’s report, was either 2°8 or 2:44 lbs. of coal per indicated horse-power per hour, according as certain experiments made under peculiarly adverse circumstances were included or excluded. The binary engine is not more economical than steam engines designed with due regard to economy of fuel; but by the addition of an ether engine, a wasteful steam engine may be converted into an economical binary engine. ADDENDUM. 502 A, Explosive Gas-Emgine.—In Lenoir's gas-engine, air and coal-gas in proper proportions are introduced into a cylinder; the admission is cut off, and the mixture exploded by electricity; the explosion causes a sudden increase of pressure; the gaseous mix- ture expands, driving the piston before it till the stroke is com- pleted, and is expelled during the return stroke. The cylinder is prevented from overheating by water circulating ina coil. Best proportion of mixture, eight volumes of air to one volume of coal- gas. Absolute pressure immediately after explosion, p, = about 5 atmospheres, or 10,580 lbs. on the square foot. Let the atmos- pherie pressure be denoted by 7; then available heat of explosion, per cubic foot of explosive mixture, H, = 2°5 (p, — yy) = 21,160 foot-lbs., nearly. (This is about éhree-eighths of the total heat of the explosion.) | Let r be the ratio of expansion, py, the final absolute pressure ; W the indicated work per cubic foot of explosive mixture; p, the mean effective pressure; then z P, = pyr * nearly; W = 25 (p, — py) — 3:5 (7 — 1) pe + (& — 1) (Pe — Po) p= W +r. Rate of expansion for greatest efficiency, 7, = (2) 7= 3-16 - 0/ nearly; then p, = Po; and W, = 25 (py — po) — 3°5 (r — 1) py 448 STEAM AND OTHER HEAT ENGINES. The preceding formule include no deductions for losses through increased back-pressure, and through abstraction of heat, from the gas which is in the act of expanding, by the cold-water coil. These losses, chiefly from the last-mentioned cause, are so great as to increase the expenditure of coal-gas per indicated horse-power per hour nearly four-fold, its actual amount being about 140 cubic feet, according to experiments by Tresca. In Hugon’s gas-engine a small jet of water in the state of spray is injected into the cylinder by a pump during each return stroke. This at once diminishes the back-pressure, and lessens the supply of water required for the cold-water coil. The expenditure of coal- gas per indicated horse-power per hour, according to experiments by Tresca, is about 85 cubic feet, or about 24 times that given by the preceding formule. The explosive mixture is fired by being put into communication with a gas-flame. In Otto and Langen’s gas-engine there is a very tall vertical cylinder containing a piston, whose rod is connected with the fly- wheel shaft by means of ratchet-work, which acts during the down-stroke ouly. The explosive mixture is admitted below the piston, and fired by being put in communication with a gas-flame. The piston, being free from connection with the fly-wheel shaft, shoots up with great speed until it is brought to rest by gravity, and by the atmospheric pressure; the burnt gas cools so rapidly by the expansion as to give out very little heat to the cylinder; and it falls at the end of the expansion to a pressure much below the atmospheric pressure. A water-jacket round the lower end of the cylinder only is found sufficient to prevent overheating. The down-stroke is performed by means of the atmospheric pressure, and of gravity, opposed by the back-pressure; which during a great part of the stroke is about + atmosphere, and towards the end rises to 1 atmosphere by compression; and then the gas is ex- pelled. The explosive mixture consists of one volume of coal-gas and nine volumes of air; the pressure immediately after explosion is from 4 to 6 atmospheres; the expenditure of coal-gas per indi- cated horse-power per hour is said to be about 35 cubic feet. (See Verhandlungen des Vereins fir Gewerbjleiss in Preussen, 1868.) ADDENDUM To ARTICLE 296, Pace 430. Empirical formula for elasticity of steam-gas at the temperature corresponding to the pressure p’ and volume v’ of saturated steam. Let yp = 1 atmosphere; then vapid +1737 (=), pv=p a (From Shipbuilding, Theoretical and Practical, page 260.) 449 CHAPTER IV. OF FURNACES AND BOILERS. Section IL—Of Boilers and Furnaces in general. 303. General Arrangements of Furnace and Boiler.—The usual relative arrangements or positions of the furnace and boiler of a steam engine may be divided into three principal classes; as follows :— I. In the External Furnace Boiler, the furnace or fire-chamber is wholly outside of, and partly in contact with, the water vessel or boiler ; so that the boiler forms part of the boundary of the furnace (generally the top). The other boundaries of the furnace are usually built of fire-brick. As to the thickness required to prevent loss by radiation, see Article 228. Examples of this are—the old hay-stack boiler and wagon boiler, the plain cylindrical boiler, without internal flues, and some boilers, such as Gurney’s, Perkins’s, and Craddock’s, in which the water and steam are contained in tubes surrounded by the flame. II. In the Yuternal-Furnace Boiler, the fire-chamber is enclosed within the boiler. Examples of this are—the boilers now most common in land.engines, with one or more furnaces contained in horizontal cylindrical internal flues ; most marine boilers ; and all locomotive boilers. III. The Detached Furnace or Oven is a fire-chamber built of brick, in which the combustion is completed before the hot gas comes in contact with any part of the boiler. This has been already referred to in Article 230, page 283. 304. The Principal Parts and Appendages of a Farnace al'e— I. The furnace proper, or fire-box, being the space where the solid constituents of the fuel, and the whole or part of its gaseous constituents, are burned. : II. The grate, being that part of the bottom of the furnace proper which is composed of alternate bars and spaces, to support the fuel and admit air. III. The hearth is a floor of fire-brick, on which, instead of on a grate, the fuel is burned in some furnaces. IV. The dead plate, or dwmb plate, being that part of the bottom of the furnace proper which consists of an iron plate, without bars and spaces. 26 450 STEAM AND OTHER HEAT ENGINES. V. The mouth-piece, being the passage through which fuel is introduced, and sometimes also air. The bottom of the mouth- piece is a dead plate. In many furnaces there is a mere doorway, and no mouth-piece. VI. The fire-door, which closes the mouth-piece or doorway, and which may or may not have openings and valves in it to admit air. Sometimes the duty of a fire door is performed by a heap of dross closing up the mouth-piece. VII. The furnace-front, above and on either side of the fire door. VIII. The ash-pit, being the space below the grate into which the ashes fall, and through which, in most cases, the greater part of the supply of air is admitted. IX. The ash-pit door, used in some furnaces to regulate the admission of air through the ash-pit. X. The bridge, being a low vertical partition at one end of the furnace (usually the back) over which the flame passes on its way to the flues or chimney. This is what is meant when “the bridge” is spoken of without qualification ; but the word bridge is also applied to any low partition having a passage for flame or hot gas above it. Bridges are usually built of fire-brick; but they are also sometimes made of plate iron, and hollow, so as to contain water within, and form part of the water space of the boiler—they are then called “water bridges.” The top of a water bridge ought to slope or curve upwards towards the ends, to admit of the rapid escape of the bubbles of steam which form on its internal surface. Sometimes a water bridge projects downwards from a part of the boiler above the furnace, leaving a passage below for flame—it is then called a “hanging bridge.” A water bridge with passages for flame, both above and below, is called a “ mid-feather.” XI. The jlame chamber, being the space immediately behind the bridge in which the combustion of the inflammable gases that pass over the bridge is or ought to be completed. It has often a floor of fire-brick, called the flame bed; and is sometimes lined with fire-brick to prevent the cooling and extinction of the flame, and sometimes, for the same purpose, filled with fire clay tiles, made of a horse-shoe form in section, to admit of the circulation of the gases. XII. Air passages, of various constructions and in various situa- tions, and with or without valves, to admit air for the combustion of the fuel, whether forced in by atmospheric pressure or by a blowing machine. XIII. Flues, being passages traversed by the hot gas on its way from the fire to the chimney. These are sometimes external, being in contact with the outside of the boiler, and bounded externally by brickwork ; and sometimes internal, being contained within, PARTS AND APPENDAGES OF FURNACE AND BOILER, 451 and forming part of, the boiler. Internal flues of small diameter are called tubes. XIV. Baflers or diffusers, being partitions so placed as to improve the convection of heat, by promoting the completeness of the circulation of the particles of hot gas over the heating surface of the boiler. The various bridges already mentioned fall under this head, and also the spiral blades for boiler tubes recently introduced by Messrs. Duncan & Gwynne. XV. The chimney (see Article 233), at the foot of which is sometimes a chamber called the smoke box, or uptake, in which the various flues terminate. XVI. Blowing apparatus, used in order to produce a draught, whether by forcing air into the furnace by means of a fan, or by driving the gases out of the chimney by means of a blast pipe. See Article 233. XVII. Dampers, being valves placed in the chimney, flues, tubes, or air passages, to regulate the draught and rate of combustion. No one furnace possesses ald the parts and appendages above enumerated ; for some of them are substitutes for others, and some are only employed in furnaces of particular kinds (see page 477). 305. The Principal Parts and Appendages of a Boiler are— I. The shell, or external boundary of the boiler, for which the usual material is iron, although sheet copper is sometimes em- ployed. The figures usually employed for the shells of boilers are, the spherical, the cylindrical, and the plane, and combinations of those three figures. The most common figure at the present day is. that of a horizontal cylinder, with flat or hemispherical ends. In some peculiar boilers, the shell is a vertical cylinder, or a cluster of vertical tubes connected by means of horizontal tubes (as in Mr. Craddock’s boiler) ; or a set of square tubes or cells (as in Mr. J. M. Rowan’s boiler) ; or a single spiral tube (as in Mr. Perkins’s boiler). Tubes which thus contain water internally are called water tubes, to distinguish them from tubes for transmitting furnace gas. In most locomotive boilers, part of the shell is a rectangular box, containing within it another rectangular box, which latter is the fire-box. The shells of ordinary marine boilers are of irregular shapes, adapted to the space in the ship which they are to occupy, and approximating more or less to rectangular figures, rounded at the corners and arched at the top. II. The steam chest, or dome, being a part of the shell which usually rises above the level of the rest of the boiler, so as to provide a space in which the steam, before being conducted to the engine, may deposit any particles of spray that it may have carried up from the water. It is usually cylindrical, with a hemispherical or segmental top ; but its form is often varied, especially in marine boilers. It 452 STEAM AND OTHER HEAT ENGINES. is advantageous that the steam chest should be traversed or sur- rounded by a flue, in order to dry or slightly superheat the steam, as explained in Article 295, page 429. Il. The furnace or fire-box (in boilers with internal furnaces) is a chamber contained within the boiler, in such a position as to be completely covered with water. In ordinary cylindrical land boilers it is usually cylindrical, being at one end of a horizontal cylindrical flue: in locomotive boilers it is sometimes a vertical cylinder, but more frequently a rectangular box. In marine boilers it is usually of a figure approaching to rectangular, with rounded corners, Many of the parts mentioned in the last Article as belonging to furnaces, become, when the furnace is internal, parts of the boiler also; for example, the ash-pit, in the cylindrical internal furnace of a horizontal cylindrical boiler, is simply the space below. the grate within the cylindrical flue which contains the furnace. Water bridges have already been described. The principal bridge at the back of an internal furnace is usually of fire-brick. Sometimes, in order to prevent the cooling of the flame by contact with the surface of a water space before the com- bustion is complete, the furnace is lined internally with a fire-brick arch; and sometimes also an internal flame chamber (Article 304, Division XT.) adjoining the furnace is lined in the same manner. One boiler may contain one, two, or more internal furnaces. IV. Internal flues, and internal tubes, being small internal flues, have already been mentioned under head XIII. of Article 304. V. A tube-plate is a plate which forms sometimes part of the shell of the boiler, and sometimes one side of an internal fire-box, flame chamber, or flue, and which is perforated with holes, into which the ends of a set of tubes are fixed. Each set of tubes requires a pair of tube-plates, one for each end of the tubes. VI. The man-hole is a circular or oval orifice in any convenient position on the top of the boiler, large enough to admit a man to the interior of the boiler to cleanse or repair it. The entrance to the man-hole usually consists of a short cylinder having a flange surrounding its upper end, to which the cover is bolted, when the cover opens outwards. The bolts must be capable of safely bearing the pressure of the steam against the cover. Sometimes the cover opens inwards, and then it is kept shut by the pressure of the steam; but to prevent its being dislodged from its seat, it is held by bolts and nuts to cross bars outside the man-hole. The cover should fit its seat very accurately. VIL. Mud-holes are orifices at or near the lowest part of a boiler, which are opened occasionally for the discharge of sediment. VIII. The feed apparatus, by which water is introduced into the PARTS AND APPENDAGES OF BOILERS. 453 boiler to supply the place of that which has been discharged in the state of steam or otherwise, is usually supplied by a pump worked by the engine. In marine and locomotive engines, the rate at which feed water is supplied is regulated by a cock under the con- trol of the engineer; the surplus water which comes from the feed pump being discharged through a valve loaded with a pressure greater than that in the boiler; but in stationary boilers, there is often a self-acting apparatus to regulate the feed, controlled by a float which rises and falls with the level of the water in the boiler. The proper dimensions of feed pumps will be considered farther on. In cases in which a float within a boiler is used, it ought to rise and fall within a casing, communicating with the rest of the boiler through small holes near the top and bottom only. The water within the casing will preserve the same mean level with that throughout the rest of the boiler, but will be free from the agita- tion which is produced in all other parts of the boiler by the disengagement of steam. (As to Injectors, see page 477.) IX. The blow-off apparatus consists, in fresh water boilers, simply of a large cock at the bottom of the boiler, which is opened occasionally to cleanse the boiler by emptying it completely of sediment and muddy water. In many marine boilers, fed with salt water, a similar cock is opened at regular intervals to discharge brine, and so prevent salt from collecting in the boiler. Another blow-off cock is sometimes so placed as to discharge occasionally the scwm, consisting of crystals of salt, which collects on the surface of the water : this is called the “ surface blow.” As a substitute for the common blow-off apparatus, Messrs. Maudslay introduced brine pumps, which draw off a fixed quan- tity of brine from the bottom of the boiler at each stroke of the engine. The hot brine, whether blown off or pumped off, is, or ought to be, passed through a set of tubes, surrounded by a casing through which the feed water passes on its way to the boiler; the currents of the brine and of the feed water flowing in opposite directions. By means of this apparatus, called the refrigerator, the greater part of the heat which would otherwise be wasted with the brine is saved by being transferred to the feed water. X. The sediment collector, used in some marine boilers, is a funnel shaped like an inverted cone, and placed within the boiler so that its mouth is somewhat above the water level. It communi- cates with the rest of the boiler through triangular slits near its upper edge. In the boiler generally, there is a continual boiling up of steam, which keeps crystals of salt and other solid particles for a time near the surface of the water. Within the cone therc is comparatively still water, so that the solid impurities collect 454 STEAM AND OTHER, HEAT ENGINES. there, and sink down to the bottom, or apex of the cone, whence they are from time to time blown off, being first stirred up if necessary. XI. The steam pipe conveys the steam from the boiler to the engine. Ag to its dimensions and resistance, see Article 290. Besides the throttle valve or regulator, by which the supply of steam to the engine is controlled, the steam pipe of every- boiler should be provided with a perfectly steam tight stop valve (being usually a conical valve worked by means of a screw) to be shut when the boiler is not in use. XII. Safety valves, for letting the steam escape from the boiler when its pressure tends to rise too high, have been partially men- tioned in Article 113, and will be further considered in a subse- quent Article. Every boiler should have two, one being placed beyond the control of the engineman. XIII. The vacuwm valve is a safety valve opening inwards, to admit air into the boiler, and so to prevent it from collapsing, in the event of the steam within it falling below the atmospheric pressure. XIV. The fusible plug is a piece of metal or alloy stopping an aperture in some part of the boiler which is directly exposed to the fire, and of such a composition as to melt at a temperature lower than that at which the pressure of the steam would become dan- gerous. As to the melting points of various metals and alloys, see Article 205, page 235. Little confidence is now placed in this contrivance; for it has been known to fail completely in various cases of boiler explosions. XV. The pressure gauge shows to the engineer the excess of the pressure within the boiler above that of the atmosphere. As to various pressure gauges, see Article 107 a. That which is now almost universally preferred for steam boilers is Bourdon’s (see pages 111, 112). XVI. The water gauge shows to the engineer the level of the water in the boiler; and especially, whether it stands high enough to cover all those parts of the boiler which are directly exposed to the fire. The old form of water gauge consists of three cocks at different levels; one at the proper level of the water, another a few inches above that level, and a third a few inches below. By opening these the engineer can ascertain the level of the water approximately. The new form which is most frequently used, consists of a strong vertical glass tube, communicating with the boiler above and below the proper water level through cocks, which can be shut if the tube is accidentally broken. The level of the water is visible in this tube. Every boiler ought to be pro- vided with both forms of water gauge, the cocks and the glass tube ; APPENDAGES OF BOILER—FIRE GRATE. 455 so that if the tube should be choked or broken, the cocks may be employed. There are other forms of water gauge, in which a float acts upon an index; but they are less used than the two forms hefore mentioned. In the ether evaporator of M. du Trembley’s binary engine, where a glass tube would be dangerous, an iron float on the surface of the zther rises and falls in a vertical brass tube, and its position is indicated by a magnetic needle outside. XVII. A steam whistle may be used, as in locomotives, merely to make signals; but it may also be acted upon by a pressure gauge, or by a float, so as to give warning of the pressure rising too high, or the water level falling too low. XVIII. A damper is sometimes so acted upon by a pressure gauge as to regulate the draught of the furnace, and prevent any great deviation of the pressure from a given intensity. This is accomplished in Watt’s low pressure stationary boilers, by having a pressure gauge consisting of a vertical column of water contained in a tube which is open at the top, and plunges into the water within the boiler at the bottom; while a float on the surface of that water column opens the damper when falling, and closes it when rising. XIX. Stays are bars, rods, bolts, and gussets for strengthening the boiler, which have already been mentioned in Article 66, and will be further referred to in a subsequent Article. XX. Clothing for the outer surface of a boiler, to prevent waste of heat, is made sometimes of a layer of coarse felt, covered with a layer of thin wooden boards, and sometimes of a casing of brick- work. The tops of land boilers, resting on brickwork, are sometimes buried under a layer of ashes; but this method is objectionable, as the moisture which collects amongst the ashes tends to corrode the boiler shell. The principal parts and appendages of engines and boilers having been enumerated and described generally, those which require it will now be treated of in a more detailed manner. 306. Grate—The area of the grate is regulated by the weight of fuel which is to be burnt upon it in an hour, and by the rate of combustion per square foot of grate, as to which, see Article 232. To the list of different rates which occur in practice, as given in that Article, at page 285, may now be added the following, which comes between Nos. 1 and 2 of that list :— Lbs. per square foot per hour. 1 a. Rate of combustion in the furnace of Craddock’s ; 6 to 10 oilers sivewcscsceoosavwersetaorrecas Cuesuseeseaany As has been already more fully explained in Chapter II., the 456 STEAM AND OTHER HEAT ENGINES, economy of fuel depends very much on the proper adjustment of the rate of combustion per square foot of grate to the draught of the furnace. A certain rate of combustion, which may be found by practical trials, is the best suited to insure perfect combustion in a given furnace; and this fixes the best area of grate: if the grate is made smaller, the combustion becomes imperfect: if larger, too much air enters, and heat is wasted in warming it. It is best, in practice, to make the grate-area at first rather too large, and then to contract it by means of fire-bricks, until the smallest area is obtained upon which the required quantity of coal can be burned without incomplete combustion. When air is admitted above the fuel to burn the coal gas, a smaller area of grate is required to burn a given quantity of fuel per hour, than when the whole supply of air has to pass through the grate. For an example of this, see the Table in Article 232, page 285, Nos. 5 and 6. The length of a grate should not much exceed 6 feet, in order that the fireman may easily throw coals to the back of it. It may be as much less than 6 feet as the dimensions and figure of the boiler require. The breadths of grates range from about 15 inches to 4 feet; the most convenient breadths for firing being from 18 inches to 2 feet, or thereabouts. The grates of stationary and marine boilers are usually long and narrow; those of locomotive boilers are usually almost square, and sometimes round. To facilitate the even spreading of the fuel, the surface of an oblong grate isin general made to slope downwards from the furnace mouth to the bridge at the rate of about one in six. Its clear height above the floor of the ash-pit should be at least 23 feet in front. A locomotive grate is usually level; and the place of an ash-pit is supplied by a rectangular wrought iron pan about 10 inches deep, which is open at the front, to catch the air as the engine rushes through it, and can be removed when required. A grate consists of fire-bars, and of cross bearers by which they are supported. The fire-bars are made in lengths of from 2 to 3 feet. They are from 2 inch to 3 inch broad on the top, and are often made to diminish to about half that thickness at the lower edge, in order to admit of the free entrance of air and escape of ashes. Their ordinary depth is about 3 inches. The breadth of the clear space between two bars is from one-half to two-thirds of the greatest breadth of a bar. At each side of each end of a bar there are snugs or projections, by which the breadth of the bar at its ends is increased so as to be equal to the distance from centre to centre of the bars. When the bars are laid upon the cross bearers with the snugs touching each other, the proper spaces are GRATES—HEIGHT OF FURNACE—HEARTH FOR WOOD. 457 left between their intermediate parts. Fire-bars are often cast in pairs, so that two bars with the proper space between them form one piece. This saves time in removing and replacing them when the grate requires repairs. (As to burning mineral oil, see page 477.) 307. Moving Grates.—Reference has been made in Article 230, page 283, to contrivances for supplying fuel to furnaces gradually and equably by mechanism, in order to insure complete combustion. Some of these inventions involve the use of moving grates. The revolving grate is circular and horizontal, and turns slowly about its centre. The fuel is dropped upon it by degrees through a fixed opening; and thus every part of it is at all times equally covered. Juckes’s grate consists of an endless web of very short fire-bars, moving on horizontal rollers, travelling from the furnace mouth to the bridge, and returning through the ash-pit. The portion of the web which at any time is uppermost, is supported on small wheels with which the bars are provided, and which rest on rails. Some- times the fire-bars, by means of cams, are made to have a short reciprocating motion up and down, and from side to side, in order to keep them clear of clinkers. 308. Height of Furnace.—The clear height of the “crown” or roof of the furnace above the grate bars is seldom less than about 18 inches, and often considerably more. In the fire-boxes of loco- motives it is on an average about 4 feet. The height of eighteen inches is suitable where the crown of the furnace is a brick arch, as in Mr. C. T. Dunlop’s detached furnaces, formerly referred to. Where the crown of the furnace, on the other hand, forms part of the heating surface of the boiler, a greater height is desirable in every case in which it can be obtained; for the temperature of the boiler plates, being much lower than that of the flame, tends to check the combustion of the inflammable gases which rise from the fuel. Asa general principle, a high furnace is favourable to complete combustion. The height of the furnace is limited in practice, sometimes by the necessity for having flues or tubes traversing the water above it; and always by the necessity for having a sufficient depth of water above the crown; that is to say, about 12 or 15 inches in marine boilers, 5 or 6 inches in locomotive boilers, and 10 or 12 inches in land boilers. 309. Hlearth for Burning Wood.— According to M. Peclet, the best furnace for burning wood under a steam boiler consists of a hearth of fire-brick, with a sort of hopper or feeding passage in front, of the full width of the hearth, made of cast iron. The wood, cut into billets whose length is a little less than the width of the hearth, is placed crosswise in the hopper, and descends gradually either by its weight alone, or by its weight aided by the pressure of 458 STEAM AND OTHER HEAT ENGINES. the feet of the stoker. As it reaches the -hearth billet by billet, it takes fire, and is completely consumed. The hearth has a slight slope forwards, towards the bottom of the hopper. The whole supply of air for the combustion of the wood passes down through the hopper amongst the unconsumed billets of wood. The ashes are swept away by the draught. 310. Dead Plate—MMouthpiece—Fire Door—Farnace Front—Ash- pit Boor.—The use of the dead plate has been stated in Article. 230, page 282. In some of Watt’s furnaces, it was nearly as long as the grate; but a length of about 20 inches has been found to answer well in some recent practical examples. When the dead plate forms the bottom of a cast iron mouthpiece, it is useful to make the roof of that mouthpiece slope downwards towards the furnace at the rate of one in six, or thereabouts. This has the effect of directing any current of air which may enter through the mouthpiece downwards upon the surface of the burning fuel, so as at once to promote rapid combustion of the coal gas, and to prevent that current from striking the crown of the fire-box, which, when that crown is part of the boiler-surface, tends both to lower its temperature, and to oxidate the plates. In some furnaces the sides and top of the mouthpiece are made thick enough to be traversed by a row of longitudinal holes, each 4 inch in diameter. These holes admit small currents of air, which have some effect in burn- ing the coal gas, but whose principal use is at once to keep the mouthpiece cool, and to carry back to the furnace the heat which would otherwise be lost by conduction through the metal of the mouthpiece. In some furnaces the dead plate is double, and a current of air is admitted through the passage. As to contrivances for preventing waste of heat through the fire- door and furnace-front, and for admitting air through them to burn the coal gas, and regulating the admission of that air, and of the air which enters through the ash-pit, see Article 228, page 279, and Article 230, pages 282, 283. To what has been stated there, it may be added, that doors consisting of several layers of wire gauze have lately been used for these purposes, and it is said with good effect; and also, that a heap of dross, slack, or sawdust (where those substances are burned), blocking up the mouthpiece, which is without a door, has been found to answer the same end extremely well in stationary boilers at St. Rollox chemical works. The heap so placed intercepts the radiant heat, and admits through its interstices enough of air to carry the sensible part of that heat back into the furnace, and to burn the gases distilled from the fresh fuel. When the fireman considers that the heap is sufficiently coked or charred, he pushes it forward and spreads it uniformly DRAUGHT—-CHIMNEY—STRENGTH OF BOILERS. 459 over the grate, and supplies its place by blocking the mouthpiece again with a heap of fresh fuel. 311. Air Passages— Blowing Apparatus—Chimney. — The means of producing a current of air through a furnace, and the principles of the action of those means, and their peculiar effects, have already (with the exception of the blast pipe) been considered in Articles 230, 231, 232, 233, and 234. It may now be added, that care should be taken not to direct streams of fresh air against the plates or other metal surfaces of the boiler; because if so directed, they produce rapid oxidation. The blast pipe will be treated of in greater detail amongst some special subjects relating to locomotive boilers. 312, Strength and Constraction of Boilers—The principles upon which the strength of boilers depends have already been stated in Section 8 of the Introduction, Articles 59, 60, 61, 62, 63, 66, 67, 68, 69, and 73. The only figures for the shells of boilers which are safe against bursting by internal pressure, without the aid of stays, are the cylinder and the sphere, as to which see Articles 62, 63, Portions of boiler-shells which are flat, or which otherwise deviate from the cylindrical and spherical figures, are strengthened by means of stays, as to which see Article 66. To the information there given, it may be added, that the usual pitch or distance apart of the stays of locomotive fire-boxes is about 44 or 5 inches, and of marine and stationary boilers 12 to 18 inches. According to Mr. Bourne, the staying of existing marine boilers is seldom sufficiently strong; and the iron of the stays ought not to be exposed to a greater working tension than 3,000 lbs. on the square inch, in order to provide against their being weakened by corrosion. This amounts to making the factor of safety for the working pressure about 20. If any part of the surface of a boiler cannot be efficiently stayed by rods reaching across to the opposite part, it may be fastened by bolts or rivets to a series of ribs crossing it, care being taken that the ends of those ribs have sufficient support. For example, the flat crown of a locomotive fire-box is hung by bolts from a series of parallel ribs, which cross it at distances of from 44 to 5 inches from centre to centre, and whose ends are supported on the front and back of the fire-box. It has been found by experience that a thickness of about 3 of an inch is the most favourable to sound rivetting and caulking of boiler-plates; and therefore they are seldom made much thicker or much thinner than that thickness. If a cylindrical boiler is required to withstand a very high pressure, the necessary increase of strength must be attained, not by increasing the thickness of the 460 STEAM AND OTHER HEAT ENGINES. plates, but by diminishing the diameter of the shell. The strongest boilers are those which are entirely composed of tubes and small cylinders, with the water and steam inside. My. Fairbairn’s experiments have shown (as stated in Article 66), that the stay-bolts of locomotive fire-boxes should have their diame- ters equal to double the thickness of the plates, if these are of iron, so that for 2 inch iron plates the stay-bolts should be ? inch in diameter. According to the principles laid down by Mr. Bourne, the factor of safety for the stays of marine boilers should be about three times the factor of safety for those of locomotive boilers; hence for plates of $ inch thick or thereabouts, the stays of marine boilers, if round, should be about 14 inch in diameter. The flat ends of cylindrical boilers are made about once and a-half the thickness of the cylindrical barrels, and are tied to each other by longitudinal stays, or to the sides of the boiler by gussets (see Art. 66.) A pair of tube-plates are tied together in the same man- ner; and it is safer to rely altogether on stay-rods, to prevent them from being forced asunder, than to leave any part of the tension to be borne by the tubes. “Tubes for the passage of flame and hot gas are made of brass or of iron, and are from 14 to 2 inches in diameter for locomotives, and from 2 to 4 inches in diameter for marine boilers. They are fixed tight in the holes in the tube-plates, either by driving ferules into their ends, or by rivetting up the edges of the ends themselves, so as to make them fit countersunk grooves which surround the holes on the outside of each tube-plate. The principles of the strength of cylindrical internal flues have been explained in Article 67. The flat ends of cylindrical boilers are very commonly connected with the barrels and flues by means of rings of angle iron; but such rings are liable to split at the angle; and therefore it is considered preferable to make the connection by bending the edges of the endmost plates of the barrel and flues. A flat end to a cylindrical shell, or a flat top to a cylindrical steam chest, connected by means of an angle iron ring alone, without stay-bars or gussets, is danger- ous at high pressures, even when of small diameter ; as the angle iron ring, although it may last for a time and be apparently safe, is almost certain to split at the angle in the end. The shells of stationary and locomotive boilers are usually single- rivetted—those of marine boilers usually double-rivetted—that is, the rivets form a zig-zag line at each joint. Horizontal overlapped joints should have the overlapping edges facing upwards on the side next the water, that they may not intercept bubbles of steam on their way upwards. The joints in horizontal flues should be so placed that the overlapping edges shall not oppose the current of gas. BOILERS—HEATING SURFACE—FLUES. 461 _ Those parts of boilers which are exposed to more severe or more irregular strains than the rest, or to a more intense heat, should be made of the finest iron, such as Bowling or Lowmoor. This applies to the sides and crowns of internal furnaces, to tube-plates, to bent plates at the ends of cylindrical shells, é:c. 313. Heatiug Surface—Dimensions and Course of Flues.—In Article 234, Division IV., there have already been given several examples of the proportions usually borne by the area of heating- surface to the area of the grate, and to the number of pounds of fuel burnt in an hour; and in that Article, and the previous Articles 219, 220, and 221, have been explained the principles ou which the efficiency of that heating-surface depends. The object of the use of tubes is to obtain a large heating-surface within a moderate space; and this was the nature of the improvement intro- duced by Booth and Stephenson into the construction of the heating-surface of locomotive boilers. The construction which insures the greatest known heating-surface relatively to the fuel consumed, is that in which the boiler consists mainly of a sort of cage of vertical water-tubes enclosing the furnace, as in Mr. Crad- dock’s boiler, where there are from sia to ten square feet of heat- ing-surface for each pound of coal burned per hour ; and the efficiency is accordingly greater than that of any other boiler which has yet been brought into continuous practical operation on the large scale. (See Article 234, Example IX., page 297.) Similar proportions of heating-surface to fuel consumed may be obiained by means of square water-tubes or cells, each containing four hot gas tubes, as in Mr. J. M. Rowan’s boiler. The sectional area of the flues of a boiler must not be’ made too large, lest it should make the boiler too bulky, nor too small, lest it should cause too much resistance to the draught. Experience has shown, that a sectional area of from one-fifth to one-seventh of the area of the grate answers well in practice. Where there is a bridge contracting the entrance to the flue, this applies to the area of the passages left by the bridge. In multitubular boilers, the area to be considered is the joint area of the whole set of tubes, which, when there are ferules at their ends, is to be measured within the ferules. The course taken by the current of hot gas through the flues and tubes of a boiler is most commonly from below upwards on the whole, even when most of those passages are horizontal. It was first shown by Peclet, and is now generally recognized, that a great advantage in point of thorough convection of heat, and con- sequently in economy of fuel, is gained by causing the course of the hot gas to be on the whole from above downwards; because then the hottest strata of the furnace gas, being uppermost, spread them- 462 STEAM AND OTHER HEAT ENGINES, selves out above the denser and colder strata which are below, and so diffuse themselves more uniformly throughout all the passages than they do when made to ascend from below. This principle was practically applied in the Earl of Dundonald’s boiler—as to .which see Article 234, Example X., page 298, also Article 334, page 476. 314. Wotal and Effective Heating Surface.—The lower horizontal or neatly horizontal surfaces of internal flues and tubes, owing to the difficulty with which bubbles of steam escape from them, are found to be much less effective in producing steam than the lateral and upper surfaces. It is therefore common amongst engineers to distinguish between the total heating surface of a boiler and the effective heating surface, from which latter the bottoms of internal flues, and one-fourth of the surface of each cylindrical horizontal tube are excluded. On an average, the effective heating surface is from $ to § of the total heating surface. In all the calculations of Article 234, it is the total heating-sur- Jace which is considered. 315, Water-Reom and Sterm-Roem are the names given to the volumes of water and steam respectively contained in the boiler when the surface of the water is at its proper mean level. A-uthori- ties differ as to the relative proportions of water-room and steam- room adopted in the practice of the most skilful engineers. .\ccording to Mr. Bourne, of the whole boiler-room, or internal capacity of the boiler, there are very nearly ? water-room, and 1 steam-room. According to Mr. Robert Armstrong, there are 4 water-room and 4 steam-room ; and that author considers that, with a less proportion of steam-room, there is risk of priming, or carrying over liquid water from the boiler to the cylinder. A cylindrical boiler is usually filled with water to three-fourths of its depth or thereabouts. The practice with regard to the absolute capacity of boilers varies very much. According to Mr. Robert Armstrong, that capacity cught to be— Lor each cubic foot of water evaporated per hour, Shea =LOOM 6s siccaiscesieetens sdeeveratar sages 134 cubic feet. Woarter-r00m, ...sscccecsecensesteaeseneces 133 ie Total boiler-rooin,......ceeceeseeeeeeeeees 27 ” BOILER-ROOM. 463 The number of cubic feet of water to be effectively evaporated per hour in a given engine, per indicated horse-power, is given by the formula, 1980000 eau Janididiscuarctenetasecuses canes (1.) where U is the work of one lb. of steam, found by the methods of Chapter ITI. Sections 5 and 6. pp. 975 — 448 A useful mode of comparing the capacities of different boilers is to divide the boiler-room, in cubic feet, by the area of heating- surface, in square feet. Thus is obtained a sort of mean depth in feet, analogous to the hydraulic mean depth of a pipe. Of the fol- lowing examples, the first three are given on the authority of Mr. Fairbairn’s “ Useful Information for Engineers :’— “Mean depth.” Feet. Plain cylindrical egg-ended boiler, with external flues below and at each side, but no internal UES iiss feivigely cassie aie stevalon x Sucbiweseiss wetee a cedesulaswienaen 3°50 Cylindrical boiler with external flues, and one cylindrical internal fluc, ........ccccceeeeeeereeeeeee 1°65 Cylindrical boiler with external flues, and two cylindrical internal flues,.............ccscceceeeeeen ee 1'00 Stationary boilers according to Mr. Robert Arm- strong’s Tues si: atcusen, saey steeds nweaN eens 3°00 Multitubular marine boilers, about...............00. 0°50 Locomotive boilers, and boilers composed of water- tubes, average about: «:0:ccesaccsesisvecssensecees oes o'lo Boilers of large and small capacity have each their advantages. In favour of large capacity are, steadiness in the pressure of the steam, ready deposition of impurities, space for the collection of sedi- ment, freedom from priming. In favour of small capacity are, rapid raising of the steam to any required pressure, small surface for waste of heat, economy of space and weight (which are of special importance on board ship), greater strength with a given quan- tity of material, smaller damage in the event of an explosion. In boilers of very small capacity in proportion to their area of heating surface, especially those composed of small water-tubes, it is desirable, and in some cases necessary, to work with distilled water, in order to avoid the priming, the choking of the water- spaces by salt or sediment, and the consequent burning of the iron, which would arise from the use of water containing salt, mud, or other impurities. For that purpose swrface condensation must be employed, which has already been treated of to a certain extent in Article 222, and will be further considered in the sequel. 464 STEAM AND OTHER HEAT ENGINES. 316. Beea and Blow-off Apparatus — Donkey-Engine — Brine Pumps.—The feed-pumps are worked by the engine itself when it is ‘in motion; but when it is standing still, and it becomes necessary to feed the boiler, they are driven either by hand, or by a small auxiliary engine called a “Donkey.” For all marine boilers of con- siderable size, a donkey-engine is necessary; and it is used not merely to feed the boiler, but to drive the starting and reversing gear of the valves when required, and perform other miscellaneous duties. (As to Injectors, see page 477.) To provide for leakage of water and steam, priming, blowing-off, and loss by the safety valves, the feed-pump of a land engine should be of such capacity as to discharge from double to two and a-half times the net feed-water required by the engine, according to Article 284, Equation 10, page 389, \. ib fea Article 287, Equation 17, page 401, - ay te, or Article 297, Equation 12, page 434, In marine engines, a further addition to the capacity of the feed- pumps must be made, to provide for the brine which is blown off or pumped out. Ordinary sea-water contains about s'; of its weight of salt. The brine in the boiler should never be allowed to rise above treble that strength ; and for that purpose the volume of brine dis- charged should be equal to half the volume of the net feed-water. But it is better still to provide that the brine in the boiler shall never rise above double the strength of ordinary sea-water; and for this purpose the brine discharged should be equal to the feed-water in volume. The result is, that the discharging capacity of the feed- pumps of a marine engine is made equal to from three to four times the volume of the net feed-water. There is, besides, a duplicate set of feed-pumps, in order that if one breaks down the other may be used. As to the effect of salt in water on its boiling point, see Article 206, Division VIIL., page 242. The brine is discharged at a temperature on an average 140° or 150° higher than that at which the feed-water is drawn from the hot-well. In order that the apparatus of tubes and casing already mentioned under head IX. of Article 305 may act with the greatest possible efficiency in transferring heat from the hot brine to the fead-water, it appears, by the application of equations 6 and 7 of Article 219, that the surface of the tubes should amount to about toth of a square foot per lb. of brine discharged per hour; or 64 square feet per cubic foot of brine discharged per hour. It may, however, be sometimes difficult or inconvenient in prac- tice to obtain so large a surface. 317. Safety Valves—(See also Article 113.)—It is considered SAFETY VALVES—-STEEL BOILERS. 465 desirable that one at least of the safety valves of a boiler should be loaded directly, and not through the medium of a lever. In stationary engines the load, whether applied through a lever or to the valve directly, consists usually of weights; and weights are used for the same purpose in marine engines also. In locomotives, whose oscillations render weights inapplicable, the load is applied through a lever, by means of a spiral spring contained in a cylin- drical case, like that of the indicator (fig. 16, page 47). One end of the spring is attached to the boiler, the other to the lever, by means of a rod whose effective length can be adjusted by a screw and nut; an index pointing to a scale marked on the case shows the tension exerted by the spring. This mode of loading is now frequently adopted for the valves of marine boilers. A valve may also be loaded directly by means of a spring. Mr. Nasmyth’s safety valve is a sphere, and has a load hung to it inside the boiler. Mr. Fairbairn Joads the safety valve by a weight and lever inside the boiler. Feed-water heaters (page 262) should have safety valves and pressure gauges. The rules followed in practice for the size of the orifice of a safety valve are very various. That given by Mr. Bourne is equi- valent to the following:—Let A be the area of the piston; V, its velocity in feet per minute; P, the excess of the pressure in the boiler above that of the atmosphere, in lbs. on the square inch. Let a be the required area of the safety valve; then Vv a=A- 300 P Another mode of determining the size of the orifice has reference to the rate of consumption of fuel, and consists in making @ in square inches = from 7s to zx of the number of lbs. of coal burned per hour.....-...scsescesseseeee (2.) This rule is applicable to boilers in which the weight of water actually evaporated per lb. of coal is about 6 Ibs.; consequently we may substitute for it the following :— @ in square inches = from xs to ris of the number of Ibs. of water actually evaporated per hour.........(3.) Another rule is @ = 3 sq. inch x nominal horse-power (see page 479),...(4.) As to the outflow of steam, see page 298. 318, Steel Boiters.—Recent improvements in the manufacture of steel have so far diminished its cost as to render it commercially 2H 466 STEAM AND OTHER HEAT ENGINES, available as a material for boilers. Its tenacity is on an average about 1:6 times that of iron; and hence, by its use, boilers of a given strength may be made much lighter than iron boilers. In the steel steamer, “‘ Windsor Castle,” constructed by Messrs. Caird & Co., the shell of the boiler is made of steel plates, with steel rivets. It has to withstand a working pressure of about 40 lbs. on the square inch; while its thickness is only 7% inch, or little more than 2 of the thickness of an iron boiler of the same strength. 319. Proving Boilers.—DBefore any boiler is used, its strength ought to be tested by means of the pressure of water, forced in by pumps. The ¢esting pressure (according to the principles of Articles 59 and 60) should be not less than double the working pressure, and not more than half the bursting pressure; that is to say, as the bursting pressure should be six times the working pressure, the testing pressure should be between twice and three times the work- ing pressure. About two and a-half times the working pressure is a good medium. In everything that relates to the strength and testing of boilers, the “pressure” is to be understood to mean the excess of the pres- sure within the boiler above the atmospheric pressure, as in Article 294. The pressure of water is to be used in testing boilers, because of the absence of danger in the event of the boiler giving way to it. 320. Explosions of steam boilers, so far as they are understood, arise and are to be prevented in the following manner :— I. From original weakness. This cause is to be obviated by due attention to the laws of the strength of materials in the designing and construction of the boiler, and by testing it properly before it is subjected to steam pressure. II. From weakness produced by gradual corrosion of the ma- terial of which the boiler is made. This is to be obviated by frequent and careful inspection of the boiler, and especially of the parts exposed to the direct action of the fire. III. From wilful or accidental obstruction or overloading of the safety valve. This is to be obviated by so constructing safety valves as to be incapable of accidental obstruction, and by placing at least one safety valve on each boiler beyond the control of the engineman. 1V. From the sudden production of steam of a pressure greater than the boiler can bear, in a quantity greater than the safety valve can discharge. There is much ditterence of opinion as to some points of detail in the manner in which this phenomenon is produced ; but there can be no doubt that its primary causes are—first, the overheating of a portion of the plates of the boiler (being in most cases that portion called the crown of the furnace, which is directly BOILER EXPLOSIONS—INCRUSTATION. 467 over the fire), so that a store of heat is accumulated—and, secondly, the sudden contact of such overheated plates with water, so that the heat stored up is suddenly expended in the production of a large quantity of steam at a high pressure. Some engineers hold, that no portion of the plates can thus become overheated, unless the level of the surface of the water sinks so low as to leave that portion of the plates above it, and uncovered; others maintain, with M. Boutigny, that when a metallic surface is heated above a certain elevated temperature, water is prevented from actually touching it either by a direct repulsion, or by a film or layer of very dense vapour; and that when this has once taken place, the plate, being left dry, may go on accumulating heat and rising in temperature for an indefinite time, until some agitation, or the introduction of cold water, shall produce contact between the water and the plate, and bring about an explosion. All authorities, however, are agreed, that explosions of this class are to be pre- vented by the following means:—1. By avoiding the forcing of the fires, which makes the boiler produce steam faster than the rate suited to its size and surface. 2. By a regular, constant, and suffi- cient supply of feed water, whether regulated by a self-acting apparatus, or by the attention of the engineman to the water gauge ; and 3, Should the plates have actually become overheated, by abstaining from the sudden introduction of feed water (which would inevitably produce an explosion), and by drawing or extin- guishing the fires, and blowing off both the steam and the water trom the boiler. 32]. Internal Deposits,—Boilers are liable to become encrusted inside with a hard deposit of the minerals contained in the water, which, by resisting the conduction of heat, impairs at once the evaporative power of the boiler, its durability, and its safety. The deposition of carbonate of lime can be prevented by dissolving sal- ammoniac in the water; for that salt and the carbonate of lime are mutually decomposed, producing carbonate of ammonia and chloride of calcium, of which. both are soluble in water, and the former is volatile. The deposition of sulphate of lime can be pre- vented by dissolving carbonate of soda in the water ; the products being sulphate of soda and carbonate of lime, of which the former is soluble, and the latter falls down in grains, and does not adhere to the boiler. The most effectual means of preventing internal incrustation are, either a regular system of blowing off the water before it becomes too highly charged with impurities, like that described in Article 316; or the use of water so pure as to yield no deposit; whether such water be obtained from a natural source, or by means of surface condensation. A peculiar deposit of an unctuous nature has been found to clog 468 STEAM AND OTHER HEAT ENGINES. the water spaces of the boilers of some of the engines in which sur- face condensation has been employed. That deposit consists of the’ grease or oil used to lubricate the cylinder, partially altered and decomposed. It can be obviated by introducing little or no grease or oil into the cylinder; and to make that practicable, the surface of contact between the packing of the piston and the interior of the cylinder must be lubricated with water. In order that a small quantity of water may remain in the cylinder in the liquid state for that purpose, the heating of the steam, whether by means of a superheating apparatus or of a steam jacket round the cylinder, must not be carried so far as wholly to prevent condensation in the cylinder. On this point, see Article 286, page 396. 322. An External Crust of a carbonaceous kind is often deposited from the flame and smoke of the furnaces in the flues and tubes, and if allowed to accumulate, seriously impairs the economy of fuel. It is removed from time to time by means of scrapers and wire brushes. The accumulation of this crust is the probable cause of the fact, that in some steam-ships the consumption of coal per indicated horse-power per hour goes on gradually increasing, until it reaches one and a-half its original amount, and sometimes more. The following isan example of that increase, from an ocean steamer of great size and power :— Coal per I. H.-P., per hour. Lbs. On trial trip, ........cceeccseeees netde dine vanaaats 3.5 On Ist day of voyage,......cecceceececteeeee neces 3°6 On DUH day jwescs psevsncecetabecesaigntiais cank tetas 4°68 On UGA days. fis cave cenidcs ncsiel saceanel eecsemacte 4°55 OD 26th: Days sii cacnss cee cd snaveanenansiustencadaiess 5°32 On. B0th day, sccseseave vincan shesnceeaucnteyeaneetoee 5°84 On: 32d days cusssvissanertisemal ves vepeenensemsaas 4°65 On 35th: days. scseccsaciieneangaaeass ospauenexsneds 6°10 The increase in the consumption of fuel, although not absolutely continuous, and sometimes even reversed to a small extent, is still sufficiently marked to prove a progressive falling off in the efficiency of the furnace and boiler. 323. Nominal Horse-power of Boilers.—Boilers, especially those of stationary engines, are sometimes stated to be of so many horse- power. This is, in fact, a conventional mode of describing the dimen- sions of the boiler, according to an arbitrary rule. The rules employed for estimating the nominal horse-power of boilers have been various, and most of them vague and indefinite. A perfectly definite rule, however, has been proposed by Mr. Robert Armstrong, as being founded on the best ordinary practice, viz. :— BOILER-HORSE-POWER—-WAGON BOILER. 469 Take a mean proportional between the area of the fire grate in square feet, and the area of the effective heating surface in square yards. The nominal horse-power of the boiler is generally much less than the indicated horse-power of the engine, to which it bears no fixed proportion. Section 2.—Fxzamples of Furnaces and Boilers. 324. Wagon Boiler.—This form of boiler, which is suitable for Dd a“ Fig. 116. low pressure steam only, was introduced by Boulton and Watt, and was for a long time the most generally used of all boilers. A , great number of wagon boilers are still in use, but as their manufacture has been almost, if not wholly, given up, they will probably disappear by degrees. Fig. 116 is a longitudinal section, showing the general arrangement of the principal appendages of the boiler; fig. 117 a cross- ' section. A is the grate; B, the boiler; 470 STEAM AND OTHER HEAT ENGINES. C, C, C, C, stay-rods; D, the bridge; N, N, flues. The flame or furnace gas proceeds from the furnace over the bridge, and back- wards along the flue below the boiler; it retwmns forwards along one of the lateral flues N, and again proceeds backwards along the other lateral flue to the chimney. This course of the hot gas is called a wheel-draught. In the figure the boiler has no internal flue; sometimes there is a cylindrical internal flue, along which the hot gas returns forwards, and then divides into two currents, which proceed backwards to the chimney along the lateral flues. This is called a split-draught. W and 8 are water-gauge cocks; M, the man-hole; I, the steam pipe; V, the safety valve; F is the stone float, partially counter- poised, whose rising and falling regulates the valve for the admis- sion of the feed-water. The column of water in the vertical feed- pipe in these old low-pressure boilers acts as a pressure gauge, and a float on the surface of that column is seen to be connected by a chain over a pulley with the damper, whose opening it regulates. 325, Cylindrical Egg-Ended Boiler.—This boiler consists simply of a cylindrical shell with hemispherical ends. Its figure is very favourable to strength and safety, with a high pressure; but it requires great length as compared with other boilers to give sufficient heating surface. In the cross- section, fig. 118, A is the grate, cecupying a length which ought not to exceed about six feet under the front end of the boiler; B, the [|_| | «6boiler; D, the bridge, made concave at the Fig. 118. top so as to be parallel to the bottom of the. boiler; N, N, the flues, through which the hot gas forms a wheel-draught, as in Article 324, This boiler, like the wagon boiler, is sometimes made with an internal flue, by which the deficiency of heating surface compared with capacity is to a certain extent made up. A serious defect of the cylindrical boiler with the furnace below it is, that the bottom of the boiler where sediment collects is the part exposed to the most intense heat. Unless, therefore, the water used is of uncommon purity, the bottom of the boiler is liable to burn. Cylindrical boilers are sometimes made without lateral flues ; the hot gas flowing straight along the bottom of the boiler from the furnace to the chimney. This arrangement is called a “flash flue.” It requires a greater length for a given heating surface than any other form of boiler. 326. Retort Boiler—This is the name given by Messrs. Dunn & Hattersley to a boiler introduced by them, in order to obtain the strength of the cylindrical egg-ended boiler, without its disadvan- RETORT BOILER—BOILER WITH IIFATERS, 41 tages in point of compactness, economy of fuel, and durability. Tt consists of a number of small cylindrical egg-ended shells laid side by side, parallel and horizontally, above the furnace and flues ; these contain water to about three-quarters of their depth, and in them the boiling takes place; they all communicate upwards with one long cylindrical egg-ended shell which acts as a steam chest, and below with another which serves as a sediment collector. ee 327. Cylindrical Boiler with Heaters—This is called in Britain the “French boiler,” from being much used in France. In France it is called “chaudiére 4 bouilleurs.” Fig. 119 shows a longitudi- Vig. 119. nal section of the furnace and flues, and side elevation of the boiler fig. 120 shows a cross-section of the boiler, furnace, and flues. A is the main boiler shell, cylindrical, with hemispherical ends 5 B, B, the heaters, or “bouilleurs,” being horizontal cylindrical shells of smaller diameter than the main shell, having their back- ward ends hemispherical or segmental, and their forward ends closed by covers, so as to serve as “mud-holes” for the clean- sing out of sediment when required ; CCC, CCC, are two rows of vertical. tubes, which connect the main boiler shell with the heaters. D is a horizontal brick partition, at the level of the 472 STEAM AND OTHER HEAT ENGINES. upper halves of the heaters; E, the furnace; F (fig. 120), the passage over the bridge from the furnace to the flame-bed. The space above the horizontal partition D is divided by two parallel brick partitions, occupying the intervals of the two rows of vertical tubes, into three parallel flues, H, G, H. L is the chimney ; M, the damper; d is the glass water-gauge in front of the boiler. On .the top of the main shell are seen the man- hole, safety valves, and other appendages. In fig. 119, at the back of the furnace, is seen one of a row of curved passages, opened and closed by a sliding valve, for admitting jets of air above the fuel through holes in the front of the bridge ; at the front of the furnace is seen a dead-plate. The flame and hot gas pass backwards through F; then forwards through G; then by a “split-draught,” backwards through the lateral flues H, H; and then to the chimney. This boiler is considered both safe and efficient. In France the heaters and con- necting tubes are often made of cast iron ; = in Britain that material is considered unsafe Fig, 120. for boilers. 328. The Cornish Boiler in its simplest form consists of a horizontal cylindrical shell B (fig. 121), with an internal cylindrical flue, whose diameter is jsths of that of the shell or thereabouts. In the front end of that flue is situated the internal furnace, of which A is the grate, and D the bridge. The external flues may be arranged either for a split-draught or a wheel-draught. The figure shows the arrangement for a split-draught. The current of furnace gas, Fig. 121. after having passed backwards over the bridge and along the internal flue, divides into two streams, which pass forwards along the side flues EH, E; then those streams re-unite, and pass backwards along the bottom flue F to the chimney. In this form of boiler the furnace gas takes a descending course, of which the advantages have been stated in Articles 220 and 313; the bottom of the boiler, where the feed-water first mingles with the rest, and where deposit tends to settle, is the coolest portion; and the hottest portion (the CORNISH BOILER—DOUBLE-FURNACE BOILER. 473 crown of the furnace) is near the surface, where the steam is given off. All these circumstances are favourable to durability and economy. The crown of the furnace, and a portion of the top of the flue beyond the bridge, are sometimes lined with a brick arch, to pre- vent the flame from being cooled and extinguished by contact with the plates of the boiler before the combustion of the coal gas is complete. The part of the internal flue behind the bridge is sometimes made a little narrower than the part which contains the furnace. Boilers of this class have in many cases given way by the collaps- ing of the internal flue. The principles upon which the strength of that flue depends, discovered by Mr. Fairbairn, have been explained in Article 67, pages 70, 71. The dotted circle C represents a heater, or horizontal water-tube, like those of the French boiler, which is sometimes placed within the internal flue of the Cornish boiler, in the part behind the bridge. It is connected by one or more vertical water-tubes, with the water-space at the bottom of the main boiler, and by a siphon- shaped tube, beyond the backward end of the main boiler, with the steam-space at the top. 329, Cylindrical Double-Furnace Boiler.—A_ cross-section of a hoiler of this class is shown in fig. 122. The boilerconsists of a cylindrical shell, witha pair of similar and parallel internal flues, whose diame- ter is xsths of that of the shell, or thereabouts. Each of these flues contains in its front end an internal furnace, like that of the Cornish boiler. Those furnaces are fired alternately, in order to promote complete combustion, as stated in Article 230, page 282. The external flues form either a wheel-draught (as shown in fig. 122), or a split-draught (as shown in fig. 121). In one form of this boiler the two internal flues run parallel to each other from end to end of the boiler. This prevents the mixing of the gases from the two furnaces until they have been considerably cooled; and to remedy that defect, in some boilers a series of trans- verse tubes have been introduced, at and near the bridges, to make an early communication between the two currents of furnace gas. In another form, the two flues unite into one at a short distance behind the bridges, so that the entire combination of flues has a forked shape. The combustion-chamber where the flues unite, is sometimes strengthened against collapsing by means of vertical water-tubes traversing it, and acting as hollow pillars or struts, to keep the top and bottom asunder, Fig, 122. 474 STEAM AND OTHER HEAT [CNGINES. 330. Cylindrical Double-Furnace Tubular Boiler.—This boiler, mo introduced by Mr. Fairbairn, is like a forkcd-flue boiler, in which, for the single part of the inter- nal flues, is substituted a set of parallel tubes. The cross-section of the two furnaces is similar to fig. 122. Fig. 123 is a horizontal section of the boiler. A, A, are the grates; B, B, dead-plates; D, D, bridges; E, mixing-chamber or flame- chamber ; F, F, front tube- ‘plate ; G, tubes; H, H, back tube- plate, and backward end of boiler. According to the usual proportions of this boiler, the length of the tubes is about one-half of the total length of the boiler. It has external flues, like the boiler of the last Article. 331. Marime Flue Boilers, as stated in Article 305, are of a shape approximating to rectangular, with the corners more or less rounded, and ‘the top more or less arched: strength to resist inter- nal pressure is given by stays and ribs. Each boiler usually contains two or more internal furnaces, of an oblong rectangular shape, often arched at the top also. These furnaces stand in a row within the boiler, near its bottom. The bridges are sometimes water-spaces, but are more generally of fire- brick. The remainder of the interior of the boiler-shell, up to within about ten inches or a foot of the proper water-level, contains a set of flues, of a form of section nearly rectangular with rounded corners. One of these flues starts from each of the furnaces, aud takes a winding course within the boiler, according to the judgment of the designer. Finally, all the flues unite in an ascending flue called the “uptake,” which leads to the chimney. The steam chest is usually a rectangular or cylindrical box, sometimes with a hemispherical dome, enveloping the upper part of the uptake and lower part of the chimney, so that the steam may be dried, and in some cases partially superheated. The variety of forms and arrangements of flues in marine boilers is such as to defy classification. One of the most remarkable forms is the spiral flue, winding round a vertical axis through the water- space and steam-space, which latter ascends to a considerable height, in order to dry and superheat the steam effectually: an invention of Mr. John Elder. The chimneys of marine boilers are sometimes made to lengthen and shorten like the tube of a tele- scope, so that they can be lowered when the vessel is going under sail only. 332, Marine Tubular Boilers —The general arrangement of parts in this class of boilers is shown in fig. 124, which is a longitudinal section, showing one furnace, with its flue, tubes, and communica- tion with the uptake and chimney. Any required number of such Fig. 123. MARINE BOILERS—-DETACHED-FURNACE BOILER. 475 furnaces, according to the breadth of the boiler, may be ranged side by side within the boiler. A, A, is the grate; B, the dead-plate; C, the ash-pit; D, the bridge; E, the rising flue, flame-chamber, or “back uptake ;’ F, F, F, F, the tube-plates and tubes; G, G, the uptake, having doors in front for the removal of soot and other dirt, and for access to the tubes to cleanse or repair them; H, the chimney. The figure shows a few of the stay-rods within the boiler. In the figure, the tubes are represented as horizontal; they are often, however, made to have a slope, parallel or nearly parallel to that of the grate-bars, The height from the furnace-crown to the lowest row of tubes should be sufficient to allow the space between them to be cleansed. The most usual diameter of marine boiler tubes is, as formerly mentioned in Article 305, three inches ; they are sometimes, however, used of smaller diameters, ranging down to 14 inch internal dia- meter. 333, Detached-Furnace Boiler-—This has already been mentioned in Article 228, page 279; Article 230, page 283; and in Articles 303, 304, and 310, pages 449, 450, and 458. Fig. 125 is a horizontal 476 STEAM AND OTHER HEAT ENGINES. section of a double furnace of this kind, used at St. Rollox, showing a small portion of the boiler; fig. 126 is a cross-section of the fur- nace ; fig. 127 a cross-section of the boiler and flues. These three figures are on a scale of xty of the real dimensions; A, A, are the ] VI / 7 WS N SG yyy Fig. 126. Fig. 125, dead-plates; B, B, the grates; C, the brick partition between the two grates and their ash-pits; D, D, air-spaces in the brickwork of the sides and roof of the furnace, to resist the conduction of heat; H, flame-chamber, tapering so as to join the internal flue E, of the boiler; F, F, side'flues; G, bottom flue. Fig. 128 is a longitudinal section of a mouthpiece and dead- plate, showing the heap of dross which acts as a fire- door (see Article 310), and the air-holes in the thickness of the top of the mouthpiece. Fig. 129 at is a front view of the mouthpiece, show- gli ing the air-holes. These two figures are ef 17] on a scale of gs of the real dimensions. In some of the boilers, the internal Fig. 129. flue, instead of traversing the boiler from end to end, is of a T-shape at the back- ward end, the two branches leading into .the two side flues F, F. In others, there is a single cylindrical fiue for half the length of the boiler, and a set of tubes, as in fig. 123, page 474, for the other half of the length. These forms of flue were introduced by Mr. John Tennent. 334, Miscellaneous Forms of Boiler.—Various kinds of boilers, presenting great diversities of form and arrangement, have already been incidentally mentioned and described generally, such as Mr. Craddock’s boiler (Articles 303, 305, 313, 315). With reference to this boiler, it may here be added, that the vertical water-tubes have a portion slightly curved, in order that when expanded by VARIOUS BOILERS. 477 heat, they may yield sideways, and not strain the framework of the boiler. The Earl of Dundonald’s boiler, mentioned in Article 234, Example X., consists of a shell like that of a marine flue-boiler, but somewhat longer and lower. Within that shell are, the fur- nace, the flame-chamber, and the uptake, all at the same or nearly the same level. The flame passes from the top of the furnace into the top of the flame-chamber, which is traversed by a great number of vertical water-tubes: from the bottom of this chamber the hot gas passes into the uptake, in contact with which is a steam chest communicating at its top with the top of the boiler. At the passage of communication is a centrifugal fan, so placed as to throw the spray that is mixed with the steam back into the boiler. Amongst vertical tube boilers may be mentioned one of Mr. David Napier’s, which has been used to some extent in practice. The shell is cylindrical and vertical, with a hemispherical top. Within it is a vertical cylindrical flame-chamber, and within the flame-chamber are numerous vertical water-tubes, communicating above with the steam space at the top of the boiler, and below with a flattened hollow disc, or “ pan,” which is above the fire, and is connected by horizontal tubes with the surrounding annular water space. The locomotive boiler will be illustrated in the next chapter. ADDENDUM TO ARTICLE 306, Pace 457. Forvaces for Wincral Oil.—To adapt the furnace of a steam-boiler to the burn- ing of mineral oil, it is lined throughout with fire-brick 4 or 5 inches thick, which at once protects the boiler-plates and maintains a temperature high enough for complete combustion. The oil runs from a closed reservoir at a rate regulated by means of suit- able cocks or valves into one or more funnels, from which it is conducted into the furnace. There are different ways of introducing the oil and the air for its combustion into the furnace; but in every case it is essential that the oil should be in a state of fine division. In some furnaces the oil flows in by gravity, in a shower, from a row of small orifices in the front; and below these is a fire-brick grating, through which the air enters, In others the oil is blown into the furnace in the state of spray, by means of a jet of highly superheated steam; and the air enters through orifices surrounding the injecting apparatus (Aydon’s system). ADDENDUM To ARTICLE 516, Pacz 464. The Injector for feeding boilers (invented by Giffard) is in fact a jet pump (Article 187 a, page 2138), in which the water is driven by a jet of steam taken from the boiler that is fed. ‘The ordinary rule for finding the proper sectional area for the narrowest cubic feet per hour gross feed water “800 4/ pressure in atmospheres ° cubic feet per hour gross feed water 630 4 pressure in atmospheres * is about fourteen times the volume of the water injected. parts of the nozzles is as follows :—For square inches, and for circular inches, The expenditure of steam 478 CHAPTER V. OF THE MECHANISM OF STEAM ENGINES. Section 1.—Of the Mechanism of Steam Engines in general. 335. Emgines Classed.— All steam engines may be divided into two great classes, according as they are or are not provided with apparatus for condensing the steam at a pressure lower than the atmospheric pressure; that is to say, with a low pressure condenser, and its appendages. These classes are— I. Condensing, or low pressure engines. II. Non-condensing, or high pressure engines. The difference between those two classes of engines, in so far as it affects the efficiency of the steam, has been treated of already in Article 280, pages 381, 382, 383, and in Article 289, pages 410, 411. The kind of locomotive mentioned in Article 412, which condenses part of its waste steam at the atmospheric pressure, belongs more properly to the second class than to the first. Engines of the second class are on the whole less economical of fuel than those of the first class; but as they have fewer parts, and occupy less space, they are much used where simplicity and compactness are considered of more importance than economy of fuel. _ A second mode of classing steam engines is founded on the mode in which the steam acts upon the piston, and is as follows :— I. Single acting engines, in which the steam performs its work by its action on one side of the piston only. II. Double acting engines, in which the steam exerts energy on either side of the piston alternately. III. Rotatory engines, in which the steam drives a revolving piston round. The way in which the difference between single and double act- ing engines affects the calculation of the power has already been explained in Article 43, page 50, and referred to in Article 260, pages 333, 334, Article 263, page 339, and elsewhere. A third mode of classification distinguishes engines into— I. Non-rotative, in which no continuous rotation is produced, as in single acting pumping engines, steam hammers, and direct acting beetling machines. - STEAM ENGINES CLASSED—NOMINAL HORSE-POWER, 479 II. Rotative engines, in which the motion is finally communi- cated to a continuously rotating shaft. Rotative engines are now the most common. Non-rotative engines are exceptional. A fourth mode of classing engines is founded on their purposes, as follows :— I. Stationary engines, such as those used for pumping water, for driving manufacturing machinery, &c. II. Portable engines, which can be removed from place to place, but are stationary when at work. III. Marine engines, for propelling vessels. IV. Locomotive engines, for propelling vehicles on land. Stationary engines exist of all the classes belonging to the three previous modes of classification. Portable engines are usually non- condensing, to save space, and to adapt them to situations where injection water cannot be obtained in sufficient quantity. Most of them are also double acting and rotative. Marine engines are in general condensing, double acting, and rotative. Locomotive engines are almost all non-condensing, and all double acting and rotative. 336. Nominal Morse-power is a conventional mode of describing the dimensions of a steam engine, for the convenience of makers and purchasers of engines, and bears no fixed relation to indicated or to effective horse-power. The mode of computing nominal horse-power, established amongst civil manufacturers of steam engines by the practice of Messrs, Boulton and Waitt, is as follows :— Assume the velocity of the piston to be 128 feet per minute x cube root of length of stroke in feet ; Assume the mean effective pressure to be 7 lbs. on the square inch ; Then compute the horse-power from those fictitious data, and the area of the piston; that is to say, Nominal H.-P. = 7 x 128 x 3/ stroke in feet x area, of piston in square inches + 33,000 _ 3] stroke in feet x area piston in inches = 47 nearly °/ stroke in feet x diam.? in inches 1 = 60 iaaturane (1.) The indicated power of different engines usually exceeds the nominal power as computed by the above rule in proportions rang- ing from 13 to 5. ; ; ; Tn the rule established by the Admiralty for computing nominal 480 STEAM AND OTHER HEAT ENGINES. horse-power, the real velocity of the piston is taken into account; but the fictitious effective pressure of 7 lbs. on the square inch is assumed; consequently, by the Admiralty rule, Nominal H.-P. = velocity of piston in feet per minute x area of piston in inches x 7 + 33,000 _ Yelocity in feet per min. x diam.? in inches (2.) 6000 The indicated power of marine engines ranges from once to three times, and is on an average about twice the nominal power as com- puted by the Admiralty rule. Both the civil rule and the Admiralty rule for computing the power of engines are applicable to low pressure engines alone. For high pressure engines there is a customary rule proposed by Mr. Bourne, which consists in assuming the effective pressure to be 21 lbs. per square inch, the other data being the same as in the rule for low pressure engines. 337, Enumeration of the Principal Parts of an Engine.— I. The boiler and cylinder are connected by means of the steam pipe, in which is the stop valve, already mentioned in Article 305, Divi- sion XI.: also, the throttle valve or regulator, for adjusting the opening for the admission of steam to the cylinder,-which in some engines is regulated by hand, and in others by a governor, as to which see Articles 55, 56, page 63: also page 551. II. The steam pipe contains sometimes also the cut-off valve or expansion valve, for cutting off the admission of the steam to the cylinder at any required period of each stroke of the piston, leaving the remainder of the stroke to be performed by the expansion of the steam already admitted. ITI. The cylinder may be single or double acting. In a single acting engine, the piston is forced in one direction by the pressure of the steam, and made to return in the opposite direction when the steam is discharged by the action of a weight or counterpoise. In a double acting engine, the piston is forced in either direction by the pressure of the steam which is admitted and discharged at either end of the cylinder alternately. IV. The admission and discharge of the steam take place through openings near the ends of the cylinder, called ports, con- nected with passages called nozzles, which are opened and closed by induction and eduction valves. Sometimes the induction and eduction valves are combined in one valve, called a slide valve. ‘Che valves are contained in the valve-chest. V. In non-condensing engines (conventionally called high pressure engines), the waste steam discharged from the cylinder escapes into PARTS OF STEAM ENGINES. 481 the atmosphere through the blast pipe; in locomotive engines, as well as some others, the blast pipe is placed in the centre of the chimney, so that the successive blasts of steam discharged from it augment the draught of air through the furnace, and cause the combustion of the fuel to be more or less rapid, according as the engine is per- forming more or less work. VI. The cylinder cover has in it.a stuffing-bow for the passage of the piston rod; in large engines there are sometimes more than one piston rod and stuffing-box, and sometimes a tubular piston rod, called a trunk. The cylinder cover is also provided with a grease cock, to supply the piston with unguent. VII. In many large engines, there is a spring safety valve, called an escape valve, at each end of the cylinder; the chief use of which is to discharge water which may condense in the cylinder, or be carried over in the liquid state from the boiler, by what is called priming. VIII. To prevent condensation in the cylinder, it is sometimes enclosed in a casing, called a jacket, the intermediate space being filled with hot steam from the boiler, or hot air from a flue (see Article’ 286). 1X. Outside the jacket, to prevent loss of heat externally, there is a clothing of felt and wood. _X. Double cylinder engines have two cylinders; the steam being admitted from the boiler into the first cylinder and then filling the second by expansion from the first. XI. The ordinary condenser is a steam and air-tight vessel of any convenient shape, in which the steam discharged from the cylinder is liquefied by a constant shower of cold water from the rose-headed injection valve. (As to the Hjector-condenser, see page 552.) XII. In land engines the injection water comes from a tank called the cold well, surrounding the condenser, and supplied by the cold water pump; in marine engines, it comes directly from the sea. XIII. In the surface condenser the steam is liquefied by being passed through tubes or other narrow passages surrounded by cur- rents of cold water, or cold air. XIV. The condenser is provided with blow-through valves, com- municating with the cylinder, usually shut, but capable of being occasionally opened, and with a snifting valve opening outwards to the atmosphere; through these valves steam can be blown to expel air from the cylinder and condenser before the engine is set to work. XV. The condenser has also a vacuwm gauge, to show how much the pressure in it falls below that of the atmosphere (see Article 107 a, pages 110, 111, 112). XVI. The water, the small portion of steam which remains 21 482 STEAM AND OTHER HEAT ENGINES, uncondensed, and the air which may be mixed with it, are sucked from the condenser by the air pump, and discharged into the hot well, a tank from which the feed pump, mentioned in Articles 305 and 316, draws the supply of water from the boiler. The surplus water of the hot well in land engines is discharged into a pond, there to cool and form a store of water for the cold well; in marine engines, it is ejected into the sea. XVII. In all, except certain peculiar classes of engines, there is a parallel motion for guiding the head of the piston rod to move in a straight line, consisting either simply of straight cheeks or guides, or of a combination of levers and linkwork, invented by Watt, and more or less modified by others. XVIII. The peculiar class of engines above excepted, are—first, trunk engines (including Mr. Hunt’s Z crank engine), where the stuff- ing-box is the guide; secondly, oscillating engines, in which the head of the piston rod is directly connected with the crank, and the cylinder oscillates on trunnions; thirdly, disc engines, in which the functions of a cylinder are performed by a vessel of the figure of a spherical zone, and those of a piston by a disc having a motion of nutation in that zone; and fourthly, rotatory engines, in which the piston revolves round an axis. Trunk engines and oscillatory engines are of common occurrence in steam-ships. The Z crank engine has not been tried on a large scale. Disc engines are said to answer well, but are of rare occurrence. Rotatory engines of various kinds have been often tried, but seldom with good results. XIX. In single acting engines for pumping water, the pump rods are worked either by direct connection with the piston rod, or through the intervention of a beam. XX. In double acting engines, the power is communicated to a revolving shaft, driven by means of a crank and connecting rod, with or without the intervention of a beam. (In oscillating engines the piston rod and connecting rod are one). XXI. In stationary engines the shaft carries a fly-wheel, to dis- tribute and equalize irregularities in the action of the power by its inertia; this function is performed in marine engines by the inertia of the paddle-wheels or screw, and, in locomotive engines, by the inertia of the driving-wheels and of the engine itself. XXII. The feed pump, and other pumps which are appendages of the engine, are worked by the mechanism ; so also are the induction and eduction valves, through what is called the valve gearing or valve motion—a part of the machinery which is under the control of the engineman, and so contrived as to enable him to stop and reverse the motion of the engines at will, and whose forms are very various. 338. Combined Engines—Most marine and locomotive engines, COMBINED ENGINES. 483 and many stationary engines, have, in order to equalize the action of the power, a pair of cranks at right angles to each other, driven by a pair of pistons in a pair of cylinders, with their appendages ; 484 STEAM AND OTHER HEAT ENGINES. and are, in fact, pairs of engines. In some cases, engines arc simi- larly combined in sets of three, driving three cranks, which make equal angles with each other. As to the effect of these combina- tions on steadiness of motion, see Article 52, page 60. 339, Parts of an Engine Mlustrated.—Most of the parts enume- rated in Article 387 are illustrated in fig. 130, which represents a longitudinal section of a rotative double-acting stationary condens- ing (or low-pressure) steam engine. That kind of engine is selected because the arrangement of its parts is well suited for exhibiting nearly all of them at one view. Amongst the parts omitted, for want of room, the chief are the beam and the parallel motion, which will be illustrated farther on. The main-centre, or axis of the beam, is above the pillar D, and its two ends are respec- tively above the cylinder A and shaft L. A is the cylinder, with its jacket, but without clothing, which is a defect in the engine represented.- B, the piston, with three metallic packing-rings. In the figure the piston is supposed to be moving downwards, pressed by the steam which is entering above it. C, the piston rod. D, one of the pillars of the frame. a, steam pipe, with throttle valve. b, valve chest. ¢, slide valve, of the kind called a “D-slide,” which regulates the “ distribution” of the steam—that is, its alternate admission and discharge above and below the piston. d, exhaust-pipe, leading into E, the condenser. g, injection cock, admitting a shower of cold water from the cold well, or cold water tank, into the condenser. H, air pump, the piston of which in the figure is supposed to be descending. K, Hot well. G, connecting rod, in the act of rising. L, shaft; LM, crank; M, crank pin, in the act of right-handed rotation (similar to that of the hands of a watch). N, feed pump, drawing water from the hot well K. In the engine represented, the supply pipe from the hot well to the feed pump traverses the cold well. That is a fault; for it tends to heat the condensation water, and cool the feed water. P, feed pipe of the boiler. Q, cold water pump. R, eccentric rod, which receives a reciprocating motion from an eccentric wheel on the shaft L, and communicates that motion to the slide valve c. STEAM PASSAGES—VALVES. 4865. 8, governor, being a double revolving pendulum of the kind men- tioned in Article 55, page 63. It is seen to act on a small lever whose axis turns in bearings fixed to the pillar D. The links and intermediate levers by which the motion of that lever is communi- cated to the throttle valve are not shown, their arrangement being a matter of convenience. Section 2.—Of Steam Passages, Valves, and Valve Gearing. 340, Steam Passages.—The principle which ought to regulate the size of the steam pipe, and of all passages by which the steam is admitted to the cylinder, has already been stated in Article 290, page 414, viz., that the velocity of the steam should not be greater than 100 feet per second, or 6,000 feet per minute, supposing its density to be the same in the steam pipe and in the cylinder during the admission. To permit the ready escape of the steam during the back stroke, the exhaust pipe should be of at least double the area of the steam pipe. For the sake of simplicity, it isan almost universal practice to make the steam enter and leave a given end of the cylinder through the same port. Mr. Joule has pointed out that this practice tends to the waste of heat, especially with high rates of expansion; because the cool expanded steam, in escaping, cools the metal of the port, which is again heated at the expense of the heat of the next cylinderful of hot steam that enters; and all the heat so trans- ferred from the entering to the escaping steam is wasted. Mr. Joule therefore recommends the use of separate admission and exhaust ports. 341. Throttle Valve.— When, the throttle valve is controlled by a governor, it is usually a disc-and-pivot valve (as to which, see Article 119, page 123, and fig. 40, page 140, U, V); because that valve is easily moved. A throttle valve to be controlled by hand may be a disc-and- pivot valve, or an ordinary slide valve moved by a screw (Article 120, page 124), or a rotating slide valve (Article 120, page 125), or a conical valve moved by a screw (Article 121, pages 125, 126). The last named form of throttle valve is now much used in locomo- tive engines, and will be illustrated in a subsequent Article. 342. Conical and Double Beat Valves. — In Waitt’s earlier engines, conical valves with vertical spindles (Article 112, page 118) were used to regulate the distribution of the steam. Now double beat valves (Article 116, pages 121, 122, figs. 33, 34) are used in all cases in which the slide valve is not employed. In a single acting engine, there are three such valves, viz. :— 486 STEAM AND OTHER HEAT ENGINES. I. The steam valve, which opens at the beginning of the forward stroke to admit steam to drive the piston, and closes to cut of the steam at the proper instant. II. The equihtbrium valve, which is closed during the forward stroke, and open during the return stroke, the expanded steam being then transferred through it from the one end of the cylinder to the other. III. The eduction valve, which is closed during the return stroke, and open during the forward stroke, to let the steam in front of the piston escape to the condenser. In a double acting engine, there are four valves, one pair for each end of the cylinder, and each of these pairs consists of— I. A steam valve, opening at the beginning of each forward stroke, and closing to cut off the steam at the proper instant. II. An eduction valve, closed during the forward stroke, and okie during the return stroke, to let the steam escape to the con- enser. 343, Plug Rod and Tappets.—The motions of conical and double beat valves, in single acting engines, and in some double acting engines also, are produced by means of a “plug rod,” which hangs vertically from the beam of the engine, near the cylinder, and rises and falls vertically along with the piston. From its sides, suitably formed pins and bars project, whose positions can be adjusted by screws; and these projecting pieces, striking levers at certain instants in the course of each stroke, produce the required motion of the valves. In single acting engines, the exhaust valve and the steam valve are not opened directly by the action of the plug rod, but by a piece of mechanism called the “cataract,” of the nature of a pump brake, already referred to in Article 50, page 58. It consists principally of a small loaded piston, moving in a vertical cylinder which contains water or oil. At the end of the forward stroke of the engine, a pin projecting from the plug rod lifts the cataract piston. That piston, on being set free, descends with a speed which is determined by the degree of opening of the regulating cock through which the liquid below it is discharged ; and towards the end of its descent it acts successively upon two catches which liberate weights that in their descent open the exhaust valve and the steam valve. Thus, by varying the opening of the regulating cock of the cataract, the engine can be caused to make more or fewer strokes per minute. The arrangement of the valve motions of single acting engines may be varied in its detail. One of its forms will be illustrated in a subsequent Article, , 344, Slide Valves, on account of the simplicity of their action, LONG SLIDE VALVE. 487 and smoothness of their motion, are almost universally employed in Europe for the distribution of the steam in double acting engines. The seat of a steam engine slide valve consists usually of a very accurate plane surface, in which are oblong openings or ports. These are at least two in number; one communicating with each end of the cylinder. The seat of the short slide valve has a third, or exhaust port, between the first two, which is the passage for the escape of the exhaust steam. In some special forms of engine the ports are more numerous still. The long slide valve, or D-slide, represented by ¢ in fig. 130, and by figs. 131, 132, and 133, might also be classed as a sort of hollow Fig. 151. Fig, 132. Tig. 185. or tubular piston valve; for the back of the valve, which is semi- cylindrical, is made to move steam-tight at its top and bottom in the semi-cylindrical valve chest, by means of two half-rings of metallic packing. Fig. 131 shows a vertical section of the valve, separate from the valve chest and cylinder. ¢, c, are the two portions of which its plane face consists: at its back near the top and bottom are seen sections of the packing half-rings. The valve rod is shown passing down through the tubular interior of the valve, and attached to a cross bar at the bottom. This bar is flat and thin, and placed with its breadth vertical, so as to contract as little as possible the passage through the interior of the valve. Figs. 132 and 133 are vertical sections of the cylinder, valve chest, and valve. The steam is admitted through the steam pipe and throttle valve to the middle part of the valve chest, which surrounds the tubular part of the valve. The two ends of the valve chest communicate with the condenser, the lower end directly, and the upper end through the interior of the tubular part of the valve. 488 STEAM AND OTHER HEAT ENGINES. In fig. 132, the valve is in its highest position: the middle part of the valve chest communicates with the top of the cylinder, admitting steam to drive the piston downward; the bottom of the cylinder communicates with the bottom of the valve chest, and so with the condenser. In fig. 133, the valve is in its lowest position: the middle part of the valve chest communicates with the bottom of the cylinder, admitting steam to drive the piston upward: the top of the cylinder communicates with the top of the valve chest, and thence through the tubular interior of the valve, with the condenser. The short slide valve is represented in figs. 134, 135, 136, 187, and 138. Fig. 134 is a longitudinal section of the valve and its seat. The cylinder is supposed to be vertical: d is the slide valve; @ the upper and ¢ the lower cylinder port; 6 the exhaust port, leading sideways to the condenser, or to the air, according as the engine is condensing or non-condensing. Fig. 135 is a front view of the valve seat and ports; fig. 136, the face of the valve. The steam is admitted from the boiler into the valve chest, round and behind the valve. In fig. 134, the valve is in its middle position, and both the cylinder ports are closed. In fig. 138, the valve is depressed so far below its middle position as to open Fig. 134. the upper port for the admission of . steam above the piston; while at the same time the lower port is connected through the interior of the valve with the exhaust port, so as to allow the steam from below the piston to escape as the piston descends. In fig. 137, the valve is raised so high above its middle position as to open the lower port for the admission of steam below the piston; while at the same time the upper port is connected through the interior of the valve with the exhaust port, so as to allow the steam from above the piston to escape as the piston rises. _ The shortslide valve is pressed againstits seat, and the joint between it and its seat kept steam-tight, by the excess of the pressure of the steam in the valve chest behind the valve, which comes from the boiler, above the pressure of the steam in the interior of the valve, which communicates with the condenser or with the atmosphere, as the case may be. SHORT SLIDE VALVE. 489 In large engines, the amount of that difference of pressure, over the whole area of the face of the valve, would be unnecessarily great, onm Cc Fig. 138, Fig. 137. causing too much work to be lost in overcoming friction. To diminish its amount is the object of the contrivance called the equilibrium slide valve, in which the interior of the back of the valve chest is a true plane, parallel to that of the valve seat; and the back of the valve is provided with a flat brass packing-ring, which is pressed against the back of the valve chest by springs. The amount of the pressure of the valve against its seat due to the pressure of the steam from behind, is the product of the inten- sity of that pressure into the excess of the area of the face of 490 STEAM AND OTHER HEAT ENGINES. the valve above the area of the packing-ring at its back, and may be reduced to any required amount, how small soever, by making that ring large enough. 345. Eccentrie.—It is obvious that to produce the proper distri- bution of the steam by a slide valve, whether long or short, the valve must have a reciprocating motion of such a nature as to bring it to the ends of its stroke, being its greatest distances from its middle position, at periods intermediate between those at which the piston reaches the ends of its stroke. The eccentric ¢ (fig. 139), which is used to give that motion, is a circular disc car- ried by the shaft, with whose axis the centre of the disc does not -coincide. It is equivalent to a crank whose length is equal to the eccentric radius; that is, the line joining the centre of the disc and the axis of the shaft ; and being encircled with a hoop, d, at one end of the eccentric rod, a, it gives to that rod a reciprocating motion whose length of stroke is the double of the eccentric radius. The eccentric rod is either directly jointed to the slide valve rod, or con- nected with it by any convenient combination of levers and link- work. One such arrangement is shown in figs. 137 and 138, of Article 394, where ¢ is the piston rod; J, the connecting rod; &, the crank; m, the eccentric; ”, the eccentric rod; 0, p, levers; pe, a link; h, the slide valve rod. The notch opposite the letter a, in fig. 189, is the gab of the eccentric rod, by which it holds a pin on the end of the lever that is directly driven by it (as 0, figs. 137, 138). By means of a handle on the end of the eccentric rod, the gab and pin can be dis- engaged and re-engaged, so as to throw the valve motion “out of gearing” and “into gearing,” and thus make the slide valve stop and resume its motion when required. LOOSE ECCENTRIC. 491 In many engines a different contrivance is used, called the “link motion,” to be afterwards described. 346. Reversing by the Loose Eccentrie.—To reverse the direction of rotation of the shaft of a steam engine, the piston must be made to come to rest and then to move the reverse way, before ecomplet- ing a stroke, and the eccentric must assume that position relatively to the crank which is proper for working the slide valve when the rotation of the shaft is reversed. That position (or the position of backward gear) is somewhat less than half a circumference from the position of forward gear, measured round the shaft in the direction of forward rotation. To bring the eccentric, therefore, into back- ward gear, it is sufficient to cause it first to stand still while the shaft nearly finishes the first half-turn backwards, and then to accom- pany the shaft in its rotation. In most stationary engines, and many marine engines, those objects are effected by having the eccentric loose on the shaft, and so counterpoised, that its centre of gravity shall be in the axis of the shaft; but prevented from turning completely round by means of two shoulders, one of which holds it in the position of forward gear, and the other in that of backward gear; care being taken that the motion of the loose eccentric round the shaft shall be forwards to go from forward into backward gear, and backwards to go from backward into forward gear. To reverse an engine with a loose eccentric, the gab is to be dis- engaged from its pin and the slide valve shifted by hand if neces- sary. When the shaft has made part of a turn backwards the gab is to be re-engaged. For example, in fig. 187, the piston is rising, and the shaft turning toward the right. To reverse that rotation the gab is dis- engaged, and the slide valve shifted into the position shown in fig. 138; so that steam from the boiler being admitted to press on the top of the piston, brings it to rest before it has completed its up stroke, and then drives it downwards, so as to make the shaft rotate towards the left. During the left-handed rotation the eccen- tric stands still until it is in the position of backward gear: then the gab is re-engaged with its pin, the slide valve resumes its motion, and the left-handed rotation goes on till the engine is stopped, or reversed again by the same process. According to a mode of reversing by the loose eccentric, used by Messrs. Randolph, Elder, & Co., the eccentric, instead of standing still till the engine has turned back, is made by a combination of wheelwork, to overtake or outrun the shaft while the engine is moving forward, until it reaches the position of reverse gearing; and the reversal of the motion of the engine follows. 347. Lead and Lap—Expansion by the Slide Valvee-—The lead of 492 STEAM AND OTHER HEAT ENGINES. the centre of the slide is the distance to which it has passed beyond the middle of its stroke at the instant when the piston arrives at either end of its stroke. The lead of the induction-edge of the slide is the extent to which the port is open for admission of steam at the same instant. The amount of the lead of the centre of the slide may be measured and expressed in three ways, viz. :— {. In absolute measure, such as inches. II. By the proportion of the absolute lead to the half-throw of the slide valve. This may be called the ratio of lead. III. By the angle at which the eccentric radius stands in advance of the position which it would require to have relatively to the crank, in order to make the middle position of the side valve occur at the same instant with the end of the piston stroke. This may be called the angle of lead. © When a loose eccentric has no lead, its positions of forward and backward gear are half a circumference apart. When it has lead, the angle between those positions is half a circumference less twice the angle of lead. If the eccentric rod is so long relatively to the eccentric radius, that the effect of its varying obliquities on the positions of the points it connects may be neglected in practice, the following cquation is sensibly accurate :— Liatio of lead of ceutre = sine of angle of lead;...... (1.) and in other cases the same equation always gives at least an “approximation to the truth. The angle of lead may be stated either in degrees, or as a frac- tion of a revolution. The lap, or cover, of a slide valve at one of its edges is the extent to which that edge overlaps the adjoining edge of the port which it covers when the slide valve is in its middle position. In fig. 134 of Article 344, the slide valve has a very small and nearly ; equal extent of lap at each of its four edges. \ i Fig. 140 is a section of the lower half of a verti- * Y LY) iY Z Yj Ue Wl, ak slide valve and its port having a greater extent y Ww of lap; Wis the lower port of a cylinder; X, the MT lower half of the slide valve, in its middle posi- ye tion; U is the induction side, and V the educ- Gy : : 5 “Y tion side of the port; C is the induction edge, and Fig. 140. P the eduction edge of the valve; UC is the lap on the induction side, and V P the lap on the eduction side. Lead of the induction-edge of the valve = lead of centre — lap; (1a.) EXPANSION BY THE SLIDE VALVE. 493 and this is what is meant when “lead” is spoken of without quali- fication. The lap, like the lead, may be expressed in three ways, viz.:— I. In absolute measure, as inches. II. By its proportion to the half-throw of the slide valve, which may be called the ratio of lap. ‘ITI. By the angle through which the eccentric must turn, in order to shift the valve from its middle position until the edge of the valve whose lap is considered touches the edge of the port— this may be called the angle of lap. When the obliquity of the eccentric rod may be neglected, we have, sensibly, ratio of lap = sine of angle of lap....esccieee (2.) The use of the lead and lap of the slide valve is to admit the steam, cut off the admission, and cut off the exhaust, at given instants of the stroke of the piston, and so to produce expansive working with a given ratio of expansion, and to compress or cushion a given proportion of the expanded steam at the end of the return stroke. When the obliquity of the connecting rod, as well as that of the eccentric rod, may be neglected, the following are methods by which the proper lead and Jap of the slide valve in any case may be determined :— First Mrruop :—By graphic construction. About a centre O describe a circle D E FI, and draw two a diameters at right angles to each other, a DF, EI. Consider D F as represent- vt % ing the stroke of the piston; and if (though on a different scale), the throw of the slide valve; and let motion of the ,{— piston from D to F be considered as a S a forward stroke. ae It is sometimes considered desirable = to begin the admission of steam a little before the end of the return stroke. If Fig. 411. so, let Q represent the point of the return stroke where the admission is to begin. If the admission and the forward stroke are to begin together, Q will coincide with D. Let R be the point of the forward stroke where the steam is to be cut off. oa T be the point of the return stroke where compression or cushioning is to begin, by cutting off the exhaust. As to the prin- Hp seeeeenen sy y AG 494 STEAM AND OTHER HEAT ENGINES. ciples which determine that point, see Article 291, Division TIL, page 420. These being the data, the solution consists of two parts, as follows :— I. Zo find the angle of lead, and the lap on the induction side:— Draw Q A, RG, perpendicular to D F, cutting the circle in A, G; measure or bisect the arc AG; from E lay off the equal arcs EB, : EA, each = ame AS, join BH, which will be parallel to D F. Then The angle of lad = -AOB==’ sin 4. r a 18 revolution, = * 7 The volume given by the formula 1 corresponds to that which, in computing the power of common double acting steam engines, is found by multiplying the area of the piston into twice the length of a single stroke. 362. Pistons and Packing Ordinary pistons agree pretty nearly as to figure and proportions, with the description of a piston for a water pressure engine already given in Article 127, page 129; but instead of the hempen packing, metallic packing is universally used, made of brass, or of cast iron. Fig. 148 represents one of the most complex arrangements of metallic packing, with the junk ring (as it is still called) removed. There are two, or some- times three, rings of packing, each con- sisting of an outer and inner circle of arcs of metal, built together so as to break joint, and pressed outwards against the interior of the cylinder by means of springs. Much simpler arrangements are often used, especially one in which there is only a single packing ring divided at one point, and pressing against the sides of the cylinder by its own elasticity, which, as it is originally made of a radius a little larger than that of the cylinder, causes it to tend to expand. The gap at the point of division is sometimes filled by a tongue piece morticed into the ends of the ring; sometimes by a small wedge-formed block, pressed outwards by a spring behind it. Mr. Ramsbottom’s piston for locomotives has a cylindrical surface turned to fit the interior of the cylinder loosely; round that cylindrical surface are three parallel rectangular grooves, each filled by. a single packing ring of square brass wire, measuring about an eighth of an inch each way; each of these rings is divided 506 STEAM AND OTHER HEAT ENGINES. at one point, and presses outwards against the cylinder by its elasticity, like the single packing ring beforementioned. The points of division are placed at the lower side, where the body of the piston touches the cylinder. The varieties of metallic packing are very numerous; but they differ chiefly in points of detail. Hemp is frequently used as an elastic material behind metallic packing, to keep it pressed against the cylinder. Metallic rings, or pieces of sheet brass, packed behind with hemp, are used also for the packing of stuffing-boxes. 363. Piston Rods and Trunks.—In most engines, each piston has but one rod, fitted at one end into a conical socket in the centre of the piston, and fixed by means of a gib and cotter, ora screw and nut. The piston rod passes through a stuffing-box in the centre of the cylinder cover. In some marine engines, two piston rods, and in some four, are attached to one piston, and traverse a corresponding number of stuffing-boxes in the cylinder cover. These arrangements form part of peculiar systems of mechanism for connecting the piston with the crank. A trunk is a tubular piston rod, used to enable the connecting rod to be jointed directly to the piston, or to a very short inner piston rod, so as to save room in marine engines. The width of the trunk must be sufficient to give room for the lateral motion of the connecting rod. As to the strength of piston rods, see Article 71, pages 73, 74. In computing the stress on a piston rod, the greatest pressure of the steam must be taken into account. The usual factor of safety is about 6 or 7; but in some cases it is as low as 5, and in others as high as 10. 364. Speed of Pistons.—The speed of the piston of an engine is usually expressed in feet per minute, the whole motion being taken into account in double acting engines, but the forward strokes only in single acting engines, as has already been explained. An opinion at one time prevailed, that there was an advantage in making the real speed of pistons follow the rule laid down in Article 336, page 479, for calculating the fictitious speed assumed in computations of nominal horse-power ; and although that opinion has been shown to be groundless, the ordinary speeds of the pistons of stationary engines and marine paddle engines do not often deviate much from those given by that rule, and range accordingly from about 120 to 300 feet per minute. But in marine screw engines, and in locomotive engines, speeds of piston are used rang- ing up to 900 feet per minute and more, with advantageous results, American engineers, by giving great length to the cylinder and crank, obtain a high speed of piston in paddle engines also. SPEED OF PISTONS—WATT’S CONDENSER. 507 Inasmuch as the work performed by the piston in an unit of time is the product of the effort into the speed, it follows that a high speed of piston involves a small stress upon the machinery, bearings, and framework, and consequently, a small amount of friction; circumstances favourable to lightness, and to economy of cost and of power. The velocity of the piston being proportional to the length and frequency of the strokes jointly, there are two means of obtaining a high velocity: great length of stroke, and great frequency. Of those two means, great length of stroke is to be preferred, when there is no reason to the contrary; because great frequency of stroke, requiring rapid reversal of the motion of the piston, and the other masses which move along with it, produces periodical strains, by reason of the inertia of those masses, which to a certain extent neutralize the benefits arising from the smallness of the mean effort exerted through the piston rod. The limit beyond which the velocity of the piston cannot with advantage be increased is not yet known. There must, however, be some such limit, because of the increase of the resistance to the motion of the steam through passages with increased velocity of its flow. (See Article 290, pages 413 to 417; Article 340, page 485.) Section 4.—Of Condensers and Pumps. 365. Watt's Condenser, being that which is most generally em- ployed, is a cast iron vessel of any convenient shape, and strong enough to bear the atmospheric pressure from without, in which the waste steam from the cylinder is condensed by a shower of cold water. The capacity of the condenser in Watt’s original engines was } of that of the cylinder; but according to present practice, it ranges from } to 4,"and sometimes even more. The area of the injection valve, by which the condensation water is introduced into the condenser from the cold well in land engines, and from the sea in marine engines, is commonly fixed by one or other of the two following rules :— rs square inch per cubic foot of water evaporated by the boiler per hour, or aby of the area of the piston. In Chapter ITT., Section 5, of this Part, formule have been given for computing the net quantity of injection water required to con- dense the steam in engines of various kinds, for each cubic foot swept through by the piston. The velocity with which the injection water flows towards the condenser at the contracted vein is about 44 feet per second. Taking 0-62 as the co-efficient of contraction, 508 STEAM AND OTHER HEAT ENGINES. the velocity of flow reduced to the area of the orifice itself is found to be 27 feet per second, or 1,620 feet per minute, nearly. To find, therefore, the proportion of the injection orifice to the area of piston, necessary in order to supply the net quantity of injection water, we have the following formula :— net area of orifice area of piston swept through by piston x velocity of piston in feel per THINTTOE A G20 Fe cccsesaasicssdssea saceen (1.) = net volume of injection water per cubic foot but it appears from ordinary practice, that to provide for contin- gences, the injection valve must be made capable of introducing, when required, about double the net quantity of injection water found by calculation; hence 810 is to be taken as the divisor in the above formula instead of 1,620. This gives results nearly agreeing with those of the practical rules first cited. In marine engines, there is sometimes an injection valve leading from the ship’s bilge into the condenser, which is opened only when the leakage of water into the ship threatens to become too great for the ordinary bilge pumps. On such occasions, the ordinary injection valve is closed. (See page 552.) 366. The Geld Water Pamp, by which in low pressure land engines the cold well is supplied with water, must be made of capa- city sufficient to supply double the computed net injection water. 367, The Air Pump (Article 337, Division XVI, page 481), when single acting, is usually of a capacity from one-fifth to one-siath of that of the cylinder; when the air pump is double acting, it may of course be made one-half smaller. The valves through which it draws the water, steam, and air from the condenser, are called foot valves; those through which it discharges those fluids into the hot well, delivery valves. A single acting air pump has bucket valves opening upwards in its piston. Flap valves, and other clacks of various forms, are used as air pump valves. As to the circular Indian rubber flap valves, now very generally employed, see Article 118, page 123. The ratio of the area of the valve passages to that of the air pump piston ranges in different engines from 4 to equality, being made greater as the speed of that piston is greater, so that the velocity of fluids pumped may not in any case exceed about 10 or 12 feet per second. (See next page.) The surplus water from the hot well, over and above that which is drawn away by the feed pumps (Article 316, page 164), is dis- charged by marine engines into the sea; and by land engines, if there is sufficient ground available, into a shallow pond, to be cooled and used again as condensation water. SURFACE CONDENSERS. 509 368. Surface Condensers possess the advantages of preserving the purity of the water, by returning to the boiler the same water over and over again, without the admixture of condensation water from without (see Article 321, page 468), and of saving the power which is expended in pumping the condensation water out of the common condenser. Surface condensation appears to have been employed at an early period by Watt, but afterwards abandoned by him for condensation by injection, on account of practical difficulties. Various surface condensers have since been tried at different times with more or less success. Those of Mr. Samuel Hall were fitted up in several steamers. A surface condenser consists generally of a great number of ver- tical tubes, about 4 inch in diameter, united at their upper and lower ends by means of a pair of flat disc-shaped vessels, or of two sets of radiating tubes, or in some other convenient manner. This set of tubes is enclosed in a casing, through which a sufficient quan- tity of cold water is driven. The steam being led by the exhaust pipe to the upper end of the set of tubes is condensed as it descends through them, and arrives in the state of liquid water at the lower end of the apparatus, whence it is pumped away to feed the boiler. ‘Where condensation water is scarce or impure, it may be de- sirable to condense the steam by the contact of cold air with the outside of the tubes. To overcome the chief difficulty of this pro- cess, which consists in producing a sufficiently rapid circulation of air over the tubes, Mr. Craddock makes the whole apparatus of tubes rotate rapidly about a vertical axis. Some results of experiment as to the efficiency of cooling surface in condensing steam have already been given in Article 222, page 266. The greatest of those results (that recently obtained by Mr. Joule) was the effect of casing each condensing tube in an outer tube, and driving a current of cold water through the annular space between the inner and outer tubes in a direction contrary to that of the motion of the condensing steam. To these data may be added the result of some recent experiments on a marine engine, in which the rate of surface condensation in half-inch brass tubes surrounded by water, estimated theoretically from the indicator diagrams, was between 3 and 4 lbs. per square foot of surface; the “vacuum” in the condenser being 13 lbs. on the square inch, and the absolute pressure, therefore, of uncondensed steam and air about 1°7 Ib. on the square inch. In a marine engine with a surface condenser, the loss of water is supplied by means of a distilling apparatus. ADDENDUM TO ARTICLE 367. ‘The Resistance of the Air Pump is equivalent to a back-pressure on fhe steam piston, ranging from 0°5 to 0-76 Ibs. on the square inch, in well-proportioned examples. 510 STEAM AND OTHER HEAT ENGINES. Section 5.—Of Connecting Mechanism. 369, Beam Engines and Direct Acting Engines.— By connecting mechanism is meant the series of pieces through which motion is communicated from the piston rod to the piece, whether a rotating shaft or a reciprocating rod, by which the useful work is performed. With respect to connecting mechanism, steam engines may be divided into two great classes :— I, Beam Engines, in which the piston rod is connected by means of a link, with one end of a beam or lever oscillating about a centre; the other end of the beam being connected by a link or connect- ing rod with the pump rod or with the crank, according as the engine * is non-rotative or rota- , tive. The engine used © ¥\ as an illustration in Ar- i ticle 389, fig. 180, is a a beam engine of the ordi- Tm aa hoe ie but as - a mT eam is there omitie TC COO TAA fig, 120 eeatded detec 2 Mig: 222: the general arrangement i s of mechanism in such an engine. II. Direct acting engines, in which the pump rod or the crank, as the case may be, is connected with the piston rod, either directly or by means of a connecting rod only. The engine used as an illustration in Article 344, fig. 187, is direct acting. 370. Forces Acting on Beam and Cylinder,—In a beam engine the velocities of the two ends of the beam at any given instant are to each other directly as the lengths of the two arms of the beam: the alternate pulls and thrusts exerted on the two ends of the beam by the piston rod and connecting rod, being inversely as the veloci- ties of their points of application, are to each other inversely as the lengths of the arms of the beam. The bearings of the “main centre,” or gudgeons of the beam, have to sustain, when the engine is at rest, the weight of the beam and the parts which hang from it: when the beam is in motion, the sum of the forces exerted by the piston rod and connecting rod is added to that weight druing the down stroke of the piston, and sub- tracted from it during the up stroke. The cylinder is pressed alternately downwards and upwards with a force equal and oposite to the effort of the steam on the piston; EFFORT ON CRANK PIN. 511 and the strength of the fastenings of the cylinder to the framework must be regulated accordingly. 371. Effort on Crank Pin—Fly-Wheel.—The whole force exerted by the connecting rod on the crank pin may be resolved into two rectangular components, as in Article 23, page 31—a lateral force acting along the crank towards or from its axis of rotation, produc- ing merely pressure on the bearings of the shaft, and an effort, acting perpendicular to the crank, in the direction of motion of the crank pin, by means of which effort the resistance of the machinery driven is overcome and work performed. To find the ratio which that effort bears to the effort exerted by the steam on the piston, in any given position of the mechanism, it is sufficient to know the ratio of the velocity of the crank pin to that of the piston; for the efforts are inversely as the velocities. The following are the methods by which that “velocity ratio” is found at any instant :— CasE I. In a beam engine (fig. 150), let C, be the axis of mo- tion of the beam; C, that of the crank shaft; T, ‘I',, the connecting rod, T, being the centre of the crank pin. Ata given instant, let v, be the velocity of T,, which can be deduced from that of the pis- ton, as in Article 370; v, that of T,. To find the ratio of those velocities, produce C, T,, C, T,, till they intersect in K; K is the “ instantaneous axis” of the connect- ing rod, and the velocity ratio in question is is Pigs SPOONS TO edie icin testes (1.) Should K be inconveniently far off, draw any triangle with its sides respectively parallel to C, T,, C, T,, and T, T,; the ratio of the two T, , Me f ay ’ + * ut Mae oe Fig. 150. Fig. 151. sides first mentioned will be the velocity ratio required. For ex- ample, draw C, A parallel to C, T,, cutting T, T, in A; then 05 ig | Oph, POG Digs wtiines varteoercnnes ean (2.) 512 STEAM AND OTHER HEAT ENGINES. Case IL, in a direct acting engine (fig. 151.) Let C, be the axis of the crank shaft, and T, R the piston rod; C, T, the crank; and T, T, the connecting rod. Draw T, K perpendicular to T, R, inter- secting C, T, produced in K ; K is the “instantaneous axis” of the connecting rod; and the rest of the solution is the same as in Case I., the formule 1, 2, giving the ratio of the velocity of the piston to that of the crank pin, which is also the ratio of the effort on the crank pin to the effort on the piston; that is to say— C, T,:C,A:: effort of steam on piston: effort of connecting POCO. CRANK Pith coeds vee evwcewepeareess (3.) It is by this process that data are obtained for determining the periodical excess and deficiency of energy exerted on the crank shaft, by the methods already explained in Article 52, pages 59, 60, 61, and thence, by the methods explained in Article 53, pages 61, 62, the required moment of inertia of a FLY-WHEEL which shall prevent the fluctuations of speed caused by that alternate excess and defi- ciency from going beyond given limits. Marine and locomotive engines require no fly-wheels; for in the former the inertia of the propeller, whether paddle or screw, and in. the latter that of the entire engine, suffice to prevent excessive fluc- tuations of speed. 372. Dead Points.—At two instants in each revolution, the direction of the crank coincides with the line of connection (or straight line joining the centres of the joints of the connecting rod). The positions of the crank pin at those instants are called dead points, and they correspond to the ends of the stroke of the piston, when its velocity vanishes, and so also does the effort on the crank pin. It is to diminish the irregular action caused by the existence of these dead points, and especially to facilitate the starting of engines when the crank happens to rest at one of them, that engines are combined by pairs or threes, as described in Articles 338 and 353, with the effect in diminishing the periodical excess and deficiency of energy stated in Article 52, page 60. 373. Guides for the Piston Bod are very accurately straight surfaces, plane or cylindrical, but best plane, on which a block fixed to the head of the piston rod slides, and which resist the tendency — of the link, or of the connecting rod, when in an oblique position, to make the motion of the piston rod deviate from a straight line. The accuracy with which smooth plane surfaces can now be made has oo guides to be more generally used than they were for- merly. ; 374, Parallel Motions are jointed combinations of linkwork, designed to guide the motion of the piston rod either exactly or approximately in a straight line, in order to avoid the friction PARALLEL MOTIONS. 513 which attends the use of straight guides. The first parallel motion is well known to have been an invention of Watt. Four kinds of parallel motion will now be described :— I. An Exact Parallel Motion, believed to have been first proposed by Mr. Scott Russell, is represented in fig. 152. The same parts of the mechanism are marked with the same letters, and different successive 9 S0077777777777 a positions are indicated by numerals afixed. The lever CT turns: about the fixed centre C, and carries, jointed preg to its other end, the bar or link P T Q, in which PT =TQ=COT. The point Q is jointed to a slider which slides in guides along the straight line CQ; and . the point P moves in the straight line Hige 402, P,CP,+CQ. A pair of the combinations here shown are used, one at each side of the cylinder; and the pair of bars PQ are jointed at their extremities P to the head of the piston rod. II. An Approximate Parallel Motion, somewhat resembling the preceding, is obtained by guiding the link P Q entirely by means of oscillating _le- vers, instead of by a lever and a slide. To find the length and the posi- tion of the axis of one of those levers, cé, select any convenient point, é, in the link P Q, and lay down on a drawing the ex- treme and mid- dle positions, t,, ty, tz, of that point, corre- sponding to the extreme and 4 middle _posi- Fig. 153. tions of the link PQ. The centre c of a circle traversing those three points will be the required axis of the lever, and c ¢ will be its length; and if the link PQ is guided by two such levers, the extreme and middle positions ef P will be in one straight line, 20 & 4 514 STEAM AND OTHER HEAT ENGINES. and the. other positions of that point very nearly in one straight line. IIL. waws Approximate Parallel Motion.—In fig. 153, Cc T, ct, are a pair of levers, connected by a link T#4, and oscillating about the axes C, c, between the positions marked 1 and 3. The middle positions of the levers, C T,, ¢¢,, are parallel to each other. It ig required to find a point P in the link TZ, such, that its middle position P,, and its extreme positions P,, P,, shall be in the same straight line perpendicular to C T,, ¢t,, and so to place the axes C, ¢, on the lines CT,, cé,, that the path of P, between the positions P,, P,, Ps, shall be as near as possible to a straight line. The axes C, ¢, are to be so placed, that the middle M of the versed sine V T., and the middle m of the versed sine v t,, of the respective ares whose equal chords T, T, = ¢,¢, represent the stroke, shall each be in the line of stroke M m. The position of the point P on the link is found by the following proportional equation :— Te:PT:Pé::0M+em:em: OM.......... (1.) The positions of the point P in the link, intermediate between its middle and extreme positions, are near enough to a straight line for practical purposes. When there are given, the axes OC, ¢, the line of stroke P, P, P, the length of stroke P, P; = 8, and the perpendicular distance Mm between the middle positions of the two levers, the following equations serve to compute the lengths of the levers and link :— : a & eee eae } Versed sines, TV= 3G? tv= San’ ea | a Oe | de v Levers, T=CM+-37; t=c +33 saeiteneds (2.) m Link, Ti=\/ { sae EH | IV. Wat's Parallel Motion Modified by having the guided point P in the prolongation of the link T¢ beyond its connected points, instead of between those points, is represented by fig. 154. In this case, the centres of the two levers are at the same side of the link, instead of at opposite sides, the shorter lever being the farther from e guided point P; and the equations 1 and 2 are modified as ollows :— Segments of the link— Te: PT: Pi::6M-—cm:em:OM.........(3) PARALLEL MOTIONS. 515 Versed sines, TV = e jv esa s8CM 8cem Levers, CT=oN+>", ci=em +S Sen sree (4.) Link, Tia 4/ {Met = 2 We _ This parallel motion is used in some marine engines, ina position inverted with respect to that in the figure, P being the upper, and ¢ the lower end of the link.’ Fig. 155. When Waitt’s parallel motion (IIT) is applied to steam engines with beams, ¢> it is more usual to guide the air pump rod than the piston rod directly by means of the point P. The head of the piston rod is guided by being con- nected with that point by means of a parallelogram of bars, shown in fig. 155. ¢ is the axis of motion of the beam of the engine, ct A one arm of that beam, CT a lever called the radius bar or bridle rod, Té a link called the back link. CT,ct,andTt, »° B form the combination already described : (IIL), and shown in fig. 153; and the point P, found as already shown, is guided in a vertical line, almost exactly straight. The total length of the beam arm, ¢ A, is fixed by the proportion PST POR OLA} ciceccncds saituctes (6.) that is, ¢ A is very nearly a third proportional to C Tandcé. Draw AB || T¢, and c PB intersecting it; then from the proportion 6 it follows that AB=Té AB is the main link: B, the head of the Rel Fig. 154. 516 STEAM AND OTHER HEAT ENGINES. piston rod. BT =and ||¢A is the parallel bar, by which the main and back links are connected. P moves sensibly in a straight line; cB:cP isa constant ratio; therefore B moves sensibly in a straight line parallel to that in which P moves. (For methods of designing parallel motions by graphic construction alone, see Rankine On Machinery, pages 274 to 280; On Shipbuilding, pages 284, 285; Rules and Tables, page 236.) ic Fig. 156. 375. Side Lever Engines are a variety of beam engines much used in paddle steamers, Figs. 156 and 157 represent the general SIDE LEVER ENGINES. 517 arrangement of a pair of such engines, driving a pair of cranks at right angles to each other: fig. 156 being a side view of the port Fig. 157. engine, and fig. 157 a view of the cylinder ends of both engines. Each engine has a pair of side levers or beams below the level of the shaft and of the cylinder cover; they are fixed on the opposite ends of one rocking shaft, which is the main centre. The piston rod carries a cross-head, like that of the letter T, from the ends of which hang a pair of side rods, connecting it with the ends of the * pair of side levers. The opposite ends of the side levers are con- nected with a cross-tail, which, being fixed on the lower end of the connecting rod, gives it the shape of the inverted letter 7. In fig. 156, @ is the cylinder, 6 one of the side levers, ¢ the sole plate with vertical flanges, which carries the engines and their frame; d the air pump rod ‘with its cross-head and side rods, ¢ the crank, hha paddle wheel, fan eccentric with its counterpoise. 518 STEAM AND OTHER HEAT ENGINES. 376. Vavieties in Direct Acting Marine Engines are so numerous that they would require a separate treatise for their description, The objects aimed at in them are, in paddle steamers, length of stroke, notwithstanding limited head room; and in screw steamers, compactness and convenience, especially in ships of war, where the whole engine has to be placed below the water line. Some of them Fig. 159. a pair of Messrs. Maudslay’s double cylinder engines, in which there are four cylinders, two for each engine. Fig. 163 shows the Fig. 158. have been sufficiently described un- der the head of cylinders, Articles 353, 354, 355, 358. Fig. 158 is a cross-section, and fig. 159 a side view, of a pair of oscillating engines, such as have been mentioned in Article 358. The air pump is worked by a crank in the middle of the shaft. Figs. 160 and 161 repre- sent a pair of “steeple engines,” in which, from each cylinder, a pair of long piston rods rise on opposite sides of the shaft, and also of the crank, carrying a cross-head from which the connecting rod hangs } downwards. In fig. 161 is seen the air pump, worked by a lever and links. Figs. 162 and 163 represent eee DIRECT ACTING MARINE ENGINES. 519 two similar and equal cylinders that belong to one engine, standing side by side; their pistons move together, and they act in all Fig. 162. respects like two parts of one cylinder. Their two piston rods are fixed to the cross-head of a pair of T-shaped pieces, the lower ends © of the stems of which move in vertical guides in the space between 520 STEAM AND OTHER HEAT ENGINES. the cylinders, and give motion through the connecting rod to the crank, The air pump is worked through a lever and links. The simplest arrange- ment of direct acting screw engines used in merchant vessels will be illustrated in a subsequent Article. In ships of war, those engines are brought below the water line, generally by placing their cylinders either hori- zontal or very much in- clined. Contrivances for this object have given rise to an incalculable variety of forms of engine. 377. Coupling Shafts of Marine Engines.—In paddle engines, the shaft consists Fig. 163. of three pieces, each with its independent bearings. The middle piece, called the intermediate shaft, or engine shaft, isin permanent connection with the pistons through the connecting rods. The two outer pieces, called the paddle shafts, carry the paddle wheels: they have cranks upon their inner ends, which can be at will connected with and disconnected from the crank pins of the cranks of the engine shaft. The details of the method of doing this vary very much in the practice of different engineers. In screw engines also, the engine shaft and screw shaft can be connected and disconnected by various contrivances. 378. Strength of Wechanism and Framing.—The principles upon which the strength of mechanism depends have been explained in Section 8 of the Introduction ; and it has also been shown how they are to be applied to the principal pieces which occur in the mechanism of steam engines, such as piston rods, connecting rods, cross-heads, eross-tails, beams, cranks, axles, wedges, keys, &e. Care must be taken in all calculations on this subject, to consider all the variations which the forces acting amongst the pieces of the mechanism undergo, whether in magnitude or in direction, and to take into account that condition of those forces in which the stress produced by them is the most severe. Care must also be taken not to consider efforts and resistances alone, but the entire forces applied to each piece, whether direct or lateral (Article 8, page 6; Article 23, page 31). For example, it is not the mere effort in the’ direction of motion of the crank pin which is to be considered in STRENGTH—BALANCING OF MECHANISM. 521 determining the requisite strength of the crank, but the whole thrust or pull exerted along the connecting rod, The framework by which a moving piece is held or supported, exerts upon that piece a force or forces sufficient to prevent it from being dislodged from its proper bearings, and must be made suffi- ciently strong to bear with safety all the forces exerted by other bodies upon the moving pieces which it carries. For example, in a beam engine, the principal parts of the frame- work are, the sole or base, and the pillars for alternately supporting and holding down the main centre of the beam. At one end of the base, the cylinder must be fixed down to it by bolts capable of safely resisting an upward pull equal to the greatest effort on the piston. At the other end, the bearings of the shaft must be fixed down with equal firmness. The supports of the main centre must be strong enough to bear the forces acting upon it, determined in the manner explained in Article 370. The base itself must possess . transverse strength sufficient to bear safely the tendency of the forces applied to its ends and middle to break it across, producing a moment of flecure (Article 73, page 75) at each instant, equal and opposite to that which acts on the beam. Similar principles apply to the side lever engine, except that the pillars support and hold down the bearings of the engine shaft. In a direct acting engine, the principal parts of the frame are the pillars or rods by which the cylinder and the shaft are kept in their proper relative positions, and which have to resist a pull and a thrust alternately. 379. Balancing of Mechanism.—All the moving parts in an engine ought as far as possible to be balanced; that is to say, that every axis about which moving parts turn or vibrate, or have a recipro- cating motion, should either exactly or as nearly as possible traverse the common centre of gravity of all the parts that its bearings sup- port, and be a permanent amis of those parts which turn with 1t. The reasons for doing this, and the principles according to which it is to be effected, have been explained in Articles 21, 22, pages 27 to 30. It is of special importance as applied to the crank shaft. The weight of, and the centrifugal force and couple produced by, any mass which is fixed to the shaft and rotates along with it, such as a crank or eccentric, can easily be balanced by counterpoises fixed to and rotating along with the shaft also. In the case of a mass which only partially partakes of the motion of the shaft, such as a piston, the balance of weight and inertia cannot be exactly realized in all positions of the engine, but must be approximated to in the way which may seem best to the judgment of the engineer. 522 STEAM AND OTHER HEAT ENGINES. In Article 347 it has been shown how the weight of the piston in vertical cylinders is approximately balanced by a proper adjust- ment of the pressure of the steam. In this case it is probably best, in order to avoid horizontal vibrations, that the weight of the piston, its rod, and half the connecting rod, should be balanced by steam Mian ne Fig. 164, COUNTERPOISES—CORNISIL ENGINE. 523 pressure alone, the crank and the other half of the connecting rod being balanced by counterpoises fixed on the shaft. In engines with horizontal cylinders, on the other hand, it is probably best to treat the whole weight of the piston, piston rod, and connecting rod, as if it were concentrated at and revolved along with the crank pin, and to fix counterpoises on the shaft suited to that supposi- tion; and this method, or one not greatly differing from it, appears to have been practised by Messrs Bourne & Co. in their horizontal single cylinder screw engine, with good results. Section 6.—Leaniples of Pumping and Marine Engines. 380. Examples of a Cornish Pumping Engine.—l'igs. 164, 165, and 166, represent a single acting non-rotative beam eugine, known as the “Cornish engine,” and used for draining mines, and for supplying towns with water. Fig. 164 is a general elevation or side view. Fig. 165 is an elevation, and fig. 166 a plan, of the valve gear. As to the general arrange- ment of the valve gear, see Ar- ticles 542 and 343, A is the cylinder; B, the piston rod; C D E, the beam; F, the main pump rod; G, the tappet rod or plug rod; H, the equilibrium pipe, which, when the equilibrium valve is open, connects the top and bottom of the cylinder ; I, the exhaust pipe ; K, the condenser ; L, the air pump; M, the feed pump; N, its supply pipe; and 0, its discharge pipe. P is the “ cataract,’ as to the general nature of which see Ar- ticle 343. Q, the chest of the throttle valve; a, its spindle; Fie. 165. bc, a lever; and dd,a rod and re handle to adjust its opening; Z, the passage through which it com- municates with the steam valve box R. §, the equilibrium valve box. T, the exhaust valve box. 524 STEAM AND OTHER HEAT ENGINES. ¢ is the pump of the cataract, standing in a small tank; its piston rod is attached to an arm projecting from the rocking shaft 7. From that shaft there projects another lever g, which is depressed by the tappet rod G when near the bot tom of its down stroke, so as to lift the piston of the pump. A third arm projecting from ‘ the same shaft // carries a weight 7, which, as soon as the tappet rod begins to rise and leave the lever g free, causes the piston to descend Fig. 166. slowly. Meanwhile the tappet rod, when at the bottom of its descent, has shut the exhaust valve by means of the tappet y, and opened _ the equilibrium valve: the piston has ascended; and at the top of the up stroke the tappet rod has shut the equilibrium valve, so that the engine is ready to begin a new stroke so soon as the exhaust valve and steam valve shall be re-opened. The weight é continues to press down the cataract piston, and to cause the lever g to rise. This lever supports a small vertical rod, hidden in fig. 165 behind the tappet rod G, from which small rod there projects a peg, that at length lifts the lever & From the lever & there projects a catch that holds a tooth projecting from the rocking shaft m, and prevents that shaft from turning under the action of the loaded road ? that hangs from a short lever projecting ; from the shaft m. When the lever & is lifted, the shaft m is set - free, whereupon / descends, m turns, the handle 7 projecting from m rises; the short lever projecting from m pulls the loaded rod op towards the right of the figure, which, through the bell crank pq7, lifts the spindle s of the exhaust valve, and opens that valve so as to let the steam from below the piston escape to the condenser. — The before-mentioned vertical rod resting on g continues to rise; a peg projecting from it lifts the lever ¢, similarly placed to 4, but higher, and in the same manner as a catch on & liberates a weight whose descent opens the exhaust valve, a catch on ¢ liberates a weight whose descent opens the steam valve. The steam is admitted, and the down stroke begins. 7 PUMPING ENGINE—SCREW ENGINES. 525 At a point of the down stroke fixed by adjusting the position of the long tappet x on the tappet rod, that tappet presses down the handle w as to shut the steam valve, and hold it shut for the remainder of the stroke, which is performed by expansion. As the down stroke is completed the cycle of operations already described recommences. The ascent of the piston while the equilibrium valve is open is produced by a slight preponderance of the weight of the main pump rod and its load above the weight and resistance of the column of water which the plungers raise. The energy exerted by the steam on the piston during the down stroke is stored in lifting the pump rod and its load, as has been explained in Article 32, page 37. The cylinders of Cornish engines are jacketed above, below, and all round, and clothed with felt and planking. In direct acting non-rotative pumping engines the up stroke is the effective stroke, the steam being admitted and expanded below the piston, then passed by the equilibrium valve from the bottom to the top of the cylinder, and then discharged into the condenser. The arrangement of the mechanism somewhat resembles that of the water pressure engine in Article 132, fig. 40—except that in general the piston rod proceeds upwards through a stuffing-box in the cylin- der cover, and carries at the top a cross-head, from the ends of which hang links, attached at their lower ends to the cross-head of the pump rod. Another arrangement is, to have a pair of similar and equal cylinders, standing side by side, whose piston rods support the ends of a cross-head, from the middle of which the pump rod hangs. 381, Double Acting Pumping Engines are now very common, in which the piston rod of a double acting pump is continuous with that of the engine. Such engines are rotative, having a fly-wheel driven by means of a crank for the purpose of making the motion steady. The cylinder and pump are often horizontal. 382. Example of Vertical Inverted Screw Marine Engines.—Figs. 167 and 168 represent the pair of engines of the “ Indian Queen,” by Messrs. Neilson & Co. These engines have been selected for the purpose of illustration, because they are very good and effi- cient specimens of engines for a screw merchant steamer, and: at the same time contain nothing unusual in their parts or arrange- ment.* Fig. 167 shows a front elevation, and a vertical section of part of the forward cylinder and part of the valve chest. Fig, 168 is a side elevation looking towards the head of the ship. The scale is Jy of the real dimensions. Each cylinder has an ordinary slide valve moved by a link motion (Article 348), and a gridiron ex- * Through inadvertence, figs. 167 and 168 have been reversed as to right and left, so that, while the actual engines face to port, the figures show them as facing to starboard. 526 STEAM AND OTHER HEAT ENGINES, pansion slide valve worked by a separate eccentric (Article 350), The cylinders are steam jacketed, and also clothed in felt and wood. A, A, are the cylinders. B,-part of the piston of the forward engine. ©, C, cylinder ports. D, exhaust port. E, ordinary slide valve. F, gridiron expansion valve. G, G, G, G, are the eccentric rods of the two link motions for working the ordinary slide valves. Of these rods only one is shown Fig. 167. in fig. 168. H, H, eccentric rods of the two expansion valves. K, the shaft. INVERTED VERTICAL SCREW ENGINES. L, in fig. 167, M, in tig. 168, the att connecting rod. N, in fig. 168, the aft piston rod. the fore crank. L, in fig. 168, the after crank, dotted. In fig. 167 the piston and connecting rods are hidden by pillars of the frame and guides. Nici =0 Tig. 168. the piston rod heads to work the pumps. condenser. 8, 8, exhaust pipes of cylinders. T, T, feed pumps, worked by rods attached to cross-heads on the air pump trunks. P, P, air pumps. R, hot well with air vessel above. O are levers driven by links connected with Q 528 STEAM AND OTHER HEAT ENGINES. U, wheel to turn the screw which shifts the links of the link motions when the engines are to be reversed or stopped, the valve rods being at rest laterally. This pair of engines, when making 75 revolutions per minute, with a ratio of expansion of 5, is of 320 indicated horse-power, and burns 3 lbs. of coal per indicated horse-power per hour; the efficiency of the steam, and of the furnace and boiler, as well as the rate of expansion, being almost exactly the same as in the engines referred to in Article 289, Example I., pages 405, 406. Szot1on 7.—Locomotive Engines. _ 383, Reference to Previous Articles—Besides the general charac- teristics which locomotive engines possess in common with other steam engines, the peculiarities of those engines have been frequently referred to in previous parts of this work, and especially in the fol- lowing places :— Article 229, page 281 (supply of air to fuel). Article 230, pages 282, 283 (distribution of air, and contrivances to prevent smoke. Article 232, page 285 (rate of combustion). Article 234, Division IV., pages 293 to 297, especially examples IV., V., VI, VII., VIII. (etficiency of furnace and evaporative power of fuel). Article 280, pages 382, 383 (back pressure). Article 286, page 396 (use of heating the cylinder externally). Article 289 a, page 412 (use of high pressure condensation). Article 290, pages 413 to 416 (resistance of the regulator). Articles 303, 304, 305, pages 449 to 452 (furnace and boiler), Article 306, page 456 (grate and its ash-pan), Article 308, page 457 (height of furnace). Article 312, page 459 (fire-box stays). Article 312, page 460 (tubes and boiler shell), Article 315, page 463 (boiler room). Article 317, page 465 (safety valves). Article 341, page 485 (throttle valve). Article 347, pages 491 to 496 (expansion by the link motion). 384, Adhesion of Wheels.—The tractive effort which a locomo- tive engine can exert is limited, not only by a quantity depending on the dimensions of the cylinder and driving wheels and the effec- tive pressure of the steam, but also by the adhesion between the driv- ing wheels and the rails, which means the friction between them, acting so as to’prevent slipping. If the resistance of the load drawn exceeds the adhesion, the wheels turn round without advancing. The adhesion is equal to the procuc’ of that part of the weight of ADHESION AND RESISTANCE ON RAILWAYS. 529 the engine which rests on the driving wheels into a co-efficient of friction which depends on the condition of the surfaces of the wheels and rails. The value of that co-efficient is from 0°15 to 0-2, when wheels and rails are clean and dry; but when they are damp and slimy, or in the condition called “ greasy,” it diminishes sometimes eee or 0:05, About 0-1 may be considered an average ordinary value. The proportion of the weight of the engine which rests on the driving wheels depends on the number and arrangement of the wheels, the number of pairs driven by the engine, and the distribu- tion of the load upon them. The number of wheels ranges from two to five pairs—the most common number being three pairs—of these from one pair to the whole are driven by the engine. The proportion of the weight of the engine which rests on the driving wheels may be estimated to range from one-third to the whole. One-half is probably the most usual proportion in six-wheeled engines with one pair of driving wheels under the middle of the engine, which is the most common arrangement in passenger engines; two-thirds, in six-wheeled and eight-wheeled engines with two pairs of wheels coupled so as to be driven by the engines, which is a common arrangement in goods engines. Engines with all the wheels coupled are used for slow and heavy trains, and in them, of course, the whole weight rests on driving wheels. The weights of locomotive engines range from 5 to 40 tons in extreme cases; but the most ordinary weights are from 20 to 25 tons. When the stock of fuel and water are carried in a tender, the weight of the engine itself is alone available to produce adhesion, unless, as is sometimes the case on very steep railways, the wheels of the tender are coupled to those of the engine by gearing chains and pulleys. Some engines, called tank engines, carry their own stock of fuel and water—the fuel on the platform behind the fire-box, and the water in a tank above the barrel of the boiler—and in them the adhesion is greatest on first starting from a station where fuel and water are taken in, and gradually diminishes as the stock is con- sumed. 385. Resistance of Engines and Trains.— The authority DOW chiefly relied upon for the resistance of engines and trains on railways is that of a series of experiments by Mr. Gooch on the broad gauge. The following empirical formula represents with tolerable accuracy the results of those experiments :— Let E be the weight of the engine and tender in tons. T, the weight of the train in tons. V, the velocity in miles an hour. ‘ i, the inclination of the line, expressed as a fraction; ascents being considered as positive, and descents as negative. 530 STEAM AND OTHER HEAT ENGINES, Resistance of the train in lbs. = {6 + 0-3 (V—10) =e 2240 PT. eee ied) Resistance of the engine and tender in lbs. = {12+ 0-6 (V—10) 22404} Bveeeeeceeeeee (2.) Total resistance in lbs, ={6+03 (V— 10)}(T+2 E) 22407 (T+E)....... (3.) At velocities less than ten miles an hour the term containing V—10 is ie omitted: the resistance being sensibly constant below that speed. Mr. D. K. Clark prefers to such formula as the above, another set of formule in which the resistance is treated as consisting of a constant part, and a part increasing as the square of the speed; as follows :— Resistance in lbs. per ton of engine and train; road and carriages in smooth running condition ; weather calm ; 6 v2 ‘ aa . + gp = 22407; ouiaheecaeaeeeeioncand (4.) Road and carriages not in smooth running condition; side wind; v2 ; 9 + 7 Gp SE 224043 Cov nsecrvercencscences (5.) The resistance on a curve exceeds that on a straight line, accord- ing to experiments by different authors, to the amount of from 0°6 Ib. to 1-4 Ib. per ton (6) radius of curve in miles To allow for the resistance of the mechanism of the engine, Mr. Clark adds one-third to the resistance, as calculated above. The mean effective effort of the steam on the pistons required to overcome a given total resistance of engine and train is given by the following equation, in which A is the total area of both pistons, and Pm —Ps the mean effective pressure. e Total resistance x circumference of driving wheel (8) A (Pn —Ps) = 2 x length of stroke of piston (See page 538.) 386. The Balancing of Engines, both as to centrifugal forces and centrifugal couples, is of great importance as a means of preventing dangerous oscillations. The principle according to which it is effected is, to conceive the mass of the pistons, piston rods, and BALANCING LOCOMOTIVES—BLAST PIPE, 531 connecting rods, and a weight having the same statical moment as the crank, as concentrated at the crank pins, and to insert between the spokes of the driving wheels counterpoises whose weights and positions are regulated by the principles explained in Articles 21 and 22, pages 27 to 30. ae following are the formule to which these principles lead :— ATA— W, total weight conceived to be concentrated at one crank pin. c, length of the crank, measured from the axis of the axle to the centre of the crank pin. a, distance of the centre of the crank pin, measured parallel to the axle, from the middle of the length of the axle. b, distance of the centre of a wheel from the middle of the length of the axle. 7, radius-vector of each counterpoise; being the distance of its centre of gravity from the axis of the axle. REQUIRED— a, angle which that radius-vector makes with a plane traversing the axis in a direction midway between the directions of the two cranks, and pointing the opposite way to those directions. The cranks being at right angles to each other, make angles of 135° with the plane in question. w, weight of each counterpoise. REsuLTs— 4 =are tan - 33 sothaeien teat eies neers (1.) c rat 02 We =W--: vtec 2. o r 2 62 J 2-rcost ee In practice, those formule may be used to find a first approxi- mation to the required position and weight of the counterpoises ; but the final adjustment is always performed by trial; the engine being hung up by chains attached to the four corners of its frame, and the machinery set in motion: a pencil attached to the frame near one angle, marks, on a horizontal card, the form of the oscilla- tions, being usually an oval; and the counterpoises are adjusted. until the orbit described by the pencil is reduced to the least: possible magnitude. When the adjustment is successful, the: diameter of that orbit is reduced to about rr of an inch. : 387. The Blase Pipe has the effect of adjusting the draught of the furnace, and consequently the rate of consumption of fuel, to the work to be performed by the engine with very different loads, and at very different speeds; and is on that account perhaps the most important of the peculiar parts of the locomotive engine. 532 STEAM AND OTHER HEAT ENGINES, Its effect upon the back pressure in the cylinder has already been considered in Article 280, pages 382, 383. The effect of the blast pipe in producing a draught depends upon its own diameter and position, on the diameter of the chimney, and on the dimensions of the fire-box, tubes, and smoke-box. Mr. D. K, Clark has investigated the influence of these circumstances from his own experiments, and from those of Messrs. Ramsbottom, Poloncean, and others, and has shown that the vacuum in the smoke-box is about 0°7 of the blast pressure: that the vacuum in the fire-box is from 4 to $ of that in the smoke-box: that the rate of evaporation varies nearly as the square root of the vacuum in the smoke-box: that the best proportions of the chimney and other parts are those which enable a given draught to be produced with the greatest diameter of blast pipe, because the greater that diameter, the less is the back pressure produced by the resistance of the orifice: that the same proportions are best at all rates of expansion and at all speeds: and that the following proportions are about the best known:— ara 1 Sectional area of tubes within ferules,...... = 5 area of grate. 1 Sectional area of chimney, .....cesseceseecseees = jp area of grate, Area of blast orifice (which should be somewhat below the throat of the tac area of grate. CHIMNEY) 2 veigase asinssniaeine diginesawiceveajaeanie Capacity of smoke-box, .....cscseeeseeeeee = 3 feet x area of grate. Length of chimney,.......ccccscseseeceteeeeee ees = its diameter x 4. If the tubes are smaller, the blast orifice must be made smaller - also; for example, if Sectional area of tubes within ferules....... = 5 area of grate, Then area of blast orifice ............:seeeeeeee = 5 area, of grate, 388, Examples of Locomotive Engines.— The examples here given are from two locomotive engines by Messrs. Neilson & Co., which are selected, like the screw marine engines of Article 382, because they are good and efficient specimens of the class of engines to which they belong, and have nothing unusual in their proportions and arrangements, Fig. 169 is a side view copied from a photograph of a six-wheeled engine, with two pairs of wheels coupled. Its scale is about sz of the real dimensions. EXAMPLES OF LOCOMOTIVES. 533 Fig. 170 is a longitudinal section of an engine of the same class with the preceding, but with somewhat larger driving wheels, being Vig. 169. intended for a less steep line and higher speeds. The scale is #5 of the real dimensions. The details of the valve gearing are omitted. Fig. 171 shows, at the left-hand side, a cross-section through half the fire-box, and at the right-hand side, a cross-section through half the smoke-box, of the saine engine. Fig. 172 is an elevation of the valve gearing of one cylinder, with the cover taken off the valve chest to show the slide valve and ports. Fig. 173 shows a plan of the valve gearing of one cylinder, and a longitudinal section of the cylinder and valve chest. The scale of figs. 171, 172, and 173, is gy of the real dimen- sions. A is the ash-pan; B, the grate; C, the fire-box. In fig. 170, the heads of the bolts which tie the outer and inner shells of the fire-box together are irregularly placed; but that is an oversight in the engraving; they ought to be ranged in vertical and hori- zontal lines. D is the fire-door. E are the tubes, extending from the fire-box to the smoke-box F. Gis the lower end of the chimney. T is one of the horizontal feed pumps, worked by a link from one of the eccentrics. H is the supply pipe from the water tank of the tender; K, the feed pipe, leading to the boiler. L is the water space round the fire-box; M, the water space and steam space above it. ; N are longitudinal ribs, to which the crown of the fire-box is stayed, as explained in Article 312, page 499. The crown receives STEAM AND OTHER HEAT ENGINES, 534 el | ,29%0 b09000 00 50000000° 700000000 3 p09000000 po70000 00 pDo0000000 n9900000 2900000009 =I 200000 EXAMPLES OF LOCOMOTIVES, 535 additional support from vertical stay bars, hanging from the sides of the steam dome. Fig. 171. O is the space above the tubes, in the barrel of the boiler. P is the steam dome, on the top of the external shell above the fire-box. This part of the shell in the engine represented is of a radius a little greater than the barrel of the boiler; but in many engines (for example, those of Messrs. Kitson & Co.) it is made of the same radius. 536 STEAM AND OTHER HEAT ENGINES. EXAMPLES OF LOCOMOTIVES—ROAD ENGINTIS, 5387 ; Q is one of the safety valves. The other safety valve is omitted in fig. 170, but shown in fig. 169, as standing on the middle of the barrel of the boiler. R, BR, R, is the steam pipe, bringing steam down from the dome, and along the top of the barrel. 8, 8, the regulator, a conical valve worked by a screw. T, branch steam pipe; U, slide valve chest; V, slide valve; W, W, cylinder ports; X, cylinder; Y, exhaust port; Z, exhaust pipe. The two exhaust pipes unite in the blast pipe a. 6, piston; ¢, piston rod; d, connecting rod, driving a crank on the front driving axle /; e, coupling rod, connecting cranks on the front driving axle 7, and hind driving axle h. g, front driving wheel; &, hind driving wheel. i, forward eccentric, and m, backward eccentric, of the left slide valve. n, forward eccentric rod; 0, backward eccentric rod. These rods are jointed to the two ends of the link p, which is jointed at the centre to and supported by a nearly vertical bridle or lever, oscillating about a fixed centre. is the slide valve rod, and g the connecting rod, through which the rod r receives motion from a slider in the link p. The radius of the centre line of the link is the length of the rod g. The slider and the rod q are shifted into different positions, so as to alter the expansion or reverse the engine when required (as explained in Article 348, page 497) by means of the rod s, connected with the lever 4 A pair of those levers, to act on the two link motions at once, project from the rocking shaft uw. On the left-hand outer end of that shaft is a vertical lever, connected through a long rod v (partly seen in fig. 170), with the reversing handle w, by means of which the engine driver controls the link motion. In the figure, the reversing handle is simply a lever: but in many engines as now constructed, it acts on the rod v by means of a screw, which is safer and more convenient. 7 x, x, x, are the springs; y, a balance lever to distribute the load equally between the two pairs of driving wheels, notwithstanding irregularities in the surface of the rails; z, training axle and wheel. 389. Locomotive Engines for Common Roads were invented by Mr. Gurney, Sir James Anderson, Mr. Scott Russell, and others. For many years they fell into disuse; but have been revived in the form of “traction engines.” These machines are adapted to drawing trains of heavily laden vehicles at a low speed, such as four or five miles an hour. To insure that the driving wheels shall take a sufficient hold of the road, without injuring its surface, they are made very broad in the tire, sometimes as much as a foot, and are sometimes transversely or obliquely ribbed. The traction engine or road locomotive of Mr. R. W. Thomson, has on each of 538 STEAM AND OTHER HEAT ENGINES. the wheels an indian rubber tire, about 12 inches broad and 5 inches thick. These are found to answer well on all sorts of ground, hard and soft, rough and smooth. (See Zhe Engineer, 4th September, 1868, page 191.) Section 8.—Of Steam Turbines. 390. The Reaction Steam Engine, in a rude form, is described in the Pnewmatics of Hero of Alexandria. It was improved and brought into use to a limited extent by Mr. Ruthven. Its principle and mode of action are analogous to those of a reaction water wheel (Article 171, page 190; Article 176, page 197.) 391. The Fan Steam Engine, invented by Mr. William Gorman, is analogous in its principle and mode of action to an inward flow water turbine, (Article 171, page 191; Article 173, page 193; Article 174, pages 194, 195, 196, &c.) An engine of this kind was used at the Glasgow City Saw Mills, and was considered equal in efficiency to an ordinary high pressure engine. ADDENDUM TO ARTICLE 385, page 530. Counter-pressure Steam im Locomotives.—Steam is said to act by counter-pressure, when the valves are put in backward gear during the forward motion of the engine, so as to make the cylinders communicate with the exhaust-pipe during the forward stroke, and with the boiler during the latter part of the return stroke. The cylinders thus act as pumps, forcing vapour into the boiler against the pressure there. The use of that action is to do the duty of a brake, in retarding or stopping the train when required, and in preventing excessive acceleration on descending gradients. When the cylinders, acting in this manner, used to draw in air at the _blast-pipe and force it into the boiler, great injury was done by the dust and heat. In order to prevent that, M. le Chatelier introduced the system of supplying the exhaust-pipe of each cylinder, when working at counter- pressure, with a mixture of liquid water and steam from the boiler, in quantity sufficient to cause a slight escape of steam from the blast-pipe, and thus to prevent the entrance of hot air and dust. The liquid water and steam are led from the boiler to the exhaust-pipes through tubes about 4 or g-inch diameter, with suitable cocks or valves to adjust the quantities sup- plied. The water, during the forward stroke of the piston, expands into steam of atmospheric pressure, filling the cylinder, and partly a at the blast-pipe ; during the return stroke that steam is compressed till it rises to a high pressure, and is then forced back into the boiler. (See M. le Chatelier’s Mémoire sur la Marche @ Contre-Vepeur des Machines Loco- motives, Paris, 1869; also the English translation of that Memoir, by Mr. Lewis D. B. Gordon, entitled Railway Economy, Edinburgh, 1869.) PART IV. OF ELECTRO-MAGNETIC ENGINES. 392, Introductory Remarks.— Although the principles of the development of mechanical energy from chemical action through the agency of electric and magnetic forces might be made the sub- ject of a voluminous treatise which would be highly interesting in a scientific point of view, the amount of experience of the actual working of electro-magnetic engines is not yet sufficient to supply those data which are necessary in order to render such a treatise practically valuable. In the present work, therefore, a brief outline only of those principles will be given, illustrated by descriptions of three forms of engine, two of which are selected on account of their simplicity, and probable efficiency, though hitherto used as pieces of philosophical apparatus only; and the third, on account of its having been for some years in practical operation. The experimental data to be afterwards referred to are for the most part due to the researches of Dr. Joule and Dr. Andrews. The theory of the subject was first correctly set forth by Professor Helmholtz, and Professor William Thomson, in a series of papers published respectively in Poggendorff’s Annalen, and in the Philosophical Transactions and Philosophical Magazine. especially two papers in the Philosophical Magazine for December, 1851. The summary of that theory which will be given is in the main extracted from a paper by the Author of this work “On the General Law of the Transformation of Energy” (Phil. Mag., 1853). 393, Energy, Actual and Potential.—Zvergy has been defined in Article 25, page 32; and the distinction between actual and potential energy has been explained, so far as it relates to mechan- ical energy, or energy of motion and of force tending to produce motion, in the same Article, and in Article 31, pages 35, 36. It has further been explained in Article 196, page 224, and Articles 235, 236, pages 299, 300, that heat isa form of energy. In order to understand the application of certain general laws respecting energy to electricity and magnetism, the definitions of energy, actual and potential, must be extended so as to become perfectly general and abstract, as follows :— A capacity for performing work is to be called AcTUAL ENERGY, when it consists in a state of present activity of a substance, such 540 ELECTRO-MAGNETIC ENGINES. as motion, heat, current electricity; and POTENTIAL ENERGY, when it consists in a tendency of a certain magnitude towards a change of a certain magnitude, such as mechanical potential energy (that is, weight or pressure capable of acting through a given space), chemical affinity, electrical tension, magnetic tension. The general law of the transformation of energy has already been stated in Article 244, page 309. The principles which will be explained in the sequel are instances of its application to the actual energy of current electricity, and the potential energy of electro- megnetic attraction. 304, The mnergy of Chemical Action is the source of the power of electro-magnetic engines, as it is of that of heat engines. Chemical affinity, or the tendency of two substances to combine chemically, is a sort of potential energy, which, when the substances actually do combine, is replaced by actual energy in the form of heat, or of current electricity, or of both combined. Examples of the quantities of energy in the form of heat produced by the com- bination of various substances with oxygen have been given under the head of “ Combustion,” in Articles 223, 224, pages 267 to 273; and those quantities can be expressed in foot-pounds of energy by multiplying by Joule’s equivalent of a British thermal urit, 772. It is sometimes difficult or impossible to obtain the whole energy produced by a given chemical combination at once in the form of heat. In that case, the energy may be obtained first in the form of current electricity, and reduced afterwards to the form of heat. The following are the data of the greatest importance in the theory of electro-magnetic engines :— I. Energy developed by the solution of one lb. of zine in Daniell’s battery, the liquid in the cells being a solution of sul- phate of copper in water— British thermal - units, Heat produced by the combination of zine with oxygen and sulphuric acid, and the solution of the compound in watery.........cccsceseceeseee eee eee 3006 Deduct— Heat consumed in separating copper in the solid state from the solution of sulphate of copper in WLC, cocoa cameseeanscecaet tues gases cocses cesceeanea dines 1587 1419 1419 x 772 = 1,095,468 foot-lbs. per Ib. of zinc. ENERGY OF CHEMICAL ACTION—COST OF WORKING. 541 __ This is less than one-tenth of the total energy developed by burn- ing one Ib. of carbon. IT. Energy developed by the solution of one Ib. of zinc in Smee’s battery, the liquid in the cells being dilute sulphuric acid— British thermal units, Heat produced by the combination of zinc with oxygen and sulphuric acid, and the solution of » 3006 the compound in water, Deduct— Heat consumed in separating hydrogen from diluted Sti) PHUTIC ACI jos. cs sac casera cobenceuiena nesses erebiavenweanene 2106 goo 900 x 772 = 694,800 foot-lbs. per lb. of zinc. This is about one-siateenth part of the energy developed by burn- ing one lb. of carbon. 395. Comparative Cost of Working Electro-magnetic Engines anid Went Engines.—It is certain that the efficiency can be made to approximate much more nearly to unity, the limit of perfection, in electro-magnetic engines than in heat engines. At present, how- ever, the ratio of their efficiencies can only be roughly estimated ; and it may be considered as a favourable view towards electro- magnetic engines, to estimate their greatest possible efficiency as jour times that of the best heat engines yet known. Taking this into account along with the results of the calculations in the pre- ceding Article, it appears that the work performed per pound of zine consumed may be estimated as follows :— I. With solution of sulphate of copper in the cells, ys of the work per Ib. of carbon consumed in a heat engine. II. With dilute sulphuric acid in the cells, %¢ = + of the work per lb. of carbon consumed in a heat engine. Before, therefore, electro-magnetic engines can become equally economical with heat engines as to cost of working, their working expense per lb. of zinc consumed must fall until it is from four- tenths to one quarter of the working expense of a heat engine per Ib. of carbon, or of coal equivalent to carbon. The present price (September, 1859) of sheet zinc is between Jifty and sixty times that of such coal. It is evident from these facts and calculations, that electro- magnetic engines never can come into general use except in cases where the power required is so small that the cost of material consumed is of no practical importance, and the situation of the 542 ELECTRO-MAGNETIC ENGINES. : machinery to be driven is such as to make it very desirable to have @ prime mover without a furnace. 396. An Electro-chemical Cirenit consists of a battery, with a conductor connecting its two ends; and its arrangement may be represented symbolically as follows :— ——KE CLZCLZCLZCLZ a =>>—> ‘This represents a battery of four cells, each cell being denoted by the symbol CL Z. Z denotes a plate of zinc, the substance to be dis- solved ; L the solvent liquid, containing the substances that combme with the zinc; C a plate of copper, silver, or some such metal which has less affinity for the solvent than the zinc has, and which acts merely as a conductor. The brace —— represents symbolically a metallic wire connecting the ends of the battery. The chemical action of the solvent on the zinc puts the entire circuit into a peculiar condition described by saying, that there is a current of positive electricity circulating through it, in each cell, from Z through L to C, and in the conductor ——~— from C to Z: not that the existence of the so-called electric fluid or fluids has been proved, but that the use of terms borrowed from those which commonly denote the motion of fluids is a convenient way of describing electrical phenomena. The endmost portions of the conductor, where it joins the battery, are called the electrodes; the positive electrode joining C, the negative Z. The strength of the electric current is a quantity proportional to the weight of some standard substance which it is capable of decomposing in an unit of time. It is expressed in units of such a kind, that a current of unit strength decomposes 02 grain of water per second, or 0103 lb. of water per hour. The strength of the current produced by a given battery is pro- portional to the quantity of zinc dissolved in a given time in one cell, To produce a current of unit strength requires the consump- tion in each cell of ‘0728 grain of zine per second, or 03744 Ib. of zinc per hour. Let y denote the strength of the current; z the zinc consumed per cell per hour, in Ibs.; then ELECTRO-CHEMICAL CIRCUIT. 543 The electro-motive force of a battery is a quantity such, that when it is multiplied by the strength of the current, the product is the energy produced by the battery in a given time (such as an hour). It is proportional to the number of cells. Let M, then, denote the electro-motive force of one cell, 1 the nutaber of cells; also, let E be the energy developed per Ib. of zinc consumed, as stated in Article 394; then Mi) SB Be ieee cs eadccadesvae eases (2.) So that M= 03744 E = for Daniell’s battery, 41014; \ (3.) for Smee’s battery, 26013. In these values of M, it is to be borne in mind, that the unit of force is one pound weight, and the unit of time an hour. In Pro- fessor Thomson’s papers, the unit of force is — of the weight of a grain, and the unit of time a second. The heat produced in a given time by a given current in the same circuit is proportional to the square of the strength of the current. That quantity of heat, then, is expressed by Where R is a quantity called the resistance of the circuit, being the heat developed in it in an unit of time by a current of unit strength. The resistance of a circuit is the sum of the resistances of the various parts of which it consists, comprehending the plates and liquid of the cells, and the conductor which completes the circuit. The resistances of conductors made of a given substance are directly as their lengths and inversely as their sectional areas, or directly as the squares of their lengths and inversely as their weights. Let 1 be the length of any one conductor in a circuit, in feet, whether solid or liquid; w its weight, in Ibs. ; then where ¢ is a co-efficient depending on the material, and called the specific resistance of that material. Professor Thomson gives values ‘of ¢ in which the unit of force is 3 of a grain weight, the unit 544 ELECTRO-MAGNETIC ENGINES. of mass, that of a grain, and the unit of time one second: to reduce these to values in which the unit of force is one pound weight, the unit of mass, that of a pound, and the unit of time one hour, they are to be multiplied by 8600 : 82:2 X 49000000 The following are examples of the results of that reduction for temperatures of 50° Fahrenheit :— Copper Wire, eecsscecessreeneseeeees e = from 176 to 128, Mereuty ss. sieessnncvesieasmemnensevetes e = 10,356. When the circuit produces no chemical decomposition out of the cells, no magnetic induction, and no mechanical or other external work, the whole of the energy developed by the chemical action in the cells takes the form of heat in different parts of the circuit. This fact is expressed by the following equation :— Enez=MnyHReY yj. cecccceseeee seeeee(6.) one of the consequences of which is the following :— Mn, : %1= TR rrr teerteserssesseteeeweeens (7.) or, the strength of the current is directly as the electro-motive force and inversely as the resistance of the circuit; being the celebrated prin- ciple known as “ Ohm’s Law.” Another consequence shows the rapidity of chemical action in a given circuit, viz. :— Many _ M?n? 8 Nez E = ER Pereer err riers r rere yy ( .) 397. Efficiency of Electro-magnetic Engines.— Equations 1, 2, 3, 4, and 5of Article 396 are applicable to all electro-chemical circuits whatsoever. Equations 6, 7, and 8 are applicable only to an idle battery, as it may be called, in which all the energy is spent in pro- ducing heat in the materials of the circuit. An electric circuit may move mechanism against resistance, and so perform mechanical work, in three ways. I. By the mutual attractions and repulsions of currents, or of parts of one current. Currents in the same direction attract, and currents in contrary directions repel each other. This method has been used in philosophical apparatus only. II. By the attractions and repulsions between currents and per- manent magnets. A magnet placed with its south pole towards the EFFICIENCY OF ELECTRO-MAGNETIC ENGINES, 545 eye of the spectator attracts currents whose direction is that of right-handed revolution relatively to its axis, and repels those whose direction is that of left-handed revolution. III. By the attractions and repulsions between temporary and permanent magnets. A conductor coiled round a soft iron bar, when a current is sent through it, magnetizes the bar in that direc- tion which makes it attract the current, according to the principle stated above under head II.; when the current ceases the magnetism ceases ; when the current is reversed the direction of the magnetism is reversed. Opposite poles of magnets attract, similar poles repel each other; so that by periodically reversing the temporary mag- netism of a soft iron bar, it may be made to take a reciprocating motion towards and from a permanent magnet. IV. By the mutual attractions of temporary-magnets. The efficiency of the engine in all those cases is governed by two principles: 1. Zhe performance of external work by an electric circuit produces @ counteractive force, opposing the electromotive force, whose magnitude ts equal to the external work performed in an unit of time divided by the strength of the current. Let U be the external work performed in an hour by the engine. This gives rise to a certain counteractive force, which causes the current to be of less strength than that which the battery produces when idle. Let y be the strength of the current in the idle circuit, as given by equation 6 of Article 396; and + the strength when the work U is performed per hour. Then the counteractive force is, U+y7’ and the strength of current y' is the same as if the electromo- U 3 tive force, instead of being Mn, were Mn — we that is to say, Mn U = eer (1). This principle might be deduced as a consequence from the law of the conservation of energy; for multiplying equation 1 by y'R, and transposing, we find, U aM iy — R25 ccc enccennsseneeeones (2), which expresses, that the useful work of the engine is the excess of the whole energy developed in the battery M.n vy’, above the energy wasted in producing heat Ry’? - : : 2, A second principle is, that the attractions and repulsions pro- duced by a given circuit and apparatus arranged in a gwen way are proportional to the square of the strength of the current (a law dis- covered by Mr. Joule) ; so that oe may make N 546 ELECTRO-MAGNETIC ENGINES, US kit neces (3) where A is a factor depending on the apparatus used. Hence equation 2 becomes Ay’? = My’ — Ry riccrsccsccceseeenvens (4.) Divide by ’ and transpose; then M =TTR lene (5) Hence are deduced the following expressions :— For the rapidity of the chemical action, _Mny' _ Mn 6 =a “Rae Eyres (6.) For the useful work, AM? n? Cay eee ath) For the efficiency of the engine, aU Wea a IT (8.) Mny Mn At enemas ; From which it appears that the efficiency of the engine approxi- mates towards unity as the factor A increases; but at the same time the absolute work performed diminishes without limit. 398. Rotating Disc En- gine.—This machine, the simplest of all electro-mag- netic engines, but hitherto used in the lecture room only, is the result of a dis- covery of Arago’s. In fig. 174, N and § are the north and south poles of a per- manent magnet, so shaped Fig. 174. as to approach very near to the two faces of a copper disc D, near its lower edge; that disc turns on an axis A, whose bearings (not shown in the figure) must rest on insulating supports. The lower edge of the disc between the poles of the magnet dips DISC ENGINE—BAR ENGINE. 547 into a cup M, containing mercury. C and Z are conducting wires, connecting respectively the axis of the disc and the mercury in the cup with the electrodes of a galvanic battery. By the ar- rangement shown in the figure, an electric current is made to pass from the positive electrode to the axis of the disc; thence through the disc to the mercury, and thence to the negative electrode of the battery. The action of the poles of the magnet on the disc is shown by the diagram, fig. 175. S is the magnet, with the south pole exposed to view; the arrow head on the circle shows the direction of the revolving current to which the magnet is equivalent. AB and A E are two portions of the current in the disc, from the axis to the mercury. According to the principle that currents in the same direction attract each other, and currents in opposite directions repel each other, the magnet attracts A B and repels A E, and so keeps up a continuous rotation of the disc in the direction BE. The direction of rotation can be reversed by reversing the current; that is, by connecting A with Z and M with C. 399, Rotating Bar Engine.—This machine, the invention of Mr. Webster, is shown in fig. 176. NS, NS, are two semicircular permanent magnets fixed within a frame of brass or other dia- magnetic material, and having two gaps between their pairs of contiguous poles, which are similar, as indicated by the letters. M is a mercury-cup of non-con- ducting material on a pedestal; it is divided into two parts by a diametral non-conducting partition, in the plane of the permanent magnets, as shown in fig. 177. In the centre of the cup stands a pivot, on which rotates the horizontal soft iron bar A B; the two arms of that bar are encircled by the two portions of a long coil of conducting wire. The two ends of that coil dip Migs into the two halves of the mercury cup, which is halves are connected with the electrodes of a battery by the wires C Z. The ends of the soft iron bar CT ex-2 pass between the poles of the permanent magnet, so ig. 177, as to come very near them, but not to touch them. ; To produce rotation in the direction indicated by the arrow, the coil round the bar AB is so arranged that when the end A is moving from SS to NN, and the end B from NN to SS, A isa south . Hed pole, and B a north pole. Then \ is { hgh aa { by SS§, and attracted repelled by NN. At the instant that the ends of the bar 548 ELECTRO-MAGNETIC ENGINES. pass the poles of the permanent magnets, the ends of the coil pass over the diametral partition into the opposite halves of the mercury cup; the current through the coil is reversed, and reverses the magnetism of A B, and the attractions and repulsions between its poles and those of the permanent magnets; and so the rotation is kept up. To reverse the rotation, the connections between the halves of the mercury-cup and the electrode are reversed. 400, The Plunger Engine, invented by Mr. Froment, and made by Mr. Bourbouze, is represented in figures 178, 179, and 180, ! | \ AA ANAT MN i I MMA i cc AA ’AWUW |’ Fg. 178. It is now used to a considerable extent in France, for driving small machines in places where it would be inconvenient to have a steam engine with its furnace and boiler. It bears some analogy in its form and arrangement to a steam engine with four cylinders, pistons, slide valves, beam, crank, and eccentric. Fig. 178 is a side elevation; fig. 179, an end view, showing two of the cylinders; fig. 180, a plan of the four cylinders. A A, BB, are four soft iron hollow cylinders, enveloped in coils of conducting wire; CC, DD, are horse-shoe magnets, each of PLUNGER ENGINE 549 which is so shaped that its ends form a pair of cylindrical plungers, moving up and down in the hollow cylinders, with just freedom Fig. 179. Fig. 180. enough to prevent contact; H GF E is the beam, from which the magnetic plungers are hung; F its centre; H K the connecting rod; K L the crank; L the shaft and eccentric. The shaft carries a fly wheel. aba isaslide moved by the eccentric, the parts a a being of ivory, and 6 of metal ; ¢ do, conducting wire from the metallic part 6 of the slide to the negative electrode; p, conducting wire from positive elec- trode; gn, conductors from p to the coil round A.A; 7m, conduc- tors from p to the coil round BB; g, conductor from the opposite end of the coil round A A, terminating in the spring ¢, which presses on the slide aa; h, conductor from the coil round B, terminating in the spring /, which presses on the slide aba. The reciprocating motion of the slide establishes the electric circuit through the coils round A A, and round B B, alternately, and thus magnetizes alternately those two pairs of hollow cylinders, which attract alternately the two pairs of magnetic plungers, OC, DD, and give a reciprocating motion to the beam, and a rotatory motion to the shaft, APPENDIX. ADDENDUM To ARTICLE 357, Page 500. Corliss Valves and Gearing.—In the Corliss valves the valve-seat is of the form of a hollow cylinder, and the valve-port is an oblong opening in one side of that cylinder. The valve itself is of the form of a sector of a cylinder of such dimensions as may be required in order to cover the port sufficiently; and the valve- face is a cylindrical surface accurately fitting the hollow cylindrical seat. In the axes of the cylindrical surfaces of the valve and its seat there is a spindle, about which the valve rotates with a reciprocating motion through an angle sufficient to make it alternately open and close the port. Motion is given to the valve by means of levers and link-work worked by an eccentric. The cylinder of a steam engine is fitted with four Corliss valves, two for admission and two for exhaust, all of which are worked by one eccentric. The two exhaust valves are simply opened and closed alternately with a motion like that of an ordinary slide-valve. ‘Ihe two admission or steam valves are opened in the same way, each by means of a rod pulling at a lever, But the rod is connected with the lever by ‘means of a detent which can be made to let go its hold at any period of the stroke by the action of a stud or wiper, whose position is regulated by means of the speed- governor; and the valve at that instant is closed by the action of a spring so as to cut off the admission of steam. In order to prevent the shocks which might arise from the too sudden closing of the valve, the speed is moderated by means of the resistance of the air to being forced through a hole in a small cylinder or dash-pot whose piston is connected with the spring for closing the valve. The suddenness of a action of the governor is also moderated by means of a dash-pot containing a iquid. This system of valves and valve-gear is remarkable for the smallness of its friction, the accuracy with which the proper form of expansion diagram is produced, and the precision with which the speed is regulated through the action of the governor upon the cut-off, AppEnDUM To ArtTictES 55, 56, anp 337; Paces 63 anp 480. Isochronous Governors.—The ordinary governor is not isochronous ; for when, in order to adapt the opening of the regulator to different loads, it rotates with its revolving pendulums at different angles to the vertical axis, the altitude h (=BC in fig. 7, page 26) assumes different values, corre- sponding to different speeds. The following are expedients for diminishing or removing this defect :— I. Loaded Governor (Porter’s).—From the balls of the common governor, whose collective weight is (say) A, let there be hung by a pair of links of lengths equal to the pendulum-arms, a load, B, capable of sliding up and down the spindle, and having its centre of gravity in the axis of rotation. _ APPENDIX. 551 Then the centrifugal force is that due to A alone; and the effect of pravi that due to A + 2B; consequently the altitude for a given speed is incase in the ratio A+2B:A as compared with that of a simple revolving pendulum ; and a given absolute variation of altitude in moving the regulator produces a smaller proportionate variation of speed than in the common governor. IL. Parabolic Governor.—In fig. B, let BX be v the axis of the spindle, and E the centre of one of the balls, which, as it moves towards or from the spindle, is oui so as to describe a parabolic arc, E, with the vertex at K. Let EF be anormal to the parabola, ete the axis in F. The vertical height of F above E is constant, being equal to twice the focal distance of the parabola ; hence this pane is absolutely isochronous. The balls may e guided by hanging each of them by means of a flexible spring from a cheek, LH, of the form of the evolute of the parabola. To find a series of points in the a and its evolute ; from the vertex K lay off K A = K B= 3h; A will be the focus, and the horizontal line BY the directrix. Draw AC Fig. B. Meta to an intended position of the ball-rod ; isect it in D; draw DE perpendicular to AC, and CE parallel to BX; E will be a point in the parabola, and ED a tangent. Then parallel toC A, draw EF ; this will be a normal, and a position of the ball-rod. From F, parallel to DE, draw FG, cutting CE produced in G; and from G, parallel to B Y, draw G, cutting E He aaciaced in H; this will be a point in the evolute. In Farcot’s governor, the rod E.H, in its middle position, is hung from a joint, H, at the end of an arm, MH; this gives approximate isochronism. Ill. Adjustable-Speed Governor (Rankine’s).—In this form of governor (see fig. C) the four cen- trifugal balls marked A are balanced, as regards gravity, about the joint on the spindle X X. B, B are sliders on the ball-rods; DB, DB, levers jointed to the slid- ers centred on a pointin the spindleat D, and ofa length DB=CD; F,a loaded circular platform hung by links BE, BE; G, an easy-fitting collar, jointed to the steelyard- lever GH, where ful- cram is at H; K, a weight adjustable on this lever. ue gover i ly isochronous ; as Ui the aa h of a revolving pendulum of equal speed is given by the equation 552 APPENDIX. cs A‘CA’. ‘=4B DB’ in which A is the collective weight of the centrifugal masses, and B the load, suspended. directly at B, to which the actual load is statically equivalent. The load B, and consequently the altitude and the speed, can be varied at will, by shifting the weight K; which can be done either by hand or by the engine itself. ‘The regulator may be acted on by the other end of the lever GH. The levers DB, DB, should be horizontal when in their middle position; and then the ball-rods will slope at angles of 45°. IV. Spring Governors (Silver’s, Weir's, Sir W. Thomson’s, &c.)—In this class of governors, which are specially suited for use on board ship, the action of gravity on the revolving masses ought either to be balanced, or to be made, by rapid rotation, so small compared with the centrifugal force as to be unimportant. The centrifugal force is opposed by springs. To make such a governor absolutely isochronous, the tension of the springs ought to vary in the simple ratio of the distance from the centres of the revolving masses to the axis. ADDENDUM TO ARTICLE 365, PacE 508. The Ejector Condenser (invented by Mr. Alexander Morton) consists essen- tially of two conoidal nozzles, one within the other, and pointing the same way. The inner nozzle brings injection-water from the cold-water tank; and the sectional area of its outlet is nearly that given by the rules of Article 365, The outer nozzle receives the waste steam from the cylinder; the diameter of the throat, or narrowest part of its outlet, is a little greater than that of the cold-water nozzle. Beyond the throat it widens slowly in « trumpet- mouthed form, its diameter at the mouth being about three times the diameter at the throat. Ifthere are two cylinders, there is an intermediate nozzle, so as to divide the steam coming from one, from that coming from another. The condensation goes on in the space between the outlet of the cold-water nozzle and the throat of the outer nozzle. The vacuum is at least as good as in the common condenser. The momentum of the cold water and of the waste steam carries the whole condensation-water, together with the air it may contain, through the throat of the outer nozzle, and out at the trumpet mouthpiece; and the power required to work an air-pum is saved: as to which, see page 509. (See Trans. Inst. Eng. Scot., 1868-69.) ADDENDUM TO ARTICLE 289, Pace 407. B Expansion of Steam (see fig. D).—Draw a straight line OC A B, in which make AB=4AC. Draw A D perpendicular to C A B; and about C describe the circular are BD cutting AD in D. Then in D A take E, so that DED A shall represent the effective cut-off (and conse uently DA~D E the rate of expansion). At E draw: EF parallel to AB, Then EF +A B will be the required ratio of mean to initial absolute pressure, nearly. TABLES. I.—Taste or HeicHTs DUE TO VELOCITIES. EXPLANATION OF SYMBOLS. v = Velocity in feet per second. h= Height in feet = v' + 64-4. This table is exact for latitude 54°%, and near enough to exact- ness for practical purposes in all parts of the earth’s surface. v h v \h v h I "01553 27 11°320 54 45'280 2 06211 28 12°174 56 48°695 3 "13975 29 13'059 58 52°235 4 24845 30 13°975 60 55901 5 38820 31 14'922 62 59°688 6 "55901 32 15‘901 64 63°602 7 76087 32°2 16°100 64°4 64°400 8 "99379 33 16:910 66 67°640 9 1'2578 34 17°950 68 71800 10 115528 35 19'022 70 76°087 II 1°8789 36 20°124 72 80°496 12 2'2360 37 21°257 74 85'029 13 2°6242 38 . 22°422 76 89688 14 3°0435 39 23°618 78 94°472 15 3°4938 40 24°845 80 99°379 16 3°9752 41 26°102 82 10441 17 4:4876 42 27°391 84 109'56 18 50311 43 28°711 86 114°84 19 5°6056 44 30°062 88 120°25 20 62112 45 31°444. 90 125°78 21 68478 46 32'857 92 131'43 22 75155 47 34301 94 137'20 23 82143 48 35°776 96 143°10 24 - 89441 49 37°283 98 149'13 25 9°7050 50 38820 100 155'28 26 10°497 52 41'987 WEIGHT, EXPANSION, AND SPECIFIC HEAT. 554 ¥.991 6.432 491 9.1Z1 €.1 LE TLE L.Qzgz €.g91 Gr.Qr “yt ¥bz.0 69£.0 L1z.0 GLS1.0 Igt.o ogt.o Gor.€ giz.o gtz.o 49 ‘amnquraduiey pue ainsserd pauorjueut- “HoyWaAYVT T-o68 St emnyeroduiey oy} Tory IOy pus ‘azoydsowyze ovo jo omsserd oy} sepun ‘sjodnpxoxe sq] Uy ‘eouBysqns ey} sus YoIod JO UOP)}IPUOD [U 9.€€1 E41.0 -98z olLf.0 g.09g1 O1F.2 Z.0Z1 gGI1.0 €.0€1 691.0 “a 0 aes OGLE ye QGQhl.t on 0669% €GL.z1 eae eee gh.z1 olf. 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TABLE OF THE ELASTICITY OF A PERFECT GAS, EXPLANATION OF SYMBOLS, T.—Temperature, measured from the ordinary zero. t,—Absolute temperature, measured from the absolute zero. P.—Pressure of a perfect gas in pounds avoirdupois on the square V.—Volume of one pound avoirdupois in cubic feet. PV.—Product of these quantities at any given temperature. P,V>—Value of that product for the temperature of melting ice. BY Oi vcccenass Centigrade. — 30° 244° SOG ae vaeceen —20 254 —15 259 —10 264 -— 5 269 O sasneanes 274 +5 279 Io 284 15 289 20 204 25 secccevee 299 30 304 35 309 4o 314 45 319 50 eerecsece 324 55 329 60 334 65 339 7O 344 75 eee + 349 80 354 85 359 go 304 wovvee Fahrenheit. t eeeverece PV PoVo o'8g05 0°9088 09270 0°9453 0°9635 0°9818 I'0000 T0182 1'0365 1°05 47 1'0730 I'ogi2 I'1095 1'12977 I'1460. I'1643 11825 1'2007 1°2190 1°2373 12555 1'2738 1'2920 I'3103 1°3285 150 155 160 165 170 175 180 185 190 Centigrade, 195- 205 210 215 220 230 240 250 260 240 280 290 300 310 320 33° 340 35° 360 37° 380 ELASTICITY OF A PERFECT GAS. TB '2 secececerees Fahrenheit. t T t 369° 203° 664:2 OTA te wiaacce seus BI? scccuvacs 673°2 379 221 682°2 384 230 6g1'2 389 239 700'2 394 248 709'2 300: cczesscwssexeas DE aceasBes 404 266 424°2 409 275 736'2 414 284 745°2 419 293 754°2 AZA cecesvecccesene 302: see eases 463°2 429 311 772°2 434 320 781'2 439 329 790°2 444 338 799°2 HAO: erase sacusanesy B47 cvcsvenss 808'2 454 356 817°2 459 305 826-2 404 374 835°2 469 383 844°2 474 seveceeer teers 3Q2 veceseeee 853'2 479 401 862°2 484 410 871°2 489 419 880°2 494 428 889'2 504 446 907°2 514 464 925°2 B24 seccccecceernes 482 cecseenee 943°2 534 500 9612 544 518 979°2 554 536 997°2 564 554 I015"2 + 574 vecses seeneeoes SY ee 1033'2 584 590 IO51'2 594 608 1069°2 604 626 1087 ‘2 614 644 1005'2 O24 coovccveereseesOO2 secseeees 1123'2 634 680 II41°2 644 698 1159°2 654 716 T177°2 eee weeecrees woe eonscrees 507 PV PoPo 1'3468 1°3650 1°3832 I'gorg 1°4197 1'4380 1°4562 14744 1'4927 I'5109 1°5292 15474 1.5657 15839 1'6022 1'6204 16387 16569 16752 16934 IVI] 1°7299 17481 17664 17846 18029 18394 18759 I'9124 19489 1'9854 2'0219 2'0584 2°0949 2'1314 2°1679 2°2044 2°2409 2°2774 2°3139 2°3504 2°3869 440 450 470° 480 490 500 520 549 600 620 eee eeee ELASTICITY OF A PERFECT GAS, Peveccsceree Fahrenheit. °o : 8 734 TI95‘2 TH 2 ciencsnes 1213°2 9770 1231°2 488 1249°2 806 1267°2 824 1285°2 842 sessvegxe 13032 860 1321'2 878 1339°2 896 1357°2 914 1375°2 O32 vseepenes 1393°2 968 1429°2 1004 1465'2 1040 I501‘2 1076 1537°2 TIT sevevsiees 1573°2 1148 1609°2 1184 1645°2 1220 16812 1256 1717'2 1202p isssens 1753°2 1328 1789°2 1364 1825°2 1400 18612 1436 1897'2 1472 szesseews 1933°2 1508 1969'2 1544 2005'2 1580 2041°2 1616 20772 TOG? cvcessies 2113'2 1688 2149°2 1724 2185°2 1760 2221°2 1796 2257°2 1832) sosessvesy 2293°2 eee eevcecoee ee eerccecece 559 STEAM BY THE FOOT. 9960.0 €001.0 6£01.0 6Lo01.0 OZII.0 yor1.0 6021.0 1921.0 11€1.0 69£1.0 Lz¥1.0 6gr1.0 G 2Qv 6919.€ 991 L.€ 1z19.€ groS.& gz6€.€ Fohz.€ GoG1.€ ¥6z0.€ £269.4 Frol.y Lg19.% g69r.4 ‘a oT 099900.0 LozGo0.0 660%00.0 L61€00.0 11¥z00.0 06g100.0 1£F100.0 oL0100.0 16 000.0 L1$000.0 g1¥000.0 G6z000.0 ‘ad ot60.0 9460.0 ZIOI.O €G01.0 €601.0 gf11.0 G§g11.0 vEzI.0 [QZ1.0 v1.0 zori.0 For1.0 ‘S019 chile 9919.€ rG1G.€ 101¥.€ gook.€ olg1.€ Sg90.€ 1S46.z 4919.2 1299.2 61+S.2 GS6E.2 TT ‘30, glis gfib LLzee 1LGz 6661 gecr tA11 £.188 z.G99 0.1gh E.ghE 9.9h% “I L[Z01.0 ¥go1.0 ZOII.O CVII.0 2811.0 €€z1.0 ZQEI.O €€E1.0 8gEI.0 ghh1.0 LoS1.0 zLG1.0 ‘ad ‘Sol Vv gh1G.z zgob.z 0362.2 SEg1.2 gtgo.z G1r6.1 €€1g.1 0039.1 zibG.1 996€.1 6Sbz.1 1ggo.1 . d oT o.Lz& 0.9Gz 9.961 9.291 1.911 oF.fg 90.89 Lg.lv LL.vE 26.bz zg.L1 12.21 ‘d ‘LOOT OINO AHL AT ALISNIQ] NAWIXV]{ JO NVALQ dO salLuadoyvd 40 AAV], ‘AT 1€1 Zz €11 For $6 98 LL 89 6g os 1v ze “L STEAM BY THE FOOT. oO ito) a g§f90.0 £890.60 glgo.o 1690.0 61L0.0 1blo.o tglo.o 06Lo.0 G1g0.0 +tgo.0 olgo.o z060.0 €£60.0 ‘a ‘S0LV GhGg.% ggg4.z o1zh.% €1G9.2 F6L5.2 EG09.z 6gzh.z COFE.z begz.z orgi.z ol60.z 3900.2 SE16.€ . a ‘doT €S1Lo.0 6+190.0 09zG0.0 ogtto.o L6LEo.0 Toz£0.0 Sg9z0.0 gfzzo.o §Sg10.0 gzG10.0 oSzI0.0 Q1010.0 +61g00.0 ‘da gogo. 8z90.0 gtgo.o 8999-9 0690.0 Exlo.o gE Lo.0 zglo.o Lglo.o 9180.0 EFg0.0 FLgo.0 9060.0 “T Sol V eS1l.F SzG9.¥ LLgS.b 6o2G.F 619+. gogt.F oLof.F gotz.r 12S1.F Solo.F z996.€ g36g.€ Z908.€ "YT Soy oz61S of6br oolgé og 1 €€ o1€gz ozotz ogzoz o1o0Ll1 oozhr og Lt £896 126k otto glgo.o oolo.0 1zlo.o Iblo.o Sglo.o 63L0.0 F1go.0 ofgo.o Logo.0 1630.0 9260.0 8960.0 660.0 “d S017 Egri9.€ EgtS.€ zolt.€ 120F.€ gSzb.€ Lovz.€ EGor.€ €190.€ 9b 66.z 6Fo6.z €z1g.2 Sgo1lz €L19.2 “I ‘BoT gtz 6€z ofz zig £o0z FOr Sgr glt Lou gS Orr ot1 561 STEAM BY THE FOOT. §Sto.0 99F0.0 LLto.o 63h0.0 €0G0.0 S1f0.9 gzfo0.0 zbGo.o | 980.0 zLS0.0 9890.0 £090.0 1290.0 ‘a 30, v 6€ 98. 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LL. Ag.t 66.1 Eig 62.2 gr.z 1L.% Sez £0.€ Gz.€ gS.€ td wre 9. gs. Gg. Gr. +. cg. €; Gz. ze Gt. Get. Ts Glo. Go. & T ‘SOILVY BLVMIXOUddy 410 atay ‘SUZGNITAQ ONILONGNOO-NON—TIA olen AMO Ren Ow. NTNAAAAA loo ef I fe) a & bo W.I. Macquorn Rankine. C.E€; 04. DB. CUT-OFF ORY SrreRatee S rene aa 0.09 0.80 0.70 0.60 050 18 L00 0.90 0.80 0.70 als 2 0.60 Zz bd x < 0.50 = : oO w bs 0.40 x re Zz ° 0.30 0.20 IN LBS. -MEAN ABSOLUTE PRESSURE,IN DECIMAL PARTS OF ABSOLUTE PRESSURE OF ADMISSION 0.10 0:50 ABSOLUTE PRESSURES Mw. 10 20 30 » 50 60 10 80 30 100 VOLUMES IN CUBIC FEET TO THE LB. Drawn by WJ MR. Maclure & Macdonald Se Entered at Utattoner’s Hall INDEX. apeorene temperature (see Temperature), Absolute zero, 228, Accelerating effort, 33, Acceleration, 18. Actual energy, 35. Adhesion of locomotives, 528. Adiabatic lines, 302, 319. for air, 345. for steam, 383. AXther (see Ether). Air engines, 345, Air engine, perfect, 847, 352. temperature changed at constant pres- sure, 354, re changed at constant volume, heat transferred at constant pressure, 371. Air, expansion and elasticity of, 229. for furnaces; supply and distribution of, 280, 281, 285, 291. flow of, Os assages, 459. ea lines for, 345, thermodynamic function for, 346. thermodynamic properties of, 318, 319. vessels, 148. Air-pump, 482, 508, pump valves, 123, Angular motion, 3. velocity, 4. Animals, power of, 81. Anthracite, 275 (see Fuel). ,Ash, 274. pit, 450, 458. Asses, work of, 89. Atmospheric pressure, 109, 225. Available heat of combustion (see Com- bustion). Axis, permanent, 27. Axles, strength of, 75, 78, 79. Back pressure (see Steam, Back Pres- sure or). Backwater of mill pond, 151. Bafflers, 261, 451. Balance of centrifugal forces and couples, 27. of effort and resistance, 31. Ball clack, 120. Bars, strength of, 66. Batiery, galvanic, 542. Beam of steam engine, 482, 510. Beams, strength of 75. Binary vapour engines, 444, Bituminous unguents, 16. ingredients of fuel, 273. coal, 275 (see Fuel). Blast pipe, 213, 285, 288, 481, 531. Blind coal, 265 (see Fuel). Blow through valve, 481. Blowing apparatus for furnaces, 282, 290, 451, 459. Blowing off apparatus, 453, 464, 521. in locomotives, 530. Boiler, parts and appendages of, 451. heating surface é (see Teste Surface). horse-power of (see Nominal Horse- power). 6 room, 462. shell, 451, 459. stays, 69, 455, 459. Boilers, efficiency of, 290. and furnaces, general arrangements, 449% examples of, 469. . strength of, 67, 70, 459, 466. Boiling points, 225, 235, 237, 241. resistance to, of brine, 242. Bolts, strength of, 66, 69, 71. Brakes, 52. Breast of a water wheel, 184. wheels, high, 160, 177. wheels, low, 161. Bridge of furnace, 450, 452. Brine, boiling points of, 242. blowing off, 453, 464, pumps, 453, 464, Bucket hoist, 105. Buckets of water wheels, £62, 180, 183. Burning (see Combustion), Bursting (see Heyipany Butterfly clack, 123. CALORIMETERS for measuring quantities of heat, 244, Capacity for heat (see Specific Heat). Carbon, 268, 272, 273. Carbonic acid gas, expansion and elasticity of, 229. acid gas, 269, 570 Carbonic oxide, 269, Cataract, 486, 524. Centrifugal force, 27. couple, 27. Channel, flow of water in, 154. Charcoal, 274 (see Fuel). Chemical action, energy of, 267, 540. Chemnitz (see Schemnitz). ~ Cheval, force de, 2. Chimney, 285, 288, 451, 459. Clacks, 117. compound, 144. relief, 144. Clearance, 418. Clothing for boilers, 455. x for cylinders, 48]. Cloudy vapour, 242. Coal, 275 (see Fuel). Cocks, 126. Coke, 275 (see Fuel), Cold well, 481. water pump, 481, 508, Collar, leather, 128. Columns, strength of, 73. Combined engines, 482. Combustion, 267. air required for, 280. available heat of, 290. rate of, 284. total heat of, 267, 270, 277. Compression (see Cushioning). heating by, 319. Concentric cylinder, 502. Condensation, 241. at high pressure, 412. of steam during expansion, 385. surface, 265. water, net, 389, 401. water, total, 481, 507. Condenser, 481, 507, 552. surface, 481, 509. Condensing engines, 478. Conduction of heat, 257. in cylinders, 421. Conical valve, 118, 485. divided, 120. Sonate mechanism of steam engines, rod, 482, rods, strength of, 74. Senta ese of stream, 94, 102, 150, 156, 824, Convection of heat, 261. Cooling surface, 265. by expansion, 319. Cornish boiler, 472. pumping engine, 37, 523. Counter, 552. Counter-pressure steam, 538, Cranes, hydraulic, 133, INDEX. Crank, 482, 511. effort on, 511. Cranks, strength of, 75, 79. Cross breaking, resistance to, 75. Cross-heads end tails, strength of, 75. Crushing, resistance to, 72. Crust, internal, in boiler (see Deposit). external, 468. increased consumption of fuel caused by, 468. Current, water wheel in an open, 188, Cushioning the fluid in engines, 336, 364. steam, 420. Cut off (see Steam, action of). valve (see Expansion valve). Cylinder, 322, 480, 500. ~ cover, 481. strength of, 67, 500. Cylindrical boiler, 470-474, 476. Dampers, 451, 455. Dead plate, 282, 449, 458. points, 512. Deposit in boilers, 467 Dene furnace boiler, 279, 283, 449, 458, 75, Deviating force, 26. Diagram, indicator (see Indicator): Diaphragm valves, 126. Direct acting engines, 489, 512, 518, 520, 525. Disc and pivot valve, 123. electro-magnetic engine, 546, steam engine, 482, 504. Donkey engine, 464. Double acting steam engine, 50, 479. beat valve, 120, 485, 500. cylinder steam engine, 50, 481, 501, 503. furnace boilers, 282, 473, 474, 476. piston engine, 503. Draught of furnace, 285. Drowned weir, 151, Dry coal, 275 (see Fuel), Duplex cylinder, 502. Dynamometers, 40, 80. Esuttitioy, 241, Eccentric, 490. loose, 491. Economizer (see Regenerator). Eduction valves, 480, 486. Effect, 40. Efficiency, 36. conditions of, greatest, in heat-engines, 344. of a fall of water, 91. of air engines, 345, of electro-magnetic engines, 544. of furnace and boiler, 290. of mechanism, 422. INDEX. of steam, 475 (see also Steam, action of), of the fluid in heat engines, 332, 342. of turbines, 193. of vertical water-wheels, 174, of windmills, 218, Effort, 30. Elasticity of gases, 229, Electro-chemical circuit, 542. Electro-magnetic attractions and repul- sions, 544, bar-engine, 547. disc-engine, 544. engines, 539, engines, efficiency of, 544. engines, their cost of working, as com- pared with heat-engines, 541. lunger-engine, 548. Electro-motive force, 543. Energy, actual, 35, 530. nd work, eee! of, 32, 340. intrinsic, 313. Jaw of the transformation of, 809, 540. of chemical action, 267, 540. of heat, 299. potential, 32, 539. Equilibrium valve, 122, 486. slide-valve, 489. Equivalent, dynamical, of heat, 299. Equivalents, chemical, 267. Escape valve, 481. Ether, formule for, 237, 445. and steam engine, 444. table for, V., 563. Evaporation, 235, 241. factors of, 256. ’ latent heat of (see Latent heat). measurement of heat by, 254. total heat of, 253, 327. Exhaust port, 487. Expansion by the slide valve, 491. cooling by, 319. free, 322. latent heat of (see Latent heat). of gases, 229. of fi uids, 232, of walide, 234. valves, 480, 498, 499. Expansive action of heat in fluids, 310. action of steam (see Steam, action of, on iston). Explosion of boilers, 466. ' Efficiency of T5Gee al 550. Faw of water, 91. energy of, 98. Fan blower, 290. Fan steam engine, 538. Feed apparatus, 452, 464, 552. pump, 452, 464, Feed-water heater, 262, 294, 465, 571 Feed-water, net, 389, 401. total, 464, Fifth powers and squares, 157. Fire bars (see Grate), Fire box, 449, 452. strength of, 69. Fire doors, 279, 282, 450, 458, Fire, temperature of, 283. Firing furnaces, 281, 291. Flame, 273. chamber, flame bed, 450. Flap valves, 122,123. Flexible tube valves, 126, Flexure, moment of, 75. Float in boiler, 453. Flow of air, 824; of steam, 298, xiv. of water, measurement of, 92. through channel, 154, through pipes, 113. Flues, 450, 452, 461. strength of, 70. Fluid condition, 236, Fly wheels, 59, 482. Foot-pound, 1. Frame and mechanism of engine,.strength of, 520 (see Strength). Friction, 14. heat produced by, 18, 299. of fluids, 56, 99. Fuel, ingredients of, 278, available heat of combustion of, 290. kinds of, 274. rate of combustion of, 284. supply of air to, 280. total heat of combustion of, 277. waste of, 290. : Furnace {tee Combustion and Fuel). and boiler, efficiency of, 290, 406, 409. and boiler, general arrangements of, 449, efficiency of, in air engines, 360, 370. examples of, 469. front, 450, 458, ee engine, 374, eight of, 457. Furnaces, parts and appendages of, 449. Fusible plug, 454. Fusion, temperatures of (see Melting- points), latent heat of (see Latent heat). Gaz, 490. Gas, perfect, 226, 556. Gases, elasticity of, 229, 310, 554, 556. flow of, 324. Gasefication, total heat of, 255, 327. Gas-engine, 447, Gasket, 129. Governors, 63, 158, 480, 551. Grate, 285, 449, 455. Grates, moving, 283, 457, 572 Gravity, 19, Grease, 16, Grease-cock, 481. Guides for piston rod, 482, 512. Gyration, radius of, 23. ; Heap of water, 91. Head, loss of, 100. Hearth, 449, 457. Heat, 224, engines, 223, 332. engines, action of fluid on piston, 337. dynamical equivalent of, 299. latent (see Latent heat). mechanical action of (see Thermody- naniics). quantities of, 243, 300. specific (see Specific heat). total actual, 305, transfer of, 257. unit of, 244, Heating surface, 262, 293, 461. total and effective, 462. Height due to velocity, 21. table of, 553. Hempen packing, 129. High pressure steam engines, 478. Hoist, water bucket, 105. Hoists, water pressure, 133. Horse engine, 550. power, 2, 40, 50 (see also Indicated power). power, effective, of steam engine, 422. power, nominal (see Nominal horse- power), Horses, work of, 88. Hot well, 482. Hungarian machine, 144. Hydraulic cranes, 133, 138. oists, 133. press, 66, 129. press, strength of, 69. purchases, 133. ram, 211. Hydrocarbons, as unguents, 16, as fuel, 273. Hydrogen, 268, 269, 272, 278. Ice, melting of, 225, 331. Impulse, 20. of fluids, 211. of water, 163, 211. Indicator, steam engine, 47. friction of, 422. position of, 422. Indicated power, 50, 51, 332, 339, 375. Indicator di gram, theoretical, 375, diagram, disturbances of, 417. Induction valves, 480, 486, 550. Inertia, 21. é INDEX. Inertia, moment of, 22. reduced, 23. Injection valve, 481, 508, Injector, 477, Integrals, spam computation of, 11. Isodiabatic lines, 345. Isothermal lines, 302. JACKET round steam cylinder, 895, 481. Jacketed cylinders, action of steam in (see Steam, dry saturated). Jet pump, 213. Journals, friction of, 16. strength of, 75, 79. Junk ring, 129. Keys, strength of, 71. Kilogrammétre, 1. Knot, or nautical mile, per hour, 2. Lap of slide valve, 491. Latent heat of expansion, 250, 309, 312,319. He of evaporation, 252, 325, 559, 563, 564. heat of fusion, 250, 331. Lead of slide valve, 491. Leather collar, 128. packed piston, 128. Levers, strength of, 75. Link motion, 497, 550. Liquefaction (see Condensation), Liquid state, 235. water in cylinder, effects of, 395, 421, Liquids, expansion of, 232. Locomotive steam engines, 469, 528. adhesion of wheels, 528. air, supply of, 281. back pressure in, 382. balancing, 530. blast pipe, 538. combustion in, 285. condensing, 412. efficiency of furnace and boiler, 293. examples of, 532. expansion in, 491, furnace and boiler, 449, 456, 457, 459, 460, 463. heating cylinder, 396. link motion, 497, 5387. regulator, 485. resistance of regulator, 413. of engine and train, 529, 538, safety valves, 465. smoke burning, 282. Low pressure steam engines, 478. _Macaryg, action of, 1. Man, work of, 84. hole, 452. Marine boilers, 474, 477. steam engines, 479, 516, 518, 525, 538. INDEX. Mass, xiv., 19. Mechanism of steam engines, 478. resistance and efficiency of, 422. Melting (see Fusion). points, 225, 235, 251. Mercurial barometer, pressure gauge, and vacuum gauge, ilo. thermometer, 233. Metallic paiene for pistons, 405. Mill pond, 150. site, 91, 150. Modulus of a machine, 89. Moment of friction, 17. of motion, 21. ‘of resistance, 8. statical, 3. Momentum, 19. Mouthpiece of furnace, 450, 458, 476. Mud hole, 452. Mules, work of, 89. Multitubular boilers (see Tubular boilers). Nomrnat horse-power of engines, 479. of boilers, 478. 6% Non-condensing engines, 478, 480. Notch board, flow over, 93. O1x, 16: mineral, as fuel, 278, 477. Orifice, flow of water through, 95. Oscillating engines, 482, 503, 518. Oven, or detached furnace, 283, 449, 475. Overshot water wheels, 160, 177. wheels at high speeds, 185. Oxen, work of, 89. Oxygen, 268, 273. Packine, hempen, 129. leather, 128. metallic, 505. Paddle engines, 516-520, 538. Paddles, efficiency of, 550. Parallel motion, 482, 512. Passages, resistance of, to flow of steam, 413, 485. Peat, 276 (see Fuel). Pendulum, revolving, 26. Petroleum (see Oil, mineral). Pillars, strength of, 78. Pins, strength of, 71. Pipes, flow of water through, 112. Piston, action of water on, 110, 128. of water engine, 128, rods, 506. strength of, 74. valves, 125, 141. Pistons of steam and other heat engines, 832, 480, 505. advantages of long stroke, 507. speed of, 506. Pivots, friction of, 17. 573 Plug rod, 486. Plunger, 127. Pond, mill, 150. Ports, steam, 418, 480, 485. Posts, strength of, 74. Potential energy, 32. Power, 40. muscular, 81. of a fall of water, 91. of an overshot wheel, 185. of an undershot wheel, 188. of turbines, 193. of windmills, 218. (see also Efficiency). Press, hydraulic, 66. Pressure, back (see Back pressure). gauges, 110, 454. intensity of, 4. loss of, 413, mean effective, 50, 51. mean effective in air engines, 358, 359, 367, 368, 373. mean efiective in heat engines, 339. mean effective in steam engines, 378, 388, 399, 401. various units of, 5, 110, 333. Pressures, customary mode of stating, 108, Prime movers defined, 13. classed, 80. Priming, 481. Proof of strength, 65. Proving boilers, 466. Pump brakes, 46. Pumping engines, 523, 525. Quantities of heat, 243. of heat expressed in foot-pounds, 300. RADIATION of heat, 257. from fuel, 228, 292. Ram, hydraulic, 211. Reaction steam engine, 538, of water, 173. water wheel, 190, 197, 206. Reciprocating force, 36. Regenerator, 344. Begnlners (see Throttle valve), 62, 115. Release, 421. Relief clacks, 144, Resistance of electric circuit, 543. of locomotive engines and trains, 529. of steam engine, 422. of steam passages, 413, of water pipes and channels (see Flow of water). to conduction of heat, 257. Retort boiler, 470. Reversing engines by loose eccentric, 491. by link motion, 496. 574 Rivets, strength of, 71 (see also Boiler shells Road locomotives, 537. Rolling resistance, 17. Rotative steam engines, 479. Rotatory steam engines, 478, 482, 503. Rupture, modulus of, 77. Sarery valve, 119, 464, 464. Sails of windmills, 217, 219. Schemnitz machine, 144, Screw engines, 523, 525. propeller, efficiency of, 550. Sector cylinders, 503. Sediment in boilers (see Deposit). collector, 453. Shafts, 482. of marine engines, 520. strength of, 75, 78, 79. Shearing, resistance to, 71. Side lever engines, 516. Single ae steam engines, 50, 333, 334, 339, 478. 47 Slide valves, 124, 480, 486, 550. long, 487. short, 488. Slip dock, hydraulic purchase for, 134. Sluices, 153, 156. Smoke, 273. box, 451, revention of, 281. Snifting valve, 481. Solids, expansion of, 234. melting points of, 235. Soot, 273. Sound, velocity of, 249, 321. Source of water, measurement of, 92. Sources of water power, 91. Specific heat of liquids and solids, 245, 555. heat, ayaiiteal, real and apparent, 307, 316. heat of gases, 248, 318, 554. Sohercitial stase of fluids, 238. Starting, 38. Stays (see Boiler stays, Fire box stays). Steam, action of, against known resistance, action of, on piston, 50, 51, 875, 377. 387, 396, 402, 407, 410, 552, 568. action of, practical examples, 404, 409. and ether engine, 444. approximate formule, 392, 402, 407. back pressure of, 881. chest, 451, 460. density of, 230, 326, 552, 559, 564. dry saturated, action of, 396. elasticity of, 230. engine, resistance and efficiency of me- chanism, 422. engines classed, 478. ? INDEX. Steam engines, parts of, 480, 484, gas, properties of, 255, 320,327, 430, 448, outflow of, 298, xiv. in non-conducting cylinder, 387. latent heat of, 252, 325. passages, 414, 485, pipe, 413, 454, 480. pressure of saturation of, 237. se 462. ; superheated, or steam gas, provisiona They of, 430. oe tables relating to action of, IV., 559; VI, 564; VIL, VILL, 568; 1X, 441; X., 442; XI, 443. tables, interpolation in, 380. thermodynamic function and thermal lines for, 383. total heat of, 327. valve (see Induction valve). whistle, 455. Steel boilers, 465. Steeple engines, 549. Stop valve, 454, 480. Stopping, 38. Stream (see Flow). Strength of machines, 64. Stroke of piston, advantages of long, 507. Struts, iron, 73. timber, 74. Stuffing box, 481. Suction pipe, 105. Superheating steam, 262, 428, 552. Surface blow, 455. condensation (see Condensation). cooling (see Cooling surface). heating (see Heating surface). TappETs, 486. Temperature, 224, 225, 306, Tenacity, 66. Testing strength, 65. Thermal lines, 302. for air, 345, for steam, 383. unit, 244. Thermodynamic functions, 209, 314. functions for air, 346. ~ functions for steam, 383. Thermodynamics, 223, 299. first law of, 299. general equation of, 310. second law of, 306, 307. Thermometers, 226, 232, 306. Throttle valve, 123, 485, resistance of to steam, 413, 480. Torsion, resistance to, 78 Total heat of combustion (see Combustion). of evaporation (see Evaporation). of gasefication (see Gasefication). Traction engines, 537. INDEX. Transport of loads by muscular power, 83. Transverse strength, 75. Treble cylinder engines, 502. Trunk, 481, 482. Tubes of boilers and tube plates, 451, 452, 460, 461, Tubular boilers, 463, 474, 476. Turbines, steam, 538. water, 189, 201. Turf, 276 (see Fuel). Twisting, resistance to, 78. and bending, 79, UspERsnort water wheels, 161, 186. Undulations of indicator diagram, 422. Ungnents, 16. Unjacketed steam engine, 387. Uptake, 451, 475. Vacuum (see Pressure, Customary Mode of Stating; also Steam, Back Pres- sure ot). gauges, 110, 481. valve, 454, Valves, 117 (see also Clacks). chest, 480. gearing, 482, 485, 486, 490, 550. slide (see Slide valves). steam, resistance of, 413. Vanes, impulse of water on, 163. best form of, 170. friction of water on, 171. Vapours, properties of, 236, 325, 326, 554, Velocity, 2. - angular, 4, of piston (see Piston). Vertical-tube boilers, 461, 476. inverted screw marine engine, 525. Vortex water wheel, 191, 193, 197, 198, 207. Wacon boiler, 469, Waste-sluice, 153. Waste weir, 150. Water blower, 213. bucket engines, 105. bucket hoist, 105. expansion of, by heat, 109. gauge, 454, impulse of, 163. measurement of flow of, 92. meters, 148. power, 91. power engines, 97. pressure engines, 107, 138. pressure hoists, 133. room, 462, tube boilers, 461, 476. wheel governors, 158. wheel in an open current, 188. wheel, vertical, choice of, 177. wheels, horizontal (see Turbines). wheels, vertical, 150, 160, 174, 177, 186, Weir, flow over, 93, 150. Windmills, 214. Wire-drawn steam, 413, 417. Wood, 276 (see Fuel). hearth for burning, 457. Work, 1. against an oblique force, 6. against gravity, 8. pc varying resistance, 9. algebraical expressions for, 5. during retardation, 35. in terms of angular motion, 3. in terms of pressure and volume, 4. of acceleration, 18. represented by an area, 8, summary of, 24. summation of quantities of, 6. useful and lost, 13. Wrenching, resistance to, 78. Z-CRANK engine, 482, Pan Aya es ae att