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Full text of "The steam-engine and other heat-motors"






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Professor of Mechanical Engineering, Tulane University of Louisiana 






Copyr-'ght 1907. 1909, 


Rnbrrl Brutnmonb an2> (Company 
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IN the second edition I have endeavored to utilize such 
constructive criticisms of the first edition as came to my atten- 
tion. Five plates are used to illustrate engine details and each 
part is named on the plate itself. The first chapter now includes 
a number of calculations of a general character which were intro- 
duced to give the student a better view of the entire subject. 
The boiler, the engine, and the condenser are brought together 
so that the functions of each form parts of one picture in the 
student's mind. The inertia of the indicator piston and two 
of the difficult cases in the Zeuner valve diagram construction 
are discussed. The addition of tables and diagrams facilitates 
finding loss of head in steam or air pipes. As the use of logarith- 
mic cross-section paper has not yet become common, a descrip- 
tion of its use in connection with PV n curves is given. The dis- 
cussion on Hirn's analysis is now followed by very complete 
tables giving the mean effective pressure and the steam per horse- 
power-hour for condensing and for non-condensing engines of the 
four-valve type. Tables of corrections for initial condensation 
under various pressures are also given. A comparison of the 
ideal and practical consumption of steam under a variety of 
circumstances may thus be made quite easily. 

The engineer has to deal with the transfer of heat through 
metal surfaces. Prof. Perry's theory of heat transfer and formulas 
for finding the mean temperature of the heating and cooling fluids, 
as well as for finding the rate of heat transfer per square foot 
per minute per degree difference in temperature, as given by 
Hausbrand, have been added. A much more complete discussion 
of the design of feed-water heaters and air-pumps both wet and 
dry for surface, jet or barometric condensers is presented. The 



theoretical discussion of fly-wheels is followed by a discussion 
of belt and balance wheels for A.C. and B.C. generators with 
tables and empirical formulas, so that practical sizes for ordinary 
cases may be easily found. 

A final chapter has been added on steam-engine details. The 
student is supposed to have had " Strength of Materials," From 
the empirical-rational formulas in this chapter, he may obtain 
practical answers which he can profitably compare with those 
derived from theory. The forms of the various details may be 
obtained from catalogues. This last chapter is due to the labor 
of students in Cornell and in the University of Wisconsin, super- 
vised by Professors Barr and Gould. 

While some students cannot afford the time to take up treatises 
on the gas-engine and on refrigeration in college, every student 
can afford to spend a week on those subjects. Two short chap- 
ters in this book include all the theory on those subjects which 
is given in quite large treatises. The student therefore discovers 
that books on those subjects should have no difficulties that he 
cannot master by himself if the occasion arise. It is, of course, 
realized that the short time so given can, in no sense, take the 
place of a regular course in these subjects if the student can find 
the time. 

The thanks of the author are due to those whose matter is 
quoted in the text and especially to Professor Peabody for his kind 
permission to insert Table IX, which is compiled from his latest 

W. H. P. C. 


THE instructor is seldom compelled to drive students who 
comprehend their text-books. The student's comprehension may 
be gauged by his ability to apply principles to the solution of 
problems containing legitimate difficulties. He cannot hope to 
overcome the difficulties that are inherent in the application of a 
number of principles if his knowledge of these principles is foggy 
and inaccurate. Therefore it is only fair to the student that 
the text should be clear and its style attractive; numerous 
illustrations should be given; especial stress should be laid on 
fundamentals; the errors that he is liable to make should be 
pointed out; prolixity in details and undue terseness should be 
avoided, and it is of extreme importance that a proper sequence 
of subject development should be maintained not only in the 
main subdivisions but also in every paragraph and sentence. All 
subjects in a technical course should be valuable not only 
for the instruction they give but also for the opportunity they 
present to train the student to think. The major value of text- 
books should be instructional. This value the student develops 
in his home study. The instructor brings out the training value 
of the subjects by problems of proper complexity. 
This book possesses the following characteristics: 
The history of the steam-engine has been omitted. After a 
student has advanced far enough to appreciate its import, the 
story of the development of heat motors may be given by the 
instructor. The first chapter is devoted to a bird's-eye view of 
the entire subject with illustrations of the main elements of a 
steam-engine plant and to the general relations of the different 


forms of energy. Similarly, each subsidiary subject is opened 
by a general picture of that subject, so that the general relations 
of the parts may be seen. 

While an earnest effort has been made to make the work 
simple, no principles have been omitted that should be contained 
in a work intended for undergraduate students of college grade. 
The Committee on Standard Rules of the American Society of 
Mechanical Engineers have formulated rules that should be studied 
by every student. These rules have been incorporated in the 
text in positions dependent upon the development of the sub- 
ject. In this way duplication of the same matter has been 

In the development of a new subject, students put the great- 
est stress of their attention upon the phases first presented, and 
then lightly assume that they can make the necessary modifi- 
cations for the more complex cases. On this account, and because 
it is easier to pull down than to build up, the author has always 
developed the most complex case first and then shown the deriva- 
tive or more simple forms. This inversion of the usual method 
gives a better picture of the subject in its entirety. 

In developing a complex subject many formulas are derived. 
In no way can these formulas be deemed of equal importance. 
In so far as the student is concerned, the formulas that give answers 
most directly are usually of the least importance. Memorizing 
the derivation of formulas or substituting in them is of little value. 
And yet there are about two dozen formulas that should be so 
well known that they are, in effect, memorized. These are mother, 
backbone, or fundamental formulas. All problems, either literal 
or numerical, should start with one or more of these formulas. 
Their incessant repetition brings a comprehension that can be 
attained in no other way. 

The text calls for many complete designs. These, of course, 
may be more or less crude, but they are of great value in develop- 
ing much unexpected ignorance of principles and giving definite- 
ness to the student's conception of a machine or of its action. 
For example, few books complete the design of both ends of a 
slide-valve and draw both indicator-cards when a finite connect- 
ing-rod is used. If the instructor insists on the student making 


a complete design, a number of mistakes will be made almost 

Attention is called to the method of drawing indicator-cards 
for compound engines directly from round numbers. The ease 
with which the different points on the diagram are found enables 
the effect of changes (as, for instance, in the L.P. cut-off or in the 
receiver volume) to be seen at once in the varying areas of the 
cards. Of course the object aimed at is the comprehension of 

The fundamental principles of thermodynamics are applied 
not only to the steam-engine but also to gas-engines and gas- 
producers, refrigerating machines, steam turbines, and boiling 
in a vacuum. In the discussion of these machines vague gen- 
eralities have been avoided, even if the discussion is limited to 
the application of general laws. The endeavor has been to make 
the foundation broad and strong enough to carry any super- 
structure that the instructor wishes to erect on it. The discus- 
sion on steam turbines starts with elementary mechanical prin- 
ciples of jet action, and by a step-by-step advance (omitting no 
proof, giving no outside references, and using diagrammatic 
sketches freely) a definite picture of the machine is built up. 

The author appreciates the courtesy of Professors Carpenter, 
Peabody, Reeve, Stodola, Thomas, and Thurston's heirs and 
that of the American Society of Mechanical Engineers and the 
American Society of Naval Engineers in giving free permission 
to use either text or plates of their publications. The author 
also thanks those manufacturers who loaned cuts of their pro- 

Letters containing honest criticism, suggestions, problems, or 
encouragement will be appreciated by the author and publishers. 

W. H, P. C. 





Elementary Principles, 1. Work and Torque, 2. Energy, 2. 
Various Forms of Energy, 3, 4. Temperature, 5. Thermal Unit, 
Mean and Standard, 5. Thermometers, 6. Absolute Temperature, 
7. First Law of Thermodynamics, 8. Mechanical Equivalent of Heat, 
9. Second Law of Thermodynamics, 9. Apparatus in a Steam- 
engine Plant, 10. Steam-boiler, 10. Draft, 13. Separator, 13. 
Origin of all Power, 15. Action of Steam in a Steam-engine, 15. 
Bearing Details, 17. Corliss Cylinder Details, 16. Governor Details, 
19. Cross-section of Cylinder, 20. Plan and Side Elevation of Cylinder, 
21, 22. Surface Condensers, 23. Air Pump, 23. Circulating Pump, 
25. Jet Condenser, 26. Bourdon Gage, 27. Mercury Column, ?8. 
Rates versus Quantities, 30. Horse-power Definitions, 31. Rates 
Equivalent to a Horse-power, 32. Brakes, 35. Efficiencies, 35. Heat 
Value of One Pound of Coal from Chemical Analysis, 36. Boiler Horse- 
power, 36. Usual Rates of Evaporation in Boilers, 36. Calculation of 
Grate Areas, 37. Usual Steam Consumption of Engines and Pumps, 
37. Power for Electric Lighting, 39. Boiler Horse-power and Pump 
Displacement for Electric Plants, 39. Combining Efficiencies, 40. 
Heat Consumption of a Steam-engine Plant, 41. What becomes of 
Heat-units, 44. Names of Engines, 44. 



Steam-engine Indicators, 46. Reducing-levers, 58. Reducing- 
wheels, 59. Method of Taking Indicator-diagrams, 61. Care of Indi- 
cator, 63. Actual Point of Cut-off, 65. Inertia of Indicator Piston, 65. 



Method of Drawing Hyperbolas, 68. Commercial Cut-off, 70. 
Clearance, 72. Ratio of Expansion, 72. Finding the Indicated Horse- 
power, 73. Testing Indicator-springs, 74. Isothermal Expansion 
Curve, 77. Diagram Factor, 81. Elimination of Clearance Steam, 84. 






Throw of Cranks and Eccentrics, 85. Piston Travel with a Finite and 
an Infinite Connecting-rod, 86. Slide-valve Definitions, 88. Width of 
Port and Port Opening, 90. Angle of Advance, 92. Valve-diagram, 
93. Geometrical Relations of Elements of the Zeuner Diagram, 97. 
Valve-diagram Problems, 99. Bilgram Diagram, 103. Dimensions of 
Steam Ports and Pipes, 110. Practical Considerations in Design, 111. 
Formulas, Tables, Diagrams for Loss of Head in Steam and Air Pipes, 
115. Pipes of Equivalent Carrying Capacity, 119. Defective Indi- 
cator Diagrams, 122-125. 



Effects of Heat, 126. Molecular Motion, 127. Evaporation, 127. 
Elemental Effects of Heat, 130. Specific Heat, 131. Specific Heat of 
Solids and Liquids, 132. Specific Heat of Gases, 132. Specific Heat of 
Gases at Constant Volume, 134. Specific Heat of Gases at Constant 
Pressure, 134. Fundamental Equation of Perfect Gases, 135. Boyle's 
Law, 137. Charles' Law, 137. General Expansion Curve, 139. Adia- 
batic Curve, 141. To Draw the Curve PV n = C, 143. Logarithmic 
Cross-section Paper and Method of Laying-off PV n Curves, 144. Rela- 
tion between T, V, and P in Adiabatic Expansion, 148. Heat Energy 
Represented by Areas, 148. Area Equal to Heat in a Perfect Gas, 149. 
Area Equal to Heat Added when the Gas is Heated at Constant 
Volume, 149. Area Equal to Heat Added when the Gas is Heated in 
any Manner, 150. Area Equal to Heat Added when the Gas is Heated 
Isothermally, 124. General Fundamental Equations of Heat Added 
152. Carnot Cycle, 154. 



Melting Solids, 160. Boiling-point of Water, 160. Heat of the 
Liquid, 162. Expansion of Water when Heated, 163. Vaporizing 
Water, 163. Heat in and Heat Required to Produce Steam, 165. 
Changes in Regnault's Tables, 167. Quality of Steam, 169. Super- 
heated Steam, 170. Equivalent Evaporation, 170. Calorimeters, 172. 
Determination of Water Equivalent, 176. Normal Reading, 178. 





Causes of Wetness of Steam, 180. Foaming, 181. Non-conducting 
Coverings, 181. Initial Condensation, 186. Laws of Compression of 
Steam, 188. Weight of Steam Accounted for by the Indicator, 191. 
Dry-steam Fraction, 193. Hirn's Analysis, 194. Heat Interchanges, 
198. Example of Hirn's Analysis, 198. Tables to Find Actual Steam 
Consumption of Four-valve and Corliss Engines both Condensing and 
Non-condensing, 201. Actual Results in Practice, with Leaky Valves, 



Entropy, 207. Construction of Water-line, 210. Construction of 
Steam-line at Constant Pressure, 212. Construction of Saturation 
Curve, 213. Construction of Adiabatic Expansion Line, 214. Work 
done during Adiabatic Expansion, 215. Velocity of Steam passing 
through a Nozzle, 216. Construction of Constant Volume Line, 219. 
Work done when the Curve of Expansion is the Curve of Constant 
Steam Weight, 222. Construction of Constant Heat Curve, 224. 
Deriving a Temperature-entropy Diagram from an Indicator-diagram, 
225. Carnot Cycle, 228. Rankine Cycle, 228. Ratio of Economy of 
an Engine to an Ideal Engine, 229. Temperature-entropy Diagram 
of a Real Engine, 230. 



Jet Condensation, 232. Jet Condensers, 233. Air Leaks, 234. 
Design of Jet Condensers, 234. Barometric Condensers, 236. Syphon 
or Ejector Condensers, 238. Surface Condensers, 239. Amount of 
Cooling Water, 241. Heat Transfer through Metals, 242. Professor 
Perry'o Theory of Transfer of Heat, 243. Finding the Mean Difference 
of Temperature between Heating and Cooling Fluids, 245. Principles 
of Open and Closed Feed Heaters, 248. Relative Value of Heaters and 
Purifiers, 254. Heating Surface in Feed Heaters, 255. Discussion of 
the Rate of Heat Transmission in Condensers, 257. Contraflo Con- 
densers, 260. Thermal Efficiency, 263. Economy in Vacuum Pro- 
duction, 264. Surface Section Ratio, 265. Cooling-towers, 265. Cor- 
rect Absolute Condenser Pressure, 267. Wet Vacuum-pump Design, 
268. Efficiency of Air-pumps under Variable Loads, 269. Edwards' 
Air-pump, 2 2. Dry-air Pump, Design 273. Practical Air-pump 
Air-pump Ratios, 274. Air-pump Cards, 275. Definitions of Air- 
pumps, 273. Design of Air-pump for Surface Condenser, 278. Wet 
Vacuum-pump for Jet Condenser, 281. Dry Air-pumps for Counter- 
current Barometric Condenser, 282. Cooling Air in Condensers, 282. 




SMALL AUXILIARIES ..... ........ ................................... 285 

Feed-pump Cards, 286. Feed-pump Design, 287. Reciprocating 
Circulating-pump Design, 288. Air-chambers on Circulating Pumps, 
289. Centrifugal Circulating-pump Design, 290. Injectors, 292. 
Weight of Feed-water per Pound of Steam, 293. Efficiency of Injectors, 
294. Operating Injectors, 294. Reheaters, 297. Oil and Water 
Separators, 298. 


MULTIPLE-EXPANSION ENGINES ....................................... 300 

History of Multiple-expansion Engines, 300. Record Tests made in 
the Last Five Years, 303. Laying Out Theoretical Cards of Compound 
Engines, 304. Tandem Compound without a Receiver, 306. Tandem 
Compound with a Receiver, 308. Cross Compound, L.P. Cut-off 
before Half-stroke, 310. Cross Compound, L.P. Cut-off after Half- 
stroke, 313. To Find the Size of the Cylinders of a Compound Engine, 
315. To Combine the Indicator-cards from a Compound Engine, 317. 
True Ratio of Expansion in Compound Engines, 320. Diagram Factor 
in Compound Engines, 322. 


REVOLUTION CONTROL ....................... ....................... 326 

Fundamental Equations, 328. Centrifugal Force, 329. Kinetic 
Energy, 330. Fly-ball Governor, 327. Sensitiveness, 333. Practical 
Forms of Fly-ball Governors, 334. Power of a Governor, 338. Fric- 
tion of a Governor, 338. Adjustable Eccentrics, 339. Valve-diagrams, 
Swinging Eccentrics, 341. Shaft-governors, 343. Angular Accelera- 
tion, 347. Springs, 347. Inertia Governors, 348. Link-motion, 352. 
Open and Crossed Rods, 356. Position of the Saddle-pin, 358. Link- 
arc, 359. Equivalent Eccentric, 359. Buckeye-engine Valve, 360. 
Meyer Valve, 365. Corliss-engine Valves, 366. Setting Corliss-engine 
Valves, 366. Poppet-valves, 370. 



Turning Effort in the Crank-shaft, 373. Net Steam-pressure, 37^. 
Variable Velocity of the Piston, 375. Pressure Required to Accelerate 
the Reciprocating Parts, 376. Reciprocating Parts Considered as 
Concentrated at the Center of the Crank-pin, 377. Accelerations, 
Finite Connecting-rod, 379. Pounding of the Engine, 380. Tangential 
Pressure Curves, 382. Approximate Formula for a Fly-wheel, 384. 



Design of Belt Wheels, 386. Empirical Formulas for Weight of 
Balance Wheels for Engines Direct-connected to A.C. or D.C. Genera- 
tors, 387. Analysis of Rites Inertia Governor Stresses, 390. Counter- 
balancing, 400. Shaking Forces, 403. Calculation of Phase Departure 
of Directly-connected Engines, 405. 



Rules for Conducting Steam-engine Tests, Standard Rules, A.S.M.E. 
Object of the Test, 411. General Condition of the Plant, 412. Dimen- 
sions, 414. Coal, 415. Calibration of Instruments, 415. Leakage of 
Steam, Water, etc., 419. Duration of Test, 421. Starting and Stop- 
ping a Test: (a) Standard Heat Test and Feed-water Test of Engine; 
(b) Complete Boiler and Engine Test, 422. Measurement of Heat-units 
Consumed by the Engine, 424. Measurement of Feed-water or Steam 
Consumption of an Engine, 425. Measurement of Steam used by 
Auxiliaries, 427. Coal Measurement, 428. Speed, 429. 



Superheated Steam, 431. Foster Superheater, 432. Purpose of 
Superheating Steam, 434. Thermal Laws, 435. Heat Required to 
Produce Superheated Steam, 435. Intensity of Superheating Required 
to Prevent Initial Condensation, 435. Data of a Test of an Engine 
using Superheated Steam, 438. Entropy Diagram of Superheated 
Steam, 441. Superheated Steam in Compound Engines, 442. Dura- 
bility of Superheaters, 443. Steam-nozzles, 443. Zeuner's Formula, 
445. Velocity and Weight of Steam Discharged from a Nozzle, 446. 
Elementary Mechanical Principles Applicable to Jets, 447. Impulse 
Due to a Jet Moving on a Curved Blade, 449. Maximum Efficiency 
Under Various Conditions, 456. De Laval Steam-turbine, 456. 
Theoretical Design of De Laval Turbine, 458. Curtis Turbine, 459. 
Theoretical Design of Curtis Turbine, 460. Friction Losses in the 
Curtis Type, 461. Parsons' Steam-turbine, 465. Analysis of Parsons' 
Steam-turbine, 473. Hamilton-Holzwarth Steam-turbine, 477. Com- 
bination of Engines and Turbines, 478. Turbine Auxiliaries, 478. 



Lenoir Cycle, 480. Beau de Rochas Cycle, 480. Practical Details 
and Data, 482. Calorific Power of Compound Gases, 484. Rise in 
Temperature in Gas Combustion, 485. Producer-gas, 486. Gas from 
Soft Coal, 489. Calculation of Theoretical Pressure in Gas-engines, 490 
Indicator- and Entropy-cards of Gas-engines, 490. Diesel Cycle, 496 



Data from a Diesel Engine Test, 499. Rules for Conducting Gas- and 
Oil-engine Tests, Code of 1901, 501: Objects of Tests, 501; General 
Condition of the Engine, 501; Dimensions, 501; Fuel, 502; Calibration 
of Instruments used in the Tests, 502; Duration of the Test, 504; 
Starting and Stopping a Test, 504; Measurement of the Fuel, 504; 
Measurement of the Heat-units Consumed by the Engine, 505 ; Measure- 
ment of Jacket-water to Cylinder or Cylinders, 506; Indicated Horse- 
power, 506; Brake Horse-power, 506; Speed, 506; Recording the 
Data, 507 ; Uniformity of Conditions, 507 ; Indicator-diagrams and 
their Analysis, 507 ; Standards of Economy and Efficiency, 507 ; Heat 
Balance, 508; Report of Tests, 509; Temperatures Computed at 
Various Points of the Indicator-diagram, 509. Complete Form for 
Gas- and Oil-engine Tests, 512-515. 



General Description of Evaporation in Vacuo in Mulitple and Single 
Effects, 516. Theory of the Multiple Effect, 519. Theory of Single 
Effect or Vacuum-pan, 520. Double Effect, 521. Triple Effect, 522 
Measurement of Density of Liquids, 524. Description of a Vacuum- 
pan, 527. 



Theory of Refrigerating by Dense Air, 530. Ammonia-compression 
System, 532. Entropy-diagram of a Compression System, 534. Re- 
fiigeration Units, 536. Complete Form for a Steam-engine Test, 537- 



Piston-rod, 544. Connecting-rod, 544. Main Journal, 545. Crank- 
pin, 546. Cross-head Pin, 548. Cross-head Shoes, 549. Steam Ports 
and Pipes, 549. Exhaust Ports and Pipes, 550. Belting, 550. Weight 
of Engine, 551. Steam Cylinder Details, 551. Fly-wheels, 553. 


Piston-rod, 556. Connecting-rod, 556. Main Journal, 557. Crank- 
pin, 558. Cross-head Pin, 560. Cross-head Shoes, 561. Cylinder 
Details, 561. Steam Ports and Pipes, 563. Exhaust Ports and Pipes, 
563. Belting, 563. Fly-wheels, 564. Reciprocating Parts, 564. 
Weight of Engine, 565. 




Table I. Properties of Familiar Substances 571 

' ' II. Hyperbolic or Naperian Logarithms 572 

" III. Heating Values of Various Substances 572 

" IV. Oxygen and Air Required Theoretically for the Com- 
bustion of Various Substances 573 

' ' V. Relative Humidity, Per Cent 573 

" VI. Weights of Air, Vapor of Water, and Saturated Mixtures 
of Air and Vapor at Various Temperatures and Con- 
stant Pressure 574 

" VII. Entropy of Water and Steam 575 

" VIII. Saturated Steam 576-581 

' ' IX. Saturated Steam Entropy (for Condenser Pressures) 582 

X. Mean Pressures for Various Methods of Expansion 584 

" XI. Mean Pressures for Various Methods of Expansion 585- 

' ' XII. Mean Pressure Ratios 586 

" XIII. Terminal Pressure Ratios 587 

" XIV. Flow of Steam through Pipes 588 

" XV. Specific Heat (C p ) of Superheated Steam at Constant 

Pressure 58$ 


INDEX . , .591 








THE student will avoid much unnecessary confusion by keeping 
always clearly in mind : 

1. The difference between an essentially elementary and a com- 

pound quantity. 

2. Elementary quantities can only equal elementary quantities. 
Twisting moments can only equal twisting moments. 
Compound quantities, derived from work or changeable into 

work, can only equal compound quantities that can be de- 
rived from work or can be converted into work. 

3. The two sides of an equation must be similar in kind homo- 


4. A pull, push, torque, or work cannot exist unless there is at 

the same time an opposing pull, push, torque, or work of 
exactly equal magnitude. 

5. While in nature neither matter nor energy is ever created or 

destroyed, there is an unceasing tendency to perfect change. 
6^ He should know the fundamental formulas of a subject as he 

knows the multiplication-table, and he should formulize his 

work as much as possible and substitute in formulas as little 

as possible. 
7. Clearness is often obscured in the terseness of a derived formula. 


Force, whether it be a push, pull, or an attraction such as 
gravitation, is an elementary quantity. Linear distance is also 
elementary. Unlike force it may be compounded with itself, as 
in areas and volumes. 

Force and distance may be combined to form two distinct 
compounds which should never be confounded with nor equated 
to one another. Force overcoming an equal resistance through a 
distance does work. The force is exerted THROUGH a distance. 
One pound lifted a foot is a foot-pound, because there is a resist- 
ance of one pound through a foot. One pound dragged a foot hori- 
zontally on a rough surface does not require a foot-pound of energy, 
because the resistance ordinarily is not one pound. If the coeffi- 
cient of friction is 4%, then the work would be .04 foot- 

Force acting AT a distance produces a turning moment, twist, 
or torque. Here there is no motion. If motion is impending, it 
is not in the direction of the distance factor of the twisting mo- 
ment. A twisting moment and work may exist at the same time, 
as in a moving crank. Imagine all the forces acting on a crank- 
pin reduced to a single force (that may vary in amount), always 
perpendicular to the crank-arm. The torque at any instant is the 
force, at that instant, multiplied by the length of the crank-arm 
=the distance from the center of the crank-pin to the center of 
the shaft. The work per revolution would be the mean force mul- 
tiplied by the distance that the center of the crank-pin moves in a 

PL = work or twisting moment (according to the conditions) 

in foot-pounds, foot-tons, or inch-pounds, according as 
P= pounds or tons; 

f length of arm in twisting moments; 

L=feet or inches-! ,. : ,, - ,, , . , 

[ distance the force moves through in work. 

EXAMPLE 1. A winch 8 inches in diameter has two crank-handles, 
18 inches radius, 180 apart. Two men use it to raise buckets of 
stone, whose total weight is 200 pounds, from a hole 40 feet deep. 
Neglect friction. What torque does each exert? What work does 
each man do per revolution? What is the best direction for each 
man to exert his strength? 


Work may be stored up; it is then called energy. Energy 
occurs in many forms that may be grouped into the three divi- 
sions potential, kinetic, and vibratory. 

Students are liable to confuse potential energy and torque. 
When work is stored up in the form of potential energy, all motion 
has disappeared; for example, the tightened spring in a watch or 
the water in an elevated tank. In these cases there is no motion, 
but we notice that it takes force acting through a distance to wind 
the spring or raise the water. Under theoretical conditions the 
spring in unwinding and the water in descending from the ele- 
vated tank have the power to perform as much work as was 
expended originally in tightening the spring or raising the water. 
It is its potency or power to do work, if required, that gives the 
name potential to this form of energy. 

Kinetic energy is energy of motion. As the number of revolu- 
tions of the fly-wheel increases above the normal it is absorbing 
foot-pounds of work that it will give out later in slowing down. 
The rifle-bullet with small mass must have high velocity to do 
the work of penetration. Any mass moving in any direction at 
any velocity possesses kinetic energy. 

Energy of vibration seems to be made up of kinetic and po- 
tential energy, and yet it is quite different from either. The most 
obvious example, of course, is the pendulum. At the bottom of 
its swing all its energy is kinetic, at the top it is all potential. 
Between the top and the bottom there is a continual interchange: 
descending the pendulum is converting potential into kinetic 
energy, and ascending this process is reversed. 

The main characteristics of this form of energy are the small 
amount of energy involved and the length of time that it 

Waves are vertical vibrations of the surface-water; sound is a 
vibration of the air, and light is a vibration of the luminiferous 
ether. Great distances are traversed by waves and sound, but 
they are insignificant when compared to the millions of millions 
of miles travelled by the feeble vibration called light. As the 
amount of energy is so insignificant the ether that transmits the 
vibrations must be wonderfully adapted for the purpose. 

Below is given a classification of different forms of en- 


ergy in which the forms already given appear as subdi- 

JForm of Energy. 

Factor of Intensity. 

Factor of Extent! 


Unit of Measure- 



Mechanical, pot. 
Mechanical, kin. 
Electrical, pot. . . 
Electrical, kin. . . 
Chemical, pot. . . 
Chemical, kin. . . 
Thermal, kin. . . . 

Thermal, pot. . . . 





Pounds -T- G 
Molecular weight 

Degrees (Fahr.) 
Degrees (Fahr.) 


From Reeve, Thermodynamics of Heat-engines. 

Most of the forms of energy tabulated are seen to be made up 
of two elemental factors and hence must be compound and of 
the second degree. 

It may be assumed that there is evidence in plenty that each 
of the above forms of energy can be transformed into one or more 
of the other forms above given. They must all be compound, 
since a number of them are evidently so. The student is probably 
more or less familiar with all the forms save the last one. We 
shall assume that we have shown that thermal energy or heat is 
compound and is made up of two factors. 

If these forms of energy can be converted into one another 
they must all be either simple or compound. If compound, they 
must be compound in the same degree (just as an area cannot 
equal a cube), and ultimately it would seem that they ought to 
be reducible to the product of the same factors. Further, it is 
not necessary, in any conversion of one form into another, that 
one of the above forms of energy should be transformed into one 
other form alone. Indeed this rarely takes place. But if any 
quantity in an equation of conversion is of the second degree, 
every quantity connected to the others by the + or sign must 
also be of the second degree. 

The following table gives tersely examples of the change of 
each form of energy into each of the others : 


f Electrical 

Mechanical into -j Chemical. 
I Thermal. 

f Mechanical 

Electrical into \ Chemical. 
I Thermal. 

Chemical into 

f Mechanical 

I Electrical. 
I Thermal. 


Cartridges (Trigger striking) 


Electric motor. 
Electric lights. 

Work done in collecting a gas arising 

from dissolving a solid in acid. 
Wet batteiy. 

Expansion of furnace walls. 


Growth of vegetation. 

f Mechanical. 

Thermal into -j Electrical. 
[ Chemical. 

Ex. 2. Give other examples of all the different forms of energy 
and of the change from one form into one or more other forms. 

Ex. 3. Give all the different forms of energy that appear when a 
heavy gun is fired at night. 

Temperature. Temperature is a quality of heat and may be 
said to measure its INTENSITY. It is obviously one of the factors 
of heat, for by doubling the intensity of heat, as measured from a. 
true zero, we double the heat in a body. It is one of the factors 
of heat, as a foot is a factor of a foot-pound. It is not heat any 
more than a foot can in any way be a foot-pound. Temperature 
is elemental in character. Its unit of measurement is called a 
degree. Each degree on any assumed scale, such as the Fahren- 
heit, Centigrade, or Reaumur, is supposed to measure equal vari- 
ations of intensity of heat. But the variation measured by the 
Fahrenheit degree is only 5/9 of that measured by the Centigrade 
degree and 4/9 of that of the Reaumur. This arises from the 
fact that the same variation of intensity of heat the variation 
that exists between the temperature of freezing and boiling water 
at atmospheric pressure is divided into 180 parts on the Fahren- 
heit scale, into 100 parts on the Centigrade scale, and into only 
80 parts on the Reaumur scale. 

Thermal Unit. Two such units are available, the standard 
British thermal unit, B.T.U., which is the quantity of heat required 
to raise one pound of water from 60 F. to 61 F., and the mean 
B.T.U., which is the 180th part of the heat required to raise water 
from the freezing to the boiling point. The latter is the more 
easily and certainly determined and corresponds to the mean 
calorie now becoming standard abroad. 


Calorie. The French unit of heat is a calorie. It is the meas- 
ure of the quantity of heat that is required to raise one kilogram 
(2.2 pounds) of water from 4 to 5 Centigrade or yfo of that 
required to raise one kilo of water from to 100 C. 

As heat is a compound quantity, its units of measure, a B.T.U. 
and a cal. are compound. One calorie =3.968 B.T.U. 

Cold. Since heat is a form of energy it has a positive exist- 
ence. This cannot be said of cold. There is no such thing as a 
quantity of cold. All bodies, then, are hot, i.e., possess heat. 
Some are hotter than others. When the latter are said to be 
colder than the former, the term colder is to be interpreted as less 

Minus Temperature and Minus Pressure. Similarly we shall 
find that there are no such quantities as minus degrees of tem- 
perature or minus pounds pressure. In fact we must take par- 
ticular pains to have all measurements in absolute units, viz., 
measured from a real zero. 

The Fahrenheit and Centigrade zeros are purely arbitrary. 
At a true zero of temperature a body will possess no heat, or, in 
other words, the molecules of the body will be at rest, all vibra- 
tion having ceased. Now the boiling-points of solid hydrogen, 
nitrogen, and oxygen are far below either of the above-mentioned 
arbitrary zeros, and hence the true zero must be still lower. 
While air is not a perfect gas, yet well-dried air will serve to make 
a good thermometer for the investigation of low temperatures. 

Air-thermometer. The principle of an air-thermometer is 
shown in Fig. 1. The bore is supposed to be absolutely uniform 
and the drop of mercury is supposed to be a frictionless, weight- 
less piston, perfectly air-tight. Let the piston be any convenient 
distance from the bottom when the whole tube is immersed in a 
tub of water and melting ice, the temperature of the mixture being 
constant at 32 F. The air below the mercury must be entirely 
free of moisture. Measure accurately the distance the piston is 
from the bottom of the tube. The atmospheric pressure (sup- 
posed to be 14.7 pounds per square inch) is constant and is the 
sole pressure on the drop of mercury. The tube is now trans- 
ferred to a vessel of clean distilled water boiling freely in the 
open air. The height to which our frictionless piston now rises 


is now marked. The increase in volume when the work is properly 
done is 0.3654 times the original volume. This corresponds on the 
Fahrenheit scale to a rise of 180, so that the rise per degree is 

3654 1 

"~"JOQ~ =0.00203 =A7yTa of the original volume. 


GT3 C 



FIG. 1. FIG. 2. 


Absolute Temperature. It is now evident that if we had cooled 
the air below the freezing-point, for each (Fahrenheit) degree of 
cooling the (original) volume, 7, would have decreased 1/492.6F, 
and, on the supposition that there would be no change of charac- 
teristics, the zero of volume, the zero of temperature, and the 
zero of heat possession would be 492. 6 below the Fahrenheit 
freezing-point or 460.6 below the Fahrenheit zero. 

In Fig. 2 the above calculation is shown graphically. 
Let ab = initial volume; 
ce= final volume; 

oa= initial temperature absolute = TI ; 
oc= final temperature absolute = T 2 . 



ce-ab:ab::T 2 -T 1 :T 1 , or 0.3654:1 : :180:7V /. T l =492.6 F.A. 

Hence the ordinary Fahrenheit temperature is converted into 
Fahrenheit absolute degrees by the addition of 460.6 degrees. In 
a similar way, the ordinary Centigrade degrees are converted into 
Centigrade absolute degrees by the addition of 273 degrees. 

As all known gases have been liquefied, it is evident that none 
of them can be reduced to zero volume, as the law ceases to hold 
with a change of state! In the case of the so-called permanent 
gases the law has been shown to be true far below any tempera- 
ture required for engineering purposes.* 

The measurement of temperatures by thermometers seems a 
very elementary process. The difficulties are only appreciated 
when great accuracy is required. In theory, the mercury of the 
ordinary glass thermometer is supposed to expand equal amounts 
for equal increments of heat, the bore of the capillary tube is 
supposed uniform and to vary uniformly or not at all with the 
addition of heat, and the glass is supposed to be in such a molec- 
ular condition that the bore will not change with age. In accurate 
work, these quantities vary and accurate calibration is requisite 
before use. Some forms of pyrometers for the measurement of 
high temperatures depend upon the difference in expansion of 
copper and steel rods. In practice they do not work well. For 
very high temperatures the increase in electrical resistance of 
platinum-rhodium wires with increase of temperature is meas- 
ured and the temperature is then calculated. 

Ex. 4. Convert 77 F., 17 F., -13 F. to Centigrade degrees. 
Ex. 5. Convert 25 C., 5 C., -15 C. to Fahrenheit degrees. 
Ex. 6. Convert 79.36 B.T.U. to calories; 45 calories to B.T.U. 
Ex. 7. Convert 350 F. to Fahrenheit absolute temperature; to 
Centigrade absolute temperature. 

First Law of Thermodynamics. Heat can neither be created 
nor destroyed. Heat and mechanical work are mutually con- 
vertible, and a definite ratio exists between the thermal units 
that disappear (or appear) and the foot pounds of mechanical 
work that appear (or disappear). 

* See Journal Franklin Inst., Nov. 1906, page 375. 


Joule determined this ratio as 772 foot-pounds to 1 B.T.U. 
More recently Rowland fixed the ratio as 778 foot-pouncls to 1 
B.T.U. The latter value will be used. 

Joule allowed a known weight to descend a known distance, 
doing mechanical work by revolving a paddle in a vessel filled 
with water. Due precautions were taken to prevent heat radia- 
tion as far as possible. The heat that did radiate was calculated. 
The tendency of the water to circulate with the paddles was de- 
stroyed by properly placed baffle-plates. The known weight 
descending slowly a known distance gave the foot-pounds of 
work, and a known weight of water heated a measured number 
of degrees of temperature gave the equivalent number of thermal 
units. Of course this experiment was performed many, many 
times with proper precautions. For instance, the containing 
vessel and the apparatus in the water became heated and this 
amount of heat had to be considered. One way to do this was 
to heat the apparatus to the maximum temperature before 
putting in the water at the original temperature. The apparatus 
would thus lose to the water as much heat as it would afterwards 

Second Law of Thermodynamics. Heat cannot pass from a 
cold body to a hot one by a purely self-acting process. Heat in 
many ways is compared to water. We say that water will not 
run up-hill. And yet, nothing is more common than water going 
up-hill. It is witnessed in the rising sap in the tree, in the evap- 
oration of water, in all forms of water-working machinery. It is 
evident that the expression should be " water will not run up-hill 
unaided by some exterior agency." Similarly, heat flows unaided 
from a hot to a less hot body, but will not flow in the reverse 
sense, viz., from a cold to a hot body unless aid is received from 
some exterior source. In refrigeration, heat is made to flow from 
water into ammonia-gas at the same or a higher temperature by 
the following artifice. The ammonia-gas is compressed and 
cooled at the same time. Suppose that the heat abstracted is 
just equal to the heat that is added by compression. The result 
is liquid ammonia at the same temperature as the original gas. 
If the liquid ammonia is allowed to expand in pipes surrounded 
by water, the ammonia will abstract the heat that is required for 


its gasification from the pipes and water. The actual flow of heat 
is from 'the water to the colder ammonia-gas. The final result 
of the whole process is that heat is, by the aid of mechanical 
work, taken from one body (the water) and put into another (the 
ammonia) that was originally warmer. 

Steam-plant. The most elementary form of steam-plant con- 
sists in: 

A steam-boiler and chimney. 

An injector or steam-pump to supply the boiler with water. 

A steam-engine with the necessary piping. 

In a complex system we may have : 

Steam-boiler with mechanical grates. 

Induced or forced draft. 


Separators in the pipe-line. 

Multiple-cylinder engines or steam-turbines. 

Steam-jackets around the cylinders or in the cylinder- 

Some form of exhaust-reheaters. 

Some form of steam-condenser. 


Circulating pump. 

Feed- water pump. 

In non-condensing engines the exhaust-steam may pass 
through a feed-water heater. 

Steam-boiler (Fig. 3). The furnace, the heat-transmitting sur- 
face and the chimney must be designed so that a certain amount 
of coal can be regularly burned and the resulting heat utilized in 
the formation of steam with the greatest practical economy. The 
furnace-grate must be placed in such position that the fireman is 
able not only to distribute the coal properly but also can keep 
the incandescent fuel properly levelled, free from holes and clear 
of clinkers Great economy of combustion is only secured by the 
admission of the proper amount of air at the right time. When 
bituminous coal is thrown on the front of the grate it needs very 
little air as long as it is only drying out and heating up. When 



the coal commences to give off combustible gases the air-supply 
should be proportionally increased. 

The heating-surface of the boiler is that surface (above the 
center of gravity of the fire) which has water on one side and hot 









gases on the other. It should be so arranged that repairs may 
be easily made, the cleaning of either the inside or outside of the 
heating-surface should not be difficult, and its position should be 
such that the steam-bubbles forming on it should free themselves 
and rise easily. 


The draft, whether produced by a chimney or by means of 
fans, should be ample at all times. Chimney-draft is called nat- 

ural draft, while all forms of mechanically produced draft are 
termed artificial draft. 








Name of Part. 

Steam-cylinder (1 and 2) (pump 
body in small duplex pumps). 


Cushion-valve stuffing-box. 

Cushion-valve stuffing-box fol- 


Steam-cylinder head. 

Steam-cylinder foot. 




Steam-piston ring. 

Piston-valve ring. 

Steam-piston nut. 




Piston-valve chest. 

Steam-chest cover. 

Piston-valve-chest heads. 











20 J 






Name of Part. 

Steam-pipe screw-flange. 


Auxiliary valve. 


Piston-valve rod. 

Valve-rod nut. 


Valve-rod gland. 

Piston-valve-rod gland. 

Valve-rod stuffing-box nut. 

Piston-valve rod stuffing-box 


Valve-rod head. 
Valve-rod-head pin. 
Long valve-rod link. 
Short valve-rod link. 
Upper rock-shaft. 
Lower rock-shaft. 
Long crank. 
Short crank. 

* Not shown on cuts or sectional drawings. 

Artificial draft is easily regulated to effect the combustion of 
various kinds of fuel at different rates of combustion. Under 
proper management it makes more economic combustion possible 
by providing a more accurate regulation of the air-supply, poorer 
coal may be burnt, and a steadier supply of steam may be fur- 
nished independent of weather conditions. 

Where the draft is produced by a chimney the temperature of 
the gases leaving the chimney is generally between 500 F. and 
600 F. In Europe it is quite usual to put less heating-surface 
in the boiler than is usual in this country and then force the feed- 
water through the tubes of an economizer placed in the path of 
the gases to the chimney. With artificial draft it is possible to 
have the final temperature of the gases less than the temperature 
of the water in the boiler. This is done by having the coldest 
feed- water heated by the coldest gases (just entering the chimney) 
and the hottest feed (just entering the boiler) heated by the hot 
gases just entering the economizer (Fig. 3). If the boiler absorbs 
70% of the heat of the fuel, a boiler and economizer together may 
absorb 82%. Against this saving must be charged the interest 
on the cost of the economizer and fan and on the value of the 


space occupied, as well as the cost of running the fans and an 
allowance for depreciation and repairs. 

Fig. 4 illustrates a section of a small piston-packed pump that 
may be used for feeding the boiler. On page 13 are given the names 
of all its parts, as well as those of the air-pump and jet condenser 
shown in Fig. 8. The student should familiarize himself not only 
with the names but also with the use of all the different parts. 
There are numerous methods of actuating the steam-valve of feed- 
pumps, and the best way to comprehend the mechanism is to take 
the pumps apart and put them together again and operate the 
pump. The work must be done over again if the pump does not 
work properly. For engine details, see pages 17-22. 

Steam-separator. Later it will be shown that it is extremely 
desirable that the steam entering any steam-cylinder should be 
as free from water as possible. Advantage is taken of the fact 
that water is much heavier than steam and, by causing the steam 
to whirl, centrifugal force carries the water to the circumference 
of the containing vessel. When this is accomplished great care 
must be taken to keep the water out of the line of action of the 
steam-current or it will be picked up again. An efficient sepa- 
rator should furnish dry steam to the engine. Fig. 5. 

The Steam-engine. It is usual to speak of the work done by 
the steam in a steam-engine. Strictly speaking this is incorrect* 
We shall find that the steam is an agent, just as the connecting- 
rod is, receiving a certain amount of energy in the boiler and very 
inefficiently delivering a very small part of it in the engine. We 
shall learn that the difference in temperature of the steam as it 
enters and as it leaves a steam-cylinder is greater than the differ- 
ence in temperature of the hottest day in summer and the coldest 
day in winter. As the weight of steam entering and leaving a 
cylinder is the same, it is evident that a large amount of heat has 
disappeared. The engine has done work, however, and there must 
be some relation between the heat that has disappeared and the 
work that has appeared. At the very outset we see not only that 
the steam-engine is a heat-engine, but also the necessity of under- 
standing the laws of heat and the laws governing the interchange 
of heat and mechanical energy. Thermodynamics is the science 
that treats of the relations of heat and mechanical work. 



The origin of all the power of any steam-engine lies in the 
coal that is burnt on the boiler-grate. When we assume that a 
certain engine will make a certain number of revolutions, we 
either assume or we must provide sufficient boiler-power to de- 
liver such a quantity of energy to 
the engine that the latter, with an 
efficiency of 3 to 15 per cent, will 
develop the required power. The 
boiler-power is determined by the 
amount of coal burnt and the 
efficiency of the boiler. 

If steam is admitted alternately 
to each side of a steam-piston, for 
evident mechanical reasons the 
motion of the latter is given to a 
piston-rod that moves backward 
and forward in the same straight 
line. Usually this motion is com- 
municated to a cross-head, and the 
reciprocating motion of the latter is 
converted into a rotary motion by 
means of a connecting-rod and 
crank. Such an engine is called a 
double-acting engine. Where steam 
is admitted to only one side, the FIG. 5. 

connecting-rod may be directly Station Separator, 

connected to a pivot-pin in the piston. When a plane can be 
passed through the connecting-rod and the crank-arm, the crank 
is said to be on a center. When the piston is nearest the crank 
it is on the crank center, when it is farthest away it is on the head 

The action of steam in a steam-engine is as follows : The pres- 
sure of the steam from the boiler causes the piston to move through 
a part of its stroke to a point at which, by some kind of automatic 
mechanism to be described later, the steam-supply from the boiler 
is cut off. The piston must complete the stroke having only the 
diminishing steam-pressure and the energy stored up in the mov- 
ing parts to supply the pressure necessary to overcome resistance. 


If the crank-pin has a uniform motion, by Newton's First Law 
the resultant of all the pressures exerted on the crank-pin must ex- 
actly equal the resultant of all its resistances just as if the crank- 
pin were at rest. If at any time there is a difference, acceleration 
(change of velocity or variable speed) positive or negative im- 
mediately follows. It is evident, then, that variation in rapidity 
of motion causes the equality that must exist between the driv- 
ing and resisting forces. 

When the piston has reached the end of its stroke all the steam 
that produced its motion must be allowed to escape to some place 
of lower pressure, otherwise the piston on the return-stroke would 
compress the steam. Compression in excess lessens the amount 
of external work done, and is neither desirable nor economical, 
as the object of an engine is the production of external work. 

The steam may be exhausted into : 

(a) A receiver or vessel that will serve as a reservoir to 
hold the steam till it is fed into another cylinder 
working in a lower cycle of pressures than the pre- 
ceding one. 

(&) The atmosphere. 

(c) A condenser. 

After an engine has been started and is running regularly, it 
is evident that, when exhausting into a receiver, the amount of 
steam entering that vessel must exactly equal the amount leav- 
ing, as otherwise the pressure in that vessel would continuously 
increase or decrease, which would prevent the engine from work- 
ing. The pressure in the receiver will fluctuate with the admis- 
sion and emission of steam and may be greater or less than the 
atmospheric pressure. 

When the steam exhausts into the atmosphere, the back pres- 
sure on the piston will be the barometric or atmospheric pressure 
increased by the pressure necessary to overcome the frictional 
resistances of the pipe system between the cylinder and the at- 
mosphere. The usual assumed back pressure then is either 14.7, 
or more roughly 15 pounds per square inch where pipe friction 
may be neglected. 

When the steam is exhausted into a condenser the back pres- 



Lilting Bolt Holes 

Side Liners 

Oil Grooves 

Babbitt ^Xx^ " Bottom SheU 

FIG. 6. Lower Brass. 

Bottom Wedge 
, Collar 

Bottom Wedge Adjusting Bolt 
Lock Nut 

Main Bearing Bottom Wedge and Adjusting Bolt 
(Furnished only when specially ordered; 

Fro. 7. 

Oil Cups 

Main Bearing Cap Cover 
Hand Hole Cover 
Main Bearing Cap 
Lock Nut 

Side Liner Setscrews 
Bottom Wedge 
Adjusting Bolt 
(Furnished only when 
epecially ordered) 

FIG. 8. Bearing Details. 






Planished Sheet Steel Laggi 
\Heat insulating Filling 

Corliss Steam Valve. 
Back Cylinder Head 

Back Cylinder Head Studs 
Baok Cylinder Head Bonne 

Exhaust Port 

Corliss Exhaust Valve 

Throttle Valve 

Planished Steel Lagging 
Heat insulating Filling 

.Corliss Steam Valve Chamber 
Front Cylinder Head 

Front Cylinder Head Studs 

Piston Rod Gland Studs 
Piston Rod Gland 

\Piston Rod Packing 


Corliss Exhaust Valve 
Planished Sheet Steel Lagging 
Heat insulating Filling 

Exhaust Chest 

Exhaust Flange 
Exhaust Opening 

Exhaust Pipe' 

FIG. 11. Cross-section of Corliss Cylinder. 

et Screw 

Built up Piston 

Piston S E ider 

Bull Ring 

Piston Nut 

FIG. 12. Pistcn Details. 

Babbit and Harris 

Brass Keeper Packing Rings 

(Coiled Spring \ 

Solid Piston with Babbit 
and Harris Packing 

FlG. 13. 






sure against the piston may be reduced to 1/2 pound per square 
inch above absolute zero of pressure with the very best condenser 
equipment, or to 3 pounds per square inch with an ordinary equip- 
ment. Keeping in mind that the temperature of steam depends 
in some way on the rate of vibration of the molecules of the 
steam, and its pressure depends on the rate or number of molec- 
ular impacts on the containing vessel, we readily see, when steam 
is deprived of 90% of its heat, and its volume reduced to 1/1500 
of the volume it possessed when entering the condenser, that 
there must necessarily be a great reduction of pressure. The 
unavoidable pressure in the condenser would be that due to 
the vapor of the feed-water if there were no leakage of air 
through the stuffing-boxes and the joints of the condenser 
and exhaust-piping, and no air and other non-condensible gases 
in the feed-water. If these gases accumulated, it is evident 
that the back pressure might finally be greater than that of the 
atmosphere. Hence an air-pump properly designed and placed 
must be used to remove all the condensed steam, vapor, and air. 
This pump discharges its contents into a tank called a hot-well. 
The vapor and air escape into the atmosphere, and the solid water 
can then drain downwards into the suction-chamber of a feed- 
pump which forces it through the feed-pipe into the boiler. There 
are two principal methods of condensation : 

(a) By means of a surface condenser. 

(b) By means of a jet condenser. 

Surface Condenser and Air-pump. One form of a surface con- 
denser with its necessary pumps is shown in Fig. 16. The exhaust- 
steam from the engine-cylinder enters the condenser at A and is 
divided into many streams by the scattering-plate 0. The steam 
is condensed into water by coming into contact with the cool 
tubes and then flows down pipe B (closed to spaces V and S) into 
space below valves S. The suction valves, S, open upward. 

It is well to keep in mind that there is no motion in steam, 
water, or air unless there is a difference of pressure. The ex- 
haust-steam flows into the condenser only so long as the pressure 
there is less than the pressure in the cylinder. There is no such 
thing as the vacuum drawing or sucking in the steam. Hence we 



see that the valve S will remain open only so long as the pressure 
in the pump is less than the pressure in the condenser decreased 
by the pressure necessary to overcome the compression of the 
spring that tends to seat S. If there is not enough water to fill 
the pump, air and steam-vapor will fill the remaining volume 
above the water. On the return- stroke, S will close and valve V 
will open. The air will be forced past the open valve V and will 
be followed by such part of the water as is not required to fill 
the clearance-space that exists in the cylinder and passageway 
between the valve V and the piston when on the dead- center. 
From the chamber above V the air escapes into the atmosphere, 
and the water runs through a pipe (shown as a dotted circle) to 
the hot-well. The vertical pipe at B connects B and space S, but 
is closed to space V. 

Circulating Pump. On the right of the same figure is a 
cross-section of a circulating pump. It is evident that the cool- 
ing-tubes mentioned above would soon acquire the temperature 
of the entering steam if the heat is not absorbed by some other 
medium. The object of the circulating pump is to take water at 
some low temperature, as 60 to 90 F., and circulate it through 
the tubes in such manner that it will absorb the greatest amount 
of heat possible. It will be found that this can best be done by 
bringing the coolest water in contact with the coolest steam and 
the hottest water in contact with the hottest steam. In this case 
the circulating water passes through the pump in the direction of 
the arrows. It then passes through the lower nest of tubes in the 
direction of the arrows, the water-t'ght diaphragms determining 
the direction of flow. It circulates through the upper nest of 
tubes in a similar manner, and when it leaves the condenser 
it has a temperature of 110 to 130 F., each pound of water 
having absorbed some 50 or 40 B.T.U. (110-60 to 130-90), more 
or less. This circulating water is often called injoction-water as 
it enters the condenser, and is called discharge-water as it leaves. 
The condensed steam is called feed-water, and tho feed-pump is 
the one that is used to force it into the boiler. Hot feed- water 
must never be LIFTED by the pump, as the pump-chamber will fill 
with vapor on the suction-stroke, and the requisite pressure will 
not be obtained on the delivery-stroke to force the water into the 



Jet Condenser. Fig. 17 represents a jet condenser and its air- 
pump. This is an old form that is rather uneconomical of space, 
but it illustrates the principles clearly, which is important. The 
exhaust-steam enters the condenser by the pipe just above the 
water-jet. The injection water and steam come into actual con- 
tact and assume a common temperature. The air-pump in this 
case is vertical (which is desirable) and contains three large cir- 
cular valves. These are made of hard rubber, are held fast in the 

FIG. 17. 

center, and are bent up in a saucer shape with an excess of pres- 
sure on the bottom side. The duty thrown on one valve should 
be distributed among several valves. The lowest is the foot- 
valve, the one in the piston is a bucket-valve, and the top one is 
the deli very- valve. Raising the piston reduces the pressure in the 
space between it and the foot-valve. If the condenser pressure 
is greater than this, the foot-valve rises and water and more or 
less air or vapor enters the air-pump. The air passes through the 
water so that when the piston descends the former passes first 
through the bucket-valves of the piston. The water passing 
through last serves to seal the valves and fill the clearance volume. 
A small modern jet condenser is shown in Fig. 18. 



The Bourdon Gage (Fig. 19). This gage is used to indicate 
pressures. These are indicated on a marked dial by the move- 
ment of a hand. The latter receives its motion through a 
mechanism which multiplies the motion of the free end of a 
curved elastic metal tube of flattened or elliptical cross-section. 
The long axis of this section is perpendicular to the plane of the 
tube. The steam or gas is admitted at the fixed end into the 
interior of the elastic tube. As the pressure increases, the 

FIG. 19. Double Spring Bourdon Gage. 

elliptical section becomes more round. This tends to increase 
the inside arcs at right angles to the section, and as a conse- 
quence, the free end tends to move away from the fixed end. 

To measure very heavy pressure in hydraulic work, the long 
axis is placed parallel to the plane of the tube or dial. The 
effect of increase of pressure is now to shorten the inner arcs 
and increase of pressure is followed by the movement of the 
free end toward the fixed end. 

This gage may also be used to measure vacuum or the differ- 
ence between the absolute pressure in some vessel and the 



absolute pressure of the atmosphere. When so used it is usual 
to mark it in inches of mercury rather than in pounds. 

Mercury Column. Let Fig. 20 represent a U-tube, about 
40 inches long, open at one end, C, to the atmosphere and 
connected to the condenser or other source of vacuum at 

D. Let it be filled with perfectly 
pure mercury free from tin or other 
adulterations to some level, AB, if 
the pressure at D and C are equal. 
If now the pressure is reduced in D, 
the mercury in the left leg will rise 
and it will fall in the right leg. At 
any instant, let the distance EF mark 
the difference of level. 

As the mercury is in equilibrium, 
the sum of the vertical forces must 
be zero, we have : The pressure in the 
condenser in pounds per square inch + 
the weight of the column of mercury, 
EF, must equal the pressure of the 
atmosphere in pounds per square 

Suppose the pressure in the con- 
denser is reduced to absolute zero and 
1 the mercury rises to some point G 
then HG represents the weight of the 
atmosphere. Evidently then GE + 
FH, or twice GE, represents the ab- 
solute pressure in the condenser when 
the vacuum therein is not perfect. Now the height HG, at the 
sea-level, is ordinarily 30 inches of mercury, and the height EF 
is the quantity marked on all forms of vacuum gages. Hence, 
ordinarily 30 inches minus EF in inches is the absolute pres- 
sure in the condenser. To be exact, instead of 30 inches 
the height of the barometer in inches should be used. If, 
for instance, the barometer reading is 29.83 inches and the 
vacuum is 26.7 inches the absolute pressure in the condenser 
is 29.83-26.7=3.13 inches. 

FIG. 20. 



If we call the atmospheric pressure 15 pounds per square 
inch and the barometer 30 inches, it is evident that 1 inch is 
equivalent to | pound pressure, but more accurately, 1 inch 
equals 0.491 pound. 

Names of Parts. It is desirable that the student learn, as soon 
as possible, the technical names of the different parts of the steam- 
engine, the steam-boiler, and the various auxiliaries and appliances 
of a steam-plant. He should recognize, know the use of, and make 


fair sketches from memory of pistons, piston-rods, cross-heads, 
cross-head pins, cross-head slipper, cross-head guides, connecting- 
rods (both strap and club end), gib and key, crank-pin, crank-arm, 
crank, crank-pin brass, crank-pin journal, bearing, liner, cap-nuts, 
frame back-bone, holding-down bolts, cylinder-bonnets or covers, 
cylinder-heads, junk-ring, follower, springs, rings, boss of a wheel, 
eccentrics, eccentric-sheaves, eccentric-rods, stuffing-boxes, pack- 
ing-glands, Stephenson link, dash-pot, reach-rod, parallel rod, 
saddle-plate, rocker, separator, steam-loop, steam-traps, sight- 
feed lubricator, indicator-cocks, reducing motion, steam-gage, 
vacuum-gage, receiver-gage, jack-shaft. He should trace the 
course of the steam from the boiler through the steam-pipes, the 
engine, the condenser, and the pumps back to the boiler. Engines 
and pumps must be taken apart that this may be done. 

Rates versus Quantities. It is important to distinguish between 
pressure and pressure per square inch. Pressure per square inch 
is a rate or an intensity. Pressure per square inch can never be 
pressure any more than velocity can be distance. Pressure per 
square inch multiplied by square inches gives pressure, just as 
velocity must be multiplied by time to give distance. 

An expression for work is used which is so terse that much con- 
fusion results unless its factors are kept clearly in mind : 

where P= pressure per SQUARE FOOT; 


Keep clearly in mind that V =AL, where A =area in square feet 
and L is distance in feet. Therefore PA = pounds and L=feet, 
so that 

PAL =PV = foot-pounds. 

Evidently the same result will be obtained if P is taken in 
pounds per square inch, if we take care to use A in square inches. 
In other words, P is now only 1 /144th of its former value, but A 
is 144 times as large. 

In steam-engine problems it is frequently convenient to use 
P in pounds per square inch. Evidently then, to obtain foot- 
pounds when P is in pounds per SQUARE INCH, we must take the 
area of the piston in SQUARE INCHES and the stroke in FEET. 


Graphical Representation of Work. As external work is the 
product of two factors, it may be represented by a closed area, as 
in Fig. 37. The ordinates represent pounds and the abscissas 
represent distance in feet. If the ordinates represent a rate or 
pressure in pounds per square inch, then the area of the piston in 
square inches is assumed as a constant multiplier. If the ordi- 
nates are laid off as pounds per square foot, the area of the piston 
in square feet is assumed. 

Horse-power. When work is done at the rate of 33,000 foot- 
pounds per minute, then that RATE is tersely, but arbitrarily, 
termed a horse-power. Hence if the total number of foot-pounds 
of work done by a machine per minute be divided by 33,000 the 
quotient is the rate of the machine in horse-power. 

Indicated Horse-power. The mean effective pressure that is 
exerted by the steam on the piston of a steam-engine may be 
found practically by means of an instrument called the steam- 
engine indicator, or it may be calculated from theory. For the 
present, we shall assume that we have the mean effective pressure 
per square inch. This multiplied by the area of the piston in 
square inches gives the total pressure. Multiplying the stroke in 
feet by the number of strokes per minute gives the distance 
through which, or over which, this pressure is exerted in a minute. 
The product of the total pressure and the total distance passed 
over per minute gives the foot-pounds per minute. 

foot-pounds of work per minute PLAN 
33,000 = 33,000' 

where P =mean effective pressure per square inch; 
L= length of stroke in feet; 
A =area of piston in square inches; T 
A' =2 X revolutions per minute (strokes) for double-acting 


= 1 X revolutions per minute for single-acting engines ; 
= the number of impulses for gas-engines. 

Ex. 8. Find the indicated horse-power of an engine having a cyl- 
inder 20 inches in diameter and a stroke of 48 inches; the mean effec- 
tive pressure per square inch of piston area is 33 pounds; the number 


of revolutions per minute is 50. The engine is double-acting. In 
practice this is expressed more tersely. The diameter of the cylinder 
is always the first dimension and the stroke is the second one. Thus 
the above may be written: Find the I.H.P. of a 20"X48" engine; 
revs. 50; M.E.P. = 33. 

Ex. 9. Required the M.E.P. of a 12"X20" engine of 50 I.H P.; 
revs. 100. 

Ex. 10. Find the diameter and stroke of an engine to give 100 
I.H.P. with a M.E.P. of 44 pounds, assuming the stroke to be 3/2 the 
diameter of the cylinder, the number of revolutions being 50 per 

The ordinary rating of a machine in horse-power should be 
the rate at which it is safe or economical to run it. Temporarily, 
engines may be made to develop power at greater rates than 
their normal ones, but in the end hot bearings, lack of economy, 
breakage, or other evil will probably arise. In some cases, how- 
ever, it is economical to drive an engine to the limit of breakdown 
and buy a new one when necessary. In design, due regard must 
be paid to demands for power for short-time intervals. This is 
illustrated in the powerful motors required in street-car work. 
Rates Equivalent to a Horse-power : 

33,000 foot-pounds per minute. 

550 foot-pounds per second. 

1,980,000 foot-pounds per hour. 

42.42 B.T.U. per minute. 

2545 B.T.LI, per hour. 

746 watts or 746 volt-amperes. 

1 kilowatt = 1000 watts =1.3405 horse-power. 
Brake Horse-power. This term applies to the power delivered 
from the fly-wheel shaft of the engine. It is the power absorbed 
by a friction-brake applied to the rim of the wheel or to the 
shaft. A form of brake is preferred that is self-adjusting to a 
certain extent, so that it will of itself tend to maintain a con- 
stant resistance at the rim of the wheel. 

"One of the simplest brakes for comparatively small engines 
which may be made to embody this principle consists of a cotton 
or hemp rope, or a number of ropes, encircling the wheel, ar- 
ranged with weighing-scales or other means for showing the strain. 



An ordinary band-brake may also be constructed so as to embody 
the principle. The wheels should be provided with interior flanges 
for holding water used for keeping the rim cool. 

"A self-adjusting rope-brake is illustrated in Fig. 21, where it 
will be seen that, if the friction at the rim of the wheel increases, 
it will lift the weight, A, which action will diminish the tension 
at the end, B, of the rope, and thus prevent a further increase in 
the friction. The same device can be used for a band-brake of 
the ordinary construction. Where space below the wheel is lim- 

FIG. 21. Hops-brake. 

Standard Engine Tests, 

FIG. 22. Rope-brake. 

ited, a cross-bar, (7, supported .by a chain-tackle exactly at its 
center-point may be used as shown in Fig. 10, thereby causing 
the action of the weight on the brake to be upward. A safety- 
stop should be used with either form to prevent the weights 
being accidentally raised more than a certain amount. 

"The water-friction brake is specially adapted for high speeds 
and has the advantage of being self-cooling. The Alden brake is 
also self-cooling. 

"A water-friction brake is shown in Fig. 23. It consists of 
two circular discs, A and B, attached to the shaft, C, and revolv- 



ing in a case, E, between fixed planes. The space between the 
discs and planes is suppliei with running water, which enters at 
D and escapes at the cocks, F, G, H. The friction of the water 
against the surfaces constitutes a resistance which absorbs the 
desired power, and the heat generated within is carried away by 
the water itself. The water is thrown outward by centrifugal 
action and fills the outer portion of the case. The greater the 
depth of the ring of water, the greater the amount of power ab- 
sorbed. By suitably adjusting the amount of water entering and 
leaving, any desired power can be obtained. Water-friction 

FIG. 23. Alden Brake. 

brakes have been used successfully at speeds of over 20,000 revo- 
lutions per minute." 

Brake Horse-power. The power that an engine can deliver is 
termed its brake horse-power, since it may be measured, when 
small in amount, by some form of brake-dynamometer (Fig. 21). 
The difference between the indicated and the brake horse-power 
is the friction horse-power. After an engine test, the load is 
thrown off the engine when possible and cards are taken. From 
these the power to run the engine with no load is determined. 
This power is evidently the friction horse-power, and by subtract- 


ing it from the indicated horse-power the brake horse-power is 

The mechanical efficiency of the engine is =j ^r p 

As seen above, the minute is used as the unit of time in meas- 
uring the rating of an engine in horse-power. For some other 
purposes a minute is too small a unit for convenience. The con- 
sumption of water and coal per minute would be small decimals 
that would be awkward to use and difficult to remember. Hence 
the consumption per hour of those articles for each horse-power 
indicated by the engine is the unit adopted. Hence such an 
expression as "Consumption of coal per H.P.-hour =2.1 pounds " 
is to be interpreted " There were burnt on the grate of the furnace 
2.1 pounds of coal per hour for each I.H.P." In other words, for 
N horse-power the total consumption of coal per hour would be 
2.1 A 7 pounds. 

Efficiency. A crude definition of efficiency is 

What you get 
What you paid for it* 

While it is not difficult to express the actual efficiency of a mech- 
anism under certain circumstances, the theoretical efficiency can 
only be expressed under ideal conditions. For instance, the 
efficiency of a wood-turning machine might be very low at low 
speeds and very high at high speeds; its efficiency might be low 
when operated by an inexpert workman and high when operated 
for a short time by an expert. 

Boiler Efficiency. The efficiency may refer to the grate and 
boiler, or the grate, boiler, and economizer (if there is one). The 
efficiency is 

B.T.U. delivered by the boiler per hour 
Heat in the coal burnt per hour 

The heat delivered is measured from the temperature of the feed- 
water taken by a thermometer placed in the feed-pipe close to 
the boiler. 

The heat in the coal may be found by calculation from a 


chemical analysis of a sample of the coal, or a sample may be 
burnt in a coal calorimeter and its heat equivalent found. 

If the percentage of carbon present in one pound of a sample = C 
"hydrogen " " " " " =H 

" li " " oxygen " " " " " " = 

the total B.T.U. in one pound of coal = 14,5000 + 62,000(H--A 

The maximum efficiency of a given boiler would only be secured 
when the coal in quality, fineness, thickness of bed, rate of burn- 
ing was best suited to the kind of grate, furnace, and intensity of 
draft. The method of firing, the amount of air admitted, and 
other variables dependent on the skill of the fireman enter into 
the result. 

To avoid these ambiguities the A. S. M. E. has adopted a 
standard boiler and a standard coal. The standard coal when 
burnt in a standard boiler is to give 12,500 B.T.U. , of which the 
boiler is to deliver 10,000 B.T.U., having consequently an assumed 
efficiency of 80%. 

Boiler Horse-power. The capacity of a boiler to form steam 
is expressed in the following terms : Suppose water, at 212 F., 
is fed to a boiler and converted into steam at that same tem- 
perature, 212 F. A boiler horse-power is the capacity to evapo- 
rate 34J pounds of water per hour from water at 212 F. into 
steam at 212 F. We shall find that it takes 966 thermal units 
per pound of water, so that to evaporate 34J pounds of water re- 
quires 966 X34J = 33,305 B.T.U., or approximately 33,000 B.T.U. 

This rate must not be confused with an engine horse-power. 
The latter is a rate in foot-pounds per minute but the former is 
a rate in thermal units per hour. They are not directly related. 
A 500-horse-power engine might require boilers of any power 
varying from 150 to 1000 boiler horse-power, depending on the 
thermal efficiency of the engine. 

Rate of Evaporation. Good water tubular boilers evapo- 
rate 8-10 pounds of water per pound of coal. Heating boilers 
below 20 horse-power evaporate 4-6 pounds of water per pound 
of coal. With the usual poor firing found in practice these 
results are frequently too high by one or two pounds of water. 



Grate Area. The grate area required may easily be found 
from the formula, 




G= grate area in square feet; 

E = pounds of water evaporated at 212 F. per pound of coal; 

C = pounds of coal burned per square foot of grate area per hour. 

It is usual to assume a combustion of 15 pounds of coal per 
square foot of grate with natural draft. It ranges from 10 or 
12 for anthracite to 25 for gaseous bituminous coal. 


Pounds of Steam per I.H.P. per 



Simple high speed 



Simple medium speed 



Simple Corliss 



Compound high speed. . . 


22-1 & 

Compound medium speed 



Compound Corliss. . . 



Compound Corliss, over 500 I.H.P 




Type of Pump. 

Pounds of Steam per 
Hour per Delivered 
Horse -power. 

Simple non-condensing 


Compound non-condensing 


Triple non-condensing 


High duty non-condensing 


The tables are arranged in the order of steam consumption, 
but the amounts given are for engines in good condition. If 
the valves or pistons leak the amounts given above may be 
exceeded by thirty to forty per cent. While the boiler supplies 
the above weights of steam per I.H.P. of the engine, each pound 
(weight} of the steam indicated above needs more heat than 
that required to convert one pound of water at 212 F. into steam 
at 212 F. This variable factor called the " Factor of Evapora- 
tion" depends upon the feed-water temperature and the boiler 
pressure. For the present, this factor may be assumed to be 


1.2. To obtain the corresponding boiler power then it will be 
necessary to multiply the total steam consumption of the engine 
by 1.2 and the quantity so found should ordinarily be increased 
by 10 to 20% to allow for auxiliaries, future expansion and over- 
loading the engine. 

For example, what boiler horse-power would be required 
for an electric light plant containing 300 I.H.P. of high-speed 
compound engines? 

If run non-condensing the engines would require 
300X28=8400 pounds of water per hour. 

The heat required to evaporate this water would be equal to 
that required to evaporate 8400X1.2 = 10,080 pounds of water 
from and at 212 F. Allow 15% of the last amount for auxil- 
iaries and unforeseen emergencies and we have 10,080X1.15= 
11,592 pounds of water to be evaporated from and at 212 F., or 

as the necessary boiler horse-power. 

The factor of evaporation may be obtained more accurately by 
substitution in the following equations. 
Let F e = factor of evaporation; 
T\ = temperature of the steam ; 
1= temperature of the feed-water; 

TH = total heat in thermal units to produce one pound 
weight of steam at temperature Ti from feed- 
water at t\. 

TH = 1091.7+ . 305(^-32) - (t -32) 


Steam Consumption of Pumps. The steam consumption 
of pumps is very great, and, in the case of pumps which are started 
and stopped at intervals, it is excessive through the condensa- 
tion that occurs (during the quiescent intervals) in the steam- 
pipe leading to the pump. Allow 120 pounds per horse-power 
hour for boiler feed-pumps running at a practical constant rate; 
allow 200-300, for power actually used, if they are started and 
stopped frequently. 



To obtain the work of the pump multiply the weight of 
water lifted by the vertical height in feet through which the 
water is lifted. This estimate must be increased by a percent- 
age based on pump slippage, friction, and other losses. An 
ordinary allowance is 50%. In case the resistance is given in 
pounds pressure per square inch, as occurs when water is pumped 
into a boiler, divide the pressure in pounds per square inch by 
0.4 and thus obtain the " head in feet." 

Electric Lighting. Direct-current arcs usually use 10 am- 
peres at 42 to 52 volts, the most satisfactory light being at 46 
to 47 volts. 

Enclosed Arcs. Direct-current enclosed arcs consume about 
5 amperes at 80 volts or 400 watts. Alternating enclosed arcs 
usually take a current of 6 amperes at 70 or 75 volts. 

The power required for electric lighting may be determined 
by assuming that one horse-power, at the lamps, is consumed 
by the number of lamps given below. 

Number of Lamps. 

Type and Power of the Lamp. 

1 to 1.5 

16 candle-power incandescent 
32 candle-power incandescent 
Half-arc open 
Full arc open 
Closed arc 

Assume the mechanical efficiency of the engine as 90%, the 
efficiency of the generator as 90%, and the line efficiency when 
the lamps are in or near the building as 90%; we have a total 
efficiency of 73% between the engine and the lamps. From 
these data the boiler horse-power may be determined. 

Example. What boiler horse-power will be required to 
furnish steam to high-speed compound non-condensing engines, 
using 28 pounds of water per I.H.P., which drive generators 
for the following lights: 2000 16 c.p. incandescents, 1000 32 c.p. 
incandescents, and 50 A.C. closed arcs. 

2000-^-12 = 167 

1000 -j- 6 = 167 

50^- 1= 50 


Dividing 384 electrical horse-power at the lamps by 0.73 we 
obtain 525 I.H.P. for the engines. 

Required the pump displacement per minute and the boiler 
horse-power to operate the feed-pumps for 300 I.H.P. of high- 
speed compound engines. Water lifted 5 feet, boiler pressure, 
160 pounds. 

If run non-condensing, the actual requirements are 300X28 
= 8400 pounds of water per hour. The theoretical displace- 
ment should be twice this amount to allow for slippage, ineffi- 
ciency of pump and emergencies. Pump displacement per 
minute should be 


60X6^5 = 4 ' 5cU ' ft - 

/160 _\8400 

\~4~ /~60~ 
The delivered horse-power will be 33 QQQ = 1.7. 

The actual horse-power may be 1.7x1.5=2.5. 

Assume a water consumption of 100 pounds per horse-power 
and it is evident that the boiler must evaporate 250 pounds of 
water per hour for the pump. Assume a factor of evaporation 
of 1.2 and the boiler horse-power required will be 


The steam needed by the engines is 525X28=14,700 pounds. 
With a factor of evaporation of 1.2 we have 


as the boiler horse-power required. 

Combining Efficiencies. If one pound of coal contains 14,000 
B.T.TJ. and the efficiency of the boiler is 75%, what percentage 
of the heat liberated in the furnace of the boiler appears as 
energy at the lights? Assume 28 pounds as the water rate of 
the engine. 


The engine receives 28x966x1.2=32,457 B.T.U. from the 

^^ ooo v fio < ( 

boiler per hour and utilizes ' "" = 2545 B.T.U. ' 7 

I I O 


Thermal efficiency of the engine is 7T A ^ = 7.8%. The com- 

bined efficiency is then .75 X. 078 X. 90 X. 90 X. 90 = .04. Hence 
14,000 X. 04 = 560 B.T.U. is consumed at the light. 

Heat Consumption of a Steam-engine Plant.* "The heat con- 
sumption of a steam-engine plant is ascertained by measuring the 
quantity of steam consumed by the plant, calculating the total 
heat of the entire quantity and crediting this total with that por- 
tion of the heat rejected by the plant which is utilized and re- 
turned to the boiler. The term engine-plant as here used should 
include the entire equipment of the steam-plant which is con- 
cerned in the production of the power, embracing the main cyl- 
inder or cylinders, the jackets and reheaters, the air, circulating 
and boiler-feed pumps if steam-driven, and any other steam- 
driven mechanism or auxiliaries necessary to the working of the 
engine. It is obligatory to thus charge the engine with the steam 
used by necessary auxiliaries in determining the plant economy, 
for the reason that it is itself finally benefited, or should be so 
benefited, by the heat which they return, it being generally 
agreed that exhaust steam from such auxiliaries should be passed 
through a feed-water heater and the heat thereby carried back 
to the boiler and saved. The indicated horse-power is that de- 
termined by steam-engine indicators. It should be confined to 
the power developed in the main cylinder or cylinders. 

"The temperature of the feed- water is the actual temperature 
under working conditions and should be taken near the boiler. 

"The heat consumption of gas- and oil-engines of the internal- 
combustion class is found by ascertaining the total heat of com- 
bustion of the particular fuel used, which should be determined 
by a calorimeter test, and multiplying the result by the quantity 
of fuel consumed. In determining the total heat of combustion, 
no deduction is made for the latent heat of the water-vapor in the 
products of combustion. 

* See Trans. A. S. M. E., Vol. XXIV. Standard Rules. 


"The indicated horse-power should be confined to the power 
developed in the main cylinder or cylinders, and should not in- 
clude that developed in the cylinders of auxiliaries. 

" The thermal efficiency is expressed by the fraction 

B.T.U. per H.P. per hour" 

The heat-unit expression of economy does not in itself show 
whether the engine is working to its best advantage any more 
than the expression of the steam consumption, since the tempera- 
ture at which the heat is supplied is a very important factor in 
determining the efficiency of engines, as there is only a limited 
choice in the temperature at which the heat is rejected. The 

m rji 

highest possible efficiency being measured by ^ b , where T a 

1 a 

is the absolute temperature of the steam entering the engine and. 
Tb is the absolute temperature of the condenser. 

Ex. 11. If the net or brake horse-power of an engine is 92% of 
the I.H.P. and the electrical horse-power is 94% of the brake horse- 
power, find the I.H.P. of an engine to give 750 kilowatts. 

Ex. 12. If the above efficiencies are assumed, find the coal re- 
quired per kilowatt-hour if 2 pounds are required per hour per I.H.P. 

Ex. 13. If the heat received by each pound of steam from the 
boiler is 1100 B.T.U. , and the engine utilizes only 10% of this in 
work as shown by the indicator-card, how many pounds of water per 
hour must be pumped into the boiler per I.H.P.? 

A graphical illustration of the answer to the question "What 
becomes of the heat-units ? " is given in Fig. 24 for an excep- 
tionally economical engine. 

Of the 186,600 B.T.U. generated by burning coal on the grate 
there is a loss of 10,000 units by radiation from the boiler; the 
remainder divides into two streams. About 70% is absorbed by 
the boiler and the rest passes through an economizer on its way 
to the chimney. The feed-water contains 5450 units when it 
reaches the economizer, and there it absorbs 15,750 more units 
that otherwise would have been wasted. The heated feed- water 
receives the hot water from the jackets and delivers (after losing 
some heat by radiation) some 27,650 units to the boiler. A total 
then of 159,250 units have been saved, and with small loss are 



delivered to the engine. Here the losses are very great, only 
25,390 units being delivered by the engine. As this result is 
obtained in a record-breaking engine, the amount delivered in an 

ordinary engine or in an uneconomical one is left to the reader. 
It is the province of this book to discuss the laws that govern the 
saving and the wasting of heat in the steam-engine and other 



In Fig. 25 we have a similar diagram for an ideal plant, show- 
ing that 104,200 B.T.U. only are necessary to do the same work 
in a purely theoretical engine working between the same tempera- 

ture limits. The ideal efficiency may be approached but never 
will be reached by any practical engine. 
The names of engines indicate: 

Their use: Marine, rolling-mill, agricultural, electric-light, 
saw-mill, donkey, switch. 


The number of revolutions : High, medium, slow-speed. 

Character of steam expansion: Simple, compound, triple- 

Treatment of the exhaust: Condensing or non-condensing. 

Position of the cylinders: Horizontal, vertical, inclined, 
direct-acting, inverted. 

Number of sides of piston acted upon by the steam : Single-, 

Character of the valve-gear: Corliss, gridiron, plain-slide, 
double-poppet, Marshall, piston-valve. 

Character of the cut-off gear : Meyer, Buckeye, Corliss, au- 
tomatic, adjustable, variable. 

Kind of governor: Throttle, fly-ball, fly-wheel, or shaft 

Position of valve-gear with reference to the cylinder and 
shaft: Right-hand, left-hand engine. 

Direction of rotation : Running over, running under. 

Movability: Stationary, portable, marine, steamboat, dredge. 

Connection to the crank-pin: Overhung, tandem, cross- 

Reversibility: Link, shifting eccentric. 

Enclosing of the moving parts : Enclosed engines. 

Concentration on one base-plate : Self-contained engines. 

Ex. 14. What I.H.P. will be required to raise 100,000,000 gallons 
of water per day through a height of 40' if the combined efficiency of 
engine and pump is 50%? 

Ex. 15. If the total B.T.U. in one pound of coal is 14,500, what 
is the combined efficiency of an engine and boiler if 200 pounds of 
coal are burnt per hour in the furnace of the boiler to run a 100-I.H.P. 
engine. . 

Ex. 16. One pound of coal contains .88 pound of carbon, .03 
pound of hydrogen, .04 pound of oxygen; the remainder is ash. 
33% of the heat generated is lost in the chimney gases. How many 
B.T.U. are absorbed per hour if 200 pounds of coal are burnt per hour? 

Ex. 17. If the work (expressed in B.T.U.) done by an engine, as 
shown by the indicator-card, is 8% of the heat that was given to the 
steam in the boiler and it is known that the boiler only absorbs 70% 
of the heat that is in the coal, find the number of pounds of coal that 
are required per hour per I.H.P. 


Steam-engine Indicator. The steam-engine indicator has but 
one fundamental requirement, namely, to give a graphical record 
of the steam or other gaseous pressure that existed on either side 
of a piston of an engine for any or all positions of that piston. 
Two quantities must be absolutely exact the measure of the 
steam pressure and the measure of the contemporaneous position 
of the piston. Some of the numerous sources of error will be 
pointed out later. Fig. 26 illustrates a cross-section of the Crosby 
indicator. Steam from one side of the engine-piston is admitted 
through 6 to the piston, 8, whose movement, resisted by the pressure 
of the atmosphere and the compression of the spring surrounding 10, 
is communicated to a parallel motion which causes a pencil, secured 
at 23 in the pencil-bar, 16, to move in a straight line parallel to 
one of the elements of the paper-drum, 24. If a paper is fastened 
to the drum by the two clips, shown broken above 25, and the 
pencil at 23 is pressed against the paper, then by rotating the 
drum, when piston 8 is exposed on both sides to the atmosphere, 
a reference-line, called the atmospheric line, will be drawn. Sup- 
pose steam, whose pressure is 40 pounds above the atmosphere, 
is admitted below piston 8. If the stiffness of the spring is 
such that it compresses 1/5" and this movement is multiplied 
five times by the lever, 16, then 23 would rise 1 inch above the 
atmospheric line, hence for measurements on the diagram on the 
drum the scale of the spring would be 40 pounds =1". If now 
the drum be rotated, a line parallel to the atmospheric line pre- 
viously drawn will be made if the pressure on piston, 8, remains 
constant. If the pressure varies, then the pencil-point will either 
rise or fall and a curved line will be made on the paper. If, 



however, any point on this curve be taken, its height above the 
atmospheric line represents the gage pressure of the steam on 
piston 8, and its abscissa represents the amount that the drum 
was rotated from its initial position. 

The record made by an indicator takes the form of a closed 
figure called a card or diagram. The length of a card does not 
exceed 3" or 4", and, in high-speed engines, it is better not to 
exceed 1" or 3". The height of the card should not exceed 2", 
and in high-speed work a height of 1J" is plenty. We have seen 
the significance of the vertical movement of the pencil, and there 
remains only the horizontal movement of the paper caused by 
the rotation of the drum. Suppose the stroke of an engine is 12" 
and we want a card 3" long, the reduction of the motion of the 
engine-piston is then 1/4. If the ends of the atmospheric line 
correspond to the dead-center positions of the engine-piston, then, 
for each 1/4" that the drum moves from its initial position when the 
pencil is at the end of the atmospheric line, the piston of the engine 
should move I" exactly from the corresponding dead-center. 

* "Part 4 is the cylinder proper, in which the movement of 
the piston takes place. It is made of a special alloy, exactly 
suited to the varying temperatures to which it is subjected, and 
secures to the piston the same freedom of movement with high- 
pressure steam as with low; and, as its bottom end is free and 
out of contact with all other parts, its longitudinal expansion or 
contraction is unimpeded and no distortion can possibly take 
place. Between the parts 4 and 5 is an annular chamber, which 
serves as a steam-jacket, and being open at the bottom can hold 
no water, but will always be filled with steam of nearly the same 
temperature as that in the cylinder." 

In the above paragraph many desiderata are pointed out, but 
no real evidence or data are given to prove the assertions beyond 
the evidence of the cut. Catalogues give much valuable informa- 
tion, but students should be trained to give only the proper value 
to the statements they contain for obvious reasons. 

"The piston, 8, is formed from a solid piece of the finest tool- 

* Quoted from Practical Instruction for Using the Steam-engine Indicator, 
Crosby Steam-gage and Valve Co. 



steel. Its shell is made as thin as possible consistent with proper 
strength. It is hardened to prevent any reduction of its area by 
wearing, then ground and lapped to fit (to the ten-thousandth 
part of an inch) a cylindrical gage of standard size. Shallow 
channels in its outer surface provide a steam-packing, and the 
moisture and oil which they retain act as lubricants and prevent 

FIG 26. -Crosby Indicator Cress-section. 

undue leakage by the piston. The transverse web near its center 
supports a central socket, which projects both upward and down- 
ward; the upper part is threaded inside to receive the lower end 
of the piston-rod; the upper edge of this socket is formed to fit 
nicely into a circular channel in the under side of the shoulder of the 
piston-rod when they are properly connected. It has a longitudinal 
slot which permits the straight portion of the wire at the bottom of 
the spring, with its bead, to drop to a concave bearing in the upper 
end of the piston-screw, 9, which is closely threaded into the lower 



part of the socket; the head of this screw is hexagonal and may be 

turned with the hollow wrench which accompanies the indicator." 

The above paragraph gives some idea of the care used in the 

design of the piston. The moving parts of an indicator should. 

FIG. 27. Crosby Indicator Outside Spring. 

be theoretically without weight (on account of inertia stresses) r 
and should be frictionless. With the advent of superheated steam 
and the use of outside springs, this firm changed the shape and 
size of the indicator-piston. For, they say (Fig. 27), "the other 
and more important difference lies in the shape and size of the 
piston. This piston is 1 square inch in area and is in form 
the central zone of a sphere, thus affording great active force with 
a very light pencil mechanism. In other words, this piston serves 
as a universal joint to take care of the torsional strains of the 
spring when it operates the pencil mechanism of the indicator. 


"The Piston-rod, 10, is of steel and is made hollow for lightness. 
Its lower end is threaded to screw into the upper socket of the 
piston. Above the threaded portion is a shoulder having in its 
under side a circular channel formed to receive the upper edge of 
the socket when these parts are connected together. When mak- 
ing this connection BE SURE that the piston-rod is screwed 
into the socket as far as it will go, that is; until the upper edge of 
the socket is brought firmly against the bottom of the channel in the 
piston-rod. This is very important, as it insures a correct alignment 
of the parts and a free movement of the piston within the cylinder. 

"The Swivel-head, 11, is threaded on its lower half to screw 
into the piston-rod more or less, according to the required height 
of the atmospheric line on the diagram. Its head is pivoted to 
the piston-rod link of the pencil mechanism. 

"The Cap, 2, rests on top of the cylinder and holds the sleeve 
and all connected parts in place. It has a central depression in 
its upper surface, also a central hole, furnished with a hardened- 
steel bushing, which serves as a very durable and sure guide to the 
piston-rod. It projects downward into the cylinder in two steps 
having different lengths and diameters; both these and the hole 
have a common center. The lower and smaller projection is screw- 
threaded outside to engage with the like threads in the head of 
the spring and hold it firmly in place. The upper and larger pro- 
jection is screw-threaded on its lower half to engage with the light 
threads inside the cylinder; the upper half of this larger projec- 
tion, being smooth vertical portion, is accurately fitted into a 
corresponding recess in the top of the cylinder, and forms thereby 
a guide by which all the moving parts are adjusted and kept in 
correct alignment, which is very important, but which is impossi- 
ble to secure by the use of screw-threads alone. 

"The Sleeve, 3, surrounds the upper part of the cylinder in a 
recess formed for that purpose and supports the pencil mechan- 
ism; the arm, X, is an integral part of it. It turns around freely 
and is held in place by the cap. 

"The Pencil Mechanism is designed to afford sufficient strength 
and steadiness of movement with the utmost lightness, thereby 
eliminating as far as possible the effect of momentum, which is 
especially troublesome in high-speed work. Its fundamental kine- 


ma tic principle is that of the pantograph. The fulcrum of the 
mechanism as a whole, the point attached to the piston-rod, and 
the pencil-point are always in a straight line. This gives to the 
pencil-point a movement exactly parallel with that of the piston. 
The movement of the spring throughout its range bears a con- 
stant ratio to the force applied and the amount of this movement 
is multiplied six times at the pencil-point. The pencil-lever, links,, 
and pins are all made of a hardened steel; the latter, slightly taper- 
ing, are ground and lapped to fit accurately, without perceptible 
friction or lost motion. 

"The Piston-spring is of unique and ingenious design, being 
made of a single piece of the finest steel wire, wound from the 
middle into a double coil, the spiral ends of which are screwed 
into a brass head having four radial wings with spirally drilled' 
holes to receive and hold them securely in place. Adjustment is 
made by screwing them into the head more or less until exactly 
the right strength of spring is obtained, when they are there 
firmly fixed. This method of fastening and adjusting removes all 
danger of loosening coils, and obviates all necessity for grinding 
the wire, a practice fatal to accuracy in indicator-springs. 

"The Foot of the Spring, in which lightness is of great impor- 
tance, it being the part subject to the greatest movement, is a 
small steel bead firmly ' staked' on to the wire. This takes the 
place of the heavy brass foot used in other indicators, and reduces 
the inertia and momentum at this point to a minimum, whereby a 
great improvement is effected. This bead has its bearing in the 
center of the piston, and in connection with the lower end of the 
piston-rod and the upper end of the piston-screw, 9 (both of which 
are concaved to fit it), forms a ball-and-socket joint which allows 
the spring to yield to pressure from any direction without causing 
the piston to bind in the cylinder, which is sure to occur when .the 
spring and piston are rigidly united, as is the case in other indi- 
cators. Designing the spring so that any lateral movement that 
it may receive when compressed shall not be communicated to the 
piston and cause errors in the diagram is of extreme importance. 

"The Drum-spring, 31, in the Crosby indicator (Fig. 27) is a 
short spiral, while in every other make a long volute-spring is used* 

"It is obvious from the large contact surfaces of a long volute- 



spring that its friction would be greater than that of a short open 
spiral form; also, that in a spring of each kind, for a given amount 
of compression, as in the movement of an indicator-drum, the 
recoil would be greater and expended more quickly in the spiral 
than in the volute form. 

"If the conditions under which the drum-spring operates be 
considered, it will readily be seen that at the beginning of the 
stroke, when the cord has all the resistance of the drum and 
spring to overcome, the spring should offer less resistance than at 
any other time; in the beginning of the stroke in the opposite 
direction, however, when the spring has to overcome the inertia and 
friction of the drum, its energy of recoil should be the greatest." 

Indicator-springs. Springs are made to the following scales: 
4, 8, 12, 16, 20, 30, 40, 50, 60, 80, 100, 120, 150, 180. The spring 
to be used is determined by the fact that the height of the dia- 
gram should not exceed If". 

* Tabor Indicator. Fig. 28 illustrates the method of making a 
pencil-point describe a straight line w r hen the pencil is attached 

FIG. 28. FIG. 29. 

to a lever that tends to describe a circular arc. "A stationary 
plate in which is a curved slot is firmly secured in an upright posi- 
tion to the cover of the steam-cylinder (or on the outside spring- 
indicator to a bracket on the steam-cylinder). On the pencil-bar 

* Quotations from " The Tabor Indicator." 



is a roller-bearing which is secured to the bar by a pin. This 
roller moves freely in the curved slot in the guide upright and 
controls the motion of the pencil-bar. The position of the slot 
and guide upright is so adjusted and the guide-roller is so placed 
on the pencil-bar that the curve of the guide slot controls the 
pencil motion and absolutely compensates the tendency of the 
pencil to move in a curve." 

"The springs used on the Tabor indicators are of the duplex 
type, made of two coils of wire fastened exactly opposite to each 
other on the bases. This arrangement equalizes the side strain 
on the spring and keeps the piston central in the cylinder, avoid- 
ing the excessive friction caused with a single coil spring forcing 
the piston unequally against the side of the cylinder." The 
springs for inside and outside use necessarily differ, due to the 
differences of temperature to which they are exposed. Those 
intended for outside springs are marked D, as in Fig. 29 ; the inside 
springs are unlettered. The table gives the safe pressures for 
springs of different strength. 

Maximum Safe Pressures to which 


springs can be subjected. 

Scale of Springs. 

Pounds Pressure per Square Inch 
with Square Inch Area Piston. 

To 200 

To 300 
























































Fig. 30 represents a Tabor indicator with outside spring. 
The motion of the indicator-piston, which is in the steam-cylinder 


below the spring, is given to the parallel motion shown in front 
of the spring. The indicator-card paper is held on the paper- 
cylinder by the two clips shown at the end of the pencil-bar. 
Motion is given to the drum by a Houghtaling reducing motion. 

It is well known that a worm and worm-wheel afford a simple 
means of securing a large reduction in the velocity ratio between 
two shafts at right angles to one another, since one complete 
revolution of the worm causes the worm-wheel to rotate through 
an angle measured by the pitch of one tooth. It is also well 
known that it is desirable to stop the motion of the paper-drum 
to change indicator-card papers without disconnecting the cord 
that gives motion to the paper-drum. 

In the Houghtaling reducing motion, the forward motion of 
the cross-head of the engine is conveyed through a cord to a 
detachable pulley whose diameter is about 1/12 the stroke of 
the engine. The motion of this pulley is given to its shaft only 
on closing the clutch shown to the left of the pulley. A worm 
turned on the shaft gears with a worm-wheel attached to the 
paper-drum. The rotation of this drum during the forward 
engine-stroke winds a volute-spring. The unwinding of this spring 
on the return-stroke furnishes the power to rotate the drum. 

In setting the valves of an engine it is very desirable to take 
cards from each end of each cylinder during the same revolu- 
tion of the engine. This may be done by the use of an electrical 
attachment to the indicator. Essentially it consists of an electro- 
magnet that draws the pencil to the paper during the passage 
of an electric current through the magnet and withdraws the 
pencil when the current is broken. 

"In cases where diagrams are to be taken simultaneously, 
the best plan is to have an operator stationed at each indicator. 
This is desirable, even where an electric or other device is employed 
to operate all the instruments at once; for unless there are enough 
operators, it is necessary to open the indicator-cocks some time 
before taking the diagrams and run the risk of clogging the pistons 
and heating the high-pressure springs above the ordinary work- 
ing temperature."' f 

t See Trans. A. S. M. E. Standard Rules. 

FIG. 16. 



Dimensions of Standard Tabor Indicator. Diameter of pis- 
ton, 0.7978 inch; stroke of drum, 5.5 inches; range of pencil 
motion, 3.25 inches; diameter of drum, 2.063 inches; height of 
drum, 4 inches; ratio of multiplication of piston motion, 5 for 1. 

Dimensions of Small Drum-indicator. Diameter of piston, 
0.7978 inch; stroke of drum, 4 inches; range of pencil motion, 
2.35 inches; diameter of drum, 1.5 inches; height of drum, 
2.875 inches; ratio of multiplication of piston motion, 5 for 1. 

Attachment of the Indicator. For accurate work the indi- 
cator connections should be short and direct, especially in high- 
speed engines. The indicator may be used at any angle, but 
the vertical position is generally preferable. The usual plan is 
to bore a hole in the side of the cylinder so as to pierce the bore 
in the clearance space out of the currents of steam and beyond 
the piston when on the dead-center. After tapping these holes 
for 1/2" pipe, a short quarter-bend of that size, threaded at 
each end, is screwed into these holes. A bushing and a straight- 
way cock which generally only fits one style of indicator com- 
plete the connection. 

When drilling holes, it is necessary either to take off the cylin- 
der-heads to remove the metal chips or to carry a low steam 
pressure that will blow the chips towards the driller. No red 
or white lead should be used, as particles of it may get into the 
indicator and injure it. 

Before drilling the holes the following should be considered: 

1. The relation of the holes to the piston and ports. 

2. The position, method of fastening, and accessibility of the 
reducing motion. 

3. The convenience of the operator in taking cards. 

"The use of a three-way cock and a single indicator con- 
nected to the two ends of the cylinder is not advised, except 
in cases where it is impracticable to use an indicator close to 
each end. If a three-way cock is used the error produced should 
be determined and allowed for. The effect of the error pro- 
duced by a three-way cock is usually to increase the area of the 
diagram. This is due to the tardiness of the indicator in respond- 
ing to the changes of pressure. In an investigation made by 
one of the committee, which was carried out both on short- 


stroke engines running at high speed and long-stroke engines 
running at comparative slow speed, it was found that the in- 
creased area of the diagram, due to the sluggish action produced 
by the three-way cock, ranged from 3 to 7 per cent as compared 
with an indicator with a short and direct pipe." f 

Drum Motion. The motion of the paper-drum may be derived 
from the cross-head or any other part of the engine whose motion 
coincides with that of the piston. Various devices have been 
invented to reduce the cross-head motion to that required by 
the drum. In most of them a cord is used. This cord should 
not stretch appreciably under the stress to which it is subjected 
and it should always maintain the same path. It should not, 
for instance, radiate in different lines from a point at different 
positions of the cross-head. 

Reducing-lever. Before the introduction of the portable 
forms of reducing motions, consulting engineers had frequently to 
devise a reducing motion on the premises visited. . A common 
form of the reducing-lever is shown in Fig. 31. The support 
for the pivot on the top has been omitted. In some cases the 
ceiling over the engine afforded the necessary base; in other 
cases a substantial frame had to be erected. As rigidity is more 
important than strength alone it is well to take a straight-grained 
piece of wood, planed on both sides, V thick, some 3" wide at 
the top and 2" wide at the bottom. It should swing without 
vibration in a vertical plane parallel to the guides of the engine. 
The top pivot should be vertically over the middle of the bot- 
tom stud when the latter is in its midposition. To maintain a 
constant length of lever-arm, the lever must carry a fixed stud 
(Fig. 31a) at the bottom and the necessary lost motion vertically 
will take place in a slotted plate carried by the cross-head. This 
stud should be at the top of the slot on both ends of the stroke. 
The length of the lever is the distance between the centers of the 
pivot and stud and this should be at least 1.5 times the stroke. 

It is evident that if the cross-head carried a stud and drove 
the lever, the connection therein being slotted, the radius of the 
lever would be variable. The cord connection shown is inaccu- 

t See Trans. A. S. M. E. Standard Rules. 


rate and a better one is shown in Fig. 32. The sector compels 
the cord to keep always in the same path. 

The Brumbo pulley (Fig. 32) is another form of the reducing 
lever that is frequently used in locomotive tests. The rim of the 

FIG. 31. 

FIG. 32. 

sector is grooved to receive the cord that connects with the 
indicator-drum. The lever and sector have a common pivot. 
The driving-link is from one-quarter to one-half of the length 
of the lever-arm. The latter should be vertical in midposition 
and the driving-pin in this position should be below the line 
of motion of the cross-head one-half the versine of one-half the 
arc of oscillation of the lever. In other words, the driving-stud 
in midposition is as much below the line of motion of the cross- 
head in midposition as it is above it on the two ends of the stroke. 
Reducing- wheels. Figs. 30 and 33 show different designs 
of reducing- wheels. When properly made and handled they 
give accurate results. They can be tested by moving the pis- 
ton inch by inch, being careful to take up all lost motion and 
measuring the corresponding rotation of the drum. In making 
calibrations of this or any other sort the student should be care- 
ful to see that the practical conditions are identical with the 
test conditions. An indicator reducing motion was calibrated in 



the above manner and gave perfect reduction when the engine 
was jacked over, but gave imperfect results when the engine 
was working. This resulted from attaching the reducing motion 

FIG. 33. 

to the lower guide, which, when the engine was under full load, 
was found to vibrate enough to distort the card. 

Pantographs theoretically give a perfect reduction. Numer- 
ous joints must be avoided, as each must be free from lost motion. 

"Fig. 34 shows a pantograph device at midstroke. This is 
made of bar iron nicely riveted together. The indicator-cord 
may be attached at 6. The end a is attached to a pin on the 
cross-head. The fixed fulcrum is at c. a, b, and c must always 
lie in the same straight line, and ed and bn must be parallel 
and equal to fg. Also af + nf= stroke of piston -f- by the length 
of the indicator diagram." * 

* Quoted from Practical Instruction for Using Steam-engine Indicator^ 
Crosby, page 32. 


"In Fig. 35, / is a rod moving in a slide parallel to the pis- 
ton-rod. Link bd is attached to /, and link ae to the cross-head, 
a, 6, and c must always lie in the same straight line, ae + bd 
and ec4-cd= stroke of pistons-length of indicator diagram." 

In Fig. 36, a and b are fixed ends of cord wrapped around 

FIG. 35. 

FIG. 34. 

FIG. 36. 

pulley D. Indicator-cord is attached to small pulley d and 
passes around guide-pulley e. D and d are attached to the cross- 
head. Diam. D-^-diam. d=strokeof pistons- by the difference 
between stroke of piston and length of card." * 

"The most satisfactory driving-rig for indicating seems to 
be some form of well-made pantograph, with driving-cord of 
fine annealed wire leading to the indicator. The reducing motion, 
whatever it may be, and the connections to the indicator, should 
be so perfect as to produce diagrams of equal lengths when the 
same indicator is attached to either end of the cylinder, and pro- 
duce proportionate reduction of the motion of the piston at 
every point of the stroke, as proved by test." f 

Method of Taking Indicator-diagrams. 1. Before attaching an 
indicator to an engine be sure to blow steam freely through the 
pipes and cock to remove any grit that may have lodged there. 

* Practical Instruction for Using Steam-engine Indicator, Crosby, page 32. 
t See Trans. A. S. M. E. Standard Rules. 


2. If the indicator has been unused for some time, or if it 
has been handled by others so that its condition is unknown, 
it should be taken apart and cleaned with gascline. " An occa- 
sional naphtha bath is good for an indicator, as it thoroughly 
cleanses every part." If any grit or other obstruction gets into 
the cylinder it will seriously affect the diagram and lead to bad 
results. It is not difficult to detect such trouble, and it should 
be remedied at once by taking out the piston, detaching the 
parts, and cleaning them as above described. 

f "It is essential to know whether the indicator is in good con- 
dition for use, especially to know that the piston has perfect 
freedom of motion and is unobstructed by undue friction. To 
test this successfully detach the spring and afterwards replace 
the piston and piston-rod in their usual position, then holding 
the indicator in an upright position by the cylinder in the left 
hand, raise the pencil arm to its highest point with the right 
hand and let it drop; it should freely descend to its lowest point." 
The piston may be dented or burred from a fall or the upper 
part of the cylinder-bore may be dirty. It is better to have 
the piston fit rather loosely than \he reverse, f "No diagrams 
should be accepted in which there is any appearance of w r ant 
of freedom in the movement of the mechanism. A ragged or 
serrated line in the region of the expansion or compression line 
is a sure indication that the piston or some part of the mechanism 
sticks; and when this state of things is revealed, the indicator 
should not be trusted, but the cause should be ascertained and 
a suitable remedy applied. Entire absence of wire-drawing of 
the steam line, and especially a sharp, square corner at the begin- 
ning of the steam line, should be looked upon with suspicion, 
however desirable and satisfactory these features might other- 
wise be. These are frequently produced by an indicator which is 
defective owing to want of freedom in the mechanism. An 
indicator which is free when subjected to a steady steam pressure, 
as it is under a test of the springs under calibration, should be 
able to produce the same horizontal line, or substantially the 
same, after pushing the pencil down with the finger, as that 
traced after pushing the pencil up and subsequently tapping 
f See Trans. A. S. M. E. Standard Rules. 


it lightly. When the pencil is moved by the finger, first up 
and then down, the piston being subjected to pressure, the move- 
ments should appear smooth to the sense of feeling. 

f " The point selected for attaching the indicator to the cylinder 
should never be the drip-pipe or any point where the water of 
condensation will run into the instrument if this can possibly 
be avoided. The admission of water with the steam may greatly 
distort the diagram. If it becomes necessary to place the indi- 
cator in such a position, as may happen when it is attached to 
the lower end of a vertical cylinder, the connection to the indi- 
cator must be short and direct, and in some cases it should be 
provided with a drip-chamber arranged so as to collect the water 
or deflect it from entering the instrument." 

3. Adjust the drum-cord so that the drum rotates freely with- 
out knocking at either end of its stroke. If the cord is too short 
it will break or turn the indicator in its coupling if the latter 
is set up too tight. Beginners therefore should not set this 
coupling up taut before attaching the cord. 

4. Lubricate the indicator-piston with ordinary cylinder oil 
for pressures above the atmosphere. 

5. Warm up the indicator by admitting steam for a few 

6. Shut off the steam by means of the cock in the in- 
dicator-plug. This admits air to the bottom of the indicator- 

Bring the pencil in contact with the paper and rotate the 
cylinder. This gives a reference line for pressures called the 
atmospheric line. Many prefer to draw this line after taking 
the card. 

7. Turn the steam on the indicator, press the pencil, and 
take one or more cards. 


The commercial indicator-cards have forms printed on one 
side of the cards. This form should be filled out and in addi- 
tion any information that has any probability of being of future 
value. One should remember that questions may arise other 

t See Trans. A. S. M. E. Standard Rules. 



than those of present interest. It is much better to have too 
many than too few data after the test is over. 

It is advisable to make notes of special circumstances such as 
the end of the cylinder which is represented by the card, the 
size of pipes and ports, pressures at the boiler and at the throttle, 
description of the boiler and special incidents and accidents. 
On a locomotive diagram note the speed from the time elapdng 
in passing mile-posts, the position of the link and throttle, the 
character and number and weight of cars drawn, the grade, the 
size and position of the blast orifice, character of the coal and 
quantity burned, amount of water taken on. 

In marine work take data that may be of value from the 
ship's log. 

Fig. 37 is an indicator-diagram from a non-condensing engine 
in good condition. In most steam-engines it is desirable that 


FIG. 37. 

the crank-pin revolve at uniform speed. We shall find that 
this necessitates a very irregular motion of the piston. As the 
latter approaches the end of the stroke it slows down, coming 
to absolute rest at the end of its stroke, since it must reverse 


its motion. On the return stroke the speed increases to a point 
near mid-stroke and then decreases as before. The card shows 
that the valve commences to open for steam just before the 
piston finishes the preceding stroke, at A, so that when the pis- 
ton is actually on the dead-center and instantaneously at 
rest the valve is open the amount is called lead and admit- 
ting steam. The pressure against the piston rises rapidly and 
remains constant as long as the opening of the port is sufficient. 
When the piston is half-way between B and C the port has its 
maximum opening and the valve starts on its return to close 
the port. With a diminishing port opening for steam-supply 
the piston is now moving faster than it did in the earlier part 
of the stroke. This combination results in a diminution of pres- 
sure in the cylinder, since an increasing difference of pressure 
is necessary to give an increasing velocity to the steam that is 
required to supply an increasing volume. It is evident that 
BCD changes curvature at C, the center for BC being below 
and that for CD being above those curves. The actual point 
of cut-off, C, or piston position at the instant of port closing, is 
at the point of tangency of these two curves. "f "This cut-off 
may be located by finding the point where the curve is tan- 
gent to a hyperbolic curve." 

Inertia of Indicator Pistons. Put a card on the drum of an 
indicator and rotate the drum uniformly. There being no steam 
on the indicator, pull the piston up by hand and let it drop during 
the uniform rotation of the drum. A figure, similar to Fig. 38, 
will be made, the spring causing the piston to vrorate above 
and below its proper position harmonically, i.e., in uniform periods 
of time. The amount of vibration is gradually lessened by the 
internal molecular friction in the spring as well as the various 
external resistances. 

The movement of the piston of an engine is very irregular, 
but the movement of the crank is generally uniform. Equal 
distances along the circle of the crank-pin then measure equal 
periods of time. If the crests and hollows in a high-speed engine 
card be projected on the crank-circle it will be found that 

t See Trans. A. S. M. E. Standard Rules. 


FIG. 38. 

150 - 

Steam Pressure 105 Pounds 
Revolutions 250 
Spring 60 

FIGS. 39 AND 40. 


they occur at uniform arc distance apart. This shows that the 
sudden impingement of the steam on the indicator piston pro- 
duces an harmonic vibration similar to that just described. 
(Figs. 39 and 40.) 

All cards from high-speed engines should show some ten- 
dency to wave as it is a natural effect. If it is taken out by 
friction, the cards are surely in error. At the same time a large 
wave motion should be avoided by using heavier springs. Fig. 
42 was taken from the engine giving card, Fig. 39, at the same 

FIG. 41. FIG. 42. FIG. 43. 

speed, tne omy difference being the use of a heavier spring. 
In slow-speed engines, the vibration spends itself in the admis- 
sion line due to the lessened amount of the blow and the length 
of time required to make the admission line. Similarly, there 
will be less vibration if the compression is heavy, as the blow 
at admission is lessened. Figs. 41 and 43. 

EXERCISES. Take an indicator apart and examine its construction 
carefully. Give a technical description of the indicator. Describe 
gage testers, reducing motions, or other apparatus in your laboratory, 
taking particular pains to express yourself clearly, to arrange your 
ideas sequentially, and to use technical words correctly. 


Methods of Drawing the Hyperbola PV =C (Fig. 44). The 
isothermal curve of expansion of perfect gases and the curve 
of expansion of steam in a cylinder is assumed to follow the law 


FIG. 44. Method of Drawing an Hyperbola. 

"The product of the absolute volume and the absolute pressure 
is constant for any stage of the expansion." To draw the curve, 
the absolute pressure, and absolute volume at one stage of the 
expansion (or the compression) is sufficient. 

First Method. From any point C draw the line of zero volume 
CB and the line of zero pressure CD. Being given the absolute 
pressure CB and the absolute volume Be of some point c of the 
curve lay them off and determine the position of c. Through c 
draw a horizontal line BA and a vertical line cb of indefinite 




length. From C draw radiating lines at random, cutting the 
vertical line cb and the horizontal line BA. Through the points 
of intersection draw lines parallel to CD and CB to intersect in 
points e, f, g, h, and a. A smooth curve drawn through these 
points will be the curve required. If the abscissa and ordinate 
for any one of these points are known, by similar triangles it is 
easy to show that their product is equal to the product of the 
same quantities for the original point c. If it is desired to pro- 
duce the hyberbola from a upward the same method may be 
employed, but the line BA is now ba and the line cb is replaced 
by a A. 

The line CB is called the clearance line. A line parallel to CB 
and tangent to the indicator-card at the extreme left will cut 
off the clearance on CD. CD is also called the perfect vacuum 

C V 4 &' d' 

FIG. 45. Method of Drawing an Hyperbola. 

Second Method (see Fig. 45). It is well known if a rectan- 
gular hyperbola and its asymptotes are given that if a straight 
line is drawn cutting the curve in two places and both asymp- 
totes the distance of one of the points on the curve from one 
asymptote is equal to the distance of the other point on the 
curve from the other asymptote. Suppose that we have the 
asymptotes CB and CD and any point a of the curve. Through 
a draw several radiating lines similar to a'aW. Only one is drawn 
to avoid confusion. Lay off W equal to aa' ' b in each will 



be a point of the curve. Any of the points b will serve as a 
did for finding other points. The same method of construction 
will serve on the compression curve FE. 

fThe Point of Cut-off ." The term 'cut-off' as applied to 
steam-engines, although somewhat indefinite, is usually con- 
sidered to be at an earlier point in the stroke than the beginning 
of the real expansion line. That the cut-off may be defined in 
exact terms for commercial purposes, as used in steam-engine 
specifications and contracts, the Committee recommends that, 
unless otherwise specified, the commercial cut-off, which seems 
to be an appropriate expression for this term, be ascertained 
as follows: Through a point showing the maximum pressure 

E C 

H G 

FIG. 46. Four-valve Engine. 

Slow-speed Commercial Cut-cf^ -~ 

during admission draw a line parallel to the atmospheric line. 
Through the point on the expansion line near the actual cut-off 
draw a hyperbolic curve. The point wheie these two lines inter- 
sect is to be considered the commercial cut-off point. The per- 
centage is then found by dividing the length of the diagram 
measured to this point by the total length of the diagram and 
multiplying the result by 100." 

"The principle involved in locating the commercial cut-off 
is shown in Figs. 46 and 47, the first of which represents a dia- 
gram from a slow-speed Corliss engine, and the second a dia- 
gram from a single-valve high-speed engine. In the latter case 
where, owing to the fling of the pencil, the steam line vibrates, 

t See Trans. A. S. M. E. Standard Rules. 



the maximum pressure is found by taking a mean of the vibra- 
tions of the highest point." 

The commercial cut-off, B, as thus determined is situated at an 
earlier point of the stroke than the actual cut-off, D, referred to. 

Fig. 37. Steam being elastic entirely fills an increasing volume, 
but its pressure diminishes, as is seen by the decreasing ordinates 
of the expansion curve CD. We have already seen that it is 
necessary to reject the steam during the return-stroke. At the 
point D, where there is another change in the curvature, the 
exhaust-valve opens and the pressure rapidly falls as the pis- 
ton moves to the end of the stroke at E. The piston now returns 
and the steam is forced out by the piston sweeping it out. As the 
resistance is constant the back-pressure line is parallel to the at- 


FIG. 47. Single- valve Engine. High-speed Commercial Cut-off 


mospheric line XY. If the exhaust-passages had been short and 
ample the line EF would have practically coincided with XY. 
We have seen how the atmospheric line was drawn. But 
pressures measured from it are not absolute pressures, as we 
well know that the atmospheric pressure is some 14.7 pounds 
per square inch above zero pressure. The steam-gages used on 
boilers indicate not the steam-pressure in the boiler but the burst- 
ing pressure, which is the difference between the steam-pressure 
inside and the atmospheric pressure outside. Hence, to obtain 
the absolute or true pressure above zero we must add the atmos- 
pheric pressure to all pressures that are measured above the 
atmosphere. The barometer gives this pressure in inches of 
mercury that can be converted into pounds per square inch by 


multiplying by --=0.491. In all localities near the sea-level 

sufficient accuracy is attained by using 14.7 pounds per square 
inch as the atmospheric pressure. 

Parallel to XY (Fig. 37) and at a distance below it equal to 
14.7 pounds to the scale of pressures of the indicator-card, draw 
a line HK. The ordinates of any point of the card measured 
to this line give the absolute pressure in the cylinder. At C 
then the pressure in the cylinder is CL. 

Clearance. Place the piston at the end of its stroke, then 
the space between the adjoining faces of the cylinder-head and 
the piston, including the volumes that lead into this space (such 
as ports up to the valve-face, drip-pipes, indicator-pipes, water- 
relief pipes), is called clearance. In well-designed engines of 
large size it is from 3 to 5 per cent of the volume swept 
through by the piston, in plain slide-valve engines the percentage 
varies from 7 to 15 per cent, in pis ton- valve engines it varies 
from 12 to 25 per cent. 

Method of Drawing Clearance-line. One writer has pro- 
posed the name cylindrus for the volume swept through by the 
piston. This is the volume shown by the indicator-card, since 
any part of the stroke passed over by the piston becomes volume 
when multiplied by the area of the piston. If the clearance 
volume at each end is 5% of the cylindrus we obtain, on dividing 
the clearance by the area of the piston, a linear distance that 
is 5% of the stroke. This distance may be added to the proper 
end of the atmospheric line when the length of that line orig- 
inally represented the length of the stroke. In Fig. 37 lay 
off XM =5% of XY. Then the absolute volume of the steam 
at any point L is NL and its absolute pressure is CL. 

t Ratio of Expansion. The ratio of expansion for a simple 
engine is determined by dividing the volume corresponding to 
the piston displacement, including clearance, by the volume 
of the steam at the commercial cut-off, including clearance. 

f For example, in a simple engine, referring to Figs. 46 and 47, 
the ratio of expansion is the entire distance HF, including clear- 

t See Trans. A. S M. E. Standard Rules. 


ance, divided by the distance EB, including clearance; that is, 



Indicated Horse-power. In finding the indicated horse-power 
(see page 31), we assumed the mean effective pressure. This 
quantity may be found if we have a correct average card or 
from the average of a number of cards. Suppose Fig. 37 is such 
a card. With a triangle erect perpendiculars HE and KB tan- 
gent to the extremities of the card. At H lay off HJ, making 
any angle with HK. Assume any distance HI and lay it off 
ten times to some point /. Join / and K. Draw IP parallel to 
JK. Bisect HP at a. Lay off HP ten times from a and through 
the points so found draw the dotted ordinates as shown. These 
ordinates are the mean ordinates of a series of consecutive trape- 
zoids. On a long slip of paper lay off these ordinates consecu- 
tively. Measure the total length and divide by the number of 
ordinates and thus obtain the length of the mean ordinate. This 
mean length multiplied by the scale of the spring used in the 
indicator when the card was taken gives the mean pressure. 

The mean gross forward pressure is the mean ordinate of 
HEDCBK. The. mean back pressure is the mean ordinate of 
HEABK. The mean effective pressure is the difference of the 
two preceding pressures. 

t"The indicated horse-power should be determined from the 
average mean effective pressure of the diagrams taken at intervals 
of twenty minutes, and at more frequent intervals if the nature 
of the test makes this necessary, for each end of each cylinder. 
With variable loads, such as those of engines driving generators 
for electric railroad work, and of rubber grinding- and rolling- 
mill engines, the diagrams cannot be taken too often. In cases 
like the latter, one method of obtaining suitable averages is to 
take a series of diagrams on the same blank card without unhook- 
ing the driving-cord, and apply the pencil at successive intervals 
of ten seconds until two minutes' time or more has elapsed, thereby 
obtaining a dozen or more indications in the time covered. This 
tends to insure the determination of a fair average for that period. 
In taking diagrams for variable loads, as indeed for any load, 

t See Trans. A. S. M. E. Standard Rules. 



the pencil should be applied long enough to cover several suc- 
cessive revolutions, so that the variations produced by the action 
of the governor may be properly recorded. To determine whether 
the governor is subject to what is called 'racing' or 'hunting' 
a 'variation diagram ' should be obtained; that is, one in which 
the pencil is applied a sufficient time to cover a complete cycle 
of variations. When the governor is found to be working in 
this manner, the defect should be remedied before proceeding 
with the test." 

Testing Indicator-springs. " To make a perfectly satisfac- 
tory comparison of indicator-springs with standards, the calibra- 
tion should be made, if this were practical, under the same 

FIG. 48. Indicator- spring Testing Apparatus. 

conditions as those pertaining to their ordinary use. Owing to 
the fact that the pressure cf the steam in the indicator-cylinder 
and the corresponding temperature are undergoing continual 
changes, it becomes almost impossible to compare the springs 
with any standard under such conditions. There must be a con- 
stant pressure during the time that the comparison is being 


" The apparatus used for testing indicators at ordinary 
pressures above the atmosphere is shown in Fig. 48. The indi- 
cator is placed at A on top of the cylinder B. The cylinder B 
is made of a piece of 6-inch standard pipe about 2 feet long. 
The pressure is measured by means of a plug-and-weight device, C, 
which is spun around so as to eliminate the effect of friction. 
The bottom of the plug is at the same level as the pipe D. The 
U-shaped pipe E is filled with oil. Before starting to calibrate 
the indicator, the pet-cock F is opened slightly in order to allow 
any air in the pipe G and the siphon H to escape. The siphon H 
is surrounded by water contained in the vessel /, which condenses 
the steam which enters it through the pipe D, so that when all 
the air present is allowed to escape through the pet-cock F, the 
pipe G and the siphon H will be filled with water. / is a pet-cock 
for removing any water that may collect at the bottom of the 
siphon E after the apparatus has been in use for a long time. 
The pressure is adjusted by regulating the amount of opening 
of the valve K in the supply-pipe L, which furnishes steam, water, 
or compressed air to the apparatus, and also by adjusting the 
valve M in the escape-pipe N. is a valve for removing any 
water which may collect in the bottom of the cylinder B when 
steam is used, and for draining out the water after calibrating 
under hydrostatic pressure. The pan of the plug-and-weight 
device C is limited in its movement by means of a fork which 
comes in contact with it only when the pan is in the extreme 
positions. The two prongs of this fork are shown in section at 
P and Q. R is a gage for showing the approximate pressure. 
The readings of the gage R are not used in testing the indicator, 
but as a general guide in the use of the apparatus. The diam- 
eter of the plug in the plug-and-weight device is 0.5" and the 
hole in the bushing is 0.505". Both the plug and bushing are 
ground true. The average area of the plug and of the hole in 
the bushing is used in calculating the weight required for a given 

"In testing indicators with steam-pressure, the steam is 
brought to the maximum pressure to which the indicator is to 
be subjected; the indicator-cock is then opened and closed 
quickly a number of times to heat the indicator. The steam 


is then released from the cylinder B, and the atmospheric line 
is taken after turning the indicator-cock to the proper position. 
In taking the atmospheric line, as well as the lines for any other 
pressure, the pointer of the indicator is first pressed upward, 
and then released and a line taken, then pressed downward and 
released and a line taken, the indicator being rapped sharply 
with a small wooden stick before taking each line, as has already 
been explained. After taking the atmospheric line, steam is 
admitted through the valve K, until the pan-and-weight device 
is balanced while being rotated. This requires a very fine adjust- 
ment, and the line is not taken until there is no tendency for 
the plug-and- weight device either to rise or fall." * 

t "We recommend, therefore, that for each required pressure 
the first step be to open and close the indicator-cock a number 
of times in quick succession, then to quickly draw the line on 
the paper for the desired record, observing the gage or other 
standard at the instant when the line is drawn. A corresponding 
atmospheric line is taken immediately after obtaining the line 
at the given pressure, so as to eliminate any difference in the 
temperature of the parts of the indicator. This appears to be 
a better method (although less readily carried on and requiring 
more care) than the one heretofore more commonly used, where 
the indicator-cock is kept continually open, and the pressure is 
gradually rising or falling through the range of comparison. 

"The calibration should be made for at least five points, 
two of these being for the pressures corresponding as near as 
may be to the initial and back pressures, and three for inter- 
mediate points equally distant. 

" For pressures above the atmosphere, the proper standard 
recommended is the dead-weight testing apparatus, or a relia- 
ble mercury column, or an accurate steam-gage proved correct, 
or of known error, by either of these standards. For pressures 
below the atmosphere the best standard to use is a mercury 

"The correct scale of spring to be used for working out the 
mean effective pressure of the diagrams should be the average 

* Jacobus, " Testing Indicators," Trans. A. S. M. E., Vol XX. 
f See Trans. A. S. M. E. Standard Rules. 


based on the calibration, and this may be ascertained in the 
manner pointed out below. 

" When the scale of the spring determined by calibration is 
found to vary from the nominal scale with substantial uni- 
formity, it is usually sufficiently accurate to take the arithmetical 
mean of the scales found at the different pressures tried. When, 
however, the scale varies considerably at the different points, 
and absolute accuracy is desired, the method to be pursued is 
as follows: Select a sample diagram and divide it into a num- 
ber of parts by means of lines parallel to the atmospheric line, 
the number of these lines being equal to and corresponding with 
the number of points at which the calibration of the spring is 
made. Take the mean scale of the spring for each division and 
multiply it by the area of the diagram enclosed between two 
contiguous lines. Add all the products together and divide by 
the area of the whole diagram; the result will be the average 
scale of the spring to be used. If the sample diagram selected 
is a fair representative of the entire set of diagrams taken during 
the test, this average scale can be applied to the whole. If not, 
a sufficient number of sample diagrams representing the various 
conditions can be selected, and the average scale determined 
by a similar method for each, and thereby the average for the 
whole run." 

Isothermal Expansion (Fig. 49). We may suppose that 
the walls allow heat to pass through them and that we have a 
source of heat so arranged that the temperature of the gas is 
not allowed to fall but is kept constant during the expansion. 
The law of isothermal expansion is PiVi=P 2 V 2 =P s V 3 =PV 
or PV=C. Note carefully that when a subscript is used the 
quantity to which it is added is no longer variable, for it denotes 
a fixed value for that problem. PI is the admission pressure 
in this discussion and could not be used for any value of the 
pressure during the expansion. On the contrary, take any point 
on the expansion curve, the ordinate at that point measures P 
and the abscissa measures its volume, V. Hence P\V\ and P 2 V 2 
are specific values of the general formula PV. As the area of. 
the piston is a common multiplier to all parts of the stroke, it 
is evident that if we take an infinitesimal part of the stroke it 



becomes an infinitesimal part of the volume when multiplied 
by the area of the piston. It may be called dV and when mul- 
tiplied by P it becomes work. It could be written (PA)dL, 
where PA is equal to the total pressure and dL is in feet. 
The work done during admission is PiFi. The work done 


during expansion is / PdV. 

But P varies with V, and to integrate we must have but one 

FIG. 49. 

variable and that must be V. The variable P must therefore 
be expressed in terms of the variable V. 

But PiV 1 =PV, therefore P= pA 

Substitute this value of P and we obtain for the area BCDE 
under the expansion curve 

Pi 7i (log, F 2 -log. Fi) =P 1 V 1 log, ? =P 1 V 1 log, r. 


As r is the ratio of the final absolute volume to the initial ab- 
solute volume of the gas it is called the ratio of expansion. 

Log s r is an abstract quantity and the expression P\V\ log s r 
shows that the work done during expansion is (log e r) times the 
work of admission. The subscript e denotes that a table of 
Naperian or hyperbolic logarithms must be used (Table II). 

The total gross forward work, HABCDG, is then 

The mean gross forward pressure would be found by dividing 
by 7 2 , 

Pi 7^1+ Ing, r) _P T (l+log e r) 
V* r 

The quantity that is actually desired is the mean pressure 
of the diagram ABCRLMA, which would be the mean pressure 
of the theoretical indicator-card. 

Let V c =GF, the volume of the clearance (when multiplied by 

A, the area of the piston); 

7 3 =GK, the volume of steam enclosed in the cylinder 
when the exhaust- valve closed; 

7 3 .. , 

-y-=r c = ratio of compression; 

' C 

P C =MF, the pressure that the compression steam would 

have if compressed into the clearance volume ; 
ML be an isothermal curve or follow the law P7=C. 

Therefore P 3 7 3 =P C 7 C 


area MLKF =P 3 F 3 log, ^--P.V e log, ?- -P C V C log.. 

' c V c V 3 


HAFG=P 1 V C , 

FMLK =P 3 7 3 log, ^ =P 3 7 3 log e r ff , 
LRDK=P 3 (V 2 -V 3 )- } 


The mean effective forward pressure = y _y = Pm e ' 

Theoretically, these formulas apply only to the isothermal 
expansion of perfect gases. Practically, they are used for the 
expansion of steam in the steam-engine. The temperature of 
the steam falls during expansion, but, owing to the re-evapora- 
tion of condensed steam, the actual expansion curve as shown 
by the indicator follows the law PV=C. 

The area of a piston is 1000 square inches; the stroke is 
38 inches; clearance 2 inches; cut-off is 6 inches from the begin- 
ning of the stroke; initial pressure is 75 pounds gage; the back 
pressure is 16 pounds absolute; the exhaust closes 4 inches from 
the end of the stroke; the engine is double-acting, making 100 
revolutions per minute. Draw the card, find the P me and the 
theoretical I.H.P., taking clearance into consideration. 

Initial pressure absolute, 75 + 15=90. 


Total area HBCDG =Pi7i(l +log< r). 

90 X 1000 X 1(1+1.6) =156,000. 

HAFG =90 X 1000 x & = 15,000 

LRDK = 16 xlOOOX ft =45,333 

4 + 2 
r loge - = 8,800 



86,867 ft.-lbs. 
At 100 revolutions per minute the wo.k would be 

86,867 X 200 =v!7,373,400 or ; = 526 I.H.P. 

= loOOxTi ' Pounds per square inch. 


Ex. 19. Air at a constant pressure of 60 pounds per square inch 
absolute is admitted into a cylinder, without clearance, till the piston 
sweeps through 3 cubic feet. The air is then cut off and the piston 
sweeps through 9 more cubic feet, the temperature remaining con- 
stantly at 100 F. On the return stroke, the air is exhausted at 15 
pounds per square inch absolute. Find the gross and net work per 
stroke, P m and P m , and the pounds of air required per stroke. Draw 
the card. How many B.T.U. were added during expansion? 

Ex. 20. Air is drawn into an air-compressor at 14 pounds per 
square inch absolute and 70 F. It is compressed till the pressure 
is 42 pounds absolute and the volume is 60 cubic feet; valves then 
open and the air is forced out at that constant pressure. If the com- 
pression were isothermal, find the net work per stroke, P m and P me) 
and the weight of dry air compressed. Draw the card. 

Ex. 21. The area of a piston is 4 square feet and its stroke is 2 
feet. Steam at 60 pounds per square inch absolute is admitted to 
the cylinder till the piston moves 8 inches from the beginning of its 
stroke when the steam is cut off. If the steam expand in accordance 
to the law PV=C, and the back pressure on the return stroke is 
15 pounds absolute, find the gross and the net forward work per 
stroke, P m and P m e- Draw the card. No clearance. 

Ex. 22. Steam at 75 pounds gage (90 pounds absolute) is admitted 
to a cylinder 20"X24" (20 inches diameter and 24 inches stroke). 
Cut-off at 1/4 stroke. Back pressure 15 pounds absolute or gage 
pressure. The engine is double-acting, making 90 revolutions per 
minute; no clearance. Draw the card. Find the P m and P me and 
the I.H.P. 

Ex. 23. In a cylinder with clearance when the piston is on the 
return stroke, the back pressure of the steam in the cylinder is 16 
pounds absolute when the exhaust-valve closes and the volume is 
3 cubic feet. At the end of the stroke the clearance volume is 1 
cubic foot. Draw the recompression curve and find the work of 
compression in foot-pounds. 

Ex. 24. Take the same data as in Ex. 22, but cut-off at 1/9 stroke, 
and find the same quantities. 

Diagram Factor. ''The diagram factor is the proportion 
borne by the actual mean effective pressure measured from the 
indicator-diagram to that of a diagram in which the various 
operations of admission, expansion, release, and compression are 
carried on under assumed conditions. The factor recommended 


refers to an ideal diagram which represents the maximum power 
obtainable from the steam accounted for by the indicator-dia- 
grams at the point of cut-off, assuming first that the engine has 
no clearance; second, that there are no losses through wire- 
drawing the steam either during the admission or the release; 
third, that the expansion line is a hyperbolic curve; and fourth, 
that the initial pressure is that of the boiler and the back pressure 
that of the atmosphere for a non-condensing engine, and of the 
condenser for a condensing engine. 

"The diagram factor is useful for comparing the steam dis- 
tribution losses in different engines, and is of special use to the 
engine designer, for by multiplying the mean effective pressure 
obtained from the assumed theoretical diagrams by it he will 
obtain the actual mean effective pressure that should be developed 
in an engine of the type considered. The expansion and com- 
pression curves are taken as hyperbolas, because such curves 
are ordinarily used by engine-builders in their work, and a dia- 
gram based on such curves will be more useful to them than 
one where curves are constructed according to a more exact law. 

" In cases where there is a considerable loss of pressure between 
the boiler and the engine, as where steam is transmitted from 
a central plant to a number of consumers, the pressure of the steam 
in the supply main should be used in place of the boiler pressure 
in constructing the diagrams. 

" The method of determining the diagram factor is best shown 
by referring to Figs. 50, 51, 52, which apply to a simple non- 
condensing engine and a simple condensing engine. 

In Fig. 50, RS represents the volume of steam at boiler 
pressure admitted to the cylinder, PR and OS being hyperbolic 
curves drawn through the compression and cut-off points re- 
spectively. In Fig. 51, the factor is the proportion borne by 
the area of the actual diagram to that of the diagram CNHSK. 
In "Fig. 52, the factor is the proportion borne to the area of the 
diagram CNHSK. In Fig. 51, where the diagram is the same 
as in Fig. 50, the distance CN is laid off equal to RS shown 
in Fig. 50, and the curve NH is a hyperbola referred to the 
zero lines CM and MJ. In Fig. 52, the distance CN is found 
in a similar way. 


S N 


FIG. 50. 

^Boiler Pressure 

C/ N' 

- "-v 

CNis equal to US in. Fig. 31a. 

> Line of Zero Pressure 
FIG. 51. 

Boiler Pressure 

CWis determined in the same way 
as ^-ST in Fig. 31a, 

Line of Condenser Pressure 

FIG. 52. 
Diagram Factor. 

Line of Zero Pressure 


Elimination of Clearance Steam. RS or CN measures the 
net steam that passes through the cycle. We shall find that an 
entropy diagram measures the heat added; that is, the heat of 
formation of the admission steam measured above its proper 
feed-water temperature. It is then necessary to eliminate the 
clearance steam from the diagram. Figs. 51 and 52 show how 
this is done. 

It is important to note that the diagram factor is based on an 
ideal diagram the back-pressure line of which is neither the zero 
line nor the expected back-pressure line, but an ideal line of back 
pressure. The ideal back-pressure line for a condensing engine is 
the assumed pressure in the condenser and in a non-condensing 
engine it is the atmospheric pressure. Compressing the steam to 
boiler pressure is in effect avoiding the complication of consider- 
ing clearance. Note further that the pressure during admission 
is the boiler pressure and hence the efficiency of the pipe line is 
included n the diagram factor. If the line loss is very great the 
steam pressure at the throttle may be used, but that fact should 
be specially noted. Hence in choosing a diagram factor or in 
finding it practically for a definite case, it is essential that these 
elements be properly applied. 



The Throw of Cranks and Eccentrics (Figs. 53 and 54;. 

The throw or radius of a crank is the distance from the center 
of the crank-pin to the center of its shaft or the distance R in 
Fig. 53. As it is evident from the definition that the length 
of the crank-pin radius does not affect the crank throw, a modi- 
fied form of the crank may be obtained by increasing the radius 

FIG. 54. 

of the crank-pin till its periphery extends beyond the shaft as 
in Fig. 54. 

This form of crank is called an eccentric. 

Its throw or eccentricity is the distance from the center of 
the shaft to the center of the eccentric or the distance SP in 
Fig. 54. 

The eccentricity or throw of an eccentric is improperly called 
the radius of the eccentric. The radius of the eccentric circle as 
shown above does not affect the properties of the eccentric as 
an eccentric. 

The travel of a valve in one direction is twice the throw 
of its eccentric (unless modified by lever-arms), viz., 2SP=AB. 



Piston Travel with a Finite Connecting-rod (Fig. 55). 
Let R=OD -crank throw; 

L = Dd = connecting-rod length; 
ab = travel of cross-head ; 

then with centers a and d, draw the arcs CAC' and Dg, using the 
length of the connecting-rod as a radius to the same scale that 
A0= crank throw. It is evident that ad = CD=Ag = the travel 
of the cross-head = piston travel for a crank rotation of 6 degrees 
from OA. 



FIG. 55. 

Drop the perpenaicular D/; then, from the figure, we see 
that the piston travel for a finite connecting-rod is equal to 

fg + fA = L-L cosa + R-R cos 6=L(l cos a) +R(1 cos (9). 

Piston Travel with an Infinite Connecting-rod. As the cen- 
ter d, Fig. 55, is moved to the left by the use of longer rods, the 
curve Dg approaches closer to Df and when d is at an infinite 
distance the arc becomes the straight line Df. 

With an infinite rod the travel is therefore 

fA =R-R cos 0. 


The equation for a finite rod gives the same result when 

and L = oo. 

Fig. 56 shows a crank-pin working in a yoke; the motion 
produced is equivalent to that which would be produced by a 
theoretical rod of infinite length. It is used in some forms of 



steam-pumps. It is usual to consider the eccentric-rod as a rod 
of infinite length, as it is often forty times the eccentric throw 
in length. The connecting-rod is usually only five to seven times 
the crank throw in length, and in accurate work the exact posi- 
tion of the piston for different crank positions must be found. 
The graphic methods given above are usually preferred in the 
solution of all valve-diagram problems. 

Position of a Slide-valve. The position of the piston is always 
found by measuring the distance it is from the beginning or end 

FIG. 56. 

FIG. 57. 

FIG. 58. 

of its stroke, as shown above. It is very convenient in finding 
the position of a valve to measure the distance it is from its mid- 
position. This is never done with pistons, but is always done 
with slide-valves. As the eccentric-rod is generally assumed as 
infinite in length we have, Fig. 57. 
if r\ = eccentric throw 

and </> =the angle that the eccentric radius is from its midposition, 
bd =7*1 sin (f) = distance valve has moved from its midposition. 

It is evident that the valve will be in its midposition when 
the eccentric is in its midposition, oc, if oa and oe are the posi- 
tions of the eccentric when the valve is at the ends of its travel. 

Effect of Finite Connecting-rod. In all steam-engines every 
effort is made to have the crank-pin move with uniform velocity, 
viz., pass over equal spaces in equal times. If the crank-pin 
does this, it will be found that the motion of the piston is quite 
irregular and the shorter the connecting-rod the greater is this 
irregularity. To prove this take any crank-circle, as in Fig. 58, 



and divide it up into equal arcs AD, DB, etc. The student 
should compare the amount of motion for equal crank-angles: 

1. At the ends and middle of a stroke. 

2. At the two ends of a stroke. 

3. During the forward and return strokes. 

4. With connecting-rods of different lengths. 

The Slide-valve. We have seen that the sum of all the impacts 
of the steam molecules on the face of the piston causes it to move 
and so converts some of the kinetic energy (or energy of motion) 
of those molecules into work. If the supply of steam be cut off 
after a certain amount of it has entered the cylinder, more energy 
may be extracted from the steam that has entered by allowing 
it to expand. It will do this if the resistance be gradually lessened. 

There are a number of variables to consider, but we may 
assume for the present that variation of velocity will bring about 
the necessary equality between the steam-pressure and the resist- 
ance, the velocity increasing if the resistance decreases and be- 
coming less with increased resistance. 

FIG. 59. 

The slide-valve controls the admission of the steam auto- 
matically, cutting it off after a certain percentage of the stroke 
has been passed by the piston, opening a relief or exhaust 
passage at or near the end of the stroke for the escape of the 
foteam from the cylinder during the return of the piston. Near 
the end of the return stroke, complete escape of steam is pre- 
vented by closing up the passage used for exhaust. The conse- 
quent compression of the steam in the cylinder serves as a 
cushion and tends to prevent pounding. 



Valve Laps. The amount the valve overlaps the outside edge 
of the port when the valve is in its midposition is outside lap 
(see Fig. 59, o, o'). Similarly the amount the valve overlaps 
the inside edge of the port when the valve is in its midposition is 
inside lap (see i, i', Fig. 59). In its motion to and fro it is evi- 
dent that the valve overlaps the ports both inside and out vary- 
ing amounts. But any valve has but one midposition in each 
stroke, hence inside and outside laps are fixed quantities for any 
valve and can only be reduced by chipping or planing off the 
valve and thus reducing o or i, 

It is not practical to draw the whole engine for each illus- 
tration, hence to the right of each figure are line sketches (not 
to scale) showing the relative crank and eccentric positions for 
any valve position. 

When the entering steam occupies the space S the outside 
lap is called steam lap and the inside lap is exhaust lap. These 
names are reversed if the entering steam occupies the space E. 
It is not necessary for the steam laps to equal one another and 
the exhaust laps may be unequal, zero, or negative. 

Throw of the Eccentric (Fig. 59). The eccentric Oe being 
directly connected to the valve it is evident if the former be 

FIG. 60. 

FIG. 61. 

FIG. 62. 

rotated from its present midposition to a horizontal position 
that the valve would move a distance Oe to the right or left in 
accordance with the direction of rotation. From an inspection 
of the figure we see that the valve must move the outside lap, o, 
to bring the valve and port edge and edge and any further move- 
ment will be called port-opening. The throw of the eccentric 
must equal the lap + the maximum port-opening. High-speed 
engine-valves are designed with considerable over-travel, as TO, 
Fig. 62, is called. 


Lead is the amount in inches that the port is open when the 
piston is at the beginning of its stroke. Examining Fig. 59, we see 
that, as the exhaust lap is always less than the steam lap, any 
movement of the valve to open one port to steam will open the 
port on the other side of the piston a greater amount. Hence 
exhaust lead is always greater than steam lead. 

We may now follow the crank through one revolution. 

Width of Port and Port-opening. By the width of the port 
is meant the invariable breadth of the port at the valve-seat, 
or p in Fig. 60. The maximum port-opening PO may be less 
than, equal to, or greater than the width of the port p, Figs. 60, 
01, and 62. 

Fig. 63: Crank OC on the dead-center, head end; piston P 
is at the beginning of its stroke; the left port is open the amount 
of the steam lead; the right port is open the amount of the exhaust 
lead; the eccentric is at some angle, coe (to be determined in 
amount later), ahead of the crank, i.e., in the direction of 

Fig. 64: The eccentric has moved to its extreme right-hand 
position; the left port has its maximum opening to steam; the 
right port has its maximum opening to exhaust; the piston has 
moved to the right to its position, P. 

Fig. 63 : W3 turn to the first figure and note the dotted posi- 
tions of crank and piston. The valve is moving to the left and 
is about to cut steam off from the left side of piston P f . 

Fig. 65: The piston is at the end of its forward stroke to the 
right and is at the beginning of its stroke to the left. The right- 
hand port is now open the steam lead and the left port is open 
the exhaust lead. 

Fig. 66: The eccentric and valve are in midposition twice in a 
revolution. Both ports are closed. The steam is expanding on 
one side and is being compressed on the other. The kinetic 
energy of the parts keeps up the motion. Note the position of 
crank and piston for the midposition of the valve. 

Practical Considerations. If the steam-pressure is the same 
at the two ends of a pipe there is no motion of the steam. To 
secure velocity, there must be a difference of pressure and to secure 
high velocity the difference becomes considerable. If the port 



opening is small the steam often has to flow at velocities of 6000 
to 20,000 feet per minute to fill the volume behind a rapidly moving 

FIG. 63. 

FIG. 64. 


FIG. 65. 

FIG. 66. 

piston. This necessitates an appreciable difference in pressure 
between the steam in the cylinder and that in the steam-chest. 


This explains the rapid falling off of steam-pressure at cut-off in 
high-speed engines. 

The following values will give approximate idea of the amount 
of steam lead given to engines. Experience will show that these 
values may be modified to suit other conditions. 

Diameter of Cylinder. Steam Lead. 

8" to 20" 1/32" 

20" " 30" 3/64" 

30" " 40" 1/16" 

Angular Advance. Fig. 63: If the eccentric were in mid- 
position, oc' ', Fig. 63, when the piston was at the beginning of its 
stroke, steam could not enter the cylinder as the valve would be 
in midposition. Keeping the crank and piston stationary we 
must move the valve to the right a distance = steam lap + steam 
lead. To do this we must rotate the eccentric ahead of the 90 
position some angle, a, such that r sin a = steam lap + steam 
lead. This angle, a, marked c'oe in Fig. 63 or DOE in Fig. 67 is 
called the ANGULAR ADVANCE. Fasten the eccentric to the shaft 
(90+ a) ahead of the crank. If the eccentric rod and valve-stem 
are the correct length the valve will be properly set. 

Amount that the Valve has Moved from its Midposition. If 
the eccentric was fixed at E, Fig. 67, when the crank is on the 

FIG. 67. 

dead-center OC the valve has been moved Ed = r sin a = lap 4- the 
steam lead from its midposition. If the crank rotates through 


an angle, 6 (carrying the eccentric through the same angle, as the 
eccentric is fixed now to the shaft), the eccentric will be found 
at E f , the valve having moved r sin (a + 0} from its midposition. 

The student should draw the crank and eccentric in various 
positions and find the corresponding positions of the piston and 
valves as in Figs. 63-66. 

Valve-diagrams. In the discussion on valve-diagrams the stu- 
dent must keep clearly in mind : 

1. When the crank is on the dead-center the piston is at the 
beginning of its stroke and the ports are open the amount of the 
steam lead on one side of the piston and the amount of the exhaust 
lead for the other port on the other side of the piston. 

2. The eccentric is ahead of its midposition an angle a of such 
magnitude that r sin a = lap + the lead. 

3. The angle a is invariable, the eccentric being keyed to the 
shaft (90 + a) ahead of the crank; so that if the crank rotates 
6 degrees from its dead-center the eccentric rotates the same 
angle. Hence the eccentric is (a +6) from its midposition, thus 
placing the valve r sin (a + 6) from its midposition. 

4. Referring to Fig. 59 we see .that if we subtract the steam 
lap from the amount that the valve has moved from its midposition 
we obtain the amount of port-opening to steam on one side of the 
piston, and if we subtract the exhaust lap on the other side of the 
valve we obtain the amount that the other port is open to exhaust 
on the other side of the piston. 

5. Negative port-opening indicates the amount that the valve 
must be moved to obtain a position where the port is just about 
to open. For instance in Fig. 59 the valve is zero inches from 
its midposition; subtracting the lap gives a minus port-opening 
(numerically = the lap) and shows how far the valve overlaps the 
port. If, in that same figure, the valve is moved to the left we 
must consider that amount as negative if motion to the right is 
considered positive. Subtracting the lap then gives a larger 
negative quantity, which we see represents the amount of the 
overlap or the amount that the valve would have to be moved 
to just open the port. 

6. Fig. 59: The opening of the central part E does not enter 
into the diagrams. Our only care must be to have it of such 



magnitude that the valve when moved to its extreme right or left 
position will still give plenty of room for the steam that is ex- 
hausting from either the right or left port. 

7. The engine and diagram must not be confused. In the 
engine, when the crank moves, the eccentric and valve also move. 
Once the diagram is constructed the only movable quantity is a 
line representing the crank, the rest of the diagram remaining 
stationary. The amount of motion of all the other elements of 
the valve is found by proper interpretation of the diagram. 

Pig. 68: Assume the crank to revolve clockwise and the con- 

FIG. 68. Zeuner Diagram. 

necting-rod to be to the left. In the diagram lay off the angular 
advance, a, negatively. On OE thus obtained lay off OF = the 
throw of the eccentric. On OF as a diameter construct a circle. 
Let the crank rotate through any angle, 0, from its dead-center 




position, OB. Then the Zeuner diagram construction depends 
upon the fact that "any intercept, OG, of the crank-line by the 
valve-circle represents the amount that the valve has moved from 


Proof. Connect F and G. OGF is a right angle, being in- 
scribed in a semicircle. 

OG = OF cos p = OF cos (90 - (a + 6)) = OF sin (a + 6) = r sin (a + 6) 

But (Fig. 67) r sin (a + 0) = distance valve has moved from its 

To the same scale lay off OK = the steam lap and draw the 
lap circle IQL. In the diagram many of the crank lines next 
mentioned are not drawn, as it would confuse the diagram. 

On the dead-center postion OB the port is open J7 = the 
steam lead. 

In the crank position OE the port is open the maximum amount 
FQ, as the port-opening decreases with further rotation of the 

In the position OL, steam has been cut off, as the port-opening 
has been decreasing and is now zero. 

In the position ON the valve overlaps the port MN\ 

In the tangential position ON' the valve is zero distance from 
its midposition or is in its midposition. 

In the position OP the valve overlaps the port PR. 

In the position OS the valve is at its maximum distance towards 
the left and overlaps the port by the lap + the eccentric throw = SF. 
The right port is consequently widest open. In each of the 
above cases the position of the left edge of the steam-valve is the 
one described. 

When the throw and angular advance have been determined 
for one end of the valve from the data, necessarily, they are de- 
termined for the other end of the valve, as there is only one 
eccentric having a fixed throw and a fixed angular advance. 
As the throw and angular advance of the eccentric are fixed 
there is. no reason why the lower circle (of the same diameter) 
constructed on the prolongation of OF should not serve to indicate 
the openings of the other steam-port for the other side of the 



piston for the return-stroke. Lay off the proper steam lap and 
proceed as before. 

Returning to the position OL we see, by referring to Fig. 68, 
that the valve is moving to the left (although the piston is moving 
to the right, the crank not having reached the right dead-center 
yet). When the crank reaches the tangential position ON' the 
valve is in its midposition. The left port, or head end, is now 
closed by the amount of the exhaust lap and any further move- 
ment to the left reduces the overlap. Now movements to the 
left of the central position are measured by intercepts on the 
lower valve-circle. Therefore describe the arc VW with a radius 
OF = the exhaust lap on the left side of the valve. From consid- 

Steam CufcQff 

FlG. 69. 

erations similar to those that have preceded we see that when 
the crank has rotated from the position OB to: 


07, the exhaust -port on the left side or head end is just 
about to open. 

OF, that the port is open the exhaust lead to permit the 

OA, the exhaust-port has its maximum opening. 

OW, the exhaust-port has closed and compression of the 
steam that has not escaped commences. 

By drawing an arc with a radius equal to the exhaust lap of 
the right side of the valve on the upper circle, in a similar manner 
the exhaust events for the right side of the piston or crank end of 
the cylinder may be indicated. 

Geometrical Relations of Elements of the Zeuner Valve Dia- 
gram. Suppose the diagram drawn (Fig. 69. Draw a crank- 
circle of any radius OA, it will represent the crank-circle to some 
scale. Then 

1. OH bisects A' OB and COD. 

2. HFO, HEO, and HIO are right angles, being inscribed in a 
semicircle, HE and HI are tangents to the lap circle. 

3. Draw a circle NHP with OH as a radius; join the intersection 
N and P of this circle with the two crank positions, steam admission 
and steam cut-off; the line NP so drawn is tangent to the lap circle. 

4. Drop the perpendiculars JL and JK, then JK = FG = ihe 
steam lead. 

In the following problems assume an infinite connecting-rod : 

Ex.25. Throw of eccentric = li", angle of advance =30, steam 
lap = ^", exhaust lap = J". Find the angle at which steam is ad- 
mitted and cut off, and the exhaust opened and closed; the steam 
lead, exhaust lead, and maximum opening of the port to exhaust. 

Ex. 26. Stroke is 4', steam is cut off at f stroke, and is admitted 
at 1" before the beginning of the stroke, the exhaust is opened at 
3" before the end of the stroke, the throw of the eccentric is 2"; find 
the proper angle of advance, the steam and exhaust laps, and the 
point on the stroke when the exhaust closes. 

Ex. 27. Stroke is 3', steam is cut off at 27", steam lead is J" ', the 
exhaust closes at 30" from the beginning of the stroke, throw of the 
eccentric is 1J"; find the maximum port-opening to steam and ex- 
haust, and position on the stroke when the exhaust opens. 

Ex. 28. Given the throw of an eccentric = 2", the external lap = 


I", steam lead = i", exhaust lap = J" (negative); find where the 
steam is cut off and where the exhaust-valve is closed if the stroke 
is 2'. 

Ex. 29. Stroke is 2', steam is cut off at 20", the lead is |", the 
outside or steam lap is f ", no exhaust lap; find the angular advance, 
throw of eccentric, and where the exhaust opened and closed. 

Problem. The amount that the port is to be open for any 
particular position of the crank, the position of the crank itself 
when the steam is cut off, and the amount of lead being known. 
To find the lap of the valve, throw off the eccentric, and its 
position with regard to the center lines of the crank. 

The solution of this and the next problem are modifications 
of those given in " Designing Valve Gearing," by E. J. Welch. 
The solutions are theoretically exact if the angularity of the 
eccentric-rod is neglected. Practically, however, the solution 
depends upon the intersection of lines making a small angle with 
each other and it is difficult to determine the exact point of 

Draw AB (Fig. 70) to represent the amount the port is to 
be open at the given position of the crank and lay off AC to rep- 
resent the required amount of lead. From the point C draw CD 
to represent the position of the crank at which the steam is to be 
cut off from the cylinder. Draw CE at right angles to CD and 
AF at right angles to AB. These lines intersect at G. Bisect 
the angle EOF by the line GH. This bisectrix is a locus of the 
required center N since EG and FG are tangents to a circle whose 
center is N. 

From C lay off CI to represent the crank position when the 
valve is open the required amount AB. If we draw CPL per- 
pendicular to CI it will be tangent to an unknown circle, aGP, 
at some unknown point, P, where TP is the required opening 
at the required angle. Similarly, if we draw BW perpendicular 
to AB, it will also be a tangent to the same circle. The bisectrix 
of the angle, PLW, so formed, will be LN, which is the locus of 
the center of this unknown circle, and it will intersect the other 
bisectrix, GH, at N, the required center of the unknown circle. 
Draw NC and the diameter of the valve circle will be obtained. 



NW are 

To check the position of the point N, see that NP and 
equal and that N lies in GH. 

Problem. The greatest amount that the port is to be opened, 
the position of the crank when the steam is to be cut off from 
the cylinder, and the amount of lead being given. To find the 
lap of the valve, the throw of the eccentric, and its position 
relative to the center line of the crank. 

Draw AB (Fig. 71) to represent the greatest amount that the 

FIG. 7?. 

port is to be opened and lay off AC equal to the given lead. 
Draw CD to represent the crank-angle at cut-off. A perpen- 
dicular to CD at C and a perpendicular to AB at A will both 
be tangent to the unknown lap circle. The bisectrix, GJ, of the 
angle EGF so formed is the locus of the point M. 

Lay off GU equal to AB and erect the indefinite perpen- 
dicular HKL Prolong the bisectrix JG till it intersects HI at 
some point K. In the completed but unknown figure we see 
that the radius PM (equal to the unknown diameter, MC, of the 
valve circle) is to GU as MK is to GK. Join C and K. With G 
as a center and GU (equal to AB the maximum port opening) 
r.s a radius draw the arc UL. Join G and L. Draw CM parallel 


to GL and intersecting the bisectrix GJ at M. The triangles 
LKG and CKM are similar and therefore MK:GK::CM:LG. 
It therefore follows, since three terms of this proportion are the 
same as three terms of the preceding proportion, that the fourth 
terms are equal, viz., that PM = CM. 

FIG. 71. 

The diameter of the valve circle having been found the re- 
maining points are easily found. 

Problem. Given ratio connecting-rod to crank = 5; steam lap 
1/2", exhaust lap 1/8", and steam lead 1/16" (all on headend); 
width of steam-ports 1/2", throw of eccentric 1J"; steam-pressure 
40 pounds per gage, back pressure 2 pounds above atmosphere, 


clearance 10%. Draw the theoretical indicator-card for the 
head end of the cylinder and sketch the valve when the piston 
is at the beginning of its stroke and again when the valve is in 
its extreme position to the right. 

Solution. Draw the indefinite straight line XOY. From any 
point lay off OG = steam lap, and GF = the steam lead on head 
<end; erect indefinite perpendicular FH, with as a center and a 
radius = the given throw of the eccentric describe an arc cutting 
FH at H] draw OH, it will be the diameter of the valve-circle and 
HOT will be the angular advance; with a radius OG describe the 
lap circle EGI] with a radius = the given exhaust lap describe the 
arc RSj with a radius OJ7 = lap + the width of port describe the 
arc UWV, then WH will be the overtravel. 

With a center at and a radius equal to the crank radius 
to some convenient scale, describe the crank-circle XBY; with a 
radius five times as great, describe the arc of the connecting-rod 
CiXC>2. Draw the various crank positions, as OB, and find the 
corresponding piston positions such as B f by laying off BCi 
from X. 

Project XY on any parallel line below the diagram and obtain 
X'Y , the length of the card; lay off X'Z to obtain the line of no 
volume or clearance line. Lay off the absolute pressures 40 + 15 
pounds and 15+2 pounds and obtain the steam admission and 
back-pressure lines Z'B" and C"S. Project B' Co Z>" and draw the 
isothermal expansion curve B"T> n ' project (7, the position of the 
piston when the exhaust closes, and obtain 6~' and draw the isother- 
mal curve of compression C"C m '. Find the points of steam 
admission and exhaust-opening and sketch in the expected 

On a parallel line lay of 12=.*team lead; 13= width of 
port; 26= the width of valve = steam and exhaust lap + width 
of port. 

To draw the valve in its extreme right-hand position lay off 
34 = the overtravel and then 47 is the width already found. It is 
evident that 79 ought to be at least as wide as the other port which 
is exhausting through 79. If the valve is thrown into its extreme 


FIG. 72. 


left-hand position it should go about an eighth of an inch beyond 
8. This prevents the formation of a ridge at that point. 

Ex. 30. If the data given in the above problem had been for the 
crank end, draw the indicator-card. 

Ex. 31. Assume the indicator-card found in Ex. 30 for the head 
end and draw the crank end of the valve. 

Ex. 32. Suppose that the eccentric in Ex. 30 was insecurely fast- 
ened and slips backwards (or ahead) some 30, draw the card. 
What is the effect on steam admission and cut-off, exhaust-opening 
and compression? 

Ex. 33. Diminish the throw of the eccentric J" in Ex. 30, and 
also increase the angular advance 30 5 . Draw the card. 

Ex. 34. Draw the indicator-card for the crank end of Ex. 29 if 
the valve-stem is made J" too long. 

There is another form of the Zeuner diagram that is frequently 
seen. In this form, instead of using a negative angular advance, 
a negative rotation of the crank is used. To illustrate this, lay 
off the diameter of the valve-circle of Fig. 68 to the right of OD 
a degrees and construct the diagram. To find how far the valve 
has moved from its midposition when the real crank has moved 
through an angle 6 clockwise from a dead-center OB, make use 
of an imaginary crank rotating the same angle anticlockwise from 
the head-center position OC. To find the piston positions make 
use of an imaginary connecting-rod that is swung from the right 
if the real one is on the left. Finally, when the indicator- card is 
found it will apparently be for the right side of the piston, when, 
of course, it belongs on the other side. The methods may be 
characterized as rights and lefts, and either may be gotten from 
the other by looking through the paper at the diagram instead 
of directly. 

Bilgram Diagram. The Zeuner diagram cannot be accurately 
constructed with certain data owing to the necessity of finding the 
intersection of lines that meet at a small angle. For instance if 
the position of the crank when the steam is cut off, the amount of 
lead, and the maximum port-opening are the data, the construction 
of the Zeuner diagram is complex and accuracy is difficult to 


attain. There are several more recently devised methods that 
are better than the Zeuner in some respects. We shall prove the 
construction of the Bilgram diagram. 

FIG. 73. 

With any point as a center and a radius equal to the throw of 
the eccentric describe the circle BFC. This circle is often used for 
the crank-circle since the scale of that circle is arbitrary. If the 
real engine is revolving clockwise from a dead-center position OB, 
lay off from the opposite center, 0(7, the angular advance, a, as 
shown and thus obtain the fixed point P. As in the Zeuner, 
nothing is to move but the crank. Further we must imagine that 
the crank has thickness and we must distinguish between the side 
marked R and the side marked L. 

The Bilgram diagram depends upon the fact that the perpen- 
dicular let fall from the point P (found as above) on any crank 
position, OF (prolonged when necessary), = the distance that the 
valve is from its midposition. Call all of one side of FG by the 
letter R and the other side by L. If the perpendicular is dropped 
on the side marked R, the valve is on the right of its mid- 
position; if it is dropped on the L side, the valve is on the left 
of its midposition. 

Let the crank move through any angle, 6, from its dead-center 
position to some position OF. Drop the perpendicular PH on 
OF (prolonged if necessary). From the diagram we see that 
PH = r sin (a + 6), which we know is the amount that the valve 
has moved from its midposition. 


As the port-opening = the distance that the valve has moved 
from its midposition minus the lap, it is evident that, if with P 
as a center and radii equal to the steam and exhaust laps we 
describe the circles Pe and Pi, we may automatically subtract the 
lap and obtain the port-opening. 

As the crank rotates from the position OF to 01 the distance 
PH increases and is a maximum in position 01, which is perpen- 
dicular to OP. 

The port-opening decreases to position 02, where cut-off takes 
place, as the valve is evidently (in this construction) moving to the 
left and is only the amount of the steam lap from midposition. 

At OP the length of the perpendicular has reduced to zero and 
the valve is no distance from midposition, i.e., is at midposition. 

The perpendicular now falls on the L side J)f Ihe crank and 
increases in length, showing that the valve is moving to the left 
from its midposition. Opposite 01 or at 08 the valve is furthest 
to the left and therefore the right or crank end port is widest open. 

The perpendicular is now becoming shorter, showing that the 
valve is returning to midposition, which it reaches in a crank posi- 
tion opposite OP or at OQ. 

Further rotation causes the perpendicular to fall on the R side 
of the crank, showing that the valve is moving to the right from 
its midposition, and when it moves the amount of the lap the crank 
is in position 04, in the prolongation of the tangent to the lap 
circle position 03, and the valve is about to open the port. 

Further rotation brings the crank to the dead-center OB and 
the diagram shows the port open the amount of the steam lead mn. 
The locus of the point H is a circle drawn on OP as a diameter. 

By referring to Fig. 59 it will be seen, if the valve has no exhaust 
lap, that exhaust-opening takes place for the head end when the 
valve attains midposition in its motion towards the left and the 
exhaust closes again in the midposition of the valve on its return 
to the right. In Fig. 73 when there is no exhaust lap, exhaust- 
opening takes place for the head end in crank position OP and 
exhaust-closure in position OQ. 

The effect of giving positive exhaust lap is to delay the opening 
and hasten the closure of the port as compared to the effect of 
no lap. Hence, if there is positive exhaust lap, Pe, exhaust- 



opening will take place in crank position 05, whilst exhaust-closure 
will take place at 06, which is ahead of OQ, where compression 
wo^ld have commenced if there had been no exhaust lap. 

These effects must be reversed if the exhaust lap, Pe, is negative 
instead of positive. In that case opening would take place at 
09 and closure at 07. 

Piston positions must be determined as in the Zeuner diagram 
by the use of arcs having the length of the connecting-rod as a 

To obtain the effects on the crank end, the point Q, opposite 
P, must be used as the center of the lap circles since the angular 
advance and throw of the eccentric are fixed quantities. The laps 
and leads may be the same or different from those on the head 
end. The effect of changes can only be determined by finding 
first the crank position of important events and then determining 
the corresponding piston positions. If the laps are the same on 
head and crank ends, the piston positions of steam admission and 

FIG. 74. 

cut-off, exhaust opening and closing, will be different at the two 

An examination of the fundamental principles of all forms of 
slide-valve diagrams will show that they depend on laying off 
the angular advance on one side or the other of either a vertical 
or a horizontal line and the measurement of a perpendicular. 


Geometrical Relations. The construction of the diagram from 
data to find other quantities requires a comprehension of the 
geometrical relations that exist between principal lines in the 
complete figure. 

The radius of the circle KPM is always the throw of the eccen- 
tric, mn is the amount of the steam lead (Fig. 74). 

The angle POC is always the angular advance laid off with an 
opposite rotation from the dead-center opposite that of the real 

The lead line KM, steam cut-off line 02, steam admission line 
04 prolonged, and a line ad drawn parallel to any crank position 
Ob at a required amount of port-opening ab for that crank position 
are all tangent to the steam-lap circle. The locus of the center of 
the lap circle must be the bisectrix of the angle between any two 
such tangents. The intersection of any two such loci gives the 
required center P. A similar series of tangents may be drawn 
to the exhaust-lap circles. 

Ex. 35. Apply the Bilgram diagram to the solution of Exs. 25 to 

Ex. 36. Stroke is 2', steam cut-off at 20" from the beginning of the 
stroke, steam lead J", valve is to be open f " when crank has made 
an angle of 30 from the beginning of its stroke. 

Ex. 37. Stroke is 3', steam lead is J" ', steam cut-off at 24", ex- 
haust opens 15 before the beginning of the return-stroke and closes 
30 before the end of the return-stroke; find the angle of advance, 
throw of the eccentric, and inside and outside laps. 

Ex. 38. Stroke is 2', steam is cut off at f stroke, maximum port- 
opening is 1"; find the throw of the eccentric, angle of advance, and 
the outside lap. 

Problem. Draw the cross-section of a plain slide-valve to 
comply with the following conditions: Width of ports 1/2"; 
overtravel on the head end 1/4"; cut-off on both head and crank 
ends 3/4 stroke; stroke 18"; steam admission commences on 
head end when the piston is 1/4" from the end of its stroke ; 
exhaust opens at 9/10 stroke on both ends; ratio of connecting- 
rod to crank = 5; initial steam-pressure 60 pounds absolute; back 
pressure 15 pounds absolute; clearance on each end 10%. Assume 
thickness of cylinder parts as 3/4". 


Construction (Figs. 75, 76). Lay off the stroke XY on 
a scale 2" = !'; draw crank-circle X2Y', lay off connecting-rod arc 

FIG. 75. 

CiXC2', lay off cut-off points B and E' and find crank positions 
02 and 02'; lay off XA = l/4" and obtain 04 crank position at 
steam admission and prolong, thus obtain 03, a tangent to the 

FIG. 76. 

lap circle, head end; the maximum port-opening, head end, being 
given, layoff arc SS' with a radius = 3/4"= width of port + over- 
travel. Three conditions for the lap circle being given, ordinarily 



the circle is easily drawn. In this case the locus of the center is 
on OP, the bisectrix of the angle 203, and it is not difficult, practi- 
cally, to obtain the center P so that a circle can be drawn tangent 
to 02, 03, and the arc SS'. The exhaust-opening at C gives crank 
position 09, and as this precedes OP the exhaust lap Pe on the 
head .end is negative. For the crank end, the throw of the eccentric 
and the angular advance (since there is only one eccentric) are- 
fixed and, therefore, the position of P' is determined. With a 
center at P f draw a circle tangent to 02', this gives the steam 

FIG. 77. 

lap. Find the crank position corresponding to exhaust-opening 
at C' and draw the crank position 09' at exhaust-opening. As 
this position follows position OP' the exhaust lap on crank end is 
positive. The leads and port-openings differ considerable from 
those on the head end. 

Dimensions of Steam-ports and Pipes. It is easy to determine 
the area of a steam-port if you have enough experience to determine 
what lineal velocity the steam may have in any particular case 
without too much loss of pressure. The roughness of castings 
does not vary much with their size, but its influence on the veloc- 
ity of steam in a passageway 1/8" wide is enormous when com- 
pared to its effects in a passageway 4 7/ wide. "TEe~aIIowaBle"^team 


velocity will vary then with the size of the ports, their roughness, 
their length, and their freedom from sharp bends. We must 
distinguish between maximum port-opening (when it is less 
than the width of the port), width of the port in the valve-seat, and 
the width of the passageway for steam below the valve-seat. 

* Formerly when engines cut off at 5/8 stroke, a lineal steam 
velocity of 100' per second ( = 72,000" per minute) was allowed. 
Nowadays 150' to 500' per second is allowed in obtaining the 
maximum port-opening with ordinary or usual cut-off in high-speed 
engines; the width of the port at the valve-seat is determined 
by allowing 125' to 150' per second, whilst the passageway, if used 
by the exhaust-steam on its return, is designed on an allowance 
of 125' per second. 

The effects of size, roughness, cut-off, and variable piston ve- 
locity are all merged in the choice of the velocity factor. Then 
the volume swept through by the piston in cubic inches per 
minute divided by the factor expressed in inches per minute = 
area of the port in square inches. 

Let a = area of steam-port, or maximum port-opening, or area 

of the steam-passageway; 
A = area of the piston in square inches ; 
L = stroke in inches; 
N = number of strokes; 
F = 72,000", 90,000", 108,000", or 144,000" per minute; 


In the case of high-speed engines with shaft-governors the student 
will note that shorter cut-off is obtained by automatically diminish- 
ing the travel of the valve. As a result the maximum port- 
opening at the economical cut-off (j- or -^ stroke) is so small that 
the factor F in many cases exceeds 360,003 inches per minute. 
This port-opening is often only one and a half to twice the 
steam lead. 

A cross-section at right angles to the one shown in Fig. 59 
should demonstrate that the exhaust-steam will not be choked in 
its exit from the cylinder. Hence the design of a cylinder should 

* For a full discussion, see Trans. A. S. Naval Engrs., Vol. XVI, No. 2. 


be examined to see that ample area for the passage of both live 
and exhaust steam into and out of the cylinder has been provided. 
The height, h, under the valve (Fig. 77) should be at least equal 
to the width of the port; a curve should be made as at c to pre- 
vent the formation of eddy-currents that would be formed with 
a right-angled corner. When the piston passes a dead-center, 
the valve will lift if much water gets into the cylinder; hence, 
to prevent the bending of the valve-stem its connection to 
the valve must be a sliding fit to permit the latter to lift off 
its seat. The trouble has been merely indicated to allow the stu- 
dent to provide suitable remedies. Steam- and exhaust-pipes 
should not be screwed into the castings, as the cast-iron thread 
is very weak and the movement of the pipes, generally having 
long lever-arms, soon causes leaks that cannot be stopped. Pro- 
vision should be made in the design for flange connections. 


Lead. The thickness of a pen-knife blade is enough lead for 
an engine up to 12 inches diameter of cylinder, 1/16" to 1/8" for 
cylinders up to 21 inches in diameter, 1/8" to 1/4" for cylinders up 
to 30 inches diameter; in large engines it often amounts to 1/2 
inch or more. In some high-speed engines where the compres- 
sion is very high, the lead is much reduced or made negative. 

Width of Port. In the steam-engine, heat is transformed into 
work at a comparatively low efficiency and, therefore, it does not 
pay practically to convert any of that work back into heat. It is 
desirable that the steam-pressure on the piston should be as near 
boiler pressure as possible. In very small engines the friction of 
the walls is a much more important factor than it is in large 
engines. For example, let L be the length of a steam-port and B 
its width in the case of a small engine and 8L and SB similar 
dimensions in a large engine. Then 

Perimeter _ 2 (L + B) 16(L + ff) 

Area LB 64L 

in the two cases, showing that, in so far as friction is influenced 
by skin-friction, the small cylinder has eight times the friction 


that the larger one has. The velocity usually allowed is 6000 
feet per minute. This is too high for cylinders of 6 or 8 inches 
in diameter and is too small for cylinder diameters of 40 inches and 
upwards. In high-speed engines, whilst the port may be designed 
for 6000 feet velocity, it will be found that, in most cases, the port 
is not fully opened by the valve when the engine is at normal 
speed. In other words, at less than normal load the port -opening 
is considerably less than the width of the port. As far as the 
valve motion is concerned, it is desirable to have a small port 
area, as valve friction and all valve dimensions may be diminished. 
In some cases the cross-sectional area of the steam-passage is 
increased just under the valve-seat. This increases the clearance 
volume and economy requires the clearance to be reduced to 
a minimum. As the area of the port is desired in square 
inches we may take the linear velocity as 72,000 inches; then 
72,000 X area of port in square inches = the volume swept through 
by the piston in cubic inches per minute. 

It is to be distinctly understood that the assumed velocity is 
a rate and that it is not influenced by the cut-off or the unequal 
piston velocities at different parts of the stroke. As the velocity 
rate is determined empirically, it is better to merge all small 
variations in that factor. The area found above is the area of 
each port and not the sum of the two ports; the cubic inches 
swept through by the piston is 

where r = radius of piston in inches; 
1 = stroke of piston in inches; 
s = number of strokes. 

Thickness of Cylinders. The thickness of cylinder walls is 
governed by the necessity of providing sufficient passageways for 
the metal in casting and of securing sufficient rigidity in the 
casting at all times but especially during boring. It is of the utmost 
importance on account of internal shrinkage stresses that all 
parts of the casting be of uniform thickness whether demanded 
by strength or not, and that all parts making angles approximately 
at right angles with each other should be well filleted. 


The following are given as approximations : 

t = Q.QQ3DVj> for small cylinders 
= 0.03v / Dp for medium and large cylinders; 
D = diameter of bore of cylinder ; 
p = maximum pressure in pounds per square inch. 

Thickness of the Bridge between the Steam- and Exhaust-port. 

In general the bridge should be the same thickness as the rest of 
the cylinder casting, but in every cass it is necessary to put the 
valve at the end of its motion in each direction to see that the 
outside edge of the valve does not go beyond the bridge and open 
a direct communication between the steam- and exhaust-passages. 
This, of course, can occur only in valves having overtravel. There 
should be at least 1/8 to 1/4 inch seal between the steam- and 
exhaust- space under the valve at all times. 

Width of the Exhaust-port. Put the valve at the end of its 
travel, then the inside edge of the exhaust lap for one port should 
not contract the passage of the exhaust from the other steam- port. 

Slide-valve Problems. The following are all the elements that 
enter into slide-valve problems. 

(1) Angle of advance. 

(2) Throw of eccentric. 
Length of connecting-rod L 

Crank radius ~R' 

Crank End. Head End. 

(4) Inside lap. (4) Inside lap. 

(5) Outside lap. (5) Outside lap. 

(6) Amount of steam lead. (6) Amount of steam lead. 

(7) Amount of exhaust lead. (7) Amount of exhaust lead. 

(8) Port-opening, or width (8) Port - opening, or width 

of port and overtravel of port and overtravel 

(+or-). (-for-). 

The crank-angle or piston The crank-angle or piston 

position of: position of: 

(9) Steam admission. (9) Steam admission. 

(10) Steam cut-off. (10) Steam cut-off. 

(11) Exhaust-opening. (11) Exhaust-opening. 

(12) Exhaust-closure. (12) Exhaust-closure. 

(3) must always be given. (1) and (2) are always the same 
for both ends. If four elements of one end and two of the other 



are given a complete solution is generally possible. Care must be 
taken that there is no conflict between the four e laments chosen. 
Valve Ellipse. Use is sometimes made of diagrams that 
represent graphically the relative and actual velocities of travel 
of the piston and of the valve. Divide the path of the crank-pin 
ABC into any number of equal parts and, by the use of the 
connecting-rod, find the corresponding piston positions. At the 
points so found, lay off an ordinate that represents the amount 
that the valve is from its midposition at that time. These ordi- 
nates are readily obtained from the crank positions on the Zeuner 
or Bilgram diagrams when there are no intermediate linkages. 

FIG. 78. 

If any such exist, as in the Corliss engine, the actual position must 
be plotted graphically. (Fig. 78.) 
Lay off 54 = outside lap; 

43 = steam lead; 

41 = the maximum port opening; 

12 = the overtravel; 

24 = exhaust-port; 

56 = the inside lap; 

67 = the exhaust-port opening; 

78= exhaust overtravel. 


Then a6 = the period of steam admission; 

bd = the period of steam expansion; 

cd = the period of prerelease; 

ef period of compression. 

A rapid variation in the length of successive ordinates indicates 
rapid movement of the valve. It is desirable that a valve should 
open and close with the maximum possible rapidity and be prac- 
tically motionless during the time that the valve is either wide 
open or closed, especially if there is heavy pressure on the back of 
the valve during such periods. 

Steam-pipe.* When steam flows through a pipe we must con- 
sider not only the properties of the steam but also that of the pipe 
and the influence of the surroundings or environment of the pipe. 

(1) We must consider the difference of pressure between two 
points on the pipe line, the quality of the steam, its volume and 

(2) The length and diameter of the pipe, the number and 
character of elbows and bends, the number and kind of valves, 
and the condition of the interior surface of the pipe influence the 
loss by friction. 

(3) The covering of the pipe, whether it is in the air or under- 
ground, the character of the ground whether wet or dry, the ex- 
posure to winds, the position of the pipe and its drainage, influence 
condensation losses. 

The heat losses, indicated above, manifest themselves in a loss of 
pressure and in the formation of water from the condensation of 
steam. The heat losses or changes may be divided into four 
divisions: (1) those caused by friction, (2) condensation, (3) 
expansion, (4) gravity. 

Let E a = initial energy at any cross-section of the pipe; 
E b = the energy at another section of the pipe; 
Ef = loss of energy due to friction; 
E c = " " " condensation; 

E e = " " " expansion; 

E g = " " " gravitation; 

* For data on the flow of superheated steam in pipes see Foster in the Trans- 
actions of A. S. M. E., Vol. 28. 


If W pounds are raised h feet the foot-pounds of work required 

v 2 
will be Wh. If h be expressed in terms of velocity we have h =- and 

therefore Wh = W^-. If a cubic foot of water weighs 

W pounds and the cross-section of a pipe is one 
square foot, then to raise the water-level one foot 
at h feet high would require approximately a pressure 
of Wh pounds exerted through one foot or Wh foot- 
pounds. If the water-level is lowered one foot, the 
water at C can exert Wh foot-pounds due to its energy. 
This is true only on the supposition that the tube is 
frictionless. Hence, in practice, the issuing velocity is 
less than that due to a head hi. This new head hu is 
the head that would be required in a frictionless 
pipe to produce the actual velocity. The difference 
hi-hii=h f is then a friction head. Another way of FIG. 79. 
expressing the same is as follows. The friction is 
proportional to v 2 (the velocity squared). By making it a pro- 

v 2 
portional part of -~- we may also express it as a proportional 

part of the head that produces the velocity. The friction is 
directly proportional to the wetted surface nDL and is inversely 

proportional to the cross-sectional area or r~, or, combining 


these two, is proportional to ^-^ == ~/v or ^ e * oss ^ head 


9 A T VAT 

friction is/ o~~n" = ^/J hence the work of friction Wh f =Wf-^--jr. 

*/ O 

If we consider a well-lagged horizontal pipe, E c and E g may 
be neglected and E t may be disregarded, as it represents change 
of the form of energy rather than its loss. Hence for this case 

v 2 L 
we have E a E b =E f ^Whf = W'f 2-^, where v is velocity in 

feet per second, L is the length and D is the diameter of the pipe in 
feet. Now, as a rule, we want to find the loss of pressure in pounds 
per square inch due to fractional losses. It requires a difference 
of pressure to produce a given velocity in a frictionless pipe, and 


considering friction, there would have to be a greater difference 
to produce the same velocity. 

If we took a column of the gas under consideration h f feet high 
and one square foot cross-section its volume would be h f cubic 
feet, and if it weighed d pounds per cubic foot its total weight 
would be hfd and the pressure per square inch would be 

f . . 

TT =pf pounds per square inch. 


p,144 f v 2 2_ T . . . . . 

~T~ =/ 7 D L * Unwm glves / = ^( X + T )> 

where K is a constant and D is the diameter in feet. 
We have therefore 

3 \v 2 2L 

If W = weight of steam delivered per minute and v is its velocity 
der second, 

_TF1_ 1 W 

~ 60 d xD 2 

3 \1 W 2 2L 

and if D be changed to d inches, 

W 2 L 

dd 5 20.664' 

The following experimental determinations of K have been 
K = 0.0027 for steam, Carpenter; 

0.0028 for air, St. Gothard Tunnel Experiments; 
0.005 for air, Arson; 
0.005 for water, Unwin. 

Substituting the value, K= 0.0027 for steam the loss of pres- 
sure is 



p/= 0.000131 


3.6\TF 2 L 
dd 5 ' 

The value 0.0027 was determined by Carpenter on pipes 1, 1J, 
2, 3, and 5 inches in diameter and of 90 to 230 feet in length. 

Table XIV was calculated by E. C. Sickles from the above 
formula, using 0.0026 as the constant. To use the table look in 
the left half -section of the table under the heading " Discharge 
in pounds per minute" for the discharge nearest to the given 
discharge. Then, on the same horizontal line in the right half- 
section under the heading " Drop in pressure in pounds, etc.," 
in the column under the given pressure will be found the drop in 
a straight pipe 1000 feet long. The heading of the column con- 
taining the nearest discharge gives the pipe diameter. 

For shorter pipes containing elbows and valves, corrections 
have to be made. In addition, on account of the eddies formed 
at the mouth of a steam-pipe when it enters squarely into the 
steam space, a correction called the " friction of entrance" has 
to be made. Complex formulas have been devised for these 
corrections, but they are practically useless. It is customary to 
add (to the actual length of straight pipe) lengths whose friction 
would be equivalent to the friction of the piece in question. 


Friction of 

Equivalent Straight Pipe. 


60 diameters 

Globe valves 

60 diameters 

90 elbows 

40 diameters 

Gate valves 

No friction 

A compound engine of 300 I.H.P. uses 18 pounds of water 
per I.H.P. Initial pressure is 135 pounds gage. The steam- 
pipe will contain two globe valves and two elbows and 90 feet 
of straight pipe. What will be the size of the steam-pipe and 
the probable drop of pressure in a well-lagged pipe? 


qrjA y -i o 

TJQ = 90 pounds of water per minute. From Table XIV 

a 4-inch pipe will supply 97 pounds of water per minute with a 
drop of 6.83 pounds, at 150 pounds absolute pressure, in a 1000 
feet of straight pipe. The given pipe is equivalent to 

Straight pipe ............................ 90 feet 

Entrance = 60X I 4 2 .................... 20 " 

Elbows = 2X40X'& ................ 27 " 

Globe valves= 2x60Xi 4 2 ................ 40 " 

177 " 


The drop in pressure will therefore be X 6.83 = 1.2 pounds 

per square inch. 

The curves below are illuminating in that they show at a 
glance the rapid drop of pressure when steam travels at high 
velocity through small pipes. The curves are practically 
derived from the formula given above. They are calculated for 
100 pounds absolute and 100 feet of pipe length and may safely 
be used up to 12,000 feet velocity and a drop of 10 pounds 
pressure. Within the above limits values taken from the figure 
may be used for other lengths and densities by multiplying the 
result taken from the figure by the given pipe length and given 
steam density and dividing the product so obtained by 22.71 
which is 100 times the density of steam at 100 pounds 

Equation of Pipes of Equivalent Carrying Capacity. While 
the cross-sectional areas of pipes are proportional to the square 
of their diameters, their carrying capacity is not so proportioned 
as friction will make a very considerable difference when there 
is a large ratio between the diameter of the pipes compared. 

Let W\ be the weight of fluid discharged by a pipe whose 
diameter is d\ and W 2 be the weight discharged by a pipe of 
diameter d 2 . Then if R is the ratio of the weights discharged 

* See Gebhardt, Power, 1907. 


by the two pipes of equal lengths and discharging the same 
fluid we shall have 







9000 4000 6000 8000 10000 12000 14000 16000 18000 
Mean Velocity-Eeet per Minute 

FIG. 80. Friction Head in Steam-pipes. 

From the formula we see that 43 two-inch pipes are required 
to equal the carrying capacity of one eight-inch pipe. 


Ex. 39. How many pounds of steam initial pressure, 125 pounds 
gage, will be delivered per minute from a 6" pipe, 1000' long, with a 
pressure drop of 16.4 pounds? 

Ex. 396. What will be the loss in pressure of a pipe 6" in diam- 
eter, 150' long, containing 4 elbows ani 2 globe valves (wide open), 
if the steam velocity is 8000' per minute. Initial pressure at the 
boiler, 125 pounds gage. 

Ex. 40. Find the size of the steam-pipe and of the steam- and ex- 
haust-ports of a Corliss engine. Assume length of port = diam. of 
cylinder. Stroke = 3 diameters, I.H.P. = 45, initial pressure, 75 Ibs. 
gage; non-condensing; cut-off \ stroke; revs. 94. 

Ex. 41. Engine 12"X12", 300 revs., I.H.P. = 100 at 100 Ibs. ini- 
tial pressure, and J cut-off, back pressure 16 pounds absolute. Design 
a valve to cut off at f stroke, head end, with an overtravel = J width 
of port. Assume exhaust lap = 0. Assume length of port = 0.8 the 
diam. of cyl. 

Ex. 42. Design the valve for the L.P. cylinder of a triple-expan- 
sion engine. Diam. cylinder is 72", stroke 5', revs. 75, cut-off at 0.7 
stroke, steam-lead angle 15, exhaust opens at 0.9 stroke, length of 
connecting-rod 15'. 


01 per cent of Ideal. 
40.0 Horse Power 

WTbs.Boi1er Press. 

90 per cent of i'dcal. 
C2.4 Horse Power 

KlbaBoiler Press. 

64 per cent of iden' 
15 Horse Power 

FIG. 81. Loss by Cylinder-condensation. 

^ i 

FIG. 82. Typical Admission-Lines. 

(From Carpenter's " Experimental Engineering.") 


Bottom of cyflnder 
Steam side. 

Vacuum side. 

FIG. 83. Unsymmetrical Valve-setting. 

FIG. 84. Variation of Load. 

(From Carpenter's "Experimental Engineering.") 



FIG. 85. 

FIG. 86. 


Fio. 88. 


High_Pressure Cylinder 12 x 20 
175 Rev.per Minute 


FIG. 89. 

Low Pressure Cylinder 14 x 20 

FIG. 90. 

Before the trouble was located 
FIG. 91. 

After the trouble was located 

FIG. 92. 
QUESTION. What caused the defects in indicator diagrams, Figs. 89 and 91? 


THE sensations produced by heat and its effects on bodies are 
matters of common experience. The hand held near the fire 
experiences a sensation that we say is produced by heat. The 
best conception of heat, however, is obtained by accurately measur- 
ing its effects. Under its influen3e solids increase in temperature, 
i.e. grow hot, usually increase in volume, diminish in strength and 
change many other physical characteristics such as the power of 
conducting heat and electricity; liquids rise in temperature, change 
many of their physical and chemical properties, and finally evapo- 

In heating bodies the rise of temperature does not continue 
indefinitely but ceases for solids when they commence melting 
and for liquids when they commence boiling. When solids are 
heated, the increasing rapidity of vibration of the molecules is 
shown by the increasing temperature; the length of the path is 
very slightly altered, as is shown by the very slight change in 
volume. At the melting-point, the rapidity of vibration is so great 
that the molecular attraction is at the point of being overcome and 
any further addition of heat cannot increase the rate of vibration, 
as the molecular attraction cannot oppose the increased stress; 
consequently the temperature remains constant and all the heat 
is spent in disgregation work. The energy of vibration is kinetic; 
the heat producing change of state or disgregation work is then 
stored up as potential energy. Similarly when liquids are at the 
boiling-point, all the heat added is spent in overcoming the molecular 
attraction, giving increased amplitude to the molecular paths and 
performing the external work inseparable with increasing volume. 
Hence as in the case of melting solids, this heat is stored up and 



is potential energy. It is called latent heat or concealed heat, 
since it is not indicated by a thermometer. 

All bodies at any temperature above absolute zero possess heat. 
This means, in accordance to the modern theory, that their mole- 
cules are in a state of vibration more or less rapid, depending 
upon the temperature of the body. 

In solids the mutual attraction of the molecules generally limits 
all movements to fixed paths. Hence, in general, solids retain their 
form and mass at ordinary temperatures. An exception must be 
made in the case of such solids as musk, camphor, arsenic, and ice, 
which may evaporate at ordinary temperatures. 

In liquids the motions of the molecules have been compared 
to that of dancers in the Virginia reel. Their motion is vibratory, 
rotatory, and progressive. The molecules revolve around one 
another, pick up a new partner as the old one is released, and 
revolve about the new one in turn. This free motion allows the 
liquid to assume a plane upper surface and the form of the 

No gas is absolutely perfect, but dry air, oxygen, nitrogen and 
hydrogen, at ordinary atmospheric temperature and pressure, are 
so far ABOVE the temperature at which their liquids boil that they 
act like perfect gases. Substances that are liquid at ordinary 
temperatures are converted by heat into vapors or imperfect 
gases. Steam, for instance, is an imperfect gas. By superheat- 
ing, however, a stage is reached where it practically follows 
the law of perfect gases. 

Liquids may be converted into the gaseous condition in two 
ways that are often confused but which are really very different 
from one another. Any liquid if left exposed to the atmosphere 
will finally evaporate. Clothes will dry in freezing weather. 
This evaporation will occur at any temperature, although usually 
there is a lower limit. For mercury, for instance, this is 14 F. 

Let us consider the evaporation of the water from a pan in 
the open air. Rapidity of evaporation will be secured 

1. By increasing the evaporating surface, putting the 

water in two pans; 

2. Changing the air frequently over the pan, by fanning 

the air; 


3. Performing the experiment on a dry day rather than on 

a wet one; 

4. By heating, but riot necessarily boiling, the water. 
The truth of the above may be demonstrated by experiment. 

To perceive why they are true we must keep in mind the motion 
of the molecules in a liquid as described above. In its vibratory, 
rotary, and progressive motion, at intervals, at the surface all 
of these movements, at the same instant, may be in one direction 
only. If that total motion in one direction takes the molecule 
out of the liquid with sufficient energy, it may move out into the 
air instead of falling back into the liquid. The gradual loss of 
molecules from the surface in this manner is evaporation. 

At the same temperature and pressure, dry air is heavier than 
moist air (see Table VI), hence the water molecule tends to rise 
till the temperature or the pressure or both are lowered, when 
equilibrium will be established. The hotter and drier the air 
the more rapid the evaporation. Usually this process is very 

The usual commercial method of forming steam by boiling is 
a very different process, governed by very different laws. Unfor- 
tunately for clearness, the term evaporation is also generally used 
for this process. In this, operation steam is not slowly formed 
at the surface of the liquid, but there is a rapid formation of steam- 
bubbles on the heating surface and therefore in the mass of the 
liquid itself. 

Consider for a moment the conditions that must exist on the 
inside of one of these little bubbles. It is evident that the mole- 
cules of steam must impinge on the water-envelope of the bubble 
with sufficient energy to form a pressure that will keep the water 
back. The intensity of this pressure must be equal to the intensity 
of the steam-pressure on the surface of the water increased by 
the weight of the column of water vertically above the bubble. 
If the steam-pressure increases, it is evident that the temperature 
of the steam inside the bubble will have to increase, since the 
required vibratory energy is proportional to the temperature. 
Consequently with each steam-pressure there is a corresponding 
steam-temperature necessary for boiling. 

In the power of increasing the length of the path of vibration 


gases differ essentially from liquids. Hence the volume of a gas 
increases to completely fill an enlarging volume, whereas the 
volume of a liquid remains practically constant under the same 

In the gaseous state, the attraction of the molecules for one 
another is extremely slight. The molecules are in incessant 
motion in straight lines, striking one another and the containing 
envelope, thus producing the pressure that they exert on the 
enveloping vessel. 

When they strike one another (if they do), they rebound 
without loss of energy. We are much interested in what happens 
when they strike the envelope. 

1. If the latter is at the same temperature as the gas, it is 
also in a state of vibration and the molecules will rebound with- 
out loss of energy. 

2. If the envelope is cooler than the gas, some of the energy 
of the molecule will be communicated to the envelope, which is, 
probably, losing heat by radiation, and the molecule will rebound 
with diminished energy. 

3. If part of the envelope is movable and (as a result of all the 
combined instantaneous impacts) motion ensues, the rebound will 
be with diminished energy as part of the energy is consumed in 
producing the motion against a resistance. When the molecules 
rebound with diminished velocity it indicates a lowering of tem- 
perature, viz., a loss of heat. 

It is of great importance to comprehend fully these effects as 
they explain how steam loses heat in doing work against a mov- 
ing piston in a steam-cylinder. Anything that tends to reduce 
the sum total of molecular velocities means a loss of heat, viz., 
a lowering of temperature. If the piston moves and the tem- 
perature of the gas (and therefore the heat in the gas) is kept 
constant, heat must be added (equal to the work clone) from some 
external source of heat. 

Heat cannot be expended without an equal quantity of en- 
ergy appearing in some other form. If the heat equivalent of 
each elementary change is known, then the total heat expended 
will be the sum of the heat-equivalents. Every heat-unit that 
disappears as heat must be balanced by the production of some 


change of equal thermal value. In the less complex cases less 
Leat is required, the decrease being equal to the heat-equivalent 
of the changes that did not take place. 

We saw above that when the molecules of a gas were allowed 
to do work they rebounded from the surface that yielded to 
their bombardment with less velocity than from an unyielding 
surface whose molecules are vibrating in unison with the gas, i.e., 
possessing the same temperature. If a gas does external work, 
it loses heat equivalent to the external work done. If work is 
done on the gas ; then the gas gains heat equal to the external 
work done on it. 

It is important to keep in mind that the difference between 

1. The total heat required to heat a substance from one 
temperature, ti, to another temperature, t 2 , and 

2. The increase cf the amount of heat in a substance 
when heated from t\ to 1% 

is always the external work. 

Let us take the most complex case possible and itemize every 
source of heat-expenditure. Heat a solid to the melting-point, 
melt it, heat the resulting liquid to the boiling-point, evaporate 
it, and heat the vapor under ONE cf several sets of conditions. 
The exceptions to the events as stated below are of little impor- 
tance to the student at present. These events are: 

1. Temperature of solid rises. 

l a . It expands against external pressure. 

2. Temperature remains constant, but melting is taking 

2 . Expansion against external resistance. 

3. Temperature of liquid rises. 

3. Liquid expands against external resistance. 

4. Temperature remains constant till all the liquid is evap- 

4 a . Change of volume against external resistance. 

5. Temperature and pressure increase, the volume remain- 

ing constant; 

or 5'. Temperature increases, pressure remaining constant; 
5 </. Volume increases against constant external pressure; 
or 5". Temperature increases; 


5o". Volume increases against varying pressure; 
or 5'". Temperature constant, volume and pressure varying. 

A careful examination of this apparently complex series of 
events will demonstrate that they may all be grouped under 
three heads, each of which is absolutely elementary in its nature. 
Heat is expended to produce 

(a) A rise of temperature: 1, 3, 5, or 5', 5" kinetic energy. 
(6) A change of state: 2, 4 potential energy, 
(c) External work : l fl , 2 a , 3a, 4 a , or 5a', 5 a ", 5'" mechan- 
ical energy. 

The heat required to produce any one of these events is not 
used to do two things. For example, when a substance is heated 
a few degrees we see that there is not only a rise in tempera- 
ture, but also that the substance either expands or contracts. 
What is meant by (a) is the heat that, theoretically, is required 
to produce the rise of temperature alone. 

When solids, liquids, or gases expand the external work is 
equal to the product of the increase in volume in cubic feet mul- 
tiplied by the mean pressure (in pounds per square foot) (page 30) 
that resisted the expansion. This product is foot-pounds of 
work, and divided by 778 will give its equivalent in thermal units. 

The expansion or contraction of a substance when heated 
may always be measured without reference to any other heat 
quantity. Hence the (c) events may always be found directly. 
Then, when there is a combination of any one (a) or any one 
(b) event with its corresponding (c) event, it is evident that, by 
measuring the total heat required to produce the two simul- 
taneous events, the value of the (a) or the (&) event alone may 
be found by subtracting the heat equivalent to the external 
work or (c) event from the total measured heat. 

Physicists, by careful measurements and determinations, 
have found the heat necessary for the (a) and (6) events for one 
pound (or unit weight) of most substances and tabulated the 
results. By proper use of these tables we may calculate the 
quantity of heat required in the most complex cases. 

Specific Heat. Different amounts of heat are required to 
raise equal weights of different substances through one degree 
rise of temperature. If a body expands, some external work 


is done equal in amount to the pressure per square foot that was 
acting on the body multiplied by the change of volume in cubic 


feet divided by 778, or ==$ . The change of volume of solids and 

/ /o 

liquids on being heated is so slight and the heat equivalent to 
the resultant external work is so minute that it may be neglected. 
Let h = total heat to raise 1 pound through 1F.; 

s=heat required to raise the temperature alone = change 
of intrinsic energy = change of heat as heat in the 

i = heat expended in overcoming the molecular attrac- 
tions = disgregation work = work done incident to 
change of state; 

e = external work due to change of volume under pressure; 
h = s +i+e (B.T.U. per pound). 

In the case of solids and liquids not only is e very small, but i 
is practically zero except close to the melting-point of solids 
and the boiling-point of liquids. Hence, in engineering questions, 
the heat required per pound per degree rise in temperature of 
solids or liquids is that required to increase their sensible tempera- 
ture alone. 

The amount of heat required to raise one pound of water 
one degree Fahrenheit, called a British Thermal Unit, or B.T.U., 
is adopted as the unit, since, from experiment, we know that more 
heat is required to increase the temperature of one pound of water 
one degree than is required by one pound of any other substance 
except hydrogen gas. See page 5. 

The Specific Heat of Solids and Liquids (C) is that fraction of 
a B.T.U. that is required to raise the temperature of one pound 
of a substance in either of those states through one degree Fahren- 
heit. Hence to raise W pounds from ti to t 2 requires 

W'C-(t 2 -ti) B.T.U. 

Specific Heat of Gases. We must distinguish between perfect 
and imperfect gases. Vapors are imperfect gases which on the 
addition of heat become more perfect and eventually may be 
made to act like perfect gases by the addition of sufficient heat. 
There is no such thing as absolutely perfect gases, but the so-called 


permanent gases, dry air, hydrogen, nitrogen, oxygen, which at 
ordinary temperatures and pressures are far removed from the 
conditions required by their liquids, may be termed perfect 
gases. Imperfect gases or vapors are not far removed from the 
conditions of their liquid, but may reach that state by the recep- 
tion of a large quantity of heat. 

In the case of perfect gases it is usual and practically correct 
to assume that no energy (heat) is required to separate their 
molecules. Theoretically the molecules, having mass, must have 
the mutal attraction called gravitation. This force of attraction 
must exist even if all other forces of mutual attraction are lost. 
As a matter of fact, in the condensation of the so-called permanent 
gases, use is made of this minute mutual attraction of the mole- 
cules. In the cases of imperfect gases, some heat is spent in over- 
coming molecular attraction. In the case of steam, for instance, 
it is now recognized that its specific heat is variable, and many 
scientists are now at work on the determination of the specific 
heat of superheated steam at various temperatures and pressures. 
Recent work in gas-engines leads to the conclusion that the 
specific heats of the gases used in those engines are not the same 
at high pressures and temperatures as they are at low ones. As 
no final conclusions have been reached, the student, in engineering 
problems, may assume i = for all gases perfect and imperfect. 

There still remains the other factor e = external work. If 
solids and liquids are not allowed to expand when heated, the 
pressure that is exerted is equal to that which would be necessary 
to compress them back to the original volume had they been 
allowed to expand freely. These pressures are enormous. On 
the other hand, in the case of gases the increase of volume is 
considerable if the gas ic allowed to expand, and it is also feasible 
theoretically to prevent all expansion. Practically, of course, the 
vessel does change volume with increase of temperature or pressure 
or both, but the change is relatively so slight as to be negligible. 

Specific Heat of Perfect Gases at Constant Volume. If a gas is not 
allowed to expand, no external work is done since work is the 
exertion of a pressure (against an equal resistance) through a 
distance. If either factor (pressure or distance) is zero, the work 
is zero. Mere increase of pressure, then, is not work. Hence if 


i and e are both zero, all the heat applied to the gas appears as 
heat in the gas, or increase of intrinsic energy. Its sole effect 
is to increase the rapidity of vibration of the molecules, and this 
results in an increase of pressure on the containing vessel and an 
increase of temperature as measured by a thermometer. Hence 

The Specific Heat at Constant Volume, C v , of a perfect gas is 
the fraction of a B.T.U. that is required to raise one pound of 
the gas through one degree Fahrenheit, the volume of the gas 
being kept constant. 

Therefore, if W pounds of a perfect gas are heated from t] 
to to F., the heat required would be 

ir-c^-fe -^ ) B.T.U. 

Another variation of the general rule occurs when a gas is 
heated and the pressure is kept constant. When one pound of 
a gas at constant pressure is heated one degree, the heat equivalent 
to the external work done is a fraction of a B.T.U. which may be 
added to C v , thus obtaining a new coefficient, C p . It is evident 
that the external work done by 10 pounds of gas heated 10 de- 
grees will be 100 times as great as that done by one pound of gas 
heated one degree. The expenditure of heat for external work 
varies with W(t 2 /i). Hence 

The Specific Heat at Constant Pressure is that fraction of a 
B.T.U. that is required to heat one pound of a gas one degree 
Fahrenheit and do the external work if the gas is allowed to 
expand against a constant resistance. To raise W pounds of gas 
from ti to t 2 and do the external work that accompanies expansion 
under constant pressure requires 

W- C p -(t 2 -ti) B.T.U. ' 

Ex. 43. In a non-conducting, non-heat-absorbing box are 30 
pounds of water at 75 F. What will be the final mean temperature 
if 5 pounds of lead at 50 C., 3 pounds of copper at 300 F., and 4 
pounds of cast iron at 50 C. are thrown into the box? (Table I.) 

Ex. 44. If \ pound of hydrogen is heated from 75 F. to 90 F. 
under constant pressure, how many B.T.U. are required? If the 
volume had been kept constant, how many B.T.U. would have been 
required? How many foot-pounds of external work were done in 
the first case? 


Ex. 45. It requires 73.2 B.T.U. to heat 3 pounds of a certain gas 
from 60 F. to 160 F. under constant pressure, and 16571.4 foot- 
pounds of external work are done. What gas is it? What is the 
increase of heat in the gas? 

Ex. 46. Two pounds of dry air at 75 F. and 20 pounds per square 
inch pressure are heated and cooled several times. At the end of the 
operations, by plotting a curve of the variations of pressure, and vol- 
ume it is found that 77,800 foot-pounds of external work have been 
done, and that the volume of the gas has been doubled and its tem- 
perature is 475 F. How many B.T.U. were expended, and what is 
the increase of heat in the air? 

Ex. 47. Two pounds of air under 20 pounds per square inch pres- 
sure and at a temperature of 200 F. are allowed to expand; heat is 
added so that, notwithstanding the fact that the gas is expanding 
and doing work, its temperature remains the same. If 100 B.T.U. 
were added to the gas, find the number of foot-pounds of external 
work that were done. 

Heretofore we obtained our answers in thermal units by using 
C p and C v . To obtain an answer in foot-pounds it was necessary 
to multiply by 778. The answer may be obtained directly in foot- 
pounds by multiplying by the corresponding constants K p and K v 
= 778C P and 778C V from Table I. The difference of these con- 
stants (KpKv) is a constant which will be called R. 

Derivation of the Fundamental Formula, PV = WRT. 

The truth of this formula is demonstrated by the correct results 
obtained by its use. 

Imagine a piston of any constant weight P resting on a perfect 
gas weighing W pounds. Cool the gas till its temperature is 
reduced to absolute zero and its volume is also reduced to an inap- 
preciable quantity. If the gas is now heated under constant 
pressure, it will take W(C P C v ) thermal units to do the external 
work per degree rise of temperature in accordance with our defini- 
tions. If the gas is heated T degrees absolute, the heat required for 
the external work is W(C P - C v ) T. Expressing this in foot-pounds, 
W(K P -K V )T, it may then be equated to the external work done 
under a constant pressure P through a volume V, or 

py = W(K P - K V )T = WRT. 

In the derivation of this formula we eliminated all internal 
heat. It cannot be used, therefore, in the determination of quan- 


titles of heat. It shows a relation that exists between physical 

conditions alone. 

In its use only one quantity must be kept constant, and that 

is the mass of the gas. Hence for any gas if 

PI = initial pressure absolute in pounds per square foot, 

F! = the initial volume (in cubic feet) absolute, 

TI = the initial temperature in degrees Fahr. absolute, 

P2 = the absolute pressure at any other instant in pounds per 

square foot, 

V 2 = the absolute volume in cubic feet at that instant, 
T 2 = absolute temperature Fahr. at that instant, 

then, whether the gas was heated or cooled, whether it did work 

or work was done on it, 

T 1 T 2 ' 

In the equation PV = WRT there are five quantities : if any four 
are known, the fifth can be found. Similarly in the equation 

P 1 V 1 P 2 V 2 

JJP = ~nn > there are six quantities; if any five are known, the 

LI -i 2 

sixth may be obtained. Note that P is a rate or intensity of 

Ex. 47. A cylinder 1 square foot in area and 4 feet long contains 
oxygen at 139 F. and 100 pounds per square inch pressure absolute. 
What is the weight of the oxygen? 

Ex. 48. A cylinder contains 1/10 of a pound of an unknown gas. 
The volume of the cylinder is 3.2 cubic feet, and the absolute pres- 
sure is 100 pounds per square inch, and the temperature is 139 F. 
What is the gas? 

Ex. 49. What volume will 1/2 pound of dry air occupy at 39 F. 
and 50 pounds per square inch pressure? 

Ex. 50. A spherical balloon, 30 feet diameter, is to be inflated 
with hydrogen gas at 70 F., with the barometer standing at 29.8 
inches. What will be the weight and volume of the gas that should 
be run in, if none is to be lost when the balloon has risen to such 
height that the barometer stands at 20 inches and the thermometer 
stands at 36 F.? 

Calculate the lifting-power when the balloon starts to rise. 

Ex. 51. Find the temperature at which one kilogram of air will 


occupy 3 cubic meters under a pressure of 5000 kilograms per square 

Ex. 52. A cylinder 1 square foot in area and 3 feet in height con- 
tains air at 100 F. under a piston weighing 576 pounds, exclusive 
of the atmospheric pressure. What is the weight of the air? 

p l V l P 2 V 2 

Boyle's Law. Taking the equation = ^ for a constant 

1 1 i 2 

mass of gas, it is evident that certain relations hold if any one 
of the three factors, pressure, volume, or temperature, is kept 
constant, allowing the other two to vary. If heat be added 
or subtracted so that the temperature is kept constant, we have 

P V 
Boyle's Law; for if T L = T 2 , then we have P^ =P 2 V 2 or -^ = ^. 

-T2 V 1 

Since the temperature is kept constant, P\Vi =P 2 V 2 must be the 
law of isothermal expansion. If V 2 is greater than V\ the gas has 
expanded; if it is smaller, then there has been isothermal com- 
pression. The law then expresses the fact that if the temperature 
is kept constant, the volumes will be inversely proportional to the 
pressures. It is generally much easier to deal with ratios thus: 
if the volume is doubled or trebled, the pressure is halved or is one 
third of the original pressure; or if the volume is one third or one 
fourth the original, the pressure is three or four times the original. 
Charles' Law. If the volume is kept constant, the equation 

P P 

becomes -^ WT If a gas be heated or cooled in a closed vessel 

1 I 2 

so that there is no change of volume, then the pressure is directly 
proportional to the absolute temperature. Put in the form of a 

P T 

ratio, -=p- = m~ t we see that doubling the pressure requires double 
"i * i 

the absolute temperature. 

Similarly if the pressure is kept constant the equation becomes 


Ti T 2 V 2 T 2 ' 

and we see that the volume is directly proportional to the AB- 
SOLUTE temperature under those circumstances. 

Joule's Law. For engineering purposes we may say that if a 
perfect gas expands and does no external work, the temperature 


remains constant. Let us examine the effect of this on the general 

T 7 ! T 2 ' 

By supposition TI = T 2 , therefore 

p,F 1 =P 2 F 2 . 

But this is the law of expansion of a gas at constant temperature. 
As T 2 is practically equal to TI, we shall assume the law to hold. 

Ex. 53. The area of a piston is 2 square feet; the pressure of the 
air against it when it is 1 foot from the beginning of its stroke is 50 
pounds. The temperature of the air is 100 F. If the air expands, 
doing work as the piston moves to the end of its stroke, find the final 
pressure of expansion, if the stroke is 4 feet and the final temperature 
of expansion is 100 F. 

Ex. 54. The cylinder of an air-compressor is 3 square feet in area 
and 2 feet stroke. If this cylinder is filled with air at 15 pounds 
pressure and at a temperature of 60 F., what will be the final pres- 
sure of compression if the air is compressed at a constant tempera- 
ture to one fourth its original volume? 

Ex. 55. A cylinder contains dry air at 100 pounds pressure per 
square inch and at 75 F. If the area of the cylinder is 3 square feet 
and its length is 2 feet, find the number of B.T.U. that it will take to 
double the pressure, if the volume remains constant. 

Ex. 56. A cylinder with a movable piston contains one half pound of 
oxygen at a pressure of 100 pounds per square inch absolute. If the 
volume of the gas under the piston is 1 cubic foot, required the num- 
ber of B.T.U. to double the volume under the above pressure. What 
is the increase of intrinsic energy of the gas? 

In using these formulas it is convenient to express the pressures 
in pounds per square inch. This can be done by expressing the 
area of the piston in square inches. All stroke dimensions must 
be in feet. 

The formulas for the net work done and the mean effective pres- 
sure are very much simplified by making the clearance equal zero 
and closing the exhaust-valve at the end of the stroke. These 
simple formulas will not apply to a cylinder that has clearance, 
and most cylinders have clearance. 



Curves of Expansion of a Gas in General. When the volume of 
a gas varies either increasing or decreasing in volume doing 
work (or the reverse) and either receives or loses heat in some 
regular way, the relation that exists between the pressure and 
the volume at any instant may generally be expressed by the 

For example, if be, Fig. 93, represent the expansion curve 

FIG. 93. 

PV n = C, from the point 6 draw other curves above or below be. 
It is evident that some relation such as 

PV n = C, 

or, in general, 

might exist between the absolute pressure and its corresponding 
volume at any instant of the expansion. 

To find an expression for the work done during expansion when 
the expanding gas either receives or loses heat in such manner 
that the relation between the varying pressures and the varying 
volumes is PV n = C. 

Work done during expansion = J PdV; 

This is readily reduced if F 2 ~ n+1 is multiplied by P 2 F 2 n (which 
is equal to PiF^) rather than by PI TV 

n+1 n-1 

This gives the work done during expansion of W pounds of 
gas (determined by PI, FI) expanding from I^ to T 2 and mean- 
while receiving or losing heat so that the law of expansion may 
bePF = C. 

p TT _ p y 

To express the work - t 2 in thermal units. From the 


general equation PF = WET we have 

The w r ork done during expansion in foot-pounds is therefore 

W(K P -K V )(T 1 -T 2 ) 

or, expressing this directly in thermal units, is 

W(C P -C V )(T 1 -T 2 ) 

The change in intrinsic energy is WK V (T 2 TI), since the gas 
has changed from Tf to T 2 . 


The total heat required is that necessary to produce the change 
in intrinsic energy and do the external work, viz., 

WK V (T 2 -T 1 ) 

Tr(gp-g.)(ri-r 8 ) 


The equations just derived are general and any value of n 
may be used except unity, and that value gives isothermal ex- 
pansion, which has already been discussed. 

Since we may suppose heat added or subtracted in any way 
we choose, a very important special case is that in which the 
supposition is made that no heat is added to the gas from any 
external source while it is expanding, neither does it lose heat 
AS HEAT by radiation nor conduction to any outside body. If 
the gas expands and does work, it must lose some heat. As we 
have made the conditions such that it is impossible to lose or 
gain HEAT as HEAT, it is evident that the external work done 
must be the sole measure of the heat that the gas has lost. This 
is adiabatic expansion. 

For Adiabatic Expansion the formula for the total heat re- 
quired niay be equated to zero, since no heat is added or sub- 
tracted. Therefore 

nK v (T 2 ~T 1 )-K v (T 2 -T l )+K p (T 1 -T 2 )-K v (T i -T 2 )=0, 

Since the temperature decreases T 2 cannot equal T\, therefore 
(nK v K p ) must be the zero factor. Hence 

T? C 1 

L*- P ^ P 

An adiabatic expansion is a particular kind of expansion and 
hence the general value n cannot be used. For this kind of 


expansion n has the definite value ^, which is constant for 


any gas but varies with different gases. For simplicity ? is 


generally used for the value of -^ for any gas. 

o v 

The equation for adiabatic expansion is then 

PVr = C. 
The work done during adiabatic expansion is 


The total work of admission and expansion is 


The net work done per stroke when there is no clearance and 
the back pressure = the final pressure of expansion 

WK v r(Ti - T 2 ) = WK P (T 1 - T 2 ) foot-pounds 

C 2375 

for perfectly dry air is - = ~ = * ' 

Y for moist air has some value between 1.4 and 1.2. 

The equation PV r = C may be easily derived from the two 
fundamental equations of thermodynamics derived on page 152: 

H = K p dT-VdP, 
H = K v dT+PdV. 

When the expansion is adiabatic H = Q: 

K p dT=VdP, 
K v dT= -PdV, 
K^ = VdP 
K v ~ r ~ ~PdV 
dV = dP 

-r- v - p- 

Integrating, C f log V = log P, 


To Draw the Curve PV n = C (Fig. 94). Suppose the curve and 
a tangent at any point m is drawn. 

FIG. 94. 

Differentiate PV n = C. 

7 n - l dV = Ois the equation of the tangent. 



From the figure, 

'* ~efe 

From similar triangles, 

'dV = ~d^' 

md cd 

n ~j > ' ~j~ 
cd ' de 


r- = n also. 

The minus sign shows that the angle, 0, that the tangent makes 
with the X axis, if measured from the X axis to the tangent, is 
greater than 90 degrees. Given one point on the curve and n, the 
value of C may be calculated. For any assumed V, the corre- 


spending P may be calculated, and then if be and cd be assumed 
to be those values, de and ab may be laid off so that the tangent 
may be drawn. Having a series of points and the tangents, the 
curve may be drawn through the points and tangent to the tangents. 

Logarithmic Cross-section Paper and PV n Curves. Loga- 
rithmic cross-section paper is invaluable in work dealing with 
equations of the form PV n =C. By the use of this kind of cross- 
section paper we find that the drawing of curves is replaced by 
the drawing of straight lines. Hence in hydraulics and in air 
or steam compression or expansion, it not only facilitates work 
immensely but it also serves as a guide to indicate any variation 
in the law of expansion as the variation of the exponent n becomes 
immediately apparent. 

The curve PV n =C has many disadvantages: 

1. It has to be laid out for each different initial P and V. 
For superheated steam the curve is rather complicated, as it will 
consist of two curves meeting at the point where saturated steam 
is converted into superheated steam. 

2. The areas in the low-pressure zone are very inaccurate, 
the PV n = G curve being there nearly parallel to the axis of V. 
It does not show at a glance what happens when the initial 
pressure is lower than the boiler pressure; what happens when 
the initial pressure is raised or lowered; what happens when 
the exhaust pressure is raised or lowered; what happens when 
both of these pressures are changed simultaneously. 

3. The whole diagram is not flexible and transparent, so 
permitting changes in the lay-out to be made rapidly and their 
effects to be visible instantly.* 

These troubles disappear when the curves PV n =G are plotted 
on logarithmic cross-section paper. (Fig. 95.) 

If we take the logarithm of both sides of the equation PV n = C 
we still have a true equation. Hence 

log P+n log V =log C or log P= -n log F+log C. 

In this form, we have the equation of a straight line as it is 
evidently of the form y=mx + b. 

Hence, if we plot the logarithms of the various values of 
P and V and the logarithm of the constant C, we shall have a 

* See Steam-turbine Characteristics, Holzworth, Trans. A. S. M. E., Vol. 28. 



straight line whose intercept on the axis of Y is log C and which 
makes with the X axis an angle whose tangent is n. It is 
readily seen how simple it is to plot a straight line and how easy 
it is to see if its inclination to the X axis varies. 





f5 ft 

4 ft 



q A 











- 1.0 

- 0.5 


- 0.2 
" 0.15 

* x- 



X " 


S E 








^ x 



N ^ 




^ N 

. .Cl 


^ x 




X N 


F y 










H to ot eo^oooo 
3 20 00000 

i f i i 1 i i 7 t 

9 too o oooo c 

^ C* * 00 C 

i f I I I ~i i I i 1 

% e d S o 

FIG. 95. 

o* o_^i4 

Those who have used the slide rule know that it is la'.d off 
to a logarithmic scale but that the divisions are marked with the 
numbers themselves rather than with the logarithms of the 
numbers. The divisions hence appear very irregular. In this 
way one multiplies or divides with the aid of the slide rule by 
the addition or subtraction of logarithms and yet never looks 
up or knows the logarithms of the quantities multiplied or divided. 


Similarly, if the subdivisions on the logarithmic cross-section 
paper are marked by the numbers instead of their logarithms 
the straight line form of the curve may be laid off without look- 
ing up the logarithms. Nevertheless, it is essential to keep 
in mind that we are really dealing with logarithms. Hence 

(1) The origin on logarithmic scale paper is at the inter- 
section of the lines 1 and 1 since the log (1) = 0. 

(2) Multiplying or dividing a number by ten changes its 
logarithm by 1.0, hence the logarithmic scale paper is divided 
into squares of a unit (logarithmic) each. 

(3) The logarithm of numbers between 1.0 and 0.1 would 
lie between and 1.0. It is better to mark the intermediary 
subdivisions 9.9, 9.8, etc., meaning 9.9 10, 9.8 10, etc. (as in 
logarithms) and so avoid the use of negative quantities. The 
tenth division line would be 9.0 and the eleventh 8.9. 

(4) The intercept on the Y axis will be log C, since if log 7=0 
we would have log P = log C. 

(5) The " unit " or " base " of the logarithmic scale cross- 
section paper is 5 inches. On a large paper these units may 
be repeated a number of times to the left or right of the Y axis 
and above or below it. On the right of the Y axis the first line 
at unit distance is marked 10, the second is marked 100, etc., 
since the logarithmic markings would have been 1, 2, etc. At 
unit distances to the left of the Y axis the first line would be 
marked 0.1, the second 0.01, etc., as the logarithmic markings 
would have been 1, 2, etc. When an origin has been selected, 
it cannot be changed during the calculations. Decimal points 
must not be disregarded. To lay off the line, P=0.15F 2 or its 
equivalent PF- 2 = 0.15. 

The logarithm of 0.15 is negative or less than zero, hence 
we find the intercept below the origin, Z, at some point A. The 
tangent of the slope is 2. This must not be measured by an 
irregular scale such as the actual numbers appear to have. From 
A lay off any distance, Aa f and at a erect a perpendicular ab 
of twice the length of Aa. Through the point b so found, draw 
the line AbB', it will be the required line. 

The converse is apparent. Given the line AB, what is its 
equation? The intercept on the Y axis is 0.15, which is there- 


fore the constant. The value of any intercept divided by its 
abscissa such as -r- is 2, which is therefore the exponent. Hence 

the required equation is Y = 0.15X 2 or P7- 2 = 0.15. 

To lay off the line Y=2X' 5 or its equivalent PF~* = 2. The 
logarithm of 2 is more than zero, hence the intercept on the 
Y axis is above the axis of X and is found at c. The tangent 
of the angle is positive and, by laying off to the left of the origin, 
Z, an abscissa, Zd = 2Zc the point d is found. The required 
line is dcD. 

To lay off the line PV' = 0.3 or F = 0.3X-- 66 . Lay off 
any distance Ze\. Then lay off Ze 2 and Zfo equal to twice and 
three times that distance respectively. Through an intercept 
on the Y axis = 0.3 draw a line EF parallel to a line joining / 3 
and 62 It will be the required line. 

Keep in mind that the subdivisions are logarithmic and are 
unequal. Note the position of 1.5 and 0.15. 

Relations between Temperature, Volume, and Pressure for a 
Perfect Gas Expanding Adiabatically. 

T 1 T 2 >" P 

The general equation is always true and is therefore true in adia- 


batic expansion. These simultaneous values of -p- may therefore 

be equated. 

V 2 TI /V 2 \ r TI /V 2 

Vi P 2 TI 
Similarly V~ = p~ T~' 

P 2 Vi /P 2 

Hence we see that ^- = 


r~i r^i 
/. T l :T 2 ::P l ' :P 2 ' , 

TV TV: TV' 1 : TV' 1 , 

Ex. 56. The area of the piston of an air-compressor is 4 square 
feet, the stroke is 2 feet. A cylinder full of dry air at 14 pounds per 
square inch pressure, temperature 60 F., is compressed adiabatically 
till the volume is reduced to 1/4 the original amount. The air is 
then rejected at constant pressure. Compressor is double-acting, 
without clearance, and makes 100 double strokes per minute. Find 
the final pressure of compression, final temperature of compression, 
heat added to the air, and horse-power to effect compression. 

Ex. 57. Find the same quantities on the supposition that the air 
is damp and the law of compression is PV l - 2 =C. 

Ex. 58. A cylinder of indefinite length contains 3 cubic feet of 
air under a pressure of 200 pounds per square foot and at a tempera- 
ture of 300 F. The pressure is varied so that the gas expands ac- 
cording to the law PVt=C till the volume is 9 cubic feet. How 
much heat is added or subtracted, what is the work of expansion, and 
what is the final temperature? 

Ex. 59. A cylinder of indefinite length contains 4 cubic feet of 
air at 539 F. and at a pressure of 400 pounds per square foot. The 
volume expands to 16 cubic feet, the pressure varying in accordance 
with the law PV~*=C. Find the heat added and the work of ex- 

Ex. 60. Assume any gas at any pressure, volume, and tempera- 
tuie. Let it be heated or cooled irregularly, and let it do work or 
have work done on it. The curve of expansion, which may be a wavy 
line, is given, viz., all the ordinates and abscissa can be measured to 
known scales. At any point of this curve find how much heat has 
been expended and the increase ( -f or ) of the heat in the gas above 
the original amount in the gas when at the original pressure, volume, 
and temperature. 

Heat Energy Represented by Areas. (Fig. 96. ) Assume any 
volume of any perfect gas, at any temperature, volume, and pres- 
sure, in a cylinder whose envelope is impervious to heat. Let the 
stroke of this cylinder be indefinite in length. Let the gas expand 
adiabatically (expending its internal heat in doing external work), 
the resistance gradually reducing to zero pounds absolute. When 
this is done it is evident that all the heat in the gas has been con- 
verted into external work. 


1. The work of adiabatic expansion is 


When P 2 = the work is = 

If the pressure is reduced to zero, it is evident that the absolute 

temperature of 
the gas is re- 
duced to zero 


and all of its 

heat has been 

expended. The 
total expendi- 
ture of heat 

equals the in- 
trinsic energy 
of the gas at 

< i 


FIG. 96. 

the beginning of expansion =WK V T\. 

Ex. 61. Treating air as a perfect gas, what is the total intrinsic 
energy in 5 cubic feet of dry air at 10 pounds per square inch pressure 
absolute and 75 F.? 

2. (Fig. 97.) Let the gas in the preceding problem be heated 
at constant volume, V\, until the pressure becomes P 2 and the 

temperature T 2 . 
As in the preced- 
ing problem, re- 
duce the resist- 
ance of the piston 
in such manner 
that the curve of 
expansion is ad- 
iabatic, and con- 
tinue it until 
both temperature 

FIG. 97. 

and pressure are reduced to zero. 

The work done during expansion will be 

P 2 7i 

The increase 



of work in this case over that in the preceding one is the area 
OO&&QO between the two adiabatics. This increase of work must 
equal the heat added to the gas. Therefore 

In this case 

The area *>BE*> = 

Ex. 62. If the dry air in the preceding example is heated to 
1000 F. absolute, at constant volume, how many foot-pounds of 
work could be obtained from it if it were expanded infinitely? 

FIG. 98. 

3. Let the gas at PI, Vi, T l gain or lose heat so that the 
expansion line BE is formed. Draw the adiabatics through the 
points B and E. Then the total heat added (positively or nega- 
tively) to the gas to do the external work and change the intrinsic 
energy from that which it possessed at PI, Vi, T l is &BEoo. 
For if to the heat in the gas at PI, Vi, 7\ (area <*>AB<x>) we add 
heat equal to the area <x>BE& (or subtract it) we obtain the 
area <x>ABE<x>. Now of the heat equivalent to this latter area 
we have expended the area A BEG in external work and hence 
that heat is not in the gas and must therefore be subtracted. 
This leaves the area ccGEoo as the heat in the gas at P 2 , V 2 , T 2 . 
As this is correct the total heat added to change the state of a gas 



from PI, Vi, TI to P 2 , V 2 , T 2 is equal to the area enclosed by 
its PV curve and the two adiabatics of the two states. 

FIG. 99. 

Ex. 63. If the dry air in Ex. 61 were heated, the temperature 
being kept constant, and its volume doubled, show that its final 
energy is the same as its initial energy. 

4. Suppose the gas in the preceding case neither gains nor 
loses heat. The heat in the gas remains constant and the curve 


FIG. 100. 

BE is isothermal. If the gas does work, it must receive heat as 
fast as it loses it in doing external work. If work is done on the 
gas, then the heat in the gas would increase unless it were cooled, 
the loss of heat being measured by the work done on the gas. 

By supposition oo AB oo = <*> GE oo ; 

but oo ABE oo = nAB + oo BE oo = wGE<x> +ABEG. 



If B represents the initial state, then the gas expands, receives 
heat as heat and loses it in doing external work. If E represents 
the initial state, then work is done on the gas in compressing it to 
B and heat must be taken from the gas to keep its temperature 

Ex. 64. If the air in Ex. 61 were expanded adiabatically till its 
volume was trebled, what would be the external work done and what 
would be its loss of heat? 

The preceding demonstrations enable us to give graphic solu- 
tion to the two fundamental equations of thermodynamics: 

dH = K v dT+PdV, 
dH = K p dT-VdP. 

The first of these was written by Clausius. 

dH = K v dT+dL+dU. 

In this equation K v dT represents, as before, the increase in 
the intrinsic energy of the gas, whilst dL represents the work of 
molecular separation and dU represents external or visible work. 
Some heat must be expended in separating even the molecules of 
perfect gases, since they must have some attraction for one another 
because they have mass. In practical work this is small enough 
to be neglected. 



Let a d e . . . represent the path of the gas. Through the points 
a, d, e, . . . pass both an isothermal and an adiabatic. The area 
between the adiabatic and the base is in each case equal to the heat 
in the gas. At a the heat in the gas is K v Ti ; at d the heat in the 
gas is K v (T!+dT). The work done badc = PdV. Let d# = heat 
added. Then 

K V T 1 +dH = K v (T 1 +dT) +PdV 

dH=K v dT+PdV. 
To derive the formula dH = K p dT-VdP. 

Let ade ... be the path of the fluid. Through a draw an 
isothermal TI and an adiabatic. Let the next higher isothermal 
Ti +dT be df. The heat in the gas at a = K v T^ 

The heat in the gas at f = K v (T l +dT). The heat added 

FIG. 102. 

in going from a to f={bafg+K v (T 1 +dT)} -I^T^I^dT +bafg 
= K p dT. 

The path of the fluid is from a to d, however. The heat in 
the ga? at d and / is the same since those points are on the 
same isothermal. To reach the point d from / the gas must be 
cooled or heat must be subtracted equal to the area dcgf. 

Since df is an isothermal, (dc) X (dk) = (fg) X (fh) . Subtract 
the common area (hm) X (me) and we have kdmh = mfgc. Adding 
the common area dfm to each side and we have kdfh = dcgf, but 
kdfh = VdP; therefore the heat expended, dH, =K p dT-VdP. 


Carnot Cycle. The term cycle may be used to indicate a period 
of time in which a series of events repeat themselves; a closed figure 
that may be a graphic description of a recurring series of events, 
or a series of operations bringing the thing operated upon to its 
original state. The Carnot cycle is a cycle of operations per- 
formed on a perfect gas working in an engine of perfect mechan- 
ical efficiency, and it will be proved that the thermodynamic 
heat converted into mechanical work efficiency of this engine 
is the highest that can be obtained by the use of any substance or 
combination of substances in any engine working in any other 
cycle between the same limits of temperature. The practical engine 
as it improves approaches this efficiency, but can never attain 
it. In other words, the nearer the efficiency of any heat-engine 
is to that of the Carnot cycle efficiency (between the same tem- 
perature limits) the nearer it is to its highest attainable perfection. 

Note carefully in the Carnot cycle that 

(1) All the heat received as heat is at one temperature and 
that is the highest. 

(2) That all the heat rejected as heat is at one temperature 
and that is the lowest. 

(3) In order that (2) may be so the heat of the substance 
must be lowered by an adiabatic expansion in which the 
heat that disappears does so in doing mechanical work. 

(4) In order that (1) may be so the gas must be compressed 
adiabatically, so that all the heat received as heat may be 
received at the highest possible temperature. 

In order that we may control absolutely the gain and loss 
of heat, let us imagine a cylinder (Fig. 103) made of a material 
that is absolutely impervious to heat and has zero specific heat. 
In other words, it takes the temperature of the gas inside imme- 
diately without requiring any heat therefor. The piston is to 
be made of the same material. Let there be three separate 
heads that may be applied, at will, to one end. One head, H, con- 
tains an indefinite amount of heat at a temperature TV Since 
the amount of heat is infinite the withdrawal of any finite amount 
will not lower its temperature. Let the other head, C, contain 
an infinite amount of heat at T 3 . Since the amount is infinite, 



the addition of a finite amount will not raise its temperature. 
Let the other head, N, be a non-conductor of similar material 
to the cylinder. Let us imagine that we may change heads in 
any desired way without losing gas, that the engine is single- 
acting (there being no head in the right side of the cylinder), and 
that the back pressure against the piston is zero pounds. 


Heat at T, 







a d b c 

Cold at F 

O V, V 4 v, v 3 

FIG. 103. 

Let N be applied at the end e, the piston to be at a; the 
volume ea to be filled with a perfect gas at PI, FI, 7\, and hence 
W may be calculated if the kind of gas is known. The resistance 
is PI. 

1. Replace N with E\ reduce the resistance gradually; motion 
will ensue as soon as the pressure is an infinitesimal amount less 
than that called for by the law PI FI = const. The temperature 
will be constantly T l . The pressures will be represented by the 
ordinates of the isothermal curve ai6i. The work done will be 

. The ratio of expansion, r, will be 

The external 


ivork will be PiVi\og f r, or its equal, P^z log r. The heat 
received will be equal to the work done, or WRTi log e r. 

2. At 6 replace H by N. Allow adiabatic expansion till the 
end of the stroke. The pressures will vary in accordance with 
the ordinates of biCi . The work will be the area of biCi V 3 V 2 , which 

E> T/- P T/" 

is equal to 2 . No heat has been received and the tem- 

perature has been reduced to T 3 , the temperature of the head, C. 
The loss of intrinsic energy equals WKy(T 3 T 2 ). To accomplish 
this, however, we now see that the point 61 in the stroke must be 

T 2 /Vi\ r ~ l 
chosen in accordance with some law. We know that - = ( TT~ ) , 

1 I \ V 2' 

T 2 /OFsV- 1 
or in our case -^ = I KTT ) Knowing T 2 , T 3 , and 07 3 , we can 

readily find OV 2 . 

3. The return-stroke must be made by the action of some 
outside force tending to compress the gas. Replace N with 0. 
Compressing the gas (by doing work on it) tends to heat it and 
therefore increase the pressure that now acts as a resistance. 
The presence of C keeps the back pressure down, as it keeps the 
temperature down to T 3 . Since C is at the lowest possible tem- 
perature T 3 , it is evident that this resistance is the least possible. 

It is evident that c\d\ is the curve of back pressures and that 
CidiV^Vs is the back-pressure work up to the point d\. The heat 
equivalent to this work is wasted. But we have made the waste 
as small as possible by using the lowest TV This wasted heat is 

4. The point d\ of the stroke must be chosen so that, if is 
replaced by N and the gas is compressed into its initial volume, 
its temperature will be increased from T 3 to the initial tempera- 

T /V \ r ~ 1 
ture TI. Since r= (r 1 ) we have 

T 4 (ovj 


but 7 7 4 =2 7 3 and 7 7 i = 7 7 2 ; therefore 

T 3 ' 


or the ratio of adiabatic compression must equal that of adia- 
batic expansion. From the above ratio of volumes we may 

OV 3 OV 2 ' 

or the ratio of isothermal expansion equals the ratio of isothermal 
compression. The work of adiabatic compression is 

or the work of adiabatic expansion. The gain of the gas in in- 
trinsic energy during compression is WK v (Ti T 4 ). 

Summing up results we have the work done in adiabatic 
expansion balanced by the work of compression, and the heat 
or intrinsic energy lost in adiabatic expansion equals that gained 
in adiabatic compression. The net work must then be the differ- 
ence between that done in isothermal expansion and that re- 
quired for the isothermal compression. This is 

PiV l loge r-P 3 V 3 log, r = log r(P l V 1 -P 3 V 3 ), 

The efficiency is then measured by the ratio of the work done to 
the heat expended or 

This efficiency is independent of the gas and the mechanism j 
since it contains no terms dependent on the gas or the mechanism^ 
it depends upon T 3 , as the efficiency evidently increases with a 
decrease of T 3 . The lowest practical limit of T 3 is the temperature 
of the atmosphere. Practically, then, increase of efficiency is to 
be sought in increasing the initial temperature of the heat transfer 
agents. That this is correct is seen in the increased efficiency of 
the steam-engine with increase of pressure and temperature in the 
boilers. Gas-engines, utilizing gas at still higher temperatures, are 
even more economical. 


The above cycle is reversible. With the non-conducting cover 
in place, permit the gas to expand adiabatically to d, replace 
N by C and allow the gas to expand isothermally, drawing heat 
from C. Exchange C for N and compress the gas adiabatically 
to b, and then, using the cover H in place of N, compress at 7\ 
until the original volume is reached. In this cycle instead of the 
gas doing work it is evident that work has been done on the gas. 
As before, the adiabatic areas will balance one another, as will the 
gain and loss of heat in the gas WK v (Ti T 3 ). The quantity of 
heat, WRT 3 log r, has been taken from the cold body, and 
WRTi log.r has been added to the hot body. Work equal to 
WR log* r(Ti T 3 ) has been done on the gas, the required energy 
being supplied from an outside source. The efficiency of this 
second engine running backward is the same as that of the first 
running forward. If there is any cycle more efficient than the 
Carnot cycle let a third engine F, using that cycle, taking heat 
h'" from the source H and rejecting heat c'" into C, drive the 
second engine which takes heat c" from C and rejects heat h" 
into H. 

' In some respects this is like a water-wheel driven by water 
from a height, h, driving another water-wheel that takes the water 
running from the first and restores it to the original height h. 

If the power of each engine is the same h'" c'" = ft" c", but 
according to supposition 

W"-c'" h"-c" 

which will only be true when h'"<h". That, is, this system is 
taking more heat from the cold body and forcing it into the hot 
body than is coming from the hot body into the cold one. This is 
a self-acting system, since each drives the other (the amounts of 
work of each being equal) and, neglecting friction, could theoret- 
ically go on forever. We thus have heat transferred from a cold 
body to a hot one by a self-acting apparatus. This is contrary to 
human experience. Since our premises bring us to an untrue 
conclusion they must be incorrect. Hence engine F cannot have 
a cycle more perfect than the Carnot cycle. 

Ex. 65. Suppose the thermal efficiency of the furnace = 50% and 


the mechanical efficiency of the hot-air engine = 65%. Let the fuel 
contain 14,000 B.T.U. per pound, and the engine make 100 cycles 
per minute. Find the B.H.P. and I.H.P. per 100 pounds of fuel for 
the following cycle. One pound of dry air at 14.7 pounds per square 
inch pressure at 60 F. is drawn in per stroke. It is compressed 
isothermally and then adiabatically to 1200 F. absolute, receives 
heat at that temperature, and expands adiabatically to the starting 




WE have seen that when heat is added to a substance a careful 
analysis will show only three elementary effects are accomplished. 
The first two are ideal since they are always accompanied by the 
third. We have found, however, that in the case of heating solids 
and liquids so long as the former are not brought too near their 
melting-point and the latter too near their point of vaporization 
the heat-equivalent of the internal and external work is practically 
negligible, and hence all the heat is expended in raising their 

If the specific heat of ice is .5, how many B.T.U. would be 
required to raise 3 pounds of ice from -43 F. to 32 F.? 

3 X.5X75 = 112.5 B.T.U. 

The above number of thermal units would be absorbed by a piece 
of ice weighing 3 pounds that had been cooled artificially to 
43 F. and then placed in open air whose temperature was 32 F. 
Melting of Solids. When solids melt and become liquids the 
variation in volume is slight, and we may say that all the heat is 
spent in overcoming certain molecular attraction forces. To melt 
the above quantity of ice or convert 3 pounds of ice at 32 F. to 
water at 32 F. would require, since the latent heat of water is 
144 B.T.U., 

3X144 = 432 B.T.U. 

Boiling-point of Water. If we heat the 3 pounds of water 
at 32 F. we have seen that there will be a slight and slow forma- 
tion of vapor at the surface of the liquid at various temperatures. 



Rapid boiling, where the steam is formed at the heating surface 
and rises through the liquid to its surface,* will always take place 
at the same temperature, in the open air, at the same locality. (It 
is well known that the presence of gases and salts in the water and 
the roughness and character of the containinig vessel may change 
the boiling-point by one or two degrees.) Hence the vapor tension 
equals the pressure on the surface of the liquid. If the atmos- 
pheric pressure is 14.7 pounds per square inch, the water will boil 
at 212 F. 

Let us put 3 pounds of water in a cylinder 13.54" in diameter, 

so that the area will be exactly 1 square foot. The height of the 

water will be , =.0483'. This calculation is only made to 


show that the volume of the water may be neglected in future 

The pressure of the atmosphere on the water may be replaced 
by a piston weighing 14.7X144 = 2116.8 pounds. To the actual 
weight of any piston that we might use, if exposed to atmospheric 
pressure, this weight must be added to obtain the absolute pressure 
on the water. 

If we determine the temperature at which the water boils 
under a series of pistons of different weights, we shall find that the 
temperature increases with the weight, but, in no simple propor- 
tion. Regnault has done this work for us in a most careful way, 
and given us the following empirical formula connecting the pres- 
sure and the observed temperature at which boiling took place : 

where A, B, m, n are determined constants and t is the temperature 
of the boiling water in degrees Centigrade. 

Rankine's formula is equally difficult to apply : 

7? C 

where A, B, and C are constants and T is temperature of the boiling 
water in degrees Fahr. absolute. 

Practically, then, it is essential to refer to a set of tables to find 

*For an extended discussion, see Rowan's Modern Steam Boilers. 


the pressure corresponding to any boiling-point or to find the 
boiling-point corresponding to any pressure. 

Heat of the Liqiid. If we assume that the specific heat of 
water is unity throughout its range from 32 F. to the boiling- 
point, we do not need tables to find the quantity of heat necessary 
to raise W pounds of water from one temperature, ti, to another, t 2 , 
as it is simply Wxi X(t 2 -ti). 

When considerable accuracy is necessary we must refer to the 
tables, as the specific heat of water is not constant. The actual 
number of B.T.U. that are required to heat water from 32 F. 
to any other temperature which is a boiling-point at some pressure 
have been calculated and tabulated. The increase in the specific 
heat at high temperatures is due to the increase of internal work 
as the water approaches the condition of steam. If the pressure is 
high enough the molecular condition of the water at the boiling- 
point does not differ from that of steam; in other words, the latent 
heat has become zero. This temperature is called the critical 

Problem. How many B.T.U. does it take to heat one pound 
of water from 62 F. to the boiling-point under a pressure of 400 
pounds per square inch? If the specific heat is assumed to be 
constant, the boiling-point (by the tables) being 445 F., 

(445 -62) =383 B.T.U. 

If the tables are used, for variable specific heat, 
419.8 - 30.12 = 389.68 B.T.U. 

In this calculation 30.12 measures the heat of the water above 
32 F. initially, and 419.8 measures the heat in the liquid above 
32 F. finally. Hence, in general, if 

qi = heat in the liquid above 32 F. initially, 
52 = heat in the liquid above 32 F. finally. 
Heat added =(g 2 -9i) B.T.U. 

The above difference of 6.68 B.T.U. is about 2% of the total. 
The error per degree at 400 pounds pressure in using the first 
method is 5.5%, hence particular care must be used at high pres- 


Expansion of Water when Heated to the Boiling-point. We 

have seen that the volume occupied by water at 32 F. is negligible, 
and we shall now indicate the importance of 
the external work that is done when water is 
heated under pressure up to its boiling-point. 

Fig. 104 represents a cylinder 13.54" diam- 
eter or 1 square foot in area containing 3 
pounds of water at 32 F. under a piston, P, 
that is to take the place of the atmospheric 
pressure, and therefore weighs 2116.8 pounds. 
Let us put on this piston a shaft of wrought iron 
12" in diameter and some 23' long. Heat is 
added till the water is brought to the boiling- 
point, which, by trial, is found to be 307 F. 
How much heat was added? and show how 
much was spent in doing the external work, i.e., 
raising the shaft by the expansion of the water. 

The absolute pressure corresponding to a 
boiling-point of 307 F. is 74.5 pounds per 
square inch. The total weight of shaft and 
piston will be 74.5X144 = 10,728 pounds. 

By formula, the heat added is 3 X 1 X (307 - 

By the table, the heat added is 3qi or 3 X 
276.9 = 830.7 B.T.U. 

The increase in volume of the water will be about 10% of the 
original volume. 

.0483 X.I = .00483 cubic feet. 

FIG. 104. 

The external work will be 

10728 X. 00483 


= .07 B.T.U., 

which may be neglected. 

Vaporizing a Liquid at its Boiling-point. Let heat be added 
to the boiling water. We note two effects, (6) and (c) : 

1. Notwithstanding the addition of heat, the temperature 

of the water remains constant at 307 F. 


2. The piston and shaft rise until they are 17.28 feet above 
the original position, or, to be more accurate, the bottom of 
the piston is 17.28 feet above the bottom of the cylinder. 

If we experimented with shafts of different weights we might 
ultimately discover Rankine's formula connecting pressure and 
volume, viz., P7" = 475. Practically, however, it is easier to use 
the table, and we there discover that one pound weight of steam at 
74.5 pounds pressure per square inch absolute will occupy a volume 
of 5.76 cubic feet, and hence 3 pounds of water converted into 
steam will, at that pressure, occupy 3X5.76 = 17.28 cu. ft. The 
actual rise of the piston is therefore 17.28 -.0483 = 17.2317 feet. 

As the temperature of the liquid does not change, but a liquid 
is changed into a gas and external work is done, we see that all 
heat is expended in doing two things only : 

(b) Separating the molecules of the liquid. 

(c) Doing external work. 

The purely theoretical value of (b) may be obtained by measur- 
ing the sum of 6 and c and subtracting the value of c, which may 
be measured directly. The sum of b and c is called the latent heat 
and is found in the tables under that title. (See Table VIII.) 

Latent heat of evaporation at 74.5 pounds per square inch 
= 898.6 B.T.U. = Li. 

.'. Latent heat of 3 pounds weight of steam at that pressure 
= 3X898.6 = 2695.8. 

The heat-equivalent of the external work is 



= 239.1 B.T.U., 

239 i 

or ~ = 79.7 B.T.U. per pound of steam = Apu. 


The value of the (b) event per pound would be 


This value will be found tabulated under the head of Heat Required 
to Overcome Internal Resistance =p. 


We may now tabulate all our results per pound of steam. 

^ = Heat in the 
the ' 


Total heat required 
to produce one 
pound of steam 
from water at 
32 F. 

Heat in 

p = Internal 
+ work heat 


External / A pu = External 

work I work heat 

Latent heat 

A +819+79.7, 

where A = 1 / 77 s' ) pi ^pressure in pounds per square foot; u= volume 
in cubic feet of one pound of steam. 

If the water were originally at some temperature t 2 so that it 
contained q 2 thermal units above 32 F., then if 
F. and q 2 = 30 B.T.U., 

276.9-30+819 + 79.7, 

Heat in Steam and Heat Required to Produce Steam. Many 
students and some authors confuse these terms. Steam cannot 
be continuously made at a constant pressure without the per- 
formance of work, as the continuous formation of steam leads 
either to an increase of pressure or an increase of volume. The 
condition of uniform pressure then necessitates increase of volume 
under a pressure, and therefore work. When steam blows off 
from a weighted safety-valve, the heat thrown away is the heat 
required to produce steam, since that steam was formed at con- 
stant pressure. The heat that is required to RAISE steam in a 
closed boiler is not the heat required to produce steam at the 
highest pressure, since the pressure has varied from that of the 
atmosphere to that of the highest pressure. 

In our experiment with a cylinder one square foot in area, 
let the piston, weighing 100 pounds per square inch, rest on a 
pound of water, at 60 F. The heat required to produce one pound 
of steam from this water is 1091.7 +.305 (327.6 -32) -(60 -32). 

If the piston is fixed at the top of its stroke and the steam is 
cooled off till the water at the bottom is 60 F., how much heat 
has been taken away? Evidently it is not the quantity put in, 
as the piston is at the top of its stroke. Further, the water at the 
bottom of the cylinder does not weigh one pound, as the cylinder 
must be filled with steam at a temperature of 60 F. If we drop 


the piston on this steam and then bring the temperature down 
to 60 F., the cycle will be complete and we will then have ab- 
stracted the total heat put in. 

To obtain the heat IN steam, subtract from the heat required 
to produce the same weight of steam the heat equivalent of the 
external work done. 

The engineer ordinarily has no need for steam- and water- 
temperatures below 32 F. As change of state occurs at that 
temperature it is wisely used as an origin in the following formula 
devised by Regnault: 

Total heat required to produce steam = 1091.7 + .305(T- 32) 

where t = temperature of the feed-water; 

T = temperature at which the steam is formed at constant 

If the temperature of the feed- water is 32 F., the last term 
disappears, and it is evident that if the feed-water is at a higher 
temperature than 32, less heat will be taken, and hence the 
last term should be negative. 

Modifications of Regnault's Results. After the student has 
used different steam tables he will notice slight variations in 
the values assigned to the same quantities. The recent accu- 
rate and extensive experiments to determine the specific heat 
of superheated steam has disclosed the inaccuracies of the steam 
tables based on Regnault's formulas. These experiments have 
shown that it is extremely difficult to produce and maintain 
steam in an exactly dry and saturated condition. Small globules 
of water may float around even in highly superheated steam and 
thorough mixing is essential to its production. Hence the diffi- 
culties experienced in the attempts to produce continuously 
exactly dry saturated steam may be imagined. 

Fig. 105 and Table A will show the variations from the Reg- 
nault table as deduced by Dr. Davis. The formula which he 
deduces is not accurate below 212 F. Its best range is from 
212 F. to 400 F. 

Total heat required to produce one pound of steam is 
H = 1150.3 + 0.3745(^-212) - 0.000550 (T-212 ) 2 . 

The tables given in this book, however, are based on Regnault's 


formulas. In the middle range of temperatures they are in error 
one-half of one per cent which is unimportant to engineers. 



















>~ " 



) 100 200 *300 400 50 

FIG. 105. Deviation in B.T.U. (from values given in Peabody Tables). 





Total Heat. 

Specific Volume. 



















































1204 . 1 










Use of Formulas. In text-books formulas are ordinarily given 
for latent heat and internal latent heat, as well as other forms for 
the total heat, such as 

1082 + . 305 T-(t- 32), 
1146.7 + .305(T -212)-(-32). 

The constant repetition by the student of one fundamental 
formula, in different phases, will result in a better comprehension, 
by him, of the meaning of each of the items of heat expenditure 
than he will obtain by the use of separate formulas. 



The student should have a few rough guides as to the relative 
importance of heat quantities and their variation with pressure. 
For instance, let him examine the amount that external-work heat 
varies from 80 B.T.U. for pressures between 80 and 250 pounds per 
square inch. Similarly note, for the same range of pressures, the 
variation of the total heat from 1190 B.T.U. (Fig. 106) Table VIII. 

Quality of Steam. Steam formed in a steam-boiler is always 
saturated steam, as the space over the water contains nothing but 
the vapor of water, i.e., the SPACE is saturated. This steam 
may be either dry saturated or wet saturated steam. If it con- 


Pounds Pressure 


FlG. 106. 

tains per pound the number of thermal units called for by the 
above formula of Regnault, it is dry saturated steam; if it 
contain a less number, it is wet saturated steam. If this dry 
steam passes through pipes or tubes and has more heat added 
to it, then it is called superheated steam. Hence dry steam 
may be either saturated or superheated steam; usually, however, 
the term dry is restricted to dry saturated steam. 

Ex. 68. How many B. T. U. are required to convert feed-water 
at70F. into steam at 327.6 F., pressure 100 pounds absolute? If 


the volume occupied by 1 pound weight of this steam is 4.4 cubic feet, 
find the internal latent heat. 

Ex. 69. A 10"X10" steam-pump using steam full stroke at 100 
pounds gage pressure makes 40 double strokes a minute. If half 
the steam that enters the pump is condensed, find the work done 
per minute in foot-pounds, the number of pounds of steam used per 
hour by the pump, and its efficiency. 

Ex. 70. The thermal efficiency of an engine is 14%. How many 
pounds of feed-water will it require per horse-power hour if the boiler 
pressure is 150 pounds and the temperature of the feed is 70 F.? 

Ex. 71. Boiler pressure 125, gage: feed 65 F.; engine uses 20.5 
pounds of feed-water per horse-power. What will be the gain in 
efficiency if there is installed a feed-heater that uses only waste heat 
and raises the temperature of the feed-water to 212 F.? 

Ex. 72. A tank 8'X8'X4' is filled 3 feet deep with water at 50 F. 
How many pounds of steam at 324 F. will be condensed in a steam- 
coil in the bottom of the tank in bringing the tank-water to the boil- 
ing-point? (The condensed steam in the coils does not cool below 
324 F.) 

Ex. 73. A certain boiler uses 12,000 pounds of water per hour. 
From a catalog pick out a feed-water pump. If it uses per stroke 
165% of the volume of its steam-cylinder, find the number of pounds 
of water pumped per pound of steam. 

When steam is formed slowly and carefully in a well-lagged 
vessel, such steam is always dry saturated steam. If the steam 
be formed rapidly and there are violent steam currents it is easy 
to see how small vesicles of water may be swept along by the 
current of the steam. More heat must be spent on these minute 
drops of water to convert them into steam. This extra heat is 
evidently a percentage of the latent alone, since the drops have 
the same temperature as the dry steam by which they are carried. 

Wet Steam. As wet steam does not contain the same number 
of heat-units as dry steam and is much less efficient for use in 
steam-engines, it is necessary to have instruments to measure its 
degree of wetness or its quality. Whether the boiler formed wet 
steam, or the wetness arose from condensation due to radiation 
losses from the steam-pipe, there is little excuse for allowing wet 
steam to enter the engine since an efficient form of separator near 
the engine should remove all the moisture. In measuring the 


evaporation of water per pound of coal, impossible results have 
been reported by experimenters through neglecting the measure- 
ment of the quality of steam produced. As the moisture is only 
water at the boiling-point and requires one-quarter or one-fifth 
as much heat as an equal weight of dry steam, it is easily seen 
how the presence of only a small percentage of moisture will ma- 
terially alter the results. 

Let =the per cent of dry steam in 1 pound of a mixture of 

steam and water, then 
100 x = the per cent of water present. 

If hi = the heat in 1 pound of water above 32 F., then h 2 -hi 
will be the number of B.T.U. required to heat this water to the 
boiling-point, t 2 , corresponding to h^. 

If only x per cent of this water at t 2 is evaporated, the total 
expenditure of heat will be 

xL 2 + h 2 hi, or less accurately, xL 2 +t 2 ti. 

Problem. If the quality of steam issuing from a boiler is 97 
per Cent, temperature of feed-water is 120 F., boiler pressure 
100 pounds, gage, how many B.T.U. are expended per pound of 

The temperature corresponding to 115 Ibs. abs. is 337.9 F, 

L = 1091.7+ .305(337.9 -32) - (337.9 -32) = 877 B.T.U. 

.97 X877 +337.9 - 120 - 1068.59 B.T.U. 
From the tables 

.97x876.3+308.7-88 = 1070.7 B.T.U. 

Superheated Steam. The specific heat of steam at constant 
pressure was determined by Regnault to be .4805, and at con- 
stant volume to be .346. These values have been accepted as 
correct for pressures and temperatures higher than those used 
by Regnault in his experiments. Recent experiments show that 
these specific heats vary with the temperature and with the press- 
ure of the superheated steam. See Fig. 228 and Table XV. 

Equivalent Evaporation from and at 212 F. To say that one 
pound of a certain coal will evaporate ten pounds of water does 
not convey exact information, as the amount of heat required to 
evaporate the water would vary, not only with the initial tern- 


perature of the water and the temperature at which it was evap- 
orated but also with the quality of the steam. Otherwise ex- 
pressed, the same number of B.T.U. would evaporate different 
weights of water as the circumstances differed. Hence it is 
usual in boiler trials to reduce the rates of evaporation actually 
obtained to those that would have been obtained under certain 
adopted standard circumstances. These are : 

1. That the feed-water should be at 212 F. 

2. That the above-mentioned feed-water should be con- 
verted into dry saturated steam at 212 F. 

The heat then would be expended in converting water into steam 
from and at 212 F. By reducing the results obtained in all 
boiler trials to this standard, a result is obtained that expresses 
the combined efficiency of the coal, the boiler, and the method 
of firing. It is desirable to separate these factors, but experience 
will prove that it is difficult to do so. 

Problem. What is the equivalent evaporation if, on a trial, 
a certain coal evaporated 9 pounds of water from feed at 120 F., 
the quality of the steam being 97%, boiler pressure 100 pounds 
per gage? 

All the water is raised from 120 to 337.9 F., and then 97% 
of it is converted into steam at 337.9. Latent heat = 876.3. 




Ex. 74. Find the heat required to produce one pound of steam 
at 324 F. from feed at 60 F. The quality of the steam is 97%. 
What will be the equivalent evaporation from and at 212 F.? 

Ex. 75. The efficiency of a boiler is 70%. If coal is burned whose 
composition is C = 86, H = 8, = 4, how many pounds of steam, 
quality 98%, will be made per pound of coal from feed at 180 F.? 
What is the equivalent evaporation? 

Ex. 76. Given one pound of wet steam at 358 F., quality 97%, 
how many B.T.U. will be required to superheat the steam 75 F.? 

Ex. 77. What is the equivalent evaporation per pound of com- 
bustible if, on a test, there is 10% ash and one pound of coal is found 
to evaporate 9 pounds of water from feed at 100 into superheated 
steam at 400 F., boiler pressure being 120 pounds, gage? 


Methods of Determining Dryness of Steam. 

1. By the Barrel Calorimeter. This method is theoretically but 
not practically accurate. The steam to be tested is conveyed 
by a pipe (the lower end of which is perforated with small holes) 
to the bottom of a barrel that rests on platform scales. The 
perforations in the pipe prevent bursting the barrel by a too free 
admission of steam. The water on being heated by the steam must 
be stirred, if necessary, to obtain water of uniform temperature. 

Let Wi = the initial weight of cool water and ti its temperature. 
If t 2 is its final temperature, 

Wi(t 2 ti) = increase of heat. 

If z=tne quality of 
the steam added, 
W 2 = final weight of mix- 

W 2 Wi = weight of wet 

steam added, 
L 3 = latent heat of steam 
at given pressure, 

is = temp3rature of steam at given 

lest by 
the steam, 

The quality of the steam, 

or more accurately, use 

\, h 2 , h 3 for t v t-2, and 3 , 

FIG. 107. The Separator Calorimeter. 

For example, suppose steam is run into a barrel of water 
weighing 200 pounds at 60 F. The final weight is 208.5 pounds 
at 105 F. Boiler pressure is 85 pounds gage, and the corre- 


spending temperature is 327.6 F. What is the quality of the 

200(105-60) = (208.5 - 200) (z884 +327 -105). 

x = 94.8%. 

2. Carpenter's Separating Calorimeter (Fig. 107). The amount 
in pounds of dry steam (at P pounds per square inch absolute) 
that will flow through an orifice of A square inches area is 


~=- (Napier's formula). 

The amount of dry steam that will 

flow through a given orifice in a given period ten minutes, 
for instance can be determined by trial or can be calculated and 
tabulated for various pressures. If wet steam flows through a 
separator for a period of ten minutes the amount of dry steam 
escaping through the orifice may be taken from the table and the 
amount of water that was separated from the steam may be 
weighed or calculated from its volume. The Carpenter calorim- 
eter depends upon the above principles. 

3. Barrus Continuous- water Calorimeter. If the wet steam is 
made to flow through a surface condenser it will give up all its 
heat to the cooling-water. The 
weight of the cooling-water, Wi, 
multiplied by (h 2 hi), corre- 
sponding to its rise of tempera- 
ture (t 2 ti), must equal the heat 
lost in the same time by the W$ 
pounds of wet steam at 3 F., 
that flowed through the calorim- 
eter and issues as water at U. 

4. The Throttling-calorimeter 

(Fig. 108) was invented by Prof. 
C. H. Peabody. As will be seen 
below it is the only form recom- 
mended by the Committee on 
Standards. Steam at high pressure contains more heat than an 
equal weight of steam at low pressure. When steam is allowed 

FIG. 108. Carpenter's Patent 



to expand suddenly from a high to a low pressure, forming eddies 
and doing no useful work, the excess of energy or heat must be 
taken up in some manner. If the steam at high pressure contains 

any moisture the first effect is to convert the moisture into steam 
at the lower pressure. If there is still an excess of heat, then all 
the steam at the lower pressure will be superheated until the excess 
is absorbed. 

In Fig. 108 the steam passes through the sampling-nozzle 


(screwed into the main steam-pipe and the valve C) into the 
chamber A. Ordinarily the exit to A is so great that the pressure 
therein is that of the atmosphere. If the exit be throttled in any 
way the pressure is shown on the U tube or manometer, which is 
filled with mercury to the zero-points before attachment to A. 

In preceding discussions we let x = the quality or dryness of 
the steam. In this case we shall let 

y = per cent of moisture present; 
TI = temperature of the moist steam; 
hi and LI = heat of liquid and latent heat corresponding to T\; 

T 2 = temperature corresponding to manometer pressure; 
h 2 and 1/2= heat of the liquid and latent heat corresponding to T 2 ', 
T s = temperature of steam as shown by the thermometer in 
the well screwed in the chamber A, where the steam 
is expanding freely. 

Then hi + (1 y)L\ =heat to produce the moist steam. 

f heat in the steam after expansion 

fi 2 +L 2 + A8(l o 1 2) = i ,1 n 
[ in the well. 

If T s is not greater than T 2 the instrument cannot be used, as it 
does not give utilizable readings. 

1091.7 + .305(7 7 1 -32) -yLi = 1091.7 + .3Q5(T 2 -32) +A8(T,-T 2 ). 
.305(7*1 - 7%) - .48(7*. - 7 7 2 ) 

Ordinarily T 2 is taken from the tables by finding the tempera- 
ture corresponding to the sum of the atmospheric and manometer 
pressures. The Standard Rules given below do not permit this, 
since T s is taken with a thermometer that is subject to radiation 
and other errors, and further it does not allow for the radiation of 
tho chamber A, which may be considerable even when well covered. 

To correct for these errors a Normal Reading is necessary. 
Either before or after the test, take steam through the end hole 
of the nozzle only, from a horizontal pipe, containing quiescent 
steam at constant pressure. This steam is, in all probability, dry 


and the calorimeter should give such a value for T that the value 
of y should = 0. Instead of this it gives some other value, T n . We 
know that y should = 0, therefore .3Q5(T 1 -T 2 )-AS(T n -T 2 )=Q. 

Therefore the true value of y corrected for indicator errors and 
radiation errors is 

A8(T n -T 2 ) - A8(T.-T 2 ) _ AS(T n -T s ) _ T n -T. 



Determination of the Water Equivalent of the Calorimeter. 
All instruments have to be calibrated to determine their error 
under the conditions in which they are used. They absorb heat 
if they are heated, and they radiate a part of the heat that they 
absorb. There are three ways of allowing for these effects : 

A. Compute from the known weights of the apparatus and 
the specific heats of the materials the quantity of heat absorbed. 
Let Ci, C 2 , C 3 be the specific heats, and W 1} W 2 , W 3 be the 
weights of the component materials of the apparatus and K the 
water equivalent per degree variation, 

\? K = C 1 W 1 +C 2 W 2 +C 3 W 3 . 

B. By drawing into the apparatus that has acquired a con- 
stant temperature by being exposed to water at a definite 
temperature, a certain amount of weighed warm water and 
measuring the resulting temperature after equilibrium has been 

Let Wi = the weight of the apparatus; 
W 2 = the weight of the water; 
7 7 3 = the original temperature of the apparatus; 
TI = temperature of the warm water drawn in; 
T 2 = the final temperature of water and apparatus. 

Then W z (T l - T 2 ) = C1F, (T 2 - T 3 ) =K(T 2 - T 3 ) . 

K W (T *- T>) ' 

A = W 2~7n - 7fT~* 
1 2 1 3 


C. By taking steam from a boiler under steam-pressure, but 
at rest. The steam is therefore dry. The variation of the cal- 
culation will therefore be due to the instrument. (See Normal 

Ex. 78. What is the quality of steam shown by a Carpenter calo- 
rimeter if 4.45 pounds of dry steam escape from the orifice and 1.15 
pounds of water are separated out? What is the diameter of the 
orifice if the run is 25 minutes long and the pressure is 81.5 pounds 

Ex. 79. An experiment with the Carpenter calorimeter gave the 
following data: Duration of run, 25 minutes; gage pressure, 78.2 
pounds; water separated out, 0.15 pound; dry steam escaping, 
5.20 pounds. Find size of orifice and quality of the steam. 

Ex. 80. If the steam escaping from the two preceding examples 
gave readings 281 F. and 281.3 F. as the temperatures in a Peabody 
throttling-calorimeter, find the quality of the exhaust-steam. 

Quality of Steam. * "When ordinary saturated steam is used, 
its quality should be obtained by the use of a throttling-calorimeter 
attached to the main steam-pipe near the throttle-valve. When 
the steam is superheated, the amount of superheating should be 
found by the use of a thermometer placed in a thermometer- 
well, filled with mercury, inserted in the pipe. The sampling-pipe 
of the calorimeter should, if possible, be attached to a section 
of the main pipe having a vertical direction, with the steam 
passing upward, and the sampling-nozzle should be made of a 
half-inch pipe having at least twenty one-eighth inch holes in its- 
perforated surface. The readings of the calorimeter should be 
corrected for radiation of the instrument, or they should be 
referred to a "normal reading/' as pointed out below. If the 
steam is superheated, the amount of superheating should be 
obtained by referring the reading of the thermometer to that of 
the same thermometer when the steam within the pipe is satu- 
rated, and not by taking the difference between the reading of 
the thermometer and the temperature of saturated steam at the 
observed pressure as given in a steam-table. 

"If it is necessary to attach the calorimeter to a horizontal 
section of the pipe, and it is important to determine the quantity 

* Standard Rules. A. S. M. E. 


of moisture accurately, a sampling-nozzle should be used which 
has no perforations, and which passes through a stuffing-box 
applied to the bottom of the pipe, so that it can be adjusted up 
and down, and thereby draw a sample at different points ranging 
from the top to the bottom. By this means the character of the 
steam in the lower portion of the pipe, where it contains the most 
moisture, can be determined, and especially that at the very 
bottom, where there is usually more or less water being carried 
along the pipe. If, by preliminary test, water is found at this 
point, we recommend that a drip-pipe be attached a short dis- 
tance in front of the calorimeter, the end of the drip being below 
the level of the bottom, and a sufficient quantity of steam be 
drawn off, while the trial continues, to remove the water and 
cause the calorimeter to show dry steam at whatever height the 
sampling-nozzle is adjusted. The quantity of water and steam 
thus drawn off should be determined by passing it under pressure 
through a separator, weighing the water after cooling it, and 
the steam after condensing. If the amount of water on the 
bottom of the pipe is so excessive that it cannot be removed by 
this means, or in cases where the main pipe is vertical and the 
calorimeter shows that the percentage of moisture varies widely, 
sometimes exceeding three per cent, we recommend that a separator 
should be introduced before making a test, so as to free the steam 
of all moisture that it is possible to remove, the calorimeter being 
attached beyond the separator. 

"To determine the ' normal reading' of the calorimeter, the 
instrument should be attached to a horizontal steam-pipe in 
such a way that the nozzle projects upwards to near the top of 
the pipe, there being no perforations and the steam entering 
through the open end. The test should be made when the steam 
in the pipe is in a quiescent state, and when the steam-pressure 
is constant. If the steam-pressure falls during the time when 
the observations are being made, the test should be continued 
long enough to obtain the effect of an equivalent rise of pressure. 
When the normal reading has been obtained the constant to be 
used in determining the percentage of moisture is the latent heat 
of the steam at the observed pressure divided by the specific heat 
of superheated steam at atmospheric pressure, which is .48. 


To ascertain this percentage, divide the number of degrees of 
cooling by the constant and multiply by 100. 

"To determine the quantity of steam used by the calorimeter 
in an instrument where the steam is passed through an orifice 
under a given pressure, it is usually accurate enough to calculate 
the quantity from the area of the orifice and the absolute pressure, 
using Rankine's well-known formula for the number of pounds 
which passes through per second; that is, absolute pressure in 
pounds per square inch divided by 70 and multiplied by the area 
of the orifice in square inches. If it is desired to determine the 
quantity exactly, a steam-hose may be attached to the outlet 
of the calorimeter and carried to a barrel of water placed on a 
platform scale. The steam is condensed for a certain time and. 
its weight determined, and thereby the quantity discharged per 

Ex. 81. The mean boiler pressure during a test was 155 pounds 
by the gage, the barometer reading was 29.5 inches of mercury, the 
mean thermometer reading of boiler steam was 367.1 F. The pres- 
sure in the manometer was equal to 6 inches of mercury and 3 inches 
of water-pressure. The same thermometer that was used in determin- 
ing the temperature of the boiler steam read 272 F. in the expansion- 
chamber. What was the quality of the steam? 

Ex. 82. Assume the data for calibrating the thermometers used 
in determining the quality of steam. 


Quality of Steam in the Cylinder. The amount of dry steam 
in a cylinder of a steam-engine at the point of cut-off is only 50 
to 90 per cent of the steam actually admitted. It is extremely 
important to account for the differences between the amount of 
steam admitted and that present at cut-off, because the economy 
of a steam-engine is fairly well measured by the number of pounds 
of feed-water that are required per horse-power. Commencing at 
the boiler, we may have 

A. Wet steam delivered by the boiler. 

B. Condensation in the steam-pipes. 

C. Leaky steam- valves. 

D. Condensation of the steam in the cylinder. 

E. Leaky piston. 

F. Condensation due to radiation of heat from the cylinder. 

G. Condensation due to the performance of work during 

A. Quality of Steam Supplied by the Boiler. A boiler is said to 
give wet steam when there is an intimate mixture of the water 
and steam. The boiler is said to be foaming or priming when the 
water is carried into the steam-pipe in solid masses. A boiler may 
furnish dry steam for months and then start foaming. This may 
be due to 

1. Bad feed-water. Feed-water containing soap, oils, salt, 
mucilaginous matter, or certain vegetable ferments will foam. 

2. The heating-surfaces of the boiler may become coated 
with oil from too free use of oil in the engine. This applies, 
of course, only to surface-condenser engines from which the 



condensed steam is returned to the boiler. New boilers and 
boilers using condensed steam from recently erected steam- 
heating systems will foam till the oil is worked out of the 

3. Sudden reductions of pressure in the boiler. These 
may be caused by the engine taking larger volumes of steam 
per stroke than the boiler can properly supply. If the steam- 
pressure falls greatly and the engine cut-off is proportionally 
lengthened to keep up the number of revolutions, foaming may 

4. A change in the boiler design, so that a bad circulation 
of the water in the boiler is obtained instead of a good one. 

If a new boiler continues foaming after the oil has been 
worked out of it, the trouble is generally due to faulty design. 
The trouble may be due to 

a. Bad circulation of the water. This may be due to 
faulty placing of the tubes or faulty movement of the hot 
gases. Retarders were placed in the central tubes of a ver- 
tical boiler that had always given dry steam, and it foamed 
till they were removed. 

6. Improper method of collecting the steam for the 
steam-pipe. Where the steam-pipe opening is only a foot 
or so above the water in a boiler, the surface of that water 
will not be level, but will curve up towards the opening. 
The lessening of the static pressure at that point, owing to 
the high steam velocity, will cause the presence of more 
steam-bubbles in the water at that point than elsewhere. 
The bursting of rising steam-bubbles will cause the spray 
to be carried by the rapidly moving steam into the steam- 
pipe. A well-drained collecting-pipe, nearly as long as the 
boiler and having its upper surface perforated for its entire 
length with numerous small holes whose total area is con- 
siderable in excess of the cross-section of the steam-pipe, 
should be used. 

All the causes of foaming may be reduced to 

1. The water temperature is too high for the pressure that 
exists in the boiler at that instant. To check foaming, cool 


the water by opening furnace or connection doors; by putting 
on a heavy feed; by increasing the pressure by partially closing 
the throttle or the stop- valve on the foaming boiler in a battery 
of boilers. If the water disappears from the glass gage, start 
the foaming again by raising a safety-valve or opening the 
throttle to keep the tubes cool and put on a heavy feed. 

2. Formation of Steam-bubbles of Abnormal Size. Any in- 
gredient in the water that adds strength to the bubble-envelope, 
or any mechanical formation that allows the bubble to grow in 
size before its detachment from the heating-surface, is con- 
ducive to foaming. Feed and blow till the ingredients are 
washed out of the boiler, or add other ingredients that will 
reduce the envelope strength. In boiling sugar solutions, tallow 
is added for this purpose. 

B. Condensation in the Steam-pipe. The amount of heat lost 
by an uncovered steam-pipe is considerable. It varies with 

1. The extent of the uncovered area. 

2. The temperature and rapidity of movement of the outside 

3. The temperature of the steam. 

4. The character of the steam. 

Ordinarily the number of B.T.U. lost is expressed by the formula 

CA(T l -T 2 ) ) 

where C is a constant = 2.5 B.T.U. per hour per square foot (approxi- 
mately), TI and T 2 are the temperatures of the steam and air 
respectively, and A is the exposed area of the pipe in square feet. 

Perfectly dry steam is a very poor conductor of heat, and it has 
been found that pipes carrying superheated steam do not lose the 
same amount of heat that they would lose if carrying saturated 
steam of the same temperature. The presence of a slight film of 
water on the inside of the pipe is an active agent in the transfer of 
heat and therefore affects the value of the constant C in exact 

Whilst the loss of heat in small pipes is less in amount than in 
pipes of large diameter, the percentage loss is enormously greater. 
This arises from the fact that the exposed area varies with the 



diameter, whilst the amount of heat passing through the pipe 
varies with the cross-section of the pipe or the diameter squared. 
The value of non-conducting covering depends upon 

1. Its non-conducting quality. 

2. Its permanence. 

3. Its inflammability or heat-resisting qualities. 

4. Its solubility or water-resisting quality. 

5. Its corrosive effects upon the pipe. 

6. Its bulk and general appearance. 


The following results were obtained by G. M. Brill, and were reported in the 
Trans. A. S. M. E., Vol. XVI. The heat loss was determined by the condensa- 
tion in an 8" steam-pipe GO' long. Steam-pressures varied from 109 to 117 pounds 
gage, the air-temperature varied from 58 to 81 F. The difference in tem- 
perature at the two sides of the heating-surface varied from 263 to 286 F., 
averaging 272 F. 

Kind of Covering. 


ti f 




H mw 
rt o 


Thickness < 
ing, Inc] 

Pounds of 
densed p 
per Hou 





Ratio of H 
Bare to 
Pipe in ] 

.+.' * 


Bare pipe 





2 819 

Magnesia .... 








Rock wool . . 








Mineral wool 
Fire felt. ... .... 








18 6 


Manville sectional 








Manv. sect, and hair-felt. . . 
Manv. wool-cement 









Champion mineral wool. . . . 
Riley cement 









Fossil meal. ... .... 



3 99 





The non-conducting quality depends upon the porosity and 
not upon the material of the non-conductor. In other words, the 
more air there is entrained in the pores of the material the better 
the non-conducting qualities. If from any cause the covering 
becomes more dense its non-conducting quality becomes less. 
For instance, wetting ruins some non-conductors that otherwise 
are excellent. Glass wool after a time breaks up into a dense 
powder and so loses in value. The situation of the steam-pipe 



to be covered is a prime factor in the choice of the covering. The 
intense heat in the confined space over a boiler would prevent the 
use of a covering that would be suitable for pipes that are subject 
to occasional wetting. The chemical action of the constituents of 
the covering when damp must be considered to prevent pipe 
corrosion. On p. 183 ara tabulated some tests of commercial 
steam-pipe coverings. 

The following results were obtained by C. L. Norton of the 
Mass. Manufacturer's Mutual Fire Insurance Co.: 

Temperature Cor- 
responding to 10 

Temperature Cor- 
responding to 200 

Pounds Steam- 

Pounds Steam- 




Name of Covering. 

ness in 

in Ounces 


Loss per 
Sq. Ft. 

Ratio of 
Loss to 


Los- per 
Sq. Ft. 

Ratio of 
Loss to 

of Pipe 

Loss from 

of Pipe 

Loss from 









Nonpareil cork 









Air-cell No. 1 





Air-cell No. 2 














Fire felt 






Bare pipe 





>2.3 45.8 33.9 27.3 

1.53 1.46 1.40 

When the difference of temperatures is small the B.T.U. 
transferred per degree difference of temperature is also decreased. 


4" Cast-iron Pipes. 
Difference of tempera- 
ture 103.7 49.4 25.' 

Heat emitted per 1 F. 
difference of tempera- 
ture per hour 2.25 2.11 1.83 

All steam-pipes should drain in the direction of the moving 
steam and should be free of pockets where water may lodge. 
It is almost impossible to prevent leakage from pipe-joints if 
water lies in the bottom of the pipes. Moving steam will carry 
water against a very considerable adverse pitch. Notwith- 
standing the fact that the water should drain towards the engine, 
none should be allowed, under any circumstances, to enter the 
engine, as it is certain to lower the economy (see p. 187). Simi- 
larly, all receivers in multiple-expansion engines should be drained 


and the water wasted rather than let it enter the following cylin- 
der. To separate the water and steam, use may be made of any 
efficient separator. The essential principles of a good separator 
consist in giving a whirling motion to the steam to throw the 
water outwards by centrifugal force and then preventing the 
water so thrown out from entering into the moving body of steam 
again. Fig. 5 shows one form of separator. The steam enters 
at A, whirls in the direction of the arrows and passes out at B. 
The amount of entrained water is shown by the sight-glass C. 
This water may be automatically trapped out and sent to the 
hot-well with the rest of the feed- water. 

It is necessary to afford the same support to a hot pipe as 
to a cold one. Frequently the expansion of the vertical part 
of a pipe will lift parts of the horizontal portion of the pipe-line 
from intended supports. All movement of the pipe should be 
calculated and proper allowances made. 

Ex. 83. What will be the probable saving per annum, if coal is 
worth $3.00 per ton, in covering (with magnesia 1.25 inches thick) a 
6-inch pipe 300 feet long; boiler pressure 100 pounds gage; average 
outside temperature 50 F.; boiler used 14 hours per day, 300 days 
in the year? 

Ex. 84. Assume that any given covering will last five years, how 
much may be paid without loss for a covering 2 inches thick (al- 
lowing 8% for repairs and interest and 15% for depreciation) on a 
12-inch pipe-line 1000 feet long, carrying steam at 150 pounds pres- 
sure; average outside temperature = 50 F.; plant runs continuously; 
coal $3.00 per ton, labor 50 cents per ton of coal? 

Ex. 85. Sketch a pipe-line connecting five compound engines of 
1000 H.P. each to a battery of boilers of 300 boiler horse-power 
each. The nearest boiler is 15 feet below and 300 feet distant from 
the nearest engine. Steam-pressure 165 pounds gage, engines use 
15 pounds water per H.P. Assume other quantities needed. 

C. Leaky Steam-valves. The steam may leak directly into the 
exhaust cavity and so tend to raise the back pressure and thus 
produce a double loss, or, in some constructions, it leaks into the 
cylinder during expansion. The leakage, of course, will be greatest 
when the piston is near the end of its stroke and the steam-pressure 
is lowest. It is easy to see that there will be a loss, but the magni- 


tude of such loss is only appreciated by those who know the 
amount of steam that will pass through an almost insignificant 

D. Condensation of the Steam during Admittance. By the use of 
a dry-pipe to collect the steam in the boiler for the steam-nozzle, 
and by the use of well-lagged steam-pipes, the amount of condensa- 
tion may be reduced, ordinarily to a small percentage of the feed- 
water, and this amount is readily taken out by an efficient separator. 
We can therefore easily give dry steam to the engine. Leaky valves 
and pistons present mechanical difficulties that are not difficult to 
overcome. We now come to a problem of different character. 
For clearness, let us deal with the events that take place on one 
side of the piston only and we shall call the stroke in which the 
steam drives the piston the forward stroke and the stroke in 
which the piston drives the steam out of the cylinder the return- 
stroke. To be concrete, let us take an engine exhausting into 
the atmosphere, using steam at 80 pounds absolute, temperature 
312 F. As the piston starts on its forward stroke, steam at a 
temperature of 312 F. is entering a volume the walls of which 
were exposed during the whole of the previous stroke to steam 
at a temperature of 212 F. The difference of 100 in tempera- 
ture is greater than the ordinary difference between a hot summer 
day and a cold day in winter.* The immediate result of the 
contact of the hot steam and relatively cool walls is the condensa- 
tion of enough steam to heat the walls (to a depth that probably 
does not exceed 1/50 of an inch) to the temperature of the in- 
coming steam. The thickness of the film of water may not exceed 
a few thousandths of an inch, but the detrimental effect on the 
engine economy is very considerable. From 20 to 50 per cent 
of the weight of the entering steam is condensed to form this 
apparently inconsiderable film and to heat the inner wall to such 
a small depth. 

Let us make a few rough calculations for a 20"X24" cylinder 
without clearance, steam-pressure 80 pounds per square inch 
absolute, cutting off at one-quarter stroke, and suppose the steam 

* Later we shall show, however, causes that will prevent the walls from 
sinking in temperature, in this case to 212 F. 


shown by the card at cut-off is 75 per cent of the steam actually 
admitted : 

Volume at cut-off 6X3.14x100 = 1884 cu. in. 

Weight of steam present 1884/1728 X .1843 = .201 pound 

Weight of steam admitted 201 X4/3 = .268 pound 

Weight of steam condensed 268 - .201 = .067 pound 

Volume of condensed steam 067/.036 = 1.86 cu. in. 

Area of internal surface 314 + 314 + 376.8 = 1008.8 sq. in. 

Thickness of film 1.86/1008.8 = .0018 in. 

Heat given up by cond's'd steam . 895 X .067 = 60 B.T.U. 
Assume weight of cast iron .26 pound per cu. in.; 

specific heat of cast iron .13; 

rise in temperature 100 F.; 
" thickness of metal affected = d.; 
Then (1008 XdX. 26) (.13 X 100) =60 B.T.U. ; 
hence d = l/55 inch approx. 

For reasons given hereafter the assumed range of 100 is 
probably too high and we have only considered the area up to 
cut-off. The calculations are only intended to give approximate 
values, as other variables will be found to enter the problem. 

After cut-off the temperature of the expanding steam decreases 
with the decreasing pressure. Therefore after cut-off the part of 
the cylinder that is being uncovered by the moving piston does 
not have to be heated to the same temperature that was required 
for the part exposed before cut-off. At some point after cut-off, 
then, condensation ceases and re-evaporation starts, since the v/alls 
are now hotter than the steam. If we have an accurate card from 
an engine whose clearance volume, diameter, and stroke are known, 
we may easily find the weight of steam present at cut-off and for 
various points on the expansion-curve. The re-evaporation, while 
not considerable, is greatest near the end of the stroke where its 
usefulness in driving the piston amounts to little. But the moment 
that the exhaust-valve opens and there is a considerable drop in 
pressure (and the corresponding temperature), re-evaporation and 
the consequent cooling of the walls proceeds rapidly. It may 
probably be taken for granted that steam of any degree of wetness 
(short of actual foaming) on entering a cylinder will be exhausted 


as practically dry steam. The heat so taken from the walls must 
be returned by the condensation of an appropriate amount of the 
dry steam that enters for the next stroke. Hence the economy of 
separating the steam and water before the steam enters the 

Considering only the facts brought out in this article, we note 

1. The condensation and re-evaporation would go on in a 
cylinder clothed in a perfect non-conductor. 

2. With an imperfect non-conducting covering there would 
be an additional loss of heat and consequent increase of con- 
densation to supply the heat flowing to the outside of the 
cylinder, and thence carried away either by conduction or 

3. In any practical case we may consider the cylinder- 
shell as made of two parts. In the inner (of greater or less 
thickness in accordance with circumstances yet to be consid- 
ered) there is a rapid fluctuation of heat from and to the steam, 
and a regular flow of heat to the outside surfaces of the 

4. The water of entering wet steam will be re-evaporated 
at the expense of the dry steam of the next stroke, and that 
this re-evaporation takes place on the return-stroke and serves 
only to tend to increase the back pressure. In the case of 
compound engines, however, this steam does some work in a 
following cylinder if there is one. 

5. In the case of the loss of heat from steam-pipes it was 
remarked that steam was a poor conductor of heat, and that 
the presence of a film of water on the surface of the walls had 
an extremely important influence on the loss of heat. We 
shall find that, in this case also, the presence or absence of this 
film modifies results materially. If, by evaporation during 
exhaust, the walls become free of the film of water, then they 
cease to fall materially in temperature and may remain at a 
considerable temperature above that of the exhaust-steam. 
Their range of temperature is thereby lessened. 

At the point of exhaust closure the steam remaining in the 


cylinder is not only dry, but may be slightly superheated. If this 
point be late in the return-stroke the whole compression curve 
may show evidence of superheating by rising more rapidly than 
an adiabatic. With a heavier ratio of compression the first part 
of the curve may rise higher than the adiabatic, owing to the recep- 
tion of heat from the hotter cylinder walls. With the rising tem- 
perature of the steam (from compression) the temperature differ- 
ence between the walls and compressed steam becomes smaller, the 
rate of pressure increase is lower, and the compression-curve crosses 
the curve of dry saturated steam. Further compression raises the 
temperature of the compressed steam above that of the cylinder 
walls and condensation ensues. Heat is now lost rapidly by the 
steam and further compression follows the laws governing the 
compression of vapors in contact with their liquid. The curious 
hook EVG is produced. In Fig. 110, taken from Thurston on Heat 
Exchanges within the Steam-engine, let GVETD'CA be the com- 
pression-curve, CDH the adiabatic from any point (7, SEI the 
saturation-curve from any point E, LM the temperature-curve 
if the compression were adiabatic, MNPR the actual temperature 
as shown by calculation from the diagram, and MPR the probable 
temperature of the metal. 

The statement has frequently been made that there would be 
no loss from clearance if compression were carried to the initial 
pressure. Accurate experiments have shown a slightly increasing 
water consumption per horse-power with increasing compression 
when all other quantities were kept constant in the same engine. 
Theoretically, increasing compression should produce a loss of 
economy for the following reason. The steam-engine is a mechan- 
ism for the conversion of heat into work. No economy can result 
by changing the expensively obtained work back into heat, since 
all changes of energy from one form into another are accompanied 
by loss. As a practical result, in engines designed for economy, 
clearance surface is reduced to the minimum by placing the valves 
in the cylinder-heads and only a moderate amount of compression, 
conducive to smooth running, is used. 

6. The amount of condensation will be affected by the size 
and proportions of the cylinder. Comparing two cylinders (the 


linear dimensions of one being twice that of the other), the 
larger one could perform eight times the work of the smaller, 
but its internal exposed area would only be four times as great, 
hence the percentage of condensation would be reduced. 
Similarly for engines of the same volume, by proper choice of 

FIG. 110. 

dimensions there would be one of minimum exposed internal 

7. Other variables also affect the result. We may men- 
tion steam-pressure, revolutions, ratio of expansion, and jack- 

Range of Temperature. The amount of initial condensation 
depends upon the range of temperature of the cylinder walls, and 


economy follows a reduction of this range. The range is de- 

1. By a late cut-off. By studying the conditions we note 
that the part exposed to the initial steam was exposed to the 
exhaust conditions for a short time only, and more of the sur- 
face is at the highest temperature. 

2. By the reduction of the amount of water present at cut- 
off. The walls part readily with their heat to a film of water 
and less readily to dry steam. Therefore the lower tempera- 
ture is raised by reducing the amount of water to be evaporated. 

3. By reducing the time of exposure. The element of time 
always affects the amount of heat that may be transferred. By 
increasing the number of revolutions the time of exposure is 

To Find the Weight of Steam Accounted for by the Indicator- 
card. At any point in the stroke, the steam-pressure is due to 
the amount of dry steam present. At any point between admis- 
sion and cut-off all the steam has not yet entered the cylinder, 
and after the exhaust opens a large percentage of the steam has left 
the cylinder. In any case, however, we can determine the weight 
of dry steam present in the cylinder at any piston position. From 
cut-off to exhaust-opening and from exhaust-closure to steam- 
opening we are dealing with a closed volume and approximately 
with a constant mass of dry steam. . At all other points of the 
stroke we are dealing with a variable mass of steam and care 
must be taken in the interpretation of results. 

The amount of dry steam present between cut-off and exhaust- 
opening differs materially from the amount of steam that entered 
the cylinder before cut-off. The reasons for this become evident 
when we consider not only the conditions that exist when steam 
is admitted, but also the exceedingly small volume occupied by 
the water formed in the condensation of steam. Two cubic feet 
of steam may readily enter a cylinder whose volume up to the 
point of cut-off is only one cubic foot. One cubic foot of the 
steam may condense and form a film about 1/500" thick on 
the walls. The volume of this film is, of course, practically neg- 


To obtain the weight of the dry steam present in the cylinder 
at any point of the stroke we need 

1. The absolute steam-pressure at that point. 

2. The absolute volume of the clearance and of the cylinder 
up to the point considered. 

3. Steam-tables that show either the weight of one cubic 
foot of steam or the volume occupied by one pound weight 
of steam at the various pressures. 

Then to obtain the weight of dry steam present at any point 
of the stroke either multiply the absolute volume in cubic feet 
by the weight of the steam per cubic foot, or divide the absolute 
volume in cubic feet by the volume in cubic feet of one pound 
weight of steam. Table VIII. 

For example, find the weight of dry steam in a 20"X24" 
cylinder at 16" from the beginning of the stroke, the pressure 
at that point being 42 pounds absolute, clearance 10 per cent. 


Volume = 


18 4x314 
Weight = . 32 pound, 

or weight = - 1 _ OQ - = .32 pound. 

1 / -o 

Analysis of Indicator-diagrams. Steam accounted for by the 
indicator-card assumes the following data : 

Clearance ............................ =E =2% 

Stroke ............................... =L ____ 

Number of strokes ..................... =N .... 

Cut-off pressure above zero ............. 75.6 Ibs. 

Weight per cubic foot at cut-off pressure =W e = .1773 Ibs. 

Proportion of stroke completed at cut-off =C = .172L' 
Compression pressure .......... . ....... 3 Ibs. 

Weight per cubic foot at compression pres- 

sure .............................. = W h = .0085 Ibs. 

Proportion of stroke uncompleted at com- 

pression .......................... =H .048L' 

Mean effective pressure ...... , ......... =M.E.P. =37.17 Ibs. 


The weight of steam as shown by the indicator-card would be 
per hour per horse-power : 

A " ;.172 + .02) (L X .1773) - (.048 + .02) (L X .0085)]# X60 

Hence the general formula is 

The symbol C may also refer to the proportion of the stroke com- 
pleted at release, and W c would be the weight of one cubic foot of 
the steam at release pressure. 

Method of Finding the Dry-steam Fraction. Let us imagine 
that we have a boiler of ample capacity in which the steam-pressure 
is kept absolutely constant. Let us have two engines driving a 
common shaft whose load is always too great for the engine that 
is to be used as an experimental engine. Block the cut-off of the 
latter engine at constant cut-off. The other engine takes steam 
from a separate boiler and its cut-off varies with the load. The 
experimental engine may easily be run at constant pressure, load 
cut-off, revolutions, and so will give a constant card. 

If the experimental engine has a surface condenser the feed- 
water per stroke may be calculated by weighing the condensed 
steam. By keeping the water-level constant in the steam-boiler 
a less accurate measure of the feed per stroke is obtained by weigh- 
ing the feed- water. 

The dry-steam fraction 

Weight of dry steam at any point of the stroke 
"Amount of steam and water present at that point 

The method of finding the numerator was shown (page 163). 
To obtain the denominator we must start at the piston position 
when the exhaust-valve closes. All authorities agree that the 
steam in the cylinder at the point of exhaust-closure is perfectly 
dry. Knowing its volume and pressure, its weight can be calcu- 

t Standard Rules. A. S. M. E. 



lated. At the end of the compression-curve this steam may be 
either wet, dry, or superheated. Knowing the pressure and volume 
at that point, the weight of dry steam present can be calculated 
and if that is less than the amount present at exhaust-closure, it 
is evident that some steam has been condensed. If the pressure 
is higher than that called for by the law, PV = C, the steam has 
been superheated. In any case, the amount of steam and water 
present when the steam-valve opens is equal to the amount of dry 
steam present at the instant the exhaust-valve closes. If to the 
amount so found we add the weight of steam and water admitted 
per stroke (as found by weighing the condensed steam or the feed- 
water), we obtain the amount of steam and water that is present 
at any point between cut-off and exhaust-opening. 

Hirn's Analysis. Mons. G. A. Him published his Thermo- 
dynamics in 1876. In that work he developed a theory of the 
real engine that has served as the basis for nearly all subsequent 
work on that subject. 

O O' 

FIG. 111. 

In this analysis we endeavor to account for every thermal unit 
of the steam that passes through the engine. To make such an 
analysis we must know accurately the volume of the clearance and 
of the cylinder at the important points of the stroke. The quality 
of the steam at admission, the pressures, revolutions, and work 
should be known and must be kept practically constant. All the 
indicator-cards would then be precisely alike, so that the expendi- 
ture of heat and water per stroke multiplied by the number of 
strokes per hour will give the actual expenditure per hour. 


Let Vb = volume of clearance in cu. ft.; 
V c = volume at cut-off in cu. ft.; 
V d = volume at exhaust-opening in cu. ft. ; 
V f = volume at exhaust-closure in cu. ft.; 
V g = final volume of compression = 7 & ; 
m = pounds of (mixture) steam and water; 

x = quality of mixture; 
xm = pounds of steam in the mixture; 
(1 x) m = pounds of water in the mixture; 

g = heat of the liquid above 32 F.; 

p= internal latent heat; 

E = external latent heat; 

I/= internal latent heat + external latent heat. 

As before, a subscript added to a letter limits its value to the 
piston position shown by the letter. Thus m/ indicates the weight 
of steam and water in the cylinder at the instant that the exhaust- 
valve closes. 

The analysis will start at the instant the exhaust-valve closes 
or at / on the indicator-card. In all ordinary cases all the water 
that may have been in the cylinder when the piston is at e will be 
evaporated by the time the piston reaches /. Knowing p f and 
Vf we may calculate m/. We know x = 100%. 

At g we know that m g = mf, as we are dealing with a closed 
volume. We do not know the condition of the steam, however. 
Knowing p g and V g , we can obtain the amount of dry steam 
present. This is (x g m g ). The water at g is then m f x g m . 

Therefore x g = -~. In a preceding paragraph it was shown 

that compressed steam may be either wet, dry, or superheated. 
This would be shown in the above by x g m g being <, =, or (appar- 
ently) > than m { . 

At g the steam-valve opens and the lines gb and be are made 
Calling the weight of steam and water admitted per stroke m t 
(found from the measurement of the condensed steam), we knov* 
that the total weight of steam and water present at c is m a +m/=m c . 
As before, the amount of dry steam present (x c m c ) can be calcu- 
lated, as we know p c and V e . The value of x c is . The 


quality of the steam admitted x a must be determined by calorim* 
eter experiments at some point just before the engine-throttle. 
The weight of steam and water present at exhaust-opening is the 
same as that at cut-off, and its quality x^ is determined as before. 
Heat Interchanges. 

Let 7 c = the work of compression o'gjo" in B.T.U.; 
U e = ihe work of expansion in B.T.U.; 
7 r = the work of rejection of exhaust = o"feo r " in B.T.U.; 
7 = the heat given to the cylinder walls in B.T.U.; 
H = the heat required to produce one pound of steam. 

In discussing heat interchanges we must start at the point of 
exhaust-closure, as we assume that the steam is dry at that point. 
This is a very safe assumption, for even if the quality of the clear- 
ance steam were only 75%, the amount of steam in the clearance 
is so small that the percentage effect on final results would be 
negligible. The amount of heat IN the steam at / on the assump- 
tion of dry steam is m f (q f +pj). 

The amount of heat in the steam and water at g is ing(q g + Xgp g ). 
Adding the heat-equivalent of the work of compression to the heat 
at /, we obtain the heat at g plus the heat given to the cylinder 
walls. Therefore 

whence the heat given to the cylinder walls, 7 C , may be found. 

We must discriminate between the heat required to produce 
m a pounds of steam and the heat in m a pounds of steam. The 
heat required to produce the m a pounds of steam that enters the 
cylinder is 

For wet steam, H a = m a (q a + x a L a ) . 

11 superheated steam, H a s = m a \q a + L a +QA8(t t -t a )}, 

where t a t a is the rise in temperature due to superheating. 

If we add the heat IN the steam and water at the beginning of 
admission (at g) to the heat required to PRODUCE the steam (wet 
or superheated) admitted, we obtain the heat in the steam at 


cut-off + the admission work (in B.T.U.) 4- the heat given to the 
cylinder walls during admission. Hence 

H a (or H a s ] + m g (q g + x g p g ) =m c (q c +x c p c ) + U a +I a . 

As I a is the only unknown it may readily be found. 

The weight of steam and water present at cut-off is the same 
as that present at exhaust-opening. The difference between the 
amounts of heat in the mixtures at cut-off and exhaust-opening is 
equal to the work of expansion + the heat given to the cylinder 
walls. Hence m c { (q c +x c p c ) (qa + xapd) } = U e + I e . If I e is nega- 
tive, then the walls have given more heat to the steam during 
expansion than they have received. 

If tests are accurately made on an engine with a surface con- 
denser, the amount of heat sent to that vessel per stroke may be 
calculated by multiplying the rise in temperature of the cooling- 
water (more accurately the difference of the corresponding q's) by 
the weight of that water used per stroke. While it is easy to cal- 
culate approximately the exhaust-heat quantities sent to the con- 
denser, it is impossible to give directly an exact measure for the 
following reason. The water that is in the cylinder is evaporated 
in varying quantities in the time that the lines de and ef are made, 
that is, at varying temperatures. If the fall of pressure, de, is not 
great, it is probable that most of the water is evaporated during 
the formation of the line ef. A check to any calculation is found 
in the fact that the heat admitted the work done (B.T.U.) must 
equal the heat sent to the condenser (neglecting radiation or heat 
received from a steam-jacket). This is an indirect but exact 
measure of the heat sent to the condenser or to the atmosphere. 
Or, H a (or H a 8 ) - the net area of the indicator-card in B.T.U. 

=H r} the heat rejected = w(qi q^ +m a q a , 

where w = the pounds of cooling- or injection-water per stroke; 

g e = the heat of the cooling-water above 32 F. as it en- 
ters the condenser; 


qi = the heat in the cooling- or discharge-water above 32F. 

as it leaves the condenser; 
q a = the heat in the feed-water above 32 F. 
In the case of a jet condenser the amount of water leaving the 
condenser includes the condensed steam as well as the injection- 

Heat Interchange, I r , during Exhaust. We know the weight of 
steam and water that is present at d, we can calculate its quality 
x d , and therefore can calculate the amounts of heat. We have 
already calculated these quantities for piston position, /. The 
difference between these two quantities of heat is the heat given 
to the cylinder walls (negative) + the heat given to the cooling- or 
injection-water + the heat, q t , given to the condensed steam above 
32 F. Or, 

m c (q d + x d p d ) - m f (q f +p f ) = I r + w(qi-q e ) +m a (q 9 ). 

As all quantities but I r are known, it may be found. 

Jacket-steam. Each pound of jacket-steam, try, gives up L 
thermal units, as the steam is condensed at constant pressure to 
its liquid at the boiling-point. The heat given up, WjLj, must be 
added to the heat that is required to produce the m a pounds of 
steam admitted. From this sum, subtract the heat-equivalent of 
the work done to obtain the heat sent to the condenser. 

The thermal efficiency is obtained by dividing the net work done 
per stroke in B.T.U. by the total heat expended to produce m a 
pounds of steam (from the temperature of the feed-water) plus the 
heat given up (WjLj) per stroke by the jacket-steam. 

Hirn's Analysis. Work out Hirn's analysis for the following 

Area of piston, 3 sq. ft. 

Stroke, 3 ft. 

Clearance, 3.33%. 

Steam-pressure, 100 pounds absolute. 

Cut-off, 6" from beginning of stroke. 

Exhaust opens at 98% of stroke. 

closes" 95% " " 
Back pressure, 15 pounds absolute. 


From a test it is found that the dry steam at cut-off is 
composed of the steam saved by compression and 80% of the 
steam mixture admitted. Quality of steam at the throttle, 
98%. Fig. 111. 

Clearance volume, 3 X3 X .033 = .3 cu. ft. 

Volume at /, 3 X (3 X .05) + .3 = .75 cu. ft. 


Pressure at g, ptVt = p g v g , - 5 - = 37J pounds. 


V/ = .75 cu. ft., p/ = 15 pounds. 

Weight of dry steam at / = . 03868 X. 75 =ra/ = . 029 pound 
dry steam. 

F<, = .3 cu. ft., p g = 37.5 pounds. 

Weight of dry steam at g = x g m g = . 09151 X. 3 = .02745. 

Weight at /weight at g = weight condensed = .029 .0274 
= .0016. 

x g = the per cent of steam = 

To find m a , the steam and water admitted. 
Volume at c = .3 cu. ft.+3X.5 = 1.8 cu. ft. 
Weight of dry steam present at c, 1. 8 X. 2303 = .41454 pound. 

" " the above dry steam that was admitted on this stroke 
= .41454 - .02745 - .38709 pound. 

" " dry steam and water actually admitted, ^ Q = .483862 


" " water in mixture admitted, .02 X .483862 = .00968 pound. 
" "dry steam actually admitted, .483862 - .00968 = .47418 

" " steam condensed on admission, .47418 .38709 = 

.08709 pound. 

" " " and water present at cut-off, .483862 + .029 = 
.512832 pound. 

Heat Exchanges. Heat at /, the heat actually contained in 1 
pound of dry steam at p f pressure multiplied by the weight of 

1074.1 X. 029 = 31. 1489 B.T.U. 


Heat at g ......... 029 X232.46 + .0274 X853.48 = 30.1693 B.T.U. 

Work of compression, U c = ' !L 



Heat given to walls, 7 C = 31.1489 + 1.908 -30.1693= 2.8876 

Heat admitted = .4839 X298.09 + .47418 X 883.773 = 563.1840 " 
Adding heat at g = 30.1693 " 

593.3533 " 
Subtracting heat present at c 

= .5128X298.03 + .41454x803. 108 = 485.7478 " 


Subtract external work .......... 100X144x1.5 = ^ ^ 

778 . __ 

Heat given to the walls, I a ................... . . 79.845 " 

Pd= Q .. =19.35 pounds. 


Weight of dry steam present at d =9.3 X. 0495 = .46035 pound. 

Work during expansion = - log* 5.17= U e 

= 54.735 B.T.U. 

Heat at d = . 51286x195.28 + .46035X882 .36 = 506.3535 

-506.3535 + 485.7478-54.735= - 76.3407 = / e = heat 

OIVEX UP by the walls during expansion. 

The data of this problem were assumed. The student will find 
the heat that is wasted and determine if any change should be 
made in the data. 



Steam Consumption. The actual consumption of steam by 
engines is a very variable quantity. It varies with the style 
of engine, its load, its speed, and a number of other quantities. 
As important as any cause is the amount of leakage past worn 
valves or pistons. Much that is called initial condensation is 
really leakage. In an engine in good condition probably one- 
third of its so called initial condensation is leakage. For com- 
parison, we give two tables and their corrections, as given by 
Helm in The Engineer, and the results of actual tests on engines 
as they were in daily use. (Paper by Dean and Wood, A.S.M.E., 
June, 1908.) 

The ideal consumption of steam per horse-power (S.P.H.) for 
non-condensing engines of the four-valve and Corliss types, with a 
back pressure of 16 pounds absolute is given in Table C. To this 
must be added the following corrections for initial condensation: 

For 80 pounds initial pressure the following amounts should 
be added to those given in Table C for non-condensing engines : 


For 2 expansions 3 . 65 pounds 

" 3 
" 4 
" 5 
" 6 
" 8 
" 9 
" 10 
" 12 
" 15 
" 16 

For condensing engines increase the quantities given in Table 
D by the following quantities based on an initial pressure of 
125 pounds. 


For 2 expansions 3 . 28 pounds 











6 70 

7 90 

9 80 

11 20 




. 21.50 


5 . 57 

6 35 

7 35 




9 80 

10 80 


12 60 

. 13.30 






o s 


r^ u 







16 Lbs. Absolute Back P 



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If the initial pressure is increased above the amounts on 
which the above tables of corrections are based, the cylinder 
condensation will be increased by J- pound for each 10 pounds 
of increase in initial pressure. For instance, in non-condensing 
engines if the pressure is 100 pounds instead of 80, then to the 
amount in the correction Table A an additional .4 pound must 
be added. In the case of condensing engines, if the initial pressure 

is 165 pounds an additional amount of ^~-X.2 = .S pound 

-must be added to the amount in the correction Table B. 

Example. What is the steam consumption of a non-con- 
densing engine, initial pressure 100 pounds, five expansions. 
From Table C, 16.42 pounds; condensation 6.70 pounds at 


80 pounds, pressure, hence at 100 it would be 6.7 H ^ X.2 

= 7.1. Total consumption = 23.52 pounds. 

In Tables C and D the mean effective pressure, M.E.P., is a 
little greater than would be realized owing to the effects of com- 
pression, release, and clearance. 

Compare results obtained as above indicated with the results 
given below. See Power, July 14, 1908. 

(1) 15 in. by 14 in.; 240 r.p.m.; horizontal, single, flat- 
valve engine with 100-kw. d.c. generator on the shaft. Average 
steam pressure 83 pounds; back pressure 4.8 pounds; cut-off 
30.7%; water per I.H.P. per hour, observed pounds, 44.7. 

(2) 16 in. by 15 in.; 240 r.p.m.; vertical, single-flat valve 
engine with two 50-kw. d.c. generators on the shaft. Average 
steam pressure 75 pounds; average back pressure, 1.6 pounds; 
average cut-off, 46.85 and 29.3%; water per I.H.P. per hour 
observed pounds, 37.3 and 39.7. 

(3) 14 in. by 12 in.; 300 r.p.m.; horizontal, single flat-valve 
engine with two 40-kw. d.c. generators on the shaft; average 
steam pressure 91 pounds; average back pressure 6 pounds; aver- 
age cut-off, 45.3 and 25.1%; water consumed per I.H.P. per hour 
observed, 37.5 and 37.3 pounds. 

(4) 16 in. by 14 in.; 270 r.p.m.; horizontal engine with four 
"flat valves and having a 125-kw. d.c. generator on the shaft; 
tested at J, f, and full load; steam pressure, 114 pounds; back 


pressure, 3.5, 5, and 8 pounds; cut-off, 16.5, 27, and 40%; water 
per I.H.P. per hour observed, 45.7, 43.4, and 42.7 pounds. 

(5) 12 in. and 19 in. by 14 in.; 230 r.p.m.; vertical, cross- 
compound condensing piston valve engine with a 100-kw. d.c. 
generator on the shaft; steam pressure, 114 pounds; average 
cut-off, H.P. cylinder 33 and 21%; average cut-off, H.P. cylinder, 
38 and 25%; water per hour observed, pounds, 25 and 20, at .8 
and .7 full load. 

(6) 18 in. by 18 in.; 220 r.p.m.; horizontal piston valve 
engine with a 100-k.w. d.c. generator on the shaft; approximate 
loads 1J, f, J; average steam pressure, 114 pounds; I.H.P. 
273, 170, 122; water per I.H.P. per hour observed, pounds, 29.7, 
34.8, 39.89. 

(7) 15 in. by 16 in. ; 250 r.p.m. ; horizontal single piston valve 
engine with a 100-kw. d.c. generator on the shaft; loads, full,, 
f, J, and J; steam pressure 87 pounds; I.H.P. 137, 102, 69, 
36; water per I.H.P. per hour observed, pounds, 34.1, 37,, 
42.3, 56.3. 

(8) 12 in. by 18 in.; 190 r.p.m.; horizontal engine with two 
flat inlet valves and two Corliss valves, and having a 75-kw. d.c. 
generator on the shaft. Loads, 1J, 1, and J; average steam 
pressure 90 pounds; I.H.P., Ill, 74, 43; water I.H.P. per hour 
observed, pounds, 34, 36.8, and 44 pounds. 

While it would be unfair to draw general conclusions from 
isolated tests such as the above it is nevertheless proper to call 
attention to the great loss in economy due to improper seating 
of valves and of pistons. Poorly made four-valve high-speed 
engines will not compare in economy with well made single-valve 
engines. The latter should have valves for which the wearing, 
process should be a tightening process. Balanced valves in 
which this process does not take place showed up badly in the 
above test. The economical loads are the heavy loads. D. K. 
Clark in the early fifties showed that the economical load for 
locomotives was that due to a cut-off at one-third stroke. 

Ex. 86. Assume data from Engine Tests by Barrus, and work out 
the analysis. 

Ex. 87. Assume card and other required data, and work out the 


Ex. 88. Corliss engine, area piston 8 square feet, stroke 4 feet, 
clearance 2 inches, cut-off 1/6 stroke, initial pressure 100 pounds 
gage, exhaust opens and closes at end of the stroke, expansion ac- 
cording to the law PF = C, revs. 100 per min., 20% of dry steam 
that was admitted is condensed, quality of steam admitted = 98%. 
Give Hirn's analysis. 


Definition. Every term on either side of an equation must be 
of the same degree. An area cannot equal a volume, and a foot- 
pound cannot equal any number of feet, pounds, or degrees of 
temperature. When the chemical energy of gunpowder is con- 
verted, through an explosion, into work, heat, light, and sound, 
all of these must be compound and of like degree. As work is a 
compound of two factors, heat must also be a compound of two 

An area is a product of two dimensions, and, just as we have 
heretofore represented work by areas, we shall now show that 
heat may be represented in a similar manner. In so doing we 
shall be able to illustrate easily certain facts that are difficult to 
understand. Let it be clearly understood from the beginning that 
as in the construction of the work diagram or PV diagram no 
thought was given to the variation of heat quantities, so in the 
construction of the heat diagram ; or <j>T diagram as it is often 
called, we must lay off heat quantities and ignore variation of 
pressures and volumes. 

As work in foot-pounds is equal to Wh or PV= (pA)U, similarly 
heat in thermal units will be found to equal <j>T, where <, or en- 
tropy, represents one factor of heat, and T, or absolute tempera- 
ture, represents the other. As the work diagram is a rectangle 
if P is constant, similarly the heat diagram is a rectangle if T 7 is a 
constant. The word entropy is derived from two Greek words en 
and t~ope, meaning a turning in or transformation, referring to the 
heat per degree which is transferred to another body or trans- 
formed into another form. 

As we must resort to calculus in PV calculations when the 
pressures vary according to some law, so we must resort to the 
same instrument if the temperatures vary in the <f>T diagram. 
4s work is made up of the sum of the infinitesimal rectangles, 



abed, =pdV, Fig. 113, so the heat added is made up of the sum 
of the infinitesimal heat changes Td$, Fig. 115. During these 




d c 

FIG. 112. 

FIG. 113. 

changes T is kept constant as P was kept constant in the work 

diagram. Hence (Fig. 115) we have 

Td(j> or d<p = -. We 

can easily integrate this expression, when we can express Q in terms 
of T. It is essential to remember that T is absolute temperature. 



FIG. 114. 


FIG. 115. 

The proper interpretation of many facts already given will 
show that absolute temperature is one of the factors of heat. The 
heat in a body increases or decreases as we increase or decrease its 
temperature. If a perfect gas is expanded adiabatically to absolute 
zero of temperature, it has lost all its heat. In other words, the 
total heat of a perfect gas is a function of its absolute temperature. 


If we agree that heat is made up of two factors and that absolute 
temperature is one of them, we may call the other factor anything 
we please. It is not possible at present to give an absolute con- 
crete meaning to entropy. It is said to be analogous to pressure 
in a PV formula, or analogous to a variable thermal mass in the 

WV 2 
formula for energy, . For the present the student will find 

the mathematical definition sufficient. In addition he should keep 

in mind that change in entropy depends upon a change of heat as 
heat. When heat is transformed into available work there is no 
change in the entropy, since there has been no loss of heat as heat. 
The student must remember that exact processes are theoretic 
ones. In adiabatic expansion there must be no friction, conduc- 
tion, nor radiation. In other words, the process is reversible. 
Evidently these assumptions are not absolutely obtained, then, 
in any practical case. 

In representing heat by an area, absolute temperatures are 
represented by ordinates, and variable entropy by variable ab- 
scissas. Further, whilst temperature must be laid off from absolute 
zero of temperature, entropy is never so laid off. We are only 
interested in the increase or decrease of the entropy of a substance, 
and not in the total amount of entropy that it may possess above 
the absolute zero of entropy. In other words, by the formula 

d(f> = -7F- we mean that the addition or subtraction of the quantity 

of heat dQ at T produces a change of entropy d(f>. The starting- 
point for measuring entropy is taken at 32 F., as we are not in- 
terested in the entropy of ice above some lower temperature. 

In drawing a PV diagram, we assume one scale for pressures 
and a different one for volumes. Similarly in entropy diagrams, 
we may assume any convenient quantity, as \" or }", to represent 
100 degrees of temperature, and 1" or 2" to represent a unit of 
entropy. Assuming 200 degrees =1" and unity of entropy = 1", 
then 1 sq. inch area = 200 B.T.U. 

If dQ thermal units raise the temperature of any liquid dT 
degrees, we know that dQ = cdT, where c is the specific heat of the 
liquid. For water we may assume c = 1.0 for all temperatures. 

Hence, for water, dQ = l.QdT, and therefore the equation d(f> = ^ 



becomes d$= ' , or -jr. The student should remember 

that the numerator dT now represents an infinitesimal quantity 
of heat and not an infinitesimal difference of temperature. 

Taking our origin for entropy at that possessed by water at 
32 F., we have for the increase of entropy, when water is heated 
from TV = 32 +461 to 3V, any other temperature in degrees Fah- 
renheit absolute, 

Construction of the Water-line. To illustrate the use of the 
above formula, let us draw the line that shows the variation of 
absolute temperature and entropy when one pound of water is 
heated from 32 F. to 350 F. 

As this line will be slightly curved, let us find the abscissa and 
ordinate for one pound of water heated to 

The ordinates are 

TO = 493; ^1 = 561; 7 7 2 = 673; T 3 = 8ll. 
The abscissas are 

.313; and 

Q-j I 


Having the abscissa and ordinate for each of the four points, they 

may be plotted as in Fig. 116, where to, ti, t 2 , t% represent the points. 

The heat required to raise the water from 32 F. to 350 F. is 

the area eotot 3 e 3 . To show this approximately multiply the mean 

ordinate by ^ or 4B3+561 ^ fl73 + 811 XJSM2-319 B.T.U.. 

or 350-32 = 318 B.T.U. These results would be equal if we had 
laid off the figure accurately and used a planimeter. 

As the curvature of the line t Q t^ is so slight, the entropy may 
be obtained directly by dividing the known area by the mean 



ordinate. For example, the area of e /o^i^i^?i <?o = 68 = 68 
B.T.U. Dividing this by the mean temperature we have 

493 +561 = .129 as the entropy or abscissa 




FIG. 116. 

The reason for choosing an arbitrary starting-point for entropy 

may now be shown. In the expression < = log -^r let T = Q 

absolute, .'. < = oo. This shows that entropy measured from an 
absolute zero of entropy is infinite, so that it is absolutely necessary 
to start at some finite point. 

In the construction of the water-line it must be distinctly 
understood that the pressure on the water increased with the 
addition of heat in such manner that there was no steam formed. 

Ex. 89. On a scale of 1" = 200 Fahr. abs. and 3" = unity of en- 
tropy, lay off the water-line for 32, 100, 150, 200, 250, 300 from 
the entropy table; measure the area with a planimeter. Table VII. 


Steam-line at Constant Pressure. Having reached any de- 
sired pressure and the corresponding boiling-point, let any further 
addition of heat go to the conversion of some of the water into 
steam. The volume increases in proportion to the steam formed 
and the temperature will remain constant. 

The heat added is the sum of the internal and external latent 
heat. Ordinarily this sum is called simply the " la tent heat." As 
the temperature remains constant, it is evident that the ordinate 
in the diagram will be constant, and that the entropy will vary 
directly with the amount of heat added or the amount of water 
converted into steam. 

If L 3 = latent heat of one pound of steam at TV Fahr. absolute, 
the increase of entropy over that of water at the boiling-point T 3 is 

T rrt T 

7;?. The total entropy above water at 32 F. is log, -^ +-^. If 
1 3 ^0 -t 3 

the water was initially at some temperature TI higher than T , the 


increase of entropy above TI will be less by log e ^r, or the entropy 

* o 

required to raise one pound of water at a temperature TI to T$ 

(m \ T 
jr) + jT 

Tz . T, T 3 

since log. ^r-log. ^r = log t TFT. 

1 -tQ ^ 1 

T is / 3 + y +JT* 

If we consider the diagram (Fig. 116) to be made by a point 
travelling along the water-line, its vertical movement being due 
to increase of temperature and its horizontal motion being propor- 
tional to increase of entropy, we know that after water reaches the 
boiling-point there is no further increase of temperature. On 
further addition of heat the point must then change direction 
abruptly and travel parallel to the horizontal axis. The distance 
travelled along this line will be directly proportional to the amount 
of water evaporated. For instance, if t 2 s 2 is the entropy added to 
one pound of water at the boiling-point to form one pound weight 
of steam at that same temperature, then t 2 m 2 is the entropy of 

~ - pounds of steam. And, of course, represents the fraction 
t 2 s 2 * t 2 s 2 

An approximate value for log. +jT is + y +JT 


of the pound of water that has NOT been converted into steam, or, 
in other words, is water. 

Expansion Curves. Draw the steam-lines due to the forma- 
tion of steam by the addition of heat to water at the following 
boiling-points: 3 =350 F.; * 2 = 212 F.; and ^ = 100 F. 

We may substitute in the formula 

Latent hea t = 1091 .7 + .305fe - 32) - (fe - 32) , 
or from the tables obtain 


Latent heat at 350 F. = 868 B.T.U., .'. e 3 e 4 = 359+461 = 1 ' 07 ' 

212 F.= 966 " e 2 e s = =1.44; 


100 F. = 1044 " 6i6 6 = ~^r =1-86. 


Evidently the area of the rectangle 63*35364 = 3= 868 B.T.U. 

e 2 t 2 s 2 e5 = -Lj 2 = 966 
6iMi6e = LI = 1044 

Ex. 90. From the values in a table of entropy, lay off the entro- 
pies for 1 pound of steam at the temperatures and on the same scales 
as in Ex. 89. 

The lines 3 s 3 , t 2 s 2 , Mi are lines of constant temperature or iso- 
thermal lines. If the points s 3 , s 2 , i, are joined, the curve so 
obtained is called the saturation curve. This is a short way of 
expressing the fact that as 3^2*1 limits the entropies of one pound of 
water at varying temperatures, so s 3 s 2 Si limits the entropies of 
one pound of dry saturated steam at various temperatures in a 
similar way. 

In discussing the expansion of steam it is easy to propose 
theoretical conditions that could not be carried out in practice. 
The information gained is of great value, however, as practical 
conditions may lie between supposed ideal conditions. 

Theoretically we may suppose the steam to expand 

1. Adiabatically. 

2. To expand receiving heat in just sufficient quantities as 
to prevent the formation of any water by the loss of heat in 
any way. The steam is kept dry, and therefore contains the 


tabular number of B.T.U. for one pound of steam at each 

3. To expand and meanwhile receive heat so that the 
steam becomes drier or perhaps superheated. 

CASE 1. What course will the tracing-point that described the 
water-line tMs and the line t 3 s 3 take (Fig. 116), if the steam is 
supposed to expand adiabatically? Keep in mind that this dia- 
gram is not concerned in variation of volume and pressure, but 
solely in the reception and rejection of heat as heat. The tracing- 
point must radically change its direction and follow the line S 3 e 4 . 

That this is true is indicated by the equation d^ = -^r, for if the 

amount of heat added, dQ, is zero, the change of entropy d$ is 
zero; therefore a line of adiabatic change is one that is parallel to 
the axis of temperature, OF. 

As the tracing-point follows the line s 3 e 4 it cuts the isothermal 
line 1282 in some point m 2 . The significance of this is important. 
The position of ra 2 , in accordance with a previous explanation, 
shows that if a pound of perfectly dry steam at a temperature of 

TS expands adiabatically to T 2} only - - will remain dry steam, 


as will be condensed to furnish heat to do work. With 
t 2 s 2 

greater expansion there is greater condensation, as is shown by the 

increased value of 

Ex. 91. At cut-off, the volume is 4 cubic feet, pressure is 100 
pounds per square inch absolute, and the card shows 80% of the steam 
admitted. If it were possible to expand the steam adiabatically to 
15 pounds per square inch, how much water would be present? 

If the steam is condensed at constant pressure, the temperature 
will remain constant. This is not so if the condensation takes 
place at constant volume, for then both pressure and temperature 
change. If, then, after expanding adiabatically to temperature 
t 2 the steam is condensed at constant pressure, our tracing-point 
will follow the isothermal line m 2 t 2 , and will reach t 2 if. all the 
steam is condensed at t 2 . If the water at t 2 is cooled, the tracing- 
point will follow the water-line t 2 ti to the temperature h of cooling. 


Work Done per Pound of Steam during Admission and Adiabatic 
Expansion We shall discuss the case of wet steam, since that of dry 
steam is easily found by making the quality of the steam mixture 
100% instead of a less quantity Fig. 116). If the whole pound of 

water at t$ is not converted into dry steam, lay off x% so that - 

equals p^ the quality of the steam. Then the position of x% indicates 
the entropy of the mixture. If this mixture expands adiabatically 
to any lower temperature t 2 , the intersection of the vertical with 
t 2 s 2 or x 2 marks the quality of the steam at that time. Calling 
this quality of the steam p 2 , we see that 

TV T 3 

' t 2 s 2 t 2 s 2 L 2 ' 

T 2 

since 1/3 = area 63^3^4 and L 2 = area e 2 t 2 s 2 e 5 . 

Example. If one pound of water at 100 F. is converted into 
steam, quality 95%, at 350 F., does work during admission and 
adiabatic expansion to 212 F., what will be its quality at the 
end of expansion? If the pressure during exhaust is constant and 
equal to the final pressure of expansion, find the theoretical heat 
expended, heat rejected, heat utilized, and the efficiency. 

811 .95X867.3 966 

Log. 573-, 18, --gjj- =1.016, 73-1.435, 



Heat expended from ti = 100 = area eitit 3 x 3 e x 

= 350 -100 + .95X867.3 = 1074 B.T.U. 

Heat rejected must be measured down to feed-water tempera- 
ture = eitit 2 x 2 e x = 212 - 100 + p 2 L 2 

= 212 -100 +.833X966 = 916.7 B.T.U. 

Heat utilized 1074-916.7 
Efficiency == -- =15%. 

This of course neglects initial condensation, friction, wire- 
drawing, etc. 



In Fig. 117 we have a theoretical indicator-card representing the 
conditions of the last example. The line ab corresponds to 

and at b there is present one pound of wet steam, quality -~. 

This steam expands adiabatically to c, the adiabatic be correspond- 
ing to 0-3X2. The exhaust opens and the steam is forced out at 

FIG. 117. 

constant back pressure equal to the final pressure of expansion, 
the line cd corresponding to x 2 t 2 . 

Velocity of Steam Passing Through a Nozzle. The above for- 
mulas apply to steam flowing through nozzles as used in steam- 
turbines. The sum of all the different forms of energy on one side 
of a section must equal the sum of all the energies on the other 
side of that section. In the case under consideration there are 

FIG. 118. 

three different forms of energy, viz., heat or intrinsic energy, E } 
external work, , and kinetic energy or energy of motion; hence, 
Fig. 118, at any two sections, AB and CD, 


The velocity of approach, Vi, in a large vessel is inappreciable and 
may be neglected. The equation becomes, per paund per second, 

V-2 2 

- (E 2 +p 2 y 2 ). 



Inspection shows that the right-hand member of this equation is 
the difference of the total heats of one pound of steam. Calling 
Hi and H 2 the total heats of one pound of the steam, differing 
according as the steam is wet, dry, or superheated, we have, omit- 
ting the subscript, 

-= (Hi -H 2 ) 778 foot-pounds. 

From theoretical conditions and experiment, it is known that 
the weight of steam flowing through an orifice increases as the 
back pressure decreases to a limit which is reached when the 
back pressure is .57 of the forward pressure (see page 445). 

Initial Pressure, 
Absolute per 
Square Inch 

P 2 =.57P,. 

Weight of Fow, Pounds per Second. 

Velocity, Feet 
per Second, at 
smallest Cross- 
section of 



By Equation 

By Napier's 








* Table from Thomas's Steam-turbines (Wiley). 

If dry saturated steam at 132.3 pounds absolute flows through 
an orifice whose cross-sectional area is .0355 square inch, against 
a back pressure of 75.2 pounds absolute, what will be the 
velocity of discharge per second, volume and weight discharged 
per second? 

Draw the entropy diagram, Fig. 119. Then the area TiT 2 s 2 mi 

represents H 2 - HI in the formula = 77S(H 2 -Hi). 

We may obtain that area by either exact or approximate 
methods If TiT 2 is assumed to be a straight line, the area of the 
trapezoid TiT 2 s 2 mi is=(T 2 -7 T 1 )J5, where 





\ would be the 

(If the initial steam were wet, the area 

... ^-^-(809-768) 

=45.1 B.T.U. 

= 64.32X778X45.1. 
= 1500 feet per second. 

FIG. 119. 

The more exact method would give 1470 feet per second. If 
the steam expands adiabatically, its quality is 

T l m l 
T lSl 

_ 1.5731 -.4465 
1.6155 -.4465 ** A/0 ' 


At 75.2 pounds the volume per pound weight of dry steam 
is 5.68 cubic feet. The volume per pound of wet steam is 
96.4X5.68 = 5.47 cubic feet. 

The volume discharged = area orifice X velocity. 


The weight discharged = ^^ = ^0637 pound. 

Ex. 92. If steam of an initial absolute pressure of 117.6 pounds 
flows through an orifice whose cross-sectional area is .0355 square 
inch, against a back pressure of 67 pounds absolute, find the velocity 
of discharge and volume and weight of steam discharged per second. 

Condensation or Expansion at Constant Volume. Fig. 120 illus- 
trates a series of events similar to those given in the example on 

FIG. 120. 

page 214 and illustrated in Fig. 117, up to the point of exhaust- 
opening, c. The line cf is made while the piston is theoretically 
stationary. Therefore the volume of the cylinder is not being 
diminished by the movement of the piston, and the steam is said 
to be condensing or expanding at constant volume. It is evident 
that the volume of the steam in the cylinder at / is precisely the 
volume that was present at c, the weight, of course, being different. 
We must therefore distinguish between the lines cf and fg in draw- 
ing our entropy diagram. The latter indicates condensation at 
constant pressure and, since that occurs at constant temperature, 
the corresponding entropy line will be parallel to the entropy axis. 
When our tracing-point described the line from t% to 3 (Fig. 
116), its position at any moment indicated the weight of steam 
formed and, therefore, its volume, since we can take from tables 
the volume of one pound of steam at any temperature and, by 


multiplication, obtain the volume of any fraction of a pound. Or, 
reversing the conditions, if we have the volume of any unknown 
weight of steam at any known temperature or pressure, by dividing 
this volume by the volume of one pound of steam at that tem- 
perature we obtain a fraction that determines the weight of the 
steam, and also the proportional part of the entropy of one pound 
of steam, measuring from the water-line. 

To illustrate a method of drawing the curve of constant volume, 
let us draw the line corresponding to cf (in Fig. 120) in the entropy 
diagram (Fig. 116). We know that x 2 indicates the conditions that 
exist when one pound of steam, quality 95%, temperature 350 F., 
has been expanded adiabatically to 212 F. We have found that 

its quality -- is 83.3%. From the tables we find that one pound 


of steam at 212 F. occupies 26.64 cu. ft. Hence t 2 x 2 marks the 
entropy of .833X26.64 = 22.19 cu. ft., or approximately 22 cu. ft. 
Taking from the tables the temperatures corresponding to volumes 
which are multiples of 22 cu. ft. per pound of steam, we obtain the 
following series: 

Volume in Degrees. Relative Entropy 

Cubic Feet. Fahr. Abs. of 22 Cu. Ft. 

44 .......... 186 647 1/2 

66 .......... 167 628 1/3 

88 .......... 154 615 1/4 

111 .......... 144 605 1/5 

132 ........ '.. 137 598 1/6 

354 .......... 100 561 1/16 

Hence the entropy of 22 cu. ft. is easily laid off at 1/2 the 
entropy of one pound of steam at 186 F., 1/3 of that at 167 F., 
etc., thus obtaining the curve x 2 m^. The back-pressure line fg of 
the indicator-card is given by mt\ of the entropy diagram. 

Second Method of Drawing the Constant-volume Curve. Let 
383 and t 2 S2, Fig. 121 7 represent two of any number of entropy- 
lines of steam at constant pressure. 

Let OT and OE be the absolute temperature and entropy axes. 
Prolong TO and lay off on the prolongation OF a scale of volumes. 
The scale must be so chosen that OF is at least equal to the volume 
of one pound weight of steam at the lowest pressure. Since the 



diagram deals with one weight of steam only, it is convenient to 
take the volumes from the tables for one pound, since it is easy 
to change the scale to give the volumes for any other weight. 
In the quadrant TOE, ordinates represent absolute temperature 
and abscissas represent entropy; in the quadrant VOE, the ab- 
scissas represent entropy as before, but the ordinates repressnt 

The line t 3 s 3 gives the increase of entropy due to the formation 
of one pound of steam. At t$ the volume of the steam is zero, and 

FIG. 121. 

the entropy is found by dropping the perpendicular 2 3 e 3 . Simi- 
larly, dropping a perpendicular s 3 e 4 from s 3 and laying off on the 
prolongation e 4 F 3 equal to the volume of one pound weight of 
steam at temperature t$ (in accordance with the scale laid off on 
OF), we obtain the point F 3 . Draw e 3 F 3 . This is a straight line, 
as the entropy measured from the water-line is directly propor- 
tional to the volume of steam formed. Suppose e 4 F 3 = 3.324 cubic 
feet. If we wished to find the entropy corresponding to any other 
volume, as three cubic feet, find that number on OF; draw a 
parallel to OE. At the intersection, i 3 , erect a perpendicular to 
OE. The intersection of this perpendicular with 3 s 3 at c 3 gives 
the required entropy 3 c 3 . In a similar manner draw e-zVz, e\Vi, 


and find c 2 and c\. Draw the curve CiC 2 c s . The line so found will 
represent the entropy at constant volume of 3 cubic feet of steam. 

We may now modify the data of the example on page 181. 

Example. One pound of water at 100 F. is converted into 
steam, temperature 350 F., quality 95%, under constant pressure, 
and is then expanded adiabatically to 212 F. The exhaust-valve 
then opens and the pressure drops to that corresponding to a tem- 
perature of 100 F.; at this pressure the remaining steam is re- 
jected to the condenser. Find the theoretical heat expended, 
.heat rejected, heat utilized, and the efficiency. See Fig. 116. 

The heat expended will be the same as in the preceding example 

The heat rejected will be that of the preceding example less 
the heat equivalent to the area t 2 x 2 ni4ti. By means of a planim- 
eter this can be obtained in square inches and the corresponding 
B.T.U. obtained by multiplying by the heat scale.. 

The value of the area t 2 x 2 mti may be obtained from the indica- 
tor-card, Fig. 120, as it is evidently equal to the area cfgh. 

c/= 14.69 -.94 = 13.75. Vol. of cyl. = 22.19 cu. ft. 

Heat rejected =916.7-56.4= 860.3 B.T.U. 
Heat expended = 1074 " 

heat utilized 1074 - 860.3 
Efficiency = heatexpended = -^- = 20%,approx. 

CASE 2 (Fig. 116). If one pound of water at ti is heated to t a 
and converted into dry steam at 3, the heat added will be e\ tit^s^e^. 
Similarly if water at t\ is heated to t 2 and evaporated into dry 
steam at t 2 , the heat added will be eitit 2 s 2 e 5 , and similarly with 
other points. The curve 352$! expresses the relation between the 
temperature and entropy of one pound of dry steam expanding 
and meanwhile receiving heat in sufficient quantity as to prevent 
liquefaction entirely. The heat taken from the jacket to do this is 
4838^5 between temperatures t 3 and t 2 . In adiabatic expansion 
the weight of steam was constantly changing on account of the 
condensation of part of the steam. This curve, on the other hand, 
is called the curve of constant steam weight for obvious reasons. 


The total heat added is the area 61/1/3533265. This area may be 
integrated by a planimeter or it may be divided up into the areas 
61/1/262, 62/2^265, and /2/3S3S2- The last area may be obtained as 
follows: The length of any elementary strip at temperature T (ab- 

solute) is , and, if the width of the strip is dT, its area is - 

This may be integrated if we express L in terms of the absolute 
temperature T. But 

L = 1091.7 + .305 (t s - 32) - (f. - 32) 
= 1091.7-.7(/ s -32 )=1114-.7/8 
= 1114-.7 (T- 481) = 1437 -.7 T. 
' r /1437 - .7 T r- T *U37 dT 



/'/1437 - .7 \ l r-*U37 dT r* 
/ -- ~ - )dT = / ^ -- / .7dT 

' J L ^ J- ^ 

This equals the net work done if the back pressure is constant and 
is equal to the final pressure of expansion. If the back pressure 
is less, the increase can be obtained from the indicator-card as in 
the preceding case. 

CASE 3. The law connecting the pressure and volume in 
Case 1 is PV^ = Ci, in Case 2 it is PV& = C 2 . Owing to the large 
amount of initial condensation in steam-engines, the steam at 
exhaust-opening is only superheated in exceptional engines, with 
high superheat at cut-off. In the case of steam-turbines the 
exhaust, in certain cases, has been found to be superheated. 
This is undesirable and is a source of loss. In such engines the 
energy of the steam is converted into kinetic energy by allowing 
the steam to expand. The curved buckets of the turbine are 
designed to reverse, to a greater or less extent, the motion of a 
mass (of steam) moving at very high velocity. The work done on 
moving blades by the steam is at the expense of its heat energy, 
and some steam should condense. It is not desirable that any of 
this steam should re-evaporate. It does so, however, and for the 
following reason. Whenever two masses of considerable density 
move past one another, friction is almost inevitable. With super- 
heated steam in a turbine the friction is considerable, and it is 


greater with wet steam, as a very slight film of water increases 
the surface friction greatly. This friction heats the buckets, and 
this heat in turn re-evaporates the condensed steam or, at low 
temperatures, if the steam be dry, tends to superheat it. The low- 
pressure steam formed in this way does some work on the following 
vanes before it goes to the condenser. 

The conversion of frictiofial resistance into heat may occur in 
another way, which forms the basis on which the theory of the 
Peabody calorimeter rests. Steam flowing through a simple 
orifice in a diaphragm forms eddies. The high kinetic energy of 
the steam in the orifice is converted back into heat in the chamber 
of the calorimeter. As no external work is clone, the heat in the 
steam at the final temperature contains as much heat as it did at 
the initial temperature. This curve of expansion may be called 
the Constant-heat Curve. If the steam at the initial tempera- 
ture was nearly dry, at the final temperature the steam may con- 
tain more heat than is required by saturated steam and the excess 
is used in superheating the steam. 

Constant Heat Curves are hyperbolas since (j>T = C. The con- 

/ \ 

/ \ 

/ \ 





FIG. 122. 

stant heat curve x 3 a, Fig. 122, has the following data : Steam at 
350 F., quality 97%, expanding in a Peabody calorimeter to 14.7 
pounds; the superheat will be 35 F., approximately. The point 


where the curve crosses the saturated steam line indicates the 
temperature at which one pound of dry saturated steam contains 
the same number of B.T.U. as an equal weight of wet steam, 
quality 97%, at 350 F. 

In the case of the constant-heat curves a definite law is fol- 
lowed ,and intermediate points may be found and plotted. In 
the case of steam expanding in an engine-cylinder or in a turbine, 
it is far from easy to find the values of the variable quality of the 
steam. Let SsWs, Fig. 122, be the curve of expansion followed by 
steam initially dry. The increase in the external work done, if the 
final pressure of expansion is equal to the back pressure, is S 3 m 8 m3. 
The additional amount of heat carried to the condenser, as com- 
pared to the case of adiabatic expansion, is m&e&emz. The heat 
utilized always equals the heat received minus the heat sent to the 
condenser. To make a comparison, let the heat received in two cases 
be the same; in one the expansion is adiabatic, in the other some 
curve, such as s 3 ms, is followed. The total heat received in each case 
is eititsSse^ the heat sent to the condenser is e\t\m^e^ in the case of 
adiabatic expansion, and is eitimses in the other case. In the case 

of adiabatic expansion the efficiency is - In the other 

case we must convert the area e 4 s 3 m 8 e 8 into some area x' 

the area x fff s 3 m 3 x r being a measure of the extra heat sent to the 

condenser and is therefore wasted. The efficiency in the second 

case is then - . These results point out a source of ther- 

mal loss in the steam-turbine. 

Ex. 93. Compare the theoretical efficiency of a steam-engine and 
that of a steam-turbine, both taking steam at 150 pounds pressure; 
the expansion in the steam-engine is adiabatic to 3 pounds back pres- 
sure absolute, and that in the steam-turbine is adiabatic to 1/2 pound 
back pressure absolute, the initial condensation being 15% in the case 
of the engine and zero in the case of the turbine. 

Deriving a Temperature-entropy Diagram from the Indicator- 
diagram. The two diagrams above mentioned involve four vari- 
ables, P, V, T, <j>. If, by graphic means, we can pass from the 
PV or indicator-card diagram to a PT diagram, any T correspond- 
ing to any P is obtained. If from the PV diagram we can pass to 


a <f>V diagram, any < is at once obtained for any V whose P we 
already have. Having and T the <j>T diagram may be con- 

As in Fig. 123, draw two axes at right angles to one another. 

On OF volumes are to be laid off from zero volume. 
On OP pressures are to be laid off from zero pressure. 
On OT temperatures are to be laid off from zero absolute tem- 


On OE entropy is to be laid off in excess of the entropy of 
water at the assumed temperature, 32 F. in the above case. 

If, in the given indi:a tor-card, the hyperbolic curve is con- 
tinued through the point of exhaust-closure to the line of steam 
admission, we have seen that RS is the measure of the steam that 
goes through the cycle, and RT can be laid off to measure the 
actual steam admitted per stroke. The indicator-card is to be 
placed in the POV quadrant with R in the line PO at such a point 
that RO measures the absolute pressure. It is convenient to lay 
off the entropy diagram as for one-pound weight of steam in this 
manner. From the tables we find that an even pressure of 27 
pounds corresponds to an even volume of 15 cubic feet for one 
pound of steam. Through 27 pounds draw a line parallel to OF, 
intersecting the hyperbolic curve at some point a. From a drop 
a perpendicular on 0V and call the intersection 15 cubic feet, 
thus determining the scale of volumes for a cycle of one pound of 
steam. After constructing the complete diagram, by merely 
changing the scale the dimensions for entropy or volume will suit 
the corresponding steam weight. For instance, if the actual 
weight were one-third of a pound, then on the new scale, three 
times as large as the present one, the volume corresponding to a 
would be 5 cubic feet. 

From steam- tables take the temperatures corresponding to con- 
venient pressures and so plot the PT curve in its proper quadrant. 
From entropy tables or an entropy diagram, the water and satu- 
rated steam lines may be laid off in the TOE quadrant. 

The diagonal (j>V lines in the VOE quadrant should be dr^wn 
as required to avoid confusion, as there will be one of them for 
each point, a, etc., in the hyperbolic curve. 

Project any point, a, in the hyperbolic curve vertically to the 
PV curve, obtaining b and c at the intersection of the projecting 
line with the indicator curves, and d the zero of volume point; 
project e on the entropy curves, thus determining / and g. Project 
/ and g vertically and d and a horizontally, thus locating the <j>V 
line hi. Project b and c horizontally and obtain j and Z; project 
the latter vertically and obtain the required points k and m on the 
steam line fg. Find other points of the <j>T diagram in a similar 
manner. (See Fig. 124.) 


Carnot Cycle. The conditions of this cycle are: 

1. All heat to be received at one temperature, the highest 

2. All heat to be rejected at one temperature, the lowest 

3. Working substance cools from highest to lowest tempera- 
ture through loss of heat equal to external work performed by 
it, i.e., expands adiabati^ally. 

4. Working substance is heated from lowest to highest tem- 
perature by gaining heat equal to the external work done on it: 
adiabatic compression. 

On the entropy diagram (Fig. 116) t^s^m 2 mQ would represent a 
Carnot cycle between temperature limits t 3 and t 2 . In the case of 
a steam-engine, assuming one pound of steam as going through 
the cycle, we should have one pound of water at the boiling-point, 
Z 3 , receiving heat equal to the area 3536463 at a temperature fe, 
expanding adiabatically, as shown byline s 3 ra 2 , to tempera ture = t 2 , 
then losing heat = e^e^mzniQ in the condenser at temperature 1%. 
The abstraction of heat must stop when conditions indicated by 
the position of m^ are attained. In some way work would have 
to be performed on the mixture of steam and water, so that it 
would all be converted into water at temperature 3. " This 
cannot be practically accomplished, but a system of feed-water 
heaters has been suggested and exemplified in the Nordberg engine, 
which is theoretically a close equivalent to it. Where steam is ex- 
panded in, say, three cylinders, the feed-water may be successively 
heated from the receiver intermediate between each pair, the 
effect of which is illustrated in Fig. 116. The expansion line follows 
the heavy line, being carried over to y by the first feed-water 
heater and to y' by the second feed-water heater. With an infinite 
number of such feed-water heaters, the line yy r would be parallel 
to 2^3 and the cycle would be equivalent to that of Carnot.* 

" Rankine Cycle. This differs from the Carnot cycle in that the 
condensation does not stop at ra 6 , but is made complete by carrying 
it to t 2 . We therefore have a pound of water at t 2 . The second 
difference is that the water is heated by external heat from t 2 to 3. 

* Trans. A. S. M. E. 


*' Efficiencies of Ideal Engines. The efficiency of the Carnot 
cycle is 

T 3 -T 2 

the efficiency of the Rankine cycle is 

t " Ratio of Economy of an Engine to that of an Ideal Engine. 

The ideal engine recommended for obtaining this ratio is that 
which was adopted by the committee appointed by the Civil 
Engineers, of London, to consider and report a standard thermal 
efficiency for steam-engines. This engine is one which follows the 
Rankine cycle, where steam at a constant pressure is admitted into 
the cylinder with no clearance, and after the point of cut-off is 
expanded adiabatically to the back pressure. In obtaining the 
economy of this engine the feed-water is assumed to be returned to 
the boiler at the exhaust temperature. Such a cycle is preferable 
to the Carnot for the purpose at hand, because the Carnot is theoret- 
ically impossible for an engine using superheated steam produced 
at constant pressure, and the gain in efficiency for superheated 
steam corresponding to the Carngt efficiency will be much greater 
than that possible for the actual cycle. 

" The ratio of the economy of an engine to that of the ideal 
engine is obtained by dividing the heat consumption per indicated 
horse-power per minute for the ideal engine by that of the actual 

Temperature-entropy Diagram of a Real Engine. In Fig. 124 
let ABCD be the ideal diagram, or Rankine cycle, of an engine 
between temperature limits, as shown by the positions of the 
points A and D. As shown in this diagram the temperature at A 
is the temperature of the steam as it enters the engine. If the 
temperature at the throttle had been chosen the line AB would have 
greater ordinates, and if the boiler temperature had been chosen 
the ordinates would have been still greater. 

t Trans. A. S. M. E. Standard Rules. 



The point B represents the theoretical point of cut-off, but the 
real point of cut-off is represented by b and the real admission line 
by Ab. The heat lost by initial condensation is represented by the 
area between AB, Ab, and the full length of the ordinates through 
b and B. 

Keeping in mind that the gain or loss of heat through doing or 
receiving external work produces no entropy change, and that 
therefore decrease of entropy means loss of heat as heat and in- 
crease of entropy means the reception of heat as heat, we see that 
the inclination of W to the left indicates the loss of heat to the 

FIG. 124. 

walls, and the inclination of &'c' to the right shows that the walls 
are returning heat, but at lower grade, i.e., lower temperature. 

The line c'd indicates the changes in temperature and entropy 
due to expansion at constant volume. Had the cylinder been 
large enough in volume, adiabatic expansion from cf would have 
added an additional amount, c'34d, to the work done. 

The line dd f indicates condensation at constant pressure and 
temperature. The fact that it does not coincide with Z)4 indicates 


that there are resistances between the engine and the condenser, 
so that a higher pressure and temperature are required in the 
former to overcome the combined resistance of the condenser and 

The departure to the left of d'e from d', the point of exhaust- 
closure, indicates that the compression is not adiabati3 and heat 
is given to the cylinder walls. The point e may be taken as the 
beginning of compression, and the cylinder clearance steam is dry 
saturated steam. The line eA may be considered as the water- 
line for the new charge of steam. It must be borne in mind that 
in the part of the cycle Abc'ddf we are dealing with a constant 
mass, as the condenser may be assumed to be part of the cylinder. 
The part d'fA, on the other hand, deals with the much smaller 
clearance mass, so that steam and water at / may have less entropy 
than a weight of water equal to th$ full cylinder charge at the 
same temperature. 

Ex. 94. A steam-boiler contains 5000 pounds of water and 50 
cubic feet of steam at 100 pounds gage pressure. The barometer 
reading is 29.3 inches. What number of foot-pounds of energy will 
be developed by the water and by the steam if the boiler explodes? 
What volume of steam will be formed? 

Ex. 95. Draw the Rankine cycle for the expansion of one pound 
of steam at 150 pounds per square inch pressure absolute to 1 pound 
per square inch pressure absolute and determine the efficiency. 

Ex. 96. If the steam in the preceding problem had a quality of 
80% (due to initial condensation) and expanded to 27 inches of mer- 
cury vacuum, barometer 29.5, find the efficiency. 

Ex. 97. The steam-pressure on a steam-pump is 100 pounds ab- 
solute during the entire stroke. If the exhaust is at atmospheric 
pressure, 30.02 inches mercury, what is the efficiency? 


A BRIEF description of two forms of condensers has been given 
already, but the influence of this vessel on the economy of steam- 
turbines and other engines using the highest possible grade of 
expansion is so great that a more detailed description of its 
requirements is necessary 

Two divisions may be made : 

1. Condensers giving a vacuum ranging from fair to excel- 

2. Condensers giving little to no vacuum. 
In the first class we have : 

(a) Jet condensers. 

(b) Barometric condensers. 

(c) Ejector-condensers. 

(d) Surface condensers. 
In the second class are: 

(a) Air-condensers. 

(b) Evaporative condensers. 

It is well known that the temperature of gases or vapors is 
some function of the rate of vibration of their molecules, and 
that the pressure exerted by the gases is some function of the rate 
of bombardment of their molecules on the containing vessel. 
When vapors condense there is an enormous decrease in both the 
amplitude and the rate of vibration, hence there is a great reduc- 
tion of pressure. In the case of non-condensible gases, such as air, 
the reduction of pressure on cooling, of course, is riot so great. 

Jet Condensation. In the jet, barometric, and ejector con- 
densers the water and steam are brought into the most intimate 



contact. The cooling or injection water is sprayed by some 
appropriate form of nozzle, and the steam is forced to travel one 
or more times through spraying cascades. 

Both the cooling-water and the steam carry large quantities of 
air with them into the condenser. All this air being incondensible 
expands enormously in volume on reaching the condenser, on 
account of the reduction of pressure and the increase of tempera- 
ture therein. 

The condensed steam and water, in jet condensation, form a 
mixture. In some cases 2% to 5% of this mixture may be used as 
feed- water for the boilers and the rest runs to waste. If the injec- 
tion water contains anything injurious to the boilers, all the water 
may be wasted. 

Jet condensers were in common nse in marine practice until 
1865-70. It was common usage to feed the boilers with part of 
the discharge water from the condensers. As the injection was 
salt water containing 1/32 of its weight in common salt, calcium 
carbonate, magnesium carbonate, etc., it is evident that a large 
weight of solids would be left in the boiler water, the density of 
which would rapidly increase, as steam contains no solids. Some of 
these solids would be deposited as scale. The density of the water 
would be reduced by " blowing off " at a fixed high density and 
replacing the water " blown off" with water of the lowest obtainable 
density. The loss of heat in the water blown off was considerable. 

The main differences in the three types of jet condensation are: 

1. The air and water must be pumped from the jet-condenser, 
and it may or may not be necessary to pump the water in. 

2. It is necessary to pump the air out of the barometric 
condenser, and the water must be pumped into an elevated 

3. In the ejector type the water is forced into the condenser 
at high velocity. This water in descending with high speed 
past a series of gills entrains or syphons air and steam from the 
main body of the condenser. The mixture of air and water 
passes away by gravity. 

Jet Condensers. This type is used in fresh-water navigation, 
in places where water is cheap and a vacuum is wanted either on 


the score of economy or from the gain in power, but oily feed- 
water is feared. The spraying-nozzles clog at times with leaves, 
fish, and other debris; hence the design should provide for their 
ready removal. The diameter of the spraying-holes may be J" ', 
and their total area may be three or more times the area of the 

The end of the suction-pipe should have a strainer and a foot- 
valve and be immersed in deep water. In rivers heavy cribbing 
is necessary to protect the pipe from ice and an accumulation of 
logs floating on the water surface. The suction-pipe should rise 
at a uniform grade without a single bend or dip. The water in 
this pipe is under less than atmospheric pressure, and the air 
therefore separates from the water and lodges at the highest bends. 
When enough air accumulates the " water will not lift " and the 
pump becomes inoperative. When the bend cannot be avoided a 
small pipe should be tapped in the top of the bend and then be 
connected to an air-pump or condenser. 

Air Leaks. It is exceedingly important to prevent the leakage 
of air into a condenser, as pumping out highly expanded air throws 
much unnecessary work on the air-pump. As the vacuum affects 
the net pressure on the L.P. piston, a loss of one or two inches of 
vacuum will reduce the economy of the engine materially. 

The principal sources of air leakage are the stuffing-boxes of 
the L.P. piston-rod and of the air-pump rod; the various joints 
of the condenser, exhaust-pipe, and L.P. cylinder; the drip-cocks, 
or drain- valves, on the main or auxiliary engines which exhaust 
into the condenser. Absolute air- tightness of joints is difficult to 
secure. Even soldered joints will leak. Metal to metal joints are 
the best. To test the tightness of a condenser wafoh the needle 
move backward the moment the engines and auxiliaries are shut 

Dimensions. As is shown in Fig. 18, jet condensers are often 
made pear-shaped, the maximum diameter being twice the diameter 
of the exhaust-pipe leading into it. This shape tends to conserve 
the velocity of the water entering the condenser and causes the 
delivery to the air-pump of a mixture of air and water. Under 
these conditions the water absorbs considerable air, and in any 
case this mixture can be handled with greater uniformity of pump 


motion than is possible when the air and water separate from one 
another. The volume of the condenser may be from one-fourth 
to one-half that of the L.P. cylinder. 

Weight of Injection Water for Jet Condensation. 

Let W = pounds of injection- water per minute; 
ti = initial temperature of injection-water; 
* 2 = final 

then W(t2 t\) is the heat absorbed by the injection- water per 
minute and must therefore equal the heat lost by the steam per 
minute. Now the total heat received by the steam per minute 
from all sources minus the external work done in the engine per 
minute is the heat above 32 F. sent to the condenser per minute, 

I.H.P.X 33,000 
= wH t = wH e , 

where H t = total heat received from all sources above 32 F.; 

# c = heat (above 32 F.) per pound of steam as it goes to 

the condenser; 
w = pounds weight of steam sent to the condenser per 

minute ; 
w(H c - (t 2 - 32)) = W(t 2 - h), or, more accurately, 

The diameter of the injection-pipe may be calculated by allow- 
ing a velocity of 600 to 800 feet per minute to the injection- water. 
A velocity in excess of this may be obtained when the condenser is 
much below the level of the surface of the water-supply. The 
pressure of the atmosphere then supplies the power to force the 
water into the condenser. Knowing the static head and assuming 
any velocity, the corresponding velocity and friction heads may be 
calculated. The sum of all the resistance heads should be less than 
the head that is equivalent to the difference of the pressure of the 
atmosphere and that in the condenser. 

Ex. 98. Design a jet condenser for a 1000 horse-power engine 
using 15 pounds of steam per horse-power. Make a sketch showing 
size of injection-pipe, form of sprayer, number and size of holes in 
sprayer. Assume other conditions. 


Ex. 99. Design a jet condenser and air-pump of type shown in 
Fig. 8 for a Corliss engine of 40 horse-power, using 25 pounds of steam 
per I.H.P. Assume other conditions. 

Ex. 100. Design the suction-pipe line for Ex. 98. This pipe- 
line must cross a levee 15' above mean low level of the river. Maxi- 
mum and minimum river heights 10' above and below mean low level. 
River bottom soft mud to a depth of 10 feet. 

Barometric Condenser. In many operations, steam must be 
condensed at some elevation above the ground. If this be over 35' 
it is evident that the discharge-water would flow away by gravity. 
All that is necessary is to seal the end of the tail-pipe (discharge- 
pipe) in a tank or barrel of water. Fig. 125 illustrates a counter- 
current barometric condenser, so called because the cooling-water 
is flowing in one direction and the air in flowing to the vacuum- 
pump is moving in the opposite direction. In this case it is evi- 
dent that only the air moves to the vacuum-pump, as all discharge- 
water flows away through the tail-pipe. It should be noticed in 
Fig. 125 that the final temperature of the air on its way to the 
vacuum pump is that of the incoming water, whilst in Figs. 17 
and 18 it is the temperature of the discharge water. The weight 
and volume of the air to be handled in barometric condensers is 
very much less than in jet condensers. Serious accidents have 
happened by the use of improperly designed condensers. For 
instance, cases have occurred in which the water inside of the con- 
denser acquired a gyratory motion and then, rising over 34' high 
in the condenser, flooded through the engine exhaust-pipe, causing 
the breakage of the cylinder-head. When this type receives a 
larger amount of steam than usual, the current of steam and water 
may reverse and flood the air-pump. If the bottom of the dis- 
charge-pipe becomes uncovered, air enters and, forming ascending 
pistons, lifts the water (as in the Pohle air-lift in wells) and may 
cause the flooding of the cylinder. As the passageway for the air 
to the pump may be very much constricted by water, ample 
passageway should be allowed. The spray-tubes are very liable 
to become choked, and the injection-pipe should deliver into a tee 
on the sprayer, so that by the removal of two blank flanges the lat- 
ter may be easily cleaned (Fig. 262). Condensers of tlds character 
are used in connection with vacuum-pans and multiple effects in 


FIG. 125. Heisler Induced Circulation Counter-current Condenser. 


sugar-houses, condensed-milk factories, and in chemical industries 
where there is much boiling done at pressures less than atmospheric 

FIG. 126. Alberger Barometric Condenser. 

Syphon, Ejector, or Injector Condensers. A remarkable degree 
of vacuum may be obtained, without the use of an air-pump, by 
means of condensers of the form shown in Fig. 127. Its most im- 
portant and essential feature is a suction-gill, so arranged that 
the steam, vapor, and air may be drawn into the discharge- 



water. This action is due to the high velocity of the water entering 
the contracted orifice above the gill, and since the sum of the 
static, velocity, and friction heads must be constant, it is evident 
that if the velocity-head is increased the static head will be de- 

In tests made with an injector-condenser of this type in winter 
in New York the condenser pressures varied from 0.82 pound to 

FIG. 127. 

1.25 pounds absolute, the engine varying from 340 to 1004 I.H.P. 
An objection to this condenser, when used with variable loads, is 
that the same volume of water is required to fill the throat regard- 
less of the load. 

Surface-condensers. The Alberger condenser (Fig. 128) has 
several unique features. The exhaust-steam enters either at the 
bottom or at the side near the bottom. The cooling-water enters 
at the top and leaves at the bottom. The object of this arrange- 
ment is to obtain a full counter-current transfer of heat. The 
steam as it rises is condensed, and the water thus produced falls 
down against the incoming steam and is removed by a hot-well 


pump. On account of this intimate contact the feed-water acquires 
the same temperature as the steam. The air left after condensa- 
tion, before being withdrawn by the dry-air pump is cooled by 
passing over the tubes containing the coldest circulation water. 

In the lower part of the condenser-shell is a diaphragm to dis- 
tribute the steam to all parts of the condenser. The method of 
changing the direction of flow of the cooling-water is similar to 
that shown by the arrows in Fig. 10. 

FIG. 128. Albarger Surface-condenser. 

A high vacuum may be obtained by the use of a surface- 
condenser. Such a vacuum is not necessarily economical in prac- 
tice. The vacuum that gives the best economy will vary with the 
ratio of expansion of the engine. When there is a big drop in the 
pressure between the engine and the condenser, increasing the drop 
by an excessively high vacuum may be very uneconomical. In 
other words, the extra gain in work does not compensate for the 
increased loss in heat-units caused by the increase in initial con- 
densation, colder feed-water, increased cost of pumping greater 
quantities of cooling-water, and the interest on the increased size 
of air- and circulating-pumps, condenser, et3. 

On the contrary, if the steam can be expanded in the engine 


to any back pressure, however low, theoretically there would be an 
enormous gain in reducing the condenser pressure to the lowest pos- 
sible amount. In the steam-turbine there is no trouble with initial 
condensation, and it was expected that there would be a great 
advance in economy from the greatly increased ratio of expansion 
possible. As a consequence machinery for the production of a 
vacuum of 29" + has been devised. The entropy diagram will 
show that if steam is expanded adiabatically to 40 or 50 times its 
original volume, theoretically some 20% of it would be converted 
into water. As it is the province of the steam-engine to convert 
heat into work, the above effect would be very desirable. Unfor- 
tunately, from causes explained under the head of turbines, much 
of this water from friction is converted back into steam. It is evi- 
dent that this causes a loss in the external work done, since the 
latter is the difference between the heat entering the turbine and 
that going to the condenser. 

Amount of Cooling-water. The amount of cooling-water per 
pound of steam entering a surface-condenser is somewhat greater 
than it is in the case of jet condensation, as the range of tem- 
perature of the cooling-water is less. As an engine converts into 
work only 10 to 15% of the heat it receives, in practical design, 
it is not important to be particular about the pressure at which 
the heat is sent to the condenser since H does not vary greatly 
with the pressure. Evidently ^ is not only indeterminate in such 
cases but is also variable and a variation of three degrees in its 
assumed value has a material effect on the value of W. 
Let ti = the initial temperature of the cooling-water; 

2 = the final temperature of the discharge-water ; 

3 = temperature of the condensed steam; 
He = heat in the steam entering the condenser above 32 F.; 

w = weight of steam entering the condenser per minute; 

W = weight of injection- water per minute. 
Then w\He-(t 3 -32)}=W(t 2 -t 1 ) ) or, more accurately, 

The outside diameter of condenser-tubes is 1/2", 5/8", or 3/4";, 
thickness of metal, .049"; the spacing is 1 1/2 diameters; length 
from 6' to 16', but supported at 5' spaces; composition Cu, 70, 
Zn, 29; Sn, 1, or Admiralty metal; packed by screwed glands 
7/8" diameter and cotton tape. 


In ordinary land service the cooling-surface is 1 sq. ft. for every 
10 pounds of steam the engine uses : with high vacua, as with tur- 
bines, 1 sq. ft. for 4 to 8 pounds of steam is allowed. The velocity 
of water through the tubes is from 150 to 200 feet per minute. 

Heat Transfer through Metals. Many experiments have been 
made on the rate of heat transfer through heating-surfaces. 
When the difference of fluid temperatures at the two surfaces is 
very high, as in steam boilers, the rate of heat transfer probably 
varies with some power, probably the second, of the difference in 
the tw r o temperatures. In surface condensers the difference of 
fluid temperatures at the inside- and outside-tube surfaces is so 
small that the rate is generally taken as varying with the difference 
of the temperatures only. 

Motion only ensues when there is a difference of pressure, and 
heat only passes when there is a difference of temperature and the 
rapidity depends upon the temperature gradient, or, in other 
words, the latter depends Upon the rapidity with which the heat 
is taken away. The temperature fall in the metal itself is always 
very small. The principal falls occur in the soot, grease, scale, 
inert gases or liquids adjacent or attached to the two metal surfaces. 

We note that 

1. As the water passes along a tube and increases in tem- 
perature the efficiency of the heating-surface gradually dimin- 
ishes; therefore 

(a) the cooler the injection the greater the efficiency. 

(6) Long tubes must be inefficient compared to short 
tubes and disregarding the amount of water used. 

(c) The higher the vacuum the lower the steam vapor- 
temperature, therefore the efficiency of heat trans- 
fer is low and the necessity of cold injection for rec- 
ord tests is greater. 

2. If the tubes are coated with any non-conductor of heat 
the efficiency will be lowered. Grease and scale are evident 
examples, but there are others of equal importance. Air in a 
condenser acts as a non-conducting blanket, and whilst it is 
important at condenser temperatures ranging from 140 to 120 
F. ; at 80 F. the presence of air having a pressure of .2" mer- 
cury is prohibitive of all heat transfer.* 

* London Engineering, 1906. 


3. Increasing the rapidity of motion of water through the 
tube increases the efficiency of heat transfer. The rise in 
temperature of the water will be less, but at high velocities the 
product of the weight of cooling-water and its rise in 
temperature will be greater than that same product at low 

Professor Perry's Theory. This theory is given as applied to 
a boiler tube, but it applies in a measure to condenser tubes as 
the steam takes the place of the hot gases and the water is the 
quantity heated in both cases. According to this theory the 
rate at which heat is imparted to a boiler tube is propor- 
tional to : 

1. The difference of temperature between the hot gases 
and the metallic surface. 

2. The density of the gases. 

3. The velocity of the gases parallel to the metallic surface. 

4. The specific heat of the gases at constant pressure. 
The heat transmitted per second per unit of heating surface is 

H=Cpv(T l -T 2 )' ) 

where #=the amount of heat transmitted; 

(7= the specific heat multiplied by a constant: 

v= velocity of gas parallel to the metallic curface;^ 

p = density of the gas. 

That the heat imparted should depend upon the difference 
of temperature is self-evident. Experiments seem to show that 
it does not depend upon a higher power of the temperature differ- 
ence than one. Weiss, for instance, makes it depend upon the 
square of the temperature difference, but Josse's experiments 
do not favor this exponent. , 

Heat is imparted by molecular impact and the greater the 
number of these impacts per unit of area and per unit of time 
the greater the molecular vibration of the metallic surface. As 
the number of impacts is proportional to gas density, it is 
evident that density should be one of the factors in the transfer 
of heat. 

The effect of a blow is lessened if there is a cushion between 
the striking and the struck object. If we imagine a number of 


inert gas molecules entangled in the spaces between the metallic 
molecules and holding other gas molecules by attraction at the 
metallic surface we have such a cushion. (See Fig. 129.) If 
the heating gas passes with a strong current so that these inert, 
non-moving, cold gas molecules are swept away it is evident 
that a stronger blow will be struck on the metallic surface and 
hence more heat will be conveyed. That the value of H will 
depend upon v is the more evident when we remember what 
poor conductors of heat all gases are. In all forms of steam 
condensation, it is noticeable how violent the boiling action is 
directly opposite the induction steam-pice if baffles or deflectors 

FIG 129. 

are not placed in front of it. A strong steam current over the 
entire cooling surface is necessary for a high mean rate of con- 
densation per square foot of cooling surface. As gas currents 
take the lines of least resistance it is evident that their direction 
of flow must be compulsory to avoid short circuits, air pockets, 
and dead ends in which there is no circulation. 

All gases at the same temperature, pressure, and volume 
contain exactly the same number of molecules. (Avogadro's 
Law.) But they require and give up different amounts of heat. 
The latter depends upon the specific heat of the gases, hence the 
heat given up should vary with the specific heat. In the case of 
condensers this factor is merged in other empirical factors. 


Heating or Cooling Surface. The value of any one of the 
four factors in the equation below is easily deduced after we 
have obtained the proper value of the other three. 

H=FAT m . 

This equation is applied to surface condensers, feed-water 
heaters, multiple effects, vacuum-pans, or any form of apparatus 
where heat is given up by a hot fluid and absorbed by a cooler 
one through some metallic surface. 
In this formula, 
HihQ total heat transmitted in B.T.U. per hour through the 

entire heating surface, A ; 

J^=the number of B.T.U. transmitted per square foot of heat- 
ing surface per degree difference in temperature in 
degrees F. between the heating and cooling fluids per hour; 
A = area of the heating surface in square feet; 
7^ = the mean difference in temperature in degrees F. between 

the hot and cold surfaces for one hour; 
TF=the pounds of cold water passing through the heater per 


7\. = temperature of steam to be condensed (at constant pres- 
sure) ; 
th= temperature of the hot liquid (if other than steam) at any 


tin an d tfo are initial and final temperatures of the hot fluid; 
t c = temperature of the cold fluid at any point; 
k, and tc 2 are initial and final temperatures of the cold fluid; 
th tc = ihe difference in degrees F. between the hot and cold 

fluid at any point. 

The Mean Temperature, T m . In an endeavor to find the mean 
temperature between the heating and cooling sides we see that 
four cases may occur: 

Fig. 130. The hot fluid maintains a constant temperature 
and there is a continuous rise in temperature in the cold fluid ; 
Fig. 131. The cold fluid has a constant temperature but 
the hot fluid varies in temperature; 

Fig. 132. Both fluids change in temperature and both flow, 
in the same direction, in currents parallel to the heating surface. 








FIG. 130. 

FIG. 131. 

FIG. 132. 

FIG. 133. 





This would occur in concentric tubes, one carrying the cold 

and the other the hot fluid ; 

Fig. 133. Both fluids change in temperature but both flow 

in opposite directions parallel to the heating surface. 

The following discussion is limited to the case of feed-water 
heaters, as is illustrated by Fig. 130. Steam at constant tem- 
perature, Ts, gives up heat to water, raising its temperature from 

tc t tO tc r 

Formula for T m . Case I. In a time dt the temperature of 
the water will rise an amount dd where 6 = T s t c . 

Wdd=heat transferred in time dt, 
FA C'dt = 


Let = 1 hour, 

As FA = the number of B.T.U. transmitted by the heating 
surface per hour for one degree difference in temperature, 

FAT m =W-\og s ^"^.7^ = total heat transmitted =W(T Cl - Tc z ). 

Is tc 2 

T C1 -T C2 (T s -t C2 )-(Ts-t Cl ) d 2 -di 
Ts-T c ~ Ts-t Cl di' 

lOgs 7p - TFT lOgc ~ - log -r 

1 s JL C2 JL s lc2 U2 

where d\ = difference in temperature between the hot and cold 

fluids initially, 
d 2 = difference in temperature between the hot and cold 

fluids finally. 

In fact, according to Grashof, Theoretische Maschinenlehre, 1, 
the mean temperature in each of the four cases is given by the 

For example, in an opposite current condenser, the cold 
liquid enters at 50 F. and leaves at 176 F. ; the hot liquid 


enters at 212 F. and leaves at 122 F. What is the mean tem- 

2fi 2 
perature. Here di=36 F., d 2 = 72 F. Hence 

51.9 F. This is a case of the cooling of water coming from 
condensed steam. 

When vapors are cooled the operation should be divided 
into two parts. In the first part the vapor is cooled and con- 
densed at constant temperature and in the second the resulting 
liquid is cooled at a varying temperature to some lower tem- 
perature. During these two operations the factor F is quite 
different, as will be seen. The mean temperature difference, T m , 
should be obtained for each operation. 

Feed Heaters. Feed heaters should accomplish much more 
than heating the feed-water important as that is. It is only 
in recent years that proper attention has been given to the 
steam-boilers and, owing to the high development of steam- 
engine economy, it is often possible to obtain greater economy by 
attention to boiler management than to refining the engine- 
room economics. For high boiler efficiency it is absolutely essen- 
tial to obtain a supply of feed-water free of salts or scale-form- 
ing substances, oil, gases, acids, alkalis or organic matter. In 
brief, feed-water should be pure and as hot as it is possible to 
get it. 

The thermal efficiency of an injector used as a boiler feeder 
is 100%, but that does not make it necessarily a better feeder 
than a boiler feed-pump whose thermal efficiency may be only 
1/50 of that of the injector. If the exhaust from the steam- 
pump is sent to an open feed heater the thermal efficiency of 
pump and heater becomes 100% approximately if radiation is 
neglected. The injector using live steam from the boiler is there- 
fore far less efficient than the pump, as its steam pumps and purifies 
the feed-water. Injectors are unreliable with hot water and are 
unreliable as pumps if the resistance is liable to fluctuation. 
Injectors cannot be used to pump water that has been heated 
in a heater nor can they be used as pumps to send water through 
heaters, since the water has been so heated in the injector as 
to make the heater inoperative. Injectors do not remove any 
foreign matter whatever from the feed-water, and the decrease 



FIG. 134. The Cochrane Heater and Purifier for use in connection with Engines 
or Pumps exhausting freely to the atmosphere. 


in economy due to the formation of scale, the destruction of the 
boiler due to acids or alkalis must be charged to the injectors. 
Feed-heaters may be divided into three classes: 

1. Open-feed heaters; 

2. Closed-feed heaters* 

3. Feed purifiers. 

Choice of a Feed Heater. In choosing a feed heater it is 
essential to keep in mind all the requirements of the situation. 

FIG. 135. A conventional illustration showing the general method of con- 
necting up a Cochrane Feed- Water Heater and Purifier, where all of the 
exhaust is passed through heater engine exhausting free to atmosphere 
at all times. Pump exhaust entered into main line ahead of heater. 
Direct and free feed line from heater to pump. Heater foundation as high, 
or preferably higher than pump foundation. Live steam drips saved 
by returning to heater through steam trap. Direct connection to cold 
water supply. Waste piped direct to sewer or other convenient point not 
higher than bottom of heater,, and without any valves in the line. 

In practically all cases the oil must be removed. Once water 
and oil are mixed it is almost impossible to separate them, hence 
the oil should be removed from the steam by the use of a sepa- 
rator. The other requirements are fixed by the composition of 
the feed-water. Volatile gases should be driven out. Some 
salts are precipitated around 212 F. but others are precipitated 
only at high temperatures. Some feed-waters form scums and 
some do not. Hence scum removers, settling-chambers, cham- 


bers holding chemicals to cause precipitation may or may not 
be necessary. 

Open-Feed Heaters (Figs. 134 and 135). Open-feed heaters 
are simple in construction, are exposed only to one or two pounds 
pressure, are efficient as the steam is brought into direct contact 
with the feed-water, neither deteriorate nor lose their heat 
transfer capacity and being of ample capacity serve as hot wells. 
All the volatile gases are expelled, thus enormously reducing 
the work of air-pumps; they are equipped with means of purify- 
ing the water of oil and various salts, carbonates of lime, and 
magnesia for instance; have settling and filtering chambers in 
addition to oil-separator. 

Exhaust steam in condensing will give up enough heat to 
raise six to ten times its own weight of water from ordinary 
temperature to 203 F., which is about as high as open-feed heaters 
can heat. Hence they cannot utilize the entire exhaust from 
the main engines for feed heating. But the exhaust from a 
few pumps will supply this heat and therefore a condensing plant 
should turn their exhaust into feed heaters. In so doing they 
far exceed the main engines in economy. 

Closed Feed Heaters (Fig. 136). Closed-feed heaters are those 
in which the heat is transferred through some form of heating 
surface to the water in a vessel which is closed, so that the water 
may be heated above 212 F. This heater is best suited to 
water which is free from scale-forming deposits and volatile 
gases. For instance, carbonates are precipitated when the C02 
is driven out of the water. In closed heaters if the C02 is not 
driven off these salts will be deposited on the boiler tubes. This 
will happen if the valve placed for this purpose on the heater 
is not opened to permit the gases to escape. 

The closed type of heater is subject to boiler pressure and the 
corresponding strains and accidents; it is not as economical as 
the open heater, and becomes less so as the tubes become covered 
with scale; it is difficult to remove the scale from its tubes; a 
coating of oil on its tubes renders them less efficient; the con- 
densed steam is ordinarily wasted; the precipitate does not 
settle owing to the agitation of the water. 

It is extremely desirable to reduce the amount of gases passing 






FIG. 136. 


into the condenser when high vacua are desired. These gases 
interfere with the economy of the condenser and increase mate- 
rially the load on the air-pump. In the open heaters these 
gases are driven out automatically. 

In the design of a closed heater, in addition to the properly 
arranged heating surfaces to abstract all the heat possible from 
the steam, other requirements arise from the necessity of main- 
taining that efficiency with the least amount of trouble. Being 
under boiler pressure the heads must be stayed if not thick 
enough to withstand expected pressures. Grease may be re- 
moved by gentle boiling in a strong alkali and scale by subse- 
quent boiling in a weak acid solution. Do not mix the acid and 

Percentage Gain in Using Feed Heaters. The theoretical gain 
in percentage by the use of feed-water heaters is easily shown. 

Let #=B.T.U. in one pound of steam at boiler pressure; 

gi=B.T.U. in one pound of water as delivered from the 


g 2 =B.T.U. in one pound of feed- water before being heated; 
p = percentage gain. 


Suppose one pound of unheated feed-water at 60 F. is raised 
to 202 F. in an open heater and is then forced into a boiler at 
100 pounds gage, what is the percentage gain? From the tables, 
H= 1184.9, 

Theoretically, then, the gain is 1% for every 12% gain in 
feed-water temperature. There are, however, a number of gains 
that cannot be calculated easily in percentage. The heater 
drives air and carbonic acid out of the water and so lessens oxida- 
tion in the boiler and makes the air-pump work much lighter 
if a condenser is used. The circulation of the water in the boiler 
is undoubtedly improved and the economy of the boiler from 
that cause is improved. An undoubted gain is the furnishing 


of pure soft water to the boilers thus reducing the formation of 
scale and prolonging the life of the boiler. Most heaters are 
provided with means to remove oil from the steam where the 
water is used to feed boilers. The percentage gain then varies 
from 1.2 to 1.4% for each increase of 10 in the feed-water. 

Relative Value of Feed-water Heaters and Economizers. 
Feed-water may be heated by the hot gases which would other- 
wise go to waste and it becomes a question as to which is the 
better source to look for economy. In England, where the 

FIG. 137. Hoppes Heater. 

boilers have less heating surface than those in this country, 
economizers are used extensively. 

Economizers cannot purify the water, neither do they serve 
to remove any of the absorbed gases. The purchaser has to 
consider the relatively high initial cost; the high cost of upkeep; 
a high rate of depreciation; the difficulty of keeping the appa- 
ratus in an efficient condition; the value of the space occupied; 
its effect on the draft or the cost of forced draft. No hard and 
fast rule can be laid down and each case must be considered on 
its merits. 

Closed Purifiers. Fig. 137 represents a closed purifier. The 
purifier is generally placed over the boiler. The water is pumped 
into the boiler and trickles over the pans. It then comes in 


contact with the steam from the boiler at boiler pressure and 
temperature. Many salts are deposited at the high tempera- 
tures attained which would not be precipitated at lower tem- 
peratures. It is important to take the steam to run pumps 
and other auxiliary machinery from the top of the purifier and 
in that way remove gases arising from the feed-water. From 
the purifier the water runs into the boiler, through the regular 
gate and check valves, by gravity. 

It is generally contended that there is an economic gain in 
taking steam from the boiler to heat the feed-water, as is clone 
in purifiers. There will certainly be a gain if salts are removed 
which would scale up the boiler. Independent of this reason, 
it is contended that the hotter feed-water causes an increased 
circulation of the water in the boiler. Recently, however, some 
experiments were made which seemed to discredit the above 
theory. The question is still open. 

Heating Surface in Feed Water Heaters. In the open heaters 
and the closed purifiers there is no heating surface as the steam 
and water are brought into intimate contact. In these vessels a 
large volume must be used to divide the steam and water into 
thin divisions to bring about the necessary intimate contact. 
In the closed-feed heater the heating surface must be calculated. 

Instead of finding the mean temperature by calculus the arith- 
metical mean is often used. In Case I, Fig. 130, for instance, 
such a mean would be 

Value of the Heat-transfer Factor F. The ability of a heating 
surface to transfer heat is far greater than the amount of heat 
which is actually transferred. The resistance to heat transfer 
does not lie in the molecular resistance of the metal but in the 
resistances at the two surfaces, as is shown in the discussion of 
Professor Perry's theory. 

In surface condensers, for instance, the factor F is dependent 
upon the density of the steam, its velocity of flow, the velocity 
of the water squared (or perhaps cubed), the amount and charac- 
ter of the incrustation of the cooling surfaces, the position and 


direction of the cooling surfaces, width and capacity of the con- 
denser space, and whether the tubes are drowned with water 
from above or blanketed by air which is not driven off by the 
current of the steam. 

In closed-feed water heaters, receiving steam at atmospheric 
pressure, the value of F is often taken to be proportional simply 
to the velocity of flow of the water. This assumes all other con- 
ditions to be normal and at their best. For instance, if the 
arithmetic mean of the temperatures be taken, practical results 
are obtained if F is taken in B.T.U. per hour the same as the 
velocity of flow of the cooling water in feet per minute. Thus, 
if the cooling water flows at 200 feet per minute then F is 200 
B.T.U. per hour per square foot per degree F. difference of tem- 
perature. If the logarithmic difference be taken, then an as- 
sumed value of .F=325 B.T.U. seems to give better results. 

Example. What amount of heating surface is necessary to 
heat 50,000 pounds of water per hour from 40 to 200 F. with 
steam at 212 F. 


200x92 = 435 sc l uare feet > 

or using the logarithmic mean temperature and 325 for the 

325A - 50,000 log, 212 _ 2QQ , 

^4. = 410 square feet. 

Primary and Secondary Heaters. If the steam on its way 
to the condenser passes through a heater we can raise the feed- 
water from 40 F. (winter conditions) to 110 F. if the vacuum 
carried is 26 inches, corresponding to a temperature of 126 F. 
The feed-water at 110 F. can be raised to 205 F. in another 
heater where exhaust steam from pumps or other non-condensing 
engines is used as the heating medium. 

The preceding method may be used to find the amount of 
heating surface in a primary and secondary heater to raise 



50,000 pounds of water per hour "from 40 F. to 205 F. if the 
main engine carries a vacuum of 26 inches. 


200 + 51 

343 square feet; 


432 square feet 

775 total area in both heaters' 

Factor F, according to Hausbrand. In finding the rate of heat 
transfer Hausbrand divides the operation into two parts. In 
the first part the factor F is large, as it is applied only to the 
cooling surface at which steam is condensed. In the second 
part a lower factor is used, as it is applied only to the cooling 
surface at which the condensed steam is cooled below its boiling- 
point to some lower temperature. 

In thermal units, B.T.U., per square foot per hour per one 
degree difference, the factor is 
F = 

where V d is the velocity of the steam in feet per second and Vj 
is the velocity of the cooling water in the same units. 

The table below is for F at various velocities of the cooling 
water in feet per second, but for a steam velocity of one foot 
per second. For any other steam velocity, with any of the 
tabulated velocities of the water, the proper F is determined by 
multiplying the tabulated value of F by the square root of the 
steam velocity in feet per second. 


V) of cooling 
water in feet . . 














Fin B.T.U 














The Coefficient of Transmission of Heat, F, between two liquids 
at different temperatures may be found from the equation 




where v^ is the velocity in feet per second of one liquid and v/ 2 
is the velocity of the other in the same units. For certain veloci- 
ties the value of F is tabulated below in B.T.U. per square foot 
of cooling surface per hour per degree F. difference of tempera- 







































































































In endeavoring to apply these formulas to a condenser the 
variety of conditions encountered therein will be made apparent. 
The formulas show possibilities for future improvement, point- 
ing out surface efficiencies that ought to be attained but are 
not and indirectly indicating the reason therefor. 

Suppose that we are required to find the cooling surface per 
100 pounds of steam, exhausted at 10 pounds absolute, 193 F.; 
temperature of injection, 60 F. ; temperature of discharge, 
90 F.; temperature of feed-water, 110F.; velocity of cooling 
water, 200 feet per minute. Assume other data as required. 

To condense the steam to water at its boiling-point, 193 F., 
will require the absorption of its latent heat or 978.8 B.T.U. 
per pound. To cool the water from 193 to 110 F. will require 
the absorption of 83 B.T.U. or about 1/12 of the former quantity. 
Ideally then the range of the injection from 60 to 90 F. should 
be divided into twelve parts and one of those parts should be 
devoted to cooling the condensed steam and eleven should be 
devoted to condensing the steam. The range of temperature of 
the injection would be 60 to 63 F. for cooling and 63 to 90 
for the condensing. 


(193 -63) -(193-90) 
Tm== ~~ =117 K > 

( 193_63)-(110-60) 00 


= 83. 

These temperatures do not differ materially from the arithmetical 

The velocity of steam as it strikes the tubes may be very 
much less than its velocity in the exhaust-pipe. Similarly the 
velocity of the descending hot water on the tubes is indefinite. 
We are not interested in its velocity in falling from tube to tube. 
Let us assume 5000 feet per minute as the velocity of the steam 
and 40 feet per minute for the velocity of the hot water on the 
tubes. Hence F<* = 83.3, ^ = .66 feet, and iy a = 3J feet. F (from 
Table A) =84; Vv d =9.1, F (from Table B) = 95. 
Heat transmitted per square foot of cooling surface 
Condensing=(9.1)(84)(117) = 89,400 B.T.U., 
Cooling = (83) (95) = 7,885 B.T.U. 

1 DO V Q7$ 8 
To condense 100 Ibs. steam requires - Qn , nn ' =1.1 sq. ft.; 

To cool 100 Ibs. water requires - = 1.06 sq. ft. 



Hence ., fa . 1 1 =46 pounds of steam are condensed and 
l.Uo H- 1.1 

cooled per square foot of cooling surface. 

As this result is not secured in practice under the given cir- 
cumstances it is important to discuss the causes of the difference. 
In the first place, it is seen that the transmission of heat in con- 
densing is ten or a dozen times that in cooling. If therefore any 
of the condensing surface is water covered all the time, since its 
rate of heat transmission is enormously reduced, it is evident 
that a very great increase must be made in the cooling surface 
to make up for the loss of the more efficient surface. 

Suppose, for example, that one-half of the condensing surface 
is water covered. Then one-half of 89,400 B.T.U. must be trans- 

mitted by water-cooled surfaces. - Then - ' - -- = 6.7 square 


feet of cooling surface will be required As the condensing surface 


is now .55 feet, we have ,, = 13.8 pounds of steam con- 

o. / T~ -OO 

clensed and cooled per square foot of cooling surface. 

In the contraflo type of condenser an average of 33 pounds 
of steam were condensed and cooled per square foot of cooling 
surface. The rate for the upper tubes was much higher than 
this. It is instructive to examine the tables and note the effect 
that the velocity of steam and cooling water has on the coefficient 
of heat transmission. 

Contraflo Condensers. " A leading feature of this type of con- 
denser is a compartment draining of the feed-water (Figs. 138, 139). 
The condenser is divided into three compartments by two dia- 
phragms somewhat inclined to the horizontal, and the water of 
condensation in each of the three compartments is drained off 
directly from that compartment, so that the surfaces in the lower 
compartments are unimpeded in their condensing action by water 
from the upper compartment flowing over them. As the major 
part of the condensation, even at fairly high rates of condensa- 
tion, is completed in the highest sections of surface on which the 
steam first impinges, the importance of this feature is apparent, 
and its influence will be seen in the results. 

" Surface Efficiency. Surface efficiency is at the root of all 
efficiency in a surface-condenser. That condenser is the most 
efficient in which each square foot of surface transfers in given 
time and conditions, as to water-supply, etc., from the steam to 
the water, the largest number of heat-units. This will, moreover, 
be the condenser which will not only register the highest vacuum, 
but will maintain it at the least cost in condensing water, and 
with the smallest surface a*nd cubical capacity per pound of steam 
condensed. It will also, in given conditions, be the one to yield 
the highest hot-well temperature. Now, in order that a surface 
may act thus, it is necessary that the steam should have free access 
to, and should pass over, sufficient surface on the one side, and 
that all the condensing water should come into direct and efficient 
contact with the surface on the other side. This clearly cannot 
be the case if, on the steam side, practically the whole surface is 
continually subjected to showers from the water of condensation, 
or if the steam can short-circuit any material amount of the sur- 
face; nor can it be the case on the water side if the condensing 





Nou.naiaj.sia unodVA 

773AI20H OJL 


water flows through the tubes in unbroken cylindrical streams, 
peripheries of which streams alone come into actual contact with 
the tube surface, and a greater or less proportion of water-core 
passes through without efficient contact. Hence the augmented 
efficiency of the surface as a whole, due to the early interception 
and removal of the feed-water, the provision for promoting steam 
circulation, and the adoption of a suitable ratio between the surface 
and the water-carrying section of each tube element, by the intro- 
duction of a solid displacing core in the tubes or otherwise, as 
shown in Fig. 139a. The effect of the use of cores, as against open 
tubes, on economy in vacuum production will be dealt 
with later on. The cores used on these trials were tri- 
angular laths of hard wood rough from the saw. They 
IG. I39a. were a | DOut two inches longer than the tubes, and were 
simply inserted in the tubes without any fastening whatever. The 
annexed figure, 139a, shows a full-sized section of tube and core in 

" Let ti = temperature of injection-water; 
t " discharge-water; 

t v = corresponding to the vacuum V. 

"Then the index of relative surface efficiency is the ratio in 


relation to t it the heat-units absorbed per pound of condensing water 
being (t 1<). The greater this quantity the less the condensing 
water required per pound of the steam condensed. Hence economy 
of condensing water is one very important result of enhanced sur- 
face efficiency. Economy of water is important from several 
points of view. First, as in the case of land installations, water 
may itself have to be purchased. Second, it has to be pumped 
through the condenser; and any saving in water means, other 
things being equal, power economy in vacuum production. 
Third, water may have to be cooled for repeated use, and in this 
case surface efficiency of condenser has a double effect. Not only 
is there less water to be pumped, but owing to its higher outlet 
temperature there will be a greater mean difference between the 
temperature of the water to be cooled and the air which cools it; 
and hence cooling-towers will be more efficient, and may therefore 
be of smaller size for given power. 

" Another important result of enhanced surface efficiency is, of 



course, economy of condensing surface. Owing to steam space 
being dispensed with in this type, a given surface is contained in 
less capacity of condenser-shell. These two features conduce to 
economy of weight and capacity. From the point of view, there- 
fore, of weight and space occupied, this type of condenser has 
important advantages, which would seem to render it peculiarly 
adapted for use aboard ship, and specially so for all classes of war- 
vessels, in which both weight and space are of supreme importance. 
In the case of marine condensers, economy of condensing water is 
of itself of secondary importance; but economy of pumping power, 
of weight and space occupied, degree of vacuum maintained, and 
hot-well temperature are all of great importance. 

"The table gives results obtained under similar conditions by 
two Contraflo condensers and one old- type condenser attached to a 
quadruple-expansion engine 7"XlOJ"Xl5i"X23", stroke 18", 
using steam at about 210 pounds, superheated 50 F. 






perSq. Ft. 
per Hour. 


ing Water 
per 1 Lb. 
Steam . 

12 Lbs. 

per H.P. 
(No.3 = l). 

= 50F. 


Sq. Ft. 

Cu. Ft. 



Sq. Ft. 

No 3 








" 2 


9 6 






Old type. . . 








" Thermal Efficiency. The higher hot- well temperature and the 
smaller amount of condensing water and surface are both due, the 
former entirely and the latter partially, to the same cause, viz., 
the compartment drainage of the condenser. At all, except very 
high rates of condensation, or with very small quantities of con- 
densing water per pound of steam, the greater proportion of the 
condensing work is done by the surface situated in the uppermost 
compartment. The great mass of the feed-water is therefore with- 
drawn from the condenser at a temperature sensibly equal to that 
obtaining in the top compartment of the condenser and without 
passing over the cooler compartments lower down, and specially 
escaping the lowest compartment of all, which is thus reserved as 
an efficient air-cooling section. The hot-well temperatures of the 
old type are from ten to fifteen degrees lower than those for cor- 


responding conditions in the new type for all degrees of vacua 
exceeding 26 inches. 

"The absolute pressure in these condensers is practically uniform 
throughout the interior; but the temperature is not uniform 
throughout. It is always higher at the top than at the bottom. 
The absolute pressure, therefore the vacuum must be a com- 
promise between that due to the top and that due to the bottom 
temperatures. As a matter of fact, in air-tight systems the vacuum 
recorded is generally somewhat higher than that corresponding to 
the top temperature, but is not so high as the bottom tempera- 
ture would indicate, especially at high vacua. 

" Economy in Vacuum Production. Conditions are conceivable 
in which a given vacuum might be too dearly purchased. Leaving 
out of account for the moment all question of the first cost or 
weight of the vacuum-producing appliances, including condenser 
and pumps, as well as any commercial value attached to the con- 
densing water, we have on one side of the account the power ex- 
pended in maintaining the vacuum and on the other side the 
power realized from it. Obviously, if a given vacuum should cost 
more in power for its attainment than it returns in the shape of 
power due to it in the engines, it would be bad policy to work at 
such a vacuum. On the above basis, the power cost of a vacuum 
will comprise the power required to drive the air- and circulating- 
pumps. The power absorbed by the air-pump will clearly depend 
upon its size and speed, but so far as degree of vacuum is concerned 
the power seems practically independent of the vacuum, at least 
for the Edwards type of pump and for vacua ranging between 
26" and 29". If there is any effect at all, it is so small, in a com- 
parative sense, as to be negligible in practice. (For proof, see 
page 270.) 

"As regards the power absorbed by the circulating-pump, this 
will, of course, depend upon several factors, according to the cir- 
cumstances of each individual case; but so far as the essential 
circumstance is concerned, viz., the production of different degrees 
of vacua in a given condenser the power will depend on two 
factors only the quantity of condensing water and the head or 
pressure against which it is propelled through the condenser. 

" The speed of the circulating water in the tubes varied from 
\y to 4}' per second with no cores, and from If to 6J' with cores, 


the corresponding maximum resistances being those due to heads 
of 10' and 32' respectively." 

Surface-section Ratio. If L is the length of one tube and the 
water circulates 4 times, the length of one element = 4L. Calling 
s the exterior surface of one element and a the cross-sectional 

area of one tube, then the surface-section ratio = ( ). The numer- 

ator of this ratio indicates proportional heat-absorbing capacity, 

and the denominator proportional condensing water-carrying 
capacity; and it might therefore be expected to have a determining 
influence upon the efficiency of condensers on the water side. In 
this type of condenser surface efficiency is independent of rate of 
condensation up to 37 Ibs. per sq. ft. per hour but it is materially 
dependent upon the value of the surface-section ratio. 

The sole advantage of cores in these trials consisted in the 
fact that they afforded a ready means of changing the surface 
section without the necessity of structural alterations in the con- 
denser. In new designs the same end can, of course, be attained 
by the adoption initially of suitable proportions and without cores. 

Maximum efficiency will occur when discharge-water tempera- 
ture is equal to the temperature at the condenser top. This is 
practically attained when the surface section has a value of some- 
thing like 2900 or 3000." * 

Cooling-towers. In many places water is either unobtainable 
in large quantities, expensive, or, if abundant, contains elements 
such as mud, salts, or acids that are objectionable. Some appli- 
ance that will reduce the amount of water necessary to operate 
condensers is desirable. Evidently if the cooling-water could be 
cooled and used repeatedly, a very great saving would be effected. 

Fig. 140 represents the Alberger cooling-tower for this purpose. 
It consists of a thin cylindrical steel shell, open at the top and 
supported on a suitable foundation, and having fitted on one side 
a fan, the function of which is to circulate a current of air through 
the tower and its filling. This filling consists of layers of cylindrical 
6-inch tiles 2 feet long, breaking joints. The hot water passes 
up through a central pipe to four perforated arms that are made 
to revolve by the discharge reaction. The water is thus sprayed 
over the tiles, down which it runs in thin layers, exposing an enor- 

* Lordjn Engineering. 



mous surface to the air rising from the fan. The area of floor- 
space occupied varies from 1 to 2 square feet per hundred pounds 
of steam used by the engine. 

FIG. 140. 

The fans must be large and run at low speed. The speed of the 
fans must vary with the temperature and humidity of the atmos- 



phere, and a direct engine-drive proves economical. The water 
lost per hour by evaporation in the tower = .8 of the feed- water 
used per hour. Hence the total water required by a condensing- 
plant with a tower is .8 of the feed-water instead of 30 to 50 
times the feed-water. The power to run the fans varies from 2% 
to less than 1% of that of the main engine. 

The following data show the effect of changes in the season : 

Temperature of atmosphere . 
' ' condenser dis 
cl.arge to cooling-tower. . . 
Temperature of injection re- 
turned from tower 

30 F. 

36 F. 



78 F. 

96 F. 

85. F. 

59 F. 

Degrees of heat extracted by 







Speed of fans at tower 
R P M 






Vacuum at condenser, inches 
Strokes of air-pump 
Boiler- pressure 







Temp, boiler- feed 







The gain by condensing is shown in the following table : * 

Type of Engine. 

Feed-water per I.H.P. per Hour. 

Per Cent 
Gained by 




for Com- 


for Com- 

Simple high-;- peed 
" low- " ... 

35 to 26 
32 " 24 
30" 22 




25 to 19 
24 18 
24 16 
20 12| 
23 14 
18 12 



Compound high-speed. . . . 
' ' low- ' ' 

Triple highspeed 

27 to 21 

" low- " 

Correct Absolute Condenser Pressure. The vacuum on a con- 
densing-engine is usually expressed in inches of mercury, whether 
a mercury column or the ordinary Bourdon gage is used. The 
latter is seldom correct enough for accurate work and ther- 
mometers properly placed give more accurate results. If the 

* See A. S. M. E., Vol. XVII. 


mercury column is used, care must be taken in interpreting its 
reading. If the barometer reads 29.6 and the corrected mercury 
column reads 27.5, the absolute pressure in the condenser is 2.1 

2 1 

inches, or 14.7^-^ = .491 X 2.1 = 1.032 pounds per sq. in., corre- 
sponding to 102.5 F. If, however, the barometer stood at 30.5 
the pressure would then have been .491 X (30.5 -27.5) = 1.473 
pounds per sq. in., corresponding to 114.5 F. This would make a 
serious difference, for example, in the adiabatic expansion of 
steam in a steam-turbine. 

Wet Vacuum-pump Design. Let us state a few laws that are 
demonstrated in books on physics : 

1. The temperature of ebullition, or the boiling-point, in- 
creases with the pressure. 

2. For a given pressure ebullition begins at a certain tem- 
perature, which varies in different liquids, but which, for equal 
pressures, is always the same in the same liquid. 

3. Whatever the source of heat as soon as ebullition begins, 
the temperature of the liquid remains stationary. 

4. The tension and consequently the quantity of vapor 
which saturates a given space are the same for the same tem- 
perature whether this space contains a gas or is a vacuum. 

5. The tension of the mixture of a gas and a vapor is equal 
to the sum of the tensions which each would possess if it occupied 
the same space alone. 

In engineering problems none of these laws is absolutely true be- 
cause the requirements of the law are not fulfilled. The conditions 
existing in the vapor-space of a jet condenser are very complex. 
The injection- and feed- waters bring into the condenser from 
5% to 7% of their volume of air when reckoned at atmospheric 
pressure and temperature. The volume that this air will occupy 
in the condenser depends upon its tension or pressure in the con- 
denser, and not on the total pressure in the condenser as shown 
by a vacuum-gage. The latter, as shown by law 5, indicates 
the sum of the pressures due to the steam tension and the vapor 

The five laws given above, governing a vapor and its liquid, 


when there is temperature equilibrium in both vapor and liquid 
(which occurs in experiments when vapor and liquid are quiescent), 
must not be applied too rigidly to masses moving with cyclonic 
velocity. The temperatures of the vapor and its liquid are not 
the same, and the temperature of both differs throughout their 
mass in engine-condensers.* 

For our purposes it is close enough to take the mean tempera- 
ture of the vapor and liquid and find the corresponding pressure. 
This is approximately the pressure due to the steam ; and the 
difference between this quantity and the pressure as calculated 
from the vacuum-gage reading is the pressure due to the incon- 
densible gases, such as air, carbonic acid, etc. If the mean tem- 
perature of the water and steam were 126 F., we know that the 
pressure due to the steam vapor is 2 pounds per sq. in. If the 
vacuum-gage shows 24", the barometer reading being 30", the 
total pressure in the condenser would be 2.94 pounds, and the 
pressure due to the air alone would be .94 pound per sq. in. 

The importance of distinguishing between the air- and steam- 
pressures will become apparent if we attempt to obtain high degrees 
of vacua in any system of jet condensation where the air is allowed 
to separate from the water. 

Air-pump. f "It is sometimes thought that a large air-pump 
is a very inefficient machine for handling comparatively small 
amounts of air, and the reason given is that the piston of the 
pump is drawing against the vacuum all the time, and there is 14 
pounds pressure on every square inch of the piston to be overcome 
by the motor. This idea is wrong, however. The work on the 
pump is nearly proportional to the amount of air handled regard- 
less of the size of the pump. If the amount of air is less than the 
pump is capable of delivering, the pressure on the atmospheric 
side of the piston itself is balanced, or nearly so, for a good portion 
of the cycle. This can be demonstrated mathematically, and has 
been demonstrated by actual measurements on these air-pumps. 
The maximum load on the pump occurs when the vacuum is about 
18J", varying with the clearance. If the vacuum is less than that, 

* Expts. Surface Condensation. J. H. Smith, Engineering, March 23, 1906. 
f Engineering Mag., April. 1906. 



the load falls off because of the decreased difference in pressure. 
If the vacuum is greater, the load falls off from the decrease in the 
mass of air handled. The curve on page 271 (Fig. 142) is a record of 

FIG. 141. 

a trial made on a pump to demonstrate this, and the analytic dem- 
onstration is also given. The record of the trial of the pump does 
not present a perfect and uniform curve, because the pump- valves 
are mechanically operated, and for the low vacuum they can be ad- 
justed only by the sound which the mechanism gives out; but the 
curve in general is correct and demonstrates the point. The read- 
ings were taken down to 18J" of vacuum. Below that point only 
one reading was to be had, i.e., that at inches. 
Analytical Proof. (Fig. 141.) 

A = area of card = piVi + I I2 pdv (piv c +P2V 2 


log, v 2 -pivi log* vi -piVc- 


piv c 


The area = a maximum when log v\ =log* v 2 1 + . 


Let p l =14.7, v 2 = l, r c = .03, log. i?i =0-1 +.03= -.97. 
(Add 2.3025 and we obtain 2.3025 -.97 = 1.3325, or the logarithm 
of ten times the required number, .*. Fi = .379.) Hence the 
area is a maximum when V\ = .379. The corresponding value of 


Amperes of Current 

n pi Vi = p 2 v 2 is 5.6 pounds, or a vacuum of 14.7 5.6 = 9. 
















) * . 4 G 8 10 12 14 16 18 20 22 24 _ 26 28 30 
" Vacuum in Inches 

FIG. 142. 

FIG. 143. 

"Edwards' Air-pump. The condensed steam flows continu- 
ously by gravity from the condenser into the base of the pump 


and is there dealt with mechanically by the conical bucket working 
in connection with a base of similar shape. Upon the descent of 
the bucket the water is projected silently and without shock at 
a high velocity through the ports into the working barrel. 

"However slowly an air-pump with foot- and bucket-valves 
may be running, the pressure in the condenser has to be sufficiently 
above that in the pump to lift the foot- valves, overcome the inertia 

FIG. 144. 

of the water, and drive the water up through the valves into the 
barrel. The higher the speed of the old type of pump the greater 
is the pressure required to overcome these resistances owing to the 
very short space of time available, and as any increase of pressure 
in the condenser is accompanied by a corresponding increase of 
back pressure in the L.P. cylinder, it"' will be seen that in an air- 
pump fitted with foot- and bucket-valves, increase of speed means 
loss of efficiency. 

"Under ordinary working conditions, when the bucket descends 
and the ports are open, there is absolutely no obstruction between 
the condenser and the pump; the air has a perfectly free entrance 
into the barrel (Fig. 142), while immediately afterwards the water 


is injected into the barrel at a high velocity. Thus, instead of 
obstructing the entrance of the air, the water tends to compress 
that already in the barrel and to entrain or carry in more air 
with it. 

"In the old type of pump the clearance between the bucket and 
head valve-seat is necessarily large, due to the space occupied by 
the bucket-valves, the ribs on the under side of the valve-seating, 
etc. Before an air-pump can discharge, all the air in the working 
barrel above the bucket must be compressed to a pressure slightly 
in excess of the atmosphere. Immediately the bucket descends, 
the air-bubbles remaining in the clearance water expand and 
occupy a space in the pump which should be available for a fresh 
supply of air from the condenser. In this type of pump the top 
clearance is reduced to a minimum." 

To obtain high vacua we should utilize one or more of the follow- 

1. Cold injection-water. 

2. Have low discharge- water temperature. 

3. Control the amount of injection- water. 

4. Increase the speed of the air-pump. 

5. Reduce the back pressure on the air-pump. 

6. Prevent the separation of air and discharge- water and 
sweep both out together by gravity. 

7. Use an air-pump that does not require suction-valves. 

8. Have the minimum possible clearance in the air-pump and 
fill that clearance with cool water. 

9. Cool the gases to the temperature of the injection- water. 

10. Use a dry-air pump. 

11. Use a surface-condenser, pump all air out of the system, 
and absolutely prevent air-leakage. 

Air-pump for Surface-condensers. At first sight it would seem 
that air-pumps used with marine engines could be of very mod- 
erate size, as the same feed-water is used continuously, and after 
it has circulated a few times it ought to be freed from all of its 
contained air. And yet on large transatlantic steamers we find 
an air-pump capacity of .23 cubic foot per pound of steam con- 
densed, the vacuum ranging from 26 to 27 inches. When dealing 


with high vacua, as required in steam-turbine work, much higher 
pump capacity is required. 

5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. 5.5 6. 6.5 7. 
jUr Jump Capacity in Cubic Feet 
fer pound of Steam 

FIG. 145. 

Professor Weighton, in experiments illustrated in Fig. 145, 

1. That when the system is fairly air-tight .7 cu. ft. per 
pound of steam condensed is as good as anything larger. 

2. When air-leakage exceeds a certain amount, larger pump 
capacities are required. This ranged from .7 cu. ft. per 
pound of steam, condensed when the engine was running under 
full power and air-leakage was consequently slight, up to 6.5 
cu. ft. at one-quarter power when the receiver pressures were 
below atmospheric pressure. 

3. That there is no apparent advantage in working pumps 
on the compound principle. 

Dimensions. When air-pumps are directly connected to the 
engine so that they make the same number of strokes, the follow- 
ing dimensions have been used : 

For jet-condensing engines having vertical, single-acting air- 
pumps the area of the air-pump piston or bucket multiplied by 
its stroke may be from 1/5 to 1/10 the capacity of the L.P. cylinder; 
if the pump were horizontal and double-acting its capacity may 
be from 1/8 to 1/16 of the L.P. cylinder. 

For surface condensing engines the single-acting air-pump 
capacity may be 1/10 to 1/18 of that of the L.P. cylinder, and 
the capacity of the double-acting pump would be 1/15 to 1/25 cf 
the volume of that cylinder. 

On torpedo-boats with main engines making 330 revolutions 
per minute the ratio of directly connected air-pump volume swept 
through per revolution is from 1/36 to 1/30 of that swept through 





TW^-PICCM c^ {Tension Hnch= 9.874 
M.E.P. 1.894 Spnng, -\ Comp , , n l inch=8 . 7 


0.-Line = 14.334 

FIG. 146. 



V.-Line= 12.549 

0.-Line-= 14.324 



FIG. 147. 

0.-Line = 14.324 


per revolution by the low-pressure pistons. On the battle-ships the 
corresponding ratio of independent air-pump piston displacement 
per revolution to the displacement of the low-pressure pistons per 
revolution was 1/25, but the pumps only made 1/4 to 1/5 the 
number of revolutions made by the main engines. 

Bauer gives 





Small cargo boat 







Medium cargo-boat 

Large cargo -boat . .... 

Mail steamer . 


KdisGT 'Wilhclm II 

Russian cruiser Booatiir 

Navy gunboat 

Small cruiser 

Large cruiser 


Definitions of Air-pumps. If we refer to Fig. 16 we see that 
this pump draws from the condenser the condensed steam and 
a mixture of air and vapor. The injection water, however, is 
forced by the circulating pump through the tubes and out of 
the condenser without coming into contact with the condensed 
steam. If we examine Fig. 17 we see that that air-pump has 
to handle a mixture of injection water and condensed steam as 
well as the mixed air and vapor. Air-pumps which must handle 
both water and a mixture of air and vapor are called wet vacuum- 
pumps. On the other hand, a vacuum-pump attached to the 
barometric type of condenser, Figs. 125 and 126, would draw 
off only the mixture of air and vapor as the mixture of condensed 
steam and injection water flows off by gravity at the bottom 
of the discharge pipe. An air-pump working in this manner is 
called a dry-air pump. The ejector type of condenser needs no 

Action of an Air-pump. Comparing the air-pumps in Figs. 
16 and 144 we notice that one is horizontal, with large clearance 
spaces and with inlet valves, S, which must be lifted. The other 
pump is vertical, with no clearance spaces and with no inlet 


valves. On the suction stroke the difference between the abso- 
lute pressure in the pump cylinder and that in the condenser is 
the force which moves the water and mixture of air and vapor. 
That this difference may be as small as possible so that the con- 
denser pressure will be a minimum it is evident that anything 
causing resistance to movement, such as valves, narrow passages or 
sharp bends, should be removed. That the pressure in the pump 
should be as low as possible there should be no pockets in which air 
is compressed on one stroke only to re-expand on the following one. 

To understand the action of the air-pump the student should 
have a clear idea of the sequence of events as they occur in the 
pump during a revolution. At the beginning of the compression 
stroke of the air-pump piston (see Figs. 16, 144, and 146), the 
air-pump chamber contains more or less water and some air and 
water vapor at the same temperature as the water and at a certain 
pressure absolute. 

Returning to Figs. 16, 144, and 146, we note that in the 
early part of the compression stroke that the curve of pressure 
rises very slowly. This is due to the fact that the water vapor 
cannot be compressed as the vapor is converted into water. Hence 
the air alone is compressed. After all the water vapor is con- 
densed, the curve of air pressures rises very rapidly to something 
over the pressure due to the atmospheric and valve resistances. 
On the return stroke, the pressure drops very rapidly if only 
water is present, but, if any air is present (at full atmospheric 
pressure) the curve drops rather slowly. (Fig. 147.) 

Designing Air-pumps. The design of an air-pump consists in 
finding the volume which the air-pump piston must sweep through 
per minute to remove all the air and water intended from the 
condenser. This amount will vary greatly. For example : 

1. If the condenser is thirty or more feet from the ground, 
it may be made self-draining. A surface condenser of that 
sort would use a dry air-pump whose volume would depend 
principally on the amount of air leakage and the degree of 
vacuum required. 

2. A barometric condenser has a dry-air pump but it must 
remove not only the air from the condensed steam but also 
the air from the injection water and the air leakage. 


3. The wet vacuum-pump attached to a surface condenser 
removes the condensed steam and the air that leaks in. 

4. The wet vacuum-pump attached to the ordinary jet 
condenser has to remove the discharge water, the condensed 
steam and the air which the feed- and injection-water con- 

Design of Air-pump for Surface Condenser. Assume the 
following data: Compound engine, 300 I.H.P.; 15 pounds of 
water per I.H.P.; injection, 70 F.; discharge, 90 F.; feed, 
110 F.; vacuum, 26 inches; barometer, 29.90 inches. 

The unit of volume generally used is the volume of one pound 
of feed-water. Let us assume that feed and injection water 
contain 1/20 or .05% of their volume of entrained air at atmos- 
pheric temperature and pressure. As soon as the water con- 
taining this air gets into the condenser the air increases in volume 
in proportion to the decrease in pressure and to the increase of 

absolute temperature according to the law, -=-=C. 

As the vacuum gage is affected by the atmospheric pressure 
we see that the absolute pressure in the condenser is 29.90 26 
= 3.90 inches. As the temperature of the water vapor is 110 F. 
we see from the tables that the pressure due to it is 2.58 inches 
or 1.29 pounds absolute. Then, from Dalton's law, we know 
that the difference, or 3.90 2.58 = 1.32 inches, is the pressure due 
to the air. 

NOTE. If over a little water at 110 F. we had a cubic foot of 
space filled with water vapor alone at 2.58 inches pressure abso- 
lute, we could take a cubic foot of air at 1.32 inches pressure and 
110 F. and force it into the cubic foot of vapor. At the end of 
the operation there would be only one cubic foot of the mixture 
of vapor and air but the pressure would be the sum of the former 
pressures. The volume occupied by a certain weight of air in 
the condenser is determined by the absolute temperature of the 
air and the air pressure and not by the condenser pressure. If 
the vapor in a condenser were at 126 F., it would be impossible 
to obtain a vacuum over 26 inches, or if the temperature of the 
vapor were 141 F. it would be impossible to secure a greater 
vacuum than 24 inches, no matter what the volumetric displace- 


ment of the air pump might be. Hence to obtain a high vacuum 
it is necessary to have the air and vapor as cool as possible. 

If F 1= =the volume of the feed-water in cubic feet per minute, 
then .05Fi is the volume of its entrained air at 29.90 inches of 
pressure and 460 + 70 = 530 F. A. From the equation, 

PV P 2 V 


rfi rfi ) 

JL 1 JL 2 

we can find its volume at 1.32 inches of pressure and at 
460 + 110 = 570 F. A. Hence, 

29.90 X.057i_ 1.327 2 
460 + 70 "460 + 110 

The theoretical volume of the air-pump would thus be 
Vi + 1.2Fi = 2.2Vi. As the volume of the feed-water is generally 
taken as the unit, we may say then that the volumetric displace- 
ment of the air-pump in cubic feet per minute is, in this case, 
2.2 times the volume of the feed-water in cubic feet. The above 
makes no allowance for air leakage or pump efficiency. On the 
other hand, the factor 2.2 is too large if the condensed steam is sent 
to the boiler continuously since such feed-water will not contain 
.05% entrained air. Neither is it true if new feed- water is used 
continuously if this feed-water is sent through an open heater 
and brought to the boiling-point approximately. The entrained 

. 460 + 70 53 
air would be then only 4590 . 210 = 67 = ; as mucn as ^ was 

in water at 70 F. 

Manufacturers of condensing apparatus are in the habit of 
calling for piping free from air leaks and then supplying air- 
pumps that are entirely too large if there are no air leaks. In 
the present case a reliable index of the amount -of leakage ex- 
pected is obtained from the size of air-pumps supplied. Manu- 
facturers of vertical twin air-pumps will guarantee '26 inches of 
vacuum with injection at 70 F. with an air-pump displacement 
of 13 times the volume of the feed-water. This allows practically 
ten or eleven volumes, at condenser pressure and temperature, 
for air leakage and pump inefficiency. Horizontal pumps are 


furnished with a displacement of 20 times the volume of the 
feed-water, thus allowing 18 volumes for leakage and inefficiency. 
A 300 horse-power engine would use 

625X60 = 1>2 CU * ft ' ^ water P er mmute - 

The theoretical displacement of the required air-pump would 
be 2.2 times and the practical displacement would be 13 or 20 times 
1.2 cu. ft. per minute, according as the air-pump is vertical or 

Bauer states that the principal dimensions of single-acting 
air-pumps are determined from the equation 

Here /= sectional area of air-pump in square inches; 

s = stroke of pump piston in inches; 
I. H. P. = indicated horse-power of the main engine; 

C = constant, equal to volume delivered by the air-pump 
per I.H.P. per minute. 

n= number of effective strokes of air-pump piston. 

The coefficient C=86 to 111 in surface condensers of triple 
or quadruple engines, with separately-driven engines. 

C=185 to 245 in surface condensers of triple- or quadruple- 
expansion engines, the air-pumps being driven by the main engine. 

C=300 to 365 in surface condensers of compound engines, the 
air-pump being driven by the main engine. 

If jet condensation is used as well as surface condensing, or 
if the former alone is used, (7=610 to 730. If instead of one 
air-pump, two pumps are fixed to and driven by the main engine, 
the volume swept through per stroke in each may be about .6 
of that above. The piston speed varies from 200 to 350 feet 
per minute in cargo boats and from 300 to 500 feet per minute 
in warships. 

The student may discuss the following data of the Glasgow 
Electric Power Station (Power, 1905): Steam handled, 60,000 
pounds per hour; vacuum, 25 inches in the condenser and 23 
inches in the engine; injection, 78 F.; discharge, 94 F.; con- 


densers, 7000 square feet; cooling surface (2690 tubes), 1 inch 
diameter; Edwards' three-throw electrically-driven air-pumps; 
diameter of cylinder, 16 inches; stroke, 12 inches; revolutions, 

Wet Vacuum-pump for Jet Condenser. Assume the following 
data: Compound engine, 300 I.H.P; water rate, 15 pounds per 
I.H.P.; injection, 70 F.; discharge, 110 F.; vacuum, 26 inches; 
barometer, 29.90 inches. 

As the amount of heat per pound of steam to be absorbed in 
the condenser is practically constant and is about 1050 B.T.U., 
we can assume that the amount of injection water required is 
1050 -Kl 10 -70) = 26 pounds. The total water is then 27 pounds 
and the volume of air is 

29.9 X .057i (29.90 - 26 - 2.58) 7 2 
460 + 70 460 + 110 

Hence V% is equal to 1.27:. As V\ is 27 times the volume of 
the feed-water then the volume of the entrained air is 27X1.2 
or 32.4 times the volume of the feed-water. The amount to be 
allowed for air leakage is largely guess work. If we allow 10 
times the volume of the feed-water we shall have the following 
allowances : 

Volumes : 1 .... Feed-water 

26 Injection water 

32.4 . . . .Air in feed and injection water 

10 Air leakage at condenser pressure and temp. 


Hence the displacement of the air-pump in cubic feet per 
minute will be 70 times the volume of the feed-water. The 
required displacement is therefore 

62.5X60 =84 CublC feet ' 

The required air-pump may now be chosen from a catalogue. 


Cooling Air in Condensers. To cool the air In its passage to 
the air-pump a large cooling surface is necessary, as the heat 
transmission coefficient is very low. Efficiency depends upon 
the air velocity, the water velocity in the pipes being of little 
importance. In Josse's experiments (Power, Feb., 1909) it 
varied from 0.172 to 0.955 B.T.U. per square foot per hour per 
degree Fahrenheit difference of temperature. 

Dry Air-pumps for Counter-current Barometric Condensers. 
If Fig. 125 is carefully examined it will be seen that the air is 
drawn off at the top of the condenser. To reach the eduction 
pipe the air has to pass in intimate contact with " cold fingers " 
containing injection water at initial temperature. The tendency 
of these cold fingers is to deprive the air of its last remnant of 
vapor and to cool the air down to (theoretically) the injection 
temperature. If the vapor is condensed, there is a marked ten- 
dency for the vapor pressure to decrease and the air pressure 
to increase as the total pressure must be very nearly uniform 
through the condenser. It is evident that the lowest total 
pressure must be at the mouth of the air-eduction pipe, as 
the gases are flowing in that direction and all flow is from 
the greater to the less pressure. But in gases so light as these, 
a very high velocity is secured by a very slight difference in 
pressure. At condenser pressures air is lighter than steam, but 
practically the velocities in the condenser are so great that it 
is easy to see that ideal conditions cannot be carried out. Hence 
in the design of an air-pump for this style of condenser the volume 
of the pump displacement is materially reduced, as it does not 
care for the feed and discharge water and receives the air not 
only at much higher pressure but also colder. 

Design a dry-air pump for a 300 I.H.P. compound engine, 
using 13 pounds of water per I.H.P. The injection is at 70 F.; 
the discharge at 110F.; vacuum is 28.5 inches; barometer, 
29.90. Counter-current condenser. 

We shall assume that the air is drawn off at 85 F. (the cor- 
responding pressure is 1.2 inches of mercury) and that the air 
leakage at condenser pressure is 15 times the volume of the feed- 

The pressure corresponding to 110 F. is 2.58 inches of mer- 


cury and, if the steam vapor were not brought below that tem- 
perature, no vacuum pump however large would give the 
required vacuum. The difference, 29.90 28.5 = 1.4 inches, is the 
maximum possible pressure of the air and could only occur if 
all the vapor is condensed. The air may be lower than 85 F., 
the minimum 70 F. being possible. Assume then 1.2 inches as 
the absolute pressure of the air. 

Assuming each pound of steam going into the condenser loses 
1050 B.T.U the amount of injection per pound of steam will be 

= 26 pounds. 

For each cubic foot of feed-water there will be 26 + 1 = 27 cubic 
feet of discharge water. The volume, V 2 , of the air in this injec- 
tion and feed-water (assuming both to have been originally at 
70 F. and 29.90 inches pressure) after reaching the condenser 
and passing the cold fingers of the injection-pipe will be, since 

29.90 X.057i 1.2F 2 
460 + 70 "460 + 85' 

1.3Fi, where Vi represents the volume of the discharge in any 
unit of time. 

The number of cubic feet of feed-water per minute will be 


The volume of the discharge, per minute, will be 

27X1.1 = 29.7 cubic feet. 

The volume of air to be discharged per minute will be 
29.7X1.3 = 38.6 cubic feet. 

If the air leakage is 15 cubic feet per minute the total dis- 
placement of the dry-air pump, per minute, will be 

38.6 + 15 = 53.6 cubic feet. 


Ex. 101. Design a surface condenser for a 100 horse-power high- 
speed engine using 18 pounds of steam per I.H.P. Assume other 
conditions. Vacuum 27". 

Ex. 102. Design a contraflo condenser for a 2000-horse-power 
engine using 13.5 pounds of steam per horse-power. Vacuum ex- 
pected = 28". 

Ex. 103a. Design a wet vacuum-pump for the jet condensers; 
26.5 inches of vacuum required. 

Ex. 1036. Design a dry vacuum-pump for the surface condensers. 


Steam-pumps (Fig. 4). The wastefulness of the ordinary 
steam-pump is not recognized by the ordinary steam user. It 
uses steam at full boiler-pressure; the clearance is inordinate when 
the piston makes a full stroke and there is no adjective strong 
enough to express its wastefulness in case it does not make its full 
stroke. The initial condensation depends upon range of tempera- 
ture which, in the case of a steam-pump, is from the boiler tem- 
perature to 212 F. As a result, the initial condensation is very 
great. In case the pump is used only occasionally and the steam- 
pipe fills with water from radiation losses, the percentage loss for 
the actual work done is very great. The ordinary steam-pump will 
use between 80 and 300 pounds of water per I.H.P. A simple 
pump will require one pound weight of steam to pump 40 pounds 
of water during the time actually employed in pumping. 

This waste may be reduced by compounding, and a still greater 
saving will be made by the use of a compound condensing pump. 
For instance, a duplex 6"X4"X6" may be replaced by a single 
compound with high- and low-pressure steam-cylinders of 6 inches 
and 10 inches diameter, water cylinder 5 inches in diameter and 
10-inch stroke. 

The greatest saving can be made by using the exhaust-steam 
in a feed-water reheater. Great care should be used not to increase 
the back pressure unduly. 

Wasteful as they are, however, they are far more economical 
than ejectors when the heat in the water ejected is thrown away^ 
as in the case of (bilge) syphons. 

To economize, auxiliaries have been belt-driven from a shaft: 




which was driven from the main engine. This arrangement has a 
number of difficulties to overcome : 

1. The need of regulating each pump to an exact speed 
depending upon requirements. In an emergency an excessive 
speed of one pump may be needed for a few moments, or for 
long intervals no speed at all may be needed. 


M.E.P. 134.15 

Spring, 1 inch -84.905 Ibs. 



M.E.P. 141.79 

Spring, 1 inch =84.905 Ibs. 



FIG. 148. 

2. The friction of heavy shafting is a large part of the power 
required, hence the arrangement is wasteful if only a few aux- 
iliaries are running. 

If the steam from the main engine is sent to a condenser, this 
arrangement is less economical in heat and less convenient than 
separate auxiliaries if the latter send their exhaust-steam to feed- 
water heaters. 

There is a practical limit to the amount of exhaust-steam that 
can be used in this way. Moreover, the use of any heater is not 
economical unless it is using heat that would otherwise be neces- 



sarily wasted. As in many other things, heating economies are 
possible in a large plant that are not practically possible in a small 
one. Similarly plants that are run for short intervals only cannot 
use apparatus on which the interest and depreciation charges 
would counterbalance the economy gained by their use for a short 


M.E.P. 132.28 

Spring, 1 inch =83.19 Ibs. 

A.-Line y 


M.E.P. 144.75 

Spring, 1 inch =83. 19 Ibs. 


Coo ley 


FIG. 149. 

period of time. Hence with a uniform load and good feed-water an 
economizer may pay for itself. 

The amount of feed- water required per horse-power varies 

40 to 25 pounds for simple engines, 
25 to 15 pounds for compounds, 
20 to 11 pounds for triples. 

Each pump should be designed to supply 1.5 to 2 times the 
theoretical quantity of water required. This allows for slip or 
imperfect filling of the pump with water. 


The velocity of the water in the suction-pipe should not exceed, 
normally, 450 feet per minute, that in the discharge-pipe being 
600 feet per minute. The net area of the valve passageway 
should be calculated at 400 feet per minute. The diameter of the 
steam-cylinder is 1.4 to 1.6 times that of the water-cylinder, thus 
affording a pressure of 2 to 2.5 times that of the boiler. 

In duplex pumps the steam-valve on one cylinder is driven by 
the reciprocating motion of the other pump. In the simplex 
pumps it is necessary to employ an independent valve. 


FIG. 150. 

Reciprocating Circulating Pumps (Fig. 18). The piston speed of 
these pumps may reach 475 feet a minute; their volume may be 
obtained by allowing 

9 to 10.5 cubic feet per hour per H.P. for compound engines: 
7 to 9 cubic feet per hour per H.P, for triple- or quadruple- 
expansion engines. 

This allows 80% efficiency for the pump. 

The number of strokes per minute made by a steam-pun: p is 
generally calculated on the basis of 100 feet of piston speed per 
minute. For continuous boiler feeding and running under heavy 



pressure the speed should not exceed 50 feet per minute. The de- 
livery is also frequently given in gallons. If the diameter of the 
water-cylinder is squared and then multiplied by 4 ; the result is 
the delivery of the pump in gallons per minute on the basis of 
100 feet of piston velocity. 

On most pumps it is deemed advisable to place an air-chamber 
on the delivery side of the pump. In most cases it is even more 

j Suction 

FIG. 151. 

essential to put an a^r-chamber, as in Figs. 150, 151, on the suction 
side. Fig. 152 is added to show how not to apply the air-chamber. 
On long suction lines this air-chamber takes up the inevitable 
surging of the water in the suction-pipe due to the irregular taking 
of water by the pump. It stops the hammer-blow noise heard in 
pumps that are " pumping dry," as in pumping bilges dry. 

Ex. 104. A compound engine of 1000 I.H.P.; cylinder ratio, 1:4; 
19 expansions; steam at 165 pounds absolute on the piston; revolu- 
tions, 94; vacuum, 26"; using 14.5 pounds of water per I.H.P.; injec- 
tion, 70; discharge, 110 F.; jet condenser; feed-water, 70 F. in 
river-mains. Find the size of the feed-pump by calculation or from 
catalog. Assume positions of machinery and other data that may be 
required. Use hand-books or other aids. 


Ex. 105. Find the size of air-pump for Ex. 104. 

Ex. 106. Find the size of reciprocating circulating pump. 

Ex. 107. Find the size of centrifugal circulating pump. 

Ex. 108. Find the size of a feed-water heater to take care of the 
exhaust-steam from the steam-cylinders of the above pumps if the 
discharge-water be unfit to use. 

Ex. 109. Design a reheating receiver to superheat exhaust-steam 
50. See page 297. 


FIG. 152. 

Centrifugal Circulating Pumps (Fig. 153). The inner diameter 
of the driving- vanes should be 1.1 to lAd, where d = the diameter 
of the single suction- or delivery-pipes, and the outside diameter is 
2 to 2.6U The width of the vane at its inner diameter is .23 
to Ad. The width of the vane at its outside diameter may be 
reduced in proportion to the increase in velocity of the water, 
Notice proportions in the cut showing double suction-pipes. 

If the water enters from one side there is an axial thrust which 
is avoided by having the water enter on both sides. 

The shape of the vanes is such that the water may enter with- 
out shock (see steam-turbine calculations). The velocity at the 
periphery must be 25 to 40 feet per second for a friction-head of 5 



to 8 feet, the revolutions varying in general from 150 to 350 per 

The engines to drive these pumps must have a horse-power 

where Q = pounds of water delivered, 
h = head in feet. 



These engines should develop this power with a pressure equal to 
.75 boiler-pressure.* 

Steam-injector. Fig. 154 is a diagrammatic sketch of an in- 
jector. We owe this invention to M. Giffard, a French engineer. 
The original invention has been much improved and many care- 
fully worked out devices have been added to make the device reli- 
able and automatic. Its use is practically confined to boiler- 
feeding, as its efficiency as a pump is very low. As a boiler-feeder 
its thermal efficiency approaches 100%, as all the heat that it 
takes from the boiler is returned, but at a lower temperature. 

FIG. 154. 

The device consists essentially of a steam-nozzle, A ; a combin- 
ing tube, B; and a deli very- tube, D. C is an overflow and E is 
the suction-pipe. 

On page 216 we found that if steam is made to expand adia- 
batically in a properly proportioned nozzle, the heat lost in 
expansion was converted into energy of motion, or, in other words, 
the steam acquired a high velocity. The amount of thermal energy 

wV 2 
converted into kinetic energy = -^~ =wh is more than sufficient to 

do the work required in forcing W pounds of feed-water = (12 to 22) w 

into the boiler against the boiler-pressure, or wh>(W+w) - 


(W +w)hb, where hb is a head of water in feet equivalent to the 
boiler-pressure P&. 

* See Bauer, Marine Engines. 


When steam is turned on the injector, the first effect is to drive 
all air out of the system through the overflow which is open. The 
partial vacuum allows the atmosphere to force water through the 
suction-pipe, E, into the combining chamber, B. The steam, issu- 
ing from A at high velocity (as soon as the reduction of pressure 
occurs due to the condensation of the steam), possesses sufficient 
energy to move a large mass of water with considerable velocity. 
The combined mass in slowing down can overcome a higher static 
pressure than its own, and can therefore enter the boiler. 

Weight of Feed-water per Pound of Steam. Assume the steam 
to be dry, and measuring all heat-units from 32 F. : 

Let qi H-Z/i =heat required to produce one pound of steam; 

#2= heat contained in the feed before entering the 


#3 =heat contained in the feed after leaving the injector; 
w = number of pounds of steam used in any given time; 
W = pounds of feed- water lifted by the injector in the 

same time; 

W+w = pounds of water delivered by the injector; 
W(qzq2) =heat gained by feed- water; 
+qi qs) =heat lost by the steam; 

V 2 1 
The last term (W +w) ~-~ X ^= is the heat-equivalent to the kinetic 

energy of the delivered feed-water entering the boiler. As it is 
very small it may be neglected, hence 

/. = - = weight of feed- water lifted per pound of steam 
w qs~q2 

used by the injection. 

Efficiency of the Injector. A large portion of the kinetic 
energy of the steam is converted back into heat, as the impact 
must be that of non-elastic bodies. 

Let MI = the mass of the steam and Vi its velocity; 
M 2 = " " " " lifted feed and 7 2 its velocity; 
V c = " common velocity of the mass MI +M 2 . 


We know that the sum of the momenta before impact equals the 
momentum of the combined mass after impact, or 

(1) MM +M 2 V 2 = (M 1 +M 2 )V 

Let EI = %M i Fi 2 + %M 2 V 2 2 = the sum of the kinetic energies be- 

fore impact; 

E 2 = %(Mi+M 2 )V c 2 =t'he energy of the total water after 
impact. Then from (1) 

/M 1 7 1 
\ M l 


+M 2 /> 2(M l+ M 2 ) 

The initial velocity of the lifted feed is so small that it may be 
neglected. M 2 V 2 2 = approximately, hence EI = \M\ Vi 2 approxi- 
mately. The energy converted back into heat is 

AW M 2 

E 2 =Wit i - = ' 

In a locomotive injector one pound of steam is required for 
every 12 pounds of water lifted; therefore from the above formula 
12/13 of the energy of the steam must be converted back into 

Disregarding V 2 we have 


Similarly, E 2 = ^ . 

If from the entropy diagram we find the velocity of the steam 
is 2400 feet per second, 

EI = -- 2^32 -- =90,000 ft.-lbs. 

The Hancock Inspirator, " Stationary " Type. 

Directions for Connecting. 

Steam, water, delivery, and overflow connections are as illus- 

Si earn. Take steam direct from the dome or highest part of 
the boiler and not from a pipe furnishing steam for other purposes, 



Place a globe valve in the steam-pipe for a starting-valve, and 
before connecting the inspirator blow it out thoroughly to remove 
any red lead, iron chips, etc. 

Suction. A TIGHT SUCTION is absolutely necessary, especially 
on a high lift and for the smaller sizes of inspirators. 


FIG. 155. Hancock Inspirator. 

The size of the suction-pipe should be in proportion to its 
length. For a high lift or long trail, use pipe one or two sizes 
larger than the suction connections. The suction-pipe should be 
as nearly straight as possible. 

Never use a foot-valve-, as the water should be allowed to drain 
from the suction-pipe when the inspirator is not in service. 


Place a globe valve in the suction-pipe to regulate the supply 
of water to the inspirator, and KEEP IT WELL PACKED. 

Delivery. Place a check-valve in the delivery-pipe, between the 
inspirator and the boiler, also a globe valve between the check- 
valve and the boiler, so that the check-valve may be examined and 
cleaned when necessary. If the inspirator is to feed through a 
"heater," there must be a check- valve between it and the in- 

Overflow. The overflow-pipe must be as straight as possible 
and the full size of the connections. The end of the overflow-pipe 
must be opened to the air and not piped below the surface of the 

We do not recommend the arrangement for an inspirator to 
take water under a head, but the use of a tank fitted with a "ball 
cock," so that the inspirator may lift the water from it. If it is 
necessary to connect the inspirator direct to water-works pressure, 
the suction-pipe must be large enough to secure a uniform pressure. 
Never take water from a pipe which supplies water for other pur- 
poses, as the water-supply may be reduced so much at times as to 
make it unreliable. 

Directions for Operating. 

Open the overflow-valves Nos. 1 and 3, close forcer steam-valve 
No. 2, and open the star ting- valve in the steam-pipe. 

When the water appears at the overflow, close No. 1 valve, 
open No. 2 valve one-quarter turn, and close No. 3 valve. The 
inspirator will then be in operation. 

NOTE. No. 2 valve should be closed with care to avoid damag- 
ing the valve-seat. 

When the inspirator is not in operation both overflow-valves, 
Nos. 1 and 3, should be open to allow the water to drain from the 

If the suction-pipe is filled with hot water, either cool off both it 
and the inspirator with cold water or pump out the hot water by 
opening and closing the starting-valve suddenly. 

No adjustment of either steam- or water-supply is necessary for 
varying steam-pressures, but both the temperature and quantity 
of the delivery-water may be varied by increasing or reducing the 


water-supply. The best results will be obtained from a little 
experience in regulating the steam- and water-supply. 

To locate a leak in the suction-pipe, plug the end, fill it with 
water, close No. 3 valve and turn on full steam-pressure. Examine 
the suction-pipe and the water will indicate the leak. If the in- 
spirator does not lift the water properly, see if there is a leak in 
the suction-pipe. Note if the steam-pressure corresponds with 
the lift, and if the sizes of pipe used are equal to the size of the 
inspirator connections. 

If the inspirator will lift the water, but will not deliver it to 
the boiler, see that the check-valve in the delivery-pipe is in work- 
ing order and does not stick. Air from a leak in the suction con- 
nections will prevent the inspirator from delivering the water to 
the boiler even more effectually than it will in lifting it only. If 
No. 1 valve is damaged or leaks, the inspirator will not work 
properly. No. 1 valve may easily be removed and ground. 

To remove scale and deposit from the inspirator parts, discon- 
nect the inspirator and plug both the suction and delivery outlets 
with corks. Open No. 2 valve and fill the inspirator with a solu- 
tion of one part muriatic acid and ten parts water. 

Reheaters. There is little use in drying steam passing from 
the high to the low-pressure cylinders, but it is economical to. 
superheat steam that has been dried by passage through a separa- 
tor. Figs. 156 and 157 show two such reheaters, in which the 
extent of heating-surface provided is at the rate of 1.25 square feet 
to the horse-power. The principal data are shown on the cuts. ,, 

Oil and Water Separators. The thermal efficiency of an 
engine is increased by removing water from the steam before 
they enter the high, or any succeeding cylinder, or a surface 
condenser. The thermal efficiency is also increased by removing 
the oil before it enters any condenser or boiler or any succeeding 
heating system. Water or oil interferes with the transfer of 
heat through condenser tubes. It is better to have a solid clean 
scale a quarter of an inch thick on a boiler tube than an amount 
of oil that could be placed there by rubbing the tube with a greasy 
rag. Water carrying oil should not be used as boiler feed-water 
and steam carrying oil should not be used in radiators or other 
heating systems. 


S I 










Fig. 5 represents a separator depending upon centrifugal 
force. Figs. 157 and 157a represent separators in which a ribbed 
baffle plate is placed at right angles to the current of steam. 
The ribbing prevents the oil or water from being brushed off by 
the deflected steam current. The water drains down and out 
away from all entraining currents.* The vacuum oil-separator 
is placed on the exhaust pipe of the engine and in addition to 
the baffle plates it has a circumferential lip to catch the oil that 

End Section 

Side Section 

FIG. 157. Vacuum Oil Sep- 
arator for Horizontal Pipes 
18 inches and larger. 

FIG. 157a. Separator. 

creeps along the interior surface of the exhaust pipe in the direc- 
tion of the steam current. 

If oil is to be removed from exhaust steam it should be 
done before condensing the steam. It is almost impossible 
and generally impractical to remove oil from condensed steam. 
The reason arises from the fact that the oil becomes oxidized on 
the surface. The, oily particles lose all tendency to coalesce 
and only break down when they are subjected to the high heat 
of the boiler. In the boiler, the oil unites with the metal of the 
boiler, forming oleates of iron which has the consistency and 
strength of graphite. 

* By enlarging the lower cylindrical body a separating receiver is formed 
which may be used between the various cylinders of multiple-expansion engines. 


THE heat in the steam exhausted from a simple or single engine 
is wasted, as far as the engine is concerned. In some cases this 
exhaust-steam is sent to a heater and its heat is saved, but the 
resulting economy may be considered as belonging to the engine 
plant rather than to the engine. If this steam is exhausted at 
considerable pressure above zero, more work might be obtained 
from it by further expansion. This would necessitate a second 
cylinder of much larger volume than the first to accommodate the 
proposed increased expansion of the steam incident to the lowering 
of its pressure before rejection. 

In no case is it economical in simple engines to lower the tem- 
perature by expansion below that which may be obtained with con- 
siderable ease by utilizing the temperature of natural substances 
around us. If water be expensive, then it is nojt economical to 
expand below the atmospheric pressure. If water is cheap, then 
we may expand the steam to a pressure not lower than three or 
four pounds per square inch above the pressure corresponding to 
the temperature of the water aS shown in steam-tables. The back 
pressure should be as close to the pressure corresponding to the 
temperature of the injection- water as possible. 

Advance in the design of economical engines had to wait on 
advance in knowledge of methods of manufacturing better mate- 
rials for use in boiler and engine construction. Lack of proper 
lubricants for high-pressure steam prevented its use for one or 
more decades. Failure to experiment restrained advance in all 
sciences till the middle of the last century. Watt advanced the 
theory that the water consumption of an engine per horse-power 
would decrease with increased ratios of expansion, the maximum 







expansion, however, being that which gave a final pressure equal 
to the back pressure. In 1840 a Cornish pump was accurately 
tested, and the water consumption was found to be 24 pounds at 
1.5 expansions and 16.5 pounds at 3.5 expansions. This was 
assumed to prove Watt's theory, and engine-builders gave all the 
expansion that their form of valve-gear would admit. Gradually 
it began to be felt that " expansion-engines were expensive engines." 
From 1840 to 1860 no authoritative experiments were made. At 
the latter date, Chief Engineer Isherwood, U. S. Navy, pub- 
lished his accurate and elaborate experiments on the U. S. Steam- 
ship Michigan, and the losses from initial condensation were re- 
vealed. A more intimate knowledge of the facts demonstrated 
that the Cornish engine experimented upon was working under 
unsuspected advantages, which accounted for its economy. The 
working end of its cylinder was not exposed to exhaust tempera- 
tures, the admission steam was superheated by excessive wire- 
drawing, and a live-steam jacket effectively reduced internal 

Rankine's analyses of Isherwood's results showed that the 
initial condensation depended upon the range of temperature to 
which the cylinder was subjected, and that by dividing this range 
among two or more cylinders economy would result. In a double- 
expansion engine, for instance, all the steam condensed in the first 
cylinder is re-evaporated, and so is capable of performing work 
in the next cylinder. The condensation in the second cylinder is 
due to its own range of temperature, which is far less than it would 
be in a simple engine having the same range of expansion as the 
compound engine. 

During the next forty years competition caused an interesting 
struggle in the production of record-breaking engines. Pressures 
rose with the advance in the art of boiler-making and the advent 
of mineral oils. Triple- and quadruple- expansion engines naturally 
followed the advance in pressures. High-speed engines showed a 
marked economy over slow-speed engines. It was claimed that the 
large clearance spaces of the former caused no loss, because the 
clearance space was filled by recompressed steam to the boiler- 
pressure. It has only been, in recent years that proper considera- 
tion has been given to the large losses that may be expected from 


high compression in engines having large ratios of expansion, large 
clearance surfaces, and early release. With small clearance, a 
slight degree of compression produces no considerable loss and is 
conducive to smooth running. 

The economy arising from enclosing the working-cylinder with 
not only non-conducting material, but also with heat-giving fluids, 
has been recognized. Hot waste gases in jackets caused unequal 
expansion and trouble in lubrication, so that the use of hot-air 
jackets soon ceased. The use of steam-jackets continues till this day, 
but with more general use of steam-superheaters they also will cease 
to be employed. In the past, however, not only the cylinder-barrel, 
but also the heads and even the piston have been jacketed. In 
tests, a gain in economy is shown by their use, because they are 
regulated properly; in practice, they cease to be economical (when 
their high cost of installation is considered) if not kept properly 
drained and the drainage returned at high temperature to the boiler. 

We have already seen that the maximum fluctuations of tem- 
perature take place only in the innermost layer of the cylinder 
walls. With a rapidly diminishing range of temperature these 
fluctuations take place in successive layers till the outermost one 
is reached. If this outside layer is kept at some constant tempera- 
ture by means of a jacket the less will be the range of fluctuation 
the higher the temperature of the steam-jacket, since the heat from 
the latter is flowing inwardly. As the steam-jacket practically 
only affects the cylinder steam that comes in contact with the 
cylinder walls, its value in the case of large cylinders is doubtful. 

Reduction of -clearance having been found to produce economy, 
clearance was reduced more and more till the shortening and 
lengthening of the piston-rod under stress became a subject of 
consideration ( !) . It is now recognized that reduction of clearance 
surface is more essential than reduction of clearance volume. To 
obtain reduction of clearance volume, the valves are placed in the 
cylinder -heads to give the shortest possible ports, and separate 
valves are used for admission and exhaust. 

High speeds of rotation having proved economical, Corliss 
speeded his engines up from 50 to 125 revolutions, and for a long 
time his engine was considered a high-speed engine. A higher 
speed with detachable valves is not practical, as the piston travels 


too far during the time that the dash-pot is operating the valve. 
The shaft-governed engines, running at speeds of over 200 revolu- 
tions per minute, have put Corliss engines with detachable valves 
in the slow-speed list. Small engines rotating 400 to 600 times 
a minute and large engines with a piston speed of 1000 feet per 
minute are in general use. 

We have seen that the second or low-pressure cylinder is larger 
than the first or high-pressure cylinder in a double-expansion or 
compound engine; in a triple the third or low-pressure cylinder is 
larger than the intermediate pressure cylinder, which is larger than 
the first or high-pressure cylinder. Ordinarily the low-pressure 
volume may be taken at 3 to 4 times the volume of the high in the 
compound system, and in the triple the relative volumes are fre- 
quently 7, 2f , 1. Rockwood designed a compound engine in which 
the ratio of the low- to high-pressure volumes was 6J to 1, or 
practically a triple with the intermediate cylinder left out. Other 
data were: Engine room gage, 172.2 pounds: superheat at throttle, 
46 degrees; cut-off, .278 stroke; clearance, 4.3 and 5%; revolu- 
tions, 80.25; vacuum, 27.7 inches; horse-power, 565.1; steam con- 
sumption, 11.22 pounds per I.H.P. A belief immediately arose 
that high ratios between the cylinder volumes of compound engines, 
combined with low clearance percentage, were essential to com- 
pound-engine economy. 

More recent compounds designed by Prof. Rockwood have given 
better results. A 16 X 40 X 48 Cross-Compound Cooper Corliss 
Engine, designed by him, consumed 11.22 pounds of water per 
I.H.P. including steam condensed in jackets and reheater coil. 
The principal data were: Steam pressure, engine room gauge, 172.2 
pounds; superheat at the throttle, 46 degrees; cut-off at .278 
stroke: clearance 4.3 and 5%; revolutions, 80.25; vacuum 27.7 
inches; horse-power, 565.1. 

The following tests, made in the last five years, will demon- 
strate that, whilst all of the above are contributing, none of them 
is an essential element to economy. A deficiency in one respect 
may be more than replaced by an economy in some other direction. 

On December 28, 1901, Jacobus on a Rice and Sargent cross- 
compound engine, cylinder ratio, 4 to 1; Corliss valve-gear, 121.5 
revolutions; steam-pressure, 151.3 pounds; pressure absolute in 
condenser, .85 pound; live steam in cylinder-head jackets of 


both cylinders and in a reheating-receiver at 627.4 I.H.P. found 
a water consumption of 12.10 pounds. The clearances were 4.7 
and 7%; expansions, 33; initial condensation, 22%. This engine, 
with ordinary cylinder ratios and ordinary clearances, gave a better 
economy than the Rockwood engine. It had a better vacuum and 
a larger ratio of expansion. 

Schroter with a Van den Kerchove poppet-valve compound 
engine, cylinder ratio, 2.97 to 1; 126 revolutions; steam- pressure, 
130 pounds; 27.6" vacuum; jackets on barrels and heads; no 
reheater; 32 expansions; 23.5% of initial condensation at 117 
I.H.P. found a dry saturated steam consumption of 11.98 pounds 
per horse-power. 

This result is slightly better than the preceding and on a smaller 

Whitham, Andrew, and Wells on a Westinghouse compound 
with twin L.P. cylinders; combined poppet and Corliss valve; cylin- 
der ratio, 5.8 to 1; 76 revolutions; clearances, 10.5% and 4%; 
steam-pressure, 185 pounds; 27.3 inches of vacuum; 29 expan- 
sions; 32% initial condensation; no jackets, no reheater at 5,400 
horse-power found a water consumption of 11.93 pounds. 

This result is a trifle better than the preceding. We are dealing 
with a large engine with a fairly large ratio of expansion, but, on 
the other hand, the revolutions are low, the clearance high. 

The only elements in common in the above engines are the high 
ratio of expansion and a high boiler-pressure. Jackets helped the 
small engine, and the large one did not need them. Reheaters are 
probably of little account unless they superheat from 30 to 100 
degrees as a minimum limit. Very high expansion may overcome 
initial condensation losses. 

Laying out Theoretical Indicator-cards for Compound Engines. 
The essential fact to keep in mind in laying out the theoretical 
indicator-cards from a compound engine according to the following 
method is: 

The weight or mass of steam entering the high-pressure cylin- 
der is the weight or mass that is rejected by the low-pressure 


From this naturally flows the following assumptions : 

The mass of steam in the high-pressure cylinder at cut-off = 
The mass of steam present in the high-pressure cylinder at 

exhaust- opening = 


The mass of steam in the low-pressure cylinder at the instant 

of cut-off = 

The mass of steam in the low-pressure cylinder at the instant 

of exhaust-opening. 

We shall assume that the exhaust opens at one end and closes 
at the oiner end of a stroke, and that there is no clearance in either 
cylinder and no steam is lost in the cycle. We are not discussing 
conditions that exist when the engine is first started up or when it 
is stopping. The engine is supposed to be rotating uniformly and 
taking regular charges; there is no initial condensation and, con- 
sequently, no evaporation. The weight of a mass of steam is known 
when its pressure and volume are known, and if steam is supposed 
to expand in accordance with the law PV = C the mass is desig- 
nated by its product PV. 

The student will obtain a better knowledge of the sequence of 
events in compound engines if he will draw the indicator-cards on 
cross-section paper from direct calculations, using simple round 
numbers, instead of substituting in derived formulas that become 
meaningless from cancellation. After obtaining a full comprehen- 
sion of the cycle of events in a compound engine, he may derive his 
own formulas. 

Definitions, Figs. 159, 160, 191. When the high- and low- 
pressure pistons are on one piston-rod, the engine is called a tandem 
compound. In a cross-compound engine the piston-rods of the high- 
and low-pressure pistons are parallel to each other, and their cranks 
are at right angles, or the piston-rods are at right angles to each 
other in a plane, which is perpendicular to the crank-shaft, and a 
single cr^nk is used. There may be more than one low-pressure 
cylinder. In triple- and quadruple-expansion engines the angle 
between successive cranks is not necessarily the same in amount, 
nor is there any compulsory sequence of cranks. In no case should 
the opening of the exhaust-valve of one cylinder occur before the 
steam cut-off of the next larger cylinder. As will be shown later, 
we shouid avoid transforming energy (that should be available for 
the production of work) into low-grade thermal energy that cannot 
be efficiently utilized. 

The maximum volume occupied by the steam admitted to a 
compound engine is the volume of the low-pressure cylinder 
minus the volume of the piston, of course and the minimum 


volume is the volume of the high-pressure cylinder up to its point 
of cut-off; therefore the total ratio of expansion is 

Volume of L.P. cyl. 
Volume of H.P. cyl. at cut-off" 

Varying the cut-off on the H.P. cyl. varies the amount of heat 
admitted, but varying the cut-off on the L.P. cyl. has no effect on 
the amount of heat rejected. The final pressure of expansion in 
the L.P. cyl. is governed by the H.P. cut-off and the relative sizes 
of the high- and low-pressure cylinders. 

The work done per stroke by any engine depends upon 

1. The mass of steam admitted. 

2. The total ratio of expansion. 

3. The back pressure at which the steam is finally rejected. 

Therefore the w r ork done per stroke is independent of the posi- 
tion of the point of cut-off in the L.P. cyl. For in any given 
engine the mass of steam admitted depends only on the high- 
pressure cut-off, and the other two quantities are independent of 
the L.P. valve. 

On the other hand, the percentage of the total power that is 
developed in each cylinder does depend upon the position of the 
L.P. cut-off. For it is evident that any cause that increases the 
back pressure on the piston of an engine decreases the power of 
that engine. If the cut-off on the L.P. cyl. is shortened, the pres- 
sure in the receiver is increased, since the same mass must be ad- 
mitted into the L.P. cyl. as before, and the volume in which it is 
to be contained has been decreased. As the receiver pressure is 
the back pressure on the H.P. piston, increasing the receiver pressure 
decreases the work done in the H.P. cyl. As the total power of 
both engines has not been altered, it follows that the work in the 
L.P. cyl. has been increased. The only use of the L.P. cut-off valve 
is, then, to regulate the percentage of the total power developed in 
each cylinder. 

Tandem Compound Engine Without a Receiver (Fig. 158). 
Draw the cards for a tandem compound engine, initial pressure, 
100 pounds abs.; back pressure, 3 pounds abs.; volume of H.P. 
cyl., 4 cubic feet; volume L.P. cyl., 16 cubic feet; cut-off in the 
H.P. cyl., 1/2 stroke. 


Since there is no receiver there can be no cut-off on the L.P. cyl. 
Practically there is always a small receiver, as the pipes leading 
to the L.P. cyl. from the H.P. cyl. always form part of the receiver. 
Theoretically, however, we may assume their volume as zero. 

Lay off on A B the pressure 100 pounds abs. 

Lay off on BC the volume of the L.P. cyl., 16 cubic feet. 

Lay off AD = 2 cubic feet = 1/2 the volume of the H.P. cyl. 

At steam cut-off in the H.P. cyl. P^i = 100x2 = 200, the con- 
stant mass passing through the system. 

At exhaust-opening in the H.P. cyl. P 2 V 2 = 2QO, but V 2 = vol- 
ume of H.P. cyl. = 4 cubic feet. .'. P 2 = 50 pounds, giving point E. 

The mass in the L.P. cyl. at the moment the exhaust-valve 
opens = 200. 

The volume of the L.P. cyl. = 16. .'. P 3 = ~ =12^ pounds, 

giving point F. 

At the end of the high-pressure stroke we have the H.P. cyl. 
full of steam at pressure of 50 pounds. The opening of the exhaust- 
valve admits this pressure on the L.P. piston without change, as 
the volume of the connecting pipe is zero. Therefore the admis- 
sion pressure in the L.P. cyl. is 50 pounds. 

Lay off J9G = 50, thus giving the point G. 

The pressure in the L.P. cyl. varies gradually from G to F, 
hence draw a smooth curve, FG. 

The back pressure of the H.P. cyl. is the same as the forward 
pressure in the L.P. cyl. 


Lay off HB = FC and draw curve EH. 

Lay off CI = 3 pounds and draw //; it will be the back pressure 
of the L.P. cyl. 

The curves GF and EH are not hyperbolic curves. Inter- 
mediate pressures may be found as follows : 

Suppose the pistons are at 1/4 stroke on the return. Then 3 
cubic feet at the exhausting end of the H.P. cyl. would be con- 
nected to 4 cubic feet on the steam side of the L.P. cyl. This 
mass in this case must = 200. 

Hence -y-=28 pounds would be the required pressure to be 

laid off, giving points K and L. 

The cards from the ends of each cylinder are similar. 

Cards from tandem compound steam- pumps are similar to the 

Ex. 110. The diameter of the H.P. cyl. = 1'; diameter L.P. cyl., 2'; 
stroke, 3'; initial pressure, 120 pounds absolute; back pressure, 3 
pounds absolute; 12 expansions. Draw the cards. Use relative in- 
stead of absolute volumes. 

Tandem Compound Engine with a Receiver (Fig. 159) . Initial 
pressure, 120 pounds abs.; volume of H.P. cyl. = 4 cubic feet; 
volume L.P. cyl. = 12 cubic feet; volume of the receiver = 6 cubic 
feet; cut-off in H.P. cyl. at 1/4 stroke; cut-off in L. P. cyl. at 3/4 
.stroke; back pressure, 3 pounds abs. 

Lay off A B = 120 pounds, 

Lay off BC = 12 cubic feet and 7)' = 4 cubic feet, 

Lay off AD = l cubic foot or 1/4 the vol. of H.P. cyl., 
then the constant mass = 120 X 1 = 120. 

The volume occupied by the steam in the H.P. cyl. as the 
exhaust-valve is about to open = 4 cu. ft. ; therefore the pressure 

= -j- = 30, giving the ordinate of point E. DE is an hyperbola. 

When the exhaust-valve is about to open in the L.P. cyl. the 
mass present = 120 and the vol. = 12 cubic feet, therefore the 

pressure = -^- = 10 pounds, or the ordinate of point F. 

At the instant of cut-off in the L.P. cyl. the mass present 
= 120, and it will be the mass rejected, since there is no clearance 




The pressure at cut-off or G will be <r- = 13J pounds, because 

the vol. of the L.P. cyl. at cut-off = f Xl2= 9 cu. ft. 
Draw GF; it will be an hyperbola. 


FIG. 159. 

We assume that the pressures in the L.P. cyl. at the instant 
before its cut-off, at its cut-off, and the instant after its cut-off are 
identical. The instant before cut-off in the L.P. cyl. the exhaust 
from the H.P. cyl. was in communication with the receiver, and the 
latter was in communication with the L.P. cyl. The pressures in all 
three must have been identical and equal to that in the L.P. cyl. at 
its cut-off. 

As the L.P. piston is at 3/4 stroke, the H.P. piston must be at 
3/4 of its stroke, so that the volume of the H.P. cyl. on the exhaust 
end must be (1 f)4 = l cu. ft. This is open to the receiver with 
a volume of 6 cu. ft. The back pressure at H on the H.P. piston 
= 13J, and the mass must be 7X13J. 

Since the cut-off valve on the L.P. cyl. is closed, further move- 
ment of the H.P. piston must compress this mass into the volume of 

the receiver alone. The rise in pressure must be 
pounds, or the ordinate of /. Draw HI. 


= 15.55 


The back pressure on one side of the H.P. piston is 15.55 pounds, 
and the forward terminal expansion pressure on the other side of 
this piston is 30 pounds. The next instant, the H.P. exhaust- 
valve opens, and these masses with these two pressures form one 
mass. A common pressure will be attained immediately. The 
masses joined are 30x4 and 6x15.5, or 120+93.3 = 213.3. As the 
volume of the combined mass is 4 +6 = 10, the common pressure is 
21.33 pounds, which is the value of the ordinates of K and J. 

Join K and G, it will be the admission curve of the L.P. cyl. 

Join / and H, it will be the corresponding back- pressure line of 
the H.P. piston. 

Lay off CM = 3 pounds and draw MN, it will be the back- 
pressure line of the L.P. piston. 

Ex. 111. Data same as in preceding example, except that there is 
a receiver whose volume is twice that of the H.P. cylinder. 

Cross-compound Engines. In cross-compound engines the 
cranks of the high- and low-pressure engines are at right angles 
to one another. There must be a receiver between the two engines, 
as the high-pressure exhaust occurs when the low-pressure piston 
is at half-stroke. In addition to the work in the preceding case 
we have to find the positions of one piston when the other is at 
critical points, such as cut-off, exhaust-opening, etc. It is essential 
to decide on the character of rotation, whether clockwise or the 
reverse, and also fix on the crank that is leading. Much help will 
be found in diagrammatic sketches for each critical position, show- 
ing piston positions and the volumes that are in communication 
at such critical positions (Figs. 159 and 160). 

Cross-compound Engines. Draw the cards from a cross-com- 
pound engine, L.P. crank leading; rotation clockwise; initial pres- 
sure H.P. cyl., 180 pounds abs.; number of expansions, 30; ratio 
of cylinder volumes, 6 to 1 ; volume of H.P. cyl., 5 cu. ft. ; volume 
of receiver, 10 cu. ft.; cut-off on L.P. cyl., 1/3 stroke; back pressure 
in L.P. cyl., 1 pound abs. 

Volume of L.P. cyl. = 6 X 5 = 30. 

Volume of H.P. cyl. at cut-off = == 1 cu. ft. 


Ratio of expansion in H.P. cyl. =-=- = 5. 



The volume of L.P. cyl. at cut-off = -^- = 10 cu. ft. 

The constant mass passing through the cycle or PiV l = 180 X 1 



The pressure at cut-off in the L.P. cyl. must equal 

lcu.ft.: their 

pounds = H. 

Lay off AB= 180 pounds; AC=30 cu. ft.; 

180 180 

EF = = 36 pounds and CV2 = = 6 pounds, and the ordinate* 

o oU 

at H is laid off for 18 pounds. Join H and G by an hyperbola. 

Diagrammatic Sketch at 
Low Pressure Cut-Off 

FIG. 160. 

Check. The pressure at H is three times that at G. 

We must now find the volume of the H.P. cyl. that is exhaust- 
ing into the receiver at an instant before L.P. cut-off takes place. 
If the length of the connecting-rod is to be considered, graphic 
construction will be found easier than by analysis. For simplicity 
we shall assume infinite rods and obtain our results analytically. 

Draw the circular diagram (Fig. 160) in accordance with the 
data. It is evident that ce represents the desired volume if ef 
represents the volume cf the H.P. cyl. 

ed = ^, od= 2 -^=- 



da=oc=efV (1/2) 2 -(l/6) 2 = . 47 ef, 

The required volume is therefore .03 X5 cu. ft. = .15 cu. ft. 

Hence the pressure in .the L.P. cyl. at cut-off, in the receiver 
and in the H.P. cyl. when the piston of the latter has .15 cu. ft. of 
exhaust-steam behind it is 18 pounds. 

Lay off AJ = .l5 cu. ft. and lay off an ordinate = 18 pounds, 
thus finding point I. 

As the H.P. piston moves to the end of its stroke all the steam 
in the H.P. cylinder on the exhaust side and in the receiver will be 
compressed into the receiver volume alone, as the L.P. valve has 
cut-off steam admission. The pressure in the receiver whose 
volume is 10 cu. ft. when the H.P. piston reaches the end of its 

stroke will be ~Tn~ ~~ = 18.27 pounds or the ordinate at K. 

There is assumed to be no exhaust lap on the high-pressure valve. 

The next instant the exhaust from the other side of the H.P. 
piston is opened to the receiver and the two masses must come to 
a common pressure. The sum of the two masses is proportional 
to 5X36+18.27X10 = 362.7, and the common volume is 5+10 cu. 
ft., or the sum of the volumes of the H.P. cyl. and receiver. 

The pressure at L is then 362.7^15 = 24.2 pounds. On this 
diagram there is no corresponding point on the L.P. diagram, as 
its valve is closed. 

The pressure having dropped from F to L at the opening of the 
exhaust-valve, the H.P. piston now starts on its return-stroke, 
sweeping steam into the receiver. This continues till the H.P. 
piston reaches half-stroke. No steam is taken from the receiver 
during that interval, as cut-off on the L.P. cyl. took place before 

A mass of 362.7 is forced into a volume of 2+10 = 12.5, and 

362 7 
the resulting pressure will be ^ - =29 pounds, which is not only 

the back pressure on the H.P. piston at the middle of its stroke at 
M, but is also the initial pressure on the L.P. piston at N. Join 



L and M , M and /, N and #. These curves are not hyperbolic 
curves and may be sketched in. Intermediate points can be found 
by calculating volumes and pressures. 

Draw the back-pressure line for the L.P. cyl. at 1 pound above 
the absolute zero line. 

Ex. 112. Diameter of the H.P. cyl. is 20"; stroke, 40"; cut-off 
H.P. ryl., 1/4 stroke; total expansions =16; initial pressure, 160 abs.; 
back pressure, 3 pounds abs.; volume of the receiver, 3/2 that of 
H.P. cyl.; cut-off in L.P. cyl., 3/8 stroke. (Assume volume of H.P. 

Cross-compound with L.P. Cut-off after Half-stroke (Fig. 161) 

FIG. 161. 

If the cut-off on the L.P. cyl. has not taken place before half- 
stroke, it is evident that, when the high-pressure exhaust opens, 
the common volume will be the volume of the H.P. cyl., the re- 
ceiver, and half the volume of the L.P. cyl. The result is a hump 
in the middle of the L.P. card. This indicates a loss of efficiency, 
for whenever high-pressure steam is allowed to enter a space filled 
with steam of a lower pressure, there is a transformation of energy 
into heat that could have been converted into work. Keeping in 
mind that the object of a steam-engine or steam-turbine is the 
transformation of heat into work, any reversal of that process is 
certain to produce a loss in the number of foot-pounds of work. 


In Fig. 160 the drop FL, known as receiver drop, is not economical 
when excessive, and hence for best results thermodynamically LE 
should be made to equal FE by cutting off shorter in the L.P. cyl. 
If this results in making the L.P. card larger than the H.P. card, 
the engines will develop different horse-powers, which will produce 
;non-uniform rotation. 

Take the same data as in the preceding problem and let the 
-cut-off on the L.P. cyl. be at 2/3 stroke. 

The points B, D, F, and G will be in the same position as before. 

At cut-off in the L.P. cyl. the volume is 20 cu. ft. and the mass 
is 180X1 = 180, therefore the pressure = V<f = 9 pounds, giving # 
.and h. 

Check. Expanding 20 cu. ft. at 9 pounds to 30 cu. ft. the pres- 
sure becomes 6, as found. 

Drawing the circular diagram and laying off crank positions in 
^accordance with the data we find 

df=& od = 4, da = oc = Al ef. .'. c/ = .97 ef. 
o o 

The volume of the H.P. cyl. exhausting into the receiver at this 
-cut-off of the L.P. cyl. is then .97x5 cu. ft. =4.85 cu. ft. 

The mass in the H.P. cyl. and the receiver at the instant of 
L.P. cut-off is then 9 X (4.85 +10) = 133.65. 

Rotate the crank-shaft till the L.P. is at the end of its stroke. 
The H.P. piston compresses the above mass into the volume of the 
.receiver and half the volume of the H.P. cyl. The pressure there- 
fore rises to -^ ^r =10.7 pounds, which is therefore the value of 

&2 ~T 1U 

the ordinate, 7, at the middle of the return-stroke of the H.P. cyl., 
and of /, which is the initial pressure in the L.P. cyl. 

Rotate the crank till the H.P. piston reaches the end of its 
stroke. During this period the volume of the H.P. cyl. exhaust is 
rapidly diminishing, but the volume of the L.P. cyl. is increasing 
more rapidly, so that the pressure in the receiver is falling till 

9 X 14 85 

half-stroke. At that time the pressure is in ' =5.34 pounds, 

1U ~r 1) 

which will be the value of the ordinates K at the middle of the 
L.P. stroke and of L at the end of the H.P. stroke. Join 7 and L, 


J and K. These curves represent the same change of pressure, 
being the back pressure on the H.P. piston and the forward pressure 
on the L.P. piston. 

An infinitesimal movement of the crank produces the next 
event, viz., opens the exhaust of the H.P. cyl. into the receiver and 
the L.P. cyl. whose steam-valve is wide open. 

The sum of the two masses united is 36x5+5.34 (10+15) = 
313.65, and the common volume is 5+10+15 = 30 cu. ft., hence 

313 65 
the common pressure is ^' -10.45, which is therefore the 

ordinate at M and N. Join N and h, h and 7, K and M, M and H. 
Draw the back-pressure line on the L.P. diagram. 

Ex. 113. Data as in preceding example, but assume cut-off at 5/8 

Ex. 114. Alter the data of the preceding example to obtain equal 
horse-power in each cylinder. 

Ex. 115. Alter the data to obtain the same range of temperature 
in each cylinder. 

Ex. 116. Alter the data in the preceding example, giving clearance 
and points of exhaust opening and closing in each cylinder, but use an 
infinite connecting-rod. 

To Find the Sizes of Cylinders for a Compound Engine. The 
power of any engine per stroke is determined by the mass of steam 
admitted and its ratio of expansion. All the power of a compound 
or other multiple-expansion engine could be developed in its low- 
pressure cylinder, disregarding for a moment the necessary strength 
of parts and condensation, since, if we admitted into that cylinder 
the same mass as was. admitted into the high-pressure cylinder, 
we may expand that mass in this cylinder the same number of 
times as in the multiple-expansion engine against the same back 

Find the diameters of the high- and low-pressure cylinders of a 
cross-compound engine, gage pressure at the boiler, 150 pounds; 
total ratio of expansion, 16; ratio of low-pressure cylinder area to 
that of the high, 4 to 1; assumed diagram factor derived from 
engines of about the same power and of the same general design, 
83%; back pressure in the condenser is 1 pound absolute; revo- 
lutions, 120; horse-power, 1000, stroke, 42". 


A B Boiler Pressure 

Low Pressure Head End 

Pressure in Coudenser 
FlG. 162. 


Expected mean effective pressure 

Yg - 1 F .83 = 31 .45 pounds. 

L J 

For cards, see Fig. 111. 

The diameter of the high-pressure cylinder is 20". Cut-off in 
the high-pressure cylinder is at a little less than 1/4 stroke. 

Assume clearance in high-pressure cylinder is 5%, and in the 
low is 7%, and that the volume of the receiver equals the volume 
of the L.P. cylinder. 

To Combine Indicator-cards of a Compound Engine. "The 
'Combined Diagram ' is a hypothetical figure, which in its essential 
features represents an indicator-diagram which would be obtained 
if the whole process of admission, expansion, and exhaust occurred 
in one cylinder, viz., the low-pressure cylinder. It is a diagram 
from which the pressure of the steam at any point in the stroke 
of either cylinder, and the volume of that steam, can be measured 
from one diagram in the same manner that it can be measured in 
the case of a single-cylinder engine from the actual indicator- 

"The general method of laying out a combined diagram is 
shown in the appended cuts, Figs. 163 and 165, the first of winch 
refers to a Corliss compound engine (receiver engine), in which the 
ratio of volumes of the two cylinders is as 3.72 to 1, and the clear- 
ance of the high-pressure cylinder is 4 per cent, and of the low- 
pressure cylinder is 4.8 per cent; and the second to a Westing- 
house compound engine (Woolf engine), in which the ratio of the 
volumes is as 2.72 to 1, and the clearance 33 per cent and 9 per 
cent respectively." f 

In the single cards the high- and low-pressure diagrams are of 
approximately the same length. Since there is a radical difference 
in the volumes represented by the lengths of the cards, there must 
be a radical difference in their scale of volumes. Similarly the 
scale of pressure in each card is different. In the combined dia- 
gram there is only one scale of volumes and one scale of pressure. 

t Standard Engine Tests. 




p. j 00 - *<-C.04 


100 . 

H. P. CYL. 

-1 13(7 












To Draw the Combined Diagram. Draw any line to represent 
the clearance line as in Fig. 163. Perpendicular to it, at any given 
point, erect a line, called the zero line, whose assumed length will 
represent the volume of the low-pressure cylinder plus the clear- 
ance. Lay off this clearance. Divide the remainder into any 
number of parts and divide the atmospheric line of the low-pressure 
diagram (limited by the end ordinates of the diagram) into the 
same number of parts. Draw ordinates through these points and 
lay off in the combined diagram (in accordance to its assumed 

H. P. CYL. 


- 80 

- 60 

- 20 

L. P. CYL. 



- 10 

- 5 

Standard Engine Tets 

FIG. 164. 

scale of pressures) the pressures as determined by the length of the 
corresponding ordinates in the single card. 

To the same scale of volumes lay off the volume of the high- 
pressure cylinder and its clearance from the clearance line or line 
of zero volume. As before, after laying off its clearance, divide 
the remainder into any number of parts and divide the length of 
the high-pressure card into the same number of parts. Convert 
the ordinates of the high-pressure card into pressures and lay off 
these pressures (to the chosen scale for the low-pressure card) in 
the combined diagram. 

Practical Diagrams. In the formation of the theoretical dia- 
grams just described many assumptions were made that are 
impossible of attainment in practice. There is 


1. The loss due to drop of pressure between the steam- 
boiler and the piston. This includes loss in the pipe, bends, 
valves, and separators. It varies from 5% of the boiler- 
pressure upwards, depending upon conditions. 

2. The steam- valve opens the port gradually, and there 
must be a considerable difference in pressure between the steam 
in the chest and that inside the cylinder to generate the high 
velocity demanded when the port is nearly closed. The corner 
at cut-off is rounded off. 

3. The loss due to drop when the H.P. exhaust- valve opens. 

4. The corresponding losses of pressure in the steam entering 
the L.P. cylinder or cylinders. 

5. The reduction of the mass of steam in the cycle. The 
steam from the H.P. cylinder should pass through a separator 
and the water separated out should be returned to the boiler, 
and hence passes out of the cycle. 

6. A loss due to deficient vacuum. One or two inches of 
vacuum make considerable difference in the total pressure on 
a L.P. piston. This amount is frequently lost through allowing 
avoidable air-leaks, greasy tubes, defective air-pump, etc. The 
loss of one inch of vacuum on an 80-inch piston would cause 
the continuous loss of over a ton of force. 

7. The exhaust opens gradually instead of instantaneously 
at the end of the stroke. This causes a small loss. 

8. Clearance space and clearance surface cause much loss. 
Ratio of Expansion. The rounding of the corners necessitates 

a definition of tne ratio of expansion in a compound engine. 

"In a multiple- expansion engine it is determined by dividing 
the net volume of the steam indicated by the L.P. diagram at the 
end of the expansion line, assumed to be continued to the end of 
the stroke, by the net volume of the steam at the maximum pres- 
sure during admission to the high-pressure cylinder. 

"For a compound engine, referring to the combined diagram 
(Fig. 166), the ratio of expansion is the distance CD divided by 
the distance AB, in which E and F are points on the compression 
and expansion lines respectively of the high-pressure diagram, the 
latter being near the point of cut-off, and H and G points on the 
compression and expansion lines of the low-pressure diagram, the 

Atmos. Line* 




FIG. 165 




latter being near the point of release, and the curves EA, FB, HC, 
and GD being hyperbolic. If it is desired to determine the ratio 
without laying out the combined diagram, it can be done by draw- 
ing on the original diagrams the hyperbolic curves referred to 
above and multiplying the ratio of volumes of the cylinders, 

Maximum pressure 
during admission. 

Ratio of Expansion 

Com.on Eng. Tetti 

FIG. 166. 

first by the ratio of the length of the high-pressure diagram to the 
distance AB, and then by the ratio of the distance CD to the 
length of the low-pressure diagram. 

" Diagram Factor. The Committee's definition of the ' Diagram 
Factor ' was given in the case of simple engines. In Fig. 167 the 
diagram factor is the proportion borne by the area of the two 

determined for the high-pressure diagram in the 
game way as 3 in Fig. 50. 

Bo.ler Pressure 

^ Zero Line of Pressure 

Line of Pressure 
in Condenser 

FIG. 167. 



combined diagrams to the area CNHSK. In Fig. 167 the distance 
CN for the high-pressure cylinder is found in the same manner as 
in the case of the simple engine. . . . The mean effective pressure 
of the ideal diagram can readily be obtained from the formula 


^(1 4- hyp. log ft) -p, 

where P is the absolute pressure of the steam in the boiler, R the 


ratio '-^j-r, and p the pressure of the atmosphere or in the con- 


Diagram factors for compound engines: 

High-speed, short-stroke, unjacketed 60 to 80% 

Slower rotational speeds 70 " 85 

" jacketed 85 " 90 

Corliss 85 " 90 

Triple-expansion 60 ' ' 70 

(See Vols. XXIV and XXV, Trans. A. S. M. E.) 

Jacketing, reheaters, and superheaters modify the diagram 

factor considerably. 

In marine engines these factors are much lower. Bauer and 

Robertson, "Marine Engines and Boilers," give: 

Expansion in a single-cylinder : 

Large slow-speed engines 70 to 75% 

Small high-speed engines 65 " 70 

Expansion in two-cylinder or compound engines: 

Large engines up to 100 revolutions per minute 60 " 67 

Small engines with a higher number of revolutions . . 55 " 60 

Triple-expansion in three cylinders : 

War-vessels with a high number of revolutions 53 ' ' 54 

Mercantile vessels up to 100 revolutions per minute. . 56 " 61 

In multiple-expansion engines the weight of authority is in 
favor of expanding in all cylinders but the low-pressure to a pressure 
equal to the back-pressure, i.e., there will be no drop in the re- 

f Standard Engine Tests. 


ceiver. The explanation of the difference lies in initial condensa- 

"The reason why condensation effects this change is not that 
some steam is condensed in the cylinder each stroke, but that the 
condensation is not in proportion to the steam admitted and the 
work done, but is nearly a fixed amount per stroke for a given set 
of conditions. If more steam is admitted, the amount condensed is 
practically the same, but the proportion which is condensed becomes 
less; and for this reason it is economical to throw away some work 
by free expansion at each end of each stroke, for in so doing the 
total amount of work done per stroke is increased and the con- 
densation, which is a total loss, becomes smaller in proportion." * 
This reasoning is applicable to expansion in the low-pressure cylin- 
der, where condensation should be reduced to a minimum. 

Terminal drop or free expansion tends to heat the steam. In 
other words, a loss of work is converted into a gain in heat. The 
highest economy is opposed to such a transfer. The required heat 
should be obtained from reheating coils placed in the receiver. 
Further, the heat so obtained should be applied to superheating 
dry steam, all water having been previously removed and sent to 
the boiler with the feed-water. 

Ex. 117. Initial pressure 120 pounds absolute, clearance H.P. 
cyl. 2J%; cut-off J stroke; clearance L.P. cyl. 5%; diam. of 
L.P. cyl. is twice that of the H.P. cyl. Vacuum 24"; piston speed 
800 feet per min. Find the following quantities for a horizontal, 
cross-compound condensing engine of 2000 horse-power capacity: 

(1) Give dimensions of each cylinder. 

(2) Number of revolutions per minute. 

(3) Size of pulleys on engine and shaft. { 

(4) Initial pressure in each cylinder. 

(5) Terminal pressure in each cylinder. 

(6) Mean effective pressure in each cylinder. 

(7) Give the point of cut-off for economy. 

(8) Draw cards from each cylinder for economy. 

(9) Draw some cards with admission late ^ of the stroke. f 

* Trans. A. S. M. E., Vol. XXI, p. 1006. 
t See Power, page 622, 1907. 
t See page 386. 


THE work done by some machines is dependent on the irregu- 
larity of motion of some one of their parts. In a punching-machine, 
for instance, the rather constant and small pull of a belt is utilized 
to store up energy in a fly-wheel by increasing its revolutions. At 
the instant the punch commences to penetrate a plate, the demand 
for the pressure and work of detrusion is supplied instantly by the 
fly-wheel. The consequent loss of speed is made up in the time 
elapsing between the commencement of the rise and the com- 
mencement of the penetration of the punch. 

The degree of uniformity of rotation exacted of steam-engines 
varies with their use. In the case of engines for certain electrical 
purposes and for cotton-mills, for instance, the closest possible 
approach to perfect uniformity is desirable. 

Uniformity of rotation may be considered under two heads: 

1. Uniformity in the number of strokes per minute. 

2. " of rotation during the stroke. 

It is evident that any governor controlling the pressure or 
volume of steam entering an engine has no control of the speed 
between the point of cut-off and the end of the stroke. The speed 
of an engine having badly set valves or a poorly designed governor 
may be incessantly changing, one stroke being made too fast and 
the next too slow, although the revolutions in a minute may be the 
required number. If the work done during one stroke is the same 
in amount as that done during the following one, then the amount 
of energy received (measured quite approximately by the weight 
of steam admitted) should be identical on each stroke. Uniformity 
of rotation requires the same mean effective pressure on both 



strokes of the piston for a fixed position of the governing mechan- 
ism. The valves of an engine are not properly set until indicator- 
cards simultaneously taken from each end of the steam cylinder 
on the same revolution show the same mean effective pressure* 
In vertical engines this pressure must be corrected for the weight 
of the reciprocating parts. 

No practical means of anticipating variation of speed have 
ever been devised. Hence momentary variation of speed has been 
used to actuate mechanism, that governs the incoming energy, to 
give practical uniformity of rotation within the limits set by tha 

The principal methods of governing steam-engines are : 

1. Throttling. By regulating the pressure, but not the vol- 
ume of the steam admitted to the engine. 

2. Variable Cut-off. By regulating the volume, but not the 
pressure of the steam admitted. 

3. Fly-wheels. By storing up surplus energy in such form 
that on demand it will be returned. 

FIG. 168. 

Throttling (Fig. 168). If a circular disc be pivoted at any 
cross-section of a pipe, a more or less efficient and easy means of 
regulating the weight of steam that passes will be secured. A. 
disc of this character arranged in a practical manner is called a 
butterfly valve or throttle. As the valve approaches its closing 
position the difference in the pressure of the steam on the two 
sides of the valve will be a considerable quantity. This difference 
of pressure is necessary to produce the high velocity of the steam 
in the contracted area of the pipe, and to overcome losses pro- 
duced by friction and eddy-making. By placing a valve of this 
character close to the engine and moving it by some kind of auto- 


ma tic mechanism we obtain a means of governing the speed of 
the engine under changing load. 

Variable Cut-off. We have already seen that, by changing the 
throw of a valve, the volume of steam admitted may be altered 
to comply with variations, either in the load or the boiler-pressure. 
The different mechanisms for doing this automatically will be dis- 
cussed in this chapter. 

Fly-wheels. We shall find that the fly-wheel has very little 
influence on the constancy of the number of revolutions made in 
a minute. We must distinguish carefully between a rate and an 
actual quantity. When an engine has no governor, as in marine 
engines, if the load decreases (as it does when the ship pitches and 
the propeller rises in the water), there is an immediate increase in 
the velocity of rotation. Whilst a fly-wheel might absorb some 
of this energy, yet the amount absorbed would be trivial compared 
to the surplus energy constantly coming into the engines. In 
marine engines, if the increase of speed becomes dangerous the 
supply of energy is controlled by regulating the throttle by hand. 
In land engines the revolutions in a minute are controlled either 
by a throttling-governor or by a variable expansion-governor. 
The duty of the fly-wheel is then almost li mi ted to securing uni- 
formity of rotation during a revolution. 

Fundamental Equations. We must distinguish carefully be- 
tween tangential and centripetal or centrifugal forces in revolving 
masses. If a mass is revolving uniformly it can neither exert any 
tangential force nor can any tangential force act on it unless such 
force is balanced by an equal and opposite force. Any unbalanced 
force means an accelerated or non-uniform speed. If there be any 
change of speed there is, on the contrary, a tangential acceleration 
that may be utilized in the production of force. On the other 
hand, in cases of uniform motion there is developed a force along 
the radius, called centrifugal force, that is utilized in nearly all 
forms of steam-engine governors. As we cannot have a pull on a 
string without the presence of two equal and opposite forces, so 
centrifugal stress (causing tension on the arms of the fly-wheel) 
requires two equal and opposite forces. A pull to the center is 
necessary to draw the particles from the straight line, that they 
tend to follow, into the curve of the circular path. The particles 



exert an outward pull, and the arm exerts a stress in the opposite 
direction. Centrifugal force then is not a force acting along a 
tangent, but is the outward radial pull exerted by the particles, 
and produces its equal and opposite centripetal force acting 
inwardly. The EQUALITY of centripetal and centrifugal forces only 
exists when there is NO motion along the radius. In the shaft- 
governor, for instance, the weight moves outwardly till the tension 
on the spring representing centripetal force overcomes the cen- 
trifugal force and tends to cause motion inwardly of the weight. 

This demonstration is limited to the centrifugal force exerted 
by a particle revolving at uniform speed in a circle. 

Let be the center, R the radius, and ds 
the length of arc described in the time dt. Q 

If dd is the length of the arc at unit radius, 

Rdd ds 

j~ = -r = F, the uniform speed in a circle. 

The acceleration along the radius may be 
taken as the difference between two successive 
velocities along two consecutive radii. If in 
each sec' or the origin is taken at the end of the 
left radius, we may take the velocity along the 
light radius as the acceleration. For example, the veloc'ty along 
the radius OA is zero and the velocity along radius OC (found by 

d 2 R 
drawing a tangent at A to intersect OC) is CB or -, so marked 


as acceleration is a second differential. 

dsdO = d 2 R, since the triangles A C and CAB are similar. 


ds ds 

d 2 R, 

ds 2 d 2 R 


Rdt 2 ~ dt 2 ~ 

V 2 

~p = a R = acceleration alone: the radius. 


The force to produce an acceleration is equal to the product of 
the mass and the acceleration. Therefore 



A body weighing W pounds revolving at a speed of V feet per 
second at R feet radius (gyration) will cause a centripetal force 
,of F pounds per second. 

Ex. 117. The student should show why F is elementary; is pounds 
and not feet. 

Kinetic Energy. If a body weighing W pounds is raise i h 
feet, Wh foot-pounds of work are required. If this body is allowed 
to fall, the instant that it has passed over h feet Wh foot-pounds 
of work are stored in it. This energy of motion may also be ex- 
pressed in terms of the velocity that it possesses at the instant of 

V 2 
passing the point h feet below the starting-point. As h = -~- we 

WV 2 
have Wh=f^ . It is immaterial how a particle acquires the 


velocity V whether by falling or by the action of forces other than 
gravity. 'Hence if a particle in a fly-wheel is moving with a velocity 

WV 2 

of V feet per second, its kinetic energy is also ~ . 

WV 2 


It is essentially a compound quantity and is reducible to foot-pounds. 
Note carefully that any equation containing g (gravity) must have 
aU linear dimensions in feet, and all measurements of time must be 
in seconds unless proper constants are used to effect the desired 

Fly-ball Governor with and without Central Rotating Weight. 
Let AC be a rotating spindle carrying revolving balls B 
and BI and a heavy rotating weight of L pounds at C. Let the 
balls B, BI, weighing w pounds apiece, be attached to links in such 
manner that if C move vertically upward to C', the linkage will 
now take the position AB'C'B'i, shown in dotted lines. 

By the action of two equal forces, P, P ly exerted vertically at 
B and BI, let the linkage attain the dotted position. Either analyt- 

yy y ~ 

Ex. 118. Separate ~ into its component parts, and show that 



ically or graphically it will be found that if the balls B, B\ move 
through a small vertical height (dh], the heavy weight L will move 
a greater height, k(dh) . The work put in must equal the work done, 

.'. 2P(dh) = 2wdh +Lk(dh) . 



If the upper and lower arms are of the same length, k = 2. 
horizontal work will evidently be zero. 


L Pounds 

FIG. 170. 

Let the mechanism shown be that of a loadsd high-speed 
governor. Let centrifugal force F, acting along E'B f and E'Bi, 
keep the balls in the dotted position shown. Then, for the reasons 
above given, we have, taking moments around A, Pr=Fh, or 

This equation contains apparently six variables, five of which 
must be given to determine the remaining one. Suppose Z/ = 0, 

This gives the equation of the simple pendulum governor, 

yjV2 Y 2 T 2 

wr = h or = -r . 

gr g h 

In this equation the weight of the balls B and BI has entirely 
disappeared. Hence, theoretically, if there were no such effects 
as friction and inertia, and if certain very necessary parts had no 
weight, we could use balls of any weight whatever. Practically, 
as there is considerable friction in valve-stem packing, as heavy 
parts must be given motion quickly and as connecting links have 
necessary weight, the balls are generally made of considerable 
weight, depending on the size of the governor and on the condi- 
tions under which it is to act. 

In the above equation V is the velocity of the governor-balls 
in feet per SECOND; a more convenient equation for use in practice 
is one in terms of the number of revolutions that the governor- 
balls make per MINUTE =N. .'. V 2 = 







per Minute. 

per Minute. 










.876 . 

























An examination of the table and the figure shows that the 
heights of the cones become very small and impractical at speeds 
much exceeding 80 revolutions per minute. This becomes more 
apparent when we remember that it is the difference in the height 
of the cones that affords the motion of the mechanism for closing 
the throttle. Thus, in changing from 80 to 85 revolutions a 



minute, the difference in height of the cones is 1 inch ; at 200 revo- 
lutions the cone height is only .88 inch, and the speed would have 
to reach 300 revolutions per minute to change the height .88 
.39 = .48 inch. These dimensions are entirely too small for any 
practical mechanism. 

Referring to our fundamental formula, page 331, let k = 2. 
This will be the case when the upper and lower arms are of equal 
length. Then 





- = N*h. 

.'. 2936(1 +-)=N 2 h. 
\ / 

The relation between this formula and that for the simple pendu- 
lum is at once apparent. For simplicity, let the heavy central 

FIG. 171. 

weight be nine times that of one of the balls, then the height of 
the cone will be ten times that of the simple pendulum. This 
makes this form of governor available in cases of governor revolu- 
tions ranging from 200 to 240 revolutions or higher. 

Sensitiveness. If N\ is the highest and N 2 the lowest number 
of revolutions permitted by the governor, the sensitiveness is 


N N 
expressed by ^ + ^ = the range of speed divided by the mean 


speed. The smaller this fraction the more sensitive the governor, 
If Ni~N 2 becomes 0, the governor ceases to act properly from 
su persensi ti veness. 

For convenience let 2936 = Ci 2 and (l +-j =C 2 2 . 
Then for the loaded governor 1 JJ = JVi, 



i i 

I , 

We would obtain the same expression for the sensitiveness of an 
unloaded governor. It is therefore evident that their sensitive- 
ness is identical if their cone heights h 2 and hi are identical. The 
greater inertia of the loaded governor makes it the more sensitive, 
as it overcomes friction the more readily. 

Practical Forms of Fly-ball Governors. The pendulum- 
governor takes many shapes and different qualities are possessed 
in varying amounts by the different forms. Fig. 172 illustrates 
a Proell governor. It consists of a hollow vessel, G, fixed to 
the rotating shaft, R, and possessing two projecting ears, E, which 
in turn provide pivots, D, for the bent lever-arms L. The rotation 



of the shaft is conveyed to the balls through G, E, and L. As 
the balls, B, B' , fly out, the inner ends of the bent lever L press 
downward on a plate resting on the spring S. The motion of the 
balls results in the motion of the sleeve, C7, whose motion in turn is 
used to actuate a lever or other mechanism. 

It is evident that the centrifugal force of the balls increases, 
as they fly out, on account of the increasing radius from the spindle 


FIG. 172. 

R, as well as from their increased revolutions. The compressive 
resistance of the spring S opposes the outward motion of the 

Three cases may arise : 

1. The compressive resistance of the spring may increase in 
exactly the same ratio that the centrifugal force exerted by the 
balls increases. 

2. It may increase less rapidly than the centrifugal force. 

3. It may increase more rapidly than the centrifugal force. 
In the first case it is evident that the balls will maintain their 

lowest position until the spindle R attains some fixed speed. The 


slightest increase over that speed sends the balls to their extreme 
outward position, which shuts off steam entirely. The consequent 
decrease in speed is followed by the return of the balls to the 
lowest position and the steam-valve is opened wide. This con- 
tinual fluctuation is called hunting. The governor is said to be in 
neutral equilibrium, unstable, astatic, or isochronous. Theoret- 
ically, the governor has only one speed (hence isochronal) for all 
positions of the balls; the equilibrium is not stable, hence the 
other terms. The sensitiveness is evidently too great. 

If we substitute another spring whose resistance on compression 
increases less rapidly than the centrifugal force, we have an arrange- 
ment that will not regulate at all not even badly for the balls 
fly to their limit and shut off steam before, the engine reaches the 
desired number of revolutions. 

Let us substitute, then, a spring whose compressive resistance 
increases with its diminishing length, only a trifle more rapidly 
than the corresponding increase of the centrifugal force of the balls, 
due to their increasing radii of action, the revolutions being kept 
constant at the lower fixed rate. If the speed of an engine is to vary 
from 180 to 182 revolutions, the spring is stronger than the centrif- 
ugal force at 180 revolutions for corresponding lengths of spring 
and radius of action of the governor-ball. But at any speed higher 
than 180 revolutions there are positions of momentary equilibrium. 
These moments are followed by decreased speed, as the steam- 
supply has been diminished for the following stroke. 

It is desirable that governors approach, but not arrive, at iso- 
chronism, since oversensitiveness practically produces more irregu- 
larity in the motion of an engine than that arising from a pre- 
determined variation from perfect uniformity of rotation. 

There are other methods of obtaining isochronal motion. 

/ kL\ 
N 2 h = 2936\l +o/ ^ or anv Si yen governor the only variables 

in the above fundamental equation are N and h. If the governor 
is so constructed that h is constant for different radii of action of 
the balls, then N becomes constant also. For example, three dif- 
ferent simple pendulum-governors having the same cone height AC y 
but the lever-arms of different lengths as shown, would all revolve 
in the same time, for, in that case, N 2 h = 2936. Hence if in a 



governor the arm AB could lengthen out as shown, the motion 
would be isochronous. 

A practical method of obtaining the above motion quite ap- 


\ s 




FIG. 173. 

FIG. 174. 

proximately is found by crossing the arms of the governor -balls 
and making use of auxiliary arms, so that the balls in ascending 
describe an approximate parabola instead of the circle. 


FIG. 175. 

On the axis XX' of Fig. 122 lay off a parabola as shown. 
Draw the ordinates BE' and erect the normals BS and B'Si. 
Draw a parallel ordinate BiBi' and erect normals as before to 


intersect the other normals in some points S and Si. It is a prop- 
erty of the parabola that the subnormal ac = bd. The cone height 
being constant, a governor operating on these lines would be iso- 

A practical form of this governor is shown in Fig. 175. By 
choosing the points Si, S f so that the subnormal slightly increases, 
a stable governor is obtained; if, however, the subnormal decreases, 
the governor would be unstable. 

Power of a Governor. There is a certain amount of work done 
in raising the weights of a governor, which is given out again on 
the descent of the weights. This work is called the power of the 
governor and is equal to the two vertical forces that are necessary to 
raise the weights multiplied by the range of elevation in feet, or 
twice the mean centrifugal force of each ball multiplied by the 
difference between the maximum and minimum radius. 

Pr = Pr 
Vh lr, . . *=- - 

By laying off the values of F for various radii as ordinates 
with the radii as abscissae, an area is obtained that expresses 
graphically the integral of Fdr for one ball. For a Porter loaded 
governor with equal arms, if L = 9w the power of the governor will 
be ten times that of a simple governor for the same variation in 
the height of the cone. Liability of the governor sticking as the 
engine slows down is diminished by increasing the power of the 

Friction of a Governor. Hitherto we have neglected friction 
in the joints of the governor mechanism, friction of the valve-stem 
packing, unbalanced steam- pressure, and the friction of the valve 
itself. But little consideration is necessary to show that all these 
resistances should be reduced to a minimum if a sensitive govern- 
ment of the steam is desired. It is better to let a little steam leak 
from the valve-stem packing than to tighten up the gland so tight 
that the governor acts irregularly. A method of measuring the 
total amount of these resistances in pounds will now be given. 


In the general formula (page 331) Pr = Fh, if r and h remain 

P F N 2 
constant we have ^ = rr = Tfi; in other words, the centrifugal 

* 2 ^2 

force varies with the square of the revolutions and P varies with 
the centrifugal force. 

Supposing all parts of the governor mechanism are in their 
proper position when NI revolutions are being made, but that 
they do not move until additional centrifugal force due to .2 
revolutions is generated, it is evident that the friction is meas- 
ured by F 2 FI or by Pz Pi. From the above equations we have 

2 l = 2 2 l . Hence the frictional resistance of one ball 
l? or the total friction = 2P l ^-^. 

Valves for Short Cut-off. The common slide-valve with a fixed 
eccentric is not used to cut off steam at less than 5/8 stroke. On 
constructing a valve diagram one sees at once that with a constant 
maximum port-opening the steam-lap, and consequently the valve- 
travel, become impractically large if a shorter cut-off is attempted. 
With simple engines the economical cut-off, using steam -pressures 
varying from 80 pounds to 120 pounds per square inch (gage), 
varies from 1/4 to 1/7 stroke. To obtain this result the following 
mechanisms have been used : 

1. Adjustable eccentrics. 

2. Links, by the use of which the greater or less valve- travel 
depends on two eccentrics, as in the Stephenson link. 

3. An independent valve driven by a separate eccentric and 
moving on an independent valve-seat over the main valve. A 
true representative of this type, the Ganzenbach or gridiron 
valve, is no longer used. We shall describe a modified type 
the Buckeye valve. 

4. An independent valve riding on the back of the main 
valve Meyer valve. 

5. Tripped valves of the Corliss type. 

6. Poppet-valves driven by cams used in connection with 
superheated steam. 

Adjustable Eccentrics. Instead of fitting and keying the 
eccentric to the shaft, let us attach the eccentric to the arms of a 



fly-wheel which is keyed to the shaft. Any rotation of the shaft 
will then cause exactly the same movement of the center of the 
eccentric as would have been caused if the eccentric had been 
fastened directly to the shaft. It will be seen, however, that this 
method of attachment allows us to change not only the angular 
advance, but also the throw of an eccentric. Fig. 176 shows a 
swinging eccentric with ears X and X' cast on the front edge ef an 

'--^ / 

FIG. 176. 

eccentric, leaving the rim to be encircled by the eccentric-strap as 
usual. The fly-wheel is supposed to be in front of the eccentric, 
and is omitted to avoid confusing the diagram. The eccentric, 
reduced to a ring-like form, fits the shaft so loosely that it may 
readily be swung around X as a pivot, thus causing the center of the 
eccentric to swing through the arc AfF. If P is the center of the 
crank-pin, it will be seen that this increases the angular advance 
DO A to DO/, and shortens the throw of the eccentric from OA to 
Of when the center of the eccentric is moved from point A to 
point /. If X' is held rigidly in this new position, then the valve 
motion will be that due to an eccentric having the new throw 
Of and the new angular advance DO/. In Fig. 176) S, P', and X are 



fastened rigidly to the fly-wheel, which is keyed to the shaft 0. 
If B moves about P' (from centrifugal force), the eccentric center 
A will move in the arc AfF. 

Keeping the center of the crank-pin as it is in the figure, it is 
evident that the arc AfF will vary with the radius XA and the 
position of the center X. If XA be made longer the arc becomes 
flatter; if XA be infinite in length or a construction is used that 
produces the effect of an infinite rod, the arc becomes a straight 
line perpendicular to the line joining the center of the shaft and the 
center of the crank-pin. This may be called a shifting eccentric, 

FIG. 177. 

to distinguish it from one that swings. If X' is made the pivot 
and X the moving center, the curvature of AfF is reversed. The 
effect of these changes of the position of the center X and of the 
length of the arm XA may be readily determined from the valve 

The student should draw a number of complete diagrams, 
including the indicator-cards to scale, keeping in mind that the 
steam- and exhaust-laps are constant (Fig. 177). Lay off nega- 
tively an angular advance DO A. With the maximum throw of 
the eccentric OA (4X(M, Fig. 176) as a diameter construct on 
OA (and OA produced) valve-circles. With steam-laps OC and 
exhaust-lap OH construct steam- and exhaust-lap circles. With a 


center on OX produced if necessary (to the right in this case) and 
a radius X'A = 4XA (Fig. 176) construct an arc AffF. Join 
and any point / and construct on Of and on an equal pro- 
longation valve-circles; they will be the valve-circles for the new 
throw and new angular advance. Note the effect on 

1. The crank-angle of admission. 

2. The amount of steam-lead. 

3. The point of cut-off. 

4. The crank-angle of exhaust-opening and exhaust-lead. 

FIG. 178. FIG. 179. 

FIG. 178. Diagram from a 12"X12" engine. 250 revs, per minute, width of 
port 1", length of port 9", steam-lap \" , exhaust-lap 0, L/R=G; center 
abou which the eccentric swings is distant 14" from the center of the shaft. 

FIG. 179. Diagram from Straight-Line engine 11 'X14". 275 revs, per 
minute, width of port I", length of port, If" crank end, If" head end; 
exhaust-lap, crank end f", head end $"; eccentricity varies from l^f" to 
2$"; steam lead .04 at quarter cut-off . (Klein's Steam-engine.) 

5. The crank-angle and piston position of exhaust-closure. 

6. The work of compression. 

7. Note the effect of choosing the center X! above and 
below the line OX'. 

8. Note the effect of sliding the eccentric in guides so that 
the center of the eccentric moves in a vertical line through A. 



9. Note the position of the point X f in the diagram and on 
the fly-wheel. 

10. Note the effect of interchanging the position of the 
fixed and moving pivots. 

The general effect of increasing the angular advance and de- 
creasing the throw of the eccentric is to hasten all events, viz., 
steam opening and closing, exhaust opening and closing, and to 
decrease the maximum port-opening very materially. In high- 

FIG. 180. 

speed engines cutting off at j- or \ stroke this port-opening re- 


quires the use of 360,000" for the factor F in the formula a = ^ 


(see page 109). The effect on the lead varies with the position and 
distance of the center X f from the point A. 

The Bilgram diagram may be equally well used for the deter- 
mination of the effects of swinging the eccentric center through an 
arc. The center X' of the arc CC'C" is, in this case, at right 
angles to its true position in the engine. (See Fig. 178.) 

Shaft-governors. As in the pendulum type of governor, there 
is no action in the fly-wheel type of governor except with non- 
uniform rotation. As long as the engine is revolving uniformly the 


centrifugal stresses are balanced by the pull of a spring of some 
description, and there is almost complete static equilibrium, viz., 
there is no motion of the parts relative to one another. With the 
slightest change in speed not only is there an unbalancing of the 
centrifugal or radial forces, but new forces producing tangential 
acceleration and angular acceleration may be brought into 

In Fig. 180, if disc 1, representing a fly-wheel, rotate in the 
direction of the arrow, being driven from a shaft, center at 0, the 
weight W, center at C, exerts a radial or centrifugal stress along 
OW that is resisted by the pull of the spring. If the speed increases 
the radius OW increases until the pull on the stretched spring 
equals the centrifugal force of W with its increased radius. The 
movement of W outwardly or inwardly is utilized, by appropriate 
lever-arms not shown, to move the adjustable eccentrics already 
described (Fig. 176). 

Suppose the weight W were centered as in 2. No such radial 
motion is possible, since the arm OW is not a spring. But suppose 
that disc 2 is suddenly stopped. The weight W being pivoted at 
is unimpeded and will continue its motion. To stop it a tangen- 
tial force must be exerted in a direction opposite to its motion in a 
tangential direction. 

In 1, as long as WC is perpendicular to OTF, all tangential 
stress is taken by the pin C, and motion, due to tangential stress 
alone, is impossible, but if the centrifugal force throws the weight 
W so that the arm WC is no longer perpendicular to OW, as in 
3 and 4, the motion will be due to a combination of the centrifugal 
and tangential forces. 

The tangential force may either increase or decrease the centrif- 
ugal force. In 3 the weight precedes the pivot, but in 4 the pivot 
precedes the weight, hence, while the disc in each case is revolving 
clockwise, the effects of the tangential force are opposite. If the 
speed of 3 is increased, the inertia of the weight produces a force, 
acting in the direction WB, which tends to increase the radius OW\ 
whereas if the disc slows down the tangential force then tends to 
decrease OW. In both cases the tangential effect has aided the 
centrifugal effect and hence made the governor more sensitive. 
The opposite effect is seen in 4. 





The amount of this tangential force is equal to Xthe tan- 


gential acceleration, and its moment is equal to the product of the 
above force and its lever-arm CA. Theoretical calculations give 
an approximation to required quantities, but the final results are 
obtained only by setting the engine up and running it at speed and 
varying the tension of the springs by trial. 

Angular Acceleration. Another method of using tangential 
force is shown in 5. Suppose two weights are connected by a bar 
pivoted in the middle to a fixed or component part of the fly- wheel .. 
If the latter slows down, the inertia of the revolving weights causes 
them to set up a rotation around the pivot C in the direction of the 
arrows. On the other hand, an increase of velocity of rotation of the 
fly-wheel will cause rotation in the opposite direction. The rotation 
around the pivot C is said to be caused by "angular inertia." 

Springs. If to the above forces we add the force of gravitation, 
we have the principal forces that are opposed in fly-wheel gover- 
nors by either leaf springs, as shown in Fig. 176, or helical springs, 
as shown in Fig. 181. The strength of helical springs depends 
upon a number of variables, among which are the modulus of 
elasticity of the wire, diameter of the wire, the helical angle, 
number and radius of the coils. 

The springs may be wound so that their resistance is exactly 
proportional to the stretch or to some increasing ratio. As in the 
pendulum type, the centrifugal force increases directly with the 
radius of the circle described by the center of gravity of the fly- 
weights, and if the stress in the spring increases exactly in the 
same proportion, the fly-weight will oscillate from its innermost 
to its outermost positions. It is then truly isochronal and super- 
sensitive and therefore useless. 

The tension of the spring must increase slightly faster than its 
rate of elongation, more especially since, with a variation from 
uniform velocity, other forces are brought into play and must be 
counteracted. On the other hand, the variable friction of the 
valve and its stem, the friction of all the joints of the governor 
mechanism and the difference between the friction of rest and the. 
friction of motion must be considered. 

In Fig. 181 is shown the governor of the American Ball-engine. 


In this design are used two pivoted parts, both of which use angular 
inertia. The smaller bar is pivoted wholly with regard to the best 
location of the pivot for centrifugal force, and is controlled by the 
help of the spring. The larger bar is located so that its center of 
gravity practically coincides with the center of the shaft, and " is 
pivoted at the most desirable point for determining the path of 
motion of the valve actuating pin." The parts are so arranged 
that a complete gravity balance exists in every position of the 
wheel. "In many cases the total departure from normal speed, 
with the whole load thrown on or off suddenly or gradually, does 
not exceed the space between two arms of the wheel, or one-sixth 
of a revolution, which at 300 revolutions per minute is 1/18 of 1%." 

Inertia Governor. The inertia governor designed by F. M. 
Rites is used on the engines manufactured by over one hundred 
firms. Originally designed for high-speed engines, it is now used 
on medium-speed four- valve engines and is displacing the revolving 
pendulum governor of the Corliss type. 

A hollow, flattened, dumb-bell-shaped bar or weight (Figs. 212, 
213) is fastened on one end of a spindle, s, that may oscillate 
through a small angle in a bearing in the hub of the fly-wheel. 
If an eccentric, E, is used it is fixed to the other end of the spindle. 
The position of the latter must be such that the total allowed 
rotation of the weight or bar from its position when the engine 
is at rest will shift the eccentric from its position of maximum 
throw at A to that of minimum throw (= steam-lap) at B. In- 
stead of an eccentric (with its considerable weight, inertia, and 
friction) an eccentric pin is used in many designs. Necessarily 
this must be an overhung pin, so that its rod may clear the shaft. 

The angle of rotation (in the arc gG) of the weight around 
the axis of the spindle (through the action of centrifugal and 
inertia forces) is governed by the action of the spring z. The 
tension of this spring may be regulated by a nut at z', and the 
length of its lever-arm cd may be altered at z" . 

While the weight is designed to look symmetrical with regard 
to the shaft, as a matter of fact the end to which the spring is 
attached is the heavier. The center of gravity of the rotating 
weights (the bar-weight, the eccentric, eccentric strap, and the 
strap end of the eccentric rod) is at some point G. To determine 


the effect of the weight due to its inertia, consider it as two weights 
concentrated at G\ and G 2 . If the engine slows down, these tend 
to spurt ahead, rotating the spindle and therefore the eccentric in 
the direction required to give increased travel to the vdve. The 
diminished centrifugal force of the weight considered as a single 
mass concentrated at G tends to produce a similar motion of the ec- 
centric. If the engine speeds up, the opposite effects are produced. 
Hence we may say that in all cases the centrifugal and inertia 
forces act together in increasing or decreasing the engine speed. 

As the force of inertia acts only at change of speed, when 
running at theoretical constant speed the forces acting on the 
governor may be grouped under four heads: 

1. Centrifugal force. 

2. Tension of the spring. 

3. Gravity. 

4. Force exerted through the valve-rod. 

Constant speed would only be possible if the sum of the moments 
of these forces around the valve-spindle was zero at all parts of a 
revolution. A more exact analysis will be given later. 

Practical Hints. If an engine runs unsteady, ascertain if it 
ever ran satisfactorily or if the unsteady running occurred after 
making repairs, overhauling, cleaning, or setting up any part 
of the engine, such as the packing, journals, dash-pot, springs, etc. 
Examine the steam-valve for leakage or undue pressure, the steam- 
piston for undue leakage or tightness, the governor for misplaced 
weights or undue friction. 

By means of a brake or a water-rheostat run the engine at 
one-third of its rated load. If the engine speed is steady but 
too low, tighten the spring. If the spring has already been set 
up to the limit, remove any attached weight from the short end 
of the bar GI, or cut out one or two coils from the spring. 

In making any alterations in the governor the following general 
principles must be kept in mind : 

Any alteration that increases the mass at G\ or increases its 
radius tends to increase its centrifugal force and tends to slow the 
engine down. The same results follow from weakening the spring 
or decreasing its arm. 

It is evident that fine adjustments are possible by changes 


whose effects partially offset one another. The bes<t results in 
steadiness are obtained when the no-load speed is about 2% 
higher than the full-load speed. Therefore the tension of the spring 
must increase a trifle more rapidly th&n the increase in the cen- 
trifugal force of the mass due solely to its increase of radius, 
i.e., at constant speed. 

If at change of load the governor exhibits the phenomenon 
called hunting, try the effect of adding a small weight to the lower 
weight 6r?> if there is no trouble due to carelessness, such as stick- 
ing at the pin from dirt or scoring. Hammering at the slops 
on starting and stopping may ordinarily be avoided by either 
increasing or decreasing the attached weights either at the spring 
end or at both ends.* 

In order to operate successfully the modern high-speed shaft- 
governed valve it is necessary to reduce the friction of the valvd 
and its stem to a small and constant quantity. The work of fric- 
tion is reduced by 

1. Removing the pressure from the valve. 

2. Diminishing its travel. 

The first is accomplished by balancing the valve or using self- 
balanced valves. The valve is balanced by working it between 
parallel scraped plates (Fig. 183), so that the steam does not get 
to the back of the valve. In piston- valves (Fig. 182) the pressure 
due to the steam is balanced, leaving the friction of the packing' 
rings to be provided for. 

The travel of the valve is diminished by the use of double 
ports or by the use of auxiliary passages in the valve. In the 
Allen or Trick valve (Fig. 183) the steam enters the cylinder not 
only directly past the valve-edge, but also through a port-passage 
in the valve itself. 

Draw the Zeuner or Bilgram diagrams for the following examples. 

Ex.119. Width of port, 5/8 in.; length of port, 12 in.; steam-lap, 
9/16 in.; exhaust-lap: head end 1/8 in., crank end in.; L/R=6'. 
eccentric-arm infinite; engine, 14 // X20 // ; 210 revolutions, double- 

Ex. 120. Width of port, 1 in.; length, 9 in.; steam-lap, 3/4 in.; 
steam-lead increases from 1/16 in. to 1/6 in. at maximum cut-off; 

* See Power, Nov., 1906. 



'C JV 



length of eccentric or swinging arm, 14 in.; its center is on the line of 
centers of shaft and crank-pin when the latter is on a dead-center. 

Ex. 121. Width .of port, If in.; length, 8 in.; 9"X10" engine; 
300 revolutions; steam-lap, 1 in.; exhaust-lap, 5/16 in.; throw of 
eccentric varies from lf~J to 1 in.; length of swinging arm, 6J in., and 
its center is 5/8 in. below the line of centers of the shaft and crank-pin 
when the latter is on its dead-center. 

Ex. 122. What change would be made if the valve took steam on 
its inside edges instead of the outside? 

Ex. 123. What changes would be made if the eccentric drove the 
valve through a reverse-lever? 

Ex. 124. Could this reverse-lever be designed to give equality of 
cut-off and equal lead at the important point of cut-off with equal 

Link Motion. The Stephenson link is in common use in this 
country and in England, whilst on the Continent the Gooch link is 
preferred. The former will be the only one described (Fig. 184). 

The Stephenson link is most generally used on locomotives and 
marine engines, as it gives not only a convenient means of reversing 
or running the engine backwards, but also affords, when carefully 
designed, a fairly efficient means of economizing steam by affording 
a variable cut-off (Fig. 185). 

This link consists in a going-ahead and a backing eccentric with 
their rods and a link. The eccentrics as a rule have equal throws 
and are placed at equal angles ahead and behind the crank. The 
eccentric-rods are attached by link-pins, P, P', to the link either 
at or near its ends. The length of a rod is the distance from the 
center of its link-pin to the center of its eccentric. When the link 
is in full gear, either ahead or backing, the valve receives its motion 
from one eccentric only. As the link is shifted from that position 
to those nearer midgear, it receives less motion from that eccentric 
and more from the other one. At midgear it is affected equally 
by the eccentrics. As the gear is shifted towards the other full 
gear, the influence of the first eccentric becomes less and less and 
that of the second greater. It will be shown that the effects on 
steam distribution caused by the change of valve motion produced 
by this movement of the link are the same as those produced by a 
swinging eccentric. 



On locomotives, owing to the relative positions of the valve 
(above the cylinder and outside the driving-wheels) and the eccen- 
trics (on the driving-axle and inside the driving-wheels) a rocker 
BTA is necessary (Fig. 185). To prevent the reversal of the 
valve motion the eccentrics must follow the crank. Hence, if the 
crank is at C the center of the go-ahead eccentric is at E, and the 

FIG. 184. Marine Engine. 

center of the backing eccentric is at E f . The link-pins P and P f are 
behind the link; the saddle-plate mo is dished to pass over the 
link-block, B, when the link is raised to bring the eccentric, E', 
into full gear. The link is suspended on one side by the hanger 
rwQ from the bell-crank RSn keyed to the reverse-shaft S. The 
reach-rod, attached to SR at R, is actuated from a reversing lever 
in the cab. The link shown is a slot link. 

A lighter and better construction is shown in Fig. 186. In this 
case the link receives and delivers centrally the stress due to driving 


FIG. 185. Stephenson Link. (From Peabody's "Valve-gears.") 










Fia. 186. Stephenson Link. (From Peabody's "Valve-gears.") 


the valve. In other words, the axis of stresses in the valve-stem 
and in the eccentric-rods coincides with the axes of those rods. 
The figure also illustrates another form of link called the side-bar 
link. The position of the link-block is adjustable to vary the cut- 
off by means of the screw M actuating the bridle NP. This is 
often desirable in regulating the distribution of power between the 
cylinders of compound and triple-expansion engines. By rotatirg 
the reverse-shaft, S, however, the link may be thrown over or 
reversed independently of the position of the screw M. 

To shift the link there are required (Fig. 185) a reverse-shaft, 
S; a bell-crank, RSn; and a suspension-rod, nwo (also called a 
hanger or bridle), attached to the saddle-pin, mo. The motion of 
any theoretical point on the theoretical link arc (shown dotted) is 
due to the motion received from the two 63centrics and from the 
connection of the link to the suspension-rod, or hanger. The curve 
made by any such point is generally some irregular form of the 
figure 8, the loops differing in shape and size. To provide for 
this motion a link-block carrying a pivot pin B is used. We must 
distinguish, then, between a point on the theoretical link arc and a 
point on the axis of the pivot-pin of the block, which coincide 
exactly in position only at the time the crossing-point of the loops 
of the figure 8 is made. At other times the link-arc point has 
slipped by the point in the block by the half-bread lh of the loop. 
This motion of the link relative to the link-block is called the 
slipping or slotting of the block. In Fig. 186 the link-block point 
must move only in a straight line, since the block is directly con- 
nected to the valve-stem; in Fig. 185 the link-block pin moves in 
the arc of a circle about T with a radius BT. A pivot connection 
is necessary in each case, on account of the slight rotation of the 
block about its axis. 

Open and Crossed Rods. It is necessary to distinguish between 
open and crossed rods. This is not so simple as it appears, since in 
what is called open-rod construction the rods become crossed 
during a revolution and then open again. Similarly the crossing 
apparently disappears in crossed-rod construction. In taking an 
engine apart, care must be taken, on reassembling the parts, not to 
convert a crossed-rod construction into an open-rod construction, 
or vice versa, as the steam distribution will be so altered that the 


engine will not turn over. This mistake is frequently made in 
overhauling steam-launch engines. 

To decide whether eccentric-rods are crossed or open, we must 
first determine whether the connection is direct or indirect. In 
direct connection the link-block must drive the valve-stem directly 
and the steam must be controlled by the outside edges of the 

In indirect connection the valve is either driven by a rocker 
or the link-block drives the valve-stem directly, but the steam 
is controlled by the inside lap of the valve. 

For direct connection (Figs. 187 and 188) put the crank on the 
dead-center away from the link. If the rods are open, the open- 

FIG. 188. 

rod construction is used. If the rods are crossed, crossed con- 
struction is used. 

For indirect connection put the crank on the dead-center 
toward the link. In open-rod construction the rods will be open, 
and they will be crossed in a crossed-rod construction. By re- 
volving the crank through 180, the diagrams will show that open 
rods become apparently crossed and vice versa. 

Considerations Affecting the Design of a Link-motion. The 
design will vary in accordance with the importance of the following 
considerations : 

1. The link-motion is to be used practically only for revers- 
ing, as in marine engines. 


2. The link-motion is not only to be used for reversing and 
giving a variable cut-off, but is to be much used at an important 

3. The link-motion is to be used as frequently in the backing 
as in the go-ahead position, as in hoisting-engines, switch- 

4. The importance of reducing slip at an important point 
of cut-off. 

5. The importance of having equal cut-off on both strokes 
at the important point of cut-off. Any inequality at short 
cut-off affects the regularity of rotation more at short than at 
long cut-off, as the percentage of power difference is greater. 

6. The available places of locating the r ever sing-shaft. 

7. The importance of reducing or increasing lead as the link 
is shifted towards midgear. 

The quantities affecting these considerations are: 

1. The position of the axis of the saddle-pin. 

2. " " " " reverse-shaft. 

3. ' l length of the hanger, eccentric-rods, suspension-rod. 

4. ' ' use of crossed or open rods. 

5. Whether or not rocker-arms are used. 

Whilst it may be easy to design a link-motion that will work, 
much care and skill is required in obtaining the best possible solu- 
tion. In locomotive works not only are full-sized drawings made, 
but full-sized models are frequently used in the endeavor to obtain 
the best design. In marine work the problem is simpler, but in 
many cases that which is desirable cannot be obtained on account 
of the interference of other practical considerations. 

The Position of the Saddle-pin. The position of the saddle-pin 
is generally determined with reference to the usual position of the 
link-block to prevent excessive slotting of the block at that position. 
The saddle may be placed on the go-ahead end of the link. The 
axis of the sa Idle-pin will then be in a prolongation of the axis of 
the link-block when the link is in full-gear ahead position. This 
construction is used in links of engines of certain types of vessals. 
It may coincide with the axis of the link-block when the latter is at 
the important point of cut-off, as in p ssenger-enginso. The center 
of the saddle-pin may be on the center of the link arc or before or 


behind that position in engines that run much in both directions. 
Offsetting the saddle-pin to equalize cut-off is necessary when 
the link-pins are behind the link-arc. A finite connecting-rod 
tends to reduce the offset as the latter increases with the length of 
the connecting-rod. 

Position of the Reverse-shaft. This shaft must be well sup- 
ported, and as a rule practical considerations bring it too clos2 to 
the link. Small variations of position do not affect results greatly. 

Length of Rods. In general, long arms tend to reduce inequali- 
ties and short arms to increase them. Advantage may be taken 
of this fact and inequalities may, in some cases, be made to offset 
each other. 

Open or Crossed Rods. If the open-rod construction is used, 
the lead will increase as the link is shifted from full to mid gear; 
with crossed rods the lead will decrease. The length of an eccen- 
tric-rod should be at least twelve times the throw of the eccentric. 

Link-arc. The length of the link-arc should be at least four 
times the throw of the eccentric. The radius of the arc is 
equal to the length of the eccentric-rod if its link-pin is on the 
link-arc. If the center of the link-pin is behind the link-arc, then 
the radius of the arc exceeds the eccentric-rod in length by the 
distance that the link-pin center is from the link-arc measured 
along the eccentric-rod. The length of the link-arc radius just 
given will give equal lead on both strokes if the valve has equal 
laps. If unequal laps are given, so that the cut-off on the two 
strokes may be equal or nearly so, then, of course, the leads will 
be unequal. A somewhat greater or less length may be used, but 
it will cause the leads to be unequal, and too large variation is not 
advisable unless the effect is worked out on a diagram. 

Equivalent Eccentric, Open Rods (Fig. 189). Suppose the 
link in its midposition to the right of the figure, the crank on the 
left center, the direction of rotation to be as shown, OC and OD 
the positions and throw of the eccentrics. With a radius equal to 
the length of the eccentric-rod, viz., from the center of the eccentric 
to the center of its link-pin, and with the centers of the link-pins 
as centers, describe arcs cutting AB at c. Then with a center on 
BA (produced) describe an arc through C, c, and D. Divide that 
portion of the link-arc travelled by the link-block into any number 



of equal parts, and also divide the arc CD into the same number of 
parts. Then if 8 be the number of parts so chosen, and if the link 
is moved 1/8 of the link-arc from full gear ahead, the motion of 

FIG. 189. 

the valve will be that due to an eccentric whose throw is Qc" r 
and whose angular advance is LOc'", where Cc'" is 1/8 of CcD. 

If the rods are crossed the construction is practically the same, 
but the curvature of the arc CcD is reversed as in Fig. 190. 

R L 

FIG. 190. 

Ex. 125. Design a Stephenson link for a tug of a vertical engine; 
boiler-pressure, 100 pounds; cut-off, 3/4 stroke; jet condenser, 26" 
vacuum; 125 revolutions; lead, 1/16"; maximum port-opening, 3/4". 
Connecting-rod = 5 cranks. Assume position of reverse-shaft and 
other required data. 

Buckeye Engine. Fig, 191 is a cross-section of a tandem 
compound engine of the Buckeye type. The valve mechanism 
is composed of a main and a cut-off valve, the latter controlling 
ports in the main valve. Both valves are of the piston type in 
which steam is admitted in the central part, and exhaust takes 




place at the ends. Admission of steam is practically controlled 
by the cut-off valve, while exhaust is controlled by the main 
valve alone. The main valve-stem is hollow and the cut-off 
valve-stem works through the main valve-stem. 

Fig. 192 illustrates the valve-gear diagrammatically. Let OB 
represent the crank rotating anticlockwise, c" be the cut-off valve 
riding on the top of the main valve m" '. In the position shown, 
the live steam is passing through ports a and b into the cylinder 
and the exhaust through the port b f is about to be closed by 
the end of the main valve. The angular advance is negative, 
since the exhaust is on the outside of the main valve. Therefore 
the main eccentric is found at some point M and the cut-off at 
some point C. 

By an ingenious system of levers the cut-off valve receives not 
only the motion due to its own eccentric, but also that due to the 

FIG. 192. 

main eccentric. Hence the motion of the cut-off valve relative to 
the main valve is due to the cut-off eccentric alone. This motion 
is similar to that of a man walking in a moving car. The motion 
of the man relative to the ground is the resultant of his own and 
the car's motion; relative to the car his motion is due to his own 
movements alone, and the car may be considered stationary. 

The main valve receives its motion directly through the eccen 
trie-rod Mm' and valve-stem m'm" . At m', however, it drives also 
a lever .pivoted at p. This lever carries another lever that pivots 
at /. The cut-off eccentric C by its eccentric-rod Cc drives this 
second lever at c. Suppose the cut-off eccentric stationary, then 
c' and m' would have the same motion, since the point c' would 
have twice the motion of the pivot / about the pivot-point c (sta- 
tionary temporarily). Any movement of c will be given to c' 
unchanged in amount, but reversed in direction. 

If the cut-off valve is put in its midposition in Fig. 192, it will 
be found to have a negative lap equal to about half the port-open- 



ing, a. To vary the point of cut-off the position of the cut-off 
eccentric center is rotated (the radius, OC, being unchanged) 
about 0. Its three principal positions are shown in Fig. 193. 

Lay off the diagram for the main valve as usual, BOP being 
the angular advance, Pe and Pi being the exhaust- and steam-laps. 
With a center C and a radius equal to the negative lap of the cut- 
off valve describe a circle tangent to OA. Draw any crank posi- 
tion 07. Drop the perpendicular C 8. Then from the construction 
of the Bilgram diagram C 8 +C 9 is the distance that the cut-off 
valve must move to close the port in the main valve, since we may 
consider the latter stationary. At crank position OC , the port is 

FIG. 193. 

open, the negative lap, and at OA the port is clored. If the port in 
the main valve is closed, it is a matter of indifference whether the 
port in the cylinder is open or closed. If the eccentric center is 
rotated to Ci, then the cut-off is in crank position 02. The latest 
desirable cut-off point of the cut-off valve is 03, or at the point of 
cut-off of the main valve. 

The width of the cut-off blocks must be such that the blocks 
will not overrun the port and open on the back edge when the 
valve is set for the shortest cut-off. The greater the throw of the 
cut-off eccentric the more rapidly the valve passes over the port 



in the main valve and the quicker the cut-off. But this also in- 
creases the width of the blocks and the consequent friction. 

Ex. 126. Make a diagrammatic sketch for a Buckeye valve-gear 
and its Bilgram diagram for a 20"X36" engine, making 125 revolu- 
tions per minute, lead of the main valve, 1/16 in.; maximum cut-off, 
.8 stroke; minimum cut-off at the beginning of the stroke; exhaust 
opens and closes at .9 stroke; connecting-rod, 9 feet long; ports in 
the main valve 2/3 of those in the cylinder. 

Meyer Valve (Fig. 191). Consists of a main valve, C, with ports 
through the valve, and two blocks, DD, forming a cut-off valve 

Connects to Condenser 


FIG. 194. Meyer Valve. 

that rides on the main valve. The main valve governs the latest 
point of steam cut-off and the points of exhaust opening and 
closure. The earlier points of cut-off can be varied by adjusting, 
by hand, the distance between the cut-off blocks. Means are pro- 
vided for rotating the cut-off valve-stem that fits with right and 
left threads of different pitches into corresponding nuts in the 
blocks. One thread is necessarily larger in diameter than the 
other, otherwise it would be impossible to put on one of the valves. 
To make the valves cut off earlier they must be separated, to cut off 
later they must be brought closer together. By giving the main 
valve unequal laps equal cut-off may be obtained at the maximum 
point of cut-off. By the unequal pitches of the right- and left-hand 
screws, equal cut-off may be secured at two points, as, for example, 
the most important point of cut-off and the earliest point of cut- 
off. At all other positions the cut-off will be unequal. In revers- 
ing engines, the cut-off eccentric is direotly opposite the crank. 


Ordinarily it has an angular advance of 75. Its throw is not an 
absolute quantity, but is generally a little larger than that of the 
main valve. 

Corliss Engine. In this type there are two steam- and two 
exhaust-valves placed in separate chambers, either in the cylinder- 
heads or above and below the cylinder at its ends. The valves 
oscillate about their axes, which are at right angles to that of the 
cylinder. For proper drainage the exhaust -valves are always the 
lower ones. The lower or exhaust valves have an invariable 
motion which they receive from a wrist-plate. The oscillating 
movement of the latter about a heavy pivot symmetrically placed 
in regard to the axes of the four valves is obtained as follows. The 
eccentric, set ahead of the crank a little more than 90 degrees, as 
the valve has very little lap, drives a rocker-arm, which, in turn, 
drives the wrist-plate B A (Fig. 195). The links, as BE, never drive 
the valve-stem directly, but indirectly, through a detachable mech- 
anism. In the figure, the governor, of the revolving pendulum type, 
moves a cam xg through the linkage NMl. On the extreme throw 
to the right of the link BE, the fork gTh is forced by the spring 
hs to engage with the block shown just above y. On the stroke 
to the left, the arm BE carries this block, whbh is rigidly attached 
to the valve-stem, with it until the arm gT of the fork comes into 
contact with the cam. This causes the fork to rotate anticlock- 
wise and to let go of the block. A piston which had been lifted in 
a dash-pot by the previous motion promptly closes the valve. 


In the design of this valve mechanism advantage is taken of 
the great variation in the rapidity of motion that may be produced 
by an assemblage of links. It is desirable that a valve should 
open-and close rapidly; when wide open or shut the motion should 
be as small and as slow as possible and the motion should be a 
minimum when the maximum pressure is on the valve. 

The student should note the variation in steam- valve move- 
ment due to variation of position of the links Ob 2 , b 2 e 2 , e 2 v for the 
movement of the wrist-plate through equal parts of the arc b 2 bi. 
Similarly he should note the corresponding movement of the 



FIG. 195. Corliss Engine. (From Peabody's "Valve-gears.") 



exhaust-valve due to changes in the relative position of the links 
Oa, aidi, diw for movement of the wrist-plate through equal parts 
of the arc a\a^. 

An examination of the automatic method of detaching the 
steam-valves will show that it can only operate through a crank 



FIG. 196. 

FIG. 197. 

movement of 90 degrees in each stroke, i.e., while Th is rising. 
We are at liberty to choose the position of these 90 degrees in a 
semi-revolution if the steam- and exhaust-valves are operated by 
independent eccentrics. If, however, only one eccentric is used, 
the necessity of having the exhaust-valve open and close at proper 
points practically limits the detachment of the steam- valve be- 
tween the dead-center and 3/8 stroke positions of the piston. 
With double eccentrics by giving the steam-valve negative steam- 
lap and its eccentric negative angular advance later points than 
that above given may be obtained. 

When the stroke is short compared with the diameter of the 
cylinder the method of connection illustrated in Figs. 195 and 198 
is used; if the stroke is long compared with the diameter of the 
cylinder, the form shown in Figs. 196 and 197 may be used. 

" The following method of setting the valves applies to single- 
eccentric engines of the following types: Reynolds, Twin City, 
Hamilton, Murray Bates, Cooper, Monarch (old), Harris, Hardy- 
Tynes, Lane and Bodley, and all others of similar valve arrange- 



FIG. 198. 


" First. Place wrist-plate D in central position as shown in 
Fig. 196, with both valves hooked on, so that mark on wrist-plate 
hub will coincide with center mark on 
stud; loosen stud-nut and place a piece 
of cardboard between washer and wrist- 
plate and tighten so that wrist-plate will 
not move. 

" Second. Loosen lock-nuts on shackle- 
rods and adjust valves until they have 
laps as found in table (which are given in 
parts of an inch opposite size of cylinder) , 
after which set up lock-nuts securely. 

" Third. Plumb rocker-arm by hang- 
ing a plumb-line over center of pins^ 
then adjust hook-rod between rocker-arm and wrist-plate. 

" Fourth. Remove cardboards so wrist-plate and rocker-arm 
can oscillate; now connect eccentric-rod to rocker-arm and revolve 
eccentric on shaft in the direction 
the engine is to run, being careful 
that mark on wrist-plate coincides 
with side marks on stud when 
making adjustments of the eccen- 
tric rod. Next adjust dash-pot- 
rods H as follows (Fig. 198): When 
rod is down as far as it will go, the 
shoulder E on brass hook should 
just clear the steel block F on valve- 
arm as shown in cut, leaving a 

clearance of 1/16 inch between block and catch-plate. Swing 
wrist-plate to opposite side and adjust in same manner. 

" Fifth. Place crank on exact dead-center and revolve eccentric 
in the direction engine is to run until valve on end nearest piston 
shows amount of lead as given in table. Now fasten eccentric and 
revolve engine in direction it is to run ; when opposite dead-center 
the opposite valve should show the same amount of lead. 

" Sixth. Set governor on starting-pin and adjust trip-rods so 
that cams will just trip valves as wrist-plate coincides with travel- 
marks on stud when oscillated. 

Diameter of 

Lap of 
Steam Valves 

Lap of 
Exhaust Valves 

Lead of 
Steam Valve* 











K S 


















































" Seventh. Now remove starting-pin and allow governor to go 
as low down as it will, then adjust safety-toes on trip-cams so that 
valves will not hook on when wrist-plate is swung to travel-marks 
on stud. 

"Caution. The adjustment of rod H is very important: if too 
long something will break, if too short the valves will not hook on. 
Adjust your dash-pots so as to maintain a good working vacuum."* 

FIG. 199. 

FIG. 200. 

Poppet-valves. Slide-valves give much more trouble than 
pistons wh n steam is ueed that has been superheated to such 

FIG. 201. 

FIG. 202. 

a degree, that it is still superheated on entering the cylinder. 
This is probably due to the cooling received by the cylinder-bore 




during exhaust, whilst there is no such effect on certain parts of 
the surfaces rubbed by the valve. 

As the steam-valve must have a variable cut-off it must also 

be a balanced valve. Exposed to high pressures, it must be very 
stiff to maintain the truth of its steam-surfaces, and it must also 
be tight when highly heated. The valve that best satisfies these 


requirements when superheated steam is used is a drop-valve 
called the double poppet-valve. It may be balanced as closely as 
desired, since the steam-pressure is made to act on the valve in 

FIG. 204. Double Poppet-valve used as a Governor. 

opposite directions at all times. Old forms are illustrated in 
Figs. 199-202. The valve of the Putnam engine is shown in Fig. 
203. (See page 440.) 


Turning Effort in the Crank-shaft. The motion of a body is 
uniform when the resisting forces of all kinds are exactly balanced 
at each and every instant by the impelling forces. For some pur- 
poses it is desirable to have the crank-shaft rotate absolutely 
uniformly. Not many years ago it was usual to describe the uni- 
formity of rotation of an engine by specifying that its revolutions 
per minute would not vary more than one or two from the mean in 
changing from no load to full load. An up-to-date engine for some 
electrical purposes is now designed not to vary per revolution more 
than a certain number of pole degrees eight, for instance from 
the position that absolute uniformity of rotation would give it. 
This would be a displacement in inches on the crank-pin circle of 


$" = o^n^oA X ^ 7rr if tne generator had 30 poles; i.e., a pole degree 

ouU X oU 

equals the degrees between two poles divided by 360. In cotton- 
mills uniformity is exceedingly desirable. Large capacity for cer- 
tain machines is secured by driving shuttles carrying cotton threads 
so fast that the threads are on the point of breaking but do not 
break. Calling this the economical speed, a lower speed would 
produce less cloth; and a momentary higher speed, causing the 
threads to break and the machine to be stopped to allow the 
operator to tie the threads, would also reduce production. The 
exactness required for various classes of machinery will be given 

Two different kinds of uniformity must be secured. If the 
load should vary after the point of cut-off, it is evident that the 
governor controlling the steam-supply can exercise no influence on 
the speed until the next stroke. Hence the engine must change 



speed to make the governor act, and it controls by regulating the 
amount of steam or the pressure on the stroke following the change 
of speed. The steam-governor affords means of controlling the 
number of strokes per minute, but it is also desirable to control 
the speed of the crank-pin during a stroke. If we suppose the 
resistance is uniform, then uniform rotation will be secured by uni- 
form tangential pressure on the crank-pin, since it is only the tan- 
gential pressure that is effective in the production of rotation. 

Net Steam-pressure. The net steam-pressure on a piston at 
any instant is the difference between the absolute driving steam- 
pressure on one side of the piston and the absolute back pressure 
on the other side at the same instant. The amount of this net 
pressure cannot be obtained from a single card, since the bottom 
line on such a card is the back pressure on the same side of the 
piston on the return-stroke. To obtain exact results we should 
have two indicators, each taking a single card during the same 
revolution of the engine. 

In Fig. 204 let A and B be cards so taken. For convenience 
of illustration both diagrams are shown on one card. Then the 
net steam-pressure at any piston position b is ab bc=ac, 
where ab= absolute forward pressure, 
be = absolute back pressure, 
ac=difference between driving-pressure of one card and 

back pressure of the other card. 

Draw a new card, 12345, whose ordinates represent the net forward 

When the back pressure exceeds the forward pressure the 
ordinates are laid off, as in the figure, below the base-line. 

Variable Velocity of the Piston. If the crank-pin revolves with 
uniform velocity it will pass over equal arcs in equal periods of 
time. The piston then necessarily passes over unequal distances 
in equal periods of time. On page 73 it was shown that these 
distances increased from the beginning to the middle of the strc ke 
and then decreased to the other end of the stroke. The pisto^, 
then, must have a positively accelerated motion from the beginning 
of a stroke to near the middle and then a negative acceleration 
to the end of the stroke. It was further shown that shortening 
the connecting-rod increased the amount of all irregularities. 



Bodies at rest or moving uniformly are under the action of 
forces that are absolutely balanced. Bodies having an accelerated 
motion are storing up work represented by the increasing kinetic 

. 205a. 

energy of the moving masses. This energy will be given out again 
if the moving masses slow down. At any point in the first half 
of the stroke a part of the net steam-pressure (acting through 
a distance) will be required to produce the necessary acceleration 


of all parts of the engine having a reciprocating motion or a motion 
of translation. On the other hand, the net steam-pressure during 
the second half of a stroke will be augmented by the pressure 
made available by the necessary slowing down of the reciprocating 

Reciprocating Parts. These are the piston, piston-rod, cross- 
head, and half the weight of the connecting-rod. (See Vol. XXVI, 
Trans. A. S. M. E.) In the discussion of accelerations and .forces 
on the assumption of an infinite rod we shall use the above propor- 
tion of the weight of the real rod in finding the forces, as the 
change required by the use of a finite rod is then easily made. 

Pressure Required to Accelerate the Reciprocating Parts (Figs. 
205 and 206). 

CASE I. Infinite Connecting-red. 

Let V= constant velocity of the crank-pin in feet per second; 
v= variable velocity of the piston in feet per second; 
r= radius of crank in feet; 

0=length of the arc, measured from the dead-center, 
swept through by a point on the crank-arm at 
unit distance from center of the shaft in t seconds; 
TP=weight of the reciprocating parts. 

Then rO = length of arc swept through by crank-pin in t seconds 
= Vt. 

rdd = Vdt, hence j- = 
at T 

( distance the piston moves in t seconds from a 
r(l cos0) =s= -J , , ,.! , ,, , Q 

( dead -center whilst the crank-pin moves rd. 

ds d(r-rcosd) r sin 6d6 T _ . rdd T _ 

dt= ~dT ~dT -^ sin ^ since -^=7. 

dv d 2 s d(Vsm0} V cos Odd F 2 cos# 

But acceleration =-rr =rz = -T. = T; = 

dt dt 2 dt dt r 

The product of the acceleration and the mass that has been accele- 
rated gives the force required to produce the acceleration; or 

W V 2 cos 6 
F = =the total force required to produce the necessary 

acceleration of the reciprocating parts at the piston position cor- 


responding to a crank-angle, 0, if the crank-pin revolves uni- 

As the indicator-cards show pressures in pounds per square 
inch it is advisable to divide the total 
pressure F by the area of the piston in 

W V 2 cos0. 
square inches. Hence / = r is the 

loss or gain of pressure in pounds per 

square inch of piston area arising from the 

necessary acceleration, positive or negative, 

of the reciprocating parts (at a piston posi- FIQ 2Q6 

tion corresponding to the crank-angle 6). 

Mass of Reciprocating Parts Considered as Concentrated at the 
Center of the Crank-pin. If the weight of all the reciprocating 
parts could be concentrated at the center of the crank-pin the cen- 

WV 2 
tripetal force of such a weight would be - . The horizontal 

WV 2 cos 
projection of this radial force would be - - or the above 

force, F. 

In the above equation for /, the only variables are / and cos 6. 
As the equation is of the first degree, it is therefore the equation 
of a straight line. This can be seen by giving 6 a few values such 

as 0, j, ~> an d TT and plotting the results. 

Hence it is only necessary to find the value of / for 0=0 and 
6 = n and join the points so found by a straight line. 

For example suppose the cards, Fig. 205, are from a horizontal 
high-speed engine.* With the following data find the pressure per 
square inch of piston area that will be required to accelerate the 
reciprocating parts at the beginning of a stroke, neglecting the 
angularity of the connecting-rod. 

Revolutions 300 

Stroke 12 inches. 

Diameter of cylinder 10 " 

Length of connecting-rod 36 " 

* Trans. A. S. M. E., Vcl. XI. 


Distance from wrist-pin (cross-head pin) to the 

center of gravity of the connecting-rod ........ 20. 15 inches. 

Principal radius of gyration of connecting-rod ..... 15 " 

Weight of connecting-rod ....................... 70 pounds. 

Weight of piston, piston-rod, and cross-head ....... 90 -". 

Weight of above and half connecting-rod .......... 125 " 

When 0=0 or TT 

. 125X4X* 

7 ' ;rX5 2 X32.16Xi fc 2X32. 16 

(Fig. 205.) Lay off IE or 5^ = 24.42 pounds to the scale of 
the indicator-card pressures. Then any ordinate as, dc, represents 
the pressure that is required to produce (or is produced by) the 
instantaneous variation of velocity in the reciprocating parts. 
Negative pressure is therefore indicated above and positive pressure 
below the reference line 15. As these pressures are always modified 
by the use of a finite rod, its effects will be discussed next. The 
equation of / and 6, when the length of the rod is considered, will 
no longer represent a straight line such as EF, but takes the form 
of a complex curve HIJ. 

CASE II. Finite Connecting-rod. In general, sufficient accuracy 
is attained if only three to five points on this curve are obtained. 
The formula to be used for each of these five points may be ob- 
tained from the general formula by the substitution of the proper 

Piston Position of Zero Acceleration. After reaching its maxi- 
mum velocity the piston begins to slow 'down. Evidently the 
acceleration changes sign and passes through zero at the point of 
maximum piston velocity. With an infinite rod this occurred at 
half-stroke, the crank arm and rod being at right angles at that 
point. With a finite rod this point will occur before half -stroke, 
and its position may be obtained graphically as follows: 

(Fig. 207.) Draw a circle with a radius OA = r, the throw of the 
crank. Perpendicular to OA draw AC and lay off AC equal to 
the length of the connecting-rod. If OAC is swung around till 
C cuts the line OD, the required point E will be obtained. To do 
this,_ measure the hypothenuse, OC, and lay off OD = OC. With 
D as a center and a radius = AC = length of the connecting-rod, 



describe the arc EF. Then OE will be the crank-pin position and 
GF the distance the piston is from its dead-center G when the 
piston has its maximum velocity and its acceleration is therefore 
zero, and hence f = 0. 

FIG. 207. 

Accelerations, Finite Connecting-rod (Fig. 55). In general, 
however, for any position of the crank-pin 6 degrees from the dead- 
center, the piston has moved 

x = r(l cos 6) +1(1 cos a). 
I sin a = r sin 0, rd = Vt, 

rdd = Vdt, sin a = sin 6, 

cos a = 

I Tr \ 2 / 1 r 2 \ 

a = vft- ( j- sin I = ( l - _ _ sin 2 6 , approximately, 
V / \ & I ] 

(By squaring the above quantity and neglecting sin 4 6 the quantity 
under the radical is obtained.) 

/. x = rl 1 cos 0n -j s 

dx rdd / . 1 r . 

^- = v(sm6^sm26}, 
ctt \ 2i I 



r \ V 2 


= cos 6jcos 20 



Forces to Produce Required Acceleration. As in the preceding 

Force = mass X acceleration. 

W V 2 / r \ WV 2 / r \ 

/. F = -- (cos 6-j-cos2d] and f = ^ ~ { cos 0ycos 26 ). 

The value of this equation for 

W V 2 
6=* 45 and 135, / = cos 45; 

The value for 0=45 or 135 is the same as in Case I and 
may therefore be used if the corresponding piston positions are 


/ W V 2 \ 
Substituting the value of ( : ) already found (24.42 pounds) 

\i/ / 

and the value of T = ^> we obtain /o = 24.42 (); / 180 = (24.42) 

i 60 

(-|); / 90 =(24.42)(-J). Plotting these results and those ob- 
tained for zero and equal acceleration (45) we obtain the curve 

Pounding of the Engine. It can be readily seen that the inertia 
of the reciprocating parts may be used to equalize the pressure 
that is exerted on the piston-rod during the entire stroke. At 
first sight this might seem desirable, and it has been so enunciated 
many times. On the contrary, it is not desirable, as it will cause 
the engine to pound on the centers, due to the sudclen change from 
positive to negative pressure. Smoothness of running is secured 
by such weight of reciprocating parts as will cause the forward 
pressure to increase gradually from zero to a maximum at the end 
of the stroke. The sudclen cessation of pressure will not produce 
a pound, but the taking up of lost motion under heavy pressure 
will produce a destructive pound that should be avoided. In 


shaft-governed engines at cut-off shorter than the normal, the lead 
is often made negative. This tends also to reduce the tendency 
to sudden reversal of stress. Heavy compression also has the 
same effect. 

Determination of Tangential Pressures. Let the ordinates of 
H2KU of Fig. 208 be the same as those of H234JK1H, Fig. 205, 
the abscissas being reduced to one-third of their original dimensions. 
With a radius equal to the length of the connecting-rod (3XHJ) 
lay off B and D from H and J and construct the circle BCD. 
Divide it up into any number of equal arcs and let C be one of 
the division points. With the length of the connecting-rod as a 
radius and C as a center, find A, the corresponding cross-head 
position. Having taken out the pressures required to produce 
acceleration of the masses, we may consider the forces that we 
are now discussing as static. 

The cross-head and crank-pin are each under the action of 
three forces produced by the action of one force acting in the 
direction of HJ and of magnitude p. The pressure in the con- 
necting-rod is greater than p, since the component of the connect- 
ing-rod pressure along HJ must equal p. 

Prolong the crank-arm OC till it intersects a perpendicular, 
AI, erected at A. The tendency to rotate around the instan- 
taneous center, /, is zero, since the forces producing change of 
velocity have been removed Taking moments about /, all forces 
disappear from the equation except p and the tangential force 
T acting on the crank-pin. 

On 01 lay off OP f = p and draw P'T' parallel to the connecting- 
rod position AC and intersecting OM, a perpendicular erected to 
BD at 0. 

The triangles OP'T' and CIA are similar, therefore 

oF~ci m '' OT '=P x cJ' 

Hence OT f is the reqiured tangential pressure at this crank-position. 



It is evident that connecting-rod positions will have to be 
drawn for each crank-position in succession to determine a new 
piston position and the corresponding net pressure, such as p. By 
laying off this pressure from the center of the shaft on the crank- 
position, prolonged if necessary and drawing a parallel to the 
new connecting-rod position as P'T' was drawn, the tangential 
pressure for the new crank-position will be indicated by the 
distance between and the point of intersection of the parallel 
and the line OM. It is not necessary to find the instantaneous 
center, as that is only necessary to prove the construction. 

The tangential pressures so found may be laid off in two ways; 
1. (Fig. 208.) At each point of division of the crank-circle 

FIG. 208. 

lay off the tangential pressure radially at right angles to its 
true position from the center of the crank-pin. CT" 1 ', for instance, 
is equal to OT'. Join the points so found. The area enclosed 
by this line and the perimeter of the circle does not measure work. 
2. (Fig. 209.) A much more useful diagram is formed by recti- 
fying the path of the crank-pin thus giving actual linear distance 
and at each point of division on the rectified perimeter erecting 
a perpendicular equal to the tangential pressure at that point. 
All areas then measure work and by means of a planimeter or by 



the method of ordinates we can obtain the excess or deficit of 
work variation from the mean that produces either positive 
or negative acceleration. 

The importance of dividing the semicircles into equal parts is 
now apparent, as it facilitates the rectification of the arcs. Accord- 
ing to Rankine the following method is accurate to Tiror- (Fig. 
210.) To rectify the circular arc AEB prolong the chord AB to C, 
making AC = %AB. With a center at C and a radius AC describe 
an arc AD. At B draw a tangent, BD, limited by the arc AD. 
Then 5D = arc AEB in length. 

Fig. 209, has many important qualities. For instance, its area 
is exactly equal to that of the original indicator-card, thereby 

FIG. 209. 

FIG. 210 

illustrating the fact that there is no loss of energy, friction 
excepted, in the conversion of the " to-and-fro" work of the piston 
into the work of rotation of the crank-pin. 

If we divide the area of the card, Fig. 209, by its length and 
lay off a line parallel to the base with the resultant pressure as the 
ordinate, we shall divide the card into two parts. The + area 
indicates work in excess of the mean, the areas indicate cor- 
responding deficits. In every case the sum of the + areas must 
equal the sum of the areas per revolution. 

In the case of a single engine one of the + areas may be called 
AE and its ratio to work per revolution or 2 (area of the rectangle) 

A W 
= 2 (the area of the indicator-card) may be called 

2/pds ' 


fraction is often called the fluctuation ratio or coefficient of un- 
steadiness. Its value ranges from 1/6 to 1/4 with single-cylinder 
expansion engines, with a pair of engines of practically equal power 
coupled at right angles its value is from 1/25 to 1/15; and for three 


engines coupled at 120 degrees apart it is 1/75 to 1/50. By 
means of a fly-wheel, the effect of all of these variations from 
the mean energy on velocity changes may be much reduced. The 
absorption of energy by the fly-wheel in speeding up reduces the 
highest velocity that would otherwise be attained and increases 
the lowest velocity by returning the absorbed energy. 

The following table gives an approximate value of allowed 

coefficients of unsteadiness in velocity = -=s -=k. 

For stamps, crushers, etc 1 / s 

' ' saw-mills and pumping-engines 1 / 20 1 / 30 

' ' weaving-machines and paper-mills V 30 1 / 40 

" spinning-machines for coarse to middle-fine yarns. . 1 / 35 l / 50 ! /eo 

" spinning-machines for finer yarns 1 / 50 . . 1 / IM 

tl belt -driven dynamo-machines 1 / 150 

' ' directly coupled dynamo-machines 1 / 300 1 / 60Q l / 3000 

Approximate Formula for a Fly-wheel. 
W = weight of the fly-wheel. 

Vi= maximum velocity of the rim, at radius R, in feet per 
* second. 

V 2 = minimum velocity of rim, at radius R, in feet per second. 
V =mean velocity of rim, at radius R } in feet per second. 

We shall assume that V --= ~ . This is not true frequently, 

as the maximum velocity may persist for a much longer or shorter 
period of time than the minimum velocity. 

The radius R is generally taken from the center of the shaft to the 
middle of the rim. The proper radius is the radius of gyration, 
as we are really dealing with the mean of the squared radii. In 
dealing with thin rims in an approximate solution, the assumption 
of the mean radius is sufficiently accurate. 

The kinetic energy of a mass, moving Vi feet per second is 



~-Vi 2 . If the velocity changes to V 2 feet per second the new 


WV 2 2 
kinetic energy is , . The change of energy is 

This must equal 

JE may be obtained in foot-pounds from the maximum + or 
area in a diagram (Fig. 209) , or it may be obtained from an 
assumed fraction of the work per revolution. 

For example, find the weight of a fly-wheel for a 100 I.H.P. 
engine making 100 revolutions per minute; fluctuation of energy 

17? 1 

= T, -- = .2; fluctuation of speed = r^; mean velocity of fly- 

wheel rim = 50 feet per second. 
100x33,000 2 

1oo^- x io x32 - 18 

*- - .01X50X50 - =849 P und& - 

Another method of reducing the difference between V l and 2 
is to reduce the amount of the + and areas. This can be done 
by having the work done by two engines coupled at right angles, 
or three engines at angles of 120 degrees apart. 

I T7T 

The formula W = ~TT^ is expressed in several forms : 

Let N = number of revolutions per minute; 
RI =mean radius of rim in feet; 
R 2 = " " " " " inches; 
R g = radius of gyration in inches; 
/ =WR g 2 = moment of inertia; 

=/ = jjjyvj inch-pounds; 

N 2 or .0000278TF# 2 2 N 2 foot-pounds. 


In Fig. 222 the curve of tangential effort of the high-pressure 
engine of a compound is given in full lines, while the curve for 
the low-pressure engine is given in dotted lines. From the posi- 
tions of the points of zero-crank effort it is readily seen that the 
cranks of the engines are at right angles to one another. In 
Fig. 223 the ordinates of the two engines have been added and 
the variation from the mean ordinate MC is indicated. 

Belt Wheels. For many purposes the belt wheel, if properly 
proportioned so that it does not look weak, will be found suffi- 
ciently heavy to serve as a regulator. It will not serve where 
very close regulation is required, as in parallel operation of A. C. 
generators. Two per cent variation on either side of the normal 
speed is close enough for steady burning of lamps and a belted 
Corliss should run that close. If power and lamps are on the 
same circuit a heavier wheel should be used. 

Horse-power of a Belt. Authorities differ but common rules 

Single belts transmit one horse-power per inch of width per 

1000 feet linear veloc ty; 

Double belts transmit two horse-power per inch of width 

per 1000 feet linear velocity; 

At 3000 feet the effect of centrifugal force becomes per- 
ceptible and 5000 to 6000 feet is the economic limit if the life 

of the belt is to be considered. 

The Arc of Contact. This is supposed to be 180. Reducing 
the arc increases slippage and causes less horse-power to be 
transmitted. The maximum ratio that should exist between 
driving and driven pulley should not exceed 5. With this large 
ratio the axes of the pulleys should be well separated. The 
bottom of the belt should be the tight side. The upper side 
should run with a perceptible sag. 

General Details. The face of a belt wheel should be crowned 
at the rate of J inch to the foot. If over 40 inches wide, double 
staggered arms are used. The rims of wheels under 13 feet in 
diameter should be at least one inch in thickness and strength- 
ened at the sides and middle by ribs. The middle rib serves to 
connect the thicker arms and rim and reduce shrinkage stresses. 

The diameter of the hub is about twice that of the shaft and 


the length of the hub is one and a half to twice the shaft diameter. 
This width is necessary to prevent the wheel from rocking on the 
shaft. The minimum weight of a belt wheel for good looking 
proportion is given in column five, Table A, page 389. 

Weight of Balance Wheels. In the analytical discussion it was 
shown that the efficiency of a fly-wheel varied with WR 2 , where 
R 2 is the squared radius of gyration. It is evident for economy 
of material that the diameter of the wheel should be as large 
as possible, yet, for good looks, it may become too large. 

When engines are used to drive generators it is convenient 
to express the weight of the balance wheel in terms of the revolu- 
tions of the engine and the kilowatts of the generator. To do 
this, primary constants will be given for single-cylinder engines, 
running at 100 revolutions per minute, the rim of the fly-wheel 
moving with a velocity of 5700 feet per minute. These constants 
will have to be modified in the case of multicylinder engines 
and in case the revolutions are not 100. Two sets of primary 
constants will be given, one for A. C. current generators running 
in parallel, and another for D. C. current generators and for A. C. 
current generators which are not in parallel operation. 

The method then is as follows: 

From Table A pick out the diameter of the wheel corresponding 
to the given number of revolutions. From Table B (page 390) 
pick out the constant K A or KD, according as the engine is to 
drive A. C. generators in parallel or A. C. generators not in 
parallel or D. C. generators. Obtain a new constant, K\ or K%, 
depending on the number of revolutions from the formulas below : 



In turn the constants K\ or K% must be modified in accordance 
with the amount of variation of energy from the mean during a 
revolution. As that of the single cylinder is a maximum it will 
be assumed as unity and K\ and K 2 must be multiplied by the 
decimals below corresponding to the type of engine: 


Single-cylinder engine .............. ........ 1 . 00 

Tandem-compound engine ................... 80 

Cross-compound engine ...................... 60 

This final constant, K/ t multiplied by the kilowatts will give 
the weight of the wheel in pounds. The effect of the WR 2 of 
the armature and rotors of the generators is only to ^ of 
that of the wheel, except in very large sizes. They may therefore 
be neglected. 

Examples. A tandem-compound engine is direct connected to 
a 500-kilowatt 60-cycle alternating-current generator, running at 
90 revolutions per minute. Find the diameter and weight of 
the wheel. 

From Table A we find that a wheel corresponding to 90 
revolutions must have a diameter of 20 feet and from Table B 
the primary constant, K A , is 145 for 100 revolutions per minute. 
Hence for 90 revolutions, 

For a tandem compound, 

K/=220X.80 = 
Total weight of wheel, 

176X500 = 88,000 pounds. 

After finding the weight, reference should be made to the 
last column of Table A, as the weight should not be less than 
the tabular amount. In the present case the tabular amount 
for a 20-foot balance wheel is 32,000 pounds, and hence the 
weight found, 88,000, may be used. If less than the tabular 
weight is used the wheels will appear out of proportion and look 

Example. A single-cylinder engine is direct connected to a 
75-kilowatt direct-current generator running at 120 revolutions 
per minute. Find the diameter and weight of the wheel. 

If we used a rim speed of 5700 feet per minute we should 
obtain a wheel with a rim section too light to look well. Even 



at 4800 feet we shall lower the amount of the radius to obtain 
a more substantial appearing rim. 

From Table A, column 2, the nearest diameter is 12 feet and 
from Table B, K D is 185. 

For 120 revolutions per minute, 

100\ 3 

: I 



X 185 = 107. 

Total weight of the wheel, 107x75 = 8025 pounds. 

Referring to Table A we find that the minimum weight that 
should be used for a 12-foot wheel is 12,500 pounds. We must 
therefore assume a 10- or 11-foot wheel and recalculate. 

For a 11-foot wheel, 

_/100\ 3 


X 225 = 130. 

The weight of the wheel is 

130X75 = 9750 pounds. 

This is a trifle above the limit for a 11-foot wheel and hence 
may be used. 



Diameter of 
Wheel in 

per Minute, 
Rim Speed 
4800 Feet 
per Minute. 

per Minute, 
Rim Speed 
5700 Feet 
per Minute. 

Fare Width 
in Inches of 
Belt Wheels. 

Weight of 
Belt Wheels 
in Pounds. 

Weight for 
Balance Wheel* 
in Pounds. J 





















































































* Power. 





K A 


i_^ameter 01 
Balance Wheel 

A.C. Current 

D.C. Current 

in Feet. 

in Paralle 



K.C. Current 
not in Parallel. 




























Analysis of the Rites Inertia Governor. The designing of 
steam-engine governors is the work of a specialist. It involves 

FIG. 211. The numbers show variable positions of the eccentric center and 
gravity center at variable cut-off. The dotted lines AO and OG are of 
variable length. is the center of the shaft ; C is the center of the crank- 
pin; s is the spindle center; G is the center of gravity of the rotating 
weights; M is an ideal center of mass placed at a distance equal to the 
radius of gyration from G; zz" is the line of action of the spring; OG is 
the ,line of action of centrifugal force; Gi is the line of action of tan- 
gential acceleration; I a is the angular acceleration couple around G. 

* Power. 


not only special knowledge of the action of such mechanism but 
also shops and funds for experimentation of no mean propor- 
tions. The analysis here given gives not only an insight into 
the action of this particular mechanism but gives an extended 
application of various principles of mechanics. In this analysis, 
there is; first, a rather long preliminary statement of principles; 
next, the proof of an equation of static equilibrium; then, the 
proof of an equation of work, or dynamic, equilibrium; and, 
finally, some equations dealing with angular inertia. 

In Fig. 211 let OC be the position of the crank; s, the position 
of the spindle center; A is the center of the eccentric and the 
dots indicate positions of A giving shorter cut-off; G is the center 
of gravity of the rotating weights of the governing mechanism, 
and the dots indicate positions of G corresponding to the different 
positions of A; cd is the lever-arm of the moment about the 
spindle centers s, due to the tension in the spring z\ ef is the 
lever-arm of the moment of the centrifugal force of the rotating 
weights' G about s, since it is equal to the perpendicular let 
fall from s on OG. See also Fig. 213. 

Division of Weights. The weights are placed in two main 
divisions : 

Reciprocating Parts valve, valve stem, slide, and the 

eccentric-rod up to the eccentric. 

Rotating Parts the eccentric, its strap, strap end of the 

eccentric-rod, and the governor bar, GiG 2 . 

The center of gravity of all the rotating weights is intended 
when the center of gravity of the bar is used in the following 
discussion. If the eccentric is heavy a material difference is 
made if its weight be neglected. 

Forces Acting through the Eccentric-rod and their Lever-arms. 
The force acting in the eccentric-rod at any instant is the 
resultant of the following forces: 

1. The inertia of the reciprocating parts of the valve 

2. The friction of the valve; 

3. The unbalanced pressure on the end of the valve stem, 
since only one end of it is exposed to steam; 

4. The weight of the reciprocating parts in vertical engines. 


The eccentric-rod will be treated as if infinite in length. 
Hence, at all parts of a revolution, it will be parallel to the center 
line of the engine. 

The resultant of all the forces in this rod, at any instant, will 
pass through the center of the eccentric. 

If in Fig. 215 the eccentric center is at the point, a\, the 
moment of the force acting in the eccentric-rod, at that instant, 
about the spindle axis, 61, will be the product of that force and the- 
lever-arm bid. At 120, the lever-arm is almost zero; at the 
next point, it is negative. 

FIG. 212. Rites-Carpenter Governor. 

Algebraic Signs of Forces, Arms, and Moments. Forces, arms, 
and moments may be either positive or negative. We shall 
call positive all moments which tend to increase the eccentricity 
of the eccentric, i.e., tend to move the center of the eccentric 
away from the center of the shaft. Movement in the opposite 
direction will be negative. Positive arms are those which com- 
bined with positive forces will produce positive moments. For 
example, the moment of the spring, z, is positive and the moment 
of the centrifugal force through OG is negative. Calling the 
stroke of the valve toward the shaft its instroke and the stroke 
from the shaft its outstroke, we have: 

1. The inertia of the reciprocating parts of the valve mech- 
anism is positive during the first half of the instroke and the 



second half of the outstroke. The inertia forces, therefore, produce 
negative stress during the second half of the instroke and during 
the first half of the outstroke. 

2. When the steam pressure is on the outside of the valve 
(exhaust inside) the unbalanced pressure on the end of the valve 
stem will produce a negative stress in the eccentric rod. 

3. Friction produces a positive stress on the instroke and a 
negative stress on the outstroke. 

4. The weight of the reciprocating parts (in vertical engines) 
produces a negative stress during both strokes. 

FIG. 213. 

FIG. 214. 

Gravity. The effect of gravity on the reciprocating parts: 

1. Will be called zero in horizontal engines; 

2. In vertical engines, will be classed as one of the forces 

acting through the eccentric-rod as above; 
The effect of gravity on the rotating parts: 

1. The attraction of gravitation being constant the force 
due to the weight of the rotating parts is constant; 

2. The lever-arm of this force will vary from a maximum 
positive, equal to the radius sG, through zero to a maximum 
negative equal to sG and back again during the next semi- 
revolution. Its effect in a complete revolution is zero and 
will not affect our static equation of equilibrium to be derived. 
Its effect in determining the weight of the bar will be dis- 
cussed. (Figs. 213 and 214.) 


Conditions of Static Equilibrium. If a body is at rest or is 
moving uniformly, it is in a condition of static equilibrium; 
hence, the sum of the vertical forces is zero, the sum of the hori- 
zontal forces is zero and the sum of the moments of all the forces 
acting on it is zero. In the case of this governor it will be shown 
that absolute static equilibrium for a number of consecutive 
instants is not obtainable owing to the incessant variation of one 
of the moments. An equation of static equilibrium for 'a revo- 
lution can be written by finding the mean moment of the forces 
and arms that vary in amount and sign. 

To find this mean moment we shall assume the engine to be 
revolving at constant speed. In the case of the fly-wheel, we 
found that it had no value in regulating the number of revolu- 
tions per minute but had very great value in regulating the speed 
during a revolution. As the fly-wheel absorbs the excess or deficit 
of work put into the crank-pin through the connecting-rod, so 
the governor bar absorbs or gives out work through exceedingly 
small variations of speed. These variations occur if the engine 
is supposed to be rotating uniformly. In case the engine speeds 
up or slows down an entirely different use of the bar arises through 
its angular acceleration aiding centrifugal force in bringing the 
eccentric center to a new position. This phase of the use of 
the bar is discussed last. 

The static equation of equilibrium for a revolution involves 
three moments. These moments are taken around the spindle 
axis and are as follows: 

1. The tension of the spring is constant for a revolution, 
its lever-arm is constant, and, as the moment of the spring 
tends to increase the eccentricity, the moment will be called 

Let Z = tension of the spring, 
cd = the lever arm. 

Moment of the spring = +Z(cd). 

2. At constant speed the centrifugal force of the revolving 
parts concentrated at G and with an arm ef, would have a 
constant moment, 

Centrifugal moment- -Q.QW34WRN 2 (ef), 


if W= weight of revolving parts; 

# = distance of the center of gravity, G, from the center of 

the shaft, expressed in feet; 
N = number of revolutions per minute. 

The negative sign is used as centrifugal force tends to decrease 
the eccentricity. 

3. The third force is the resultant force in the eccentric-rod 

passing through the eccentric center. Not only is this a variable 

force but its lever-arm about the spindle, s, is variable. 

When we remember, however, that a point on the surface of a 
crank-pin revolves once around the axis of the crank-pin in one 
revolution of the latter about the axis of the shaft we perceive 
that the center of the eccentric and the center of gravity of the 
rotating weights revolve in circles about the axis of the spindle. 
The radii of these circles are the distances of those centers from 
the spindle axis. 

To find the mean moment of the third force we shall divide the 
path of the eccentric center in its revolution around the spindle 
axis into equal parts, say, twelve. We shall find the amount of 
the force in the eccentric rod when the eccentric center is at each 
of these points and multiply the force so found by the perpen- 
dicular let fall from the spindle center on the axis of the eccentric-rod 
produced. The mean of the products found arithmetically is the 
mean moment required. 

To find the resultant pressure acting at each of the twelve 
positions of the eccentric center, it is best to rectify the path of 
eccentric center, 2na\bi, Fig. 215, and at each point lay off the 
positive or negative pressures as follows (Fig. 217) : 

The force due to the inertia of reciprocating parts is 

/= 0.0000284 wrN 2 cos 0, 

where w= weight of reciprocating parts of valve mechanism 4 , 
r = eccentricity in inches] 
N = the number of revolutions per minute; 
= angle swept through. 

By laying off the values of / so found, some such curve as 
A (Fig. 217) is obtained. Had valve positions instead of eccen- 



trie center positions been used two straight lines would have 
replaced the double curve, A. 

The friction of the valve is a variable quantity. It varies 
with the construction of the valve, the amount of wear and the 
lubrication. In the diagram, the unbalanced steam pressure on 
the end of the valve stem, the friction and the weight of the 
reciprocating parts is indicated by that part of each ordinate 
included between the curves A and B so that the ordinates of B 
indicate the resultant pressure in the eccentric-rod at the corre- 
sponding positions of the eccentric center. From Fig. 217, we 

FIG. 215. 

see that these ordinates pass through zero value at 90 and 300 

The corresponding lever-arms are shown in Fig. 215, b\c\ 
being the arm for the force in the eccentric-rod when the eccentric 
is on the dead center; b 2 C2 being the arm for the force in the 
rod when the eccentric center is 30 from its dead center, etc. 

The next step is to scale off each force and its lever-arm and 
find the arithmetical product. The mean of all the products is 
the mean turning moment due to the forces in the eccentric-rod 
during a revolution. This operation is not performed in the 
text. We can then write: 

Constant centrifugal moment constant spring moment ^-the 
mean moment of the eccentric-rod forces. 



To Find the Weight of the Bar to Absorb Unbalanced Work. 
The second part of the analysis is devoted to a discussion of a 
method of finding the weight of the bar to absorb excess or 
deficit of work caused by the unbalanced pressure in the eccentric- 
rod and by the weight of the rotating parts. As work is the 
product of a mean pressure and the distance through which that 
mean pressure is exerted, it remains to show the distance through 
which the force in the eccentric-rod and the weight of the rotating 
parts is exerted. 

Work of Eccentric-rod Forces about the Spindle Axis. Refer- 
ring to Fig. 216, we see that if abi is the pressure in the eccentric- 
rod when the eccentric is at a\ then the turning effort of the 
pressure, abi (about the spindle bi), is equal to that of a force 


2 10 1 


FIG. 217. 


FIG. 218. 

ao acting normally to a radius, a i&i. Note that the forces and 
their normal components in the figure are drawn at the spindle 
centers instead of the eccentric centers to avoid confusion of 
lines. By taking all the pressures normal to the line joining the 
eccentric and spindle centers, it is evident that the mean normal 
pressure multiplied by the circumference of a circle whose radius 
is a\b\ would represent the work done by the resultant eccentric- 
rod pressure during a revolution. In Fig. 218 the line, ef, repre- 
sents 27rai&i and the ordinates of the full line curve marked aC 
represent pressures in the eccentric-rod resolved normally to 
the lines joining the eccentric and spindle centers. The area 
between the curve aC and the base 360 represents the work. 
Work of Rotating Weights about the Spindle Axis. The 
rotating weights are constant in weight, are concentrated at G, 


and have variable lever-arms, since the. perpendicular let fall 
from the spindle axis on a vertical through G is variable. In order 
to combine the work of the rotating weights with that of the 
eccentric-rod forces just found, it is best to lay off the work 
diagram to the same base line as that of the eccentric -rod forces 
and to vary the pressures proportionately. Note that the radius 
of the circular path of G about the spindle axis differs from the 
radius of the eccentric centers' circle. Therefore take the moment 
of the rotating weights concentrated at G about the spindle axis 
for each 30 of revolution of the eccentric center and divide this 
moment in each case by the distance between the eccentric center 
and the spindle axis. Lay off the pressure so found at the corre- 
sponding degree position on the line 360 in Fig. 218 and 
obtain the curve in full line marked D. The total work done 
during a revolution is seen to be zero. 

Combining the curves, C and D, we obtain the broken-line 
curve, EHG, Fig .218. The mean ordinate of curve C is of. The 
cross-hatched area, GHE, is the fluctuation of energy which 
must be controlled by the governor acting similarly to a fly- 


GHI in inch-pounds; 
/ = moment of inertia of governor weights in inch-pounds; 
k = desired regulation, viz., greatest allowed variation of speed 

= k times the mean speed; 
N number of revolutions per minute; 

V = velocity of the point at the end of the radius of gyration 
in feet per second.* 

Variation of Load. Inertia governors depend upon centrifugal 
force, linear acceleration, and angular acceleration. Variation 
in the type of governor is due to the variation in the amounts 

* See Power, Nov. 1906. 


of each of the above means of regulation. In one type, for 
instance, a powerful centrifugal force is -developed, aided at change 
of speed by a powerful inertia effect which is largely linear. In the 
Rites type, for instance, the centrifugal force action is relatively 
small, the linear acceleration is also small as the center of gravity 
G is close to the spindle axis s. The angular acceleration, how- 
ever, is very powerful and acts as a steadying influence. 

Inertia Governor during Change of Speed. The centrifugal 
force acts along OG and its moment about the spindle is 

if W = weight of revolving parts concentrated at G', 
R = radius OG (which is variable) in feet; 
N = number of revolutions per minute. 

While the speed of the shaft is changing, the above cen- 
trifugal force will be augmented by a small amount of linear and 
by a considerable amount of angular inertia. 

If the fly-wheel receives the angular acceleration, a), the center 
of mass G receives the linear acceleration OGco, and the weight 

W- develops the inertia force I =OGa), acting along Gi with 


an arm hi about the spindle center s. If this arm is small it 
is evident that the turning moment will be small. 

While the center of gravity of the rotating weights is at G 
if we take the polar moment of inertia of the mass of the rotating 
weights about G as a center we can find the polar radius of 
gyration by dividing the polar moment of inertia by the mass 
and extracting the square root. Let MG = k be the polar radius of 
gyration. During change of speed an angular acceleration equal to 

is developed about G, as shown by the couple marked 7 a . As 
indicated in the figure this inertia effects acts with centrifugal 
force to hasten the movement of the governor bar. 


Counterbalanc.'ng. If the piston, piston-rod, cross-head, con- 
necting-rod, crank-pin, and crank-arms of an engine had no mass, 
the engine would be in equilibrium under what we may call the 
static pressures, or pressures not used in causing non-uniform 
motion of the engine mechanism. As these bodies possess mass 
and variable velocity, unbalanced forces exist that cause shaking 
or vibration. 

Those of the above-mentioned bodies that have a motion of 
rotation can be balanced by other rotating bodies of proper mass 
and radii of action. On the other hand, it is impossible to counter- 
balance any reciprocating mass by any rotating mass. What can 
be done, however, is this. Rotating weights can be so placed as 
to transfer the direction of the unbalanced force from one plane to 
another. If, for example, horizontal shaking forces are undesirable 
(from lack of proper means of absorbing them) by means of rotat- 
ing weights, these forces may be made vertical. 

If we consider the connecting-rod as a beam supported at the 
crank-pin and cross-head pin, the support afforded by each will be 
inversely proportional to its distance from the center of gravity of 
the rod. This is true no matter what the inclination of the rod 
may be. It therefore applies to vertical engines. Therefore (Fig. 

W = weight of the connecting-rod; 
L = length of the rod in inches; 
a = distance the center of gravity of the rod is in inches from 

the cross-head; 

b = distance the center of gravity of the rod is in inches from 
the crank-pin; 

Then Wj- is to be considered as a rotating weight concentrated at 

the center of the crank-pin and Wj- is to be considered as a recip- 


rocating weight concentrated at the cross-head. If this is done 
the connecting-rod may be considered as having no mass. 

In discussing the effect of the inertia of the reciprocating parts 
on the distribution of power we assumed that the connecting-rod 
would have its weight equally distributed between the crank-pin 
and the cross-head. When the inertia of the mass and not the 




weight of the reciprocating parts is considered, the proper division 

K 2 
is W-j^j concentrated at the crank-pin and considered as a rotating 

/ K 2 \ 
weight, and (1 J 2 )^' concentrated at the cross-head and 

sidered as a reciprocating weight, K 2 being the squared radius of 
gyration of the rod about the cross-head axis. In most cases 

K 2 

~j2=%, and for all practical purposes may be so taken. If the 

shaking forces are desired, it is a little more accurate to use W-j 

and W- as the two divisions. (Trans. A. S. M. E., Vol. XXVI.) 

Equivalent Weight at the Center of the Crank-pin. All the 

various rotating weights with their lever-arms may be reduced 
to one weight at the center of the crank-pin. For example, let 
the crank shown in Fig. 219 have a connecting-rod weighing 136 

FIG. 219. 

pounds with a center of gravity at 55% of its length from the 
cross-head pin. 

Weight of one arm(solid), { (10 2 X.78) + (10X10) }2 X .28= 99.68 

of both arms =200 

" . of crank-pin, 9X- 2 /X7X.28 = 55 

Moment of all parts about the center of shaft, 200X5 + 55X10 = 
1550. Dividing by 10", the distance from the center of the crank- 
pin to the center of the shaft, and we find that 155 pounds concen- 
trated at the crank-pin would have the same moment. In addi- 
tion there is 55% the weight of the connecting-rod to be con- 
centrated at the same point or a total of 155 and 75 = 230 pounds. 

WV 2 

The above weight would have a centrifugal force of p-. 




At 210 revolutions per minute this would be 

32 \ 7X7X6X60X60 / 

2900 Ibs. 

WV 2 

The horizontal shaking force would be 5- cos 6 = 2900 cos 

WV 2 

and the vertical shaking force would be rr SU1 

2900 sin 6. 

A good counterbalance can be obtained by the addition of weights 
formed by prolonging the crank-arm in single- or overhung-crank 
engines and prolonging both arms in double-crank arm engines. 
The product of the added weight and the distance of its center 
of gravity from the center of the shaft must be 1550 in the above 
case, or in general the product of the weight and its gravity arm 
equals the sum of the moments of all the rotating weights. 

FIG. 220. 

In general, rotating weights cannot be balanced by a single 
rotating weight, as it is not practically possible to put the center 
of gravity of the counterweight in the plane of revolution of the 
center of gravity of the unbalanced weights. For equilibrium 
it is essential that the moments of all the forces exerted by the 
weights about any axis should be zero. In statics, the force 
exerted by a weight is equal to the weight; in dynamics, the force 
may be put proportional to the product of the weight and its lever- 
arm if the comparison is restricted to bodies having the same 
number of revolutions; if the number of revolutions of the bodies 
compared differed, then their forces would be proportional to the 
product of their weight, their lever-arm, and the square of the 
number of their revolutions, as is apparent from the formula for 


centrifugal force, ~ . 


In Fig. 220, suppose that we wish to counterbalance equivalent 
weights W h and W l concentrated at the crank-pins of a compound 
engine having two cranks at right angles to one another. Let 
W h be balanced by the weights WI H and w 2 h placed opposite the 
crank-pin as shown. Since all parts of the shaft have the same 
angular velocity the moment about the axis of the shaft is zero 

But the moments of the centrifugal forces of Wi h and w 2 h about 
the rotating axis X h X\ h must also be zero to prevent shaking 
about that axis. 

(wi h rfya = w 2 h r 2 h (b + c). 

Similarly, W l R l = wfa 1 + w 2 l r 2 l , 

and w\ l ri l (a + b) = w 2 r 2 (c) . 

The weights on each wheel may be combined into one weight. 
Let W r be the desired resultant weight and R r its radius (distance 
of its center of gravity to the axis of shaft). Then 

The direction and magnitude of the product W r Rr can be easily 
obtained by laying off wi h ri h and wi l ri l as the two sides of a 
right triangle and WrRr will be the hypothenuse. The direction 
in which W r is to be laid off on the wheel is shown by the angle 
at the base of the triangle. In a similar manner a single weight 
may be obtained for the two weights on the other wjieel. 

Shaking-forces. The following method may be used in find- 
ing the shaking-forces due to the inertia of the reciprocating 
masses . and the centrifugal force of the unbalanced rotating 
masses as represented by an equivalent weight rotating at the 
crank-pin center. 

In Fig. 221 the force required to accelerate the reciprocating 
parts in Fig. 205 at every 30 degrees (to a different scale) has 
been combined with an assumed centrifugal force. The direc- 
tion in which forces act is indicated by the order of the let- 

In any horizontal engine let Oa\, Fig. 221, be the centrifugal 


force of all the unbalanced rotating parts. It produces a hori- 
zontal shaking-force Oc\ and a vertical shaking-force cia\ at 
crank-angle aoOai. Let a\A\ be the horizontal shaking-force 
exerted against the left cylinder-head at this crank-angle. It is 
equal to 3(d'c), Fig. 205. Then OA\ indicates the shaking-force at 
the crank-angle a 0ai. Its horizontal component is evidently the 
sum of Oc\ and a\A\. a^A^ and a^A^ are equal to HI and 5/ 
respectively to the new scale (Fig. 205.) 

Suppose counterweights are added in such manner that their 
centrifugal force is equivalent to a force b 2 acting at the crank- 
pin. This force not only counteracts the centrifugal force of the 
unbalanced rotating parts Oa 2 , but also alters the horizontal 
and vertical components of the shaking-forces due to the recipro- 

cating parts. The amount of these alterations is evident when 
we join 61 and A\, b 2 and At, etc. For the previous shaking-force 
OAi is now to be combined with the introduced force bi 0, and the 
result is a shaking-force b\A\, OA 2 is to be combined with b 2 y 
giving b 2 A 2 . Lay off OB\, OB'2, etc., parallel to b\A\, b 2 A 2 , etc. 
Join #o, Bi, B 2 , etc. It is accidental that A 2 falls on the line Obi. 
It is well to note the peculiar direction taken by OB\ and OB 2) 
etc., with reference to the crank-positions to which they belong. 
The effect of increasing and decreasing the value of 61 should be 
noted. In the addition of counterweights it must be remembered 
that their effect varies with the square of the revolutions. If a 
balance exists at one speed it will exist at all speeds ; the shaking- 


force only varies with some function of the square of the speed 
of the parts out of balance. 

It is evident that these circular diagrams may be laid off in 
the following way also. Rectify the crank-circle; lay off the hori- 
zontal or vertical components of the shaking-forces at right angles 
to the rectified circle at the division point indicated by the crank 

For a single-crank horizontal engine without counterbalance 
the horizontal shaking-forces are a maximum at the ends of the 
stroke, and are zero just before and just after the 90-degree position, 

For two cranks 180 degrees apart, with infinite rods the inertia 
of the reciprocating masses, if of equal weight, would balance one 
another; with finite rods this is not the case, and there are two 
maxima and two minima. The shaking, however, is much less 
than in the single-crank engine. 

For a triple^crank engine of equal weights of reciprocating 
parts for each engine the sum of the inertia effects, no matter 
what the length of the connecting-rod, is zero. This can be shown 
by adding /j, / 2 , and / 3 in the following equations and showing 
that the sum is zero. 


cos W +120) 

(0+240) +y cos 2(0 +240) V 

gAri\ L 

The ordinary form of two engines with cranks at right angles 
has smaller shaking-forces than a single engine of equal size, but 
greater shaking-forces than any of the other types mentioned. The 
shaking-force diagrams should not be confused with the tangential- 
force diagrams. 

Determination of Angular Displacement. To insure the satis- 
factory operation of two alternating-current generators when work- 
ing in parallel, the maximum amount of angular variation or dis- 
placement should not exceed 2.5 degrees of phase departure from 
the. mean position (shown by a theoretical engine moving with 
uniform velocity) during any revolution. 


Having designed all the reciprocating and rotating parts and 
their counterweights, and having determined their centers of grav- 
ity, it is necessary to calculate the phase departure of an engine 
intended for work in the class described above. 

At Top 

FIG. 222. 

Curve ol' Displacement 

FIGS. 223, 224, 225. 

The following description is taken from Vol. XXII, Trans. 
A. S. M. E. The method of obtaining the crank diagram will be 
omitted, as the only practical difference between the author's 
method and our own is that he uses the total pressure on the 
piston of each engine, and we used the pressure per square inch in 


obtaining the diagram of crank effort. Twelve crank positions 
are used as in Fig. 205. Fig. 222 represents the individual and 
Figs. 223-225 the combined cards, MM being the line of mean 

"We will now consider the equivalent mass of the rotating 
parts of the engine concentrated at the crank-pin, and as having 
no other velocity than that produced by the positive and negative 
forces represented by those portions of the curve of crank effort on 
either side of the line MM. For convenience in estimating we will 
assume that the applied force is uniform within each of the twelve 
spaces; i.e., this tangential force for each space, expressed in 
pounds above or below the normal MM, is equal to the mean 
height of each space above or below the line MM and is exhibited 
in Table A, page 408. 

" The velocity gained or lost during each twelfth of a revolution 
is deduced as fellows : 

" The equivalent weight of the revolving parts at crank radius 
(2.5') equals 3,367,000 pounds. The velocity of the crank-pin is 

2.5' X2x3.1416x75 revs. 

fi( . - =19.63 feet per second. As the number 

of revolutions per second equals ^ = 1.25, the number of spaces 

traversed per second equals 15, and the time for each space .0667 

, W 3,367,000 

second. The mass of the revolving parts equal ; = O IT^ = 

g 6Z.4 

T 06666 
104,584. Hence -^ = ' g , = .000,000,637,4 equals the accelera- 


tion for a force of one pound. Therefore -TT xF equals the velocity 

gained or lost during each interval, as shown in column A, Table 
A, page 408. 

" Now, if the velocity of the pin be assumed normal at the begin- 
ning of the stroke, the velocity attained up to the end of the various 
spaces will be equal to the algebraic sum of the velocities gained 
during each of the preceding spaces. These velocities attained up 
to the end of each space are shown in column V". As the actual 
velocity of the crank-pin at the beginning of the stroke was not 
normal as assumed, it becomes necessary to correct the values of 



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V" accordingly. The integrated sum of the velocities above and 
below normal attained during one revolution must be zero, there- 
fore the correction to be applied equals the algebraic sum of the 
velocities V" divided by the number of spaces (twelve in this case) . 
Thus the correction is .033, and this amount must be deducted 
from the values of V" in order to arrive at the true velocity attained 
up to the end of the successive intervals. With these true veloci- 
ties, given in column V of Table A, as ordinates, plot the curve 
of velocity V (Fig. 224), where BB represents the mean velocity 
of the pin. 

"From the curve of velocity V (Fig. 224), ascertain the average 
velocity above or below the mean velocity, BB, during each space, 
shown in column V of the table. With these velocities given, the 
space actually passed over during each interval can be readily 
calculated by multiplying the value's of V by .0667, the time for 
one space. The figures in column S" were deduced in this way. 

" If the position of the pin be assumed normal at the beginning 
of the stroke, its distance from normal up to the end of the respective 
intervals will be equal to the algebraic sum of the spaces actually 
passed over, ahead of or behind the mean position, during each 
interval. Therefore the figures in column S' are equal to the 
integrated sum of the preceding figures in column S". As the 
position of the crank-pin at the beginning of the stroke was not 
zero, as assumed, a correction must be applied to the values of S'. 
Since the integrated sum of the distances ahead of or behind the 
mean position must be equal to zero, the value of the correction 
is equal to the ratio of the algebraic sum of the values of S' to the 
number cf spaces. The value of the correction is .0019, and is to 
be added to the values of S' to get the true displacement or dis- 
tance from normal of the pin at the end of each interval, the figures 
for same being shown in column S. Since one foot corresponds to 
22.92 degrees of arc, measured on the crank-pin circle, the number 
of degrees of arc from normal equals the product of the true dis- 
tances in feet from normal (column S) by 22.92. The number of 
degrees of arc from normal deduced in this way are shown in the 
next to the last column of Table A. Finally, as there are 40 
poles on the generator, there will be 20 cycles or changes of phase 
per revolution, therefore one degree of arc equals 20 degrees of 


phase, and the displacement (shown in the last column of table) 
at the end of each interval may be calculated by multiplying the 
corresponding degrees of arc by 20. With the values of the dis- 
placement in degrees of phase from normal as orclinates, the curve 
of displacement (Fig. 225) was plotted, in which CC represents the 
mean position of the crank-pin." 



Rules for Conducting Steam-engine Tests. Code of 1902 A. S. 
M. E.* A large part of this code has been given in the text 
(markedf). Such parts will not be repeated. 

I. Object of the Test. Ascertain at the outset the specific ob- 
ject of the test, whether it be to determine the fulfilment of a 
contract guarantee, to ascertain the highest economy obtainable, 
to find the working economy and defects under conditions as they 
exist, to ascertain the performance under special conditions, to 
determine the effect of changes in the conditions, or to find the 
performance of the entire boiler and engine plant, and prepare 
for the test accordingly. 

No specific rules can be laid down regarding many of the prep- 
arations to be made for a test, so much depends upon the local 
conditions; and the matter is one which must be left mainly to 
the good sense, tact, judgment, and ingenuity of the party under- 
taking it. One guiding principle must ever be kept in mind, 
namely, to obtain data which shall be thoroughly reliable for the 
purposes in view. If questions of contract are to be settled, it 
is of the first importance that a clear understanding be had with 
all the parties to the contract as to the methods to be pursued 
putting this understanding, if necessary, in writing unless these 
are distinctly provided for in the contract itself. The preparations 
for the measurement of the feed-water and of the various quantities 
of condensed water in the standard heat-unit test should be made 
in such manner as to change as little as possible the working 
conditions and temperatures of the plant. 

* Trans. A. S. M. E., 1903. 



II. General Condition of the Plant. Examine the engine and 
the entire plant concerned in the test; note its general condition 
and any points of design, construction, or operation which bear on 
the objects in view. Make a special examination of the valves 
and pistons for leakage by applying the working pressures with 
the engine at rest, and observe the quantity of steam, if any, 
blowing through per hour. 

If the trial has for an object the determination of the highest 
efficiency attainable, the valves and pistons must first be made 
tight and all parts of the engine and its auxiliaries, and all other 
parts of the plant concerned, should be put in the best possible 
working condition. 

The method of testing the valves and pistons for leakage in a 
Corliss engine, or one in which the admission-valves can be operated 
independently of the exhaust-valves, is as follows : Close the two 
steam-valves, open the two indicator-cocks, and admit a full pres- 
sure of steam into the chest by opening the throttle- valve. The 
movement of the starting-bar, first one way and then the other, 
so as to close one exhaust-valve and then the other, causes the 
leakage through the steam- valves to escape from the open indicator- 
cock, where it becomes visible. The quantity of leakage is judged 
by the force of the current of steam blowing out. 

To test the exhaust-valves and piston, the best method is to 
block the fly-wheel, so that the piston will be at a short distance 
from the end of the stroke, and turn on the steam. The leakage 
escapes to the exhaust-pipe, and can be observed at the open 
atmospheric outlet. If the outlet is not visible, and there is a 
valve in the exhaust-pipe, this can be shut and the indicator- 
cock opened, thereby deflecting the steam which leaks and causing 
it to appear at the indicator-cock. In the case of a condensing 
engine where no atmospheric pipe is provided, and there is no 
opening that can be made in the exhaust-pipe in front of the 
condenser, some idea can be obtained in regard to the amount of 
leakage by observing how rapidly the condenser is heated. It is well 
to make these tests with the piston in different positions so as 
to cover the whole range of the length of the stroke. 

Another but more approximate method of testing leakage is 
called the "time method." Instead of observing the steam that 


actually blows through the valves or pistons to be tested, they are 
subjected to full steam-pressure, and when the parts are thoroughly 
heated, the throttle- valve is shut and the length of time observed 
which is required for the pressure to disappear. In testing the 
piston and exhaust-valves, the fly-wheel is blocked as before, and, 
preferably, an indicator is attached, and a line drawn on a blank 
card at intervals of, say, one-quarter of a minute after the valve 
is shut, thereby making a record of the fall of pressure. In a tight 
engine the fall of pressure is slow, whereas in a leaky engine it 
is sometimes very rapid. The relative condition of the engine 
as compared with a tight engine must be judged by an observer, 
who must, of course, have had experience in tests of this kind on 
engines in various conditions. 

The leakage of a piston can always be determined by removing 
the cylinder-head and observing what blows through the open 
end with the pressure of steam behind it. The advantage of the 
"time method" is that it saves the labor and time required in 
removing the cylinder-head and replacing it, which, in cases of 
large engines, is considerable. 

Leakage tests of single-valve engines cannot be made as satis- 
factorily as those of the Corliss type and other four-valve engines. 
The best that can be done as regards the valve is to place it at or 
near the center of its travel, covering both ports, and then make 
the test under full pressure. The valve and piston can be tested 
as a whole by blocking the fly-wheel and opening the throttle- 
valve in the same way as in other engines. 

In testing compound engines for leakage, the work is somewhat 
simplified in case of any one cylinder as compared with a single 
engine. For example, leakage of the high-pressure cylinder can 
be revealed by opening the indicator-cock on the proper end of 
the low-pressure cylinder, the steam-valve of that cylinder being 
open. The test of leakage of the low-pressure exhaust-valves 
and piston when the "time method" is used can be based on the 
indications of the receiver gage instead of using an indicator. 
In that case the fall of pressure due to leakage is read from the 

The tests thus far referred to are qualitative, and not quantita- 
tive. It is practical in some cases to determine the quantity of 


leakage under any set of conditions by collecting the steam which 
passes through, condensing it and weighing it. This can be readily 
done when there is a surface condenser, and it can be done in the ab- 
sence of such a condenser by attaching a small pipe to the exhaust 
and carrying the steam which escapes into a tank of water and 
condensing it. How much dependence can be placed upon the 
results of such a quantitative test as showing the actual quantity 
of leakage which occurs when the valves and pistons are in motion 
must be left to the judgment of the person who makes the test. 

When full information is desired, it is well to test the valves 
and pistons in several different positions, so as to cover the whole 
range of action. 

In Corliss engines the leakage of the piston with the engine 
in operation can be observed by removing the cylinder-head, 
disconnecting the steam- and exhaust-valves at the head end, and 
setting the engine to work with steam admitted at the crank end. 

III. Dimensions, etc. Measure or check* the dimensions of 
the cylinders in any case, this being done when they are hot. If 
they are much worn, the average diameter should be determined. 
Measure also the clearance, which should be done if possible by 
filling the spaces with water previously measured, the piston 
being placed at the end of the stroke. If the clearance cannot 
be measured directly, it can be determined approximately from 
the working drawings of the cylinder. 

Measure also the dimensions of auxiliaries and accessories, 
also those of the boilers so far as concerned in attaining the objects. 
It is well to supplement these determinations with a sketch or 
sketches showing the general features and arrangement of the 
different parts of the plant. 

To measure the clearance by actual test, the engine is caref illy 
set on the center, with the piston at the end where the measurement 
is to be taken. Assuming, for example, a Corliss engine, the best 
method to pursue is to remove the steam-valve so as to have 
access to the whole steam-port, and then fill up the clearance space 
with water, which is poured into the open port through a funnel. 
The water is drawn from a receptacle containing a sufficient quan- 
tity which has previously been measured. When the whole space, 
including the port, is completely filled, the quantity left is measured, 


and the difference shows the amount which has been poured in. 
The measurement can be most easily made by weighing the water 
and the corresponding volume determined by calculation, making 
proper allowance for its temperature. The proportion required 
is the volume in cubic inches thus found, divided by the volume 
of the piston displacement, also in cubic inches, and the result ex- 
pressed as a decimal. In this test care should be taken that no 
air is retained in the clearance space when it is filled with water. 

The only difficulty which arises in measuring the clearance in 
this way is that occurring when the exhaust-valves and piston are 
not tight, so that, as the water is poured in, it flows away and is 
lost. If the leakage is serious, no satisfactory measurement can be 
made, and it is better to depend upon the volume calculated from 
the drawing. If not too serious, however, an allowance can be 
made by carefully observing the length of time consumed in pour- 
ing in the water; then, after a portion of the water has leaked out, 
fill up the space again, taking the time, and measuring the quantity 
thus added, determining in this way the rate at which the leakage 
occurs. Data will thus be obtained for the desired correction. 

IV. Coal. When the trial involves the complete plant, embrac- 
ing boilers as well as engines, determine the character of coal to be 
used. The class, name of the mine, size, moisture, and quality of 
the coal should be stated in the report. It is desirable, for pur- 
poses of comparison, that the coal should be of some recognized 
standard quality for the locality where the plant is situated. 
For New England and that portion of the country east of the 
Alleghany Mountains good anthracite egg coal containing not 
over 10% ash, and semi-bituminous Clearfield (Pa.), Cumberland 
(Md.), and Pocahontas (Va.) coals are thus regarded. West of the 
Alleghany Mountains, Pocahontas (Va.) and New River (W. Va.) 
semi-bituminous and Youghiogheny or Pittsburg bituminous coals 
are recognized as standards. 

V. Calibration of Instruments. All instruments and apparatus 
should be calibrated and their reliability and accuracy verified by 
comparison with recognized standards. Such apparatus as is 
liable to change or become broken during a test, as gages, indicator- 
springs, and thermometers, should be calibrated before and after 
the test. The accuracy of scales should be verified by standard 


weights. When a water-meter is used special attention should be 
given to its calibration, verifying it both before and after the trial, 
and, if possible, during its progress, the conditions in regard to 
water-pressure and rate of flow being made the same in the cali- 
brations as exist throughout the trial. 

(a) Gages. For pressures above the atmosphere, one of the 
most convenient, and at the same time reliable, standards is the 
dead-weight testing apparatus which is manufactured by many 
of the prominent gage-makers. It consists of a vertical plunger 
nicely fitted to a cylinder containing oil or glycerine, through the 
medium of which the pressure is transmitted to the gage. The 
plunger is surmounted by a circular stand on which weights may 
be placed, and by means of which any desired pressure can be 
secured. The total weight, in pounds, on the plunger at any time, 
divided by the average area of the plunger and of the bushing 
which receives it, in square inches, gives the pressure in pounds 
per square inch. 

Another standard of comparison for pressure is the mercury 
column. If this instrument is used, assurance must be had that 
it is properly graduated with reference to the ever- varying zero- 
point, that the mercury is pure, and that the proper correction is 
made for any difference of temperature that exists, compared with 
the temperature at which the instrument was graduated. 

For pressures below the atmosphere an air-pump or some other 
means of producing a vacuum is required, and reference must be 
made to a mercury gage. Such a gage may be a U tube having a 
length of 30 inches or so, with both arms properly filled with 
pure mercury. 

(b) Thermometers. Standard thermometers are those which 
indicate 212 F. in steam escaping from boiling water at the 
normal barometrical pressure of 29.92 inches, the whole stem up 
to the 212-clegree point being surrounded by the steam; and 
which indicate 32 F. in melting ice, the stem being likewise com- 
pletely immersed up to the 32-degree point, and which are 
calibrated for points beyond and between these two reference 
points. We recommend, for temperatures between 212 and 400 
F., that the comparison of the thermometer be made with the 
temperature given in Regnault's Steam Tables, the method required 


being to place it in a mercury well surrounded by saturated steam 
under sufficient pressure to give the desired temperature. The 
pressure should be accurately determined, as pointed out in sec- 
tion (a), and the thermometer should be immersed to the same 
extent as it is under its working condition. 

Thermometers in practice are seldom used with the stems 
fully immersed, consequently when they are compared with the 
standard the comparison should be made under like conditions, 
and practically under the working conditions, whatever those 
happen to be. 

If pyrometers of any kind are used, they should be compared 
with a mercury thermometer within its range, and if extreme 
accuracy is required, with an air-thermometer, or a standard 
based thereon, at higher points, care being taken that the medium 
surrounding the pyrometer, be it air or liquid, is of the same uni- 
form temperature as that surrounding the standard. 

(c) Indicator-springs. See text. 

(d) Water-meters. A good method of calibrating a water- 
meter is the following, reference being made to Fig. 226: 

Two tees, A and B, are placed in the feed-pipe, and between 
them two valves, C and D. The meter is connected between the 
outlets of the tees A and B. The valves E and F are placed one 
on each side of the meter. When the meter is running, the valves 
E and F are opened, and the valves C and D are closed. Should 
an accident happen to the meter during the test, the valves E 
and F may be closed and the valves C and D opened, so as to 
allow the feed-water to flow directly into the boiler. A small 
bleeder, (r, is placed between the valves C and D. The valve G 
is opened when the valves C and D are closed, in order to make 
sure that there is no leakage. A gage is attached at H. When 
the meter is tested, the valves C, D, and F are closed and the 
valves E and / are opened. The water flows from the valve / 
to a tank placed on weighing-scales. In testing the meter the 
feed-pump is run at the normal speed, and the water leaving the 
meter is throttled at the valve / until the pressure shown by the 
gage H is the same as that indicated when the meter is running 
under the normal conditions. The piping leading from the valve 
/ to the tank is arranged with a swinging joint, consisting merely 



of a loosely fitting elbow, so that it can be readily turned into the 
tank or away from it. After the desired pressure and speed 
have been secured, the end of the pipe is swung into the tank the 



\ f 

* IG. 226. 

instant that the pointer of the meter is opposite some graduation 
mark on the dial, and the water continues to empty into the 
tank while any desired number of even cubic feet are discharged, 
after which the pipe is swung away from the tank. The tests 
should be made by starting and stopping at the same graduation 
mark on the meter-dial, and continued until at least 10 or 20 cubic 
feet are discharged for one test. The water collected in the tank is 
then weighed. 

The water passing the meter should always be under pressure 
in order that any air in the meter may be discharged through 
the vents provided for this purpose. Care should be taken that 
there is no air contained in the feed-water. Should the feed- 
water pump draw from a hot-well, the height of the water in the 
hot-well must never be as low as the suction-pipe of the pump. 
In case the speed of the feed-pump cannot be regulated, as occurs 
in some cases where it is driven directly from the engines, a by- 
pass should be connected with the pipe leading from the pump 
to allow some of the water to flow back into the hot-well, if the 


pump lowers the water in the hot-well beyond a given mark, 
The meter should be tested both before and after the engine 
trial, and several tests of the meter should be made in each case 
in order to obtain confirmative results. It is well to make pre- 
liminary tests to determine whether the meter works satisfactorily 
before connecting it up for an engine trial. The results should 
agree with each other for two widely different rates of flow. 

VI. Leakages of Steam, Water, etc. In all tests except those 
of a complete plant made under conditions as they exist, the 
boiler and its connections, both steam and feed, as also the steam- 
piping leading to the engine and its connections, should, so far 
as possible, be made tight. If absolute tightness cannot be 
obtained (in point of fact it rarely can be), proper allowance should 
be made for such leakage in determining the steam actually con- 
sumed by the engine. This, however, is not required where a 
surface condenser is used and the water consumption is determined 
by measuring the discharge of the air-pump. In such cases it is 
necessary to make sure that the condenser is tight, both before 
and after the test, against the entrance of circulating water, or 
if such occurs to make proper correction for it, determining it 
under the working difference of pressure. Should there be exces- 
sive leakage of the condenser it should be remedied before the test 
is made. When the steam consumption is determined by measur- 
ing the discharge of the air-pump, any leakage about the valve 
or piston-rods of the engine should be carefully guarded against. 

Make sure that there is no leakage at any of the connections 
with the apparatus provided for measuring and supplying the feed- 
water which could affect the results. All connections should, so 
far as possible, be visible and be blanked off, and where this cannot 
be done, satisfactory assurance should be obtained that there is 
no leakage either in or out. 

It is not always necessary to blank off a connecting-pipe to 
make sure that there is no leakage through it. If satisfactory 
assurance can be had that there is no chance for leakage, this is 
sufficient. For example, where a straightway valve is used for 
cutting off a connecting pipe, and this valve has double seats with 
a hole in the bottom between them, this being provided with a 
plug or pet-cock, assurance of the tightness of the valve when 


closed can be had by removing the plug or opening the cock. 
Likewise, if there is a drain-pipe beyond the valve, the fact that no 
water escapes there is sufficient evidence of the tightness of the 
valve. The main thing is to have positive evidence of the tight- 
ness of the connections, such as may be obtained by the means 
suggested above; but where no positive evidence can be obtained, 
or where the leakage that occurs cannot be measured, it is of the 
utmost importance that the connections should be broken and 
blanked off. 

Leakage of relief-valves which are not tight, drips from traps, 
separators, etc., and leakage of tubes in the feed-water heater must 
all be guarded against, measured, and allowed for. 

It is well, as an additional precaution, to test the tightness of 
the feed-water pipes and apparatus concerned in the measurement 
of the water by running the pump at a slow speed for, say, fifteen 
minutes, having first shut the feed-valves at the boilers. Leakage 
will be revealed by the disappearance of water from the supply- tank. 
In making this test, a gage should be placed on the pump discharge 
in order to guard against undue or dangerous pressure. 

To determine the leakage of steam and water from a boiler and 
steam-pipes, etc., the water-gage glass method may be satisfactorily 
employed. This consists in shutting off all the feed-valves (which 
must be known to be tight) or the main feed-valve, thereby stop- 
ping absolutely the entrance or exit of water at the feed-pipes to 
the boilers - then maintaining the steam-pressure (by means of a 
very slow fire) at a fixed point, which is approximately that of the 
working pressure and observing the rate at which the water falls 
in the gage-glasses. It is well in this test, as in other work of this 
character, to make observations every ten minutes, and to con- 
tinue them for such a length of time that the differences between 
successive readings attain a constant rate. Generally the condi- 
tions will have become constant at the expiration of fifteen minutes 
from the time of shutting the valves, and thereafter the fall of 
water due to leakage of steam and water becomes approximately 
constant. It is usually sufficient after this time to continue the 
test for one hour, thereby taking six ten-minute readings. When 
this test is finished, the amount of leakage is determined by calcu- 
lating the volume of water which has disappeared, using the area 


of the water-level and the depth shown on the glass, making due 
allowance for the weight of one cubic foot of water at the observed 
temperature. If possible, the gage-glass for this test should be 
attached close to the boiler. 

If there is opportunity for much condensation to occur and 
collect in the steam-pipe during the leakage test, the quantity 
should be determined as closely as desirable and properly allowed 

In making a test of an engine where the steam consumption is 
determined from the amount of water discharged from a surface 
condenser, leakage of the piston-rods and valve-rods should be 
guarded against; for if these are excessive, the test is of little use, 
as the leakage consists partly of steam that has already done work 
in the cylinder and of water condensed from the steam when in 
contact with the cylinder. If such leakage cannot be prevented, 
some allowance should be made for the quantity thus lost. The 
weight of water as shown at the condenser must be increased by 
the quantity allowed for this leakage. 

VII. Duration of Test. The duration of a test should depend 
largely upon its character and the objects in view. The standard 
heat test of an engine, and likewise a test for the simple determina- 
tion of the feed-water consumption, should be continued for at 
least five hours, unless the class of service precludes a continuous 
run of such duration. It is desirable to prolong the test the 
number of hours stated to obtain a number of consecutive hourly 
records as a guide in analyzing the reliability of the whole. 

Where the water discharged from the surface condenser is 
measured for successive short intervals of time, and the rate is 
found to be uniform, the test may be of a much shorter duration 
than where the feed-water is measured to the boiler. The longer 
the test with a given set of conditions, the more accurate the 
work, and no test should be so short that it cannot be divided into 
several intervals which will give results agreeing substantially with 
each other. 

The commercial test of a complete plant, embracing boilers as 
well as engine, should continue at least one full day of twenty-four 
hours, whether the engine is in motion during the entire time or 
not. A continuous coal test of a boiler and engine should be of at- 


least ten hours' duration or the nearest multiple of the interval 
between times of cleaning fires. 

VIII. Starting and Stopping a Test. (a) Standard Heat Test 
and Feed-water Test of Engine. The engine having been brought 
to the normal condition of running, and operated a sufficient 
length of time to be thoroughly heated in all its parts, and the 
measuring-apparatus having been adjusted and set to work, the 
height of water in the gage-glasses of the boilers is observed, 
the depth of water in the reservoir from which the feed-water is 
supplied is noted, the exact time of day is observed, and the 
test held to commence. Thereafter the measurements determined 
upon for the test are begun and carried forward until its close. 
If practicable, the test may be commenced at some even hour 
or minute, but it is of the first importance to begin at such time 
as reliable observations of the water heights are obtained, what- 
ever the exact time happens to be when these are satisfactorily 
determined. When the time for the close of the test arrives, 
the water should, if possible, be brought to the same height in 
the glasses and to the same depth in the feed-water reservoir 
as at the beginning, delaying the conclusion of the test if necessary 
to bring about this similarity of conditions. If differences occur 
the proper corrections must be made. 

Care should be taken in cases where the activity of combustion 
in the boiler furnaces affects the height of water in the gage-glasses 
that the same condition of fire and drafts are operating at one 
time as at the other. For this reason it is best to start and stop 
a test without interfering with the regularity of the operation of 
the feed-pump, provided the latter may be regulated to run so as 
to supply the feed-water at a uniform rate. In some cases where 
the supply of feed-water is irregular, as, for example, where an 
injector is used of a larger capacity than is required, the supply 
of feed-water should be temporarily shut off. 

It is important to use great care in obtaining the average height 
of water in the glasses, taking sufficient time to satisfactorily 
judge of the full extent of the fluctuation of the water-line and 
thereby its mean position. It is important also to refrain from 
blowing off the water column or its connecting pipes either during 
the progress of the test or for a period of an hour or more prior 


to its beginning. Such blowing off changes the temperature of 
the water within and thereby affects its specific gravity and height. 

To mark the height, of water in a gage-glass in a convenient way, 
a paper scale mounted on wood and divided into tenths of inches 
may be placed behind it or at its side. 

(b) Complete Boiler and Engine Test. For a continuous 
running test of combined engine or engines, and boiler or boilers, 
the same directions apply for beginning and ending the feed-water 
measurements as that just referred to under section, (a). The 
time of beginning and ending such a test should be the regular 
time of cleaning the fires, and the exact time of beginning and 
ending should be the time when the fires are fully cleaned, just 
preparatory to putting on fresh coal. In cases where there are 
a number of boilers, and it is inconvenient or undesirable to clean 
all the fires at once, the time of beginning the test should be 
deferred until they are all cleaned and in a satisfactory state, 
all the fires being then burned down, to a uniformly thin condition, 
the thickness and condition being estimated and the test begun just 
before firing the new coal previously weighed. The ending of the 
test is likewise deferred until all the fires are satisfactorily cleaned, 
being again burned down to the same uniformly thin condition 
as before, and the time of closing being taken just before replenish- 
ing the fires with new coal. 

For a commercial test of a combined engine and boiler, whether 
the engine runs continuously for the full twenty four-hours of the 
day or only a portion of the time, the fires in the boilers being 
banked during the time when the engine is not in motion, the begin- 
ning and ending of the test should occur at the regular time of 
cleaning fires, the method followed being that already given. In 
cases where the engine is not in continuous motion, as, for example, 
in textile mills, where the working-time is ten or eleven hours out 
of the twenty-four, and the fires are cleaned and banked at the 
close of the day's work, the best time for starting and stopping a 
test is the time just before banking, when the fires are well-burned 
down and the thickness and condition can be most satisfactorily 
judged. In these, as in all other cases noted, the test should be 
begun by observing the exact time, the thickness and condition 
of the fires on the grates, the height of water in the gage-glasses of 


the boilers, the depth of water in the reservoir from which the 
feed-water is supplied, and other conditions relating to the trial, 
the same observations being again taken at the end of the test, 
and the conditions in all respects being made as nearly as possible 
the same as at the beginning. 

IX. Measurement of Heat-units Consumed by the Engine. The 
measurement of the heat consumption requires the measurement 
of each supply of feed-water tp the boiler, that is, the water 
supplied by the main feed-pump, that- supplied by auxiliary 
pumps, such as jacket-water, water from separators, drips, etc., 
and water supplied by gravity or other means; also the deter- 
mination of the temperature of the water supplied from each 
source, together with the pressure and quality of the steam. 

The temperatures at the various points should be those apply- 
ing to the working conditions. The temperature of the feed- 
water should be taken near the boiler. This causes the engine 
to suffer a disadvantage from the heat lost by radiation from 
the pipes which carry the water to the boiler, but it is, never- 
theless, advisable on the score of simplicity. Such pipes would 
therefore be considered a portion of the engine-plant. This con- 
forms with the rule already recommended for the tests of pumping- 
engines, where the duty per million heat-units is computed from 
the temperature of the feed-water taken near the boiler. It 
frequently happens that the measurement of the water requires 
a change in the usual temperature of supply. For example,, 
where the main supply is ordinarily drawn from a hot-well, in 
which the temperature is, say, 100 F., it may be necessary, 
owing to the low level of the well, to take the supply from some 
source under a pressure or head sufficient to fill the weighing- 
tanks used, and this supply m.ay have a temperature much below 
that of the hot-well, possibly as low as 40 F. The temperature 
to be used is not the temperature of the water as weighed in 
this case, but that of the working temperature of the hot- well. 
The working temperature in cases like this must be determined 
by a special test and included in the log-sheets. 

In determining the working temperatures, the preliminary or 
subsequent test should be continued a sufficient time to obtain 
uniform indications and such as may be judged to be an average 


for tjie working conditions. In this test it is necessary to have 
some guide as to the quantity of work being done, and for this 
reason the power developed by the engine should be determined 
by obtaining a full set of diagrams at suitable intervals during 
the progress of the trial. Observations should also be made of 
all the gauges connected with the plant and of the water heights 
in the boilers, the latter being maintained at a un form point, 
so as to be sure that the rate of feeding during the test is not 
sensibly different from that of the main test. 

The heat to be determined is that used by the entire engine 
equipment, embracing the main cylinders and all auxiliary cylin- 
ders and mechanism concerned in the operation of the engine, 
including the air-pump, circulating-pump, and feed-pumps, also 
the jacket and reheater when these are used. No deduction is 
to be made for steam used by auxiliaries, unless these are shown 
by the test to be unduly wasteful. In this matter an exception 
should be made in cases of guarantee tests, where the engine 
contractor furnishes all the auxiliaries- referred to. He should, 
in that case, be responsible for the- whole, and no allowance should 
be made for inferior economy, if such exists. Should a deduction 
be made on account of the auxiliaries being unduly wasteful, the 
method of waste and. its extent, as compared with the wastes of 
the main engine or other standard of known value, shall be 
reported definitely. 

The steam pressure and the quality of the steam are to be 
taken at some point conveniently near the throttle- valve. The 
quantity of steam used by the calorimeter must be determined 
and properly allowed for. 

X. Measurement of Feed-water or Steam Consumption of 
Engine. The method of determining the steam consumption 
applicable to all plants is to measure all the feed-water supplied 
to the boilers and deduct therefrom all the water discharged by 
separators and drips, as also the water and steam which escapes 
on account of leakage of the boiler and its pipe connections and 
leakage of the steam main and branches connecting the boiler 
and the engine. In plants where the engine exhausts into a surface 
condenser the steam consumption can be measured by determining 
the quantity of water discharged by the air-pump, corrected for 


any leakage of the condenser, and adding thereto the steam used 
by the jackets, reheaters, and auxiliaries as determined inde- 
pendently. If the leakage of the condenser is too large to satis- 
factorily allow for it, the condenser should, of course, be repaired 
and the leakage again determined before making the test. 

In measuring the water it is best to carry it through a tank 
or tanks resting on platform weighing-scales suitably arranged 
for the purpose, the water being afterwards emptied into a reservoir 
beneath, from which the pump is supplied. 

The simplest apparatus of this kind, having a capacity of, say, 
6000 pounds of water per hour, consists of a small hogshead con- 
nected to the suction-pipe of the pump or injector, and an ordinary 
oil-barrel mounted on a platform scale, the latter being supported 
by the hogshead on one side and by a suitable staging on the 
other. The barrel is filled by a cold-water pipe leading from the 
source of supply, and this should be a IJ-mch pipe for pressures 
not less than 25 pounds per square inch. The outlet- valve to the 
barrel is attached to the side close to the bottom and should be at 
least 2J inches in diameter for quick emptying. Where large quan- 
tities of water are required the barrel can be replaced by a hogs- 
head, and two additional hogsheads can be coupled together for a 
lower reservoir. The capacity reached by this arrangement, when 
the weighing-hogshead is supplied by a 2J-inch valve under 25 
pounds pressure and emptied through a 5-inch valve, is 15,000 
pounds of water per hour. For still larger capacity it is desirable 
to use rectangular tanks made for the purpose and having the 
weighing-tank arranged so that the ends overhang the scales and 
the reservoir below, the outlet- valve, consisting of a flap-valve, 
covering an opening in the bottom 6 or 8 inches square. With 
rectangular tanks this system can be employed for any size of 
stationary engine ordinarily met with. 

Where extremely large quantities of water must be measured, 
or in some places relatively small quantities, the orifice method of 
measuring is one that can be applied with satisfactory results. In 
this case the average head of water on the orifice must be deter- 
mined, and, furthermore, it is important that means should be at 
hand for calibrating the discharge of the orifice under the condi- 
tions of use. 


The corrections or deductions to be made for leakage above 
referred to should be applied only to the standard heat-unit test, 
and tests for determining simply the steam or feed-water consump- 
tion, and not to the coal tests of combined engine and boiler equip- 
ment. In the latter no correction should be made except for leak- 
age of valves connecting other engines and boilers, or for steam 
used for purposes other than the operation of the plant under test. 
Losses of heat due to imperfections of the plant should be charged 
to the plant, and only such losses as are concerned in the working 
of the engine alone should be charged to the engine. 

In measuring jacket-water or any supply under pressure which 
has a temperature exceeding 212 F., the water should first be 
cooled, as may be done by first discharging it into a tank of cold 
water previously weighed, or by passing it through a coil of pipe 
submerged in running and colder water, preventing thereby the 
loss of evaporation which occurs when such hot water is discharged 
into the open air. 

XI. Measurement of Steam Used by Auxiliaries. Although 
the steam used by auxiliaries embracing the air-pump, circulating 
pump, feed-pump, and any other apparatus of this nature, suppos- 
ing them to be steam-driven, also the steam-jackets, reheaters, etc., 
which consume steam required for the operation of the engine is 
all included in the measurement of the steam consumption, as 
pointed out in Article X, yet it is highly desirable that the quan- 
tity of steam used by the auxiliaries, and in many cases that used 
by each auxiliary, should be determined exactly, so that the net 
consumption of the main-engine cylinders may be ascertained and 
a complete analysis made of the entire work of the engine plant. 
Where the auxiliary cylinders are non-condensing, the steam con- 
sumption can often be measured by carrying the exhaust-steam 
for the purpose into a tank of cold water resting on scales or through 
a coil of pipe surrounded by cold running water. Another method 
is to run the auxiliaries as a whole, or one by one, from a spare 
boiler (preferably a small vertical one) and measure the feed- 
water supplied to this boiler. The steam used by the air and cir- 
culating pumpb may be measured by running them under, as near 
as possible, the working conditions and speed, the main engine and 
other auxiliaries being stopped, and testing the consumption by 


the measuring apparatus used on the main trial. For a short 
trial, to obtain approximate results/measurement can be made by 
the water-gage-glass method, the feed-supply being shut off. When 
the engine has a surface condenser, the quantity of steam used 
by the auxiliaries may be ascertained by allowing the engine 
alone to exhaust into the condenser, measuring the feed-water 
supplied to the boiler and the water discharged by the air-pump 
and subtracting one from the other, after allowing for losses by 

XII. Coal Measurement. (a) Commercial Tests. In com- 
mercial tests of the combined engine and boiler equipment, or those 
made under ordinary conditions of commercial service, the test 
should, as pointed out in Article VII, extend over the entire period 
of the day; that is, twenty-four hours, or a number of days of 
that duration. Consequently the coal consumption should be 
determined for the entire time. If the engine runs but a part of 
the time, and during the remaining portion the fires are banked, 
the measurement of coal should include that used in banking. It 
is well, however, in such cases to determine separately the amount 
consumed during the time the engine is in operation and that con- 
sumed in the period while the fires are banked, so as to have com- 
plete data for purposes of analysis and comparison, using suitable 
precautions to obtain reliable measurements. The measure- 
ment of coal begins with the first firing, after cleaning the furnaces 
and burning down at the beginning of the test, as pointed out in 
Article VIII, and ends with the last firing at the expiration of the 
allotted time. 

(6) Continuous-running Tests. In continuous-running tests 
which, as pointed out in Article VII, cover one or more periods 
which elapse between the cleaning of the fires the same principle 
applies as that mentioned under the above heading (a), viz., the 
coal measurement begins with the first firing after cleaning and 
burning down, and the measurement ends with the last firing 
before cleaning and burning down at the close of the trial. 

(c) Coal Tests in General. When not otherwise specially under- 
stood, a coal test of a combined engine and boiler plant is held to 
refer to the commercial test above noted, and the measurement of 
coal should conform thereto. 


In connection with coal measurements, whatever the class- 
of tests, it is important to ascertain the percentage of moisture 
in the coal, the weight of ashes and refuse, and, where possible, 
the approximate and ultimate analysis of the coal, following, 
all the methods in detail advocated in the latest report of 
the Boiler Test Committee of the Society. (See Vol. XXI, 
page 34.) 

(d) Other Fuels than Coal. For all other solid fuels than coal 
the same directions in regard to measurement should be followed 
as those given for coal. If the boilers are run with oil or gas, the 
measurements relating to starting and stopping are much simplified 
because the fuel is burned as fast as supplied, and there is no- 
body of fuel constantly in the furnace, as in the case of using; 
solid fuel. When oil is used it should be weighed, and when 
gas is used it should be measured in a calibrated gas-meter or 

XIII-XVI. See text. 

XVII. Speed. There are several reliable methods of ascer- 
taining the speed or the number of revolutions of the engine 
crank-shaft per minute. The simplest is the . familiar method 
of counting the number of turns for a period of one minute with 
the eye fixed on the second-hand of the timepiece. Another 
is the use of a counter held for a minute or a number of minutes; 
against the end of the main shaft. Another is the use of a reli- 
able tachometer held likewise against the end of the shaft. The 
most reliable method, and the one we recommend, is the use of a, 
continuous-recording engine register or counter, taking the total 
reading each time that the general test data are recorded and 
computing the revolutions per minute corresponding to the differ- 
ence in the readings of the instrument. When the speed is above 
250 revolutions per minute, it is almost impossible to make a 
satisfactory counting of the revolutions without the use of some 
form of mechanical counter. 

The determination of variation of speed during a single revo- 
lution, or the effect of the fluctuation due to sudden changes of 
the load, is also desirable, especially in engines driving electric 
generators used for lighting purposes. There is at present no 
recognized standard method of making such determinations j and 


if such are desired, the method employed may be devised by the 
person making the test and described in detail in the report. 

One method suggested for determining the instantaneous 
variation of speed which accompanies the change of load is as 
follows : 

A screen containing a narrow slot is placed on the end of a 
bar and vibrated by means of electricity. A corresponding slot in 
a stationary screen is placed parallel and nearly touching the 
vibrating screen, and the two screens are placed a short disance 
from the fly-wheel of the engine in such a position that the ob- 
server can look through the two slots in the direction of the spokes 
of the wheel. The vibrations are adjusted so as to conform to 
the frequency with which the spokes of the wheel pass the slots. 
When this is done the observer viewing the wheel through the 
slots sees what appears to be a stationary fly-wheel. When a 
change in the velocity of the fly-wheel occurs, the wheel appears 
to revolve either backward or forward according to the direction 
of the change. By careful observations of the amount of this 
motion the angular change of velocity during any given time is 

Experiments that have been made with a device of this kind 
show that the instantaneous gain of velocity upon suddenly 
removing all the load from an engine amounted to from 1/6 to 
1/4 of a revolution of the wheel. | 

XVIII-XXV. The greater portion of the matter contained in 
these paragraphs will be found in the text. 

t Trans. A. S. M. E. Standard Rules. 


Superheated Steam. Steam in contact with its liquid, all 
temperature changes having cease-d, is a vapor and obeys the laws 
of vapors. The pressure or tension of a vapor can neither be 
increased nor decreased by changes of its volume as long as its 
temperature is kept constant. 

If steam is not in contact with its liquid its temperature may be 
raised; in other words, it may be superheated. In a cylinder we 
may have superheated, dry, and wet steam at the same instant. 
This is due to the fact that dry steam is a very poor conductor 
of heat. It will be found, in fact, that the great value of super- 
heated steam lies in its quality as a poor conductor of heat. The 
term contact is to be interpreted as immediate contact. 

If the steam in the upper portion of the steam-space of a 
vessel containing steam and water is heated, either the pressure 
or the volume or both will increase. Steam from a boiler may be 
superheated by passing it through a series of highly he: ted tubes 
on its way to the engine. The fact that the volume of the super- 
heater is constant does not prevent the steam from being heated 
at constant pressure, since the steam is used in the engine as fast 
as it is generated and theoretically the reciprocating piston might 
be replaced by one moving in a cylinder of indefinite length. 

This process of heating the steam is performed in a superheater. 
This consists in a series of cast-iron or steel tubes or steel tubes 
clad in cast iron placed in the back connection or behind the 
bridge-wall of fire tubular boilers, over the tubes at the mid- 
third of their length in water tubular boilers, or they may be placed 
in a separate setting with a separate grate which is independently 
fired. The furnace-gases at temperatures between 600 F. and 
1500 F. flow around the superheater tubes and the steam passes 
through them. 

Saturated steam at a high pressure contains more heat than 
the same weight of steam at a lower pressure. If therefore steam 
at a high pressure is allowed to expand, forming eddies, but (with- 
out doing external or useful work) to a lower pressure, the excess 



of heat mentioned above will be utilized, first in drying the 
steam if it be wet, and then in superheating it. This effect is due 
to the formation of eddies. This form of superheating takes 
place in throttle-governed engines, in high-speed engines at 
short cut-off, and in the Peabody calorimeter. In nozzles, 
eddying is prevented and the energy is utilized in giving the 
mass of steam additional velocity. 

Adheating is a term applied to the superheating of saturated 
steam by mixing it with highly superheated steam in such propor- 
tions that the mixture will possess a prescribed degree of superheat. 

Foster Superheater. The Foster superheater is made up of 
elements each of which consists of two steel tubes, one inside 
of the other and so connected that the steam from the boiler 
passes through the annular space between the tubes, the inner 
tube being closed at both ends. Cast-iron discs that taper in a 
cross-section from the inner to the outer periphery are shrunk 
on the outer tube. These annular gill-flanges are placed close 
to one another and not only protect the steel tube from cor- 
rosion but possess a large surface for the absorption of heat, 
and also provide a large mass for the retention of heat and so 
prevent rapid fluctuations of temperature in the superheat of 
the steam. 

This superheater is designed with a view to avoid the necessity 
for flooding devices or any form of connection between the water- 
space of the boiler and the superheater. The protection afforded 
by the external covering of cast iron is ample to prevent damage 
to the surface during the process of steam-raising. It is evi- 
dent that if water is admitted to the interior of a superheater 
there is danger of scale forming in the tubes, which must result 
in a loss of efficiency or stoppage of the circulation. It is also 
evident that care and intelligence must be exercised in drain- 
ing out a superheater which has been flooded before putting it 
into service, and in properly setting the valves in the pipes to 
prevent the engine receiving a charge of water." * 

The economic advantages of superheated steam have been 
known since 1826. After a large number of trials its use was 
abandoned on account of troubles arising from improper lubri- 
cants and improper packing for flange-joints and piston-rod 

* Catalog of makers 



and valve-stem stuffing-boxes. The superheaters becoming in- 
crusted internally were burnt out or were eaten up by the sul- 
phuric acid formed in damp soot; the cylinders were scored 
because the tallow used for lubrication was decomposed at high 
temperatures into non-lubricating elements; the joints leaked 
from the increased stresses due to increased expansion caused 
by higher temperatures. Fortunately the advent of mineral 

Detail of Return Header 

FIG. 227. 

oils, metallic packing, and the general advance in the manufac- 
ture of structural material used in engineering processes and 
increased scientific knowledge now make its use possible and 

Four methods of reducing cylinder waste, due to initial con- 
densation, are open to us compression, jacketing, compounding, 
and superheating. It is pretty well settled that economy lies in 
reducing clearance surface to the smallest possible amount and 
that heavy compression in many cases causes loss. Jackets are 
expensive, are seldom properly operated, and are of value only 


in special cases, arid these cease to exist with a proper degree 
of superheating. Superheaters have also reduced the number of 
cylinders required in compounding. A test will be given of a 
compound engine and superheater that produced results un- 
rivalled by many triple-expansion engines. In connection with 
steam-turbines marked advance in economy is produced by the 
use of superheaters. 

The greatest percentage increase in economy is obtained 
when superheaters are applied to uneconomical engines. Wasteful 
little engines with a superheater have nearly the same economy 
as large engines of the same type with a superheater. In other 
words, the economy of the small one has been increased more 

FIG. 227 Foster Superheating Tube. 

than that of the large one. If the reheaters placed in the re- 
ceivers of multiple-expansion engines do not superheat they are 
worse than useless. Using high-pressure steam to re-evaporate 
water to low-pressure steam in a receiver is uneconomical. The 
water should be taken out by a separator and returned to the 
boiler, whilst the dry steam should be superheated to prevent 
initial condensation in the next cylinder. 

"The purposes of superheating steam, as practised in the 
past and as recognized at present, are the following: 

"1. Raising the temperature which constitutes the upper 
limit in the operation of the heat-engine in such manner as to 
increase the thermodynamic efficiency of the working fluid. 

''2. To so surcharge the steam with heat that it may surrender 
as much as may be required to prevent initial condensation at 
entrance into the cylinder and still perform the work of expan- 
sion without condensation or serious cooling of the surrounding 
walls of the cylinder. 

"3. To make the weight of the steam entering the condenser, 
and its final heat charge, a minimum, with a view to the reduc- 
tion of the volume of the condensing water and the magnitude 
and cost of the air-pump and condenser system to a minimum. 


"4. To reduce the back pressure and thus to increase the 
power developed from a given charge of steam and the efficiency 
of the engine. 

"5. To increase the efficiency of the boilers both by the reduc- 
tion of the quantity of the steam demanded from the original 
heating-surface and by increasing the area of the heating-sur- 
face employed to absorb the heat of the furnace- and flue- gases, 
and also by evading the waste consequent upon the production 
of wet steam. 7 ' (Thurston.) 

If the steam entering a cylinder is only superheated enough 
to give dry saturated steam at cut-off the range of temperature 

_ m 

of the Carnot cycle is unchanged and there is no increase 


of economy from 1. The other four sources of economy de- 
pend upon one fundamental fact the poor conductivity of dry 
steam. When steam-gas passes through the cylinder, the walls 
of the latter do not fluctuate so much in temperature. The 
hot gas gives up its heat slowly to the walls, and on the exhaust- 
stroke the latter give up their heat slowly. In other words, the 
slightest film of water on the cylinder walls renders possible a 
wider fluctuation of metal temperature with its consequent waste 
of heat than occurs when superheated steam is used. If one 
thermal unit is wasted in superheating steam it prevents the 
waste of 2| thermal units caused by initial condensation. 

Thermal Laws. From experiments Regnault determined the 
specific heat of steam to be .48. The best values, at present, are 
those of Knoblauch and Jacobs. Their values show that the 
specific heat is a variable ranging from .48 to .6, increasing with 
increasing pressure, but decreasing with increasing temperature at 
the same pressure. As no authoritative figures have been decided 
upon, we shall assume the specific heat at constant pressure to be 
constant and to be .48. See Fig. 228 and Table XV, 

Hence the total heat required to heat feed-water from ti to T 2 , 
evaporate it at that temperature and then superheat it under a 
constant pressure (corresponding to T 2 ) to some temperature T s is 

or , = 2 

Intensity of Superheating Required. If L = latent heat of steam 
entering a cylinder, A = its weight in pounds per stroke, x --= the 


percentage of initial condensation, then zAL=the amount of heat 
lost by the steam in condensing. 























s v 



o s 



N N 

s s 








N ' 


V N 





,- - 






















*" * 












A i 






















572 a 

212^F 302F 392 

Temperature * 
FIG. 228. C p of Superheated Steam. (Knoblauch and Jacobs.) 

FIG. 229. Separately Fired Superheater. 

If superheated steam had to possess that number of thermal 
units in excess of those it possesses as saturated steam, it is evident 



that the necessary temperature of the superheated steam would 
be obtained from the equation 

ASA(T s -T 2 )=xAL, or 

where T s is the temperature of the superheated steam, 
T 2 is the temperature of the saturated steam. 

If the above were true there would be very little gained by 
the use of superheated steam, as we would simply substitute one 

FIG. 230. Foster Superheater and Water Tubular Bailer. 

waste for another. It is found in practice that a very much lower 
and more feasible degree of superheat is necessary. It varies, of 
course, with the size and type of engine, ratio of expansion, etc. 
In some cases it is only .4 or .5 of the amount indicated by the for- 
mula above. For example, assume the latent heat of steam to aver- 
age 875 B.T.U. For each per cent of initial condensation there is a 
loss of 8.75 B.T.U. If only .4 of this amount is required when the 
steam is superheated, the number of degrees of superheat required 

for each per cent of initial condensation would be 
degrees approximately. Hence the (approximate) rule. 

.4 X8.75 


= 7 



To have the steam dry at cut-off, the necessary number of 
degrees of superheat of the steam on entrance to the cylinder is 
equal to the percentage of initial condensation that would exist 
without superheating multiplied by 7. The superheat on leaving 
the superheater would depend on the length, character, and cover- 
ing of the steam-main and valve-chest. 

The following data (Trans. A. S. M. E., Vol. XXV) are instruc- 
tive in showing loss of pressures and temperatures in the steam- 
cycle as well as the economy in the use of superheated steam in an 
engine that is economical when using saturated steam.* 

1 Date of test 

May 27 

June 19 

July 17 

July 24 

2. Condition of steam: superheated or sat- 





3 Net water per hour to boiler. 





4c Gage-pressure at boiler 





5. Gage-pressure near throttle 





6. Gage-pressure receiver 





7 Vacuum near engine inches 





8 <<! at condenser inches 





8a c Barometer temperatures of steam, de- 
grees Fahrenheit f 

30 16 

29 80 

30 01 


9. Leaving the superheater. . 

766 4 



10. At the engine- throttle 


736 3 


11 Entering the H.P. cyl 


658 6 


12. Leaving the H.P cyl 





13. Entering the L.P. cyl 
14. Leaving the L.P, cyl 

Amount Steam was Superheated, 
Degrees Fahrenheit. 
15. Leaving the superheater, 
16 At the engine-throttle 


352 5 


374 5 


393 3 


17 Entering the H.P. cyl 




18 Leaving the H P cyl 

84 7 



19 Entering the L P cyl . 

146 2 

141 4 



Horse-power and Economy. 
20 Revolutions per minute 

103 28 

102 34 

102 49 


21 I H P developed by engine 

474 5 

420 4 



22 Water in pounds per I. H.P. . 

9 76 




23. Maximum temperature to which the feed- 
water could be heated by the exhaust 
of the engine 





24. Coal in pounds per hour (Standard of 
Civil Engineers of London) . 

1 265 

1 257 



Bore of cylinders, 16.07" and 28.03", measured when hot. 
Length of stroke, 42 inches 
Revolutions, 103. 

* See also Trans. A S M E. ; Vol XXII. 


Average data and results of (Schmidt) separate superheater test : 

1. Heating-surface in square feet 642 

2. Grate-surface in square feet 4 

3. Duration of test in hours 14 

4. Pressure of steam furnished superheater (gage) 147.4 

Temperatures in Degrees Fah. by Mercury Thermometer: 

5. Steam entering the superheater 365 . 6 

6. ' ' leaving " 809 . 1 

7 Amount steam was superheated 443 . 5 

Total Quantities. 

8. Steam passing through the superheater in pounds 58,025 

9. Heat imparted to the steam in B.T.U 12,352,000 

10. Total moist coal fire in pounds 1,473 

11. " dry coal consumed in pounds 1,426 

12. Coal burnt per square foot of grate-surface per hour in pounds. . 25.5 

13. Heat imparted to the steam in the superheater per pound of coal 

burned in B.T.U . 8.662 

14. Equivalent evaporation from and at 212 F. in pounds per pound 

of dry coal. . 8.97 

15. Heat of combustion of the dry coal in B.T.U. per pound 14,060 

16. Efficiency of the superheater based on the heat of combustion of 

the coal in per cent 61.6 

Combined Economy of Boiler and Superheater. 

17. Actual evaporation of the boiler per pound of dry coal in pounds. . 8 . 586 

18. Coal burnt in the superheater in pounds per pound of steam 

passing through it . 02458 

19. Coal burnt in superheater in pounds per pound of coa burned at 

boiler, Item 17Xltem 18 211 

20. Actual evaporation of the combined boiler and superheater 7.090 

21. Factor of evaporation of the combined boiler and superheater. . 1 .421 

22. Equivalent evaporation in pounds per pound of dry coal from 

and at 212 F. for the combined boiler and superheater 10.07 

23. Efficiency of the combined boiler and superheater based on the 

heat of combustion of the coal in per cent 69 . 2 

From the above data the student should calculate : 

1. The loss of heat in the main steam-pipe. 

2. The probable superheat at cut-off, assuming 20% conden- 
sation would occur in tests 1 and 2 if dry steam were used. 

3. Obtain the paper in the Trans. A. S. M. E., Vol. XXV, 
and check one or more percentages of superheating. 

4. Assume the mean temperature of flue-gases in super- 
heater at 1500 F., what is the rate of transmission per square 
foot per degree difference of temperature per hour? 

5. Draw a diagram similar to that on page 197, showing the 
thermal losses in the engine cycle. 

6. Assume a cross-compound Corliss engine 24" x44" x60"; 
870 I.H.P.; revs., 72; clearance H.P. cyl., .03%; cut-off, .33 
stroke; initial pressure abs., 114; pressure at cut-off, 104.4 
abs.; steam accounted for at cut-off, 12.28 pounds; proportion 


of feed-water accounted for at cut-off, .866; steam-pipe, 80 feet 
long. . .Find the diameter of the steam -pipe; assume charac- 
ter of lagging and bends and find probable heat loss. Design a 
Schmidt separate superheater that will supply dry steam at 
cut-off, viz., answer the following requirements: Heating- 
surface; grate-surface; coal; degree of superheat leaving the 
superheater, at the throttle, entering cylinder. 
The designer calls attention to the following points in the design : 
"The double-beat poppet-valves have seats surrounded by the 
inlet steam in such a way that the expansion of the seat is equal 
in extent and effect to that of the valve, thus overcoming com- 
pletely the characteristic defect of ordinary designs of their type of 
valve, namely, excessive leakage at any temperature other than 
the particular one at which they were originally ground. The 
inlet-valves are driven by the ordinary trip-gear of the builders, 
with vacuum dash-pots, with the addition of a simple linkage 
which controls the closure of the valve independent of the extent 
of closing motion imparted by the dash-pot, and thus prevents 
slamming or partial closing of the valve. The exhaust-valves are 
actuated by a system of links devoid of cams, always in connection 
with the eccentric, except when hand-actuated at starting or stop- 
ping, and which keeps the valve stationary during the forward 
stroke, as is necessary when using the poppet type, arid all joints 
are adjustable for wear. 

"The stuffing-boxes are on long necks to take them well away 
from the superheat, and the piston-rod stuffing-boxes have metallic 
packing provided with water-jackets, which, however, have never 
been used. The piston-packing consists of two simple iron spring 
rings with joint plates. 

"The high-pressure cylinder is so designed that the working 
portion of its band is a simple cylinder without ribs, all connections 
to the cylinder, such as valve-cleats, lagging-bosses, inlets, and 
exhaust -gages, etc., being at the ends. . . . 

"The only trouble noticed with lubrication was a smoking due 

to the carbonization of the animal or vegetable constituents of 

the original oil used. On notifying the oil-makers of this trouble 

they at once produced an oil which eliminated all complaint. 

"The operation of the superheater has proved to be simple; 


in fact it is easier to run than a boiler, since the pyrometer-dial 
is the only thing to be watched. Fire is never built in the super- 
heater without a flow of steam through the coils, under which 
conditions there is no sign of deterioration. The temperature is 
readily regulated, even when the engine is shut down for changes. 
in the mill, which happens once or twice in twenty-four hours in 
regular operation. If the shutdown is for more than a few minutes 
a small flow of steam is secured by "cracking" the throttle- valve 
and allowing a little steam to blow through the engine, but for 
short stoppages this is not necessary. The pipes, cylinders, and 
receiver are covered with 3 inches of a standard magnesia covering 
over pipes and flanges." 

Temperature-entropy Diagram for Superheated Steam. In Fig. 
231 let erfitzSse^ represent the heat-units expended in heating 
one pound of water from ti F. to t 3 F. and converting it into 
dry saturated steam at that temperature. To superheat this 
steam at constant pressure to some temperature T a requires 

Q = .48(T.-T 3 ) thermal umts=fdQ=f T8 A8dT. 
Hence the entropy 

where T s and T 3 are absolute temperatures in degrees Fahrenheit. 
This increase of entropy may be laid off from e 4 to some point e t 
and erecting a perpendicular = T s the point T 8 is found. By assum- 
ing a series of values for T 8 a series of points in the curve s 3 T 8 f 
may be found. The curve when drawn to the usual scale is 
practically a straight line and may be so assumed. That being the 

case the value of e 

1 s 
2 * 

If this steam expands adiabatically the line 7 7 /5 2 w 4 indicates 
the thermal changes that occur. When the temperature dropped 
to ^ the intersecting of the vertical and the saturated steam 
Aines show that at that instant the steam is dry saturated steam. 
Fuither expansion to ti is followed by the condensation of a part 

of the steam equal in amount to - of a pound. 


If the fraction -j^- = x , its value may be obtained from the 

+e 3 e4+e 4 e 5 , 

AS(T S -T 3 )2 


rri i 

* o 

whence x may be determined. 

The efficiency of the added heat is theoretically ' If 


the practical gain were no greater than this superheaters would 
not repay their cost and trouble. 

Superheated Steam in Compound Engines. It is practical to 
superheat steam to such a temperature that it will be superheated 

: ! 

FIG. 231. 

at exhaust-opening in the high-pressure cylinder, but it would 
not be practical, nor is it indeed necessary, to have the initial 
temperature so high that the steam is superheated at cut-off in 
the low-pressure cylinder. It is better to divide the superheating 
into two stages and put superheating coils in the receiver between 
the two cylinders. Elsewhere it has been pointed out that any 
moisture in the steam from the high-pressure cylinder should be 
separated out so that the superheating is only applied to dry 
saturated steam. It was further pointed out that the receiver 


steam should be superheated from 50 to 100 degrees; this would 
require 1.5 square feet of pipe surface to the I.H.P. 

Durability of Superheaters. Superheaters are best preserved 
by keeping a continual supply of steam flowing through them. 
The amount of this steam should be proportional to the amount 
of coal burning on the grate. In case the engine should slow down 
or have a reduced load the amount of steam passing through the 
superheater should not be diminished. It is better to bleed 
the excess into heaters or into steam used for other purposes. 
If this cannot be done the fires in superheating boilers should be 

In tests of a B. & W. boiler, 5000 sq. ft. heating-surface, 1000 
sq. ft. of superheating surface, a chain grate-stoker 75 sq. ft. 
surface, the following facts are stated: 

1. Superheat varied from 125 to 175 as the boiler horse- 
power varied from 350 to 750. 

2. The horse-power of the superheater varied from 35 to 
100 as the boiler horse-power varied from 350 to 700. 

3. From 7 to 17% of the b.h.p. was produced in the super- 
heater as the b.h.p varied from 100 to 900. 

When the main boilers were forced there was a greater weight 
of gases at a higher temperature passing around the superheating 

Steam-nozzles. When steam flows through a nozzle it was 
shown (page 216) that 

V 2 

At first sight it would appear that the weight and velocity 
of steam delivered by a steam-nozzle would continually 
increase with a continuous lowering of the back pressure 
or the pressure at the exit end of the nozzle. A close 

V 2 
inspection of the formula for ^~ shows that it includes also the 

final volume of expansion, which increases and therefore tends 
to diminish the value of the velocity of exit. The demonstra- 

* Trans. A. S. M. E., Vol. XXVI. 


tion below of what is known as Zeuner's formula shows that 
the maximum weight of steam that an orifice can deliver is ob- 
tained when the back pressure, p 2 , is .57 'p^ 

For steam, if p 2 becomes less than .57pi, the delivered weight 

160 150 140 130 120 110 100 90 80 TO 60 50 40 30 20 10 .10 

FIG. 232. 

remains constant. For perfect gases, if p 2 becomes less than .528pi, 
the delivered weight decreases. If p 2 is kept constant and p\ 
is increased the weight delivered of steam or perfect gases is 

A nozzle must be designed to give definite results under defi- 
nite conditions. It can be shown that a very slight alteration 


of the conditions may produce a very considerable change 
in the results. Nozzles may easily be 'too long or too short, 
may expand too rapidly or not rapidly enough, and the orifice 
at the entrance may be too well rounded or the reverse for exist- 
ing conditions. If the nozzles are too long the work of friction 
is carried off as heat. Short nozzles are desirable with low pres- 
sures; with high pressures longer nozzles may be used. If 
the cross-section of the nozzle increases too rapidly the stream 
acquires too many cross-eddies. 

The maximum weight of steam discharged through a simple 
orifice is determined by the maximum velocity in the orifice, 
although there may be higher velocities on the discharge 
side accompanied by very low gas density. The maximum 
velocity in the orifice never exceeds 1500 feet per second no 
matter how great the difference between the initial and dis- 
charge pressures. 

Given the ratio , p b and the weight of steam discharged 

per second by Zeuner's formula the necessary cross-section at 
any part of the nozzle can be found. For a maximum Wi the 

value of should be .57. The best results are obtained when 


the steam-pressure in the nozzle gradually decreases to the back 
pressure, otherwise vibratory waves shown in Fig. 232 are set up. 

Hence if p 2 is less than .57p l} design the throat or narrowest 
part of the nozzle for a p 2 = .57pi and design the exit for a p% 
equal to the pressure at the discharge end of the nozzle. 

Zeuner's Formula. We have seen that the work of adiabatic 

expansion is T^> which becomes * if the expansion is 

carried to p 2 = Q. .*. l ^ = E, the intrinsic energy. 
T~ 1 

V 2 2 
The formula -~- = (E 1 + piV 1 )(E 2 +p 2 v 2 ) may be writtea 


It is desirable to get rid of v 2 and obtain results in terms of 


If the area of the orifice in square feet is A, the volume dis- 
charged per second will be AV. As the above formulas apply 
to one pound weight, it is evident that v 2 is the specific volume 
per pound at p 2 , the pressure at the section of area A. 

Weight discharged per second = = W. 

But V 2 = i>i >". Therefore 
Weight discharged per second 

- w 

To obtain the maximum weight discharged per second let 

= r Then the weight W becomes a maximum when 

2. i+ r 

(r) r (r) r becomes a maximum. 

Differentiating and equating the first differential to zero, 

i / 2 \-L_ 

Dividing by rr we obtain r= ( Tij r ~ 1 - 

Substituting the values of ^=77 for steam and air we have: 
For air, 7- = 1 .41 ; r = .528 = -A 

For dry saturated steam, 7- = 1 . 135 ; r = .577 = -. 


The restriction in the weight discharged is caused by the 
actual formation or the tendency to form in the orifice a vend 
contractd, or contracted vein, in which the pressure does not drop 
below the value of p 2 indicated above, no matter what the 
final or exterior pressure may be. From the contracted orifice 
the pressures should decrease to the final pressure. 

Steam-turbines. To understand the action of steam on the 
blades of a steam-turbine, the student should review the deriva- 
tion of certain formulas in hydraulics. 

We have seen that it requires the expenditure of Wh foot- 
pounds of energy to raise W pounds through a height of h feet; 
that in falling freely through this height the body would acquire a 

V 2 
velocity of V feet per second; that h = -^- , and hence the energy 

V 2 

possessed by the body due to its velocity of motion is W-~- . 

Bodies at rest or moving uniformly, whether in straight or 
curved lines, cannot be under the influence of any unbalanced 
force. In other words, all forces acting on a body moving uni- 
formly must be reducible to pairs composed of equal and opposite 
forces. A train of cars moving uniformly down a grade has all 
resistances exactly equal to the impelling force of gravity; a fly- 
wheel moving uniformly does no work it is actively useful only 
when it is moving non-uniformly. 

The force necessary to produce a change of velocity in a body 
is proportional to the product of the mass of the body and the 
amount of change in the velocity produced in the time that the 
force has been acting on the body. 






where m measures the increase in velocity, i.e., acceleration per 

unit of time 

A small force- F, acting for a long time, T, or a large force, F, 
acting for a short time, T, will change the velocity of a body of mass 


M from to V feet per second, or add V feet per second to any 
previously acquired velocity. If a body has any velocity, V feet 
per second, we may suppose that such velocity was acquired from 
zero velocity in one second; therefore 


If a body took T seconds to acquire a velocity of V feet per 

second (initial velocity = 0), the mean velocity would be -~ and 


the space passed over would be T. If, however, a body has a 

velocity of V feet per second, we may suppose that velocity was 


acquired in one second, hence the space passed over would be -^ 

under the action of a force F=AIV. 

As energy is the product of a force and the distance through 
which that force was exerted, the energy exerted on the body will 

F MV 2 WV 2 
be the product of M F and -^ or 5 or ^ . In other words, the 

z z zg 

energy put into the body is equal to the energy it possesses in 
virtue of its acquired velocity. 

As g is always expressed in feet per second, it is wise to express 
all other quantities, in the same equation, in terms of units homo- 
geneous with it. Hence, in dealing with a continuous stream, it is 
convenient to express M, the mass of the fluid stream passing per 

second, by - , where w is the weight of the fluid per cubic foot, 


A is its cross-sectional area in square feet, and F is its velocity in 
feet per second. The force in pounds that could be exerted by 
such a stream, if its line of action were diverted through 90, would 

wAV 2 
be FQQ=MV or , since the velocity in the original direction 


is reduced to zero. Hence the force exerted is proportional to the 
velocity squared. Analyzed, the expression is (wAV) pounds mul- 
tiplied by feet per second divided by feet per second. The pro- 
duction of this force causes no loss of energy so long as no portion 
of the force is exerted through a distance. In fact, if the stream is 
bent through 180 by means of a frictiomess bend, the force that 


the stream exerts on the bend in the direction of the original 
stream is twice the above amount, or 


V 180 ^ 

Friction, of course, causes a reduction of energy, since the frictional 
resistance has its line of action parallel but opposite to the line of 
motion of the stream. 

A derivation of a general formula for the force exerted when 
the line of action of a stream is bent through any angle a will now 
be given. 

Impulse Due to a Jet Moving on a Curved Blade. Let a 
stream, cross-section A square feet, weight w pounds per cubic 
foot, velocity V feet per second, measured where cross-section of 
stream is A square feet, strike a frictionless vane, BC, of such 
curvature that the stream is deflected through a degrees, as shown 
in Fig. 170. Each ds of the vane will react radially an amount 
exactly equal to the radial force exerted by the stream through 
having its line of action diverted. The amount of this radial force 
on any elementary ds is equal to the centrifugal force of the 
weight of the fluid that is on that area at that instant. 

wA-ds-V 2 
dr r = . 

The horizontal component of this force, dF x , = dF r sin 0. 

The vertical component of this force, dF y , = dF r cos 6. 

The total force exerted on the whole vane along the X and Y 
axes will be equal to the integral of the above quantities between 
the limits, and a, for the angle 6. 

/* a /* - 

^0:= / dF x = / <iFrsin# = / - 1 sin# 

^t/O t/O t/0 $r 

/" /* a /* a t^7lc?sF 2 

^= / ^7,= / dFr cos 6= I - cos 6 

t/o t/o t/o </r 

Keeping in mind that 6 and dd measure the lengths of arcs at unit 
radius, we may get rid of the variable, r, by substituting ds = rdd. 


Hence Fx== f Q 


wAV 2 

sin Odd = (1 - cos a) , 

i7 t7 


*A* WAV2 ' 

cos dad = sin a. 


FIG. 233. 

But the weight of fluid flowing per second, W, =wAV. Hence 

WV WV WV / _ 

F x = - (1 -cos a), F y = -- sin a, F r = -- v 2(1 cos a). 

O \J u 

Knowing the totals, F x and F v , the direction of the resultant 
impulse F r is given by 

F x 1-cosa 

r y sin a 
(/? being the angle between the totals F y and F r .) 

NOTE. The above formulas may be gotten more simply thus: If 
the stream is turned through 90 and the velocity in the original 

direction becomes zero the force is -- . Hence for any other angle, 


= and 2F = ; we have F x = ---- (1 cos a) and F v = -- sin a. 

y y 



The values of F given for the angles 90 and 180 may be ob- 
tained from these general equations by making a = 90 or 180. 
The value of cos a is additive if the angle through which the 
stream is turned is greater than 90 and subtractive if it be less 
than 90. 

In the derivation of the formula a indicated the angle through 
which the stream is turned. Frequently, however, the supple- 
mentary angle or the angle beween the entering and departing 
streams is used. Hence the preceding formulas often appear as 


F x = --- (1+cosa), 


WV . 

F y = -- sin a, 


F r = --- \2(l + cosa). 

A modification of the preceding lines of motion is seen in 
Fig. 171, where the entering and leaving streams are inclined at 

FIG. 234. 

angles a and /? with F, the line of action of the required force. 
For a stationary and frictionless vane the entering and departing 
velocities must be equal since there can be no loss of energy. The 


WV t 

impulse due to V f in its line of action is - . The reaction due to 

V 2 in its line of action is - . Resolving these forces along the 


line of action of F and we have 

WV e 

PI = F e cos a = - cos a, 



As V . = V 2 , ^ = - -'(cos a + cos /?) . 


The action or the impulse of the stream against the bucket when 
stationary, as in the preceding examples, or when moving, as in 
the examples that follow, and whether friction is regarded or dis- 
regarded, may be found by the application of the following rule. 

Draw the line of motion of the vane or bucket. Find the 
velocities of entrance and departure of the stream relative to the 
bucket section. Resolve these velocities along the line of motion 
of the bucket. To obtain the impulse multiply the algebraic sum 

W wAV 
of these components by = - . Hence 

u \J 

iv AV 
F = - (T t -cosa-f F/cos/?), 


where A is the cross-section in square feet at the section where V 
is measured, Vi is the relative velocity of entrance and V f is the 
relative velocity of exit from the wheel. 

The same result will be obtained if F t - is the absolute velocity 
at entrance and V f the absolute velocity at exit from the wheel, 
since the sum of the components of these velocities is the same 
as the sum of the components of the relative velocities. 

The work done per second will evidently be the above force 
multiplied by the velocity per second of the vane. If v is that 
velocity then the work = Fv. 

In Fig. 235 let the bucket move in the direction of F with the 
velocity v. The velocity of entrance relative to the bucket sec- 
tion is V v. The velocity of departure is necessarily the 



same. Resolving the velocity of entrance along F and we obtain 
(V v) cos = V v. Resolving the velocity of departure relative 
to the bucket section along F and we obtain (F v) cos a. As 

FIG. 235. 

the stream has been turned through more than 90 these quan 
tities are to be added. 


F= -V- 


In Fig. 236 let the bucket move in the direction F with the velocity 
v. If the absolute velocity of entrance of the stream be V e , its 
velocity relative to the bucket section on entrance is F; in the 
direction shown and, on departure, the relative velocity is V f =Vj, 
neglecting frictional and other resistances. Resolve the relative 
velocities along the direction of F and obtain 

F= V f (cos a + cos ft) 


Vf equals V+ since there is no friction, v is the velocity of 
the bucket and F 2 is the absolute final velocity of the stream. 
From the velocity diagrams, other equivalents may be obtained 

for F 


F = (V t cos A-D + F/cos/?), 


F = (F e cosAF 2 cos). 


Blade Angles. If the entering stream struck the back of a 
revolving blade the motion of the latter would be impeded and 
the efficiency would be lowered. The angle a of the back 
of the blade on the entering side in Fig. 236 is determined by 

FIG. 236. 

the relations that exist between V e , v and A. Hence a can be 
determined from the relation found as follows : 

sin (a A) sin a cos A cos a sin A 

V t sin a 

sin a 
cot a= cot A 

= cos A cot a sin A, 

F e sin A* 

Shock is avoided, then, by having the entering angle of the 
back of the blade parallel to the relative motion of the 
entering stream. On the other hand, the angle of leaving is 
one of the principal factors in determining the efficiency of the 
mechanism. The difference in the energy of a stream on entering 
and on leaving a blade must appear either as friction or as useful 
work. Efficiency is increased by making the energy rejected as 
small as possible. 

If a stream has an absolute velocity, V, before it meets a 
resistance and an absolute velocity of V 2 afterwards the loss of 



energy of the stream is 

W(V?- V 2 2 ) wA.V t (V 2 - 7 2 2 ) 


2g 2g 

loss of energy may appear as the work of friction, useful work in 
moving the vane against a resistance or both combined. 

Disregarding friction, let us determine the conditions of maxi- 
mum efficiency. It will evidently depend upon making V% or bd, 
Figs. 236 and 237, a minimum. 

bd 2 = ed 2 +eb 2 -2(ebxef). 
Disregarding friction, 

ab = bc = ed, 

bd 2 = ab 2 +eb 2 -2(ebxef), 
ae 2 =ab 2 +eb 2 +2(eb xbg), 
bd 2 = ae 2 ~2(eb xbg) -2(eb xef), 
bd 2 = V 2 2 = V 2 -2v(Vi cos a +Vi cos /?), 
V 2 2 = V? -2vVi(cos a +cos /?) . 

Maximum Efficiency under Various Conditions. 1. If the 
stream is turned through 180 both a and y9 will be zero, hence 
cos # = cos/? = l. 

F 2 = and v = Vt=-^. 

For the highest theoretical efficiency the stream should be 
turned through 180 and the velocity of the vane should be one- 
half the velocity of the entering stream. 

Fig. 237. 

2. As a rule, it is not feasible to have a = ^ = 0. When V s , 
a, and /? are fixed, V 2 has a minimum value when (vV;) is a maxi- 
mum. If V s and a are fixed in amount, a circular arc can be 


passed through a, b, and e, since we have given a chord and the angle 
subtended by the chord and as Vi must be less than V . Let abe 

., XT lJ Vi sm a 
be the circular arc and b the varying point on it. JNow - - - 

is the area of the triangle abe and so is ae multiplied by the 
altitude. Since sin a is a constant, anything that increases the 
area of the triangle increases the value of vVi. The altitude 
perpendicular to ae is a maximum when b is the middle point of 

the arc abe. Hence vV is a maximum when v = Vi or ^ = 9' 

Therefore, when F, a, and /5 are fixed, the best economy occurs 
when the speed of the blade, v, is such that vcos-^=-^. 

3. If V f is fixed in direction, and we know that /?=a, but 
we do not know the value of either. (Fig. 237.) 

As F is fixed in direction, A and F e cos A are constant. 
Fs cos /? = Fi cos a. F2 2 is made a minimum by making vVi cos /? 
= (eb xbg) a maximum. As egr is a constant, the maximum rectangle 
or product of its parts, when divided into two parts, occurs when 

the parts are equal, viz., form a square of which ^r is a side. 

Hence v = JF cos A is the condition of maximum efficiency. 

De Laval Steam-turbines. In the De Laval steam-turbine, 
Fig. 238, steam-jets issuing from suitably designed nozzles im- 
pinge against the vanes or buckets of a single turbine- wheel 
designed and constructed to revolve at revolutions varying from 
30,000 per minute in the 10-H.P. size to 11,000 per minute 
in the 300-H.P. size. The steam enters the passageway be- 
tween buckets at one side of the wheel, passes through at 
constant pressure, but with rapidly diminishing velocity, and 
is discharged on the other side into the atmosphere or con- 
denser. The diagrammatic sketch, Fig. 239, shows how the 
pressure in the nozzle decreases from that of the boiler to 
that of the atmosphere or condenser. The turbine-wheel re- 
volving in this low pressure has, therefore, low frictional resist- 
ance on the sides and the thrust in the direction of the axis 


is practically very small. It further shows that the maximum 
velocity of the steam is generated in one nozzle in one stage and 
the total absorption of this velocity takes place in one running 
wheel. The simplicity of this arrangement is as remarkable 
as are the velocities that it necessitates. 

The centrifugal stresses generated in the turbine-wheels of 
this design requires not only the use of special metal but special 

FIG. 238. The De Laval Turbine Wheel and Nozzles. 

forms and special care in balancing. The wheels are made of 
forged nickel steel, flaring (in a cross-section) from the periphery 
to the hub, solid in the larger sizes to avoid loss of strength due 
to perforation even for the axle, and mounted on a flexible shaft 
to avoid the vibration stresses that are inevitable when an imper- 
fectly balanced mass is rotating with a rigidly fastened shaft. 
Even if the wneel were perfectly symmetrical in shape, at the 
high speeds at which these wheels rotate the slightest difference 
in mass density would set up vibration waves which would pro- 


duce enormous stresses. The velocity of rotation of the tur- 
bine-shaft is reduced by one or more pairs of spiral gears, ratio 
of ten to one, meshing in opposite directions to transfer all axial 
thrust to the slower-moving shaft. 

Theoretical Design. The expansion in the Laval nozzle is 
practically adiabatic. From the entropy diagram we may easily 

Condenser or 
exhaust pressure 

Condenser or 
'exfiaust pressure 

FIG. 239. Diagrammatic Sketch of De Laval Turbine. 

calculate the loss of heat as heat when steam expands adiabatic- 
ally from any given pressure to that of the atmosphere or to a 
given pressure in a condenser. The heat so lost is the value of 

V t 2 

(HiH 2 ) in the equation -^- = (Hi~H 2 )778. Hence we may 

Z 9 

obtain the value of V t (theoretical velocity). In the De Laval 
nozzles this velocity may reach 2500 or 3000 feet per second 
or more. The practical value of F = . 


It was shown on page 456 that when V t is given in direction 
and amount and that a=/? the maximum efficiency of the tur- 
bine is obtained when the lineal velocity of the vanes, v, = 7, cos A. 

This makes bd at right angles to the direction of v and gives a 

y e 2 _ 7 2 2 
maximum value to ~ ^ ^ ' ls 20 degrees, JF cosA = the 

required lineal velocity of the buckets = v = .477*. Hence if V e 
has a value of 2500-3000 feet per second, the velocity of the buckets 
will have to be 1175 to 1410 feet per second. The actual velocity 
of the periphery of the wheel in the 10-H.P. size is 525 feet per 
second and 1100 in the 300-H. P. size. The makers claim that 
these reductions are made not so much for the difficulties arising 
in the turbine construction as for economic reasons. 

In the discussion of efficiencies, for the sake of simplicity all 
references to the quantitative effect of friction were omitted. In 
practice this feature merits close attention. In the chapter on 
entropy, it was shown that when one mass moved over another 
friction was created. This friction increases in turbines with the 
density of the steam and velocity of the moving vanes. In adia- 
batic expansion, considerable quantities of water are formed and 
the presence of this water materially increases the friction. Hence 
we see the economic reason of reducing the velocity of the vanes. 
Whilst other forms of turbines have much lower velocities, the 
amount of surface that the steam passes over is also materially 
increased and it is doubtful if the friction is any less in them. 

In practice A = 17-20, a=/? = 30, 7 3 = .707 Z - to .857* The- 

, V? .057,2 Vt* 7 2 2 

indicated work per pound of steam = ~ .3rr TT-- 

2g 2g 2g 2g 

With the large machines the .3 may decrease to .10 or .15.* 

Curtis Turbine. In this turbine the total expansion of the 
steam is divided between two to four sets of nozzles in place of 
being confined to one set. Further, instead of one rotating wheel 
absorbing the kinetic energy of the steam from each of these sets 
two or more such wheels are used. The latter are separated from 
each other by stationary discs carrying fixed vanes which alter the 
direction of the steam as it leaves the rotating wheels in such 
manner that its velocity may be partially utilized in the next 

* Stodola. 



rotating wheel. The diagrammatic sketch, Fig. 240, shows the loss 
of pressure and the gain in velocity of the steam in two sets of 
nozzles. In its flow through each set of stationary and rotating 
wheels the static pressure is practically constant whilst the velocity 
head is absorbed in the work of the rotating wheels. The cross- 
hatched area shows the division of the actual work among the 

Loss from ^x ^ 
Eddies, Nozzles, 
Bemaining Velocity 

FIG. 240 Diagrammatic Sketch ol Curtis Turbine. 

moving wheels, the dotted line showing the limits of the theoretical 

In the De Laval turbine it is necessary to make V 2 as small as 
possible, as it represents waste velocity. We have seen that the 
velocity of steam leaving a frictionless and stationary vane is the 
same as the entering velocity. If the energy in the steam leaving 


a rotating wheel is not wasted, but can be utilized in a succeeding 
rotating wheel, there is no necessity to reduce V 2 . This permits 
a reduction of v, the lineal velocity of the turbine- vanes. In fact, 
if there are six rotating wheels, their velocity may be theoretically 
one-sixth that which is required when there is only one rotating 

This reduction in the required velocity of the rotating vanes 
without too great loss in efficiency is extremely desirable for 
many mechanical reasons. In the first place the problems of 
construction in the turbine itself are rendered less difficult, and, 
in the next place, direct connection with generators becomes pos- 
sible. The high speed of the De Laval turbine has to be reduced 
by gearing, which is not practical in large sizes; for instance, the 
largest De Laval turbine is a 300-kw. unit, whilst that of the Curtis 
type is 6000 kw. 

In the De Laval turbine a defect was found in the friction 
that resulted from wet steam moving at high velocity past the 
vanes. In the Curtis turbine the velocity is lowered and the 
steam is drier, but there is a considerable increase in the surface 
over which the steam must pass. Rateau * claims that the Curtis 
design is an inefficient one and will disappear. On the other hand,, 
Jacobus t asserts that "if we take the figures given for the water 
consumption of the De Laval, Rateau, and Curtis wheels and 
compare them with the results obtained for corresponding powers 
and pressures of the Westinghouse-Parsons turbine we will 
find that they are practically the same." In making comparisons 
care must be taken to compare turbines of similar dimensions 
operating at equal power. In turbines, only the delivered or 
brake horse-power is measured. As the friction is practically the 
same at all powers, it is evident that at low powers the water 
consumption will be excessive when compared to that at high ones 
of the same machine. 

Fig. 241. The turbine-blade may be sketched in if we have the 
velocity of entrance AB, the peripheral velocity CB, and the bL de- 
angle J. For A C will be the angle of the back of the blade at entrance, 
and if there is no friction CD = AC will be the relative and CE the 

* Trans. A. S. M. E., Vol. XXV, p. 788 
f Ibid., p 774. 



FIGS. 241 and 242. (From Thomas' Steam-turbines.) 



absolute velocity of departure, as DE = CB. For a series of buckets, 
as in the Curtis turbine, where AB represents the initial velocity 
and NP the final velocity a diagram similar to Fig. 179 may be 
drawn. In this theoretical diagram AC = CD, EK=KL, etc. If 
the friction is to be considered then CD = (1 - f)AC, KL = (1 - /') EK, 
etc., where /, /' are the coefficients of friction. 
Stodola has the following (Fig. 243) : 

FIG. 243. 

The friction in a nozzle has the effect of decreasing the exit 
velocity to the value 

where c denotes the theoretical value 

= \ / 2g(H l - # 2 )778. 

The coefficient <j> can be taken in long nozzles with condensation 
at .95 to .90; in short nozzles with free exhaust at .95 to .975. 
Combinir.g GI with u again gives (relative velocity) w 1} but this 
is decreased by friction and eddy currents during exhaust to the 
smaller value 


in which depends upon the velocity Wi, on the form of the 
blades and other factors. It appears that the smallest value of 
</> is .7; with smaller values of w 1} <f> would increase, and wi h 
Wi = 820 feet might approximately be estimated at from .85 to .9. 
Finally w 2 and +u give the velocity of exit c 2 . 

These losses by friction expressed as loss of work are, in the 

in the blade-channel, 

The "indicated work " per pound of steam is 

__ p __ 
Ll ~ 

c 2 2 

__ __ __ 

2g 2g 2g 2g' 

The indicated efficiency, 


" = r - 

The indicated power in H.P., 


Ni = --~, where (W = weight of steam per second). 

Deducting from NI the wheel and bearing friction we get the 
effective power at the turbine-shaft, >? e = Tp. 

In any case, if the absolute velocities at entrance to, and exit 
from, any wheel be resolved in the direction of motion of the 
buckets, or, in other words, 

Let c e and c a = the peripheral components of the initial and 

final absolute velocities, 
P = total peripheral force, 
M = mass of steam flowing per second, 
u = peripheral velocity of the wheel, 

then work per second, Pu, =M(c a c e )u. (See page 452.) 


The following data and Fig. 244 are taken from Thomas on 
Steam Turbines: 

T corresponding to 160 pounds abs. = 824 F. abs. 
T " " 14 " " =670F. " 

Steam initially dry. Velocity of turbine- blades = u =400 feet 
per second. Angle of nozzles = 20. 

In the second stage the quality has been increased from the 
heat arising from friction from .868 to .912. In this stage, steam at 
14 pounds, quality .912, is to expand to a ; vacuum of 29" or a 
temperature of 540 absolute. 

Fig. 247 illustrates the general arrangement of the Curtis 
turbine. The fly-ball governor at the top regulates in a positive 
manner the opening of one or more small pistons, shown at the 
right of the cut. These control the admission of steam and there- 
fore the power of the governor. 

Parsons Turbine (Fig. 248). An examination of the dia- 
grammatic sketch of the Parsons turbine will disclose the following 
peculiarities : 

1. The buckets or vanes of the rotating discs of the Parsons 
type are carried on revolving drums. 

2. The stationary vanes are carried from the casing and 
have no diaphragm reaching to the axle or shaft. 

3. There are no nozzles as in the Curtis type. In their 
place are stationary vanes uniformly spaced over the entire 
periphery. As a result all the vanes of the turbine are in con- 
tinuous use. 

4. If we call a circle of stationary and a circle of revolving 
vanes a stage, that the number of stages is very great, ranging 
from 50 to 100. They are not shown in this sketch because of 
the scale required for clearness. 

5. That the velocity of the steam increases in the stationary 
circle of vanes. In the revolving vanes it first decreases and 
then increases. 

6. That the fall of pressure is practically uniform and occurs 
in both the stationary and revolving circles of vanes. 

7. That the entering angle of the rotating vanes is almost a 
right angle and the leaving angle is quite acute, the shape differ- 



FIG. 244. 




FIG. 245. 



The entrance and exit angles of the buckets, 
whether moving or stationary, are not neces- 
sarily made equal to each other, but are 
modified to suit the energy distribution aimed 
at in any given case. 

FIG. 246. 


FIG. 247. 


, Stationary 

Condenser or 
Exhaust Pressure 



cc 5j 








Steam Velocity 


Condenser or 
Ekhaust Pressure 

FIG. 248. Diagrammatic Sketch of Parson's Turbine. 


ing materially from the lunes of the Curtis type, and hence is 

easily recognized. 

The outlet-opening between two buckets of a rotating vane 
being smaller than the inlet opening, compels the steam to expand 
and accelerate its motion, since a constant mass must pass between 
the vanes. Force is required to produce this acceleration, and 
this force produces a reaction which acts in the direction of the 
rotating vane. Therefore the steam acts by impulse on the enter- 
ing face of the vane and by reaction on the leaving face. 

In the De Laval turbine we noted that the wheel revolved in 
low-pressure steam, and that the pressure was nearly the same on 
both sides of the wheel. The Parsons turbine-vanes revolve in 
high-pressure steam, and the pressures are unequal and must be 
balanced either by balancing pistons or by an opposing turbine. 
The general construction of the Parsons turbine is shown in the 
cross-section, Fig. 249. 

Clearance is objectionable, but often unavoidable. The sta- 
tionary blades in the Parsons turbine are carried by the casing, and 
they must come as close as possible to the revolving drum to compel 
the steam to pass between the blades. This clearance area is annu- 
lar in shape in the Curtis and in the Parsons turbine, the inner 
diameter of the ring in the one being the diameter of the shaft 
and in the other that of the steam-drum. Any vibration of the 
axis, due to whipping, causes a considerable motion at a radius as 
large as that of a drum, hence the clearance in the Parsons turbine 
must be greater than that in the Curtis type. 

Analysis of the Parsons Turbine. In discussing this turbine we 
shall consider a stationary and a revolving row of blades as mak- 
ing a set or stage. The kinetic energy generated by the fall of 
pressure in the stationary row is absorbed through its impulse 
on the blades of the revolving row. The reaction caused by the 
increase in the relative velocity from Vi to v 2 (Figs. 250 and 250# is 
absorbed in the revolving row. The work done is then made up 
of three parts. 

1. The total kinetic energy created by fall of pressure 
in the first row. 

2. The reaction due to the increase of relative velocity 
in the second row. 


3. The kinetic energy in the steam due to its absolute 
velocity at exit from .the revolving row. 

Since the velocity at entrance to the first row of stationary 

Stationary M M & JS M 

FIG. 250a. 

blades is negligible, the total kinetic energy generated there is 
per pound of steam per second 



The reaction work due to the increase of relative velocity 
from Vi to V2 is 

The kinetic energy due to the absolute velocity of the steam 
at exit from the first row of revolving blades is -^- . Hence 

The net work done in the first stage is K=K 8 +K m -^- . 

The total work done in the moving blades is K t =K a +K m . 

The fraction called the "degree of reaction " is-^. 

In the second stage, if Vi is the absolute velocity of entrance 
to the stationary row of blades and F 2 the absolute velocity at 
exit from the revolving row, and if the relative velocity in the 

Stag? A 

Stage B < 

Stage C <t 

FIG. 251. 

second row is increased from Vi to v% as before, the net work done 
will be (Fig. 251) 

Fi 2 -F 2 2 v 2 2 -v l 2 


Condenser or 

Exhaust Pressure 

Fia. 252. Diagrammatic Sketch of Hamilton-Holzwarth Turbines. 


If there are (n 1) similar stages the total work for n stages, 
including the first, will be 

2g 2g 

+ (n 

The Hamilton-Holzwarth turbine is, like the Parsons tur- 
bine, a full-stroke turbine; that is, the steam flows in one con- 
tinuous belt or veil in screw line through the turbine. 

The steam works only by impact, not by reaction, thus avoid- 
ing the balancing pistons of Parsons. 

In the stationary blades, which reach up to the shaft in order 
to restrict the dangerous clearance to a minimum, the steam 
has a chance to expand and reach a certain velocity and a cer- 
tain direction in which it impinges the next running- wheel. 

The absolute velocities of the steam in this turbine are higher 
than in the Parsons turbine, but they are lower than in the Curtis 
and much lower than in the De Laval. In this turbine the steam 
is expanded in every stationary blade down to a certain pressure 
and accelerated up to a certain velocity, which is nearly exhausted 
in the following running-wheel. 

Steam-Engine versus the Steam-Turbine. The steam-engine 
and the steam-turbine are often compared and it is desirable 
to point out the advantages of each. The steam-engine finds 
its most efficient territory in the high ranges of pressure whilst 
the turbine is best adapted to low ranges.* To deal with low 
pressures the steam-engine cylinders become enormous in size 
hence difficult to construct, operate, and repair the mechanical 
friction losses are excessive and the same is true of thermal losses 
due to varying temperature of the cylinder walls due to thermal 
cyclic changes. At low pressures the steam-turbine is free of 
these excessive mechanical and thermal losses. 

A combination of the steam-engine and steam-turbine is 
rapidly coming into favor. A good Corliss engine with cylinder 

* At high ranges of pressure the steam turbine is handicapped by the 
small specific volume of steam and the consequent high leakage and rotation 
losses which increase directly with the pressure. In reciprocating engines 
these losses are about constant no matter what the pressure. 


ratios of 1 to 2.5 or 1 to 3.5, exhausting at 15 or 20 pounds abso- 
lute, will have at normal load an efficiency of 72% of that of 
the Rankine-Clausius cycle. The steam-turbine working from 
15 or 20 pounds absolute down to a moderate vacuum will give 
73% efficiency and 70% is guaranteed in the market. The com- 
bined efficiency (65 to 75% of the ideal cycle) is considerably 
higher than that given by either engine or turbine alone. 

In many cases the steam-turbine can be profitably added to 
existing plants. The low-pressure turbine may be used in rolling 
mills or in certain cases where it is desirable to: (1) Increase 
the capacity of an efficient engine plant. (2) Increase the effi- 
ciency of an inefficient engine plant. (3) Replace an inefficient 
condensing plant. 

That these effects may be accomplished is easily seen when 
we remember that a plant of non-condensing engines with a 
water rate of 30 or 35 pounds of water per kilowatt hour may 
be converted into a turbine-engine plant with a consumption 
of 15 or 18 pounds of water per kilowatt hour even in compara- 
tively small sizes. In other words, for the same consumption 
of coal and water an increase of 80 to 100% of capacity has been 

Turbine Auxiliaries. Ideally, the efficiency of the turbine 
increases with each increase in the vacuum, but practically the 
increase is not in proportion. In other words, the efficiency, as 
measured at the coal pile, must consider the costs of producing 
excessively high vaccua. If the injection water is warm the 
condenser becomes inefficient owing to its inability to work with 
small temperature differences between the discharge water and 
the steam. As a result of the improvement in jet condensers 
there has been an interchange in the efficiency position of the sur- 
face and jet condensers. 

A good surface condenser should operate within 15 difference 
of temperature between steam and discharge water and a good 
barometric condenser should operate within 10. In practice, 
twice these differences are often tolerated. There are on the 
market condensers of the jet type that are able to operate within 
2 to 5 of the steam temperature without bulky or wasteful 
auxiliaries. For example, assuming a cooling tower capable of 


cooling the water down to the temperature of the air, 75 F., 
what vacuum will it be possible to maintain? 

(1) A perfect condenser (no temperature difference between 
steam and discharge water) would require 220 volumes of water 
for 29 inches of vacuum. For 28 inches it would require 35 

(2) An efficient condenser of the jet type, working within 5 
difference of temperature, can maintain 28 inches with 43 volumes. 

(3) An ordinary jet condenser, working on 10 difference will 
require 57 volumes to maintain 28 inches. 

(4) The ordinary surface condenser, working with 20 differ- 
ence, cannot maintain 28 inches of vacuum without using the 
impracticable amount of 140 volumes of water. 

The more efficient jet type is responsible for reducing the 
water consumption to one-third of that possible with the surface 
condensing type.* 

Among the recent improvements may be mentioned the Le- 
blanc rotary air-pump attached to ejector condensers, illustrated 
and described in Engineering, May 7, 1909. With this type of 
plant it is stated that the vacuum obtained is never less than 
98.5% of that theoretically possible and that 99% is often ex- 
ceeded, provided the joints are maintained reasonably air-tight. 

Steam-turbines. In a turbine-engine station suppose that 
one-half of the 500 horse-power of auxiliaries circulating air, feed, 
and oil-pumps, fans for furnaces, coal-, and ash-conveyors, coal- 
crushers, mechanical stokers, and low-pressure water service 
are in continuous use, using 100 Ibs. of steam per I.H.P. and 
exhausting into a feed-water heater. Assuming 13,000 horse- 
power for the turbine and an efficiency of 14 Ibs. of water per 
horse-power, what would be the gain in economy by driving the 
auxiliaries electrically and heating the feed-water by steam from 
an opening in the turbine casing where the normal steam-pressure 
is 15 Ibs. per sq. in. absolute? (Engineering, May-April, 1906.) 

*See papers in Power, by J. R. Bibbins, 1905-1909, and Rateau and 
Hood, 1907. 



The Lenoir Cycle. This, the earliest gas-engine cycle, natu- 
rally followed the characteristics of the steam-engine cycle. It 
has been practically abandoned from its lack of economy In 
the Lenoir cycle (Fig. 253) 

FIG. 253. 

1. Gas and air are sucked in for less than half-stroke. 

2. The charge is fired and there is an immediate rise in 
pressure at practically constant volume at this point in the 

3. Expansion follows during the remainder of the stroke. 

4. The piston returns, sweeping out the gases for the full 

The Beau de Rochas or Otto Cycle. We shall see from the 
entropy diagrams that it is economical to compress the gases 
in a cylinder before igniting them. The Lenoir engine was double- 
acting and gave trouble from overheating. To avoid these diffi- 
culties, the Otto engine is single-acting, so that the cylinder-bore 
and the piston, on one end, are exposed to atmospheric tem- 
perature. The following is the Otto cycle (Fig. 254). 

1. The gas to be burnt and the air to support combustion 

are drawn past some form of governor into the cylinder during 

the whole of one stroke, AB. 




2. On the return-stroke, BC, this gas mixture is com- 
pressed into the clearance space of the engine. 

3. The gas is exploded, the piston being practically on 
the dead-center, and expansion during the entire stroke fol- 
lows, CD and DE f '. 

4. The burnt gases must be swept out during the return- 
stroke, E'E and BA. 

It is evident that there can only be one explosion and one 
effective stroke in four strokes or two revolutions. 

In one form of the two-cycle single-acting engine, a closed 
vessel is obtained by encasing the engine. We must examine 

the cycle first on the crank side of the piston and then on the 
other side. On the compression stroke, or the stroke towards 
the head, air is drawn into the case. On the next or explosion 
stroke this air is slightly compressed. We must now examine 
into the. events that occurred on the other side of the. piston 
during these two strokes. After the explosion of the charge and 
before the expansion is completed, ports are uncovered to allow 
the air in the case to sweep through the cylinder and displace 
the burnt gases. This action is called scavenging. A further 
movement of the piston closes the air-ports and opens gas-ports 
and the gas charge is admitted. The piston now being at the 
end of its stroke, the return-stroke is made, compressing the mix- 
ture of gas and air. 


Gas-engines, then, are divided into four-cycle, two-cycle, single- 
acting, double-acting, scavenging, and non-sea vengi ig types. 
The more regular action of the two-cycle type is offset by its 
necessary air- and gas-pumps (in large engines). The short 
time for suction may prevent proper scavenging. Improper 
scavenging produces premature ignition which is unsafe in 
large engines. Where the burnt gases are thoroughly swept 
out, or where water is injected on the suction-stroke, high com- 
pression up to 400 Ibs. per sq. in. may be used even with gases 
containing large amounts of hydrogen. The water about a 
pint to the horse-power although heated to 3500 F. will not 
dissociate on account of the high pressure. It, therefore, acts 
as a thermal fly-wheel. Combustible liquids like alcohol or kero- 
sene could be similarly used. One great advantage of the four- 
cycle engine is that the time required to make the double stroke 
tends to secure a charge that is more thoroughly mixed and 
at a higher temperature than is possible in other types. 

In governing-engines of any considerable size the cutting out 
of an entire charge is a method that is no longer used. If the gas 
alone is throttled, below half -load the mixture is too weak and may 
not explode. By throttling both air and gas the mixture will 
ignite properly at all loads, but with heavy throttling the internal 
pressure may be 6 or 7 pounds below the atmosphere, and this 
becomes a load on the engine. With this system, unless the com- 
pression is heavy initially under light loads, the compression will 
be too light and lean mixtures will not explode. In large engines 
the compression ranges from 170-200 pounds per square inch. 

Igniters furnish much vexatious trouble. The hot-tube is no 
longer used except with small sizes. Low-tension magnetos are 
now much used, but they will give place to high-tension systems 
with the introduction of reliable insulation. Mica tubes and 
washers furnish the best insulation at present. 

To keep the metal of the engine cool, much attention must be 
paid to the water circulation. The water must not leave deposits 
of any kind, the circulation must be positive in all parts, the 
cylinder-heads and valve-chambers meriting much attention. Pis- 
tons are cooled through hollow piston-rods. 


Cooling- water required per B.H.P.-hour for engines of 200 to 
1000 H.P. (quoted from the "Gas-engine ") : 


''Cylinders, cylinder-heads, and stuffing-boxes 4 to 5J 

Pistons, piston-rods If " 2f 

Valve boxes and seats and exhaust-valves " 1} 

" These figures imply water entering at 53.6-59 F. and leaving 
the cylinder-jackets at 77-95 F., the pistons at 95-104 F., and 
the valve seats and boxes at 113 F." 

The following are approximate heat balances : 


Heat converted into work 











Heat lost to jacket-water 

Heat carried off by exhaust-gase 3. . 
Radiation etc 

Brake horse-power. . . 

Mechanical efficiency, per cent. . . . 

. . 

Cost per B.H.P. Cost 20 H.P. 

Relative Costs. per Hour, for 300 Days 

Cents. of 10 Hours. 

''Electricity, 5 c. per Kw 5.00 $.-$,000 

Gasoline. 20 c. per gal 2.95 1,770 

Steam, coal $3.50 2.49 1,494 

Gasoline, 15 c. per gal 2.33 1,398 

City gas, $1 per M 2.25 1,350 

Crude oil, 5 c. per gal 2.10 1,260 

Gasoline, 10 c. per gal * 1 .70 1,020 

Suction-producer, coal $4.25 1 . 23 738 

" Depreciation, interest, and repairs were figured at 15 per cent of 
the first cost; oil, fuel, attendance, etc., were all added in the costs." 
(Quoted from " Gas-engines.") Changes in the cost of electricity 
and in the cost of coal, where anthracite must be used for the pro- 
ducer, may change these figures materially. Allow 20 cu. ft. of 
gas and one-eighth gallon of gasoline per B.H.P. 

Alcohol may be made from substances containing either starch 
or sugar. In the former class we find potatoes, corn, rice, barley, 
and wheat; in the other class are sugar-beets and molasses from 
cane- or beet-sugar. Alcohol can be made from otherwise waste 
material, as from diseased potatoes, bitter molasses, sawdust, corn- 
pith, etc. By denaturizing the alcohol it may be made unfit for 
human consumption. This is accomplished by adding substances 


that vary with the subsequent use of the alcohol. Such substances 
are pyradin, picolin, benzene, wood alcohol, gasoline, acetone oil 
derived from the grease of sheep-wool. Wood alcohol is CH 4 0. 
Ethyl alcohol (spirits of wine), C 2 H 6 0, is from the fermentation 
of grape-juice or glucose. 

The use of small motors is growing enormously. The produc- 
tion of gasoline is limited, being about 2% of the petroleum ob- 
tained. The price is therefore limited by the demand. The fol- 
lowing sums up the advantages of alcohol when compared to 
gasoline : 

1. It can be produced as cheaply as gasoline. 

2. The raw materials are illimitable, hence no fear of 

3. It is far safer. Fires can be extinguished with water. 

4. It is clean and sanitary and leaves no deposits in the 

5. It can stand far more compression than gasoline in small 
non-scavenging engines. 

6. In boats the leakage from a defective pipe will be mixed 
with the bilge- water and unexpected explosions prevented. 

7. With high compression more power can be obtained from 
alcohol in small motors than from gasoline, since it is dangerous 
to compress the latter to an equal extent. The consumption is 
1.1 pints to the B.H.P. in a 10-H.P. motor. 

Calorific Power of Gases. The calorific power of a compound 
gas, w^hich can be burnt or oxidized, should not be computed from 
the calorific power of its component elements, as heat may have 
been given out or may have been absorbed when its elements 
united in its formation. For example, the calorific power of 16 
pounds of marsh-gas, CH 4 , computed from its elements would be 

= 12x14,500 = 174,000, 
H= 4x63,000 = 252,000, 

or -25,600 per Ib. 

By actual experiment the calorific power is 23,600, or a differ- 
ence of 3000 B.T.U. On the other hand, acetylene gives out 


more heat than that derived from a theoretical computation. In 
one pound of acetylene there is .923 pound of C and .077 pound 
of H. Therefore 

C = 14,500 X. 923 = 13,383 

H = 63,000 x. 077= 4,851 


From experiment the actual heat-equivalent is 21,500, or an excess 
of 3266 B.T.U. 

We shall need the following calorific powers : 

Marsh- gas (methane), CH 4 21,000 B.T.U. 

defiant gas, or ethylene, C 2 H 4 18,900 " 

Acetylene 20,750 " 

From the above the heat-equivalent of any mixture of these 
gases may be obtained, as in the following example : 


Marsh-gas 2 . 34 X 21,000 = 49,140 

Ethylene (olefiant gas) 13 X 18,900 = 2,457 

Hydrogen .. .60X63,000= 37,800 

Carbon monoxide 20.32X 4,500= 91,440 

Nitrogen 60. 17 

Carbon dioxide and oxygen 16.44 

100.00 180,837 

Thermal units per pound = 1808 

If the weight of the gas per cubic foot is known, then the thermal 
value per 1000 cubic feet may easily be calculated. 

Rise in Temperature in Gas Combustion. The theoretical rise 
in temperature due to the heat liberated in combustion may be 
calculated if we make certain assumptions : 

1. That the gases are burnt in a non-heat-absorbing cham- 
ber, so that all the heat is spent in raising the temperature of 
the gases. 

2. That we know the weights of the gases composing the 
mixture and their specific heat either at constant volume or at 
constant pressure, depending upon the corresponding conditions 
of combustion. 

Hence, if W i} W 2 , Wa, TF 4 , W 5 represent the weight of the gases 


present, and Ci, C 2 , CB, C*, C 5 represent the proper specific heats, 
then H = WC 

where H = total heat of combustion, 
T = nse in temperature. 

It is evident if W and W 5 represent gases that were not 
or could not be burned that the resulting rise in temperature 
would be very much less than it would have been had they been 
absent. Thus, when gases are burned in air the necessity of 
raising the temperature of the non-combustible nitrogen decreases 
very materially the possible rise in temperature of the whole 

Producer-gas (Figs. 255, 256, and 257). In the gas-producer 
air passes in and burrs part of the fuel coal or coke into C0 2 . 

FIG. 255. 

The nitrogen of the air and the C0 2 rise, and the latter, if the 
temperature is high enough, may break up into 2 (CO). Very 
little use could be made of this CO on account of the large amount 
of inert nitrogen that accompanies it. 

Suppose, however, we blow steam on the red-hot coals also, 
the steam will be decomposed, thus: C+H 2 = CO+2H. 

The CO obtained in this way is unaccompanied by inert nitro- 
gen, but, on the contrary, carries with it a large percentage of H 
which has high calorific power. Evidently the more steam that 
is decomposed the better, but it requires heat to decompose the 
steam and this heat must be supplied by the heat evolved when 
the air unites with carbon to form carbon monoxide. The rela- 
tion that exists between the amount of CO formed by the "air- 



burned carbon" and that formed by the " steam-burned carbon" 
is, theoretically, that of equality as indicated below. 

In the formula C+H 2 = CO+2H we may say that 2 pounds 
of H and 16 pounds of united with 12 pounds of C to form 
28 pounds of CO and 2 pounds of H. 

FIG. 256. 

Heat absorbed (per pound of H) in the separation of H 
and when combined in the form of steam 
= 63,000-9[966 + (212-32)] -52,500 

Heat given out in burning 6 pounds of C to CO = 6 X4500 +27,000 

Heat absorbed for each pound of carbon burned by the 
steam = 25500/6. 



As 4500 thermal units are liberated by the "air-burned 
carbon" per pound, and this must provide for all heat radiated 
and otherwise wasted, it is evident that the percentage of car- 



bon that may be steam-burned must be very much less than 
that which is air-burned. It is feasible to burn 3 pounds of 
carbon with air to 1 pound of steam-burned carbon. 

If air is a mixture of 

Ibs. CO @ 12.8 cu. ft. per lb.= 89.6 
" N 12.77 " " " =178.78 

3 Ibs. C+4lbs. O = 7 

Nitrogen with 4 Ibs. O =14 
1 Ib. C burned to CO by 

steam = 2.33 " CO 12.8 " " " 

To furnish 1J Ibs. of O 

requires f-i- 8 = .17 " H @ 178.93 " " " 

Cubic feet per pound of 


FIG. 257. 

Expressed in percentage the gas has the following volume and 

Volume. Weight. 

Carbon monoxide, CO ........... 36 . 4% 39 . 7% 

Hydrogen, H ............ 9.1 .7 

Nitrogen, N ............ 54 . 5 59 . 6 

In finding the heat liberated when one pound of CO is burned 
to C02 it is necessary to find the amount of C burned. Further, 
we must remember that if one pound of C burned to CO gives 
4500 B.T.U. and 14,500 if burned to C0 2 it will follow that 
for each pound of C in carbon monoxide only 10,000 B.T.U. 
will be liberated when that gas is converted into C0 2 . 

The heat-equivalent of the above gas will be: 

.397 x 

= 1707, 

.007X53000=2^ B.T.U. 



148 B.T.U. per cu. ft. 


We have seen that the adiabatic compression of air is accom- 
panied by a great waste of power if the air is to be conveyed 
through long pipes, as the air will lose all heat due to tempera- 
ture above its surrounding envelope from conduction, radiation, 
etc. In a similar way producer-gas often loses all its heat above 
that due to atmospheric temperature. To purify the gas it 
is led through scrubbers and it comes into intimate contact with 
streams of water. Producer-gas is, in general, an agent to pro- 
duce heat at some place other than at the place where the gas 
was generated. It is desirable, then, to convert all heat gen- 
erated in the producer into some form of latent energy similar 
to the molecular separation in the case of steam. 

Gas from Soft Coal. Anthracite and coke are alone used as 
fuel in gas-producers in combination with gas-engines in small 
plants. The high cost of anthracite prevents competition with 
steam-engines in many cases. By the use of soft coal a much 
richer and cheaper gas may be made. The difficulties to be over- 
come lie in the presence of tar, ammonia, dust, and other 
residual matter. Caking coals cannot be used, as they melt 
and stop the passage of the gases. In large plants, scrubbers 
of various kinds are used as well as dust-collectors. 

The tarry deposits have always given trouble. In recent 
producers, however, by the use of under-feeding, these deposits are 
brought into contact with hot fuel and are decomposed, giving free 
H and marsh gas. Professor Fernald, at a meeting of the 
A. S. M. E., read a paper on "Results of the Preliminary Pro- 
ducer-gas Tests by the U. S. Geological Survey Coal-testing 
Plant at St. Louis." A brief summary of this paper in the 
shape of tables of twenty-four of the principal tests is given 
in Power, .January, 1906. "The experience gained during these 
tests showed that neither a purifier nor an economizer is required 
in order to use bituminous coal." These tables give the average 
composition of the gas from coals from various parts of the coun- 
try by volume, the number of cubic feet per pound of coal, and 
the heat-units per cubic foot of gas. The third table gives eco- 
nomic results of the use of the gas. In general, a cubic foot of 
gas gave 140-150 B.T.U., but the number of cubic feet of gas 
-per pound of coal varied from 25 to 82. 


Calculation of Pressure in the Gas-engine. Theory and prac- 
tice always agree when the theory has been derived from a con- 
sideration of all the facts. If a definite weight of gas of known 
composition mixed with a definite weight of air is fired, af ier hav- 
ing been drawn into a gas-engine and compressed into a definite 
clearance space, the resulting pressure will ordinarily be less than 
half the expected pressure. As a definite amount of heat is liber- 
ated which should result in a definite rise in temperature and pres- 
sure, there must be a source of heat loss. This is found in the heat 
absorbed by the cylinder walls. This one fact compels us to resort 
finally to experiment under actual conditions to obtain accurate 

For example, the mixture that gives the highest pressure will 
not develop the most power hi a given engine. Suppose a mixture 
of one part gas and four parts air gave a very high theoretical tem- 
perature and pressure, the heat loss to the walls would be high, 
due to the high temperature of the gas. Suppose that to the same 
weight of gas double the volume of air were used, the temperature 
of the gas would be lower, the heat loss less, and the heat remaining 
in the gas greater. We may or may not get more work out of the 
new mixture. Whilst there is more heat in it, this heat is at a 
lower temperature. 

Brannt records experiments made with mixtures of oil-gas 
specific gravity .68: 

Oil-gas, Volumes. Air, Volumes. Explosive Effect. 

1 4.9 None 

5. 6 to 5. 8 Slight 

6 to 6 . 5 Heavy 

7 to 9 Very heavy 

10 to 13 Heavy 

14 to 16 Slight 

17 to 17.7 Very slight 

18 to 22 None 

Even if the best mixture of gas and air is used, three-fourths to 
four-fifths of the heat is wasted either in the jackets, exhausts, or 

Indicator- and Entropy-cards. The theoretical cards from 
4-cycle and 2-cycle engines using any explosive mixture are iden- 
tical. The card from the Diesel oil-engine, however, differs in 



a few particulars. The practical card, Fig. 1896, differs very 
materially from the theoretical one, taking some such form as 
ABCD'FBA, or, when the engine is not properly adjusted, some 
such form as that indicated by ABCD"E"BA. 

The entropy analysis given below is based on an article by 
Professor Reeve, Trans. A. S. M. E., Vol. XXIV. 

The line AB of the indicator-card (Fig. 254) is represented by 
the point B in the entropy diagram (Fig. 258), since the position 

FIG. 258. 

of B is sufficient to indicate the thermal characteristics of the fujl 
gas charge. If the compression is truly adiabatic, BC is the 
course of our tracing-point. If the walls absorb heat there will be 
a loss of entropy, and the tracing-point will wander to the left. 
The charge is fired and the gas is heated at constant volume, so 
that the piston is practically stationary during the formation of 
lines CD or C'D'. To prevent overheating the cylinder walls, a 
water-jacket which abstracts heat and wastes it must be applied 
for mechanical reasons. Its effect in decreasing economy is seen 
in the difference of the positions of D and D'. If the expan- 
sion were truly adiabatic the straight line DE would be followed. 
A careful plotting of the entropy changes would give some such 


line as D'ZE' '. The initial decrease in entropy of the line D'Z 
indicates a very rapid loss of heat, but the swerving of the curve 
ZK to the right indicates the reception of heat by the gas from the 
cylinder walls. This action is similar to the re-evaporation of 
condensed steam toward the end of the stroke in a steam-engine. 
The line EB indicates expansion at constant volume. 

To draw the entropy diagram of the Otto cycle the following 
artifice and form will be found useful. 

On the indicator-card (Fig. 254) and the entropy diagram 
(Fig. 258) let us suppose the suction-stroke line AB has been 
made. Let us ideally compress the gas from B at constant pres- 
sure (abstracting heat) along the line BA till some point y is 
reached. Then let the gas be heated at constant volume, thus 
tracing the line yXZ perpendicular to AB in the indicator card. 
At the points X and Z the temperature and entropy of the gas 
would be identical with that required by those points on the indi- 
cator diagram. The point y is an auxiliary that will disappear. 
At the points B and y we are dealing with the same mass of a 
perfect gas, hence 

T B T v 
Cooling constant mass at constant pressure, 

T " V ' 

1 y v y 

Heating at constant volume, 


rp p * rp r> 

J- x 1 x 1 z * z 

At the points X and B we are dealing with the same mass of a per- 
fect gas, hence we may write 


The ratio of .one pressure to another, or of one volume to another, 
is easily found if both are measured on a fine decimal scale. Divide 
the indicator-card into a series of two points, such as (X, Z), 
(X', Z'), etc., and tabulate the ratio 

^ ?L ?*L *JL * V** Yj I* 

PB'PB'PB' ?B ' ' V x > V f > V x ,> V,,' ' 

The value of T B must be assumed. It lies between 600 F. 
and 670 F. (absolute). The absolute values of all derived quan- 
tities are affected by the uncertainty in the absolute value of T Bf 
but the relative values are absolutely unaffected. Making this 
assumption the values of the temperatures at all points are obtained 
from the equation 

. T P x V B 

From the ideal method of obtaining the points y and X we may 
write our entropy equation 

T T 

<t>x-<l>y = C v \Qge~- and <t>B-<f>y = C P logt^~, 

1 y 1 y 

Cy and Cp being the thermal specific heats at constant volume and 
constant pressure. 
By subtraction 

m m 

<t>x~ 4>B = C V log, ~- C P loge TiT 

-C F (log.J 2 1.404 log. J? 

= 2.3026 C F (log 10 Jpl.404 lo glo ~ 

= 2.3026 C v (log - 1.404 log 

As a rule only relative values of entropy are required, hence the 
coefficient 2.3026 C v may be omitted. 


In the following form the term 1.404 log pF is placed first, 

to bring together the two quantities whose difference is desired. 

Suppose TT = 1.49, its log = . 1732 . . (1) 

T r. 

A x " " =.06928 
.004 x " " =.00069 


jr = 1.778, " " =.2499 (2) 


^ = 3.602, its log = .5565 (3) 

* JC 

P 2 
as (j> x </>B +log TT = </>z <t>B .5632 


T x P x V B 

Subtracting (1) from (2), since log - =log p- log y-, 

* B *- B ' x 

log - .0767. 


Assume T B = 600 F. A., log 600 = 2.7781 

log T x = 2.8548 ... (4) 

7^ = 715.8 F. A. 


Adding log ^ to log T x , (3) + (4) = log T z = 3.41 13 

-t x 

r z =2578F.A. 

Therefore, noting the use of ratios: 

1. With the slide-rule set to the initial absolute pressure, 
take each point on the card in turn, divide the pressure at 


that point by the initial pressure, and note the logarithm of 
the result. 

2. With the slide-rule set to the total length of the indi- 
cator-card (including clearance) divide it by the total volume 
at each point of the card in turn, and obtain the logarithm of 
the quotient. 


3. Add to (2) TTTTT: of itself by slide-rule or by arithmetic. 

4. The difference found by subtracting (3) from (1) is 
the entropy of the desired point. 

5. The difference found by subtracting (2) from (1) is the 
logarithm of the temperature ratio; this logarithm should be 
set down at one side. 

6. With the slide- rule set to the initial absolute tempera- 
ture enter the table of logarithms with (5), and multiply 
its number by the initial absolute temperature; the result 
is the absolute temperature of the desired point. Thus, let 
!T 5 -600 F. A.: 

(1) log - =0.2499 

(2) log |JS =0.1732 


^ of ditto =0.06928 

(4) Entropy =0.0067 
(5) log ~ =0.0767 
(6) T absolute = 715.8 

of ditto =0 . 00069 460 . 9 

(3) = . 2432 T Fahrenheit =255 F. 

In this way some twenty points, or sufficient for an entire 
analysis, can be calculated and plotted inside of an hour. 
A natural gas has the following composition : 

Carbon dioxide (and H 2 S) . * ........ 1 . 80 per cent 

Oxygen ........................... 70 " " 

Hydrocarbon ...................... 50 " " 

Carbon monoxide .................. 55 tl " 

Hydrogen ......................... 60 " " 

Methane ......................... 92.05 " " 

Nitrogen ......................... 3.80 " " 


What is the thermal value of this gas per cubic foot? Assum- 
ing its value at 1000 B.T.U per cubic foot, what would be the 
efficiency of a gas-engine using 12.7 cubic feet per B.H.P. With a 
thermal efficiency of 27.6%, how many cubic feet of gas will a 
13" Xl4" engine use making 257 revolutions per minute? Assume 
a clearance of 20% and a mixture of gas and air in the proportion 
of 1 to 11, what will be the theoretical temperature and pressure 
after an explosion, the piston being on the dead-center? 

Diesel Cycle. In this remarkable cycle 

1. The air alone and not the explosive mixture is compressed. 

2. The degree of compression exceeds that of all other types. 

3. This compression is adiabatic and nothing is done to 
make it isothermal. 

4. The degree of compression is so great that the tempera- 
ture causes spontaneous combustion, as the charge or com- 
bustible is forced in at a higher pressure. 

5. Just as powder for cannon is made in grains as large as 
an inkstand to delay combustion and produce a uniform rather 
than a rapidly diminishing pressure, so in this motor the charge 
is supplied gradually for the same purpose. 


PIG. 259. 

FIG. 260. 

The indicator-card and entropy diagram are represented in 
Figs. 193 and 194, but not to scale. The diagrams are lettered to 

FIG. 261. Valves of Diesel Engine. 




indicate the same events. AB is the suction ; BC is the compres- 
sion; CD is the preliminary and DB the after or isothermal heat 
lines due to the gradual combustion of the injected oil; EF is the 
adiabatic expansion line; and FB is the expansion line at constant 
volume. Operating between 500 and 35 pounds per square inch, 
this motor has an efficiency ranging between 36 and 45%. The 
following data are from the Journal of the A. S. N. E., November, 


Feb 13 

Feb. 14 

Feb 14 

Feb 14 


f 3.55P.M. 

! to 



il.21 15 

2.01 30 

Duration minutes.. 

I 5.55 

11. 12 15 
115 25 

1.30 15 

2.59 3 


Diam. of cylinders, inches 
Stroke of pistons feet 

2 4605 

Revs, per min 





Jacket-water per min 

166 8 

169 85 

157 85 


Initial temp, of jacket-water, F 
Final temp, of jacket-water, F 
Temp, of outside air, F 








Temp, of exhaust-gases, F 





Analysis of exhaust-gases: CO 2 





" " " Air 

51 5 

41 9 

75 3 

Oil used pounds 

390 3 


221 1 

44 23 

Oil used per hour pounds 

195 1 

207 2 

102 8 

45 76 

Blast pressure, atmospheres 

Max. pres. shown by indicator dia- j 
grams in pounds per sq. in 1 







M.E.P., pounds per square inch: 
On first piston 


82 9 

80 7 

51 6 

23 2 

On second piston 

92 3 

93 9 

52 6 


On third piston 


115 6 

64 8 


Average in the three cylinders. . 
Indicated horse-power 


634 8 



Oil per I.H.P. per hour-pounds 





Output of dynamo kw 



168 2 


Brake HP of engine 

475 5 

502 5 



H P absorbed in friction 

133 8 

132 8 

118 6 

10 87 

B H P /I H P 





Power absorbed by motor, kw 
H P given out by motor 

44 8 


48 3 

36 8 

26 2 

I.H.P. in compressor cylinders 
Power absorbed in belt and compres- 
sors HP. 







Estimated B H P of engine 

435 1 

458 7 

213 8 


Estimate of mech. effic. if pump had 
been driven by engine 
Oil per brake H.P., pounds 










1 II. 


Per Cent. 


Per Cent. 

To calorific value of one pound of oil 





By heat-equivalent to work done 

7 944 

39 6 



By heat carried off in jacket-water 

4 070 

20 3 



By heat carried off in exhaust-gases 
By radiation and error 

1 006 




To calorific value of oil used per H. P. per min. 
By heat-equivalent to work done 


39 6 




By heat carried off in jacket-water 


20 3 



By heat carried off in exhaust -gases 

37 5 




By radiation and error 










Per Cent. 


Per Cent. 

To calorific value of one pound of oil 





By heat-equivalent to work done 


44 9 



By heat carried off in jacket-water 
By heat carried off in exhaust-gases 
By radiation and error. ... 

1 438 


7 2 

} 4,402 


To calorific value of oil used per H.P. per min 
By heat-equivalent to work done 
By heat carried off in jacket-water 
By heat carried off in exhaust-gases 
By radiation and error 









"The air for pulverizing the oil and spraying it into the cylinders 
was compressed in an independent pair of three-stage vertical air- 
compressors, worked by a two-throw crank-shaft, belt-driven by a 
motor receiving current from the dynamo upon the engine crank- 
shaft. This wasteful arrangement as compared to driving the 
compressors direct was adopted to meet special conditions." 

A study of the tables will furnish problems, and will give a 
more definite conception of the engine than can be obtained from 
a description. 


CODE OF 1901.* 

I. Objects of the Tests. At the outset the specific object of 
the test should be ascertained, whether it be to determine the ful- 
filment of a contract guarantee, to ascertain the highest economy 
obtainable, to find the working economy and the defects as they 
exist, to ascertain the performance under special conditions, or to 
determine the effect of changes in the conditions, and the test 
should be arranged accordingly. 

Much depends upon the local conditions as to what prepara- 
tions should be made for a test, and this must be determined 
largely by the good sense, tact, judgment, and ingenuity of the 
expert undertaking it, keeping in mind the main issue, which is 
to obtain accurate and reliable data. In deciding questions of 
contract, a clear understanding in regard to the methods of test 
should be agreed upon beforehand with all parties, unless these are 
distinctly provided for in the contract. 

II. General Condition of the Engine. Examine the engine and 
make notes of its general condition and any points of design, con- 
struction, or operation which bear on the objects in view. Make 
a special examination of all the valves by inspecting the seats an 1 
bearing surfaces, note their condition, and see if the piston-rings 
are gas-tight. 

If the trial is made to determine the highest efficiency, and the 
examination shows evidence of leakage, the valves, piston-rings, 
etc., should be made tight and all parts of the engine put in the 
best possible working condition before starting on the test. 

III. Dimensions, etc. Take the dimensions of the cylinder or 
cylinders whether already known or not ; this should be done 
when they are hot and in working order. If they are slightly worn, 
the average diameter should be determined. Measure also the 
compression space or clearance volume, which should be done, 
if practicable, by filling the spaces with water previously meas- 
ured, the proper correction being made for the temperature. (See 
Section III, Steam-engine Code.) 

* Trans. A. S. M. E. 


IV. Fuel. Decide upon the gas or oil to be used, and if the 
trial is to be made for maximum efficiency, the fuel should be the 
best of its class that can readily be obtained, or one that shows 
the highest calorific power. (See Section IV, Steam-engine Code.) 

V. Calibration of Instruments Used in the Tests. All instru- 
ments and apparatus should be calibrated and their reliability 
and accuracy verified by comparison with recognized standards. 
Apparatus liable to change or to become broken during the tests, 
such as gages, indicator-springs, and thermometers, should be 
calibrated both before and after the experiments. The accuracy 
of all scales should be verified by standard weights. In the case of 
gas- or water-meters, special attention should be given to their 
calibration, both before and after the trial, and at the same rate 
of flow and pressure as exists during the trial. 

(a) Gages. (See Section V, Steam-engine Code.) 

(b) Thermometers. (See Section V, Steam-engine Code.) 

(c) Indicator-springs. The indicator-springs should be cali- 
brated with the indicator in as nearly as possible the same condi- 
tion as to temperature as exists during the trial. This temperature 
can usually be estimated in any particular case. A simple way of 
heating the indicator is to subject it to a steam-pressure just before 
calibration. Compressed air or compressed carbonic-acid gas are 
suitable for the actual work of calibration. These gases should be 
used in preference to steam, so as to bring the conditions as near 
as possible to those w r hich obtain when the indicators are in actual 
use. When compressed carbonic-acid gas is used, and trouble 
arises from the clogging of the escape-valves with ice, the pipe 
between the valve and gas-tank should be heated. With both air 
and carbonic acid the pipes leading to the indicator should also be 
heated if it is found that they are below the required temperature. 
The springs may be calibrated for this class of engines under a 
constant pressure if desired, and the most satisfactory method is 
to cover the whole range of pressure through which the indi:ator 
acts : first, by gradually increasing it from the lowest to the highest 
point, and then gradually reducing it from the highest to the lowest 
point, in the manner which has heretofore been widely followed 
by indicator-makers; a mean of the results should be taken. The 
calibration should be made for at least five points, two of these 


being for the pressures corresponding to the maximum and mini- 
mum pressures, and three for intermediate points equally distant. 

The standard of comparison recommended is the dead-weight 
testing apparatus, a mercury column or a steam-gage, which has 
been proved correct by reference to either of these standards. 

The correct scale of spring to be used for working out the mean 
effective pressure of the diagrams is the average based on this cali- 
bration, ascertained in the manner pointed out in Section XIV, 
Steam-engine Code. 

(d) Gas-meters. A meter used for measuring gas for a gas- 
engine should be calibrated by referring its readings to the dis- 
placement of a gasometer of known volume, by comparing it with 
a standard gas-meter of known error, or by passing air through the 
meter from a tank in which air under pressure is stored. If the 
latter method is adopted, it is necessary to observe the pressure of 
the air in the tank and its temperature, both at the tank and at 
the meter, and this should be done at uniform intervals during the 
progress of the calibration. The amount of air passing through 
the meter is computed from the volume of the tank and the ob- 
served temperatures and pressures. 

The volume of the gas thus ascertained should be reduced to 
the equivalent at a given temperature and atmospheric pressure, 
corrected for the effect of moisture in the gas, which is ordina ily 
at the saturation-point or nearly so. We recommend that a 
standard be adopted for gas-engine work, the same as that used 
in photometry, namely, the equivalent volume of the gas when 
saturated with moisture at the normal atmospheric pressure at a 
temperature of 60 F. In order to reduce the reading of the volume 
containing moist gas at any other temperature to this standard, 
multiply by the factor 

459.4+60 6- (29.92- s) 
459.4+ t ' 29.4 

in which b is the height of the barometer in inches at 32 F., t the 
temperature of the gas at the meter in degrees F., and s the vacuum 
in inches of mercury corresponding to the temperature of t obtained 
from steam-tables. 


For calibrating water-meters refer to Section V, Steam-engine 

VI. Duration of Test. The duration of a test should depend 
largely upon its character and the objects in view, and in any case 
the test should be continued until the successive readings of the 
rates at which oil or gas is consumed taken at, say, half -hourly 
intervals become uniform and thus verify each other. If the 
object is to determine the working economy, and the period of 
time during which the engine is usually in motion is some part of 
twenty-four hours, the duration of the test should be fixed for this 
number of hours. If the engine is one using coal for generating 
gas, the test should cover a long enough period to determine with 
accuracy the coal used in the gas-producer; such a test should be 
of at least twenty-four hours' duration, and in most cases it should 
extend over several days, 

VIIc Starting and Stopping a Test. In a test for determining 
the maximum economy of an engine, it should first be run a suffi- 
cient time to bring all the conditions to a normal and constant 
state. Then the regular observations of the test should begin and 
continue for the allotted time. 

If a test is made to determine the performance under working 
conditions, the test should begin as soon as the regular prepara- 
tions have been made for starting the engine in practical work, 
and the measurements should then commence and be continued 
until the close of the period covered by the day's work. 

VIII o Measurement of Fuel. If the fuel used is coal furnished 
to a gas-producer, the same methods apply for determining the 
consumption as are used in steam-boiler tests. (See Vol. XXI, 
p. 34.) 

If the fuel used be gas, the only practical method of measure- 
ment is the use of a meter through which the gas is passed. Gas- 
bags should be placed between the meter and the engine to diminish 
the variation of pressure; and these should be of a size proportion- 
ate to the quantity used. Where a meter is employed to measure 
the air used by an engine, a receiver with a flexible diaphragm 
should be placed between the engine and the meter. The tem- 
perature and pressure of the gas should be measured, as also the 
barometric pressure and temperature of the atmosphere, and the 


quantity of gas should be determined by reference to the calibration 
of the meter, taking into account the temperature and pressure of 
the gas. 

If the fuel is oil, this can be drawn from a tank which is filled 
to the original level at the end of the test and the amount of oil 
required for so doing being weighed; or, for a small engine, the oil 
may be drawn from a calibrated vessel such as a vertical pipe. 

In an engine using an igniting flame the gas or oil required for 
it should be included in that of the main supply, but the amount 
so used should be stated separately if possible. 

IX. Measurement of Heat-units Consumed by the Engine. 
The number of heat-units used is found by multiplying the number 
of pounds of coal or oil or the cubic feet of gas consumed by the 
total heat of combustion of the fuel as determined by a calorimeter 
test. In determining the total heat of combustion no deduction 
is made for the latent heat of the water vapor in the products of 
combustion. There is a difference of opinion on the propriety of 
using this higher heating value, and for purposes of comparison 
care must be taken to note whether this or the lower value has 
been used. The calorimeter recommended for determining the 
heat of combustion is the Mahler for solid fuels or oil, or the 
Junker for gases, or some form of calorimeter known to be equally 
reliable. (See Poole on "The Calorific Power of Fuels.") 

It is sometimes desirable, also, to have a complete chemical 
analysis of the oil or gas. The total heat of combustion may be 
computed if desired from the results of the analysis, and should 
agree well with the calorimeter values. (See Section XVII, 
Boiler-test Code.) 

In using the gas calorimeter, which involves the determination 
of the volume instead of the weight of the gas, it is important that 
the results should be reduced to the same temperature as that 
corresponding to the conditions of the engine trial. The formula 
to be used for making the reduction is that already given in Section 

For the purpose of making the calorimeter test, if the fuel used 
is coal for generating gas in a producer, or oil, samples should be 
taken at the time of the engine trial and carefully preserved for 
subsequent determination. If gas is used, it is better to have a 


gas-calorimeter on the spot, samples taken, and the calorimeter 
test made while the trial is going on. 

X. Measurement of Jacket-water to Cylinder or Cylinders. 
The jacket- water may be measured by passing it through a water- 
meter, or allowing it to flow from a measuring-tank before entering 
the jacket, or by collecting it in tanks on its discharge. If measur- 
ing-tanks are used, the same system of arrangement is recommended 
as that employed for feed-water measurements in boiler- and 
steam-engine tests. (See Section XI, Steam-engine Code.) 

XI. Indicated Horse-power. The directions given for deter- 
mining the indicated horse-power for steam-engines apply in 
all respects to internal-combustion engines. (See Section XIII, 
Steam-engine Code.) 

The pipe connections for indicating gas- and oil-engines should 
be removed as far as possible from the ports and ignition devices 
and made preferably in the cylinder-head. The pipes should be 
as short and direct as possible. Avoid the use of long pipes, other- 
wise explosions of the gas in these connections may occur. 

Ordinary indicators suitable for indicating steam-engines are 
much too lightly constructed for gas- and oil-engines. The pencil 
mechanism, especially the pencil arm, needs to be very strong to 
prevent injury by the sudden impact at the instant of explosion; 
a special gas-engine indicator is required for satisfactory work, 
with a small piston and a strong spring. 

XII. Brake Horse-power. The determination of the brake 
horse-power, which is very desirable, is the same for internal com- 
bustion as for steam-engines. 

XIII. Speed. The same directions apply to internal-combus- 
tion engines as to steam-engines for the determination of speed, 
and reference is made to Section XVII, Steam-engine Code, for 
suggestions on this subject. 

In an engine which is governed by varying the number of 
explosions or working cycles, a record should be kept of the num- 
ber of explosions per minute, or, if the engine is running at nearly 
maximum load, by counting the number of times the governor 
causes a miss in the explosions. 

One way of mechanically recording the explosions is to attach 
to the exhaust-pipe a cylinder and piston arranged so that the 


pressure caused by the exhaust-gases operates against a light 
spring and moves a register, which is provided for automatically 
counting the number. 

XIV. Recording the Data. The time of taking weights and 
every observation should be recorded and note made of every 
event however unimportant it may seem to be. The pressures, 
temperatures, meter-readings, speeds, and other measurements 
should be observed every twenty or thirty minutes when the con- 
ditions are practically uniform, and at more frequent intervals if 
they are variable. Observations of the gas or oil measurements 
should be taken with special care at the expiration of each hour, 
so as to divide the test into hourly periods, and reveal the uni- 
formity or otherwise of the conditions and results as the test goes 

All data and observations should be kept on suitably prepared 
blank sheets or in note-books. 

XV. Uniformity of Conditions. When the object of the test is 
to determine the maximum economy, all the conditions relating 
to the operation of the engine should be maintained as constant 
as possible during the trial. 

XVI. Indicator Diagrams and their Analysis. (a) Sample 
Diagrams. Sample diagrams nearest to the mean should be 
selected from those taken during the trial and appended to the 
tables of the results. If there are separate compression- or feed- 
cylinders, the indicator diagrams from these should be taken and 
the power deducted from that of the main cylinder. 

XVII. Standards of Economy and Efficiency. The hourly 
consumption of heat, determined as pointed out in Article IX, 
divided by the indicated or the brake horse-power, is the standard 
expression of engine economy recommended. 

In making comparisons between the standard for internal- 
combustion engines and that for steam-engines it must be borne 
in mind that the former relates to energy concerned in the genera- 
tion of the force employed, whereas in the steam-engine it does not 
relate to the entire energy expended during the process of com- 
bustion in the steam-boiler. The steam-engine standard does not 
cover the losses due to combustion, while the internal-combustion 
engine standard, in cases where crude fuel, such as oil, is burned 


in the cylinder, does cover these losses. To make a direct com- 
parison between the two classes of engines considered as complete 
plants for the production of power, the losses in generating the 
working-agent must be taken into account in both cases, and the 
comparison must be on the basis of the fuel used; and not only 
this, but on the basis of the same or equivalent fuel used in each 
case. In such a comparison, where producer-gas is used and the 
producer is included in the plant, the fuel consumption, which will 
be the weight of coal in both cases, may be directly compared. 

The thermal efficiency ratio per indicated horse-power or per 
brake horse-power for internal-combustion engines is obtained in 
the same manner as for steam-engines, referred to in Section XXI, 
Steam-engine Code, and is expressed by the fraction 



B.T.U. per H.P. per hour* 

XVIII. Heat-balance. For purposes of scientific research a 
heat-balance should be drawn which shows the manner in which 
the total heat of combustion is expended in the various processes 
concerned in the working of the engine. It may be divided into 
three parts: First, the heat which is converted into the indicated 
or brake work; second, the heat rejected in the cooling-water of 
the jackets; and third, the heat rejected in the exhaust-gases, 
together with that lost through incomplete combustion and radia- 

To determine the first item, the number of foot-pounds of 
work performed by, say, one pound or one cubic foot of the fuel 
is determined; and this quantity divided by 778, which is the 
mechanical equivalent of one British thermal unit, gives the num- 
ber of heat-units desired. The second item is determined by 
measuring the amount of cooling-water passed through the jackets, 
equivalent to one pound or one cubic foot of fuel consumed, and 
calculating the amount of heat rejected, by multiplying this quan- 
tity by the difference in the sensible heat of the water leaving the 
jacket and that entering. The third item is obtained by the 
method of differences; that is, by subtracting the sum of the first 
two items from the total heat supplied. The third item can be 
subdivided by computing the heat rejected in the exhaust-gases as 


a separate quantity. The data for this computation are found by 
analyzing the fuel- and the exhaust-gases, or by measuring the 
quantity of air admitted to the cylinder in addition to that of the 
gas or oil. 

XIX. Report of Tests. The data and results of a test should 
be reported in the manner outlined in one of the following tables, 
the first of which gives a complete summary when all the data are 
determined, and the second is a shorter form of report in which 
some of the minor items are omitted. (The complete form only 
is given, pp. 510-513.) 

XX. Temperatures Computed at Various Points of the Indi- 
cator Diagram. The computation of temperatures corresponding 
to various points in the indicator diagram is, at best, approximate. 
It is possible only where the temperature of one point is known 
or assumed, or where the amount of air entering the cylinder along 
with the charge of gas or oil, and the temperature of the exhaust- 
gases, is determined. 

If the amount of air is determined for a gas-engine, together 
with the necessary temperatures, so that the volume and tempera- 
ture of the air entering the cylinder per stroke, and that of the gas, 
are known, we may, by combining this with other data, compute 
the temperature for a point in the compression-curve. In this 
computation we must allow for the volume of the exhaust-gases 
remaining in the cylinder at the end of the stroke. The tempera- 
ture at the point in the compression-curve where it meets or 
crosses the atmospheric line will be given by the formula 

-459.4, (A) 

V" + V'"+V 

where V is the total volume corresponding to the point where the 
compression-curve meets or crosses the atmospheric line; V ff 
the volume of the air at atmospheric pressure entering the cylinder 
during each working cycle, reduced to the equivalent volume at 
32 degrees Fahr.; V" the volume of the gas consumed per cycle 
reduced to the equivalent at atmospheric pressure and 32 degrees 
Fahr.; and V"" the volume of the exhaust-gases retained in the 
cylinder reduced to the same basis. To reduce the actual vol- 
umes to those at 32 degrees Fahr. multiply by the ratios of 


491.4-r- (T f +459.4), where T' is the observed temperature of the 
air and of the gas used as fuel. For the exhaust-gases retained 
in the cylinder at the end of the stroke T' may be taken as the 
temperature of the exhaust-gases leaving the engine, provided 
the engine is not of the scavenging type. 

Having determined the temperature of a point in the com- 
pression-curve, the temperature of any point in the diagram may 
be found by the equation 

T^(T +459.4)^5^-459.4 (B) 

Here T\ is the desired temperature of any point in the diagram 
where the absolute pressure is PI and the total volume V\; and 
P and V are the corresponding quantities for the point in the 
compression-line having the temperature T computed from the 
formula (A). 

Formula (B) holds only where the w r eight of the gases contained 
in the cylinder is constant. It is also assumed in this formula 
that the density of the gas compared to air at the same temperature 
and pressure is the same before and after explosion. 

A second method may be employed, provided the air which 
enters the cylinder is measured. This will allow for any difference 
in the density of the gas before and after explosion, and more 
exact values for temperatures on the expansion-curve may be 
obtained than by the first method. 

In this method the density of the exhaust-gases compared to 
air at the same temperature and pressure is computed, assuming 
perfect combustion, and including the effect of the water vapor 
present, and from this density the volume of the gases exhausted 
per cycle is determined. If the volume exhausted per cycle, 
added to the volume of the gas retained in the clearance-space at 
the end of the stroke, be called V in equation (B) and T be the 
observed temperature of the exhaust-gases, this equation may be 
used for determining the temperature of any point in the diagram 
in the way already described. This method is more complicated 
than the first, as it involves the determination of the theoretical 
density after explosion, but it possesses the advantage that it 
may be applied to an oil- as well as to a gas-engine. 


A third method of computing the temperature of various 
points in the diagram may be employed where analyses of the 
exhaust-gases as well as of the fuel have to be made. This method 
is more complicated than the first, but, in common with the sec- 
ond, it possesses the advantage that it may be applied to an oil- 
as well as to a gas-engine. 

In applying the third method the volume of the exhaust-gases 
discharged per working cycle would be given by the formula 


where D is the density of the exhaust-gases at their observed tem- 
perature, computed from the analysis, assuming the vapor of 
water produced through burning the hydrogen in the fuel to be in 
a gaseous state, R the weight of the air which enters the cylinder 
per pound of fuel, and w the weight of the fuel consumed per work- 
ing cycle. The value of R, providing there are no unconsumed 
hydrocarbons, may be computed by employing the formula 


where N, C0 2 , and CO represent the proportions, by volume, of 
the several constituents of the exhaust-gases, and C the weight of 
carbon consumed and converted into C0 2 or CO per pound of 
fuel burned, computed from the analysis of the fuel and of the 
exhaust-gases. t 

Having determined the volume V 2 of the exhaust-gases, formula 
(B) may be used in computing the temperature, in which case T 
will represent the temperature of the exhaust-gases as in the second 
method, P the pressure of the exhaust, and V the volume of the 
exhaust-gases V 2 discharged per stroke, added to the volume of 
the gases retained in the cylinder at the end of the stroke. 

The value of R given in equation (D) is approximate, on account 
of the fact that the percentage of N should be that due to the air 
alone, and not that due to the air in addition to that contained 
in the fuel gas. Where extreme accuracy is desired, the value 
found for R may be used to determine the percentage of N which 
in the analysis of the exhaust-gases is due to the N in the fuel 
gas, and this value may be subtracted from the total N showa 


by the analysis of the fuel gases in order to obtain the correct 
value of N to be used in equation (D). 


CODE OF 1902. 

1 . Made by of 

on engine located at 

to determine 

2. Date of trial 

3. Type of engine, whether oil or gas 

4. Class of engine (mill, marine, motor for vehicle, pumping, or other) .... 

5. Number of revolutions for one cycle, and class of cycle 

6. Method of ignition 

7. Name of builders 

8. Gas or oil used 

(a) Specific gravity deg. Fahr. 

(6) Burning-point ' ' " 

(c) Flashing-point " " 

9. Dimensions of engine: 

IstCyl. 2dCyL 
(a) Class of cylinder (working or for compressing the 


(Vertical or horizontal) 

(c) Single- or double-acting 

(d) Cylinder dimensions 

Bore in. 

Stroke ft. 

Diameter of piston-rod in. 

Diameter of tail-rod " 

(e) Compression space or clearance in per cent of vol- 

ume displaced by piston per stroke: 

Head end 

Crank end 


(/) Surface in square feet (average) 

Barrel of cylinders 


Clearance and ports 

Ends of piston 


(g) Jacket surfaces or internal surfaces of cylinder 

heated by jackets, in square feet 

Barrel of cylinder 


Clearance and ports 

(h) Horse-power constant for one Ib. M.E.P., and 
one revolution per minute 


10. Give description of main features of engine and plant, and illustrate 

with drawings of same given on an appended sheet. Describe the 
method of governing. State whether the conditions were constant 
during the test. 


11. Duration of test hours 

12. Gas or oil consumed cu. ft. or Ibs. 

13. Air supplied in cubic feet cu. ft. 

14. Cooling-water supplied to jackets " 

15. Calorific value of gas or oil by calorimeter test, determined 

by calorimeter B.T.U. 


16. Gas or oil consumed per hour cu. ft. or Ibs. 

17. Cooling-water supplied per hour Ibs. 


18. Pressure at meter (for gas-engine) in inches of water ins. 

19. Barometric pressure of atmosphere: 

(a) Reading of height of barometer ins. 

(6) Reading of temperature of barometer deg. Fahr. 

(c) Reading of barometer corrected to 32 F ins. 

20. Temperature of cooling- water: 

(a) Inlet deg. Fahr. 

(6) Outlet " 

21. Temperature of gas at meter (for gas-engine) " " 

22. Temperature of atmosphere: 

(a) Dry-bulb thermometer " " 

(6) Wet-bulb thermometer " " 

(c) Degree of humidity per cent. 

23. Temperature of exhaust-gases deg. Fahr. 

How determined 


24. Heat-units consumed per hour (Ibs. of oil or cu. ft. of gas per 

hour multiplied by the total heat of combustion) . . . .B.T.U. 

25. Heat rejected in cooling- water: 

(a) Total per hour " 

(6) In per cent of heat of combustion of the gas or oil 

consumed per cent 

26. Sensible heat rejected in exhaust-gases above temperature 

of inlet air: 

(a) Total per hour B.T.U. 

(6) In per cent of heat of combustion of the gas or oil 

consumed per cent. 

27. Heat lost through incomplete combustion and radiation per 


(a) Total per hour B.T.U. 

(6) In per cent of heat of combustion of the gas or oil 

consumed per cent. 



28. Revolutions per minute rev. 

29. Average number of explosions per minute 

How determined 

30. Variation of speed between no load and full load rev. 

31. Fluctuation of speed on changing from no load to full load, measured 

by the increase in the revolutions due to the change 


32. Pressure in Ibs. per sq. in. above atmosphere: 

1st Cyl. 2d Cyl. 
(a) Maximum pressure 

(6) Pressure just before igni.ion 

(c) Pressure at end of expansion 

(d) Exhaust pressure 

33. Temperature in deg. Fahr. computed from diagram: 

(a) Maximum temperature (not necessarily at maximum pressure). . . . 
(6) Just before igniton 

(c) At end of expansion 

(d) During exhaust 

34. Mean effective pressure in Ibs. per sq. in 


35. Power as rated by builders: 

(a) Indicated horse-power H.P. 

(6) Brake " 

36. Indicated horse-power actually developed: 

First cylinder H.P. 

Second cylinder " 

Total " 

37. Brake H. P., electric H.P., or pump H.P. according to the 

class of engine 

38. Friction indicated H.P. from diagrams,, with no load on 

engine and computed for average load '. . " 

39. Percentage of indicated H.P. lost in friction per cent 


40. Heat-units consumed by the engine per hour: 

(a) Per indicated horse-power B.T.U. 

(6) Per brake horse-power 

41. Heat-units consumed by the engine per minute: 

(a) Per indicated horse-power " 

(6) Per brake horse-power 

42. Thermal efficiency ratio: 

(a) Per indicated horse-power per cent 

(6) Per brake horse-power ' ' " 


43. Cubic feet of gas or Ibs. of oil consumed per H.P. per hour: 

(a) Per indicated horse-power 

(6) Per brake horse-power 



44. Quantities given in per cents of the total heat of combustion of the fuel: 
(a) Heat equivalent of the indicated horse-power. .... .per cent 

(6) Heat rejected in cooling-water " lt 

(c) Heat rejected in exhaust-gases and lost through radia- 
tion and incomplete combustion " " 

Sum = 100 " " 
Subdivision of Item (c): 

(cl) Heat rejected in exhaust-gases 

(c2) Lost through incomplete combustion 

(c3) Lost through radiation, and unaccounted for 

Sum = Item (c). 


Add any additional data bearing on the particular objects of the test 
or relating to the special class of service for which the engine is to be used. 
Also give copies of the indicator-diagrams nearest the mean and the corre- 
sponding scales. Where analyses are made of the gas or oil used as fuel, 
or of the exhaust-gases, the results may be given in a separate table. 


Multiple Effects, Vacuum-pans, and Fresh-water Distillers. 
Many substances can only be evaporated properly at tempera- 
tures below 212 F., as, for instance, sugar solutions, milk, and 
many substances used in chemical preparations. The pressure 
at which these substances are boiled must be reduced below 
atmospheric pressure by condensing their vapors and removing 
air or non-condensible gases by means of an air-pump, as in the 
case of condensing-engines. 

Omitting radiation losses from consideration, all the heat 
applied to the liquid that is being boiled is contained in the 
vapor that is sent to the condenser. If this heat is wasted, the 
economy of the operation is very low. This method is called 
boiling in a single effect. It is the method employed in boiling in 
the vacuum-pans of cane- and beet-sugar houses. 

The steam arising from the boiling liquid in an effect can 
be used to evaporate more of the same liquid in a second effect 
if the temperature of boiling in the second one is thirty or more 
degrees lower than that in the first one. This necessary difference 
of temperature to make the heat flow is obtained by making 
the pressure in the second effect lower than that in the first. The 
amount of this pressure is easily obtained from a table of boiling- 
points and the corresponding pressures of the substance boiled. 

In a similar manner the vapor arising from the second effect 
may be used to evaporate a further quantity from the given 
liquid in a third effect in which the temperature and absolute 
pressure is less than in the second effect. 

At first sight it would seem that this process could be carried 
on indefinitely. It has its limits, however. The vapor from the 




last effect must be condensed and its temperature must be thirty 
or more degrees above the temperature of the discharge-water 
cf the condenser. Hence the lowest pressure or the pressure 
in the last effect is that maintained in the condenser. The upper 
limit is determined by other conditions. Having the upper and 
lower limits or total range of temperature and an assumed range 
in each effect, the number of effects is easily found by dividing 
the total range by the range of temperature in each effect. 

In cane- and beet-sugar houses, the exhaust-steam from the 
main and auxiliary engines is the source of supply of steam to 

FIG. 262. 

Section on AB. 

the first effect. As a rule, its pressure is from 7 to 10 pounds 
above the atmosphere, hence its temperature is from 230 F. to 
240 F. If a vacuum of 27 inches is maintained in the last effect 
corresponding temperature is 115 F. there is a difference of 
240-115 = 125 F. If a triple effect is used there will be a 
difference of some 40 between the two sides of the heating- 
surface in each effect. 

In Fig. 262 the first, second, and third effects are marked 
1, 2, 3, respectively; the steam-pipe bringing steam to the first 
effect is marked $; the vapor arising from the first effect is brought 


down and delivered to the second effect at a point corresponding 
to that in No. 1 ; the vapor-pipes of the second and third effects 
differ in diameter, as the volume of the vapor delivered in- 
creases greatly as the pressure is decreased. The vapor from the 
third effect is condensed by coming into contact with the injection- 
water flowing through the pipe /. The air is drawn off through 
the pipe A, protected by a shelf, by the dry-air pump. The dis- 
charge-water flows away by gravity,, 

Examining No. 1 more in detail we find that it is made of 
four belts called the dome, the calander, the tube-belt, and the 
bottom. The effect is supported by the tube-belt in order that 
the bottom may be readily dropped for repairs. 

In none of the effects is the steam admitted directly among the 
tubes. The steam passes around the effect in an annular belt 
and is admitted to the tube-space through narrow slots, shown 
much enlarged in the No. 2 effect. This distributes the steam 
and prevents the foaming that would otherwise occur near the 
steam-pipe opening. The circulation of the juice is up through 
the small tubes 2 inches in diameter and 30 to 40 inches long 
and down through the downcomer 24 inches or more in diameter 
marked D. 

The action then is as follows: Steam, pressure 25 pounds 
absolute, temperature 240 F., enters the steam-space of No. 1 
effect. The temperature of the juice on the other side is 40 de- 
grees lower, or 200 F. ; therefore the gage G\ should show 7 inches 
mercury vacuum = 11 pounds absolute. The steam at 200 F. 
passes into the steam-belt of No. 2. The juice on the other 
side of its tubes must be ai 200 -40 = 160 F. Hence gage G 2 
should show 20 inches of mercury vacuum. The steam at 
160 passes into No. 3, and the gage G% should show 26.5 inches 
of mercury vacuum. It is the custom to show the vacuum in the 
effects rather than the absolute pressure. The efficiency of 
the heating-surfaces would be greatly increased by increasing 
the vacuum to 28 inches. 

As the condensed steam in No. 1 belt is at a pressure higher 
than that of the atmosphere it is easily drained off. As the pres- 
sure in the other two belts is less than that of the atmosphere an 
air-pump, called a sweet-water pump, is necessary to draw off 


the condensed steam and produce the necessary vacuum that 
exists over the juice surface in Nos. 1 and 2; that in No. 3 is pro- 
duced by the air-pump connected to the condenser at A. If the 
multiple effect is more than 34 feet from the ground the con- 
densed steam in the tube-belts of the second and third effects 
will drain off automatically through drip-pipes terminating in 
barrels of water on the ground. It is wise to connect by a half- 
inch pipe the steam-space to the vapor-space over the top tube- 
sheet in each effect, as shown in No. 1 at V. This permits the 
easy withdrawal of air and (in beet-sugar factories) ammonia that 
accumulate in the upper part of the steam-space and interfere 
with the efficiency of the tubes. 

The raw, clarified juice enters No. 1 at / and the syrup of 
proper density 28-30 Beaume is drawn off by a pump at 
Sy 3 , a uniform level being kept in all three effects by regulating 
valves Sy% and /. The juice therefore passes through the three 
effects, becoming denser as it loses water that has been evaporated. 

Theory of the Multiple Effect. 

Let = temperature of the juice entering the apparatus; 
TI = temperature of the boiling juice; 
T 2 = temperature of the steam for heating this juice; 
C=rate of transmission in thermal units per unit area per 
degree difference of temperature between the steam 
and juice side, =22 calories per square meter per 1 
Cent., diff. = 4.5 B.T.U. per square foot per 1 Fahr. 
diff. of temperature between the two sides per minute; 
A =area of the heating-surface; 

Q = amount of heat transmitted per minute =AC(T 2 TI) ; 
;,i = total heat of steam, above 32 F., at T! = 1091. 7 + 

.305 (T 7 !- 32); 
1/2 = latent heat of steam given off in condensing = 1091. 7 -f 

.305(r 2 - 32) -(T 2 - 32); 

S c = weight of steam condensed in the intertubular space; 
W v = weight of water evaporated from the juice. 

If the substance evaporated from any liquid is any other than water, 
the proper changes must be made in the specific heat and heat of 
vaporization. Then the fundamental equations are: 


Q = S C L 2 , .. S c =j. 



Taking the normal back pressure of the exhaust-steam from 
all engines at 10 pounds, gage, the corresponding temperature is 
240 F. Assume that the temperature of the thin beet-juice from 
the filters or the thin cane-juice from the clarifiers at 170 F. This y 
of course, varies, but a few degrees either more or less will not be 
important. Assume that the highest vacuum is 26.5 inches of 
mercury, so that the temperature of the thick juice is 120 F. The 
difference of temperature between the highest steam and the coolest 
juice is 240 -120 = 120 F. 

With the above data we shall derive the theoretical equations 
for single, double, and triple effects. It will then be seen that the 
capacity of a double or triple effect is no greater than that of a 
single effect working between the same range of temperature 
120 in this case but that the economy of a double effect is 
twice, and that of a triple effect is three times, that of a single 
effect (theoretically). In practice the economy of the double 
effect is one and a half, and that of a triple effect twice that of a 
single effect. 

The theory given applies to the distillation of fresh water 
by multiple effects. By the use of live steam instead of exhaust 
steam the number of effects (and hence the economy of opera- 
tion) may be increased due to the increased total range of tem- 


TI = 120 F. juice entering the effect is hotter than boiling juice 

T 2 = 240 F.; 

T 2 -T 1 = 240 - 120 = 120 F. ; 
C = 4.5 B.T.U. per minute; 


A = one square foot, therefore Q = l x4.5x!20 = 540 B.T.U. 
per square foot; 

S c = Y~ = steam condensed per square foot of heating-surface 
L 2 


~ 1091.7 +.305(240 -32) -(240 -32) ~* 57p 
W v = water evaporated per square foot cf heating -surf ace 


"1091.7 +.305(120 -32) -(170-32)" 

Therefore a single effect will evaporate, under these conditions, 
.55 pound of water per minute per square foot of heating-sur- 
face and will require .57 pound of steam, or, in other words, 
one pound of steam in condensing evaporates .96 pound of water. 


In a double effect the range of temperature in each effect will 


First Effect. 

be one-half that in a single effect, or with our data ^ = 60. 

T 2 ' = 240 F. as before; 

T 1 f = T 2 ^- = 240- 60= 180 F. = temperature of boiling 

juice in the first effect; 

o = 170 F. temperature of juice entering (he first effect; 

Q =A'C(T 2 f -T l '} = l x4.5 X60 = 270 B.T.U. ; 
Jli- (t -32) = 1091.7 +.305(180 -32) -(170-32) =998 B.T.U.; 
Z, 2 ' = 1091. 7 +.305(240-32) - (240-32) =946 B.T.U.; 

. 285 pound; 


Second Effect. 

The steam entering the second effect will have the temperature 
of the boiling juice in the first effect, and as the juice is run from 
the first to the second effect the temperature of the juice entering 


the second effect will be the same as that of the boiling juice 
in the first effect. 

S c " = steam condensed in the second effect; 
Wi" = water evaporated in the second effect; 
7Y' = 180 F. = temperature of steam entering second effect; 
t ' = 180 F. = temperature of juice entering second effect; 
TI" = 120 F. = temperature of boiling juice in the second effect; 
L 2 " = 1091. 7 +.305(180 -32) -(180 -32)= 988 B.T.U.; 
V- (to -32) = 1091.7 +.305(120-32) -(180-32) =970 B.T.U. 

In the first effect we assumed one square foot of heating surface. 
We cannot assume one square foot of heating-surface in the Second 
effect, for we must have such an area in the second effect as will 
transmit (under the assumed conditions) the heat that is sent 
from the first effect. 

The heat that is transmitted through the heating-surface of the 
second effect is Se'Lz". But S C " = W V ', the water evaporated 
from the first effect. Therefore 

Q = . 272x988 = 268.7 B.T.U. =^"x4.5(180-120); 
.A = .99 square foot; 

< ~ 970 

In the two effects we have 1.99 square feet of heating-surface 
required for the evaporation of .272 +.277 = .55 pound of water, 
or the evaporation for two square feet in the double effect is the 
same as that for one square foot in the single effect. But the 
amount of steam condensed from the source of supply is only 
.285, or one-half that required from the outside by the single 


In the triple effect between the same temperature limits 240 
to 120 the range in each effect is 40 F. The area of heating- 
surface in the second and third effects must be found as it was 
found in the case of the second effect of the double effect. In 
general it will be found theoretically that three square feet are 
required to do the work of one square foot in the single effect, 



Density o 

Co co id id 
id O 00 05 

f Thin Juice ir 

id id id h-k 

tf> id O 00 

i Degrees Bea 

_ _ _ _ 

05 ^. id 


CD 00 a 05 

to os 


i- 1 tO CO rfi. 

O H* fcO h- 



to CO 4^ Cn 

en o 

00 Cn CO O 



co ^j o 

4^. Cn Cn os 




( ' tO 

to en os -q 

tO CO t*x Cn 


3 g SS 

Cn Cn OS -<I 


Cn OS OS <! 

OS OS <! -<J 

CO 00 tO OS 






Density of Cc 

H* tO tO 


CO 4^ Cn OS 
CD <! Cn CO 

5 2 3 o 


% % o 3 

S 3 

^ to co 

CO 00 OS Cn 

2 g g 

S 4^ 3 g 



f 3 J| 


>- tO CO 4^ 

-a os co t > 

4^ Cn OS OS 

<! <! M 00 

to os oo to 



|! 6 S o 

00 05 

to CO > 4^ 

en co o -vi 

Cn OS OS <! 

co o os i 1 

<I J 00 00 

rf^ 00 1 rfx 


5 " I g 

00 Cn CO 

co co >. en 

00 4^ 

Cn OS OS -vl 

-a to cp co 

^J 00 00 00 
<l O tO Cn 


S * s 1 


l- tO CO 

<i en to o 

^ _ _ ;_ r 

^j CO CO rf*- 

O OS h- OS 

<i oo oo oo 

CO tO 4^ OS 


W 9 Q 

a a ^ 

^ to to to 

rf^ i-^ 00 en 

4^. 4^ en Cn 

i oo co oo 

OS OS <! ^J 

4^ CO CO 00 

8 SSZ3 


3 ' ^ 

^ SS 


4^ Cn Cn OS 
OS tO -^ i 

os <i <i oo 
-vj i os O 

oo oo oo. oo 

t i Cn OS 00 


to to co 4^ 
os to so 4^ 

gen os os 
en o co 

OS <! <J 00 

CO CO 00 I 

00 00 00 00 
CO OS ^1 CO 



CO CO *> 4^ 

to oo co co 

Cn en OS OS 
rf^" 00 tO OS 

<I <! <I 00 

I-* Cn CO tO 

00 00 00 CO 


CO ^ tf>. en 

oo to oo to 

J i k en 00 

<i <i oo oo 

CO M 1 CO 

ro oo oo co 

Cn 00 co i-' 



Ox rfx Cn en 
to OS i- 4 en 

SOS os J 
co -vi o 

^i <r oo oo 

en oo to. en 

00 00 CO CO 
OS CO O i 1 


rfs- en Cn en 

OS O Cn co 

to os o co 

-a oo oo oo 

^j O to Cn 

<I 00 00 00 
00 to * M 

00 CO CO CO 
M O i- 1 i 

00 CO CO CO 
00 O t- 1 fcO 





but there will only be required one-third the quantity of steam 
from the source of supply. 

Actual Design of Multiple Effects. The actual design of 
economical multiple effects is considerably more complicated 
than would be indicated by the preceding theory. As a matter 
of fact the coefficient of heat transfer is not the same in each of 
the effects. This is easily seen from Professor Perry's theory. 
In the last effect the molecules of steam are far apart, their rate 
of vibration is low, they have far less power of brushing away 
the water on the heating surface than in the first effect. As a 
result of numerous experiments Claassen gives the following 
values for C, the calories per square meter per degree Cent., differ- 
ence of temperature between the heating and boiling fluids per 
minute; for the first body, 40; for the second body, 30; for 
the third body, 20; and for the fourth body, 10, when the sur- 
faces are clean. 

While it is possible to attain the rates indicated above when 
the surfaces are clean it is not possible when the surfaces become 
foul. It is better then to assume the following rates for C. For 
the first body, 32; for the second body, 25; for the third body, 
17; for the fourth body, 9. Instead of having equal fall of tem- 
perature in each effect, it is better to make the product of the 
fall of temperature in any effect and the heat transfer coefficient 
in that effect a constant. Thus, if the fall in temperature in the 
first effect is 10 and 32 is the coefficient in that effect then the 
fall in the last effect should be 35.5, viz., the product 10X32 = 

The specific heat of the boiling liquid is not constant in the 
different effects and it should therefore be considered. Further, 
a very considerable economy arises if steam coming from the 
different effects is diverted from entering the following effect 
and is used to raise the temperature of the raw juice gradually 
to the temperature needed in the clarifiers. The heat coming 
from the condensed steam in each effect may also be so utilized. 
If steam is diverted, however, from its regular course a change 
must be made in the heating surface of the effects for it is 
essential that each effect should only be able to condense the 
steam from the preceding effect. 


For example, the juice from the mill at 20 C. might be raised 
by steam passing into the condenser from 20 to 48 C. By 
vapor from the second effect it might be heated to 88 C. It 
could be heated from 88 to 94 by vapor from the first effect. 
In case the raw juice is sent through the filters and cooled it may 
be heated a second time to 94 C. As a result of this method 
the heating surfaces in a quadruple effect for a house grinding 
1000 tons of cane per day would be : 

453 square meters for the first effect; 325 for the second; 
264 for the third, and 280 for the fourth. This multiple 
effect would operate on exhaust steam alone and no coal or 
wood boilers would be necessary. The bagasse would furnish 
sufficient heat. The solution of this problem is interesting, 
but too long for this treatise. 

Measurements of Density of Liquids. The density of liquids is 
taken by means of hydrometers whose indications are called 
degrees. The hydrometer is generally made of glass. It con- 
sists of a graduated stem with two bulbs. When floating in a 
liquid it is maintained in an upright position by its low center of 
gravity, due to the presence of shot in the bottom bulb. The 
upper bulb containing only air gives the necessary buoyancy. 
The zero reading is at the top of the scale for liquids heavier 
than water and at the bottom for liquids lighter than water. 

With sugar solutions either the Beaume or the Brix hydrometer 
may be used. To convert Beaume (or Baume) readings into 
specific-gravity readings see Kent's Handbook, page 165. 

To find the amount of water evaporated from a sugar solution 
when its density is increased from one hydrometer reading to 
another : 

Let <r = the specific gravity of liquid driven off; 

GI = the specific gravity corresponding to the lower reading; 
G 2 = the specific gravity corresponding to the higher reading; 
Vi = original volume of liquid ; 

x = percentage of original volume that is evaporated; 
Vi(lx) = final volume ; 

GxVi= weight of the vapor driven off; 

If the part evaporated is water, G 1; 


Tabulating the results obtained for the evaporation from one 
Beaume reading to a higher one, we obtain the preceding table. 

If a mill grinds 500 tons of sugar-cane per day, with an extrac- 
tion of 80%, what will be the heating-surface required theoretically 
in a triple effect working between 240 and 120 F., and reducing 
the juice from 6 to 26 Beaume? 

Weight of juice in pounds, 


Volume of juice in cubic feet, 

sp.gr.). / 

From table, volume of juice evaporated 
800,000. X .80 

" 62.5xl.041 
Weight of water evaporated in 24 hours 

800,000 x. 80x62.5 

62.5X1.041 = 615 > 00 ' 

Weight of water evaporated per minute 

The required heating-surface would be 


-7^= 2250 square feet. 



This quantity must be multiplied by a factor of safety to cover 
(1) the maintenance of a less range of temperature; (2) the direction 
of the tubes whether horizontal or vertical; (3) amount of scale 
on the tubes; (4) the drawing off of air in the intertubular space; 

FIG. 263. 

(5) improper care, not keeping the pressures in each effect at the 
proper point ; (6) inequality in the daily tonnage of cane. 

The factor of safety is sometimes as high as 2. 

Fig. 263 represents a diagrammatic sketch of a vacuum-pan, 
as used in sugar-houses and refineries. In theory it is a single 
effect, as the steam arising from the sugar solution, boiling under 
20 to 26 inches of vacuum, goes immediately to a condenser. 


The economy of the process is low in reality only a small 
amount of evaporation is performed in the pan. An approximate 
idea may be obtained from the following terse summary of results. 
Start with 10 cubic feet of juice as it comes from the sugar-cane, 
boil it down in the multiple effect to 2 cubic feet by evaporating 
8 cubic feet of water away. The resulting liquid has the consist- 
ency of table syrup. Evaporate the 2 cubic feet of syrup to 
1 cubic foot in the vacuum-pan The residue is a mixture of 50 to 
60% of molasses and 50 to 40% of crystallized sugar. This mass 
flows slowly, and when cold hardly flows at all. Hence the 
peculiar construction of the pan. It must be built so that the 
massecuite will flow out 

The boiling is done by a series of coils, each one with its own 
steam-valve, drain, and trap. Coils are from 4 to 6 inches in di- 
ameter and 40 to 60 feet long. Most of the boiling is done by the 
lower coils, as the upper ones are used only at the end of the process. 

In a pan containing seven rows of coils an expert sugar-maker, 
who knows the kind of syrup he is getting, will draw in syrup till 
three or more coils are covered. He will boil it down, shutting off 
coils that will soon become uncovered, until he has the syrup at the 
proper density. He will then cause crystallization or " form grain " 
by a sudden chilling of the mass as he has a saturated hot solution, 
which when chilled becomes supersaturated and will form grain. 
To do this he increases the vacuum (thus lowering the boiling- 
point) or gives a strong feed of .cold syrup. The remainder of 
the process consists in building up the grain. 

The transfer of heat per square foot of surface per degree 
difference of temperature is low not over 1.4 B.T.U. because of 
the density and stiffness of the mass during a large part of the 
process and also because of the small amount of time that the 
upper coils are in use. 

The principal broad point of interest is the relative length of 
a coil and its diameter. Only a definite weight of steam can pass 
the cross-section of any tube, and it is useless and in fact detri- 
mental to have more surface than is required to transfer the heat 
to the liquid that is being boiled. To be efficient the tubes must 
be kept clear of water. The circulation of the boiling mass is of 
great importance, and the width of the central channel is at least 


one-quarter the diameter of the pan. Vibration stresses are high, 
and the tubes must be strongly secured to prevent rubbing. A 
pinhole in a tube necessitates shutting it off. 

Problem. What should be the maximum length of a 6-inch 
tube using steam at 80 pounds gage; vacuum 22 inches; rate of 
heat transfer 2.1 B.T.U.? 


Refrigerating Machinery. When a gas is compressed, heat 
equal to the work done on it is added to the gas and its tempera- 
ture rises high above the normal. If this compression is performed 
in a tubular vessel, the gas may be cooled by passing water at 
ORDINARY temperature through the tubes. The third step is to 
allow the gas to expand, either freely or doing work. As a result 
of this expansion the temperature of the gas may be lowered far 
below 32 Fahr. If the heat had not been abstracted by the 
water, as shown above, the final temperature of the expanded 
gas would have been the original temperature. Having the cold 
gas, there are many obvious ways of using it (fourth stage) in 
cooling a room or freezing water in cans. The third and fourth 
stages may bs combined in practice. 

The refrigeration cycle has, then, four stages and is the in- 
verse of the heat cycle, and the theoretical heat equations apply 
equally well to both cycles. There are many systems of refrigera- 
tion. The absorption system is more economical than the com- 
pression system, but the latter is the more practical and is used 
more extensively. The use of a compressor may be avoided by 
absorbing the ammonia in water and then driving it off under 
high pressure by heat. We shall give short descriptions of a Com- 
pressed Air System as used on board ships and of the Ammonia 
Compression System as commonly found ashore. 

First Stage. From formulas, page 118, we find if w pounds 
of dry air are compressed from P , Vo, T Q to PI, F 1; 7\, and are 
expelled at PI, with a constant pressure, P , on the other side of 
the piston. 

AI= jy(Pi7i-PoFo)=net work in foot-pounds required per 



w r K v (T l -TQ} foot-pounds, or wK p (T l -T Q ). 
The final temperature of compression is 


Second Stage. Let the air be cooled at constant pressure 
(Pi = P 2 ), its temperature falling to T 2 ( = T theoretically) and 
its volume to V 2 . The amount of heat abstracted = 

Q 2 = wK p (Ti T 2 ) foot-pounds; 
The amount of cooling-water in gallons = 

c = Q 2 


ti = temperature of discharge-water from the condenser, 
" " injection " to " " 

Third Stage. The air is now allowed to expand in an expansion 
cylinder doing net work = 

A 2 = wK p (T 2 -T 3 ), 

/P 3 \ r-l 
when T 3 = final temperature of expansion = 7 7 2 ( -p- ) * , 

as Pi = P 2 . 

Fourth Stage. The cold air at T 3 is allowed to absorb the 
heat equal to C foot-pounds from the substance to be chilled. 
.The amount of heat gained by the air equals the refrigeration 
effect on the substance to be chilled, 

where T 4 = final temperature of the cold air. 

Theoretically, to produce a cycle, 7 7 4 should equal T . 

In other words, the initial temperature of the substance to be 
chilled the final temperature of the cold air that caused the chill- 


ing and the initial temperature of the air entering the compressor 

The power required per stroke = A i - A 2 ; 

rp _ rp 

rp _ rp 



T T 
Theoretically, ^ = TJT- 

1 2 i \ 

Ammonia Compression System. Fig. 264 is a diagrammatic 
sketch illustrating the fundamental elements of an ammonia com- 
pression system. In a reservoir, R, is a supply of liquid and 
gaseous ammonia under a pressure of 150-200 pounds per square 
inch. By opening a valve, a, capable of very fine adjustment 

I,''!''' 1 .;. 1 !! 1 ! 1 ,!'!! 1 '!!''!! 1 ilV''!-!."!' 1 '.'-''! '' 'I'Vi'Vii-Kll'ltlil,.,! ''''' 

li! 1 !!!! 1 '!'!"!!!!! 11 !::!!;!!' 1 !! 1 -'^ 

FIG. 264. 

generally a needle-valve the liquid ammonia is admitted into 
the tubes, B, enclosed in . brine. The pressure and temperature 
in these tubes are quite low, some 30 pounds absolute and F., 
for instance, as they are on the suction side of the compressor 
cylinder. On the delivery stroke of the piston of this cylinder 


the ammonia that had become completely gasefied and finally 
superheated by its free expansion at the low pressure in the 
tubes, B, is compressed up to a pressure as high or a trifle higher 
than that in the reservoir. The high superheat arising from this 
compression is removed by the action of the cooling-water on 
the tubes of the condenser, C, through which the gas flows on 
its way to the reservoir R. Under practically constant pressure the 
gas gives up first its superheat and then its latent heat, and 
trickles back into the reservoir as liquid ammonia. 

The conversion of the liquid into gaseous ammonia in the 
tubes, B, requires heat. This is supplied by the brine which is 
thereby cooled to some temperature between and 32 F. The 
brine is forced through pipes in the room to be chilled or around 
the cans containing the water distilled so as to be free of air- 
bubbles to be frozen. The brine is used : 

1. To prevent sudden changes of temperature in the cooling- 
room, its effects being similar to those of a fly-wheel on the rota- 
tion of an engine. 

2. To prevent the damage that would occur with an ammonia 

As ammonia disintegrates brass, none of that metal should 
be exposed to that alkali. All the tubes and fittings should be 
of extra-strong metal, and all screwed joints must be soldered to 
insure tightness. For efficient compression the compressor clear- 
ance must be very small and preferably filled with heavy oil at 
the end of the stroke; the valves must be perfectly true, as the 
slightest wear reduces the economy. The compressor is exposed 
to heavy pressure and high temperature, hence great strength is 
necessary. The piston and valve-stems must have very deep 
packing-boxes, as ammonia leakage is extremely difficult to 

In Fig. 265 let A represent the state of the liquid ammonia to 
the immediate left of the valve, a, Fig ; 264. The expansion that 
takes place when the liquid passes through the valve, a, is expan- 
sion at constant heat (Fig. 122, page 224), consequently AB is not 
a straight line. The heat of the vapor and liquid at B is the 
same as the heat of the liquid alone at A in excess of that at g 
assumed as an origin. Heat from the brine is absorbed in pro- 



ducing the evaporation represented by the line BC. In passing 
through pipes in the air and into the warm compressor the gas is 
superheated, as shown by CD. DE represents the rise in tempera- 
ture due to adiabatic compression in the compressor cylinder. If 
the mean pressure existing in the condenser-tubes be taken, it will 
be found that the gas entering the condenser, C, from the com- 






FIG. 265. 

pressor has a temperature far in excess of that corresponding 
to that pressure as shown in Table X of Peabody's tables, or as 
shown in Kent, page 993. The cooling-water absorbs the super- 
heat and then the latent heat of the ammonia gas, and finally 
some of the heat of the liquid ammonia, as shown by the lines 
EF, GF, and GA. 

The data for the entropy diagram were taken from Kent, 
page 998, where other data may be found. 

Average high ammonia pressure above atmosphere 151 Ibs. 

Average back ammonia pressure above atmosphere 28 " 


Pounds ammonia circulated per minute 28. 17 

Probable temperature of liquid ammonia, entrance to 

brine-tank 71.3 F. 

Temperature of ammonia corresponding to average back 

pressure +14 F. 

Average temperature of gas leaving brine-tanks 34.2 

Temperature of gas entering compressor 39 

Average temperature of gas leaving compressor 213 

Average temperature of gas entering condenser 200 

Temperature due to condensing pressure 84.5 

Heat given ammonia : 

By brine, B.T.U. per minute 14,776 

By compressor, B.T.U. per minute. 2,786 

By atmosphere, B.T.U. per minute 140 

Heat taken from mmaonia : 

By condenser, B.T.U. per minute 17,242 

By jackets, B.T.U. per minute 608 

By atmosphere, B.T.U. per minute 182 

The heat given and received per pound of ammonia may be 
found by dividing those quantities per minute by 28.17. Assume 
the specific heat at constant pressure of ammonia vapor = 1.1 and 
that of the liquid = .52. The minimum entropy is that of liquid 
ammonia at 14 F. = 475 F. Abs. Let it be the starting- 
point for entropy measurements. Assume one pound of ammonia 
passing through the cycle. The heat required to raise the tempera- 
ture of the liquid to 71.3 F. =532.3 F. Ab3. will be .52(532-475), 

and dividing by - 2 - will give the entropy of A. More 

532 3 

accurately the difference of entropies of g and A = .52 log '-. 


The difference between the heat in the liquid at B and at A 
is available in evaporating liquid between B and A. The entropy 

.52 '532 -475) 

At C all the liquid has been evaporated. The temperature at 
D is 39 +461 =500 F. Abs. The heat required to superheat from 


475 to 500 is 1.1(500-475), and hence the increase of entropy 
from 475 to 500 is readily found. 

The compression is assumed to be adiabatic and the point E 
is laid off. The excess of the entropy of F over that of G is readily 

The data show variations from this theoretical cycle. The 
heat areas are given and may be plotted approximately, and 
compared with those of the theoretical diagram. The area 
beneath BC or the heat abstracted from the brine is the effective 

Refrigeration Units. The unit adopted to measure the cooling 
effect, or the refrigeration, is the heat required to melt one pound 
of ice, which is 144 British thermal units. Dividing the refrig- 
eration, measured in British thermal units, by 144, the ice-melting 
capacity in pounds is obtained. The unit for a ton (2000 Ibs.) of 
ice-melting capacity is therefore 288,000 British thermal units. 

The commercial tonnage capacity is the refrigerating effect, 
expressed in tons of ice-melting capacity, produced by a machine 
in 24 hours, when running continuously under the standard set of 

Considering the matter from the standpoint of cost of plant 
and of steam and water economy, the best set of conditions to 
adopt seems to be those which often exists in ice-making, namely, 
that the temperature of the saturated vapor at the point of lique- 
faction in the condenser be 90 F., and the temperature of evap- 
oration of the liquid in the refrigerator be F. 

The ice-making capacity is not the ice-melting capacity of a 
machine, but is less, being usually about one-half the latter, be- 
cause in making a pound of ice more refrigeration than 144 British 
thermal units is required, owing to cooling the water to 32 F. 
and certain unavoidable losses incident to the process. 

The commercial tonnage capacity of any refrigerating machine 
using liquefiable vapor is based upon the actual weight of the 
refrigerating fluid that is circulated between the condenser and 
the refrigerator, and that is actually evaporated in the refriger- 
ator. Under the conditions specified above twenty-five pounds of 
anhydrous ammonia per hour must be evaporated in the refrig- 
erator for one ton of commercial tonnage capacity. For other 


refrigerating fluids we do not at present make any recommenda- 
tions as to the weight of the fluid that must be circulated. 

The actual refrigerating capacity (in tons) of a machine may 
be determined from the quantity and range of temperature of brine, 
water, or other secondary fluid circulated as a refrigerant. The 
actual refrigerating capacity under the standard set of conditions 
should correspond closely to the commercial tonnage capacity. 



1. Made by of. 

on engine located at 

to determine. .. 

2. Date of trial 

3. Type of engine (simple, compound, or other multiple expansion; con- 

densing or non-condensing) : 

4. Class of engine (mill, marine, locomotive, pumping, electric, or other) 

5. Rated power of engine. 

6. Name of builders 

7. Number and arrangement of cylinders of engine; how lagged; type of 


8. Type of valves 

9. Type of boiler 

10. Kind and type of auxiliaries (air, circulating, main, and feed-pumps; 

jackets, heaters, etc.) 

IstCyl. 2dCyl. 3d Cyl. 

11. Dimeadons of engine 

(a) Single- or double-acting 

(6) Cylinder dimensions: 

Bore in. 

Stroke ft. 

Diameter of piston-rod in. 

Diameter of tail-rod in. 

(c) Clearance in per cent of volume displaced by piston per stroke: 

Head end 

Crank end 


* Quoted from Vol. XXIV, A. S. M. E. 


(d) Surface in square feet (average): 

Barrel of cylinder 


Clearance and ports 

Ends of piston 

(e) Jacket surfaces or internal surfaces of cylinder heated by jackets, in 

square feet: 

Barrel of cylinder 


Clearance and ports 

Receiver jackets 

(/) Ratio of volume of each cylinder to volume of high-pressure cyl- 

(gr) Horse-power constant for one pound mean effective pressure and 
one revolution per minute 

12. Dimensions of boilers: 

(a) Number 

(6) Total grate surface sq. ft. 

(c) Total water-heating surface (external) sq. ft. 

(d) Total steam-heating surface (external) sq. ft. 

13. Dimensions of auxiliaries: 

(a) Air-pump. 

(6) Circulating pump 

(c) Feed-pumps 

(d) Heaters 

14. Dimensions of condenser 

15. Size, length, and number of turns in main steam-pipe leading from the 

boiler to the engine 

16. Give description of main features of plant and illustrate with drawings 

to be given on an appended sheet 


17. Duration of test hours. 

18. Length of time engine was in motion with throttle open hours. 

19. Length of time engine was running at normal speed " 

20. Water fed to boilers from main source of supply Ibs. 

21. Water fed from auxiliary supplies: 

(a) Ibs. 

(6) " 

(0 " 

22. Total water fed to boiler from all sources Ibs. 

23. Moisture in steam or superheating near throttle per cent or deg. 

24. Factor of correction for quality of steam, dry steam being unity , 


25. Total dry steam consumed for all purposes .......... Ibs. 

(In case of superheated steam-engines determine, if practicable, the tem- 
perature of the steam in each cylinder.) 

26. Total coal as fired .......... Ibs. 

(Where an independent superheater is used this includes coal burned in, 
the superheater.) 

27. Moisture in coal .......... per cent. 

28. Total dry coal consumed .......... Ibs. 

29. Ash and refuse .................. " 

30. Percentage of ash and refuse to dry coal .......... per cent. 

31. Calorific value of coal by calorimeter test, per pound of dry coal, de- 

termined by ........................ calorimeter ............ B.T.U. 

32. Cost of coal per ton of 2240 Ibs .................. $ 


33. Water fed from main source of supply .......... Ibs. 

34. Water fed from auxiliary supplies: 

(a) .......... Ibs. 

35. Total water fed to boilers per hour .............. Ibs. 

36. Total dry steam consumed per hour .............. " 

37. Loss of steam and water per hour due to drips from mains, steam-pipes^ 

and to leakage of plant .......... Ibs. 

38. Net dry steam consumed per hour by engine and auxiliaries .......... Ibs. 

39. Dry steam consumed per hour: 

(a) Main cylinders ................ , ., Ibs. 

(6) Jackets and reheaters. . , ........... " 

(c) Air-pump. , . ...................... " 

(d) Circulating pump .................. " 

(e) Feed-water pump. ................. ' ' 

(/) Other auxiliaries ................. " 

40. Dry coal consumed per hour: 

(a) During running period.. . , .......... Ibs. 

(6) During banking period . ., .......... " 

(c) Total ............................. ' 

41. Injection or circulating water supplied condenser per hour .......... cu. ft 


42. Steam-pressure at boiler by gage ................... Ibs. per sq. in. 

43. Steam-pipe pressure near throttle by gage ........... " " 

44. Barometric pressure of atmosphere in inches of mercury .......... ins. 

45. Pressure in first receiver by gage ................... Ibs. per sq. in. 

46. Pressure in second receiver by gage ................ " lt 

47. Vacuum in condenser: 

(a) In inches of mercury .......... ins. 

(6) Corresponding total pressure ................. Ibs. per sq. in. 

48 Pressure in steam-jacket by gage .................. " " 

49. Pressure in reheater by gage ...................... " " 

50. Moisture in steam or superheating at boilers ...... per cent or deg. Fahr* 


51. Superheating of steam at first receiver ................... deg. Fahr. 

52. Superheating of steam in second receiver ................. " " 

53. Temperature of main supply of feed-water to boilers ...... " " 

54. Temperature of auxiliary supplies of feed-water: 

(a) .......... deg. Fahr. 

(b) .......... " " 

(c) .......... " " 

55. Ideal feed-water temperature corresponding to the pressure of the steam 

in the exhaust-pipe, allowance being made for heat derived from jacket 
or reheater drips ............ deg. JFahr. 

56. Temperature of injection or circulating water entering condenser .......... 

.......... deg. Fahr. 

57. Temperature of injection or circulating water leaving condenser ..... 

deg. Fahr. 

58. Temperature of chimney gases entering economizer .......... deg. Fahr. 

59. Temperature of chimney gases leaving economizer ........... " " 

60. Temperature of water entering economizer .................. " " 

61. Temperature of water leaving economizer .................. " " 

62. Temperature of air in boiler-room ......................... " " 

63. Temperature of air in engine-room ......................... ll tf 


64. Heat-units per pound of feed-water, main supply ........... B.T.U. 

65. Heat-units per pound of feed-water, auxiliary supply ....... '' 

(a) ............. B.T.U. 

(c) .............. " 

66. Heat-units consumed per hour, main supply ............. B.T.U. 

07. Heafc-units consumed per hour, auxiliary supplies: 

(a) .......... ..B.T.U. 

(6) ............ " 

(c) ............ " 

68. Total heat-units consumed per hour for all purposes .......... B.T.U. 

69. Loss of heat per hour due to leakage of plant, drips, etc ...... "* 

70. Heat-units consumed per hour 

(a) By engine alone ............ B.T.U. 

(6) By auxiliaries .............. 

71. Heat-units consumed per hour by the engine alone, reckoned from tem- 

perature given in line 55 .......... B.T.U. 


1st CyU 2u Cyi. 3d Cyl. 

72. Commercial cut-off in per cenc of stroke ........ 

73. Initial pressure in Ibs. per sq in. above atmos- 

phere .................................. 

74. Back pressure at mid-stroke above or below 

atmosphere in Ibs. per sq. in, ............. 

75. Mean effective pressure in Ibs, per sq, in, .......... 

76. Equivalent mean effective pressure in Ibs, per sq. in: 

(a) Referred to first cylinder. - ............ 


(&) Referred to second cylinder 

(c) Referred to third cylinder 

77. Pressures and percentages used in computing the steam accounted for by 

the indicator diagrams, measured to points on the expansion and 

compression curves 

Pressure above zero in Ibs. per sq. in.: 

(a) Near cut-off 

(6) Near release 

(c) Near beginning of compression 

Percentage of stroke at points where pressures are measured: 

(a) Near cut-off 

(6) Near release 

(c) Near beginning of compression 

Percentages of stroke at points where pressures are measured: 

(a) Near cut-off 

(6) Near release 

(c) Near beginning of compression 

78. Aggregate M E.P. in Ibs. per sq. in. referred to each cylinder given in head- 


79. Mean back pressure above zero Ibs. per sq. in. 

80. Steam accounted for in Ibs. per indicated horse-power per hour: 

(a) Near cut-off 

(6) Near release 

81. Ratio of expansion 

82. Mean effective pressure of ideal diagram Ibs. per sq. in. 

83. Diagram factor per cent. 


84. Revolutions per minute rev. 

85. Piston speed per minute ft. 

86. Variation of speed between no load and full load rev. 

87. Fluctuation of speed on suddenly changing from full load to no load, measured 

by the increase in revolutions due to the change rev. 


88. Indicated horse-power developed by main-engine cylinders: 

First cylinder H.P. 

Second cylinder " 

Third cylinder " 

Total " 

89. Brake H.P., electric H.P., pump H.P., or dynamo H.P., according to the 

class of engine H.P. 

90. Friction I. H.P. by diagrams, no load on engine, computed for average 

speed... H.P. 

91. Difference between indicated and brake H.P H.P. 

92. Percentage of indicated H.P. of main engine lost in friction per cent. 

93. Power developed by auxiliaries: 

(a) H.P. 

(5) " 

(c) ' 



94. Heat-units consumed by engine and auxiliaries per hour: 

(a) Per indicated horse-power B.T.U. 

(fe) Per brake horse-power ' ' 

95. Equivalent standard coal consumed by engine and auxiliaries per hour, 

assuming calorific value such that 10,000 B.T.U. are imparted to the 

boiler per lb.: 

(a) Per indicated horse-power Ibs. 

(6) Per brake horse-power ' ' 

96. Heat-units consumed per minute : 

(a) Per indicated horse-power B.T.U. 

(5) Per brake horse-power " 

97. Heat-units consumed by engine per hour corresponding to ideal maximum 

temperature of feed-water given in line 55, British standard: 
(a) Per indicated horse-power B.T.U. 

(6) Per brake horse-power " 


98. Thermal efficiency ratio : 

(a) Per indicated horse-power per cent 

(6) Per brake horse-power ' ' 

(c) Ratio of efficiency of engine to that of an ideal engine working 
with the Rankine cycle per cent 


(The horse-power on which the above efficiency results (94 to 103) are based 
is that of the main engine exclusive of the auxiliaries.) 
99. Dry steam consumed per I.H.P. per hour: 

(a) Main cylinder including jackets Ibs. 

(6) Auxiliary cylinders, etc " 

(c) Engine auxiliaries " 

100. Dry steam consumed per brake H.P. per hour: 

(a) Main cylinders, including jackets Ibs. 

(6) Auxiliary cylinders, etc " 

(c) Engine and auxiliaries " 

101. Percentage of steam used by main-engine cylinders accounted for by 

indicator diagrams; 

1st Cyl. 2d Cyl. 3d Cyl, 

(a) Near cut-off 

(6) Near release 

102. Dry coal consumed by combined engine and boiler plant per I.H.P. per 


(a) During running period Ibs. 

(6) During banking period . ' 

(c) Total " 

103. Dry coal consumed by combined engine and boiler plant per brake H.P. 

per hour: 

(a) During running period Ibs. 

(6) During banking period " 

(c) Total " 


104. Water evaporated under actual conditions per Ib. of dry coal Ibs. 

105. Equivalent evaporation from and at 212 F. per pound of dry coal 


106. Efficiency of boilers based on dry coal per cent. 

107. Combined efficiency of boiler and engine plant " 



108. Duty per 1,000,000 heat-units imparted to the boiler ft.-lbs. 

109. Duty per 1000 pounds of dry steam " 

110. Duty per 100 pounds of actual coal consumed by plant " 

111. Number of gallons of water pumped in twenty-four hours gals. 


112. Dynamometric horse-power H.P. 

113. ' 'Standard Coal" of 10,000 B.T.U. value consumed, per dynamometric 

horse-power per hour Ibs. 



114. Current amperes 

115. Electromotive force volts 

116. Electrical power generated in watts watts 

117. Electrical horse-power generated H.P. 

118. Efficiency of generator per cent 

119. Heat-units consumed per electrical horse-power per hour B.T.U. 

120. Dry steam consumed per electrical horse-power per hour Ibs. 

121. Dry coal consumed per electrical horse-power per hour: 

(a) During running period Ibs. 

(6) During banking period * ; 

(c) Total " 

Additional Data. Add any additional data bearing on the particular objects 
of the test or relating to the special class of service for which the engine is used. 
Also give copies of indicator diagrams nearest the mean and the corresponding 


THE purpose of the investigation here described was to derive 
from reliable data constants to be used in the design of the 
steam-engine. The work is confined to the general class known 
as " slow-speed " engines, principally of the Corliss type. Printed 
forms, enumerating all the most important particulars to be 
considered, were sent to nearly all the builders of this class of 
engine, with the request that they insert the data desired. 
Seventy engines by a dozen different makers, ranging from 60 
to 800 horse-power in size, are represented in the work. 

The method of obtaining the constants is a graphical one, 
and may be most clearly explained by means of an example. 
The diameter of the piston-rod is calculated in order to insure 
sufficient stiffness, the rod being treated as a long compression 
member. Using Euler's formula, and assuming the length of 
the rod to be the same as that of the stroke, it can be readily 
shown that 

d = C'VSD 2 L 2 , . , ..... (1) 

where d is the diameter of the rod, S the steam pressure, D the 
diameter of the piston, L the length of stroke, and C' a constant. 
Assuming a constant value for S and combining it with C', 


Values of d and VDL taken from the data were plotted upon 
co-ordinate paper, the series of points for each make of engine 

* Sibley Journal and Trans. A. S. M. E., Vol. XVIII, and Bulletin of the 
University of Wisconsin. 



being connected in order by straight lines. A double circle 
indicated two co-incident points. A straight line representing 
in position and direction the mean of the different series was 
then drawn as a heavy full line, and two others marking the 
extremes were drawn as heavy broken lines. The location of 
these mean and extreme lines was determined simply by inspec- 
tion; they were drawn through the origin of co-ordinates when 
possible. The slope of these lines determine the mean and 
extreme values of the constant C in equation (2). 

The same general method was employed in the case of each of 
the other parts treated, a rational formula being used when 
practicable. In all work involving the power of the engine, 
the rating has been taken at 100 pounds per square inch gauge 
pressure, cut-off at quarter stroke, non-condensing. Where the 
steam pressure is a factor in the constant, values of the constant 
at other pressures than 100 pounds have been computed and 
tabulated. Factors of safety and stresses are calculated on 
the assumption that the unbalanced pressure on the piston is 
100 pounds per square inch. 

The notation used is as follows: 
D = diameter of piston ; 
L = length of stroke; 
A = area of piston; 
S = steam pressure (gage) ; 

H. P. = rated horse-power; 

N = re volutions per minute; 
C and B = constants. 
All dimensions are in inches unless otherwise stated. 

Piston-rod. The formula is d = C\ / DL and 

d = .112V7)Z for the mean, 
= .136V / DL for the maximum, 
= .098V5L for the minimifm. 

If LI, the free length of the piston-rod is taken at 1.1L we 
have, on substitution in Euler's formula, 


4 : 4X1.21L2X64' 

The factors of safety in the above cases are ("gg ) , ("AQ") ' 

and ( gg ) , since the strength varies as the fourth power of the 

diameter of the rod. 






















Connecting-rod. Only rods of circular mid-section are con- 
sidered. The formula is similar to the preceding, so that 
d = C'^SIPLf = CV5ZT, where LI is the length of the rod 
from center to center and d is the diameter in the middle. The 
constants obtained give 

.0935\ / DL 1 for the mean, 

= .105 v DLi for the maximum, 
for the minimum. 

The factors of safety are (1.94) 4 , (2.18) 4 , and (1.69) 4 . The 
values of L vary from 2.75L to 3L, or from 5} to 6 " cranks." 






















* Barr and Trooien give practically the same values. 

Main Journal. The well-known formula for torsion is used, 

/TT T) 

<j=(7\ ' ' and the constants obtained give 

' for the mean, 


= 7.8 \-Tf-" f r the maximum, 

ITT p 

= 5.66 \ rp for the minimum. 

The stresses in the outer fiber corresponding to these constants 
are respectively 1250, 678, and 1775 pounds per square inch. 

The corresponding constants by Barr are 6.8, 8.0, and 6.0 
respectively for one journal only, side-crank engines. 

Trooien gives the following values for the constants in the 

,7 C ' R 

c ~~ 

= .30; 

0=7.2 mean value; 

= 8.0 maximum value; 

= 6.4 minimum value. 

The length of the bearing necessary for cool running is given 

TT T) 

by the formula l=C ^ ' , 

TT T) 

I = 1 .56 7 + 7 for the mean, 


TT T) 

= 2.27 7* + 7 for the maximum, 

TT T) 

= 0.86 f-^ + 7 for the minimum. 

Using the empirical formula l = Cd the constants obtained 
by Barr and Trooien give 

Z = 1.9d for the mean, 
=2.1d for the maximum, 
=*= I. Id for the minimum. 


To prevent " seizing/' the bearing area must be made pro- 
portional to the total pressure. The formula used is dl = C'SA 
= CD 2 and the constants obtained give 

* dl = AID 2 for the mean, 

= .503Z) 2 for the maximum, 
= .36Z) 2 for the minimum. 

Neglecting the weight of the fly-wheel and the pull of the belt, 
the bearing pressures corresponding to the constants are respec- 
tively 178.5, 156, and 218 pounds per square inch of projected 

Steam Mean Maximum Minimum 

























Crank-pin. Only " overhung " cranks are considered. The 
constants obtained give for the length 

TT p 

Z = .515 j- L + 2" for the mean, 

TT T) 

= .655 j-^ + 2" for the maximum, 


= .345 V~ + 2" for the minimum. 

Barr uses the same formula with constants 20% greater, 
namely, .6, .8, and .4 respectively. 


The base formula =(7^ is derived from the fact that 

the projected area of the pin should be proportional to the heat 
(arising from lost work of friction) which must be dissipated. 

* Barr and Trooien give practically the same values. 

The empirical formula d = CD gives 

d= .278D for the mean, 
= .339D for the maximum, 
= .221D for the minimum. 

Trooien gives .27, .32, and .21 as the constants from over- 
hung crank-pins of Corliss type, using I = l.l4d as the mean 
relation of length to diameter of pin. The constants in the 
formula l = Cd are 

C=1.14 mean value, 
= 1.30 maximum value, 
= 1.0 minimum value. 

The formula for the diameter of the pin is d = C'VSD 2 l = 
C^D 2 l and the constants given 

d = . 384f / D 2 T for the mean, 
= .5QQf D 2 l for the maximum, 
= .320^^" for the minimum. 

Assuming the whole load to be concentrated at the outer end 
of the pin, the stresses corresponding to these constants are re- 
spectively 14,150, 6,400, and 25,000 pounds per square inch. 






















The projected area is given by 

= .07D 2 for the mean, 

= .09D 2 for the maximum, 

= .05D 2 for the minimum. 

* Barr gives the same constants. 


The corresponding pressures are respectively 1120, 865, and 
1640 pounds per square inch. 

CRANK-PIN, dl = CD\ 





















Cross-head Pin. The length is usually the same as that of 
the crank-pin. In the formula I = Cd, Trooien gives 

C = 1.43, Barr gives C = 1.3 mean value, 
= 1.9 =1.5 maximum value, 

= 1.0, =1.0 minimum value. 

For cross bending if l = l.25d Trooien gives for C in formula 

C = .25 mean value, 
= .28 maximum value, 
= .17 minimum value 

The bearing area is given by 

* d/ = .058Z) 2 for the mean, 
= .083Z) 2 for the maximum, 
= .042D 2 for the minimum. 






















* Barr gives the same values. 


Cross-head Shoes. The area of the shoe. or shoes on which the 
pressure comes is given by the formula 

* Area = .37 D 2 for the mean, 

= .52Z) 2 for the maximum, 
= .23D 2 for the minimum. 

The greatest pressures on the guide corresponding to these 
constants is 36.1, 58, and 25.6 pounds per square inch respectively. 


Steam Mean Maximum Minimum 

Pressure Constant. Constant. Constant. 

80 .296 .416 .184 

100 .370 .520 .230 

120 .444 .624 .276 

150 .555 .781 .345 

Steam Ports and Pipes. The areas of the ports are given by 
the formula, area port = CA X piston speed and the constants 
obtained give 

Area steam port = .000152A X piston speed for the mean, 

= .000208Ax piston speed for the maximum, 
= .000 108 Ax piston speed for the minimum, 

Area exhaust port = .000181 Ax piston speed for the mean, 

= . 000256-4. X piston speed for the maximum, 
= .000239^4. X piston speed for the minimum. 

As the piston speed is generally 600 feet per minute (with 
800 for a maximum and 400 for a minimum) we have more simply, 

Area steam port = .09 A for the mean, 

= .10A for the maximum, 
= .08A for the minimum, 
and Area exhaust port = .11^1 for the mean, 

= .125A for the maximum, 
= .10 A for the minimum. 

* Ban* and Trooien use the same values. 

The velocity of steam in 

Steam ports is 6.800 for the mean, 

9.000 for the maximum, 
5.000 for the minimum. 

Exhaust ports is 5500 for the mean, 

7000 for the maximum, 
4000 for the minimum. 

Steam pipes is 6000 for the mean, 

8000 for the maximum, 
5000 for the minimum. 

Exhaust pipes is 3800 for the mean, 

4700 for the maximum, 
2800 for the minimum. 

The diameter of the steam-pipe is given by 

d = .324L> for the mean, 
= .373D for the maximum, 
= .253D for the minimum. 

The diameter of the exhaust-pipe is given by 

d = AOOD for the mean, 
= .463Z) for the maximum, 
= .3577) for the minimum. 

Belting. The mean belt speed is 3900 feet per minute, vary- 
ing from 2600 to 5600 feet per minute. The following constants 
were also observed : 

Square feet belt per minute = 27.4 H.P.-f- 1250 for the mean, 

= 29.0 H.P. + 3000 for the maximum, 
= 23.2 H.P. - for the minimum. 
Barr gives 

Square feet belt per minute = 35 H.P. for the mean, 

= 42 H.P. for the maximum, 
= 30 H.P. for the minimum. 


Trooien gives 

Square feet belt per minute = 21 H.P. + 1000 mean value, 

= 35 H.P. + 1000 maximum value, 
= 18.2 H.P. + 1000 minimum value. 

The Weight of the Engine, including the fly-wheel, is given by 

Total weight = 148 H.P. for the mean, 

= 195 H.P. for the maximum, 
= 112 H.P. for the minimum. 
Trooien gives 

= 132 H.P. for the mean, 

= 164 H.P. for the maximum, 

= 102 H.P. for the minimum. 

The Steam Cylinder. The mean thickness of the cylinder is 
given by the formula = .024Z) + .66 inch. 

Barr gives t = .05Z) -f .3 inch, 

= .054D + .28 inch mean value, 

Trooien, = .072D + .28 maximum value, 

= .035D + .28 minimum value. 

for both high and slow speed engines. 

Flanges. The mean thickness of the flanges and heads is 
1.25, with extremes of l.Ot and l.7t. 

Bolts. The number of cylinder-head bolts is expressed by 
N = CD, where C = .7 and N = number of bolts. 

The sizes of bolts vary from f " to If", generally being from 
f" to 1|". The least number used is eight. Neglecting the 
load due to screwing up, the total cross-section of the bolts at 
the root of the thread is given by a = C'SD 2 = CD*. The con- 
stants obtained give 

a = .0199D 2 for the mean, 
= .0405D 2 for the maximum, 
= .0138D 2 for the minimum. 


The stresses on the bolts corresponding to these constants are 
respectively 3950, 1940, and 5960 pounds per square inch. 


Steam Mean Maximum Minimum 

Pressure. Constant. Constant. Constant. 

80 .0159 .0324 .0110 

100 .0199 .0405 .0138 

120 .0239 .0486 .0166 

150 .0298 .0607 .0207 

Barr gives d =-777+7^ inch, where d is the nominal diameter 

4U Zi 

of the stud. Trooien gives d = .04D + f inch. 

Piston. The face or length of the piston is given by 

Face = .330D for the mean, 

= .4457) for the maximum, 
= .257D for the minimum. 

Barr and Trooien give the same values. 

The thickness of piston shell is .6 to .7 of the thickness of 
the cylinder walls. 

There are generally two piston rings turned to a diameter 
} inch larger than the diameter of the cylinder. 

Clearance volume varies from 2 to 5 per cent in Corliss engines. 
Ratio of length of stroke to cylinder diameter in engines having 
a speed less than 110 revolutions per minute. 

5 = 8 in., 

C=1.63 mean value, 

= 2.40 maximum value, 

= 1.15 minimum value. 

For engines having a speed between 110 and 200 revolutions 

per minute, 


C = 1.36 mean value, 
= 1.88 maximum value, 
= 1.03 minimum value. 


Fly-wheels. Some makers consider only the effect of the rim, 
others take various proportions of the weight of the hub and arms 
into consideration. For standard Corliss engines Trooien gives 


B = . 000,000,004,5, 

C= 890,000,000,000 mean value, 
= 1,330,000,000,000 maximum value, 
= 625,000,000,000 minimum value 

The corresponding values of K are 

K = 4000 mean value, 
= 6000 maximum value, 
= 2800 minimum value. 

The diameter of the fly-wheel in inches is CL. 

C = 4.4 mean value, 
= 5.25 maximum value, 
= 3.25 minimum value. 

The width of the face is 

W = C(D l -B), 
or W 

5 = 50; 

C = .22 mean value, 
= .30 maximum value, 
= .18 minimum value. 

K = 13 mean value, 
= 15 maximum value, 
= 9 minimum value. 

Velocity of the rim is 

68 feet per seconu mean velocity, 

82 feet per second maximum velocity, 

40 feet per second minimum velocity. 


A note with respect to the materials used may be of interest. 
Piston-rods usually are made of mild steel, indifferently specified 
as " open-hearth " or " machinery " steel, but one maker using 
crucible steel. Connecting-rods are made of both wrought-iron 
and steel, with no marked preponderance in favor of either. For 
crank-shafts, most builders use wrought iron, but open-hearth 
and crucible steel are also employed. Crank-pins and cross-head 
pins are usually the same as the piston-rod; a few cross-heads 
are cast solid with the pin, both steel and iron being used. 


In designing the modern high-speed automatic engine, it has 
been found that the constants used for the slower type of engine 
do not give satisfactory results. It was for the purpose of 
obtaining these constants that the present thesis was under- 

Printed blanks were sent to all the manufacturers of high- 
speed automatic engines, with the request to fill in the dimen- 
sions and weights asked for. Ten responded in time to permit 
the use of their data. About six or eight sizes of center crank 
engines of each maker were selected, ranging from 35 to 250 horse- 

Rational formulae were selected for all the important parts of 
the engine. To illustrate the method of deriving the constants, 
we will take a particular case. The formula for the diameter of 
the piston-rod is 

d = VsC'D 2 L*, (1) 

where d is the diameter of rod, S the steam pressure (100 pounds 
gage), C" a constant, D the diameter of the piston, and L the 
length of stroke. Combining S and C ; into one constant, C, we 

d = CV5T, (2) 

* See Sibley Journal, Trans. A. S. M. E., Vol. XVIII, and Bulletin of Uni- 
versity of Wisconsin. 


We substituted in (2) the values of d, D, and L, taken from 
the data, and then plotted d as one co-ordinate and VDL as the 
other. The points were marked by a small circle, and where 
two points coincided, by a double circle. All the points of each 
engine were connected by a certain broken line. A mean line, 
and two extreme lines were drawn, and from their equations, 
the constants were obtained, x = diameter of piston-rod, y = \/DL; 

therefore, since d = CvDL, c = , -- = - = cotangent of the angle 

with the horizontal. In some cases, as in equation (1), the con- 
stant varies as some power of the steam pressure. For these 
cases tables have been constructed giving the constant for each 
increase of 10 pounds, from 50 to 200. These tables have been 
abbreviated for the purposes of this abstract. For simplicity all 
dimensions are in inches unless otherwise specified, and whenever 
the steam pressure is a factor, it has been taken at 100 pounds 
gage. In the case of engines not so rated, that pressure has 
been stated as safe. The complete derivation of the formulas 
here given may be found by reference to the original thesis. 
In this work the following conventions have been used: 

A = area of piston; 

D = diameter of piston; 

L = length of stroke; 
H. P. = horse-power; 

S = steam pressure per square inch; 

N = revolutions per minute; 

d = diameter of part under discussion, 

1 = length of part under discussion; 

h = height of part under discussion ; 

b = breadth of part under discussion. 
Piston-rods. The formula is d = C\ / DL, and 

d = .145 VDL for the mean, 
= .1775v / DL for the maximum, 
= .119 VDL for the minimum. 

Barr gives the same values. 



Steam Mean Maximum Minimum 

Pressure. Constant. Constant. Constant. 

50 .1220 .1490 .1000 

80 .1372 .1675 .1125 

110 .1487 .1815 .1219 

140 .1579 .1928 .1294 

170 .1659 .2023 .1359 

200 .1726 .2109 .1415 

For steam pressures other than 100 pounds, Table I gives 
the constants for the various pressures. 
Connecting-rods. The usual formula is, 

T the breadth, 
and the constants obtained give 

6 = .0545v / 5ZTfor the mean, 
= . 0693 v'DL" for the maximum, 
= .0443 v Z)L for the minimum. 

The steam pressure is the same function of the constant as in 
the connecting-rod formula. 


CONNECTING-ROD, 6 = C\ // )L. 

































* Barr gives these values approximately, 
t Trooien. 


Table II gives values of the constants for rectangular section 

The height of the rod is generally considered to be twice the 
breadth, plus a certain percentage to compensate for the inertia 
of the rod itself. The following values of the height were 
obtained : 

h = 2.73b for the mean, 

= 4.006 for the maximum, 
= 2.186 for the minimum. 

Trooien gives 2.28, 3.0, and 1.85 for the value of these constants. 
The mean factor of safety of the connecting-rod with Barr's 
constants is 27; with Trooien's constants it is 60. 

Also for the length of the rod we found, 

/ = 3.00L " cranks " for the mean, 
= 3.32L for the maximum, 

= 2.46L for the minimum. 

Main Journal. For the prevention of heating, the length 
should be 

(TT T> \ 

^ + 5.23 j for the mean, 

(TT p \ 

Y-- + 9.04 ) for the maximum, 

(TT "P \ 

'j- 1 - + 3 ) f or the minimum. 

The ratio of length to the diameter was found to be 
Z = 2.03(d + .49) for the mean, 
= 2.05(d + .17) for the maximum, 
= 1.63d, for the minimum. 

Barr gives 2.2, 3.0, and 2.0; Trooien gives 2.1, 2.9, and 1.6. 

For the prevention of expulsion of lubricant, the bearing area 
should be sufficiently large, and proportional to the area of 
piston, or 

dl=C'SA = CA. 


The values found for the constant give 
dl = .489 A for the mean, 
= .739 A for the maximum, 
= .3675A for the minimum. 
Barr gives .46, .70, and .37; Trooien gives .48, .78, and .32. 






























The constant in this case varies directly as the steam pressure, 
and Table III gives values for the constant for the different 

In all these engines, the main shaft has the same diameter 
throughout its length, and for strength the formula is 

N ' 
The constants found give 

ITT p 

d = 7.56\ r^ for the mean, 

ITT p 

= 8.76 \ n. 7 ' for the maximum, 

/TT p 

= 5.98 \^ for the minimum. 

Barr gives 7.3, 8.5, and 6.5; Trooien gives 6.6, 8.2, and 5.4. 
Crank-pin. For value of the constant, in the formula, 


which gives the length necessary to avoid heating, we found, 


/ = .333-^ + 2.2 for the mean, 

= .417 T-- + 3.92 for the maximum, 

TT T> 

= .192 ' + .88 for the minimum. 

Barr gives .30, .46, and .13 as values of C and 2.5" as the value 
of B. 

For bearing area, we found, from dl = CS'A = CA, 
dl = .22 A for the mean, 
= A4A for the maximum, 
= .0693 A for the minimum. 
Barr gives .24, .44, and .17 as the values of the constant (7 k 


CRANK-PIN, dl = CA. 





























As a check the ratio of length to diameter was found and is 

l = d for the mean, 

l = l.22d for the maximum, 

/= .9<i for the minimum. 

Trooien gives .87, 1.25, and .66 as the constants. 

In center-crank engines, assuming that the distance from 
center to center of main bearings is 4.2d, Trooien finds, in calcu- 
lating d for strength, the following constants in the formula, 

d = CD, 

C=.40 mean value, 
= .526 maximum value, 
= .28 minimum value, 

Cross-head Pin. For the bearing area the formula is 

and the values of the constant found give 

d = .1045A for the mean, 
= .346A for the maximum, 
= .0664 A for the minimum. 






































The ratio of length to diameter was found to be 

/ = 1.335d for the mean, 
= 2d for the maximum, 
= 1.07d for the minimum. 

Trooien gives 1.25, 1.5, and 1.0. 
Barr gives 1.25, 2.0, and 1.0. 

Cross-head Shoes. For the bearing area of the cross-head 
shoes, the constants found give, in the equation, 

Area = .61 1 ( A + 25) for the mean, 

= .69801 + 123) for the maximum, 
= .46 (A 2) for the minimum. 



Steam Mean Maximum Minimum 

Pressure. Constant. Constant. Constant. 

50 .3055 .3490 .230 

80 .4888 .5584 .368 

110 .6721 .7678 .506 

140 .8554 .9772 .644 

170 1.0387 1.1866 .782 

200 1.2220 1.3960 .920 


100 .63 1.60 .45 


125 .53 .72 .37 

For the maximum pressure per square inch of shoe, Barr gives 

27 for the mean, 

38 for the maximum, 
10.5 for the minimum, 

Trooien gives 39.5 for the mean, 

57 for the maximum, 

28 for the minimum. 

Cylinder Dimensions. The ratio of length of stroke to diam- 
eter of cylinder in engines having a speed greater than 200 revo- 
lutions per minute, 

L = CD. 
C=1.07 mean, 
= 1.55 maximum, 
= .82 minimum. 

Clearance volume varies from 5 to 11 per cent. 

The thickness of the cylinder cover at the center varies con- 
siderably, but may be taken at 2.75 times the thickness of cylin- 
der walls. The thickness of the flanges for holding cylinder 
covers may be taken at 1.12 times the thickness of the cylinder 
walls. For number and size of bolts, see Slow-speed Engine Design. 

Piston and Piston Speed. For obtaining the dimensions of 
the face of piston there is no rational formula applicable, but 


an empirical formula was constructed; the ratio of face to 
diameter being found thus for horizontal engines, 

Face = .4375D for the mean, 

= .65D for the maximum, 
= .299D for the minimum. 

Trooien gives .40, .47, and .30 as the constants. 

For ascertaining the piston speed a curve was plotted with 
revolutions per minute as one co-ordinate, and length of stroke 
as the other. The resulting mean curve is an equilateral hyper- 
bola showing that for this class of engines the piston speed is 
constant, and is 600 feet per minute. 

Trooien gives 

600 = mean speed, 
900 = maximum speed, 
320 = minimum speed. 

Steam Ports and Pipes. In designing ports it is customary to 
consider the velocity of steam through the passage as equal to 
the ratio of the area of the piston to the area of the passage, 
multiplied by the piston speed. Since the piston speed is quite 
constant, about 600 feet per minute, the area of these passages 
is proportional to the area of the piston. For the steam ports 
the relation is 

Area of steam ports = .0936 A for the mean, 

= .136A for the maximum, 
= .0544A for the minimum. 

Barr gives for the velocity of steam through steam ports, 
5500 mean, 
6500 maximum, 
4500 minimum. 
Area steam ports = .11 A mean, 

= .13 A maximum, 
= .09A minimum. 
For the steam-pipes, 

Diam. of pipe = .452D 1.42 for the mean, 

= .54D 1.02 for the maximum, 
= .382D-1.07 for the minimum. 


Barr gives for the velocity of steam through pipes, 
6500 mean, 
7000 maximum. 
5800 minimum. 
Diam. of pipe = .30Z) mean, 

= .32D maximum 
= .29Z) minimum. 
For the exhaust-pipe, 

Diam. of pipe = .503Z) 1.4 for the mean, 

== .5D for the maximum, 

= .57) 2.24 for the minimum. 

Barr gives for the velocity of steam through exhaust pipes, 
4400 mean, 
5500 maximum, 
2500 minimum. 
Diam. of exhaust pipe = .37Z) mean r 

= .50-D maximum, 
= .33D minimum. 

Belting. The relation between the square feet of belting per 
hour and horse-power transmitted was found to be 

Square feet belting per hour = 2000 (H. P. + 50) for the mean, 

= 2000(H.P.+95) for the maximum, 
= 2000(H.P.-50) for the minimum. 
Barr gives 

Square feet belting per minute = 55 H.P. mean, 

= 70 H.P. maximum, 
= 40 H.P. minimum, 

Fly-wheel. For governing, Professor Thurston in his " Manual 
of the Steam Engine," shows that the weight of the rim of fly-wheel 

TT T> 

is proportional to Trifp. where DI is the diameter of wheel in 
inches. The constants found give 


TT T) 

Weight of rim = 833,000,000,000^ 2 ^ 3 for the mean, 

TT T) 

= 2,780,000,000,000 ^ ' ' for the maximum, 

TT T) 

= 341,000,000,000^^ for the minimum, 

Barr gives 1200, 2000 and 650 billions for the constants. 
Trooien gives 1300, 2800, and 660 billions for the constants 
for engines up to 175 H.P. For large engines, however, the 

TT T) 

formula W = Cx + B seems better. 

= 1000, 

C= 720,000,000,000 mean, 

= 1,140,000,000,000 maximum, 

= 330,000,000,000 minimum. 

The relation between the length of stroke and the diameter of 
the fly-wheel is given by Di = CL. 

C = 4.4 mean, 
= 5.0 maximum, 
= 3.4 minimum. 

For the linear velocity of the periphery, we averaged the 
velocities of each maker, and then took a total average. This 
average gave 4232 feet per minute, and varies from 5730 to 
3060 feet per minute. 

Reciprocating Parts. The weight of reciprocating parts is 

D 2 

proportional to =- and the constants give 

Z> 2 
Weight of parts = l,850,000-^p, 

the mean curve being an equilateral hyperbola. 
Trooien gives 

2,000,000 mean, 
3,400,000 maximum, 
1,370,000 minimum. 


In cases, where obtainable, the balance weight opposite the 
crank-pin was about 75 per cent of the weight of the reciprocating 

Weight of Engine. It being of possible interest, the relation 
between the total weight of engine and rated horse-power was 
found, and is 

Weight of engine = 117(H.P. -7). 

For belt-connected high-speed engines Trooien gives for in 
formula TF = CxH.P., 

C= 82 mean, 
= 120 maximum 
= 52 minimum. 

For direct-connected engines the weight of the engine without 
the generator was 10 to 25 per cent greater than the weight of 
belt-connected engines of the same capacity. 




Water, 1. 

Water, 1. 

Degrees Fahr. 

Weight in 

Metals from 32 to 212 










Per cu. ft. 




Copper . . 

Iron, cast 
" wrought . . . 


Mercury at 32 . . 





Alcohol (mean). . . 
Oil, petroleum . . 
Steam at 212 . 
Water 62 

Ice at 32 


32 F. 




C P. 


Specific Heat 
*Z. &P 

131.40 184.77 

per Cu. 
Ft. at 
32 F. 



Acetylene gas 


Carbon monoxide, C< 
Carbon dioxide CO 2 . 

3. . . 




Ethylene, C 2 H 4 . . . . 

Hydrogen. . . 

Methane CH 4 

Nitrogen. ... 


Sulphur dioxide, SO 2 


Cu. Ft. 
at 62 F 


. 32 F. 

$ of One 

(1, at 

62 F. 

Specific Heat per Cubic Foot 

at Co 
32 F. 

62 F. 

at Con 
32 F. 

62 F. 

Air. . 


3 178.2 






Carbon monoxide. . . 
Carbon dioxide. . . 






































6. .50 



























































































































































1 . 1474 






























































1 . 5581 










1 . 5686 




2 7081 






1 . 5790 







The following table gives the heating values of different pure fuels as deter- 
mined by burning them in oxygen in a calorimeter. 





Acetylene, C.H 2 to CO 2 and H 2 O . . 
Alcohol, methyl or wood, CH 4 O. . . . 
'' ethyl or sugar C H 6 O. . .. 

\ 10,102 
\ 9,915 
/ 8,080 
1 8,137 
/ 2',403 
\ 2,385 
fl 1,858 
\ 11,957 
/ 34,462 
\ 34,342 
/ 13,120 
\ 13,063 



Favre and Silberman 
< . < i t ( 

Favre and Silberman 
St ohman 
Favre and Silberman 

Favre and Silberman 

1 1 ft < i 


Favre and Silberman 
< < 

Favre and Silberman 

t i 

Favre and Silberman 
N. W. Lord 

Benzole gas, C 6 H to CO 2 and H 2 O. . 

Carbon (wood charcoal) to CO 2 . . . 
Carbon to CO 

CO to CO per unit of CO 

CO to CO 2 per unit of C 

Ethylene (Olefiant gas), C 2 H 4 to 

Gas illuminating . 

Hydrogen gas to H^O . . . 

Methane (Marsh gas), CH 4 to CO 2 
and H 2 O 

Sulphur to SO* 





Pure dry air is a mixture made up of 20.91 parts of O and 79.09 parts of N 
by volume (viz., in the ratio of one part of O to 3.782 parts of N), or 23.15 parts 
of O and 76.85 parts of N by weight (viz., in the ratio of 1 part of O to 3.32 
parts of N). 

Lbs. of 
O per Ib. 

Lbs. of N 

Air per Ib. 
= 4.32X0 

per Ib. 

Carbon to CO 2 C+20 = CO" 




12 52 

Carbon to CO . C + O=CO 




6 76 

Carbon monoxide to CO 2 . .CO + O = CO 2 
Alcohol . . C-H 6 O + 60 = 2CO 2 + 3HoO 




9 94 

Acetylene C 2 H 2 +50 = 2CO 2 +H 2 O 
Ethylene C 2 H 4 + 6O = 2CO 2 +2H 2 O 
Hydrogen' 2H + O = H- O 




34 56 

35 56 

Methane . . .CH 4 +4O = CO 2 +H 2 O 



17 28 

18 28 

Sulphur S+ 2O = SO 2 




5 32 



Difference between the Dry and Wet Thermometers, Degrees F. 





























Relative Humidity, Saturation being 100. (Barometer = 30 ins.) 






































































































































































































































































Mixtures of Air Saturated with Vapor. 




03 P 



Force of 

Weight of Cnbic Foot of the 
Mixture of Air and Vapor. 





the Air in 



Weight of i 
of Dry Ail 

Elastic Foi 
Inches of 


of Air and 
Inches of 

of the Air, 

of the 

Weight of 

with 1 Ib. 
of Air, 











































29 583 





































































































































The weight in Ibs. of the vapor mixed with 100 Ibs. of pure air at any given 
temperature and pressure is given by the formula 

62.3 X E 29.92 
29.92 - E X ~y ' 

where E = elastic force of the vapor at the given temperature, in inches of mer- 
cury; p absolute pressure in inches of mercury, = 29.92 for ordinary atmos- 
pheric pressure. 





'" . 






Specific Heat 
of Water. 





Entropy of 1 
Ib. of Steam 





si 1 . 

1 &< 




Specific Heat 
of Water. 







Entropy of 1 
Ib. of Steam 
from 32 F. 






+ <]> 















805 6 











807 9 


1 076 









813 6 


1 063 








816 4 







1 532 





1 051 









833 7 



1 019 








838 2 










844 . 5 




















IToTB. The following table gives the data required by the engineer in this connection as based upon the expr?toents of Regnault. The temper*- 
fores, pressures, and heat-iaeasures are all from Regnault s experiments. The other quantities were calculated by Mr. R. H. Huel.* adopting the for- 
mulas of kankine already given to obtain quantities not ascertained by direct experiment. The two parts of thf latent heat of vaporization are separately 
determined, and the internal thus distinguished from the external work of expansion. British measures are adopted. The nomenclature is sufficiently 
well explamed by the table-headings. 

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Values of . Adiabatic Expansion of Steam 

Ratio of 

Cut-off, -. 

Percentage of Steam and Value of n. 








































T 4 T 




















T 4 3 






































































T 2 T 





























































































Values of for Steam, Air Gas. and Mixtures. 




Steam and Leakage, 
Actual Engines. 







.S - 

w . 

x'" u ' = 

>'Sb . 





n, 0.50. 

n, 0.75. 


mal, n, 




SQ e 

'o ft 

go " 


n, 141. 

































T 4 T 


















T 4 3 



























T 4 F 




































T 2 T 


















T a j 













































B v 



























.503 .488 









1. 0001. 000 1.000 






.194 ! .218 .204 










.310 .338 



.192 .216 .202 














.190 .215 .200 














.189 .214 .199 














.187 .212 .197 


.928 .934 











.185 .210 .195 














.183 .208 .193 














.182 .207 .192 














.180 .205:. 190 








.440 11.0 





.179 .204 .189 








.435 11.2 






.202 .187 


.8171 .830 







.275'. 301 



.177 .2001.186 









11.6 .272i.298 






.780 .795 




.436 .4211 11.8 





.196 .183 







.432 .417 I 12.0 

.264 .290 












.428!. 4131: 12.2 















.408 12.4 

























.705 .723 




















































.406!. 3901 














.402 .386 


.239 .265 



.162 .185!. 171 









.236 .262 











.396 .380 


.234 .260 




.183 .169 







.392 .376 






.1591.182 .168 







.389:. 373 







.180;. 167 







.385 .370 







.179'. 165 















.178 .164 










.221 . 247 1. 232 






























.217 .242 















.215 .240 















.213 .238 






























.209 .234 








































































, .515 







.197 .222 











.195 .220 


Column r, the ratio of expansion = 

iQ_Q r s f For dry steam, expanded with- 

" A, ratio of mean to initial pressure, = \ out gain or loss of heat, in 

Pi r { a non-conducting cylinder. 


Pm = 1+hyp. log, r t For damp steam, ex- 
pj r t panded receiving heat. 

i7_ifi r ^ fFor dry steam, expanded 

ii iHI I receiving heat sufficien* 

Pi r [ to prevent liquefaction. 

' \Jl VilJT .-IftlJll, CAJJHH-*C;VJ. 

C, " " " * ^ = -{ receiving heat sufficient 

Pi r [ to prevent liquefaction. 

RULE. To find the mean pressure exerted throughout the stroke, multiply the initial 
pressure by the number opposite the ratio of expansion, in the column corresponding with the 
conditions of expansion. (From Northcott.) 
































































































































































































































































































23.3 17.0 
































17.4 20.8 












































12 5 


































25.4 18.4 















25.7 18.6 






























26.3 19.0 















































k 4.0 
























17.0 12.8 
































5 18 












32. 6 23. 028. O 














34.1 24.029.3 





Column r, ratio of expansion = 

" A, ratio of initial to final pressure p 2 =- 



For dry steam, expanded without 
gain or loss of heat in a non-con- 
ducting cylinder. 

For damp steam, expanded receiv- 
ing heat. 

For dry steam, expanded receiving 
sufficient heat to prevent liquefac- 

RULE. To find the final pressure obtaining with any ratio of expansion, divide the initial 
pressure by the number opposite the ratio of expansion, in the column corresponding with the 
conditions of expansion. 



W S 

C | 


Cd ffi 

K * 

* % 

g O 

< K 

K 3 

H E 

^ g 

s 1 






g.l g 


Q X 

CO 1C 1C "t CO fC CM CM CM -H < i -H fH t i O 

-. . v s_ 


O 2; 

S -*i |. 




co p CM x *** co CM t-- rc 01 io i i r>- ?o 

c "^ cM-HOOiXXt^r^t^-cocoic>C'*Tficcrcc ? 



3 3 



fe.tf v CC-Hr^-fT-HO>XCOiCCOCMOO5t^COTfCM^H 

a^ o T f r f-^^ : 5t- l ^r' 


CU CM CO ' O X CO >C Tf Tf CO CM ^H O O5 O5 X t>- CO O 


S -a 
5 Q 






(According to the experiments of Knoblauch and Jacobs.) 

Lbs. per Sq. 
In. Absolute. 



Lbs. per Sq. 
In. Absolute. 


































56 93 




























Absolute zero, 7 

pressure, correct, 267 
Absorption, refrigeration by, 531 
Accelerated motion, 347, 448 
Action of clearance steam, 189 
Adheating, 432 
Adiabatic compression, 141 

curve, 143 

expansion, 141, ratio of tempera- 
tures in, 143 
Advance, angle of, 92 
Air, and vapor, weights of, Table VI 

composition of, Table IV 

cooling in condensers, 282 

leaks in condensers, 234 

specific heat of, Table I 

thermometer, 6 
Air-pump, 23, 269 

action of, 276 

design, 218, 224, 225 

dry, 282 

Edward's, 272 

efficiency, 270 

for surface condenser, 273, 278 

wet, 281 
Alcohol, 53 
Alden brake, 34 
Allen dense-air machine, 531 
Ammonia ice-machines, 531 
Angles, blade, 454 
Angular acceleration, 348 

advance, 92 

displacement, phase degrees, 405 
Areas representing heat, 147-153, 208 
Astatic, 336 
Atmosphere, Table VI 
Auxiliaries, measurement of steam used 

by, 427 

Balance wheel, design, 387 
Balancing engines, 400-403 
Barometric condenser, 236 
Barrel calorimeter, 171 
Barrus calorimeter, 173 
Baume hydrometer, 524 

degrees converted into specific grav- 
ity, 524 

Bearing, details of, 17 
Belting, 552, 564 

Belt wheel, design, 386 
Bilgram valve-diagram, 103; geomet- 
rical relations of, 107 
Blade angles, steam-turbines, 455 
Boiler efficiency, 35 

feed-pump, 13, 285, 287, 289 

horse-power, 36 
Boiling and evaporation, 128 

in vacuo, 534 

Boiling-points of water, Table VIII 
Bolts, number and size, 553 
Boulvin's temperature-entropy dia- 
gram, 221 
Boyle's law, 137 

Brake horse-power, definition of, 32 
Brakes, friction, 32 
Bridge, thickness of, 113 
British thermal unit, definition of, 5 
Buckeye valve-gear, 364 

C P , C v , for perfect gases, Table I 
Calibration of gages, 386, 427 

indicator-springs, 74-76, 502 

thermometers, 8, 419 
Calorific power of gases, 476 

Barrus continuous water, 173 

Carpenter, 172 

Junker, 506 

Mahler, 506 

normal reading of, 175, 178 

Peabody, 173 

separator, 173 

throttling, 173 

water equivalent of, 176 
Carbon, air-burnt, 488 

steam-burnt, 488 
Carnot cycle, 154, 228 
Centrifugal force, 329; derivation of 

formula for, 330 
Charles' law, 137 
Circulating pump, 25, 288, 290 
Circulation of water in the boiler, 181 
Clearance, definition, 72 

line, 72 

steam, elimination of, 84 

surface, 186 

surface, effect of, 188 

volume, 72, 416 




Coal, heating value of, 35 

in gas-producers, use of, 490 

measurement of, 429 

per horse-power-hour, measurement 
of, 35 

standard, thermo value of, 36, 417 
Coal-gas, analysis of, 486 

heating value of, 489, 490 
Column, mercury, 28 
Coefficient, heat transmission, 256, 257, 


Combining indicator-cards, 318 
Combustion, heat of, 36, 485 

of coal, rate of, 137 

temperature arising from, 486 
Compound engines: 

combining cards of, 317 

diagram factor of, 322 

distribution of work in, 308, 311, 316 

method of laying out the cards for, 
304, 311 

ratio of expansion in, 306, 320 

records made by, 304 

size of, to find, 315 

theory of, 307 
Compound quantities 2, 4 
Compressed-air formulas, theoretical 

and practical, 142 

Compression, and expansion of air, 

of steam, 188 

work done during, 142 
Concentration of cane-juice, 527 
Condensation in steam-engines, 158 

pipes, 182, 186 
Condensation at constant volume, 219 

initial, 326 
Condensers : 

barometric, 236 

condensing surface in, 241 

correct pressure in, 267 

design of, 235 

dimensions of, 234 

ejector, 238 

increasing surface efficiency of, 262 

jet, 238 

pressure in, 28 

surface, 23, 239 

syphon, 238 

transmission of heat in, 243 

tubes, of 241 
Condensing, gain by, 267 

water, 235 
Condensing water, coolers for, 265 

use of, 233 

Connecting-rod: design, 546, 558; 
division of mass for turning mo- 
ment, 401 ; division of mass for 
shaking forces, 401 ; effects caused 
by the obliquity of, 88 
Constant heat curve, 224 

temperature curve, 213 

Constant volume, condensation at, 186 

curve, 219, 220 

Constants (R) for perfect gases, Table I 
Contraflo condenser, 260 
Cooling-tower, 265 

effect of change of season on opera- 
tion of, 267 
Cork insulation, 183 
Corliss engines, 18, 366, 368 
Counterbalancing engines, 400, 402 
Coverings for steam-pipe, 183 
Crank-pin, design, 548, 560 
Crank-shaft, turning effort in, 382, 406 
Cranks, combination of, 405 

throw of, 85 

twisting moment in, 382 
Critical temperature, 152 
Cross compound engines, 311-314 
Cross-head pin, design, 550, 562 

shoes, 565 

Crossed rods, definition, 358 
Cross-section paper, logarithmic, use 

of, 144 

adiabatic, 141 

constant heat, 219 

constant volume, 221 

general expansion, 139, 143 

hyperbolic, 83, 139 

isothermal, 78 

saturated steam, 78, 213 

superheated steam, 441 

water-line, 210 
Cut-off, actual, 65 

commercial, 65 

real or actual, 65 
Cycle, Beau de Rochas, 481 

Carnot, 154, 228 

Diesel, 497 

Lenoir, 481 

Rankine, 228 
Cylinders, details of, 201 

dimensions, 562 

Cylinder walls, thermal action of, 188, 

thickness of, 112, 553 
Cylinder waste, reducing, 435 

Degree of reaction, 476 
De Laval turbine, 457 
Dense-air machine, 531 
Design of, see part required 
Diagram, Bilgram, 103 

compound engine, 308 

crank-pin pressure, 382, 406 

of effective driving pressure, 382, 406 

of shaking forces, 404 

of turning moment, 382 

Zeuner valve, 93, 94 
Diagram factor, compound engi es, 

simple engines, 81 


Dimensions of steam ports and pipes, 
110, 434, 502, 551, 564 

Distillation, 517 

Division of mass of connecting-rod for 
pin pressures, 401 ; shaking-forces, 
401 ; turning-moment, 401 

Double poppet-valves, 371, 451 

Dryness of steam, methods of deter- 
mining, 171 

Dry-steam fraction, 193 

Eccentric, throw of, 85, 89 
equivalent, 360 

rod, 87, 357 
Eccentricity, 85 
Economizer, 13 
Economy of vacuum production, 264 

ratio of, of an engine to ideal engine, 


Effects, multiple and single, 517 
Efficiencies, combining, 40 

definition of, 35 

gas-engine, 508 

maximum, of jets, 456 

mechanical, 35 
Efficiency, of injectors, 297 

of steam-engines, 267 

thermal, 42, 263 
Ejector condenser, 322 
Electrical units, 32 
Elementary quantities, 1, 2, 131 
Ellipse, valve, 114 
Energy, definition of, 3 

forms of, 4 

kinetic, 3, 331 

potential, 126 

sources of, 14 

transformation of, 4, 126, 378, 456 

ratio of economy of, to an ideal 

engine, 229 
Engines, see kind of 

average steam consumption of, 37 

details of, 17-21 
Entropy, chart, 590 

definition of, 207 

derived from indicator-card, 225, 491 

diagram of a real engine, 229 

tables, 575, 582 
Equivalent, eccentric, 360 

evaporation, 170 

factors of evaporation, 170 

weight at crank-pin center, 402 
Evaporation, factor of, 37 

rate of, in boilers, 36 
Evaporation and drying, 129 
Evaporation by the multiple system, 

latent heat of, 164 

table of, Table VIII 

total heat of, 164 
Evaporators, 517 
Exhaust-ports, width of, 113 

Expansion, adiabatic, 141 

at constant volume, 219, 220 

following the law PF" = C, 139 

hyperbolic, 77 

of water, 163 

of water when heated, 163 

proper ratio of, 325 

real ratio of, 72 

valve, Meyer, 370 

External work in adiabatic expansion, 
142, 215 

in isothermal expansion, 79, 213 

Factors of evaporation, 170 
Feed-pump, 73, 285, 287, 289 
Feed-water heaters, 248 

choice of, 250 

closed, 251 

heating surface of, 256, 257 

open, 251 

percentage of gain in, 253 

versus economizers, 254 

measuring, 427 
Flanges, 553 
Flow of air, in pipes, 117 

through orifices, 447 
Flow of steam through pipes, 117 
Fly-wheels : 

accurate weight of, 407, 555, 565 

approximate weight of, 384 
Foaming, cause and prevention, 181 

definition of, 180 
Force, centrifugal, 330 

exerted by a deflected stream, 449 

moment of, 2 

required to produce acceleration, 347 
Form, steam-engine tests, 537 
Formula for: 

adiabatic expansion, 141 

Barrus calorimeter, 173 

calorimeter correction, 175, 178 

Carpenter calorimeter, 172 

centrifugal force, 330 

energy of reciprocating parts, 379- 

fly-wheels, 385, 407 

heat to produce wet steam, 169 

I. H. P. of an engine, 31 

impulse trom jets, 449, 453, 456 

Peabody calorimeter, 177 

perfect gases, 135, 142, 148, 153 

revolving pendulum governor, 332 

Rites governor, 349, 386 

shaft governors, 341 

steam velocity in nozzles, 216 

superheated steam, 437 

the total heat of evaporation, 165 

turning force and moment, 2 

weight of steam accounted for by 

the indicator, 193 
Friction brakes, 32, 34 
Friction of elbows, valves, pipes, 118 



Friction of a governor, 339 

of air in pipes, 118 

of steam in pipes, 118 
Fuel economizers, 13 

gas, 485, 495 

heat of, 486 

measurement of, 505 
Fundamental equations of thermo- 
dynamics, 152 

Gage, Bourdon, 27 

vacuum, 28 
Gages, see Calibration 
Gallons, displacement of a pump in, 329 
Gas, alcohol, 482 

ammonia, Table I 

calorific equivalent of, 486 

combustion, rise in temperature, 486 

efficiency of, 484 

test, form of, 538 

test, rules for, 502 
Gas, flow of, in pipes, 117 

illuminating, fuel valve of, 486 

meters (see Calibrating), 504 

producers, 487 
Gases, Charles' law of, 137 

Joules' law of, 137 

specific heats of, 571 

weight and specific gravity of, 571 
Gasoline-engines, 484 
Governors : 

details of, 19 

fly-ball, 332 

friction, 338 

Hartnell, power of, 339 

practical forms of, 334 

Proell, 335 

Rites inertia, 348, 386 

sensitiveness of, 334 

shaft, 343 

throttling, 328 

weighted, 332 
Xjrate area, to find, 37 
Green's fuel economizer, 13 

Hamilton-Holzwarth turbine, 480 
Heat balance of gas-engines, 484, 508 

consumption in a gas-engine, 505 

consumption in a steam-engine 
plant, 36, 41 

curve of constant, 224 

effect on solids, liquids, gases, 130 

expansion by, 131 

graphical illustration of expenditure 
of, 43 

interchanges, 196 

internal work, 132 

latent, of evaporation, 132 

mechanical equivalent of, 9 

of combustion, 35, 486, 490 

of the liquid, 162 

Heat represented by areas, 148-153 

required at melting-points, Table I 

required to produce steam, 165 

specific, 132, 134 

storing, 127 

total, in steam, 132, 164 

transmission of, in boilers, 242, 245 

in condensers, 242 ; in cylinders, 303 ; 
in feed-water heaters, 298 ; in mul- 
tiple effects, 520 ; in vacuum-pans, 

Heaters, feed-water, 248, 256, 298 
Heating surface of boilers, definition 
of, 11 

values of various substances, 572 
Heat-units, 132 
Helical springs, 348 
Hirn's analysis, 194 
Horse-power, boiler, 36 

to supply electric lamps, 39 
Horse-power, definition, 31 

brake, 32 

equivalents of, 32 

hour, 35 

indicated, 31, 42 

of steam-engines, 31, 42 
Hot water, transmission of heat 

through pipes carrying, 184 
Hot-well, definition of, 23 
Houghtaling reducing motion, 54 
Humidity, relative, Table V 
Hyperbola, equation of, 68, 69 

construction of, 68, 69 
Hyperbolic logarithms, Table II 

Ice, specific heat of, 160 

latent heat of, 160 

making machines, 510 

making, units of, 484 
Ideal engines, ratio of economy to, 


Impact of bodies, 295 
Indicated horse-power, 31, 42, 73 
Indicator-diagrams : 

analysis of, 192 

area of, 79 

converting, into entropy diagram, 
225, 491 

correction of, for clearance, 82; for 
energy of reciprocating parts, 381 

of gas-engines, 492; converted into 
entropy diagrams, 225 

pendulum rig for taking, 59 

reducing motions for, 59 

water consumption shown by, 191 
Indicators, see Calibration, 46 

Crosby, 46 

Tabor, 52 

Indicator-springs, testing, 74-76 
Inertia governors, theory of, 349, 000 
Inertia of indicator pistons, 65 
Initial condensation, 186, 302, 326 



Initial amount of superheat required 

to prevent, 437 
Injection water, 235, 241 
Injectors, theory of, 292 

method of using, 296 
Interchange of heat in cylinders, 196, 

198, 303 

Internal energy, 164 
Isochronous, 337 
Isothermal expansion, 68, 69, 77 

work done during, 79 

Jacket steam, 198, 303 

water, 426 
Jet condenser, 26, 233 

impulse due to, 450 
Joules' equivalent, 9 
Journal, main, design, 547, 559 

Kinetic energy, 3, 131, 164, 330 

Lap and lead of valves, 89, 111 
Latent heat: 

of evaporation, 1G3, Table VIII 

of fusion, 120, Table I 
Leakage of air, 234 ; gas and oil, tests 
for, 502 

of steam, tests for, 414, 421 

of water, tests for, 421, 427 
Lenoir cycle, 481 
Link arc, 353, 360 
Links, 352 
Liquids, expansion of, 131, 132 

heat of, 162 

molecular movement in, 127 

vaporizing, 130 

weight and specific gravity of, 

Table I 

Locomotives, 568 

Logarithms, converting hyperbolic to 
common, 494 

hyperbolic, Table II 
Marine engines: 

air-pump for, 274 

circulating pump for, 290 

diagram factors for, 325 

link for, 354 

ratio of expansion in, 325 
Mass of connecting-rod, division of, to 
find effective and shaking forces, 
377, 401 

Maximum efficiency of jet action, 426 
Measuring clearance, 417 

engines, 416 

revolutions, 430 

Mechanical equivalent of heat, 9 
Melting-point of solids, 290 
Metals, specific gravity, of Table I 
Meyer valve-gear, 370 
Mid-position of valve, 92 
Moisture in steam, 169 
Molecular motion, 128 

Moment of a force, 294 

of inertia, 400 
Momentum, 294 
Multiple distillation, 517 
Multiple effects, 517 

expansion engines, proper ratio of 
expansion, 325 

Naperian logarithms, Table II 

Napier's formula, 172, 178 

Normal reading of a calorimeter, 175, 

Nozzles, flow in, 444, 446 
in calorimeters, 170 
in steam-turbines, 457, 464 - 
velocity of steam in, 216 

Open rods, definition, 358 
Orifices, flow of steam from, 172, 178 
flow of water from, 416 
thermal effects on steam flowing 

through, 216, 224, 446 
Oxygen required for combustion, 
Table IV 

Parabolic governor, 338 
Parsons' steam-turbine, 466 
Peabody calorimeter, 173 
Pendulum, or conoidal governor, 332 
Perfect gases, definition of, 127 

primary laws of, 135, 142, 145 
Phase degrees, 373, 406 
Pin, pressure on crank-, 382 
Pipes, equivalent, 119 

exhaust, 552, 564 

flow of air in, 115 

flow of gas in, 116 

flow of steam in, 116 

loss of head in, 118 

steam-, covering for, 183 

steam-, sizes of, for engines, 110, 118, 

551, 563 
Piston, design, 562 

details of, 20, 554 
Piston movement, 86 
Piston-rod, design, 545, 557 
Pole degrees, 374 
Poppet-valves, 371 
Port, width of, 90, 111, 551, 563 
Port-opening, 90 
Potential energy, 3 
Pounding of engines, 380 
Power of a governor, 339 

of an electric circuit, 32 

rate of work, 31 
Pressure, bearing, 548 
Pressure from producer-gas, 491 

net steam, 375 

volume and temperature, relations 

in perfect gases, 147 
Priming, 181 
Producer-gas, 487 



Producer-gas, pressure from, 491 
Proell governor, 335 
Properties of substances, 477 
Pumps : 

air, 23, 277-284 

average steam consumption of, 37 

boiler-feed, 13, 285 

capacity of, 289 

cards from, 283, 286 

centrifugal, 290 

circulating, 25, 288 

displacement of in gallons, 289 

efficiency of, 285 

piston speed of, 289 

sizes of, 289 

speed of water through, 288 
Purifiers, 254 
Pyrometer, see Calibration, 419 

Quality of steam, 166, 177, 180 

R, for perfect gases, Table I 
Radiation in steam-calorimeters, 175 
Rankine cycle, 228, 229 
Rankine's formula for flow of steam 


Rates, 30 
Ratio of expansion, 72, 321 

proper, in multiple-expansion en- 
gines, 325 

Reaction, degree of, 476 
Receivers, definition of, 16 

design of, 298, 325 

effect of, 325, 326 

reheating in, 298 

size of, 326 
Reciprocating parts, 375 

concentrated at crank-pin, 377 
Recompression, 189 
Reducing motion, 59 
Reducing- wheels, 54 
Re-evaporation, 187 
Refrige rat ing-machines, 530 

Allen dense-air, 530 

ammonia absorption, 530 

ammonia compression, 532 

entropy diagram of, 535 

ice-melting capacity, 537 
Regnault's formula, 166 
Reheaters, 297 
Revolutions, measuring, 420 

Saddle-pin, position of, 358 
Saturated steam, dry, definition of, 166 

expansion curve of, 213 

line, 213 

pressures, Tables VIII to XIII 

wet, definition of, 166 
Scavenging, 482 
Sensitiveness of a governor, 334 
Separator calorimeter, 173 

Separators, 13, 297 
Shaft-governor, 3'41 
Shaking forces, 404 
Simple engine, diagram factor, 81 
Slide-valve : 
balanced, 351 
diagrams, 93, 101 
lap and lead of, 88 
Solids, melting-point of, 160 

properties of, Table I 
Specific gravity: 
of gases, Table I 
of liquids, Table I 
of solids, Table I 
Specific heat, definition of, 132 
of gases, 132, 134, 571 
of liquids, 132 
of solids, 132 

of superheated steam, 589 
Speed, measuring, 430 
Springs, calibration of, 76 

for governors, 348 
Standard boiler, 41 

efficiency, 41 
Standard coal, 41 
Standard form for testing gas-engines, 

512, see Tests 

rules for testing gas-engines, see 
Tests; for testing steam-engines, 
see Tests; for testing rules, see 

steam-boiler, 41 
Standards of efficiency and ecnoomv. 


Starting and stopping tests, 424 
Steam, accounted for by indicator, 191 
actual consumption of, 37, 201 
condensation of, due to expansion, 


condensation of, initial, 186, 302, 326 
dry saturated, 169 
expansion curves, 213 
expansive working of, 301 
flow, 110, 588 
in nozzles, 216, 445 
in orifices, 172, 178 
in pipes, 115 
jacket, 198, 303, 305 
lead, 111 

line at constant pressure, 212 
loss of pressure of, 321 
moisture in, 169 
nozzles, 447 
pipe covering, 183 
pipes, 116 
plant, 425 
ports, 90, 110 
quality, see Calorimeter 
separator, 13 

superheated, see Superheater 
table, Table VIII, IX 
velocity of, in nozzles, 216 



Steam, weight of, accounted for by 

indicator, 191 
Steam-boiler, economy of, 13, 35 

heating-surface of, 1 1 
Steam-calorimeters, 171 
Steam-engines : 

compound, 305 

Corliss, 366, 368 

counterbalancing, 400-403 

expansion work in, 68, 69, 77 

leakage of steam in, 185, 414, 421 

mean effective pressure in, 77, 79 

measurement of steam in, 438 

measure of duty in, 36 

most economical point of cut-off, 

proportions of cylinders of, 304, 

ratio of expansion in, 70, 321 

steam consumption in, 186 

tests of, rules for conducting, see 

using superheated steam, 441 
Steam-pipes, 551, 563 
Steam-ports, 551, 563 
Steam-turbines, economy at various 
loads, 462 

economy at various speeds, 462 

economy of various sizes, 462 

effect of water in, 462 
Superheated steam, data of test, 436 

efficiency of, 363, 437 

engines using, 438 

entropy diagram of, 441 

in compound engines, 442 

lubrication when using, 440 

regulation of, 440 

specific heat of, 170, 436 

total heat of, 435 

turbines, 434 
Superheater, Foster, 432 

data of, 438 

durability, 443 

Superheating, intensity required, 435 
Surface section, ratio, 265 
Streams, measurement of force due to 

turning the path of, 449 
Sugar, manufacture of, 517 
Surface condenser, 23 

Tandem compound engine, 307 
Tangential pressure on crank-pin, 382 
Temperature, absolute, 7 

definition of, 5 

mean, to find, 245 

volume and pressure, relations be- 
tween, 147, 510 
Temperature-entropy diagram, 225 ; 

from indicator-card, 225, 491 
Test of Diesel engine, 500 
Testing, indicator springs, 505 

Tests, standard form for gas-engine, 
513-537 ; standard for steam- 
engine, 537 

standard method of making gas- 
engine, 502 ; complete engine and 
boiler, 425; steam-engine, 32, 36, 
54, 57, 62, 63, 70, 72, 73, 74-78, 
193, 229, 318, 321, 325, 411-30 
Thermal action of cylinder walls, 187 
Thermal efficiency, definition, 42, 263 
Thermal unit, definition of, 5 
Thermodynamics, definition of, 14 
first law of, 8 

fundamental equations of, 152 
second law of, 9 
Thermometers, definition of, 5 

calibration of, 8, 419 
Thickness of cylinder walls, 112 

of bridge, 113 
Throttling-calorimeter, 173 
Torque, 2 
Total heat, in steam, 165 

required to produce saturated steam, 

165 ; superheated steam, 437 
Turbines : 
Curtis, 460 
De Laval, 454 
Hamilton-Holtzwarth, 480 
Parsons, 466 
steam, 445 

Turning forces, analysis of, 386, 406 
Twisting moment, 2 

Unit of heat, 5 ; of temperature, 5 ; of 
work, 2 

Vacuum gage, true meaning of reading, 

pan, 517, 528 

production, economy in, 264 

pumps, 268 

Valve, Corliss, drop or detachable, 356 
Valve-diagrams, 93, 94, 100 

geometrical relations, 97 
Valve ellipse, 114 

lap or travel, 88, 89 

seats, area through, 110 

slide, 88 

Vaporizing water, 163 
Vapors, definition of, 127, Table VI 
Velocity and acceleration of pistons, 

Velocity of steam in nozzles, 216 . 

in passages and ports, 107 
Volume, temperature and pressure, re- 
lations of, in perfect gases, 147 

one pound of steam, 576, 582 

Water, boiling-point of, equation of, 

boiling-point of, Table VIII 



Water, equivalent of a calorimeter, 175 

expansion of, 163 

friction brake, 34 

gas, 488 

line, 210 

meters, see Calibration, 429 

per horse-power-hour, definition of, 

pumping engines, tests, 542 

specific heat of, Table VII 
Weight of engine, 553, 567 
Weight of gases, Table I 

of liquids, Table I 

of one pound of steam, 576, 582 

of solids, Table I 

of steam accounted for by the indi- 
cator, 191 

of steam discharged from a nozzle, 

Weights of air, vapor of water, and 
saturated mixtures of air and 
vapor at various temperatures 
and constant pressures, 574 
Wet steam, 169 

saturated steam, 167 
Woolf type of compound engine, 322 
Work, definition of, 2 
of acceleration, 448 
done in accelerating a steam-jet, 476 
during expansion, 142, 215 
Working steam and clearance steam, 
82, 227 

Zero, absolute, 7 
Zeuner valve-diagram, 94, 100 
Zeuner's formula for the flow of per- 
fect gases from a nozzle, 446 
Zinc in condenser tubes, 24.1 








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