EXPERIMENTAL ENGINEERING. FOR ENGINEERS AND FOR STUDENTS IN ENGINEERING LA BORA TORIES. BY ROLLA C. CARPENTER, M.S., C E., M.M.E., ASSOCIATE PROFESSOR OF F.XPERIMJNTA; ENGINEERING, CORNELL UNIVER3TY. SECOND RE VISED EDI T10N. FIRST THOUSAND. JOHN WILEY & SONS, 53 EAST TENTH STREET. 1893- ROLL VR1GHT, 1892, BY C. CARPENTER. 5~l "5 6 ; ROBERT Electrotyper, 4 & 446 IVarl Street, York. F3BEJS BK08., Printers, 326 Pearl Street. New York. PREFACE. THE present work is a third edition of " Notes to Mechani- cal Laboratory Practice," published in 1890; of which a second edition was published in 1891, and soon exhausted by an unexpected demand from engineering schools and the profes- sion. These earlier editions were prepared especially for the use of students in the Laboratory of Experimental Engineering, Sibley College, Cornell University, for the ^purpose of facili- tating investigation of engineering subjects, and of providing a systematic course of instruction in experimental work. The book has been rewritten and very much enlarged, so that the change in title to Text-book of Experimental Engineer- ing seems to be justified. Its principal object is the same as that of the earlier editions, but it is also believed that the volume will not be without value as a reference-book to the consulting and practising engineer, since it is the only work on the subject which contains in a single volume the principal standard methods which have been from time to time adopted by various engineering societies for the test ng of materials, engines, and machinery. The book is, however, chiefly intended fr use in engineer- ing laboratories, and presents information which the exper- ience of the author has shown to be necjs ary to carry out experiments intelligently and without gr~P 4 . loss of time on the part of students. The importance of engineering laboratories is now so fully recognized in colleges of engineering that it is hardly VI -PREFACE. necessary to refer to the advantages which they confer on such engineering students as avail themselves of the oppor- tunities they present. The principal function of such a laboratory should doubtless be to afford the student an opportunity of obtaining practical knowledge of the application and limitation of theoretical principles by personal investiga- tion, under such direction as will insure systematic methods of observation, accurate use of apparatus, and the proper methods of drawing conclusions and of making reports of any experimental investigation. One other function of an engineer- ing laboratory is that of furnishing facilities by means of which skilled observers may undertake by systematic research to dis- cover laws or coefficients of value to the engineering profession. This work deals principally with the educational methods, the use of apparatus, and the preparation required for becoming a skilled observer. In order that an engineering laboratory should best meet the educational needs of students, a systematic schedule of experiments should be adopted parallel to the course of in- struction in theoretical principles. While such a laboratory course cannot be laid down here as applicable to any general course of instruction in engineering, the following scheme of laboratory experiments is presented for consideration as one which has been successfully followed for students in the Junior and Senior classes in Sibley College, Cornell University. The order of the experiments was largely determined by the attempt to make a limited amount of apparatus do maximum duty, and the course is presented more as an illustration of one that has been practically tested than as a model for other institutions to follow. COURSE OF EXPERIMENTS, SIBLEY COLLEGE ENGINEER- ING LABORATORY. JUNIOR YEAR. Fall Term. Strength of Materials Tensile and Transverse ; Calibration Indi- cator-springs and Steam-gauges; Weirs and Water-meters; Mercurial Thermometers ; Pyrometers ; Transmission-dynamometers. PREFACE. vii Winter Term. Strength of Materials Compression and Torsion ; Lubricants -Co- efficient of Friction ; Steam-engine Indicator-practice ; Flue-gas Analysis ; Temperature Pyrometers, Air-thermometers ; Calibration Indicator Drum-springs. Spring Term. Strength of Materials Impact ; Flexure ; Lubricants Viscosity ; Chill-test; Flash-test; Steam-engine Valve-setting; Efficiency-tests Water-moter; Steam-boiler; Steam-pump; Steam-engine. SENIOR YEAR. Fall Term. Strength of Materials Brick; Stone; Cement; Calorimetry Barrel and Continuous, Throttling and Separator ; Efficiency-tests }\Q\.-&\* Engine; Gas-engine; Injector; Centrifugul Pump; Hydraulic Ram; Belting ; Compound Engine. Winter Term. Steam-engine Calorimetric Test by Hirn's Method; Efficiency-tests Air-compressor ; Triple-expansion Engine ; .University Electric-lighting Plant; Turbine Water-wheel ; Windmill; Manufacturing Plant; Re- search and Thesis Work. Spring Term. Steam-engine Compound and Triple-expansion Engine by Hirn's Method ; Special Research ; Thesis Work. NOTE. The course is arranged to give ten experiments in the fall term, nine in the winter, and eight in the spring ; several important tests being repeated to make the requisite number. Students work in groups of three. This work, being intended as a hand-book for laboratory use, in connection with a course similar to that mentioned, gives in a very brief manner, in connection with each experi- ment, a statement of the theoretic principles involved, a description of the apparatus or machines used in the experi- ment, and a full statement of the methods to be employed, followed by forms for data and report. It also gives, for the convenience of the practising engineer as well as the student, a statement of the more important Vlll PREFA CE. standard methods of testing adopted, and an extensive series of tables useful in computing results of experiments, or in comparing such results with those previously obtained. A few demonstrations are given in full when references could not readily be given, but in general a simple statement of the methods of deriving the formulae has been thought sufficient. An attempt has been made, by dividing the book into several chapters of moderate length, by making the paragraphs short, and by placing the paragraph-numbers at the top of the page, to make references to the book easy to those who care to consult it. The references to the more complete treatises on the various subjects discussed will, it is believed, be found ample for all purposes of the student or engineer. The general design is presented in the following condensed Table of Contents. That portion of each chapter which relates to the theory or principles is in general compiled from authorities named in the references, but some sections are for the first time printed in a form available for engineers. As illustrations, atten- tion might be called to part or all of the following chapters : Testing-machines ; Dynamometers ; Measurement of Flow of Fluids ; Moisture in Steam ; Heating Value of Fuels ; Steam- injector ; Experimental Determination of Inertia. The author desires to express thanks for co-operation and assistance in preparing the volume to Dr. R. H. Thurston, Director of Sibley College, Cornell University; Prof. C. W. Scribner, of the University of Illinois ; Mr. E. F. Williams, of Buffalo, N. Y. ; and to his colleagues and colaborers in the various departments of Sibley College. ITHACA, N. Y., July i, 1892. TABLE OF CONTENTS. ARTICLE PAGE 1. Objects of Engineering Experiment xvii 2. Relation of Theory to Experiment ... .xviii 3. The Method of Investigation xviii 4. Classification of Experiments xix 5. Efficiency-tests xx CHAPTER I. REDUCTION OF EXPERIMENTAL DATA. 6. Classification of Errors r 7. Probability of Errors 2 8. Errors of Simple Observations 3 10. Combination of Errors 5 12. Deduction of Empirical Formulae 6 1 5 . Rules and Formulae for Approximate Calculation 1 1 16. Rejection of Doubtful Observations 13 17. Errors to be Neglected . . . , 14 18. Accuracy of Numerical Calculation , 15 19. Graphical Representation of Experiments . . 16 21. Autographic Diagrams 17 CHAPTER II. APPARATUS FOR REDUCTION OF EXPERIMENTAL DATA. 23. The Slide-rule 20 25. The Vernier 23 26. The Polar Planimeter 24 30. The Suspended Planimeter 33 31. The Coffin Planimeter 33 34. The Roller Planimeter 37 36. Care and Adjustment of Planimeters 42 37. Directions for Use of Planimeters 43 ix X TABLE OF CONTENTS. ARTICLE PAGE 38. Calibration of Planimeters 44 39. Errors of Planimeters 47 40. The Vernier Caliper 49 41. The Micrometer 50 42. The Micrometer Caliper 51 43. The Cathetometer 54 CHAPTER III. GENERAL FORMULAE STRENGTH OF MATERIALS. 45. Definitions 58 46. Strain-diagrams 59 47. Viscosity 60 48. Notation 62 49. Tension . . . . 62 51. Compression.... 63 52. Flexure . 66 54. Shearing 71 55. Modulus of Rigidity 73 58. Combination of Two Stresses 74 60. Thermody namic Relations 76 CHAPTER IV. TESTING-MACHINESSTRENGTH OF MATERIALS. 61. General Description of Machines 78 65. Shackles or Holders 80 66. Emery Testing-machine , 82 68. Riehle Bros.' Testing-machine 89 70. Olsen Testing-machine 92 73. Thurston's Torsion Machine. 96 75. Riehle Torsion Machine , 99 76. Impact Testing-machine 101 77. Cement-testing Machines 101 78. Testing-machine Accessories 106 80. Extensometers 107 87. Deflectometer 115 CHAPTER V. METHODS OF TESTING MATERIALS OF CONSTRUCTION. 88. Form of Test-pieces 114 93. Ductility Fracture 123 TABLE OF CONTENTS, xi ARTICLE PAGB 94. Strain-diagrams 1 24 95. Tension Tests 125 99. Compression Tests I3 4 100. Transverse Tests I35 102. Elastic Curve i 39 103. Torsion Test. 140 105. Impact Test 143 107. Special Tests of Material 145 109. Method of Testing Bridge Materials 148 no. Admiralty Tests , 152 in. Lloyd's Tests for Steel used in Ship-building 153 112. Tests for Cast-iron Water-pipe 154 114. Testing Stones ; 155 115. " Bricks 158 116. " Paving Material ,. 159 117. " Hydraulic Cements 161 CHAPTER VI. FRICTION TESTING OF LUBRICANTS. 122. Friction Definitions Useful Formulae 170 127. Friction of Teeth 173 128. Friction of Cords or Belts 173 129. " of Fluids 174 130. " of Lubricated Surfaces. .. 175 131. Testing of Lubricants Density 176 136. " " " Viscosity 178 143. " " " Gumming 182 144. " " " Fire-test 182 147. Testing of Lubricants Cold Test 185 151. Oil-testing Machines Rankine's 187 152. " " Thurston's 189 155. Coefficient of Friction 194 157. Richie's Oil-testing Machine 196 158. Durability Test of Lubricants 198 159. Ashcroft's Oil-testing Machine 199 160. Boult's " " 199 162. Experiment with Limited Feed 203 163. Forms for Report of Lubricant Test 205 CHAPTER VII. MEASUREMENT OF POWER. 165. Absorption Dynamometer. The Prony Brake 207 I73 . " " The Alden Brake 213 Xll TABLE OF CONTENTS. ARTICLE PAGE 178. Practical Directions for Use of Brake 215 179. Pump-brakes 217 180. Fan-brakes 217 181. Traction Dynamometers 218 182. Transmission Dynamometers Morin 219 186. " Steelyard 222 187. " Pillow-block 224 188. *' Lewis 224 189. " " Differential 227 192. " " Emerson 231 194. " Van Winkfe 233 195- " " Belt 235 197. Belt-testing Machine, with Directions , 236 CHAPTER VIII. MEASUREMENTS OF LIQUIDS AND GASES. 200. Theory of the Flow of Water . 242 201. Flow of Water over Weirs Formulae 244 203. " " " through Nozzles Formulae 247 205. " " " underPressure Formulae 248 206. " " " in Circular Pipes 249 207. " " " through a Diaphragm Formulae 251 209. Method of Measuring the Flow of Water by Weirs 253 213. " " " " " " " Meters 255 217. " " " " " " " Nozzles 259 219. " " " " " " " Diaphragms 260 220. " " " " " " " " in Streams 261 222. " " " " " " " Pilot's Tube 264 225. Flow of Compressible Fluids through an Orifice 267 229. " " " " in a Pipe 271 230. " "Steam 272 232. Gas-meters 274 233. Anemometer 278 CHAPTER IX. HYDRAULIC MACHINERY. 235. Classification , , . . . 280 239. Water-pressure Engines 281 241. Overshot Water-wheels 283 242. Breast- wheels 285 TABLE OF CONTENTS. xiii ARTICLE PAGE 243. Undershot Wheels 285 244. Impulse-wheels 286 245. Turbine , 287 248. Reaction- wheels . , . 291 249. The Hydraulic Ram 293 250. Methods of Testing Water-motors. , , .* 294 253. Pumps ,. 299 256. Test of Pumps. 302 258. Form for Data and Report of Pump-test 304 CHAPTER X. DEFINITIONS OF THERMODYNAM1C TERMS. 260. Text-books and Definitions , 307 260. Units of Pressure 308 261. Heat and Temperature 309 265. Properties of Steam, 312 267. Steam-tables 316 CHAPTER XI. MEASUREMENT OF PRESSURE. 268, Manometers 317 271. Mercury Columns 321 273. Draught-gauges 323 277. Steam-gauges 329 281. Apparatus for Testing Gauges 335 CHAPTER XII. MEASUREMENT OF TEMPERATURE. 285. Mercurial Thermometers 341 288. Air-thermometers 343 295. Calibration of Thermometers 352 296. Metallic Pyrometers 352 298. Air and Calorimetric Pyrometers 353 299. Determination of Specific Heat 354 302. Electric Pyrometers . 357 XIV TABLE OF CONTENTS. CHAPTER XIII. METHODS OF MEASURING MOISTURE IN STEAM. ARTICLE PAGE 305. Definitions 360 307. General Methods 361 314. Errors in Calorimeters 366 315. Sampling the Steam 369 317. Water Equivalent of Calorimeter 371 318. Barrel Calorimeter ; 372 321. Hoadley Calorimeter. 378 323. Barrus Continuous Calorimeter 380 326. Barrus Superheating Calorimeter 386 328. Throttling Calorimeter 388 336. Separator Calorimeter 398 341. Chemical Calorimeter , ... 404 CHAPTER XIV. HEATING VALUE OF COALS FLUE-GAS ANALYSIS. 343. Combustion Definition and Table 407 344. Heat of Combustion 408 345. Determination of Heat by Welter's Law 410 346. Temperature produced by Combustion 412 347. Composition of Fuels 414 348. Fuel-calorimeters Principle 415 352. " Favre and Silbermann's 417 353. Thompson's 419 354. Berthier 420 355. '* Berthelot 420 356. Continuous 421 357. Value of Fuel by Boiler-trial 422 358. Analysis of the Products of Combustion 423 360. Reagents for Flue-gas Analysis 425 363. Elliot's Flue-gas Apparatus 429 364. Wilson's " " 431 365. Fisher's " " 431 366. Hemple's " " 433 367. Deductions from Flue gas Analysis 436 CHAPTER XV. METHOD OF TESTING STEAM-BOILERS. 369. Objects of Boiler-testing 442 371. Efficiency of a Boiler . . . 443 TABLE OF CONTENTS. XV ARTICLE PAGE 375. Standard Method of Testing Steam-boilers 445 377. Concise Directions for Testing Boilers a . 458 CHAPTER XVI. THE STEAM-ENGINE INDICATOR. 378. Uses of the Indicator 459 380. Early Forms 461 381. Richards. . . . 462 382. Thompson 463 383. Tabor 464 384. Crosby 465 385. Calkins 467 387. Bachelder, Straight-line, and Arc Indicators 469 390. Reducing-motions 472 393. Calibration 479 397. Method of Attaching to the Cylinder 485 398. Directions for Use 486 CHAPTER XVII. THE INDICATOR-DIAGRAM.. 400. Definitions 489 401. Measurement of Diagrams 493 403. Form of Diagram 495 406. Weight of Steam from the Diagram 499 407. Clearance from the Diagram 502 408. Cylinder condensation and Re-evaporation 503 409. Discussion of Diagrams 505 410. Diagrams from Compound Engines 507 411. Crank-shaft and Steam-chest Diagrams 509 CHAPTER XVIII. METHODS OF TESTING THE STEAM-ENGINE, 412. Engine-efficiencies 511 414. Measurement of Speed 513 417. Surface Condenser ...,.... 518 418. Calibration of Apparatus , ...... 520 419. Preparations for Testing . 523 421. Quantities to be Observed 525 Xvi TABLE OF CONTENTS. ARTICLE PAGE 422. Preliminary Indicator-practice 526 423. Valve-setting 528 424. Friction-test 531 425. Efficiency-test . 53* 126. Hirn's Analysis 532 430. Hirn's Analysis of Compound Engines , 545 CHAPTER XIX. ENGINES FOR SPECIAL USES. 433. Standard Method of Testing Pumping-engines 552 434. Standard Method of Testing Locomotives 57? 435. Experimental Engines , 594 CHAPTER XX. EXPERIMENTAL DETERMINATION OF INERTIA. 436. General Effects of Inertia , 598 437. The Williams Inertia-indicator. 599 438. The Inertia-diagram 602 CHAPTER XXI. THE INJECTOR AND PULSOMETER. 439. Description of the Injector 608 440-1. .Theory 610 442. Limits of 614 443-5. Directions for Testing 617 446-7. The Pulsometer , . 621 CHAPTER XXII. HOT-AIR AND GAS ENGINES. 448. General Principles 624 449. Ericsson Hot-air Engine 624 450. Rider Hot-air Engine 625 451. Theory , 627 452-3. Method of Testing 627 454. The Gas-engine 630 455. Method of Testing 632 TABLES 637 INDEX 695 INTRODUCTION. I. Objects of Engineering Experiments. The object of experimental work in an engineering course of study may be stated under the following heads : firstly, to afford a practical illustration of the principles advanced in the class-room ; sec- ondly, to become familiar with the methods of testing; thirdly, to ascertain the constants and coefficients needed in engineer- ing practice ; fourthly, to obtain experience in the use of vari- ous types of engines and machines ; fifthly, to ascertain the efficiency of these various engines or machines ; sixthly, to de- duce general laws of action of mechanical forces or resistances, from the effects or results as shown in the various tests made. The especial object for which the experiment is performed should be clearly perceived in the outset, and such a method of testing should be adopted as will give the required informa- tion. This experimental work differs from that in the physical laboratory in its subject-matter and in its application, but the methods of investigation are to a great extent similar. In per- forming engineering experiments one will be occupied princi- pally in finding coefficients relating to strength of materials or efficiency of machines ; these, from the very nature of the ma- terial investigated, cannot have a constant value which will be exactly repeated in each experiment, even provided no error be made. The object will then be to find average values of these coefficients, to obtain the variation in each specific test xvii xviii INTRODUCTION. [ 3. from these average values, and, if possible, to find the law and cause of such variation. The results are usually a series of single observations on a variable quantity, and not a series of observations on a con- stant quantity; so that the method of finding the probable error, by the method of least squares, is not often applicable. This method of reducing and correcting observations is, how- ever, of such value when it is applicable, that it should be familiar to engineers, and should be applied whenever practi- cable. The fact that single observations are all that often can be secured renders it necessary in this work to take more than ordinary precautions that such observations be made correctly and with accurate instruments. 2. Relation of Theory to Experiment. It will be found in general better to understand the theoretical laws, as given in text-books, relating to the material or machine under inves- tigation, before the test is commenced ; but in many cases this is not possible, and the experiment must precede a study of the theory. It requires much skill and experience in order to deduce general laws from special investigations, and there is always' reason to doubt the validity of conclusions obtained from such investigations if any circumstances are contradictory, or if any cases remain unexamined. On the other hand, theoretical deductions or laws must be rejected as erroneous if they indicate results which are con- tradictory to those obtained by experiments under the condi- tions supposed to exist in both cases. 3. The Method of Investigation is to be considered as consisting of three steps : firstly, to standardize or calibrate the apparatus or instruments used in the test ; secondly, to make the test in such a way as to obtain the desired information ; thirdly, to write a report of the test, which is to include a full description of the methods of calibration and of the results, which in many cases should be expressed graphically. The methods of standardizing or calibrating will in general consist of a comparison with standard apparatus, under the 5-] INTRODUCTION. XIX conditions as. nearly as possible the same as those in actual practice. These methods later will be given in detail. The manner of performing the test will depend entirely on the con- ditions. The report should be written" in books or on paper of a prescribed form, and should describe clearly: (i) Object of the experiment ; (2) Deduction of formulae and method of per- forming the experiment ; (3) Description of apparatus used, with methods of calibrating ; (4) Log of results, which must include all the figures taken in the various observations of the calibration as well as in the experiment. These results should be arranged, whenever possible, in tabular form ; (5) Results of the experiment ; these should be expressed numerically and graphically, as explained later ; (6) Conclusions deduced from the experiment. Compare the results with those given by theory or other experiments. 4. Classification of Experiments. The method of per- forming an experiment must depend largely on the special object of the test, which should in every case be clearly com- prehended. The following subjects are considered in this treatise, under various heads : (i) The calibration of apparatus ; (2) Tests of the strength of materials; (3) Measurements of liquids and gases ; (4) Tests of friction and lubrication ; (5) Efficiency-tests, which relate to (a) belting and machinery of transmission, (b) water-wheels, pumps, and hydraulic motors, (c) hot-air and gas engines, (d) air-compressors and compressed- air machinery, (e) steam-engines, boilers, injectors, and direct- acting pumps. 5. Efficiency-tests. Tests may be made for various ob jects, the most important being probably that of determining the efficiency. The efficiency of a machine (Rankine's " Steam-engine," page 88) is a fraction expressing the ratio of the useful work to the whole work performed or to the whole energy expended. The limit to the efficiency of a machine is unity, which denotes the efficiency of a perfect machine. The whole work performed in driving a machine is evi- XX INTRODUCTION. [ 5- dently equal to the useful work, plus the lostwork. The lost work of a machine often consists of a constant part, and of a part bearing some definite proportion to the useful work ; in some cases all the lost work is constant. Efficiency-tests are made to determine the ratio of useful work to total work, and require the determination of, first, the work done or energy expended in driving the machine ; sec- ond, the useful work delivered by the machine; third, the lost work, which for any given observation is the difference between the total work and the useful work. In case the efficiency of the various parts of the machine is computed separately, the efficiency of the whole machine is evidently equal to the prod- uct of the efficiencies of the various component parts, which transmit energy from the driving-point to the working-point. The work done or energy transmitted is usually expressed in foot-pounds per minute of time, or in horse-power, which is equivalent to 33,000 foot-pounds per minute, or 550 foot- pounds per second of time. The time of run of efficiency-tests should be as long as possible, in order to overcome errors of starting and stopping, and also to obtain a greater number of observations. In ac- tual plant tests the length of test should never be less than ten hours, with forty observations, if conditions permit it; but in the laboratory practice-tests the time of run and time be- tween observations is necessarily much shortened. MANUAL OF EXPERIMENTAL ENGINEERING. REDUCTION OF EXPERIMENTAL DATA. METHOD OF LEAST SQUARES-NUMERICAL CALCULATIONS- GRAPHICAL REPRESENTA TION OF EXPERIMENTS. CHAPTER I. APPLICATION OF THE METHOD OF LEAST SQUARES. IN the following articles the application of this method to reducing observations and producing equations from experi- mental data is quite fully set forth. The theory of the Method of Least Squares is not given, but it can be fully studied in the work by Chauvenet published by Lippincott & Co., or in the work by Merriman published by John Wiley & Sons. 6. Classification of Errors. The errors to which all ob- servations are subject are divided into systematic and accidental. Systematic errors are those which affect the same quanti- ties in the same way, and may be further classified as instru- mental and personal. The instrumental errors are due to imperfection of the instruments employed, and are detected by comparison with standard instruments or by special methods of adjustment. Personal errors are due to a peculiar habit of the observer tending to make his readings preponderate in a certain direction, and are to be ascertained by comparison of 2 EXPERIMENTAL ENGINEERING. [ 7- observations : first, with those taken automatically ; second, with those taken by a large number of observers equally skilled ; third, with those taken by an observer whose personal error is known. Systematic errors should be investigated first of all, and their effects eliminated. Accidental errors are those whose presence cannot be fore- seen nor prevented; they may be due to a multiplicity of causes, but it is found, if the number of observations be sufficiently great, that their occurrence can be predicted by the law of probability, and the probable value of these errors can be com- puted by the METHOD OF LEAST SQUARES. Before making application of the " Method of Least Squares," determine the value of the systematic errors, elimi- nate them, and apply the method of least squares to the de- termination of accidental errors. 7. Probability of Errors. The following propositions are regarded as axioms, and are the fundamental theorems on which the Method of Least Squares is based : 1st. Small errors will be more frequent than large ones. 2d. Errors of excess and deficiency (that is, results greater or less than the true value) are equally probable and will be equally numerous. 3d. Large errors, beyond a certain magnitude, do not occur. That is, the probability of a very large error is zero. From these it is seen that the probability of an error is a function of the error. Thus let x represent any error and y its probability, then By combination of the principles relating to the probability of any event Gauss determined that in which c and h are constants, and e the base of the Napierian system of logarithms. 9-] APPLICATION OF METHOD OF LEAST SQUARES. 3 8. Errors of Simple Observations. It can be shown by calculation: i. That the most probable value of a series of observations made on the same quantity is the arithmetical mean. 2. If the observations were infinite in number the mean value would be the true value. 3. The residual is the difference between any observation and the mean of all the observations. The mean error of a single observation is the square root of the sum of the squares of the residuals, divided by one less than the number of observations. 4. The probable error is 0.6745 time the mean error. 5. The error of the result is that of a single observation divided by the square root of their number. Thus let n represent the number of observations, 5 the sum of the squares of the residuals ; let e, e lt e 9 , etc., represent the residual, which is the difference between any observation and the mean value * let 2 denote the sum of the quantities indi- cated by the symbol directly following. Then we shall have Mean error of a single observation \ / V n I (2) Probable error of a single observation 0.6745/1 / . (3) Mean error of the result \ , r. . (4) Probable error of the result 0.6745 In every case S 9. Example. The following example illustrates the method of correcting observations made on a single quantity: A great number of measurements have been made to determine the relation of the British standard yard to the EXPERIMENTAL ENGINEERING. [9- meter. The British standard of length is the distance, on a bar of Bailey's bronze, between two lines drawn on plugs at the bottom of wells sunk to half the depth of the bar. The marks are one inch from each end. The measure is standard at 72 Fah., and is known as the Imperial Standard Yard. The meter is the distance between the ends of a bar of platinum, the bar being at o 9 Centigrade, and is known as the Mitre des Archives. The following are some of these determinations. That made by Clarke in 1866 is most generally recognized as of the greatest weight. COMPARISON OF BRITISH AND FRENCH MEASURES. Name of Observer. Date. Observed length of meter in inches. Difference from the mean. Residual = e. Square of the Residuals. t*. Kater 1821 39.37079 0.001460 O . OOOOO2 1316 Hassler 18-32 ^o. -38103 4- 8780 0.0000770884 Clarke 1866 39. 370432 1818 O.OOOOO33I24 188.1 on -2701 5 2IOO o 0000044100 Comstock . 1885 ^q. ^6085 O.OO24OO o 0000057600 39.372250 0.0000907024 = S = 0.0000907024, n 5, n(n i) = 20. Mean error of a single observation = \l ^ _ ^ = 0.00476 Probable error of single observation = 0.00317. Mean error of mean value = Probable error of mean value = 0.00142. 11.] APPLICATION _OF METHOD OF LEAST SQUARES. 5 That is, considering the observations of equal weight, it would be an even chance whether the error of a single obser- vation were greater or less than 0.00317 inch, and the error of the mean greater or less than 0.00142. 10. Combination of Errors. When several quantities are involved it is often necessary to consider how the errors made upon the different quantities will affect the result. Since the error is a small quantity with reference to the re- sult. we can get sufficient accuracy with approximate formulae. Thus let X equal the calculated or observed result, F the error made in the result ; let x equal one of the observed quantities, and f its error. Then will (6) j y in which -r is the partial derivative of the result with respect to the quantity supposed to vary. In case of two quantities in which the errors are F, F' , etc., the probable error of the result = VF* + F'\ ....;. (7) II. As an example, discuss the effect of errors in counting the number of revolutions, and in measurement of the mean effec- tive pressure, acting on the piston, with regard to the power furnished by a steam-engine. Denote the number of revolu- tions by n, the mean pressure by/, the length of stroke in feet by /, and the area of piston in square inches by a\ the work in foot-pounds done on one side of the piston by W. Then W = plan, F = lanf, F dW 7=-% - 1 , F ' F' dW '~~''~= P 6 EXPERIMENTAL ENGINEERING. [ 12. The error/ in the mean pressure is itself a complicated one, since/ is measured from an indicator-diagram and depends on accuracy of the indicator-springs, accuracy of the indicator- motion, and the correct measurement of the indicator-diagram. These errors vary with different conditions. Suppose, however, the whole error to be that of measurement of the indicator- diagram. This is usually measured with a polar planimeter, of which the minimum error of measurement may be taken as O.O2 square inch ; with an indicator-diagram three inches in length this corresponds to an error of 0.0067 of an inch in ordi- nate. In a similar manner the error in the number of revolu- tions depends on the method of counting: with a hand-counter the best results by an expert probably would involve an error of one tenth of a second ; with an attached chronograph the error would be less, and would probably depend on the accu- racy with which the results could be read from the chronograph- diagram. The ordinary errors are fully three times those given here. Take as a numerical example, a 100 square inches, 12 feet, n = 300, / = 50 pounds, /= 0.335, /' = 0.5. F =. 20,100, F = 5,000, W= 3,000,000. Probable error = VF* + F*= 20,712 ft.-lbs., which in this case is 0.0069 of the work done. 12. Deduction of Empirical Formulae. Observations are frequently made to determine general laws which govern phenomena, and in such cases it is important to determine what formula will express with least error the relation between the observed quantities. These results are empirical so long as they express the re- lation between the observed quantities only; but in many cases they are applicable to all phenomena of the same class, in which case they express engineering or physical laws. In all these cases it is important that the form of the equa- tion be known, as will appear from the examples to be given later. The form of the equation is often known from the 1 3-] APPLICATION OF METHOD OF LEAST SQUARES. 7 general physical laws applying to similar cases, or it may be determined by an inspection of the curve obtained by a graphical representation of the experiment. A very large class of phenomena may be represented by the equation y = A + Bx + 6> 2 + Dx* + etc (8) In -case the graphical representation of the curve indicates a parabolic form, or one in which the curve approaches parallel- ism with the axis of X, the empirical formula will probably be of the form y = A + Bx*+Cx* + Dx*+etc. ... (9) In case the observations show that, with increasing values of x, y passes through repeating cycles, as in the case of a pendulum, or the backward and forward motion of an engine, the charac- teristic curve would be a sinuous line with repeated changes in the direction of curvature from convex to concave. The equation would be of the form 4- 6, sin m m m 4-,cos- 2^-j-etc. ( IO ) m Still another form which is occasionally used is y = A -|- B sin mx -f- C sin 2 mx -f- etc. . . (i i) 13. General Methods. The method of deducing the em- pirical formula is illustrated by the following general case : In a series of observations or experiments let us suppose that the errors (residuals) committed are denoted by e t /, e" t 8 EXPERIMENTAL ENGINEERING. [ X 3- etc., and suppose that by means of the observations we have deduced the general equations of conditions as follows: e = h -f- ax -\- by + cz, e " = h" + a"x + b"y + c" z, e'" = //" + a'"x + b'"y + c'"z, etc. etc. etc. Let it be required to find such values of x, y, z, etc., that the values of the residuals e, e f , e" , e"', etc., shall be the least pos- sible, with reference to all the observations. If we square both members of each equation in the above group and add them together, member to member, we shall have f + ,' + ," _[_ ,"" _f etc. = x\a* + a"* + a"* + etc.) + 2x{(ah + a'k' + a"h" + etc.)+ a(by +cz + etc.) + a' (b f y + c'z + etc.) + etc. } + h* + ft* + etc. This equation may be arranged with reference to x as follows : u = e* + e'* + e"* + etc. = PS + 2Qx+R + etc. ; in which the various coefficients of the different powers of x are denoted by the symbols P, Q, R, etc. Now in order that these various errors may be a minimum, e 1 -\- e' 9 -f- e"* -f~ etc. = u must be a minimum, in which case its partial derivative, taken with respect to each variable in succession, should be separately equal td zero. Hence or, substituting the values of P and Q, x(a? + a'* + etc.) + ah -f ah' + etc. -\- a (fy + c* + etc.) + a'(p'y + c'z + etc.) + etc. = o. Similar equations are to be formed for each variable. 1 4-] APPLICATION OF METHOD OF LEAST SQUARES. 9 From the form of these equations we deduce the principle that in order to find an equation of condition for the minimum error with respect to one of the unknown quantities, as x for example, we have simply to multiply the second member of each of the equations of condition by the coefficient of the unknown quantity in that equation, take the sum of the products, and place the result equal to zero. Proceed in this manner for each of the unknown quantities, and there will result as many equations as there are unknown quantities, from which the required values of the unknown quantities may be found by the ordinary methods of solving equations. 14. Example. As an illustration, suppose that we require the equation of condition which shall express the relation be- tween the number of revolutions and the pressure expressed in inches of water, of a pressure-blower delivering air into a closed pipe. Let m represent the reading of the water-column, and n the corresponding number of revolutions. Suppose that the observations give for m = 24 inches, n = 297 revolutions ; " m = 32 " n = 340 " " m =. 33 u n 3^ " " m = 35 " n 376 " Average values for m = 31 inches, n = 342 revolutions. Arranging the results in the following form, we have : Water-column. Revolutions. Observations. Residuals. Observations. Residuals. 24 32 33 35 - 7 + 1 + 2 + 4 2Q7 340 355 3/6 -45 2 + 13 + 34 Assume that the equation of condition is of the form IO EXPERIMENTAL ENGINEERING. [ 14* To find those values of A, B, and C which will most nearly satisfy the equation, as shown in the experiment : Taking the values of x, as the residual or difference between the mean and any observation in height of water-column, and the value of y as the corresponding residual in number of revolutions, we have the following equations of condition : A - 7 B + 4gC= -45, 1 A+ B + C=- 2, I A + 2B+ 4 C= + i A+ 4 +i6C=+ 34 . J Multiplying each equation by the coefficient of A in that equation, we have Equations of minimum condi- ' tion of error with respect to A. 4A + oB + 70(7 = o. III. Sum of equations in group II. Multiplying each equation in group I by the coefficient of B in that equation, we have 31 q .-_ _ Equations of minimum . z? i or o^ r IV. condition of error with 2Si -+- 4-B \~ *v 2O = 136 respect to ^. oA + joB 2?oC = 475 Sum of equations in group IV. Multiplying each equation in group I by the coefficient of C in that equation, we have 343^ + 2401^= 2205 } -''-. f A\ R\ f^_ Equations of minimum 4^+ 83+ i6C= 52 f V ' condition of error with 16^+645+256^- 544 J Aspect to C. 268^ + 2674(7 == 161 1 Sum of equations in group V. 1 5-] APPLICATION OF METHOD OF LEAST SQUARES. II The sums of these various equations of minimum condition are the same in number as the unknown quantities, and by com- bining them the various values of A, B, C, etc., can be deter- mined. We have, in the following case : 4A + cx#+ oA + 7 2?oC = 475 V VI. joA 26ZB + 2674^ = 161 1 ) Solving the above, A = i. 608 ; B = 7.140 ; C = 0.0919. Substituting in the original equation of condition, y 1. 608 + 7.140^ 0.0919^. To reduce this form to an equation expressing the probable relation of the number of revolutions to the height of the water- column, we must substitute for y its value, n 342 ; and for x its value, m 31. In this case we shall have n - 342 = i .608 + 7.14(0* - 30 ~ 0.0919(0* - 3i) 2 ; which reduced gives the following equation as the most proba- ble value in accordance with the observations: n = 34.952 + 13.02/0 0.091 9*0"; which is the empirical equation sought. 15. Rules and Formulae for Approximate Calculation. When in a mathematical expression some numbers occur which are very small with respect to certain other numbers, and which are therefore reckoned as corrections, they may often be ex. pressed with sufficient accuracy by an approximate formula, which will largely reduce the labor of computation. 12 EXPERIMENTAL ENGINEERING. [ 15- On the principle that the higher powers of very small quan- tities may be neglected with reference to the numbers them- selves, we can form a series by expansion by the binomial formula, or by division, in which, if we neglect the , higher powers of the smaller quantities, the resulting formulae become much more simple, and are usually of sufficient accuracy. Thus, for instance, let# equal a very small fraction ; then the expression (a -j- d) m = a m -(- ma m ~ l d -j- m a m ~\d 2 -\- etc., will become a m + ma" 1 ^, if the higher powers of # be neglected. If # is equal to y^Vfr P art f a > tne err o r which results from omitting the remaining terms of the series becomes very small, as in this case the value of & = Toiriirou^' The following table of_approximate formulae presents several cases which can often be applied with the effect of materially reducing the work of computation, without any sensible effect on the accuracy : (i + 3) m = I + md, (i d} m I md ; .... (12) (i + d) 2 =i+2tf, (i->' cos />'> ; but ED ' D = EDO from similar triangles. Hence . i ,. ' . ::c; , . : V f Denote the length of arm EJ by m, the length of arm A^* f rom pivot to tracing-point by /, the distaneeyZ? from pivot to record- wheel by n, the angle EJD \sffB. Let fall a perpendicular from E on FD, or FD produced at O. Then we have ED cos EDO = OD =JO JD = m cos B n. Hence (i) Third, the infinitesimal area FtF"t i > lying adjacent to the zero-circle. Let EF === r, let EF" .= r x ,. the radius of the zero-circle. Let d!/4 = the area sought. Let dO = FEt. Then area FEt = and area F"E? = %r"dO. Then . . . (2) From the f oblique triangle r 2 = m* + / 2 + 2mtcosB ...... (3) 28 EXPERIMENTAL ENGINEERING. From the right triangle ED'F", [ 2/. (4) Substituting the values of r* and r' 2 in equation (2), we have dA = l(mcosB n)dB ....... (5) By comparing equation (5), the differential equation for the area, with equation (i), the corresponding equation for the FIG. 4. POLAR PLANIMETER. record, we see that dA = IdR ; , (6) or by integration between limits o and R, since i is a constant, A = IR (7) This shows that the area is equal to the length of arm from pivot to the tracing-point, multiplied by the space registered 28.] APPAKA TUS. 29 on the circumference of the record-wheel, and is independent of the other dimensions of the instrument. That this is true for areas not adjacent to the zero-rcircle, or for areas partly inside and out, can readily be proved by subtracting the areas between the zero-circle and the given area, or by a similar process. Hence the demonstration is general. The Amsler instrument is usually constructed so that the arm / is adjustable in length, and consequently it may be made available for any scale or for various units. Gradua- tions are engraved on the arm which show the length required to give a record in a given scale or for given units. The area of tJie zero-circle is usually engraved on the top of the arm /. In case it is not given, it may be found by evaluating the areas of two circles of known area, each greater than the area of the zero-circle nr'" 1 . Let the areas of such circles be respectively C and C', and the corresponding read- ings of the record-wheel R and R' y in proper units. Then we have X C = nr'* + R and C = nr"* + R', from which 3 ') ........ (8) Having found r fg , we can compute n, since r' 2 = m* -f- / 2 -f- 2nl t and ;;/ and / can both be obtained from measurement 28. Design of Polar Planimeters. Polar planimeters are made in two forms : I. With the pivot/, Fig. 4, fixed. 2. With pivot J movable, so that the arm / between pivot and tracing- point may be varied in length. Since the area is in each case equal to the length of this arm, multiplied by the lineal space R moved through by the record-wheel, we have in the first case, since / is not adjustable, the result always in the same unit, as square inches or square centimeters. In this case it is 30 EXPERIMENTAL ENGINEERING. [28. customary to fix the circumference of the record-wheel and compute the arm / so as to give the desired units. For example, the circumference of the record-wheel is assumed as equal to 100 divisions, each one-fortieth of an inch, thus giving us a distance of 2.5 inches traversed in one revolu- tion. The diameter corresponding to this circumference is 0.796 inch, which is equal to 2.025 centimeters. The distance from pivot to tracing-point can be taken any convenient dis- tance : thus, if the diameter of the record-wheel is as above, and the length of the arm be taken as 4 inches, the area described by a single revolution of the register-wheel will be 2.5 X 4 = IO.O square inches. Since there were 100 divisions in the wheel, the value of one of these would be in this case o.i square inch. This would be subdivided by the attached vernier into ten parts, giving as the least reading one one-hundredth of a square inch., By mak- ing the arm larger and the wheel smaller, readings giving the same units could be obtained. The formula expressing this reduction is as follows: Let d equal the value of one division on the record-wheel ; let / equal the length of the arm from pivot to tracing-point ; let A equal the area, which must evidently be either i, 10, or 100 in order that the value of the readings in lineal measures on the record- wheel shall correspond with the results in square measures. Then by equation (7) we shall have, supposing 100 divisions, 100 dl A ; (8) If A = 10 square inches and d = -fa inch, 2.5 .29.] APPARATUS. 31 If A = 10 square inches and d = -fa inch, The length of the arm from centre to the pivot has no effect on the result unless the instrument makes a complete revolu- tion around the fixed point E, in which case the area of the zero-circle must be considered. It is evident, however, that this arm must be taken sufficiently long to permit free motion of the tracing-point around the area to be evaluated. The second class of instruments, shown in Fig. 2, are arranged so that the pivot can be moved to any desired posi- tion on the tracing-arm KF, or, in other words, the length can be changed to give readings in various units. The effect of such a change will be readily understood from the preceding discussion. 29. The Mean Ordinate by the Polar Planimeter. If we let/ equal the length of the mean ordinate, and let L equal the length 'of the diagram, then the area A = Lp, but the area A IR [eq. (7)]. Therefore Lp = IR, from which (10) In an instrument in which / is adjustable, it may be made the length of the area to be evaluated. Now if / be made equal Z,, p = R. That is, if the adjustable arm be made equal to the length of the diagram^ the mean ordinate is equal to the reading of the record-wheel, to a scale to be determined. The method of making the adjustable arm the length of the diagram is facilitated by placing a point U on the back of the planimeter at a convenient distance back of the tracing- point Fand mounting a similar point Fat the same distance back of the pivot C\ then in all cases the distance UV vt\\\ be equal to the length of the adjustable arm /. The instrument is readily set by loosening the set-screw S and sliding the frame 32 EXPERIMENTAL ENGINEERING. [ 2 9* carrying the pivot and record-wheel until the points /Fare at the respective ends of the diagram to be traced, as shown in Fig. 5- In the absence of the points U and V the length of the diagram can be obtained by a pair of dividers, and the distance of the pivot C from the tracing-point F made equal to the length of the diagram. In this position, if the tracing-point be carried around the diagram, the reading will be the mean ordinate of the diagram FIG. 5. METHOD OF SETTING THE PLANIMETER FOR FINDING THE MEAN ORDINATE. expressed in the same units as the subdivisions of the record- wheel ; thus if the subdivisions of this wheel are fortieths of one inch, the result will be the length of the mean ordinate in fortieths. This distance, which we term the scale of the record- wheel, is not the distance between the marks on the graduated scale, but is the corresponding distance on the edge of the wheel which comes in contact with the paper. The scale of the record-wheel evidently corresponds to a linear distance, and it should be obtained by measurement or computation. It is evidently equal to the number of divisions in the circumference divided by nd, in which d is the diameter, or it can be obtained by measuring a rectangular diagram with a length equal to /, and a mean ordinate equal to one inch, in which case the reading of the record-wheel will give the num- ber of divisions per inch. A diameter of 0.795 inch, which corresponds to a radius of one centimeter, with a hundred sub- 32.] APPARA TUS. 33 divisions of the circumference, corresponds almost exactly to a scale of forty subdivisions to the inch, and is the dimension usually adopted on foreign-made instruments. 30. The Suspended Planimeter. In the Amsler sus- pended planimeter as shown in Fig. 6, pure rolling motion without slipping is assumed to take place. The motion of the record-wheel, not clearly shown in the figure, is produced by the rotation of the cylinder c in contact with the spherical FIG. 6. SUSPENDED PLANIMETER. segment K. The rotation of the segment is due to angular motion around the pole (9, that of the cylinder c to its posi- tion with reference to the axis of the segment. This position depends on the angle that the tracing arm, ks, makes with the radial arm, BB. The area in each case being, as with the polar planimeter, equal to the product of the length of tracing arm from pivot to tracing point multiplied by a constant^ factor. / 31. The Coffin Planimeter and Averaging Instrument. This instrument is shown in Fig. 7> from which it is seen that it consists of an arm supporting a record-wheel whose axis is parallel to the line joining the extremities of the arm. This instrument was invented by the late John Coffin, of Johnstown, in 1874. The record-wheel travels over a special surface; one end of the arm travels in a slide, the other end passes around the diagram. 32. Theory of the Coffin Instrument. This planimeter may be considered a special form of the Amsler, in which the point P, see Fig. 8, page 35, moves in a right line instead of 34 EXPERIMENTAL ENGINEERING. [ 3 2 - swinging in an arc of a circle, and the angle CPT, correspond- ing to B in eq. (i), is a fixed right angle. The differential equation for area therefore is dA=lndti, (ii) FIG. 70 THE COFFIN AVERAGING INSTRUMENT. and the differential equation of the register becomes dR = ndd 12) Hence, as in equation (7), A=IR ." . (13) 32.] APPARATUS. 35 That is, the area is equal to the space registered by the record- wheel multiplied by the length of the planimeter arm. This instrument may be made to give a line equivalent to the M. E. P. by placing the diagram to be measured so that FIG. 8. COFFIN AVERAGING INSTRUMENT. one edge is in line with the guide for the arm ; starting at the farthest portion of the diagram, run the tracing-point around in the usual manner to the point of starting, after which run the tracing-point perpendicular to the base along a special guide provided for that purpose until the record-wheel reads as at the beginning. This latter distance will be equivalent to the M. E. P. 36 EXPERIMENTAL ENGINEERING. [33- To prove, take as in Art. 29 the M. E. P. =/, the length of diagram = Z, the perpendicular distance = 5. Then A = pL = IR (14) Let' C be the angle, EPT, that the arm makes with the guide, Fig. 8. In moving over a vertical line this angle will remain constant, and the record will be R = 5 sin C. (15) For the position at the end of the diagram sin C = L ~ /; therefore R= SL-i- L Substituting this in equation (14), pL = lR = ISL + l=SL. Hence/ = 5 (150), which was to be proved. From the above discussion it is evident that areas will be measured accurately in all positions, but that to get the M. E. P. the base of the diagram must be placed perpen- dicular to the guide, and with one end in line of the guide produced. It is also to be noticed that the record-wheel may be placed in any position with reference to the arm, but that it must have its axis parallel to it, and that it registers only the perpen- dicular distance moved by the arm. 33. New Planimeter. A planimeter, termed the New Planimeter, is manufactured by the Mechanical Specialties Co. of Boston, Mass. This instrument consists of a single arm, one end of which moves in a fixed groove ; the other end carries a tracing-point which is moved around the diagram to be 34] APPARATUS. 37 evaluated, and in this respect is similar to the Coffin Planim- eter. The perpendicular motion of the arm is measured by the slipping of a sharp-edged wheel on a graduated axis per- pendicular to the arm. The mathematical demonstration is exactly as for the Coffin Planimeter, but in this case it is evident that the perpendicu- lar distance which is registered on the axis is independent of the circumference of the wheel. The only conditions of accuracy are, that the axis of the wheel shall be at right angles to the arm of the planimeter, and that its graduations shall be equal to the area to be measured divided by the length of the arm. Although not especially designed for this purpose, the mean ordinate may be obtained by proceeding exactly as in the Coffin Planimeter; that is, place the diagram so that the dimension representing the length will be perpendicular to the guides, and one extremity will be in the line of the guides. Start at the farthest point, and after passing around the dia- gram, move in a parallel direction to the guides until the initial reading is obtained. This last distance is equal to the mean ordinate. The Engineers' Instrument Company of New York are manufacturing a form of the Amsler Polar Planimeter for large areas, in which the total number of revolutions of the record- wheel is given by a scale carried by a revolving-screw in the axis of the record-wheel. 34. The Roller-planimeter. This is the most accurate of the instruments for integrating plane areas, and is capable of measuring the area of a surface of indefinite length and of limited breadth. This instrument was designed by Herr Corradi of Zurich, and is manufactured in this country by Fauth & Company of Washington, D. C. A view of the instrument is shown in Fig. 9. The features of this instrument are : firstly, the unit of the vernier is so small that surfaces of quite diminutive size may be determined with accuracy; secondly, the space that can be encompassed by one fixing of the instrument is very large; thirdly, the EXPERIMEN TAL E NGIN BERING. [34- results need not be affected by the surface of the paper on which the diagram is drawn ; and, fourthly, the arrangement of its working parts admit of being kept in good order a long time. The frame B is supported by the shaft of the two rollers R l R l , the surfaces of which are fluted. To the frame B are fitted the disk A, and the axis of the tracing-arm F. The whole apparatus is moved in a straight line to any desired length upon the two rollers resting on the paper, while the tracing- point travels around the diagram to be integrated. Upon the shaft that forms the axis of the two rollers J^ 1 R 1 a minutely FlG. 9. ROLLER-PLANIMETER, divided mitre-wheel R^ is fixed, which gears into a pinion jR 3 . This pinion, being fixed upon the same spindle as the disk A, causes the disk to revolve, and thereby induces the roll- ing motion of the entire apparatus. The -measuring-roller E, resting upon the disk A, travels thereon to and fro, in sympathy with the motion of the tracing- arm F, this measuring-roller being actuated by another arm fixed at right angles to the tracing-arm and moving freely between pivots. The axis of the measuring-roller is parallel to. the tracing-arm F. The top end of the spindle upon which 35-] APPARATUS. 39 the disk A is fixed pivots on a radial steel bar CC l , fixed upon the frame B. 35. Theory. The following theory of the roller-planim- eter is partly translated from an article by F. H. Reitz, in the Zeitsclirift fur Vennessungs-Wesen, 1884. According to the general theory of planimeters furnished with measuring-rollers, it is immaterial what line the free end of the tracing-arm travels over ; nevertheless there is some practical advantage in the construction of the apparatus to be obtained from causing that end to travel as nearly as possible in a straight line. Still it is obvious that a slight deviation from the straight line would not involve any inaccuracy in the result. Seeing that the fulcrum of the tracing-arm keeps travelling in a straight line, it appears advisable, in evolving the theory of the apparatus, to assume a rectangular system of co-ordinates, and fix upon the line along which that fulcrum travels as the axis of abscissae. The passage of the tracing-point around the perimeter of a diagram maybe looked upon as being made up of two motions one parallel to the axis of abscissae and the other at right angles to that axis. Inasmuch as the latter of these two motions, in the direction of the axis of ordinates, is after all but an alternate motion of the tracing-point which takes place in an equal ratio until the tracing-point has returned to its starting-point, no one point of the circumference of the measur- ing-roller is continuously moved forward in consequence of this motion. Therefore it is only necessary to take the differential motion of the tracing-point in the direction of the axis of abscissae into consideration. In Fig. 10 the same letters of reference denote identical parts or organs as in Fig. 9, and the position of the parts in the two figures correspond exactly, the letter D denoting the distance between the fulcrum of the tracing-arm and the axis of the disk A. The amount of motion of a point on the record- wheel E, while the tracing-point travels to the extent of dx, must be determined. If the construction of the planimeter is EXPERIMENTAL ENGINEERING. [35- correct, this quantity must be the product of a constant derived from the instrument, multiplied by the differential expression for the surface. This latter quantity with reference to rectan- gular co-ordinates is ydx. It is readily seen that as the tracing-point moves an amount equal to dx, a point in the circumference of the rollers R l R l must be shifted the same amount, since the axes of these rollers are parallel to the ordinate y. Any point in the pitch-line of the mitre-wheel J? 2 must move r> an amount equal to ~dx. FIG. 10. Suppose that while the tracing-point moves a distance dx, the disk A moves a distance ab, Fig. 10, since this disk is turned by the mitre-wheel whose pitch-circle is R z , and ad is the dis- tance from record-wKeel to the axis of this wheel, we must have ad (16) APPARA TUS. Because of the position of the axis of the record-wheel E y the motion of the disk A to the extent of ab produces a shifting of a point in the circumference of E equal to cb, while the record-wheel slips a distance ac. The distance cb is the reading of the record-wheel and is the quantity required. We have dab = 90, cag 90 ; hence caf = a, and fab = ft, and cab = a -|- ft. So that since acb = 90, cb = ab sin (a-\- ft) = ab (sin a cos ft -f- cos a sin ft). , (17) But it is seen that sin a = . Hence cos a = V l F*' af sin or ad ~ Fad' df ad Substitute these values in equation (17): cb=.ab & <* Substitute the value of ab in (16), = (constant) ydx, (19) which was to be proved. 42 EXPERIMENTAL ENGINEERING. [ 36. The differential distance cb is the reading of the record-wheel ; let this be represented by dr, denote by C the constant - then dr = Cydx ; ^dfcr = -^ ; / ydx = ~ I dr. This expression integrated gives in which r, and r a are the initial and final readings of the record-wheel. In the construction of the instrument R 19 7? 3 , D> and R^ are fixed quantities, but the length of the tracing-arm F can be varied, with a corresponding variation in the unit of measure- ment. 36. Care and Adjustment of Planimeters. From the preceding discussion it is seen that the area in every case is the product of the distance actually moved by the circum- ference of the record-wheel into the length of the arm from the tracing-point to the pivot, into a constant which may be and is, in the polar planimeter, equal to one. It is also to be noticed that the record-wheel is so arranged as to register the distance moved by a point in a direction perpendicular to that of the tracing-arm, and that for other directions it slips. This indicates that any change whatever in the diameter of the record-wheel or gear-wheels, due to wear or dirt, will require a corresponding change in the length of tracing-arm ; and further, any irregularities in the edge of this wheel will make the rela- tive amounts of slipping and rolling motion uncertain, and con- sequently impair its accuracy. Again, the plane of the record-wheel must be perpendicular to the tracing-arm, otherwise an error will result. In the planimeter the moving parts usually have pivot- 37-] APPARATUS. 43 bearings which can be loosened or tightened as required. The revolving parts should spin around easily but at the same time accurately, and the various arms should swing easily and show no lost motion. The pitch-line of the record-wheel should be as close as possible to the vernier, but yet must not touch it ; the counting-wheel must work smoothly, but in no way inter- fere with the motion of the record-wheel. 37. Directions for Use. i. Oil occasionally with a few drops of watch or nut oil. 2. Keep the rim of the record-wheel clean and free from rust. Wipe with a soft rag if it is touched with the ringers. 3. Prepare a smooth level surface, and cover it with heavy drawing-paper, for the record-wheel to move over. Stretch the diagram to be evaluated smooth. 4. Handle the instrument with the greatest care, as the least injury may ruin it. Select a pole-point so that the instru- ment will in its initial position have the tracing-arm perpen- dicular either to the pole-arm or to the axis of the fluted rollers, as the case may be ; for in this position only is the error neutralized, which arises from the fact that the tracer is not returned to its exact starting-point. Then marking some starting-point, trace the outline of the area to be measured in the direction of the hands of a watch, slowly and carefully, noting the reading of the record-wheel at the instant of start- ing and stopping. It is generally more accurate to note the initial reading of the record-wheel than to try and set it at zero. 5. Special Directions. To obtain the mean ordinate with the polar planimeter, make the length of the adjustable arm equal to the length of the diagram, as explained in Art. 28, page 30, and follow directions for use as before. 6. In using the Coffin planimeter, the grooved metal plate / is first attached to the board, upon which the apparatus is mounted as shown in the cut, page 34, being held in place by a thumb-screw applied to the back side. The diagram will be held securely in place by the spring-clips adjacent, A and C, Fig. 7. The area may be found by running the tracing-point around the diagram, as described for the 44 EXPERIMENTAL ENGINEERING. [ 38. polar planimeter, for any position within the limits of the arm. The mean ordinate may be found by locating the diagram as shown in the cut, with one extreme point in the line of the metal groove produced, and the dimension representing the length of the diagram perpendicular to this groove. Start to trace the area at the farthest distance of the diagram from the metal guide produced, as shown in Fig. 7; pass around in the direction of the motion of the hands of a watch to the point of beginning; then carry the tracing-point along the straight- edge, AK, which is parallel to the metal groove, until the record- wheel shows the same reading as at the instant of starting : this latter distance is the length of the mean ordinate. 38. Calibration of the Planimeter. In order to ascertain whether the instrument is accurate and graduated correctly, it is necessary to resort to actual tests to determine the character and amount of error. It is necessary to ascertain: I. If the same readings are given by different portions of the record-wheel. 2. Whether the position of the vernier is correct, and agrees with the con- stants tabulated or marked on the tracing-arm. 3. Whether the scale of the record-wheel is correct, and agrees with the constants marked on the tracing-arm. These tests are all made by comparing the readings of the instrument with a definite and known area. To obtain a defi- nite area, a small brass or German-silver rule, shown at L, Fig. II, is used; this rule has a small needle-point near one end, and a series of small holes at exact distances of one inch or one centimeter from the needle-point. To use the rule the needle-point is fixed on a smooth surface covered with paper, the planimeter is set with its tracing-point in one of the holes of the rule, and the pole-point fixed as required for actual use. With the tracing-point in the rule describe a circle, as shown by the dotted lines (Fig. 11) around the needle-point as a centre. Since the radius of this circle is known, its area is known; and as the tracing-point of the planimeter is guided in the circumference, the reading of the record-wheel should give the correct area. 38.] APPARA TUS. 45 The method of testing is illustrated in Figs. II, 12, 13, and 14. Figs. II and 13 show the method with reference to the polar-planimeter, Figs. 12 and 14 show the corresponding methods of testing the rolling-planimeter. In Figs. 11 and 13 P is the position of the pole, B the pole-arm, and A the tracing- arm. In Figs. 12 and 14 B is the axis of the rollers and A is the tracing-arm. First Test. This operation, see Figs. 11 and 12, consists in locating the planimeters as shown, and then slowly and \ t/ I - ] *. . 1 . T r p y a .^s A. A ( E > i "\ \ U . ... i i .... p, 4-x FIG. ii. y Vf./ FIG. 12. carefully revolving so as to swing the check-rule as shown by the arrow. Take readings of the vernier at initial point, and again on returning to the starting-point : the difference of these readings should give the area. Repeat this operation several times. The instrument is now placed in the position shown in Figs. 13 and 14 when the circlet appears on the rtg/tt-hand side of the tracing-arm A, a$d the passage of the tracer takes place in exactly the same way. If the results obtained right and left of the tracing-arm be equal to one another, it is clear that the axis ab of the measur- ing-wheel is parallel to the tracing-arm, and, this being so, the second test may now be applied. But if the result be greater in the first case, that is to say, when the circle lies to the left EXPERIMENTAL ENGINEERING. [38. of the tracing-arm, the extremity a of the axis of the measur- ing-wheel must be further removed from the tracing-arm ; if it be less, that extremity must be brought nearer to the tracing- arm. Second Test. The tracing-arm is adjusted by means of the vernier on the guide and by means of the micrometer-screw, in accordance with the formulae for different areas ; it then is fixed within the guide by means of the binding-screw. The circumference of circles of various sizes are then travelled over r / L \ J5C -_-- FIG. 13. 1 , b \ 1 i a A r ( : S -{ 1 1 V - FIG. 14. with the check-rule, and the results thus obtained are multi- plied into the unit of the vernier corresponding to the area given for that particular adjustment by the formula. The fig- ures thus obtained ought to be equal to the calculated area of the circles included by the circumferences. If the results ob- tained with the planimeter fall short of the calculated areas to the extent of of those areas, the length of the tracing-arm, that is to say, the distance between the tracer and the fulcrum of the tracing-arm, must be reduced to the extent of of that length ; in the opposite case it must be increased in the same proportion. The vernier on the guide-piece of the tracing-arm shows the length thus defined with sufficient accuracy, usually 39-1 APPARA TUS. 47 in half-millimeters, or about fiftieths of an inch, on the gauged portion of the arm. In order to test the accuracy of the readings according to the two methods just described, some prefer the use of a check-plate in lieu of the check-rule. The check-plate is a cir- cular brass disk upon which are engraved circles with known radii. It is advisable to apply the second test also to a large dia- gram drawn on paper and having a known area. The instrument having been found correct or its errors de- termined, it may now be used with confidence. The following form is used to record the results of the test: Calibration of Planimeter 189. . by Dia. register- wheel, in Formula of Instrument Length of arms, pole to pivot, in. ... Pivot to register-wheel, in. . % . Pivot to tracing-point, in. ... In Roller Pla. radius roller, in Pitch radius Gears, No. I No. II. . COMPARISON WITH STANDARD. AREA. MEAN ORDINATE. No. Inst. Reading. Difference from Mean. e * Inst. Reading, o Difference from Mean. e e* Mean Mean error of one observation, Mean error of result, Probable error of one obs., 0.67 Probable error of result, -f- (n i) in area. . . ., in ordinate. . .in. -f- n(n i) in area. . ., in ordinate. . .in. T ) in area. . . ., in ordinate. . .in. 0.67 \^2e*-i-n(n i) in area. . . ., in ordinate. . .in, 39. Errors of Different Planimeters. Professor Lorber, of the Royal Mining Academy of Loeben, in Austria, macle 4 8 EXPERIMENTAL ENGINEERING. [39- extensive experiments on various planimeterSj with the results shown in the following table : The error in one passage of the tracer amounts on an average to the following fraction of the area measured by AREA IN Rolling Planimeter The ordinary Stark's Linear Suspend ed Polar Plan- imeter Unit of Vernier: Planimeter Unit of Ver- nier: Planimeter Unit of Ver- nier: Unit f Ver- nier: Unit of Ver- nier: i Square cm. Square inches. :o sq. mm. = .015 sq. in. ir>sq. mm. .015 sq. in. i sq. mm. = .0015 sq. in. i sq. mm. = .0015 sq. in. .1 sq. mm. = .0001 sq. in. IO i-55 V rff iff TTJW 20 3.10 tif TliW Ilk TtfW 50 7-75 iif T?V 5- l vD F7 l o 1WV IOO 15-50 "S~k~S wsVr ?iW s sVs" g ^'jJ-Q- 200 31.00 I'sW T^ST TTT rVW 715V'3 300 46-50 .... Tooo" TO"5"0"0 The absolute amount of error incre*ases much less than the size of the area to be measured, and with the ordinary polar planimeter is nearly a constant amount. The following table is deduced from the foregoing, and shows the error per single revolution in square inches : Error in one passage of the tracer in square inches AREA IN Polar Planim- eter Unit of Vernier: 10 sq. mm. = .015 sq. inches. Suspended Plan- imeter Unit of Vernier: i sq. mm. = .0015 sq. inches. Rolling Planimeter Unit of Vernier: i sq. mm. = .0015 sq. inches. Unit of Vernier: .1 sq. mm. = .0001 sq. inches. Square cm. Square inches. IO 20 50 IOO 2OO 300 1-55 3.10 7-75 15-50 31 .00 46.50 0.0207 O.O2O6 O.O22I 0.0227 0.0243 0.0025 O.OO28 0.0031 O.OO35 0.0043 0.0049 O.OO25 o . 003 i 0.0038 0.0043 0.0060 0.0058 0.00155 0.00158 0.00258 0.00310 o . 00403 0.00465 These errors were expressed in the form of equations, as follows, by Professor Lorber. Let f equal the area corre- 40.] APPARA TUS. 49 spending to one complete revolution of the record-wheel; let dF be the error in area due to use of the planimeter. Then for the different planimeters we have the following equations : Lineal planimeter, Polar planimeter, Precision polar planimeter, Suspended planimeter, Rolling planimeter, dF o.ooo8i/+ 0.00087 VFf\ dF 0.00126/4- 0.00022 M Ff\ dF 0.00069/4- 0.00018 VFf] dF o.ooo6/ -f 0.00026 VFf ; dF = 0.0009/ 4- 0.0006 VFf. 40. Other Instruments much more complicated than those described have been made for special purposes, of which we will mention Atnsler's planimeter for rinding the moment of inertia, and an instrument described by Sylvanus Thompson for drawing the derivative of any curve, the principal curve being known. * DarlmyBro.ntEhorp. Pnmdcnc. B.I. FIG 15. VERNIER CALIPER. 40. Vernier Caliper. This instrument consists of a slid- ing-jaw, which carries a vernier, and may be moved over a fixed scale. The form shown in Fig. 15 gives readings to ^ - inch on the limb, and ^ this amount or to one-thousandth of SO EXPERIMENTAL ENGINEERING. [4-1- an inch on the vernier. The reading of the vernier as it is shown in the figure is 1.650 from the scale, and 0.002 on the vernier, making the total reading 1.652 inches. This instru- ment is useful for accurate measurements of great variety ; the especial form shown in the cut has a heavy base, so that it will stand in a vertical position and may be used as a height-gauge. To use it as a caliper, the specimen to be measured is placed between the sliding-jaw and the base ; the reading of the vernier will give the required diameter. 41. The Micrometer. This instrument is used to meas- ure small subdivisions. It consists of a finely cut screw, one revolution of which will advance the point an amount equal to the pitch of the screw. The screw is provided with a gradu- ated head, so that it can be turned a very small and definite portion of a revolution. Thus a screw with forty threads to the inch will advance for one complete revolution ^ of an inch, or 25 thousandths. If this be provided with a head sub- divided to 250 parts, the point would be advanced one ten- thousandth of an inch by the motion sufficient to carry the head past one subdivision. The micrometer is often used in connection with a micro- scope having cross-hairs, and in such a case represents the most accurate instrument known for obtaining the value of minute subdivisions; it is also often used in connection with the vernier. The value of the least reading is determined by ascertaining the advance due to one complete revolution, and dividing by the number of subdivisions. The total advance of the screw is equal to the advance for one revolution multiplied by the number of revolutions plus the number of subdivisions multiplied by the corresponding advance for each. The accuracy of the micrometer depends entirely on the screw which is used. Accuracy of Micrometer-screws. The accuracy attained in cutting screws is discussed at length by Prof. Rogers in Vol. V. of Transactions of American Society of Mechanical Engineers, from which it is seen that while no screw is perfectly accurate, still great accuracy is attained. The following errors are those 4 2.] APPARA TUS. in one of the best screws in the United States, expressed in hundred-thousandths of an inch, for each half-inch space, reckoned from one end. CORNELL UNIVERSITY SCREW. TOTAL ERRORS IN HUNDRED-THOUSANDTHS OF AN INCH. No. of Space. Total Error. No. of Space. Total Error. No. of Space. Total Error. 12 4 24 -S I ~f" ^ 13 7 25 - 7 2 + 8 14 - 9 26 -7 3 + 9 15 7 27 9 4 + 7 . 16 10 28 9 5 + 9 17 ii 29 - 7 6 + 7 18 ii 30 7 + 4 19 10 31 -6 8 + 5 20 IO 32 7 9 21 - 9 33 7 10 i 22 ii - ; 34 3 ii 2 23 IO 35 2 36 o A recent investigation made by the author of the errors in the ordinary Brown and Sharpe micrometer-screw, failed to detect any errors except those of observation, which were found to be about 4 hundred-thousandths of an inch for a distance equal to three-fourths its length. The errors in the remaining portion of the screw were greater ; the total error in the whole screw being 12 hundred-thousandths of an inch. As the least reading was one ten-thousandth, the screw was in error but slightly in excess of the value of its least subdivision. In another screw of the same make the error was three times that of the one described. 42.' Micrometer Caliper consists of a micrometer-screw shown in Fig. 16, which may be rotated through a fixed nut. To the screw is attached an external part or thimble, which has a graduated edge subdivided into 25 parts. The fixed nut is prolonged and carries a cylinder, termed the barrel, on which are cut concentric circles, corresponding to a scale of equal parts, and a series of parallel lines, which form a vernier with refer- EXPERIMEN TA L ENGINEERING. [42. ence to the scale on the thimble, the least reading of which is one tenth that on the thimble. If the screw be cut 40 threads per inch, one revolution will advance the point 0.025 inch ; and if the thimble carry 25 subdivisions, the least reading past any fixed mark on the barrel would be one thousandth of an inch. By means of the vernier the advance of the point can be read to ten-thousandths of an inch. Thus in the sketches of G4ttlS. I .0156 3 .0468 5 .0781 7 .1093 9 .1406 II .1718 THIMBLE FIG. 16. MICROMETER CALIPER. the barrel and thimble scales in Fig. 16 the zero of the vernier coincides in the upper sketch with No. 7 on the thimble ; but in the lower figure the zero of the vernier has passed beyond 7, and by looking on the vernier we see that the 3d mark coincides with one on the thimble, so that the total reading is 0.007 + 0.0003, which equals 0.0073 inch. This number must be added to the scale-reading cut on the barrel to show the complete reading. The principal use of the instrument is for measuring external diameters less than the travel of the micrometer-screw. The Sweet Measuring-machine. The Sweet measuring- machine is a micrometer caliper, arranged for measuring larger diameters than the one previously described. The general 42.] APPARATUS. 53 form of the instrument is shown in Fig. 17. The micrometer- screw has a limited range of motion, but the instrument is fur- nished with an adjustable tail spindle, which is set at each FIG. 17. SWEET'S MEASURING-MACHINE. observation for distances in even inches, and the micrometer, screw is used only to measure the fractional or decimal parts of an inch. The instrument is furnished with an external FIG. 18. scale, graduated on the upper edge to read in binary fractions of an inch, and on the lower edge to read in decimals of an inch ; this scale can be set at a slight angle with the axis to correct for any error in the pitch of the micrometer-screw. 54 EXPERIMENTAL ENGINEERING. [ 43- The graduated disk is doubly graduated ; the right-hand grad- uations corresponding to those on the lower side of the scale. The scale and graduated disk is shown in Fig. 18, and the read- ings corresponding to the positions shown in the figure are 0.6822, the last-number being estimated. The back or upper side of the seale, and the left-hand disk, are for binary fractions, the figures indicating 32ds. Fig. 19 shows the arrangement of the figures. Beginning at o and following the line of chords to the right, the numbers are in regular order, every fifth one being counted, and coming back to o after five circuits. This is done to eliminate the factor five from the ten-thread screw. In Fig. 18 the portion to the left of o in Fig. 19 is seen. The back side of the index-bar is divided only to i6ths, the odd 32ds being easily estimated, as this scale is simply used for a "finder;" thus: In the figure the reading line is very near the \\ mark, or six 32ds beyond the half-inch.. This shows that 6 is the significant figure upon this thread of the screw. The other figures belong to other threads. The figure 6 is brought to view when the reading line comes near this division of the scale. Bring the 6 to the front edge of the index-bar, and the measurement is exactly \\ without any calculation. Thus every 32d may be read, and for 64ths and other binary fractions; take the nearest 32d below and set by the interme- diate divisions, always remembering that it requires five spaces to count one. 43. The Cathetometer. This instrument is used exten- sively to measure differences- of levels and changes from a horizontal line. Primarily it consists of one or more telescopes sliding over a vertical scale, with means for clamping the tele- scope in various positions and of reading minute distances. The" one shown in the engraving (Fig. 20) consists of a solid brass tripod or base supporting a standard of the same metal, the cross-section of which is shown at different points by the small figures on the left. A sliding-carriage upon which is 430 APPARA TVS. 55 secured the small levelling instrument, and which has also a vernier scale as shown, is balanced by heavy lead weights, sus- FIG. 20. THE CATHETOMETER. pended within the brass tubes on either side by cords attached to the upper end of the carriage, and passing over the pulleys 56 EXPERIMENTAL ENGINEERING. [ 43. shown at the top of the column. The column is made ver- tical by reference to the attached plumb-line. The movable clamping-piece below the carriage is fixed at any point required, by the screw, shown at its side, after which the telescope can be raised or lowered by rotating the micro- meter-screw attached to the clamp. The telescope is provided with cross-hairs, which can be adjusted by reversing in the wyes and turning 180 degrees in azimuth. The vertical scale is provided with vernier and reading- microscope. STRENGTH OF MATERIALS. CHAPTER III. GENERAL FORMULA. IN this chapter a statement is made of the principal for- mulae required for the experimental work in " Strength of Materials."' The full demonstration of these formulae is to be found in " Mechanics of Engineering," by I. P. Church ; " Strength of Materials," by D. V. Wood ; " Materials of Con- struction," by R. H. Thurston: N. Y., J. Wiley & Sons. 44. Object of Experiments. The object of experiments relating to the " Strength of Materials " is to ascertain, firstly, the resistance of various materials to strains of different char- acter ; secondly, the characteristics which distinguish the different qualities, i.e., the good from the bad ; thirdly, experi- mental proof of the laws deduced theoretically ; fourthly, general laws of variation, as dependent on form, material, or quality. The following methods of testing are ordinarily employed : (i) by tension or pulling; (2) by compression; (3) by trans- verse loading; (4) by torsion; (5) by impact; (6) by repeated loading and unloading, or fatigue. 45. Definitions. Stress is the distributed force applied to the material ; it may be internal or external. Stress is of two kinds, normal or direct, and shearing or tangential, the latter force acting at right angles to the first. A direct stress on an element is always accompanied by a shearing stress, which tends to move the particles at right 57 58 EXPERIMENTAL ENGINEERING. [45- angles to the line of action of the force. This is well shown in the simple break by tension, in which case the particles are not only pulled apart, but they are moved laterally, since the break is accompanied with an elongation of the original specimen, and a corresponding reduction in area of the cross-section. Strain is the distortion of the material due to the action of the force, and within the limits of elasticity is proportional to the stress. Each stress produces a corresponding strain. Elasticity is the property that most materials have of re- gaining their original form when the forces acting on them are removed. This property is possessed only to a limited extent, and if the deformation or strain exceeds a certain amount, the material will not regain its original form. The critical condition beyond which the body cannot be strained without a permanent distortion or set is termed the elastic limit ; this point is gradually reached in most materials, and is indicated by an increase in the increment of strain due to a constant increment of stress. Rigidity or stiffness is the property by means of which bodies resist change of form. The coefficient of ultimate strength is the number of pounds per square inch required for rupture, and is obtained by calcu- lation from the known area and actual breaking-load. The co- efficient of strength at the elastic limit is the number of pounds per unit of area acting upon the material when a failing in strength is shown by an increased increment of distortion for an equal increment of load. The resilience is the potential energy stored in the body, and is the amount of work the material would do on being re- lieved from a state of strain. Within the elastic limit, it is the work done by the force acting on the body, and is evidently equal at any point to the product of one half the load, into the distortion of the piece, this latter being the space passed through. The ductility is the total relative strain ; it is usually expressed in percentage of the full length, and is calculated for the point of rupture. In connection with 46-] STRENGTH OF MATERIALS GENERAL FORMULAE. 59 this should be measured the reduction of area of cross-section. The modulus of elasticity is the ratio of the stress per unit of area to the corresponding increment of distortion. The modulus of rigidity is the amount of . tangential stress per unit of area, divided by the deformation it produces, expressed in angular or n measure. The maximum load is usually greater than the load at rupture. The safe load must always be less than the load at the elastic limit, and is usually taken as a certain portion of the ultimate or breaking load. The ratio of the breaking-load to the safe load is termed a factor of safety. The different . kinds of stress, consequently the different kinds of strain produced, are : Longitudinal, divided into tension and compression ; Transverse, into shearing and bending ; and Twisting or Torsional. 46. Strain-diagrams are diagrams which show the rela- tions which the increments of strain bear to the stress. If the strain-diagrams of several specimens be drawn on the same sheet, the relative values of stress and of strain at elastic limit and at breaking can be determined by inspection. Within the elastic limit the diagram will be a straight line. Strain-diagrams are constructed (see Article 19, p. 16) by lay- ing off the strain on the horizontal axis to a scale that is readily apparent to the eye, and the corresponding loads as ordinates to a convenient scale, as 3000 or 5000 pounds per inch : a curve drawn through the extremities of these various ordinates will be the strain-diagram. When no part is perfectly elastic, as in cast-iron or rubber, no portion of tire curve will be straight. The general form of the strain-diagram, as drawn auto- graphically, is shown in Fig. 21. In this diagram the strain is represented by distances parallel to OX, the stress as a certain number of pounds per inch" parallel to OY. For a short dis- tance from O to A the diagram is a straight line, showing that the increments of strain arid stress are uniform; at A there is a sudden increase in the strain, without a marked increase in load, shown by the curved line A to B. The point A is often spoken of as the yield-point. In most of the ductile materials 6o EXPERIMENTAL ENGINEERING. [47- this sudden increase of strain is accompanied with an apparent reduction of stress, as shown by the curve from B to C. This reverse curvature is often well marked on curves taken auto- matically, and is probably due to the fact that the increase in FIG. 21. THE STRAIN-DIAGRAM. strain is so great that the scale-beam of the machine falls until the stress is increased. The curve then continues to rise, reach- ing its maximum position at D, and falling soon after when the specimen breaks, as shown at E. 47. Viscosity or Plasticity. This is the term applied to denote the change of form or flow that results from the appli- cation of stress for a long time. It is the result of internal molecular friction, and the resistance exerted is proportioned to the rapidity of the change. The definition of viscosity is given by Maxwell (see Theory of Heat) as follows: "The vis- cosity of a substance is measured by the tangential or shearing 47-] STRENGTH OF MATERIALS GENERAL FORMULA. 6 1 force on the unit of area of either of two horizontal planes at the unit of distance apart, one of which is fixed, while the other moves with the unit of velocity, the space between being filled with the viscous substance." Let the substance be in contact with one fixed plane and with one plane moving with the velocity^; denote the dis- tance between the planes by c. Let F be the coefficient of shearing-force, or the force per unit of area tending to move the substance parallel to either plane. Let yw be the coefficient of viscosity. Then we have If we let b = the breadth and a the length of the plane and R the total force acting, R = abF. Hence __ ~ v ~~ vab When c, a, and b each equal unity, // R. If R is the moving force that would generate a certain velocity v in the mass M in time /, R will equal Mv -i- / ; from which Mvc of which quantities may be determined by experiment. 62 EXPERIMENTAL ENGINEERING. [49- 48. Notation. The notation used is the same as that in Church's " Mechanics of Engineering," and is as follows : Syir bol. Quantity. Maximum Load. 'Breaking- Load. Elastic Limit. Safe Limit. Load applied . . . P m P P" P' P" Moduli of tenacity . T m T 7"' r' " " compression c C" C " " shearing e s S" A A A" A' Increment of elongation . . A-\ JA. z/A" Relative elongation 1M f E" [J U U" U' Bending-moment . . M M M" M' Relative shearing distortion m s 8" Transverse load total W W W W Transverse shear / r T" /' J J Compression. EC Shearing. Tension. Modulus of Elasticity E t Area sq. inches F Length, " / Factor of safety n Ordinary moment of inertia. / Polar moment of inertia Ip Maximum fibre-distance e 49. Formulas for Tensile Strength. (Church's Mechanics, pp. 207-221.) Since in tension the stress is uniformly distrib- uted, we have P=FT; (2) P = f J " (3) (4) The modulus o"f elasticity by definition equals the load per square inch divided by the strain per inch of length, within the elastic limit. Hence p p pi PI * SS T**T SS T~ JK* ' ' ' (5) /" 51-] STRENGTH OF MATERIALSGENERAL FORMULA. 63 Resilience U = mean force X total space = e"l = \T"e"FL But Fl equals the volume V. "I. .... (6) 50. Modulus of Elasticity from Sound emitted by a Wire. Let / equal the length of the wire, d equal its specific gravity, n equal the number of vibrations per second, v equal the velocity in feet per second. Determine the number of vibrations by comparing the sound emitted, caused by rubbing longitudinally, with that made by the vibration of a tuning-fork. In this manner de- termine the note emitted. The number of vibrations per second can be found by consulting any text-book devoted to acoustics. We shall have finally v = 2nl\ also rsg from which g g This result usually gives a larger valueby one or two per cent than that obtained by tension-tests, owing to the viscosity of the body. 51. Formulae for Compression-tests. The compression- tests are of value in determining the safe dimensions of mate- rial subject in use to a crushing or compressive stress. Nearly 64 EXPERIMENTAL ENGINEERING. [ 5 1. all bearings in machinery, a portion of the framework, the connecting-rod of an engine, during some portion of a revo- lution, are illustrations of common occurrence, of members strained by compression. Columns and piers of buildings, masonry-walls, are familiar illustrations in structures. The subject is naturally divided into two heads, the strength of short specimens and the strength of long specimens, since the strain is manifestly different in each case. Short Pieces, or those in which the length is not more than four diameters, yield by crushing, and the force acts uniformly over each square inch of area, so that formulae similar to those used in tension apply. (For notation see article 48, page 62.) We have (8) (9) *--?- Resilience U c = \P"\" = $P"e"/= \C"e"Fl. . . The compression-strain is accompanied with a shearing- strain acting at right angles to the specimen equal to P sin a cos a, being a maximum when a = 45. Hence, brittle materials tend to fly to pieces at that angle, leaving two pyra- mids with facing points. Long Pieces, in which the length equals ten or twenty diam- eters, yield by bending on the side of least resistance. Rankine's formwla is most used for this case (Church's Mechanics, page 374). Breaking-load for flat ends, (12) 5 1 -] STRENGTH OF MATERIALS GENERAL FORMULA. 65 Breaking-load for round-ended or two-pin column, * (i2a) Breaking-load for one round end and one square end orpin and square end, , = rc -s- (i +/? VALUE OF COEFFICIENTS AS GIVEN BY RANKINE. Coefficients. Cast-iron. Wrought-iron. Timber. C in pounds per sq. inch 80000 36000 72OO fj (abstract number) ... . I -5- 6400 I - 1 - 36000 I " ^OOO Notation in above Formulas. F = area in square inches. / = length in inches. K radius of gyration. K* I -r- F. See page 68 for values of I. In case the modulus of elasticity is required, Ruler's for- mula should be used ; in this for round-ended columns, in which I" I A, (13) For a column with flat ends, For a column with one pin or round end and the other end square, ' Ruler's formula has only been approximately verified by experiment. 66 EXPERIMENTAL ENGINEERING. [52. 52. Transverse Stress. Theory. In case of transverse stress the force, or a component of the force, is applied at right angles to the principal dimensions of the material. The material is generally in the form of a beam, and the strains produced make the beam assume a concave form with refer- ence to the direction of the force applied. The result of this is a compression of the fibres nearest the force, and a corre- sponding elongation of those farthest away. The fibres of the beam not strained or deformed by any longitudinal force lie in what is called the neutral axis. The curve which the neutral axis assumes due to the forces acting is termed the elastic curve. The weight carried tends to rupture the beam at right angles to the neutral axis ; this stress is equal to the resultant force acting at any point, and is termed the transverse shear. In addition to this there is a shearing-force tending to move the fibres of the beam with reference to each other in a longitudi-, nal direction, which is termed parallel shear; this force is a small one compared with the other forces, and for that reason is difficult to measure experimentally. Formula. In this case the external load is applied with an arm, and tends to produce rotation ; the result is termed the Moment of Flexure or Bending-moment, which is denoted by M. The internal moment of resistance is equal to pi -r- ^, in which / equals the intensity of strain on the .outermost fibre of the piece, 7 equals the moment of inertia, e equals the distance of the outermost fibre to the neutral axis. Since these moments must be equal, we have M = pl+e, (14) which formula may be used for strength. We also have EI+p = M, .'.. . (15) which may be used for flexural stiffness (Church's Mechanics, X X centre of gravity >.; (18) below) . ) ( from that axis. ) 68 EXPERIMENTAL ENGINEERING. [52. in which /is equal to the moment of inertia, J the total trans- verse shear, and b the thickness of beam in the neutral axis. In the ordinary cases of shearing-forces, such as act on rivets or pins, the intensity is uniform ; this case is considered later. The following tables of moments of inertia, of transverse loads, and of external moments will be useful in working up the results of the experiments. TABLE NO. I. MOMENTS OF INERTIA. Ordinary Moment. / Polar Moment. Ip Max. Fibre Dist. e Rectangle width b depth h iV^ 3 Jv6A(&* 4- h*} \h Hollow rectangle, symmetrical.... Triangle, width = b, height == h. , ^(Mi'-M. 8 ) &** litr 4 litr* \k I* Ring of concentric circles 7r(n 4 r^) -iTrfn 4 rJ\ Rhombus h = vertical diagonal.. . Square with side (^) vertical ' iJ- 1 * ^ " H ^ ^ ^ N H M ICQ o_c - 04(/)&H S MM M T ji^j" t r ^ C sJ .2853 f u B < ( >w 5 5 -o 1 "* "* ^xj.>, G C C G C O rt a a a a 1 C/3 - * J J kA\J t?/"^^ 1 I ^ -* I , - H ^lx J , v, Ox |]5l > >< H 1 | H H H' t ni *< H H 8 c c 1 s ? 00 ^ ^ 1 ^ - 1^. 4 3 1 ! J?i!l 1 5-1 ! 5 : li \ ^^f 1 : 1 j*||I |1|| ||f 1 |^|s|il s rt^-rfi-rgs ^ ^i tt, ^i; m "5ti*io om i2 * - rf g j g ^ s g 7O EXPERIMENTAL ENGINEERING. [53- 53. Moment of Inertia by Experiment. If the body can be suspended on a knife-edge so that it can be oscillated back- ward and forward like a pendulum, its moment of inertia can be found as follows : First, balance the body on a knife-edge, and find experimentally the position of its centre of gravity; denote the distance of the centre of gravity from the centre of suspen- sion by 5. Weigh the body, and compute its mass M\ denote its weight by W. Suspend the body on the knife-edge, and set it swinging through a very small arc ; find the time of a single vibration, by allowing it to swing for a long time and divid- ing by the number of vibrations. Let t equal the time in seconds of a single vibration or beat ; let K equal radius of gyration, so that MK* equals moment of inertia. Then, by mechanics, M = W + g; TT" or, by reduction, **=.. 09) In this equation K is reckoned from the point of suspension, and the moment of inertia is the moment around the point of suspension. The moment of inertia about a parallel axis through the centre of gravity, may be denoted by MK?, and we shall have MK; + MS* = MK* ; *See Weisbadi, Vol. I., page 662. 55-] STRENGTH OF MATERIALS GENERAL FORMULA. 71 from which and M K; = 54. Shearing-strain. This strain acts in a transverse direction, without an arm, and thus tends to produce a square break ; it acts uniformly over the whole section, so that P=SF; S = P+F. . . . . . (20) The strain produces on the molecules of the material an angular distortion, which is usually expressed in n measure, or the linear length of the degree of distortion to a radius unity, and is denoted by tf. Let/ s be the stress per square inch. E s is termed the modulus of rigidity. The coefficient of shearing-strength 5 can be obtained by direct experiments, by using the specimen in the form of pins or rivets holding links together, the links being fitted to go in the machine like tensile specimens, and tensile force applied ; if the specimen is a plate, its resistance to shearing-strain can be found by forcing a punch through, as in compression- strains. The angular distortion cannot be measured directly, but may be determined by tests in torsion, as described. 55. Torsion. The strain produced by torsion is essentially a shearing-strain on the elements of the specimen. The effect of torsion is to arrange the outer fibres of the specimen into the form of helices, as can readily be seen by examining a test- piece broken by torsion stress ; each one of these fibres makes an angle with its original position or axis of the piece, equal to its angular distortion, or 6, which is expressed in TT measure. This has the effect also of moving any particle in the surface of ?2 EXPERIMENTAL ENGINEERING. [55- the specimen, through an angle lying in a plane perpendicular to the axis and with its vertex in the axis. This last angle is called a. Letting / equal the length of the specimen, e equal its radius, we have, neglecting functions of small angles, ea ld, . . . . ..... (22) from d = ea -f- /. ........ (220) But since E s = p s -f- #, E t =pJ-s-ea\ ....... (22b) from which f , the modulus of rigidity, may be computed. Since the external moment of forces is equal to the internal moment of resistance, if we let P equal the external load, a its lever-arm, and I P the polar moment of inertia, we will have t ....... (23) from which p s = Pae + I f ....... (24) For a circular rod of radius r, , T nr i 1 IP = , also e = r. Let the external moment Pa. = M t . Then 57.] STRENGTH OF MATERIALS GENERAL FORMULAE. 73 The torsional resilience, or work done, will equal the aver- age load multiplied by the space, or (25) 56. Modulus of Rigidity of a Wire by swinging under Torsion. The transverse modulus of elasticity, or the modu- lus of rigidity, can be determined by hanging a heavy weight on the wire, and swinging it around a vertical axis passing through its point of suspension. Let /equal its length in feet, r its radius in feet, I p the polar moment of inertia of the swing- ing weight, / the time in seconds of an oscillation. Let E s be the modulus of rigidity. Then 57. Relation of E s and E t . Let the distortion in direc- tion of the stress equal e, the angular lateral distortion = #, the lineal lateral distortion m ; then f o $\ i m tan [45 1 = =i m e, nearly. But since 8 is small, tan (45 1 = I tf, nearly. Hence, by substituting, d = m + e. Now t = and E s = ; e o 74 EXPERIMENTAL ENGINEERING. [ 58. Hence E s _ e e 2T,~~2tf ~ = 2(m+e) In cast-iron, by experiment, Prof. Bauschinger found for cast-iron m = .236; hence for this case E s = 0.407^. 58. Combination of Two Stresses. Intensity of combined Shearing* and normal Stress. Let q be the intensity of the shearing-stress, which acts on the transverse section and on a parallel section, and let/ be the intensity of the normal stress on the transverse section ; it is required to find a third plane such that the stress on it is wholly normal, and to find r the intensity of that stress; let this plane make an angle 6 with the transverse section. Then, from equilibrium of forces, ( r ~~ /)cos 6 ^"sin 6, and r sin 6 = q cos 6. Hence q* r(rp\ tan 26 = 2q - p '. . (27) r = \p Vq* -f lp\ . . . . (28) 58a. Twisting combined with Longitudinal Stress. In a circular rod of radius r 1 , a total longitudinal force P in the direction of the axis gives a longitudinal normal stress p : = P -T- area = p -=- Ttr*. A twisting-couple M applied to the same rod gives a shearing- stress whose greatest intensity q, = iM t -r- nr?. * Encyc. Britannica, art. " Strength of Materials." 59-] STRENGTH OF MATERIALS GENERAL FORMULAE. 75 The two together give rise to a pair of principal stresses, as above, P //2M\* . P 8 . .., r=rri\/brT +T-rr (29) 59. Twisting combined with Bending. This important practical case is realized in a crank-shaft. Let P be the force applied to the crank-shaft ; let R be the radius of the crank-shaft ; let B equal the outboard bearing, or the distance between the plane of revolution of the centre of the crank-pin and the bearing. If we neglect the shearing-force, there are two forces acting: a twisting-force M l = PR, and bending-moment M 9 = PB. The stresses per unit of area on the outer fibre would be/, = 4J/ 3 -T- itr* (in which r l is the radius of the crank-shaft) from formulae for transverse strength, and p t = 2M l -j- nr* from for- mula for torsion. Combining these as in equation (27), we find for the prin- cipal stress r = 2M, By substituting values of M l and J/ a , r = 2P(B VB* + R) -i-7r r,* ..... (30) The greatest shearing-stress equals 7rr l 9 ....... (31) The axes of principal stresses are inclined so that tan 20 = M, -f- M a = R + B ....... (32) 7^ EXPERIMENTAL ENGINEERING. [ 60. 60. Thermodynamic Relations.* Thermodynamic theory shows that heat is absorbed when a solid is strained by opposing and is given out when it is strained by yield- ing to any elastic force of its own, the strength of which would diminish if the temperature were raised. As, for example, a spiral spring suddenly drawn out will become lower in temperature, but when suddenly allowed to draw in will rise in temperature. With an india-rubber band the reverse condition is true, which indicates that the effect of heat is to contract instead of to expand the rubber. From this theory the rise in temperature can be calculated for a given strain. Thus let / equal the absolute temperature of the body; the elevation of temperature produced by sudden specific stress/ ; let e equal the corresponding strain ; J Joule's equivalent ; k the specific heat of the body under constant stress ; 8 its density. Then in which both e and/ are infinitesimal, or very small quantities. *See paper by Wm. Thomson in 1'hilosophical Magazine 1877, also vol. in, page 814, ninth edition Encyc. Britannica. CHAPTER IV. STRENGTH OF MATERIALS TESTING-MACHINES. 61. General Description. The testing-machine consists essentially of a weighing device, head and clamps for holding the specimen, apparatus for applying the power to strain the specimen, and a frame to hold these parts together and to re- sist the stress caused by a rupture of the specimen. Some testing-machines have in addition, or as a substitute for the weighing device, means for producing an autographic record of the strain. The same machine is frequently adapted for ten- sile, compressive, and transverse strains. The testing-machipes of recent construction generally have a platform, to which is rigidly- connected, by cast-iron columns, a fixed head in which is a rectangular opening, the platform and fixed head being a portion of the weighing system ; inter- mediate between these and connected by rods to the power system is a head, which is adjustable, to accommodate speci- mens of different length. If the specimen is to be pulled apart, it is held by clamps between the upper fixed head and the movable one; if it is to be compressed or broken transversely, it is held by suitable supports between the movable head and the lower platform. In most machines the specimen is vertical for tension or compression tests, and such machines are termed vertical machines. Vertical machines are now generally pre- ferred to horizontal ones, as they take less room and are some- what more convenient in form. 62. Weighing System. The weighing system in the pres- ent English machines, and in former ones built in this country, consists of a single lever or scale-beam, along which can be 78 63.] STRENGTH OF MATERIALS TESTING-MACHINES. 79 moved a poise, and which can be connected by one or more levers to the test specimen. Such machines are objectionable principally from the space occupied. The weighing device in nearly all recent machines consists of a series of levers, arranged very much as in platform-scales, finally ending in a graduated scale-beam over which a poise is made to move. The machines are usually so constructed that the effect of the strain on the specimen is transmitted into a downward force acting on the platform, and the effect of a given stress is just the same as a given load on the plat- form. The weighing-levers usually consist of cast-iron beams car- rying hardened steel knife-edges, which in turn rest on har- dened-steel bearing plates. This is the system adopted by most scale-makers for their best scales. In the Emery testing-machines, which are especially noted for their accuracy and sensitiveness, the knife-edges and bear- ing plates are replaced by thin plates of steel, the flexibility of which permits the necessary motion of the levers. The weighing device should be accurate, and sufficiently sen- sitive to detect any essential variation in the stress. The amount of sensitiveness required must depend largely on the purposes of the test. An amount less than one tenth of one per cent will rarely make any appreciable difference in the re- sult, and probably may be taken as the minimum sensitiveness needed for ordinary testing. Means should be provided for calibrating the weighing device. This can be done, in the class of machines under consideration, by loading the lower platform with standard weights and noting the corresponding readings of the scale-beams. Testing-machines may be calibrated with a limited number of standard weights, by the use of a test- specimen, which is not to be strained beyond the elastic limit. The weights are successively added and removed, and strain is maintained on the test-piece, equal to the reading on the cali- brated portion of the scale-beam. 63. The Frame. The frame of the machine must be sufficiently heavy and strong to withstand the shock produced 8O EXPERIMENTAL ENGINEERING. [ 65, by a weight equal to the capacity of the machine suddenly ap- plied. The weighing levers must sustain all the stress or force act- ing on the specimen, without sufficient deflection to affect accuracy of the weighing, and the frame must be able to sus- tain the shock consequent upon the sudden removal of the load, due to breaking, without permanent set or deflection. 64. Power System. The power to strain or rupture the specimen is usually applied through the medium of a train of gears or by a hydraulic press, operated by power or hand. The hydraulic machine is very convenient when the stress is less than 50,000 pounds; but if there is any leakage in the valves, the stress will be partially relieved the instant the pump ceases to operate, and difficulty may be experienced in ascer- taining the stretch for a given load. 65. Shackles. The shackles or clamps for holding the specimen vary with the strain to b. applied. These clamps for tension tests usually consist of truncated wedges which are in- serted in rectangular openings in the heads of the testing-ma- chines, and between which the specimen is placed. The inte- rior face of the wedges is for flat specimens plane and serrated, but for round or square specimens it is provided with a trian- gular or V-shaped groove, into which the head of the specimen is placed. When the strain is applied to the specimen these wedges are drawn closer together, exerting a pressure on the specimen somewhat in proportion to the strain and often in- jurious to its strength. In tensile testing it is essential to the correct determination of the strength of the specimen that the force shall be applied axially to the material; in other words, it shall have no oblique or transverse component. This requires that the wedge clamps shall be parallel to the specimen, and that the heads which contain the clamp shall separate in a right line and parallel to the specimen. This construction is well shown in the following description of the clamps used in the Olsen and Riehle testing-machines. A plan and section of the draw-heads used with the Olsen machine is shown in Fig. 23. The small numbers refer to 65.] STRENGTH OF MA TERIALS TESTING-MACHINES. 8 1 the same part in each view, and also in Figs. 29 to 33, so that any part can be easily identified ; 60, 59 is a counterbalanced lever used to prevent the wedges falling out when the strain is relieved ; 63, 63, is a screw connected to a plunger for ad- justing the space into which the wedge-clamps are drawn. A lateral motion of the specimen is obtained by unscrewing on one side and screwing up simultaneously on the other side : 63. fo 5 o] 3$ _aM^ CO I P ^ 2] ii i^ JSJ, lo 55 FIG. 23. DRAW-HEAD TO OLSEN'S TESTING-MACHINE. this adjustment is of advantage in some instances in centering the specimen. For use of the other parts shown in Fig. 20, see Art. 64, page 91. The clamps used by Riehle Brothers for holding flat speci- mens are shown in Fig. 24 and Fig. 25, as follows: 82 EXPERIMENTAL ENGINEERING. Fig. 240 is a plan of wedge-clamp, with specimens in position ; CC, curve-faced wedges ; D, specimens ; e is a pin that is used to guide the specimen to the centre of the testing- tools. FIG. 24. FIG. FIG. Fig. 25 is a sectional view of same. Fig. 24 is a view of the wedge-faced clamp. The inclination of the surfaces of the wedges are exaggerated in the drawings,so as to distinctly set forth their features. Wedges have been made with spherical backs, and a por- tion of the draw-heads mounted on ball surfaces in order to insure axial strains. Special holders into which screw-threads have been cut have been used with success, and in many instances the specimens have been fastened to the draw-heads by right and left threaded screws. 66. Specifications for Government Testing-machine. The large machine in use by the United States Government at the Watertown Arsenal was built by Albert H. Emery. The machine is not only of large capacity, but is extremely delicate and very accurate. A perspective view of the machine is. shown in Fig. 22. The requirements of the United States Government as ex- pressed in the specifications, which were all successfully met, were as follows : 66.] STRENGTH OF MATERIALS TESTING-MACHINES. 83 84 EXPERIMENTAL ENGINEERING. [ 67. ist. A machine with a capacity in tension or compression of 800,000 pounds, with a delicacy sufficient to accurately reg- ister the stress required to break a single horse-hair. 2d. The machine should have the capacity of seizing and giving the necessary strains, from the minutest to the greatest, without a large number of special appliances, and without special adjustments for the different sizes. 3d. The machine should be able to give the stresses and receive the shocks of recoil produced by rupture of the speci- men without injury. The recoil from the breaking of a speci- men which strains the machine to full capacity may amount to 800,000 pounds, instantly applied. The machine must bear this load in such a manner as to be sensitive to a load of a single pound placed upon it, without readjustment, the next moment. 4th. The parts of the machine to be at all times accessible, 5th. The machine to be operated without excessive cost. 67. Description of Emery Testing-machine. These ma- chines are now constructed by Wm. Sellers & Co. of Phila- delphia, under a license from the Yale & Towne Mfg. Co. of Stamford, Conn. The following description will serve to explain the principle on which the machine acts : The machine consists of the usual parts: i. Apparatus to apply the power. 2. Clamps for holding the specimen. 3. The weighing device or scale. 1. The apparatus for applying power consists of a large hy- draulic press, which is mounted on wheels as shown in the en- gravings, Fig. 22 and Fig. 26, and can be moved a greater or less distance from the fixed head of the machine. Two large screws serve to fix or hold this hydraulic press in any position desired, according to the length of the specimen : and when rupture is produced the shocjj is received at each end of these screws, which tend to alternately elongate and compress, and take all the strain from the foundation. 2. Clamps for holding the specimen. These are peculiar to the Emery machine, and are shown in Fig. 26 in section. This 6/.] STRENGTH OF MATERIALS TESTING-MACHINES. 85 figure also shows a section of the fixed head of the machine, and a portion of the straining-press, with elevation of the holder for the other end of the specimen. The clamps, numbered 1484 in Fig. 26, are inserted between two movable jaws (1477), which are pressed together by a FIG. 27. ELEVATION OF THE VERTICAL MACHINE. FIG. 28. SCALE-BEAM AND CASE. hydraulic press (1480), resting on the fixed support (1476). By this heavy lateral pressure force equal to i, 000,000 pounds can be applied to hold the specimen. The amount of this force is shown by gauges connected to the press cylinder, and can be regulated as required. 86 EXPERIMENTAL ENGINEERING. [_ ^7- For the vertical machines these shackles or holders are ar- ranged so as to have sufficient lateral motion to keep in the FIG. 29. THE BASE-FRAME AND ABUTMENTS. line of the test-piece. 3. The weighing device. This is the especial peculiarity of 6/.] STRENGTH OF MATERIALS TESTING-MACHINES. 8/ the Emery machine : instead of knife-edges, thin plates of steel are used, which are flexed sufficiently to allow the neces- sary motion of the levers. The steel used varies from 0.0x34 to FIG. 30. BEAM FOR PLATFORM-SCALE. 0.05 inch thick, and the blades are so wide that the stress does not exceed 40,000 to 60,000 pounds per square inch. Fig. 31 shows the form of fulcrums used for light forces when the steel fulcrums are in tension. FIG. 31. CLAMPING SUSPENSION FULCRUMS. The method of measuring the load is practically that of the hydraulic press reversed, but instead of pistons, diaphragms having very little motion are used. Below the diaphragm is a very shallow chamber connected by a tube to a second 88 EXPERIMENTAL ENGINEERING. [ 67. chamber covered with a similar diaphragm, but of a different diameter. Any downward pressure on the first diaphragm is transmitted to the second, giving a motion inversely as the squares of the diameters. This latter motion may be farther increased in the same manner, with a corresponding reduction in pressure, or it may at once be received by the system of weighing levers. The total range of motion given the first diaphragm in the 5O-ton testing-machine is T -ooWo P art f an inch, but the indicating arm of the scales has a motion of T fa of an inch for each pound. This increase of motion and cor- responding reduction of pressure is accomplished practically without friction. These parts will be well understood by Figs. 28, 29, and 30, showing the Emery ioo,OOO-pound vertical test- ing-machine. Fig. 27 shows the elevation of the vertical machine arranged for transverse tests. Fig. 28 shows the scale-beam and case, and Fig. 29 is a section of the base-frame and hydraulic supports. In this last figure the diaphragm, filled with liquid, is placed between the frames EE. These frames are allowed the neces- sary but slight vertical motion by the thin fulcrum-strips b and c, but at the same time are held from lateral motion. The frame EE and diaphragms are supported by springs d, so as to have an initial tension acting on the test-piece. The dia- phragm and its enclosing rings fill the whole space between the frame to within 0.005 inch, which is the maximum amount of motion permitted. The pressure on the diaphragm between the frames EE is communicated by the tube f to a similar diaphragm in com- munication with the weighing-levers. Fig. 30 represents the weighing-levers for platform-scales. In case a diaphragm is used it is placed beneath the column A ; the motion of the column A is communicated to the scale-beams by a system of levers as shown. The scale-beam of the testing-machine is shown in Fig. 28, and is so arranged that by operating the handles on the out- side of the case the weights required to balance the load can be added or removed at pleasure. The device for adding the 68.] STRENGTH OF MATERIALS TESTING-MACHINES. 89 weights is shown in Fig. 32. a, b, c, d, e, and /are the weights, which are usually gold-plated to prevent rusting. These when not in use are carried on the supports A and B by means of pins. When needed, these supports can be lowered by the out- side levers, and as many weights as are needed are added to the weighing-poise CD. 68. Riehle Brothers' Hydraulic Testing-machines. The testing-ma- chines built by Riehle Brothers of Phil- adelphia vary greatly in principles and methods of construction. In the ma- chines built by this firm, power is ap- plied either by hydraulic pressure or by gearing, and the weighing device con- sists of one or more levers working over steel knife-edges, as in the usual scale construction. Machines have been built by this firm since 1876. The form of the first machine constructed was essentially that of a long weighing-beam sus- pended in a frame and connected by differential levers to the specimen, the power being applied by a hydraulic press. The later forms are more com- pact. The standard hydraulic machine as constructed by this firm is shown in Fig. 33. In this machine the cylin- der of the hydraulic press, which is i * - , i i ,> , , . FIG. 32. DEVICE FOR ADDING situated directly beneath the specimen, OR REMOVING WEIGHTS. is movable, and the piston is fixed. This motion is transmitted through the specimen, and is resisted by the weighing levers at the top of the machine, which are connected by rods and levers to the scale-frame. Two platforms connected by a frame are carried by the weigh- ing levers: the upper one is slotted to receive the wedges for 9O EXPERIMENTAL ENGINEERING. [_ 69. holding the specimen : the lower one forms a plane table. The intermediate platform, or draw-head, can be adjusted in dif- ferent positions by turning the nuts on the screws shown in the cut. For tension-strains the specimen is placed between the upper and intermediate head ; for compression it is placed between the intermediate and lower heads. An attachment is often added to the lower platform, so that transverse strains can be applied. The cylinder is connected by two screwed rods to the intermediate platform or draw-head, and when it is forced FIG. 33. downward by the operation of the pump this draw-head is moved in the same direction and at the same rate. 69. Riehle Power Machines. The machines in which power is applied by gearing are now more generally used than hydraulic machines. Fig. 34 shows the design of geared ma- chine now built by Riehle Bros., in sizes of 50,000, 100,000, and 200,000 pounds capacity. In this machine both the gearing for applying the power and the levers connected with the weighing apparatus are near the floor and below the specimen, thus giving the machine great stability. The heads for hold- ing the specimen are arranged as in the hydraulic machine, and power is applied to move the intermediate platform up or down 69.] STRENGTH OF MATERIALS TESTING-MACHINES. 9! as required. The upper head and lower platform form a part of the weighing system. The intermediate or draw-head may be moved either by friction-wheels or spur-gears at various speeds, which are regulated by two levers convenient to the operator standing near the scale-beam. The poise can be moved backward or forward on the scale- 9 2 EXPERIMENTA L ENGINEERING. [70- beam, without disturbing the balance, by means of a hand- wheel, opposite the fulcrum on which the scale-beam rests. The scale-beam can be read to minute divisions by a vernier on the poise. 70. Olsen Testing-machine. General Form. The ma- FIG. 35. THE OLSEN TESTING MACHINE. FRONT VIEW. chines of Tinius Olsen & Co. of Philadelphia are all operated by gearing, driven by hand in the machines of small capacity, and by power in those of larger capacity. The general form of the machine is shown in Figs. 35 and 36, from which it is seen that the principles of construction are the same as in the machine last described. 7 1 -] STRENGTH OF MATERIALS TESTING-MACHINES. 93 The intermediate platform or draw-head is operated by four screws instead of by two, and there is a marked difference in the arrangement of the weighing-levers and in the gearing. The machine can be operated at various rates of speed in either direction, and is readily controlled by convenient levers. FJG. 36. THE OLSEN TESTING-MACHINE, REAR VIEW. 71. The Olsen Autographic Apparatus. This apparatus for drawing strain-diagrams is entirely automatic, and is operated substantially as follows : The diagram is drawn on a drum (103), parallel to the scale- beam, by a pencil actuated by a screw-thread cut to a fine pitch 94 EXPERIMEN TA L ENGINEERING. on the end of the rod which actuates the poise (106), so that the pencil will move in a definite ratio to that of the poise. The drum is actuated by the stretch of the specimen. This is brought about by four fingers shown in Fig. 35, and on a larger scale in Fig. 38 by numbers 82 and 83. These fingers, shown in plan in Fig. 38, tend to separate and follow any motion of the collars (65) placed on the test-piece, as shown in Fig. 35 ; the motion of these fingers is multiplied five times, 77 FIG. FIG. 351 and connected by steel bands to the drum, IO2, in such a man- ner that the resultant force only is effective to rotate the drum. The poise is moved by a friction device attached to the main power system, which is thrown into or out of gear auto- matically by an electric current, as required to keep the beam floating ; the current passes through the scale-beam in opposite directions, according as the place of contact is above or below 72.] s TRENG TH OF MA TERIA LSTES TING- MA CHINE S. 95 the beam. Finally, an alarm-bell is rung whenever the scale- beam operates beyond its normal amount, thus calling the at- tention of the operator. Gauge-marking Device. A special and very ingenious ar- rangement, shown in Fig. 39, is used to hold the test-piece and mark the extreme gauge-marks in any position desired. 72. Parts of Oisen Machine. The following reference numbers to the parts of the Olsen machine will serve to show the construction : 1. Entablature. 61 2. Columns. 62 3. Platform supporting columns. 63 4. Pivots. 64 5. Lower moving head. 22. Sleeve on driving-shaft. 72. 24. Rock-shaft operating lever shifting 73. 22. 74. 25. Hand-lever operating 24. 75. 26. 27. Pulleys rotating driving-shaft. 78. 28, 29. Friction-clinches engaging 26 82, with driving-shaft. 85. 30. Sleeve operating clutches. 86. 31. Forked lever controlling sleeve 30. 95. 33. Hand-lever operating 30. 96. 34. Grooved wheel on driving-shaft. 97. 40. Tilting bearing. 98. 41. Band-wheel. 99. 42. Endless band. 100. 44. Helical spring. 101. 46. Fulcrum of lever 117. 102. 48. Specimen under test. 103. 49. Gripping jaws. 104. 50. Projecting flanges on jaws 49. 105. 51. Block-slide. 106. 52. Grooves in 51. in. 53. Slotted slide supporting 49. 117. 54. Opening in 53. 118. 55. Eye in 53. nS'. 56. Bolt connecting 53 and 57. 119. 57. Lever to open and shut jaws. 144. 58. Fulcrum of 57. 145. 59 Counterweight. 146. 60. Handle of lever 57. Plungers for slides 51. Screws for 61. Screw-bolt. . Collars or clamps for caliper bear- ing. . Guiding-block. , Cam. Lever moving 87. Sliding-blocks. Polygonal prism in 75, 83. Calipers. Arm of caliper. Clamps. Cord operating recording-cylinder Pulley. Lever. Fulcrum to 97. Pulley or sheave. Drum or winding-barrel of IO2. Link. Recording-cylinder. Pencil. Screw. Screws shifting 106. Poise or weight. Balancing pivot of beam. Force multiplying lever. Weighing-beam. Slide to small poise on 118. Link. Endless band for moving poise. Guiding-pulleys. Grooved wheel. EXPERIMEN TA L ENGINEERING. [73. 73. Thurston's Torsion Testing-machine. Both the breaking-strength and the modulus of rigidity can be obtained from the autographic testing-machine invented by Professor Thurston in 1872. FIG. 40. THURSTON'S AUTOGRAPHIC TORSION TESTING-MACHINE. In this machine the power is applied by a crank at one side, tending to rotate the specimen, the specimen being con- nected at the opposite end to a pendulum with a heavy weight. The resistance offered by the pendulum is the measure of 73-] STRENGTH OF MATERIALS TESTING-MACHINES. Q/ the force applied, since it is equal to the length of the lever- arm into the sine of the angle of inclination, multiplied by the constant weight P. A pencil is carried in the axis of the pendulum produced, and at the same time is moved parallel to the axis of the test-piece by a guide curved in proportion to the sine of the angle of deviation of the pendulum, so that the pencil moves in the direction of the axis of the specimen an amount proportional to the sine of this angle. A drum carry- ing a sheet of paper is moved at the same rate as the end of the specimen to which the power is applied. Now if the pencil be made to trace a line, it will move a distance around the drum which is equal to the angle of torsion (a) expressed in degrees or n measure, and it will move a distance parallel to the axis of the test-piece proportional to the moment of ex- ternal forces, Pa. The diagram Fig. 41, from Church's " Mechanics of En- gineering," shows the working portions of the machine very clearly. In the figure P is the pendulum, the upper end of FIG. which moves past the guide WR, and is connected by the link FA with the pencil A T. The diagram is drawn on a sheet of paper on the drum, which is rotated by the lever b. The 98 EXPERIMENTAL ENGINEERING. [ 73. drum moves through the angle a, relatively to the pendulum which moves through the angle ft. The test-piece is inserted between the pendulum and drum. The value of a in degrees 'can be found- by dividing the distance on ,the diagram by the length of one degree on the surface of the paper on the drum, which may be found by measurement and calculation. Application of the Equations to the Strain-diagram. For the breaking-load apply equation (23) of Chapter III., page 72, (23) The external moment Pot equals Pr sin ft, in which P is the fixed weight, r the length of the pendulum, ft the angle made with the vertical. Hence Pr sin ft = pj p -r- e. In this equation P and r are constant, and depend upon the machine ; I P and e are constant, and depend upon the test- piece. sin ft is the ordinate in inches to the autographic strain- diagram, and can be measured ; knowing the constant, /, may be computed. /, = Pr sin fte -r- I P . For the modulus of rigidity, apply equation (220), Chapter III., page 72. E s =p s l -r- ea Plr sin ft ~ I p a. In this equation sin ft is the ordinate to the strain-diagram, and a the corresponding abscissa, the other quantities are constant, and depend on the machine or on the test-piece. The Resilience (see equation (25), page 73) is the area of the diagram within the elastic limit, expressed in absolute units. U = \Poia = \Pr sin fta. 75-] -S TRENG TH OF MA TE RIA LSTES TING-MA CHINES. 99 The Helix Angle (see equation (22), page 72) 6 = ea -j- /, in which / is the length of the specimen in inches. The elongation of the outer fibre can be computed by multiplying / by secant tf. The per cent of elongation is equal to secant d. (Sec tf is equal to the square root of I -|- tan 2 d.) 74. Machine Constants. To obtain the Constants of the Machine. First, the external moment Pa. This is obtained on the principle that it is equal to any other external moment which holds it in equilibrium. Swing the pendulum until its centre-line is horizontal ; support it in this position by a strut resting on a pair of scales; the product of the corrected reading of the scales into the distance to the axis on the arm will give Pa. Check this result by trials with the strut at different points. Correct for friction of journal. Second, the value of the scale of ordinates can be obtained by measuring the ordinate for ft = 90 and for /3 = 30, since sine 90 = I and sine 30 = . Third, the value of the scale of abscissae can be obtained by dividing the abscissa on the diagram by the radius of the drum including the paper. This may be expressed in degrees by dividing by the length of one degree. Constants of the Material are obtained by measuring the dimensions of the specimen. The values of /and e are given on page 68. Conditions of Accuracy. In obtaining these values, the fol lowing conditions are assumed : Firstly, the test-piece is exactly in the centre of motion of the pendulum and of the drum ; sec- ondly, the pencil is in line of the pendulum produced ; thirdly, the curve of the guides is that of the sine of the angle of devia- tion ; and, fourthly, the specimen is held firmly from rotation by the shackles or wedges, and yet allowed longitudinal motion. These constitute the adjustments of the machine, and must be carefully examined before each test. Any eccentricity of the axis of the specimen will lead to serious error. 75. Riehle Torsion-machine. This machine is shown in Fig. 42. Power is applied at various rates of speed by means of the gearing shown. The specimen is held by means of two chucks: the one on the left is rotated an amount shown by the IOO EXPERIMEN TA L ENGINEERING. graduated scale in degrees ; the one on the right is prevented from rotating by a lever connected with the scale-beam. The external moment is the product of the reading of the scale- beam P into the fixed arm, which is taken as one foot, or unity. 77-] STRENGTH OF MATERIALS TESTING-MACHINES. IOI The angle of torsion a is given by reading of the attached graduated arc. The heads are movable, and the machine is adapted to specimens of varying length and cross-section. Olsen's Torsion-machine differs from the above principally in details of construction. 76. Impact-testing Machine. The Drop Test Testing by Impact. This test, see page 143, is recommended for material used in machinery, railroad construction, and generally when- ever the material is likely to receive shocks or blows in use. This test is usually performed by letting a heavy weight fall on to the material to be tested. The Committee on Stand- ard Tests of the American Society of Mechanical Engineers recommend that the standard machine for this purpose consist of a gallows or framework operating a drop of twenty feet, the weight to be 2000 pounds, the machine to be arranged sub- stantially like a pile-driver. The impact machine designed by Mr. Heisler consists of a pendulum with a heavy bob, which delivers a blow on the centre of a bar securely held on two knife-edge supports affixed to a heavy mass of metal. This machine is especially designed for comparative tests of cast- iron ; it is furnished with an arc graduated to read the vertical fall of the bob in feet, and a trip device for dropping the ram from any point in the arc. A paper drum can be arranged for automatically recording the deflection of the test-pieces. Let W ' the weight of the bob; h = the distance fallen through ; P= centre load ; A = deflection. Then Wh = PA. Hence P = 2 Wh + A. 77. Machines for Testing Cement. Cement mortar can be formed into cubes, and after hardening can be tested in the 102 EXPERIMENTAL ENGINEERING. [77* usual testing-machines for compression ; but tensile tests are usually required, and for this purpose a delicate machine with special shackles is needed. In order that the tests may give correct results, it is necessary that the power be applied uni~ FIG. 43. FAIRBANKS' CEMENT-TESTING MACHINE. formly, and absolutely in the line of the axis of the specimen ; and to make different tests comparable, the specimen, or as it is called, the briquette, must be always of the same shape and size, and made in exactly the same manner. The engraving (Fig. 43) shows Fairbanks Automatic Cement Tester, in which the power is applied by the dropping of shot into the pail/ 7 . The specimen is held between clamps, which are regulated at the 77-] S TRENG TH OF MA TERIA LSTES TING-MA CHINE S, I O.3 proper distance apart by the screw P. At the instant of rup- ture the scale-beam D falls, closes a valve, and stops the flow of shot. In Fig. 43 M is a closed mould for forming a briquette, 5 the mould opened for removing the briquette, T a briquette which has hardened, and U one which has been broken. Directions. Hang the cup F on the end of the beam D, as shown in the illustration. See that the poise R is at the zero- mark, and balance the beam by turning the ball L. Place the shot in the hopper B, place the specimen in the clamps NNy and adjust the hand-wheel P so that the gradu- FIG. 44. OLSEN'S CEMENT-TESTING MACHINE, ated beam D will rise nearly to the stop K. Open the automatic valve / so as to allow the shot to run slowly. Stand back and leave the machine to make the test. When the specimen breaks, the beam D drops and closes the valve /. Remove the cup with the shot in it, and hang the counterpoise-weight G in its place. Hang the cup F on the hook under the large balance-ball , and proceed to weigh the shot in the ordinary way, using the poise R on the graduated beam D and the weights H on the counterpoise-weight G. The result will show the number of pounds required to break the specimen. An automatic machine designed by Prof. A. E. Fuertes has been in use a long time in the cement-testing laboratory at 104 EXPERIMENTAL ENGINEERING. [ 77, Cornell University. In this machine water is supplied flowing from a constant head through a small glass orifice. The fall of the beam consequent on the breaking of the specimen in- stantly stops the flow of water ; the weight of this water, mul- tiplied by a known constant, gives the breaking-load on the briquette. The Olsen Cement tester is shown in Fig. 44. The power is applied by the hand- wheel and screw, so that it strains the WBS&IUP J.WF.ST FIG. 45. RIEHLE BROS.' CEMKNT-TESTING MACHINE. briquette very slowly. The poise on the scale-beam is moved by turning a crank so that the beam can readily be kept float- ing. The peculiar method of mounting the shackles or hold- ers to insure an axial pull is well shown in the engraving. The Riehle cement-tester is shown in Fig. 45. The briquette to be tested is placed between two shackles mounted on pivots so as to be free to turn in every direction. Power is applied to the specimen by the hand-wheel below the machine, and is measured by the reading on the scale-beam at the position of the poise. Special crushing tools, consisting I 77-] S TRENG TH OF MA TERIA L S TESTING-MA CHINES. 1 05 of a set of double platforms, which may be drawn together by application of the force, is furnished with this machine. The specimen to be crushed is placed between these platforms, and the power applied as for tension. Besides the machines described, various machines for special testing are manufactured ; these machines have a limited use, and do not require special description. TESTING-MACHINE ACCESSORIES. 78. General Requirements of Instruments for Measur- ing Strains. In the test of materials it is necessary to meas- ure the amount of strain or distortion of the body in order to compute the ductility and the modulus of elasticity. The ductility or percentage of ultimate deformation can often be obtained by measurement with ordinary scales and calipers, since the latter is usually a large quantity. Thus in the tension-test of a steel bar 8 inches long, it will increase in length before rupture nearly or quite 2 inches ; if in the meas- ure of this quantity an .error equal to one fiftieth of an inch be made, the resulting error in ductility is only one half of one per cent. In the measure of deformation or strain oc- FIG. 46. THE WEDGE SCALE. curring within the elastic limit the case is very different, as the deformation is very small, and consequently a very small error is sufficient to make a great percentage difference in the result. The instruments that have been used for this purpose are called extensometerS) and vary greatly in form and in principle of construction. The instrument is generally attached to the test-piece, either on one or on both sides, and the strain is ob- tained by direct measurement with one or two micrometer- screws, or by the use of levers which multiply the deformation so that the results can be read on an ordinary scale. As a 1 06 8 1.] TF STING-MACHINE ACCESSORIES. IO/ rule, instruments which attach to one side of the test-piece will give erroneous readings if the test-piece either be initially curved, or strained so as to draw its axis out of a right line, and this error may be large or small, as the conditions vary. 79. Wedge-scale. The wedge-shaped scale, Fig. 46, which could be crowded between two fixed points on the test-piece, was one of the earliest devices to be used. In using the scale two projecting points were attached to the speci- men, and as these points separated, the scale could be inserted farther, and the distance measured. 80. The Paine Extensometer. This instrument, shown in Fig. 47, operates on the principle of the bell-crank lever, the long arm moving a vernier over a scale at right angles to the axis of the specimen. It reads by the scale to thousandths of an inch, and by means of the vernier to one ten-thou- sandth of an inch. Points on the instru- ment are fitted to indentations in one side of the test-piece, and the instrument is held in place by spring clips. It is of historical importance, having been invented by Col- onel W. H. Paine, and used in the tests of material for the Brooklyn Bridge, and also on the cables of the Niagara Suspension Bridge when, a few years since, the question of its strength was under investigation. 81. Buzby Hair-line Extensometer. This is an extensometer in which the strain is utilized to rotate a small friction-roller connected with a graduated disk as shown in Fig. 48. A projecting pin placed in the axis of the graduated disk is held between two parallel bars, each of which is connected FlG - 47. to the specimen. The strain is magnified an amount proper- io8 EXPERIMENTAL ENGINEERING. [8l. tional to the ratio of diameters of the disk and pin. The amount of strain is read by noting the number of subdivisions FIG. 48. BUZBY HAIR-LINE EXTENSOMETER. of the disk passing the hair-line. To prevent error of parallax in reading, a small mirror is placed back of the graduations, and 82.] TESTING-MACHINE ACCESSORIES. 109 readings are to be taken when the graduations, the cross-hair, and its reflection are in line. In the late styles of this instru- ment the disk is made of aluminium, with open spokes, to re- duce its weight. To operate this instrument it is only necessary to clamp it to the specimen, to adjust the mirror and cross-hair, and then to revolve the disk by hand until the zero-line corresponds with the cross-hair and its reflection. Strain is then applied to the specimen, and readings taken as desired in the mariner de- scribed. 82. Thurston's Extensometer. This extensometer was designed by Prof. R. H. Thurston and Mr. Wm. Kent, and FIG. 49. THURSTON'S EXTENSOMETER. was the first to employ two micrometer-screws, at equal dis- tances from the axis of the specimen. These were connected to a battery and an electric bell in such a manner that the con- tact of the micrometer-screws was indicated by sound of the bell. The method of using this instrument is essentially the same as that of the Henning and Marshall instrument, to be described later. With instruments of this nature a slight bending in the no EXPERIMENTAL ENGINEERING. ['83- specimen will be corrected by taking the average of the two readings. The accuracy of such extensometers depends on 1. The accuracy of the micrometer-screws. 2. The screws to be compensating must be two in number, in the same plane, and at equal distances from the axis of the specimen. 3. The framework and clamping device must hold the mi- FIG. 50. THE HENNING MICROMETER. crometers rigidly in place, and yet not interfere with the ap- plication of stress. 83. The Henning Extensometer. This instrument, which was designed by G. C. Henning and C. A. Marshall, is shown in Fig. 50. It is constructed on the same general principles as the Thurston Extensometer, but the clamps which are attached to the specimen are heavier, and are made so that they are held firmly in position by springs up to the instant of rupture. This extensometer is furnished with links connecting the two parts together. The links are used to hold the heads exactly eight inches apart, and are unhooked from the upper head 84-] TESTING-MACHINE ACCESSORIES. Ill before stress is applied to the specimen. The micrometer is connnected to an electric bell in the same manner as the Thurston extensometer. FIG. 51. THE MARSHALL EXTENSOMETER. 84. The Marshall Extensometer. This extensometer, shown in Fig. 51, is the latest design of the late Mr. C. A. Marshall. Its principal difference from the Thurston exten- 112 EXPERIMENTAL ENGINEERING. [ 8jJ. someter is in the convenient form of clamps, which are well shown in the cut, and in the spring apparatus for steadying the lower part. The micrometer-screw used with this instrument has a motion of only one inch. When the motion exceeds the range of the micrometer-screws, the movable bars BP, B ' P r are changed in position, and a new series of readings taken with the micrometer- screw. To facilitate the change of posi- tion of these bars, and allow the microme- ter-screw to return to zero at each change, the arrangement shown in Fig. 52 is adopted, which consists of a nut to which FIG. 52. is attached a slotted taper-screw, on which screws a second nut, which serves to clamp the lower nut to the bar ; by turning the lower nut when clamped, the desired adjustment can be made. The following are the directions for use: Run wire (Fig. 51) from one terminal of battery to lower clamp at A, from B and B' to binding-post C on the electric bell, from the other binding-post marked D to switch E, and from there back to the other terminal of battery. To measure strain, screw up micrometer-screws at P and P r until each of them makes connection and bell rings ; then take the readings on both sides. 85. Boston Micrometer Extensometer. This instru- ment consists, as shown in Fig. 53, of the graduated microm- eter-screw, reading in thousandths up to one inch, and having pointed extension-pieces attached, for gauging the distance between the small projections on the collars fastened to the specimen at the proper distance. These collars are made partly self-adjusting by the springs which help to centralize them. They are then clamped in place by means of the pointed set-screws on the sides, and measurements are made between the projections on opposite sides of the specimen and com- pared, to denote any changes in shape or variations in the two sides. 86.] TESTING-MACHINE ACCESSORIES. The Brown and Sharpe micrometer can readily be used with similar collars, thus forming an exten- ' someter ; the accuracy of this form is considerably less than those in which the micrometers are fixed, but it will, however, be found with careful handling to give good results. Of the various extensometers de- scribed, the Paine, Buzby, Marshall, and Riehle are manufactured by Riehle Bros,, Philadelphia ; the Thurston, by Olsen of Philadelphia ; the others, by the respective de- 86. Combined Extensometer and Autographic Apparatus. An extensometer designed by the author, and quite extensively used in the tests of materials in Sibley College, is shown in Fig. 54 in ele- vation and in Fig. 55 in plan. In this extensometer micrometers of the kind shown in Fig. 16, Article 42, p. 52, with the addition of an exten- sion-rod for holding, are used. This rod sets into a socket A, which holds the micrometer in position. Read- ings are taken on the thimble B, as explained on p. 52. Connections are made with bell and battery at ;;/, n, and m', n', so that contact of the micrometer- screws is indicated by sound. The construction of the clamp- ing device is fully shown in the plan view, Fig. 55. The principal peculiarity of this extensometer consists in the addition of four pulleys, C l , C^ , C a and C 4 , which are arranged so that a cord ab can be fastened at C 3 and passed down and around the pulley C 19 thence over the guide-pulley W, Fig. 55, to pulley C 9 , thence over the pulley C t , and thence to a paper FIG. 114 EXPERIMENTAL ENGINEERING. [86. drum. It is at once evident that any extension of the speci- men SS' will draw in the free end of the cord at twice the rate of the extension; moreover, any slight swinging or rock-' ing of the extensometer head will produce compensating effects on the length of the cord. By connecting the free end of the cord to a drum, the drum will be revolved by the stretch FIG. 54. FIG. 55. of the specimen. As this work may be done against a fixed pull, there may be a uniform tension on the cord so that the motion of the drum would be uniform and proportional to the stretch. A pencil is moved along the axis of the drum pro- portional to the motion of the poise. An autographic device constructed in this way has given excellent diagrams, and in addition has served as an extensom- eter for accurate measurements of strain within the elastic limits. Wire has been used to connect extensometer to drum in place of the cord with success. A suggested improvement is 8/.] TESTING-MACHINE ACCESSORIES. 11$ to rotate the drum by the motion of the poise, and to move the pencil by the stretch of the material, using two pencils, one of which is to move at a rate equal to fifty times the strain, the other at a rate equal to five times the strain ; thus producing two diagrams one on a large scale, for use in deter- mining the strains during the elastic limit; the other on a small scale, for the complete test. 87. Deflectometer for Transverse Testing. Instru- ments for measuring the deflection of a specimen subjected to transverse stress are termed deflectometers. The deflectometer usually used by the author consists of a light metal-frame of the same length as the test-piece, and arched or raised sufficiently in the centre to hold a micrometer of the form used in the extensometer described in Article 86, above the point to which measurements are to be taken. In using the deflectometer it is supported on the same bearings as the test-piece, and measurements made to a point on the specimen or to a point on the testing-machine which moves downward as the specimen is deflected. This instrument eliminates any error of settlement in the supports. A steel wire is sometimes stretched by the side of the specimen, and marks made on the specimen showing its original position with reference to the wire. The deflection at any point would be the distance from the mark on the specimen to the corre- sponding point on the wire. The cathetometer, see Article 43, page 55, is very useful in determining the deflection in long specimens. The deflection is often measured from a fixed point to the bottom of the specimen, thus neglecting any error due to the settlement of the supports. One of the most use- ful instruments of this kind is made by Riehl Bros., and is shown, together with the method of attachment, in Fig. 56. FIG. 56. CHAPTER V. METHODS OF TESTING MATERIALS OF CONSTRUCTION. Standard Methods. The importance of standard methods of testing material can hardly be overestimated if it is desired to produce results directly comparable with those obtained by other experimenters, since it is found that the re- sults obtained in testing the strength of materials are affected by methods of testing and by the size and shape of the test- specimen. To secure uniform practice, standard methods for testing various materials have been adopted by several of the engineering societies of Germany and of the United States, as well as by associations of the different manufacturers. The general and special standard methods adopted by these asso- ciations form the basis of methods described in this chapter. 88. Form of Test-pieces. The form of test-pieces is found to have an important bearing on the strength, and for this reason engineers have adopted certain standard forms to be used. The form recommended by the Committee on Standard Tests and Methods of Testing, of the American Society of Mechanical Engineers is as follows:* " Specimens for scientific or standard tests are to be pre- pared with the greatest care and accuracy, and turned accord- ing to the following dimensions as nearly as possible. The tension test-pieces are to have different diameters according to the original thickness of the material, and to be, when ex- pressed in English measures, exactly 0.4, O.6, 0.8, and i.o inch in diameter; but for all these different diameters the angle, but * See Vol. XI. of Transactions. 116 88.] TESTING MATERIALS OF CONSTRUCTION. 1 1/ not the length, of the neck is to remain constant. This neck is a cone, not a fillet connecting the shoulders and body. The length of the gauged or measured part to be 8 inches, of the cylindrical part 8.8 inches. The length of the coned neck to be 2J- times the diameter, increasing in diameter from the cylindrical part to \\ times the cylindrical part. The shoul- ders to have a length equal to the diameter, and to be con- nected with a round fillet to a head, which has a diameter equal to twice that of the cylinder, and a length at least ij the diameter. Fig. 57 shows the form of the test-piece recommended for tension ; the numbers above the figure give dimensions in <-25--*l*-20-4 ! 50 H< 220 millimetres - -* 50 *K-20>(^-2{ -T-T ! I J_T^ : -H r-^^z ^fillet O.I"R. FIG. 57. STANDARD TEST-PIF.CS IN TENSION. - 1 ^fillet 0.1 R. I -4 u.b-H*- - 2 4*~ 8.8-inches -H 2 *4 < 0,8f- -1 >j millimeters, those below in inches. For flat test-pieces the shape as shown in Fig. 58 is recommended : such specimens T I i ^ R. FIG. 58. TEST-PIECE FOR FLAT SPECIMENS. are to be cut from larger pieces ; the fillets are to be accurately milled, and the shoulders made ample to receive and hold the full grip of the shackles or wedges. The length for rough bars is to remain the same as for fin- ished test-pieces, but the length of specimen from the gauge- mark to the nearest holder is to be not less than the diameter EXPERIMENTAL ENGINEERING. [89^ of the test-piece if round, or one and a half times the greatest side if flat. For commercial testing the standard form cannot always be adhered to, and no form is recommended.* It is recommended in all cases that the specimens be held by true bearing on the end shoulders, as gripping or holding devices in common use produce undesirable effects on the cylindrical portion of the specimen. The forms of test-specimens which have been heretofore used are somewhat different from the standards recommended. These forms are shown in Fig. 59, No. I to No. 5, and are as follows : No. i. No. 2. No. 3. No. 4. No. 5. No. i. Square or flat bar, as rolled. No. 2. Round bar, as rolled. No. 3. Standard shape for flats or squares. Edges must be smooth and true. Fil- lets, one half inch radius. Specimens not over three inches wide. No. 4. Standard shape for rounds. No: 5. Government shape for marine-boiler plates only. Not in general use, as it gives too high a test. FIG. 59. FORMS OF SPECIMEN FOR TENSILE STRAINS FORMERLY USED. 89. Test-pieces of Special Materials. Wood. Wood is a difficult material to test in tension, as the specimen is likely to be crushed by the shackles or holders. The author has had fairly good success with specimens, made with a very large bearing-surface in the shackles, of the form shown in Fig. 58, * A discussion of the effect of varying proportion of test-pieces is given in Thurston's " Text-book of Materials," pages 356-7. 89.] TESTING MATERIALS OF CONSTRUCTION. \\g page 117 for flat specimens, but with the breadth of the shoul- ders or bearing-surfaces increased an amount equal to one half the diameter of the specimen over that shown in Fig. 58. Cast-iron. Cast-iron specimens of the usual or standard forms are very likely to be broken by oblique strains in tension tests much before the true breaking-point has been reached. To insure perfectly axial strains Riehle Bros, propose a form of specimen shown in Fig. 60, A, B, and C, cast with an enlarged FIG. 60. PROPOSED FORM FOR CAST-IRON SPECIMENS. head, the projecting portion of which, as shown in C, has a knife-edge shape. The specimen is carried in holders or shackles, A and B, which rest on knife-edges extending at right angles to those of the specimen. This permits free play of the specimen in either direction, and renders obfique strains nearly impossible. Chain. In the case of chain, large links are welded at the ends, as shown in- Fig. 61 ; these are passed through the heads of the testing-machine and held by pins. FIG. 6.1. CHAIN TEST-PIECE. I2O EXPERIMENTAL ENGINEERING. [89- Hemp Rope. A similar method is used in testing hemp rope, the specimen being prepared as shown in Fig. 62. FIG. 62. RO?E TEST-PIECE. Special hollow conical shackles have also been used for hold- ing the rope with success. Wire Rope. Wire-rope specimens may be prepared as shown in Fig. 63, or they may be prepared by pouring a mass FIG. 63. WIRE-ROPE TEST-PIECE. of melted Babbitt metal around each end and moulding into a conical form, taking care that the rope is in the exact centre of the metal. Cement. Cement test-pieces for tension are made in moulds and permitted to harden for some time before being tested. It is found that the strength is affected by the form of the speci- FIG. 64. STANDARD SPECIMEN FOR CEMENT. men, by the amount of water used, and by the method of mix- ing the cement. To get results which may safely be compared, it is necessary to have the test-specimens or briquettes of exactly the same form, and pulled apart in shackles or holders 89.] TESTING MATERIALS OF CONSTRUCTION. 121 which exert no side strain whatever, and the strain applied uniformly and without any jerky motion. Various standard forms of briquettes have been adopted, but the one in most common use is that adopted by the American Society of Civil Engineers, and shown full size in Fig. 64. The form of the mould used in making the briquettes and the holders or shackles used in the Riehle machine are shown in Fig. 65. FIG. 65. CEMENT MOULDS AND BRIQUETTES. The form of briquette adopted in the standard German tests differs from the above in having a distinct necking or indentation at the points of least section. The German form applied to briquettes of the American size is used in the cement- testing laboratory of Cornell University. FIG. 66. STANDARD GERMAN BRIQUETTE. This form of briquette is shown in Fig. 66, abed. The form of the briquette is determined by arcs struck from various centres in order as follows: o, i, 2, 3, 4, 5, 6, 7 and 8. The radii of the arcs are as follows : oa = ob = oc = od = l 122 EXPERIMENTAL ENGINEERING. [ 9 2 inches, la = 2b etc. = -J inch, 01 02 = I inch, 05 = 06 = i J inch, 07 = 08 = f inch. The distance AB =. i inch. The angle aob = 60. The enclosing mould , F y G, H, is in two pieces, EG and HF, and is prevented from moving endwise by the pins shown in dotted lines at C and D. The two parts of the mould are held together when in use by spring clips, not shown in the figure. 90. Compression-test Specimens Test-pieces. Test- pieces are in all cases to be prepared with the greatest care, to make sure that the end surfaces are true parallel planes normal to the axis of the specimen. 1. Short Specimens. The standard test specimens are to be cylinders two inches in length and one inch in diameter, when ultimate resistance alone is to be determined. 2. Long Specimens. For all other purposes, especially when the elastic resistances are to be ascertained, specimens one inch in diameter and ten or twenty inches long (see No. 2, Fig. 59) are to be used. Standard length on which strain is to be measured is to be eight inches, as in the tension-tests. Great- est care must be taken in all cases to insure square ends, and that the force be applied axially. The specimens are to be marked and the compression measured as explained for tension-test pieces, page 126. 91. Transverse-test Specimens. For standard trans- verse tests, bars one inch square and forty inches long are to be used, the bearing blocks or supports to be exactly thirty, six inches apart, centre to centre. For standard or scientific tests of cast-iron, such bars are to be cut out of a casting at least two inches square or two and a quarter inches in diameter, so as to remove all chilling effect. For routine tests, bars cast one inch square may be used, but all possible precau- tions must be taken to prevent surface-chilling and porosity. Test bars of wood are to be forty inches in length, and three inches square, in section. 92. Torsion-test Specimens. For standard tests, cylin- drical specimens with cylindrical concentric shoulders are to be used ; the two are connected by large fillets. The specimen 93-] TESTING MATERIALS OF CONSTRUCTION. 123 is to be held in the chuck or heads of the machine by three keys, inserted in key-ways -J inch deep, cut in the shoulder. 93. Ductility Fracture. The character of the fracture often affords important information regarding the material. The structure of the fractured surface should be described as coarse or fine, either fibrous, granular, or crystalline. Its form, whether plane, convex, or concave, cup-shaped above or below, should in each case be stated. Its location should be accu- 15 14 13 12 11 10 FIG 67. rately given, from marks on the specimen one half inch or less apart. The reduction of diameter which accompanies fracture should be accurately measured. Accompanying the report should be a sketch of the fractured specimen. Fracture occurs usually as the result of a gradual yielding of the particles of the specimen. This at first, when the stress is well within the elastic limit, is distributed nearly uniformly over the specimen, but after the yield-point is passed the dis- tortion becomes nearly local ; a rapid elongation with a corre- sponding reduction in section is manifest as affecting a small portion of the specimen only. This action in materials with sensible ductility takes place some little time before rupture ; in very rigid materials it cannot be perceived at all. This peculiar change in form is spoken of as " necking." The drawing Fig. 67 shows the appearance of a test speci- men in which the "necking" is well developed. Rupture occurs at b b, a point in the neck which may be near one end of the specimen. In order to measure the ductility of the specimen fairly, a correction should be applied, so that the reduced elongation shall be the same as though the stretch either side of the point 124 EXPERIMENTAL ENGINEERING. [94- of rupture were equal. This can only be done by dividing up the original specimen into equal spaces, each of which is marked so that it can be identified after rupture. Supposing that twenty spaces represent the full length be- tween gauge-marks : then if the rupture be nearest the mark o, Fig. 67, three spaces from the nearest gauge-mark, the total length to compare with the original length is o to 3 on the right, plus o to 10 on the left, plus the distance 3 to 10 on the left. These spaces are to be measured, and the sum taken as the total length after rupture. The stretch is the difference between this and the original length ; the per cent of stretch, or ductility, is the stretch divided by the original length. This method is stated in a general form as follows : Divide the standard length into m equal parts, and repre- sent the number of these parts in the short portion after rupture by s. Note two points in the long portion, A and B, at s and \m divisions respectively from the break. Lay the parts to- gether, and measure from the gauge-mark in the short por- tion to point A. This distance increased by double the measured distance from A to B gives the total length after rupture. Subtract the original length to obtain the total elon- gation : thus the elongation of the standard m parts will be obtained as though the fracture were located at the middle division. 94. Strain-diagrams. The results of measurements of the strain should be represented graphically by a curve termed a strain-diagram. Strain-diagrams are drawn (see Art. 46, page 60) by taking the loads per square inch (/>) as ordinates, and the relative stretch or strain (e) to a suitable scale as abscissae. The curve so formed will be a straight line from the origin to the elastic limit, and the tangent of the angle that it makes with the axis of X (p -+- e = ) will be proportional to the modulus of elas- ticity. The area included between the axis of Jf and that por- tion of the curve preceding the elastic limit will represent the Elastic Resilience or work done by the resistance of the material to that point. 95-] TESTING MA TERIA LS OF CONS TR UC TION. 1 2 5 Autographic Strain-diagrams are drawn automatically on a revolving drum. In most machines the drum is revolved by the stretch of the material and a pencil is moved parallel to its main axis and proportional to the motion of the weigh- ing poise, although in some devices for drawing autographic diagrams the drum is actuated by the poise motion, the pencil by the stretch. The Olsen autographic apparatus is described in Article 71, Figs. 37 to 39, page 93. This apparatus is very perfect in all its details, and produces a diagram similar to that shown in Fig. 68. The ordinates on this diagram are proportional to the load, the abscissae to the strain. The lines are straight and nearly vertical until the yield-point ; then for a time the strain rapidly increases, with little increase of stress as shown by the line of stress ; this is followed by an increase of both stress and strain, until the point of maximum loading is reached. After passing the elastic limit the strain increases very rapidly, the stress but little. The autographic attachment is a valuable addition to a testing-machine, especially if its use does not interfere with the measurement by micrometers ; but if the scale of the dia- gram does not exceed five or ten times that of the actual o strain, it is of value only in showing the general character of the strain, and is not to be considered of value in obtaining coefficients or moduli within the elastic limit. TENSION - TESTS. 95. Objects of Tension Tests. Tension tests are con- sidered valuable as affording information of the qualities of material, and a certain tensile strength is required of nearly all materials used, even though in practice they may be sub- jected to different kinds of strain. The breaking-strength is frequently specified within limits, and is to be accompanied with a certain amount of ductility. Directions for Tension Tests. Examine the test-piece care- 95-] TESTING MATERIALS OF CONSTRUCTION. 12? fully for any flaw, defect, irregularity, or abnormal appearance, and see that it is of correct form and carefully prepared. In- dentations from a hammer often seriously affect the results. In wood specimens, abrasions, slight nicks at the corners, or bruises on the surface will invariably be the cause of failure. Next, carefully measure the dimensions, record total length, gauge-length (or length on which measurements of strains are made), also form and dimensions of shoulders. Divide the specimen between the gauge-marks into inches and half inches, which may be marked with a special tool, or by rubbing chalk on the specimens and marking each division with a steel scratch. ..; *> ; :<;,h. i FIG. 69 LAYING-OFF GAUGE. A special gauge as shown in Fig. 69 is con/enient for this pur- pose. These marks serve as reference points in measuring the elongation after rupture, and this elongation should be meas- ured, not from the centre of the specimen, but from the point of rupture either way, as explained in Art. 93, page 123. See that the testing-machine is level and balanced before each test ; insert the specimen in a truly axial position in the machine by measuring carefully its position in two directions, and by applying a level. Calculate from the known coefficients of the material the probable load at elastic limit. Take one tenth of this as the increment of load. The Committee on Standard Tests, American Society of Mechanical Engineers, recommend that the increment be one half or one third that of the probable load at the elastic limit, thus giving larger strains but fewer observations. Apply one increment of load to the specimen before measurements of elongation are made, since by loading specimens up to 1000 or 2000 pounds per square inch the effect of initial errors, such as occur generally at the com- mencement of each test, are lessened. The auxiliary apparatus 128 EXPERIMENTAL ENGINEERING. [ 96. adjusts itself somewhat during this period of loading, and the specimen assumes a true position should any slight irregularity exist. 96. Attachment of Extensometer. Attach the auxiliary apparatus for measuring stretch, or obtaining autographic dia- grams. The method of attaching extensometers will depend on the special form used (see Articles 80 to 86), but this act should always be carefully performed, and the specimen exactly centred in the extensometer, and the gauge-points arranged 8 inches apart. The following directions for applying and using the Henning extensometer will serve to show the method to be used in all cases. The Henning extensometer (see Article 83, Fig. 50, page 110) is attached and used as follows: Before attaching the in- strument, adjust the knife-edges in the clamps by means of the two milled nuts so that they are equally distant from the frame and not so far apart as the diameter of the test-piece. Then, since the springs acting on the knife-edges are of equal strength, the instrument will adjust itself in the plane of the screws symmetrically with respect to the test-piece. Advance or withdraw the set-screws until their points are equally distant from the frame and far enough apart to admit the test- piece. Separate the upper portion of the instrument, put it around the test-piece (already inserted in the machine) near the upper shoulder, with the smaller part to the right, force together and fasten securely. Advance the set-screws simultaneously until their points indent the test-piece. Separate the lower portion, put it around the test-piece with the vertical scales to the front, force together and secure. Hang the links on the proper bear- ings on both portions of the instrument. Then advance the set-screws as above. Throw the links out, take readings of the micrometers, apply the first increment of load, and proceed with the test as directed. To read the micrometers make the electrical connections ; advance one micrometer until the bell rings announcing contact, back off barely enough to stop ring- ing, and advance the other until the bell rings. Back off as 98-] TESTING MATERIALS OF CONSTRUCTION. I2Q before, and read both micrometers. The vertical scale and the micrometer head are graduated so that readings to y-g-J--^ inch can be obtained directly. 97. Tension Test. The test is made by applying the stress continuously and uniformly without intermission until the instant of rupture, only stopping at intervals long enough to make the desired observations of stretch and change of shape. The stress should at no time be decreased and re- applied in a standard test, but should be maintained continu- ously. The auxiliary apparatus for measuring strain must be removed before rupture takes place, except it is of a character not likely to be injured. It should usually be taken off very soon after the elastic limit is passed ; although for ductile material it may be left in place for a longer time after the elastic limit has been passed than for hard and brittle materials. The material is then to be loaded until fracture takes place, keeping the beam floating, after which the distortion for each part is to be measured by comparison with the reference divi- sions on the test-piece, measured from the point of rupture as previously explained. It is to be noted that measurements within the elastic limit are of especial importance, since materials in use are not to be strained beyond that point. '98. Report. Remove the fractured piece from the machine ; make measurements of shape, external and fractured surface ; give time required in making the test.* When fracture is cup- shaped, state the position of cup whether in upper or lower piece. In recording the results of tests, loads at elastic limit, at yield-point, maximum, and instant of rupture are all to be noted. The load at elastic limit is to be that stress which produces a change in the rate of stretch. The load at yield-point is to be that stress under which the rate of stretch suddenly increases rapidly. * See Report of Committee on Standard Tests, Vol. XL, Am. Society Mech. Engrs. 130 EXPERIMENTAL ENGINEERING. [ 98. The maximum load is to be the highest load carried by the test-piece. The load at instant of rupture is not the maximum load carried, but a lesser load carried by the specimen at the instant of rupture. In giving results of tests it is not necessary to give the load per unit section of reduced area, as such figure is of no value; (i) because it is not always possible to obtain the load at in- stant of rupture ; (2) because it is generally impossible to obtain a correct measurement of the area of section after rupture; (3) lastly, because the amount of reduction of area is principally dependent upon local and accidental conditions at the point of rupture. The modulus or coefficient of elasticity is to be deduced from measurements of strain observed between fixed increments of load per unit section ; between 2000 pounds per square inch and 12,000 pounds per square inch; or between 1000 pounds per square inch and 11,000 pounds per square inch. With this precaution several sources of -error are avoided, and it becomes possible to compare results on the same basis. In the report describe the testing-machine and method of testing, form and dimensions of specimen, character and posi- tion of rupture. Calculate coefficients of elasticity, rrfaximum strength, breaking-strength, strength at elastic limit, and resili- ence, and submit a complete log of test. Also, draw a strain- diagram on cross-section paper; make a sketch of surface of rupture. The curve of stress and strain is to be drawn as follows: Plot a curve of stress and strain up to a point beyond the elastic limit, using for ordinates values of />, on the scale I div. = 2000 Ibs. per sq. in,, and for abscissae values of e, on the scale I div. o.oooi"; compute E and /. Then plot the complete curve of stress and strain to the point of rupture, using scales of I div. = 10,000 Ibs. per sq. in., and I div. = o.Oi inch for ordinates and abscissae, respectively. A blank form for the log is shown below; which is to be filled out and filed. On this log is to be entered, value of the 98-] TESTING MATERIALS OF CONSTRUCTION. modulus of elasticity, load at elastic limit, character of rupture, area of least section, and measurements between each mark made on the specimen. The following form is used by the author for both tension and compression tests : Test of .by. Kind of Test Material from Machine used Time of Testing .min. Date .189 Tempt degrees F. No. * Load. Micrometer- readings. Extension. Modulus Elasticity. E Actual. Per sq. in. . / I II Mean. Actual. A Difference. AA. Per in. e Original length in. Diameter in. Area. . . . . . .sq. in. Final " , in. Diameter ....in. Area " Form of section Fractu re : position ; character Moduli: resilience ; breaking-strength Load per sq. inch: elastic limit max breaking Equivalent elongation for 8 inches inches per cent. Ductility Reduction area per cent. Local elongation each half-inch, from top, ist ; 2d .......; 3d ... ; 4th ; 5th ; 6th ; yth ; 8th ; Qth ; loth ; nth ; I2th ...; I3th ; I4th ; I5th ; i6th .. The following form, from Vol. XL Trans. American Society Mech. Engineers, is excellent for reporting the principal results of a series of tests. Attention is called to the full descriptions accompanying the report. 132 EXPERIMENTAL ENGINEERING. gl (X S s a |. as s ! % o-i 5 i ! il 2 1 W " 1 u M j.ll 1 ! 1 !.! ^8 ^*J ^ y^ 5"o.w - 1> So 2^ 2^ 2'55^ i/5 3 -u to M jsai jo uopuanQ : c c c c c. ; a B a 'a 'a IO Stress in Ibs. -dru jo 30115 iv N N C? r 'P3AJ3S m O O O O O 1 ^ oo vo J? ^J J*j C^ JO V^ ,, ra!I o, )S8 , 3 ,v O O 00 O ON O O N co M usuipsds jo pus 5S3JB3U raojj sjnj -OBJJ jo juiod jo aouEisiQ qj *- . || || S^ "3 ^?3 ^S> S >So so 5o M 'ajniDBjj J31JB UOH33S mniaiuij^ a : a a a * .2 .2 .2 .2 -a : TJ -a -a S in co M oo m ; oo m r-. 6 ; d d d 2 -SBJ3 ITS UOI3D3S tiintUIUlp^ c, Length between gauge-marks. gjnidnj J31JV 00 00 O> CO CO 00 UIHJ1S jspun 3iiq.\\ 3iui;i onsHp iv J? 8 8 8 fl- CO VO N VO "*" O O O O O ^ *DirosuM D O H M O c o o o o 10 ao sduS usaAuaq qjaubq g O> ON ON OS ON m Dimensions be- fore test. UOIJ33S a a 2^ ? ^ c - .2 .26^ II II .S -a -a --_ _*_ ^^_ 00 00 O-CO p) 00 ON (~> * qiSuai teiox ^ (^ tx ^ t^ r^ co usuipads jo rajoj OJ3 73 ^3 "OJ3 "OJ3 T3J3 ^ '3 ^ '3 ^ 'a ^ '3 ^ '3 ^frw ^H.*J i- ^H> b ^f4-i H **** S|l3flu||3||u|| M uauipads jo ^JBUJ JO 'o^ || |s || p || l| 93.] TESTING MATERIALS OF CONSTRUCTION. 133 Prof. G. Lanza of the Massachusetts Institute of Tech- nology uses the following forms for log and report of tension- tests : TENSION-TEST. No Date Specimen , Length between clamps Tested by. Original section Loads. Micrometer-readings. Differences. Mean. Remarks. Actual. Per sq. in. i 2 i 2 Actual. Per inch. Fractured section Breaking-stress per sq. in. fractured section. , Reduction of area of cross-section Modulus of elasticity Ultimate extension. Modulus of elastic resilience Cross-section at maximum load Modulus of ultimate resilience. Tensile limit per sq. in REPORT. No Date ,..., Specimen Length between clamps Original section, Elastic limit, Breaking-load Fractured section, Reduction of area of cross-section, Ultimate extension, Breaking-stress per square inch fractured section, Modulus of elasticity, Signed 134 EXPERIMENTAL ENGINEERING. [ 99> COMPRESSION-TESTS. 99. Methods of Testing by Compression, i. Short Pieces: Method of Testing. In case of short pieces, measure- ments of strain cannot be made on the test-piece itself, but must be made between points on the heads of the testing- machine. It is necessary to ascertain and make a correction for the error due to the yielding of the parts of the testing- machine. This is done as follows : Lower the moving-head until the steel compression-plate presses on the steel block in the lower platform with a force of about 500 pounds. Attach the micrometers to the special frame, which is supported by the upper platform, and read to a point on the movable head. With load at 500 pounds, read both micrometers. Apply loads by increments of 1000 pounds up to three fourths the limit of the machine, taking corresponding readings. Plot a curve of loads and deflections with ordinates I long division = 1000 pounds, and abscissae I long division = o.ooi inch. From this curve obtain corrections for the deflections caused by the loads used in the compression-test. In making the test calcu- late the increment of load as explained for tensile strain, Arti- cle 98. Conduct the experiment in the same manner as for tension, except that the stress is applied to compress instead of to stretch the specimen. If the material tested is hard or brittle, as in cast-iron, care should be taken to protect the person from the pieces which sometimes fly at rupture. Report and draw curve as for tension-tests, and in addition show why brittle material breaks in planes, making angles of about 45 with the axis of the piece ; compare the results obtained for wrought- iron in compression with those obtained in tension. 2. Long Pieces : Me'thod of Testing. In this case the exten- someters used for tension-tests can be connected directly to the specimen, and the measurements taken in substantially the same way, except that the heads of the extensometer will approach instead of recede from each other; this makes it IOO.] TESTING MATERIALS OF CONSTRUCTION. 135 necessary to run the screws back each time after taking a meas- urement a distance greater than the compression caused by the increment of load. In case large specimens are tested horizontally, initial flexion is to be avoided by counterweight- ing the mass of the test-piece. Calculate the increment of load as one tenth the breaking- load given by Rankine's formula, Article 51, page 64. Apply the first increment and take initial reading of micrometers; continue this until after the elastic limit has been passed, after which remove the extensometer, and apply load until rupture takes place. Protect yourself from injury by flying pieces. Compute the breaking coefficient C by Rankine's formula, and compare with the usual results. Compute the modulus of elasticity by Euler's formula: (1) /> " =^/7r 2 ^-/ //a (Church, " Mechanics of Materials," p. 366). (2) E = l"*P Q ff -T- rfl. I" = / - A.". (3) E = (/ - KJP' -f- 7T 2 /. Also by the method used in testing short specimens. In the above approximate formula the notation is the same as in Article 48, page 62. Note in the report, load at elastic limit, yield-point, and ultimate resistance, as well as increase of section at various points, and total compression calculated as explained for tension. Submit a strain-diagram, and follow the same general direc- tions as prescribed in the report for tensile strain, Article 98. TRANSVERSE TESTS. IOO. Object. This test is especially valuable for full-sized pieces tested with the load they will be required to carry in actual practice. The deflections of such pieces, with loads at centre or in various other positions, afford means of computing the coeffi- cients of elasticity and the form of the elastic curve. Method of Testing. Arrange the machines for such tests 136 EXPERIMENTAL ENGINEERING. [ IOO. by putting in the supporting abutments, and by arranging the head for such tests, or else by using the special transverse testing-machine. In this experiment the test-piece is usually a prismatic beam, 3 feet long (see Article 91, page 121), and it is supported at both ends, the stress being applied at the centre. The same data are required to be observed as in the preceding experiment, viz., loads and deflections, or stresses and corre- sponding strains. Sharp edges on all bearing-pieces are to be avoided, and the use of rolling bearings which move accurately with the angular deflections of the ends of the bars are recommended ; otherwise the distance between fixed supports measured along the axis of the specimen is continually changing. Place the test-bar upon the supports, and adjust the latter 36 inches apart between centres, and so that the load will be applied exactly at the middle. Obtain the necessary dimen- sions, and calculate the probable strength at elastic limit and at rupture by means of the formula/ = Wle -j- 4/. (See Arti- cle 52, page 66.) Adjust the specimen in the machine in a horizontal plane, and apply the stress at the centre normal to the axis of the specimen, and in a plane passing through the three points of resistance. Measure the deflections at the centre from a fixed plane or base, allowing for the settling of the supports, or by the special deflectometer (see Article 87, page 1 14), from which compute the coefficient of resilience and the modulus of elasticity. Balance the scale-beam with the test-bar in position and the deflectometer lying on the platform. Set the poise for one increment of load and apply stress until the beam tips. Place the poise at zero, and balance by gradually removing the load. Place the deflectometer in position on the supports, and with the micrometer at zero make contact and record zero-reading and zero-load. Apply the load in uniform increments equal to about one fifth the calculated load for the elastic limit, stopping only 1 01.] TESTING MATERIALS OF CONSTRUCTION. 137 long enough to measure the deflections. Wrought-iron is to be strained only until it has a sensible permanent set, but cast- iron and wood are to be tested to rupture. Wood specimens generally rupture on one side only : in that case turn over and make complete test as in the first instance. 101. Form of Report In the report describe the ma- chine, method of making test, form of cross-section, peculi- arities of the section, and make a sketch showing position and form of rupture. Submit a complete log of the test, together with drawing of the elastic curve, to be filed for permanent record. The following is a form for data and results of a transverse test : DATA OF TRANSVERSE TEST OF, Form of cross-section .... Length between supports ins. On Testing-machine. Time hrs .mins. Date.. Observers: No. Load W. Deflection. Remarks. Reading. Net. REPORT OF TRANSVERSE TEST. Wt. per cu. ft Ibs. Material Form Composition Specific Gravity Load Applied V esting-machine Time hrs min. Pate ,189 . Observers: 138 EXPERIMENTAL ENGINEERING. Dimensions. Length Diameter Breadth Height Max. fibre distance. Moment of inertia. in. in. in. in. in. Load. Elastic limit Maximum. . Actual. Deflection. Elastic limit. Maximum... Symbol. D b h Reduced per sq. in. in Outer Fibre. Modulus of elasticity. Modulus of resilience. Remarks: ,lbs. per sq. in. ..ft. Ibs, . The following forms are used by Prof. Lanza in the labora- tory of the Institute of Technology for log and report of trans verse test : LOG. Date . . No., Specimen Span Wt. of beam Position of load Wt. of yoke, etc. Loads. Micrometer-readings. Mean. Differences. Remarks. i 2 I 2 Modulus of elasticity Modulus of rupture (including weight of beam). Maximum intensity of longitudinal shear IO2.] TESTING MATERIALS OF CONSTRUCTION. 139 REPORT No Date. Specimen Span, . . . , Dimensions, Weight of beam, , Weight of yoke, etc., Deflection, Modulus of elasticity, . . . . . . . . . . . Modulus of rupture (including weight of beam), Maximum intensity of longitudinal shear, . . (Signed) 102. Elastic Curve. The object of this experiment is to determine the coefficient and moduli of the material, by loads less than that required at the elastic limit. The required general formulae are to be found in Art. 52, page 67. A table of deflections corresponding to various centre loads is to be found on page 69. The beam is to be supported at both ends on rounded supports or on rollers. The loads consist of weights of known amount that can be suspended at various points. Apparatus needed. Cathetometer or other suitable instru- ment for measuring deflection. Directions. Obtain dimensions of beam, compute moment of inertia of cross-section ; note material of beam, and com- pute probable deflection and corresponding load at elastic limit. Carefully divide the length of the beam into equal parts, and mark these divisions on the centre-line of the beam. With no load on the beam, take cathetometer-readings of each point, then apply successive increment of loads, each equal to one fifth the probable load at the elastic limit, and take correspond- ing readings of the cathetometer. From readings, obtain the deflections for each point, and plot the elastic curve. Compute the deflections for the corresponding points from the formula, using tabulated values of E, and plot the correspond- ing theoretical curve. Make deductions concerning the rela- tion of the two curves. I4O EXPERIMENTAL ENGINEERING. [ 103. The above experiment is to be performed with the load at center, and again with the load at a point one fourth or one third the length of the beam. Similar experiments may be performed on beams fixed at one end, or fixed at one end and supported at the other. TORSION-TEST. 103. Object. The object of this experiment is to find the strength of the material to resist twisting forces, to find its general properties, and its moduli of rigidity and shearing- strength. Thurstoris Machine. The special directions apply only to Thurston's torsion-machine (see Article 73, Figs. 40 and 41, page 96). In the use of the machine the constants are first ob- tained, the test-piece inserted between the jaws of the machine, stress applied, and the autographic strain-diagram obtained. This diagram is on a large scale, and gives quite accurate measures of the stresses or loads. The diagram is, however, drawn by attachment to the working parts of the frame, and consequently any yielding of the frame or slipping of the jaws appears on the diagram as a strain or yield of the specimen. The angular deformation , as obtained from the diagram, is likely to be too great, especially within the elastic limit. This error should be determined in each test by attach- ing index arms at each end of the specimen, and corrections made to the results obtained from the diagram. The characteristic form of diagram given by the torsion- machine is shown in Fig. 70* * n which the results of tests of several materials is shown. In the above diagrams * the ordi- nates are moments of torsion (Pa), the abscissae are develop, ments of the angle of torsion (a). The value of one inch of ordinate is to be found by measuring the ordinate correspond- ing to a known moment of torsion, and the abscissa corre- * See " Mechanics of Materials," page 240, by I. P. Church. Published by- Wiley & Son, N. Y. ICXJ.] TESTING MATERIALS OF CONSTRUCTION. 141 spending to one degree of torsion is to be calculated from the known radius of the drum. Knowing these constants, numerical values can readily be obtained, and the coefficients of the strength of the material can be computed. During the test, relax the strain occasionally : if within the elastic limit, the diagram will be retraced ; but if beyond that FIG. 70. limit, a new path is taken, called an " elasticity "" line by Thurston, which is in general parallel to the first part of the line, and shows the amount of angular recovery BC> and the per- manent angular set OB. 104. Methods of Testing by Torsion with Thurston's Autographic Testing-machine. (See Articles 55 and 73.) Method. Determine first the maximum moment of the pendulum. This may be done by swinging the pendulum so that its centre-line is horizontal, supporting it on platform- scales and taking the weight and the distance of the point of support from the centre of suspension of the pendulum. The product of these two quantities is the maximum moment of the pendulum. Make three determinations, using different lever-arms, and take the mean for the true moment of the pendulum. A correction for the friction of the journal of the pendulum must be made. When hanging vertically, measure with a spring-balance, inserted in the eye near the bob, the force necessary to stall the pendulum. Add this moment to that obtained above, and the result is the total maximum moment of the pendulum. From this the value of the mo- ment for any angular position may be calculated. 142 EXPERIMENTAL ENGINEERING. [ 104- .fi o ffl S C/J Vi w b^ ^ Q J2 Ctf OH 1! . ri ^ o o*S c2 III ws-g S-N co t> m 111 ft O O O in c< ON ^ 'bio ^ II O r- oo C (5Pn b? CO M ON ^ o*l A O co O 9 ^6 ^ ^ oo r^. |l <5'r- la^ ON O "* oo m .S M o - R *^ o^ V SJ M o .-0 ii. O S^ 1 ^ M M \o "rf in - co . O r -C .,_? C s 7 c IH r 1 OJ c 13 : S > o ; f e . 1 * i u T X c "' C : 03 3 ^ CN 5 " CO d t J ^-N ( g oT C : td 3 i i 8 'H '5 S- o "o c tn 1* O ^c a S s 1 G CU (A i "^ OJ *C i 3 II ^* C r II o C U U .5 "c ^rt \T> "t p ^N C (3 HH c dj * 3 s ' d X 'S Q Cu 1-1 ^"^ O u o c cf O tx invovcj minvo NOOVOVOOOO ^ c o bc.y I ^' m M oo moo oo o\oo fO(>N t^M o ^MV puBag 121.] TESTING MATERIALS OF CONSTRUCTION. 169 121. Coefficients of Strength. It is desirable to know in advance of the test the probable load the material under in- vestigation will safely bear, in order that increments of stress may be so proportioned as to make a reasonable number, of observations. It is also often desirable to know how the results obtained compare with the standard values for the material under investigation. To provide this information a brief statement of the results of various tests are tabulated in the Appendix. These results are mainly obtained from " Ma- terials of Construction," by R. H. Thurston (3 vols.; N. Y., Wiley & Son); and from "Applied Mechanics," by Prof. G. Lanza (N. Y., J. Wiley & Son) ; and " Materials of Engineer ing," by Prof. W. H. Burr (N. Y., J. Wiley & Son). These books will be found of great value for reference in the testing- laboratory. CHAPTER VI. FRICTION TESTING OF LUBRICANTS. 122. Friction. This subject is of great importance to en- gineers, since in some instances it causes loss of useful work, and in other instances it is utilized in transmission of power. The subject is intimately connected with that of measurement of power by dynamometers, treated in Chapter VII. ; in con- nection with these two chapters, the student is advised to read " Friction and Lost Work in Machinery and Mill-work," by R. H. Thurston ; N. Y., J. Wiley & Sons. Definitions. Friction, denoted by F, is the resistance to motion offered by the surfaces of bodies in contact in a direc- tion parallel to those surfaces. The normal force ', denoted by R, is the force acting perpen- dicular to the. surfaces, tending to press them together. The coefficient of friction, f, is the ratio of the friction, F, to the normal force, R ; that \s,f=F-R. The total pressure, P, is the resultant of the normal pressure, R, and of the friction, F, and its obliquity or inclination to the common perpendicular of the surfaces is the angle of repose, or friction, whose tangent is the coefficient of friction. The angle of repose or friction, = iitnrfW '-f- y i -\- f*. s 3 " . bo Weight on journal (general). . . Intensity of pressure at 6 = 90 Weight, perfect fit of journal. . Pressure per square inch . ... W p' w f) / + plr cos 0t/0. fl / -f- COS 0. /J^TT cos 2 0d9 = i.57//jr. J^TT o 64 W^ cos 6 -J- /?* c 1 Maximum pressure persq. inch Total pressure on bearing pm P' F /g 0.64 /^ / cos 0^0 = 1.27 JF. / - /"/>' W \ 2.1 fW. 1 i 27/^CsDace) Moment of friction. ........ M P'fr i yjflVr Work of friction per minute . . U Ma = 1.21/lVr = i.^TtfnrW. "1 Maximum pressure per sq. inch Total pressure . . . . P' P' P ' litr \it \V i 57 IV a o Total force of friction . . F P'f i 57/W 7 u C Moment of friction M P'fr i tffWr. Work of friction per minute. . . U Ma = \.nafWr = rffWrn. 125. Friction of Journals in V or Triangular Bearings. Force of friction F= P cos sin -f- cos a, in which P equals the force transmitted through the shaft. When cos = I, F~ Psin -=- cos <*. 126. Friction of Pivots on Flat Rotating Surfaces. Intensity of pressure =/; total pressure = P. Moment of 128.] FRICTIONTESTING OF LUBRICANTS. 173 friction, M = \fPr. Work of friction, U^^nnfPr. For a conical pivot, M j/Pr -r- sin a. a \ angle of cone. For Friction on a Flat Collar. Moment of friction, M f//Xr 3 -/ 3 )-Kr*-r' 2 ) ; r = radius of collar ; r'=radius of shaft on which it is fitted. 127. Friction of Teeth Rolling Friction. Work lost in a unit of time, UnFPs, in which s equals the sliding or slip- ping ; n, number of teeth ; other terms as before. For in volute teeth, in which C l length of arc of approach, C t that of arc of recess, the obliquity of action, r 1 and r 2 respective pitch-radii, we have for involute teeth U = nfPs = nfP(Q + C*)(- + -} + r r 2 cos This is nearly accurate for any teeth. (See article " Me- chanics," Encyc. Britannica.} 128. Friction of Cords and Belts Sliding Friction. Let T 1 be the tension on driving side of belt, T t on the loose side, T the tension at any part of the arc of contact ; let be the length of the arc of contact divided by the radius, i.e., ex- pressed in circular measure ; let c equal the ratio of the arc of contact to the entire circumference; let d equal the number of degrees in the arc of contact, e the base of the Napierian logarithms = 2.71828, m the modulus of the common loga- rithms = 0.434295 ; let F equal the force of friction. nr d nd = Ito7=i85' ..... * W d e 7t The tension at any point, dT, is equal to the resistance TfdO. Hence dT= TfdB, ....... (d) or 1/4 EXPERIMENTAL ENGINEERING. [ 129. This integrated between limits T l and T z gives T i T fO = log ~ = (common) log ^ ; . . . . (e) 1 2 Wl -L 3 hence ~ yww -- 1 = ff* = io^ m = 10 I8 " = io 27r/ ^ = B l ...(/) * From the nature of the stress, T -~ = the number corresponding to the logarithm, which is fndm , equal fum, or - , or 27tfcm. 1 80 Substituting numerical values, fit dm f6m = o.434/#, -^ = o. oofS&fa, and in f cm 2.72&&/C. I oO From equations (/), common log L^j = 0.434/0 = 2.7288/2:. By solving equations (/) and (g), I2Q. Friction of Fluids (i) is independent of pressure ; (2) proportional to area of surface ; (3) proportional to square of velocity for moderate and high speeds and to velocity for low speeds ; (4) is independent of the nature of the surfaces (5) is proportional to the density of the fluid, and is related to viscosity. The resistance to relative motion in case of fluid friction, R =fA F 2 = 2ghfA = 131.] FRICTION TESTING OF LUBRICANTS. the work of friction, U= Rs = RVt = A V*t = In the above formulae R resistance of friction, A area of surface, V ' velocity of slipping, h =. head corresponding to velocity, w = weight, f fehe resistance per unit of area of surface, f = coefficient of liquid friction,/'' = -- . Viscosity and density of fluids do not affect to any appreci- able extent the retardation by friction in the rate of flow, but have some influence upon the total expenditures of energy. Molecular or intern-al friction also exists. 130. Lubricated Surfaces. Lubricated surfaces are no doubt to be considered as solid surfaces, wholly or partially separated by a fluid, and the friction will vary, with different conditions, from that of liquid friction to that of sliding fric- tion between solids. Dr. Thurston * gives the following laws, applicable to perfect lubrication only: 1. The coefficient of friction is inversely as the intensity of the pressure, and the resistance is independent of the pressure. 2. The coefficient varies with the square of the speed. 3. The resistance varies directly as the area of journal and bearing. 4. The friction is reduced as temperature rises, and as the viscosity of the lubricant is thus decreased. Perfect lubrication is not possible, and consequently the laws governing the actual cases are likely to be very different from the above. The coefficient of friction in any practical case is likely to be made up of the sum of two components, solid and fluid friction. TESTING OF LUBRICANTS. 131. Determinations required. The following determina- tions are required in a complete test of lubricants : 1. The composition, and detection of adulteration. 2. The measurement of density. * See Friction and Lost Work, by Thurston, 176 EXPERIMENTAL ENGINEERING. [ 133- 3. The determination of viscosity. 4. The detection of tendency to gum. 5. The determination of temperatures of decomposition, vaporization, ignition, and solidification. 6. The detection of acids. 7. The measure of the coefficient of friction. 8. The determination of durability and heat-removing power. 9. The determination of its condition as to grit and foreign matter. 132. Adulteration of Oils. Adulteration can be detected only by a chemical analysis.* Animal oils may be distinguished from vegetable oils by the fact that chlorine turns animal oil brown and vegetable oil white. 133. Density of Oils. The density or specific gravity is usually obtained with a hydrometer (see Fig. 71) adapted for this special purpose, and termed an oleometer. The distance that it sinks in a vessel of oil of known temperature is measured by the graduation on the stem ; from this the specific gravity of the oil may be found. The density is usually expressed in Beaum's hy- drometer-scale, which can be reduced to correspond- ing specific gravities as compared with water by a table given in the Appendix. Beaum's hydrometer is graduated in degrees to accord with the density of a solution of common salt in water ; thus, for liquids heavier than water the zero of the scale is obtained by immersing in pure water; the five-degree mark by immersing in a five-per-cent solution ; the ten-degree mark in a ten- FIG. 7 i. per-cent solution; etc. For liquids lighter than HYDROMETER. r ... water the zero-mark is obtained by immersing in a ten-per-cent solution of brine ; the ten-degree mark by im- mersing in pure water. After obtaining the length of a degree the stem is graduated by measurement. * See Friction and Lost Work, by R. H. Thurston. 1 35-] FRICTION TESTING OF LUBRICANTS. IJJ The density may be found by obtaining the loss of weight of the same body in oil and in distilled water. The ratio of loss of weights will be the density compared with water. It may also be obtained by weighing a given volume on a pair of chemical scales. The density of animal oils varies from .62 to .89; sperm-oil at 39 F. has a density of .8813 to .8815 ; rape-seed oil has a density of .9168; lard-oil (winter) has a density of .9175 ; cotton-seed oil a density of .9224 to .9231 for ordinary, and of .9128 for white winter; linseed-oil, raw, has a density of .9299; castor-oil, pure cold-pressed, a density of .9667. 134. Method of finding Density. A. With Hydrometer Thermometer, and Hydrometer Cylinder. Method. I. Clean the cylinder thoroughly, using benzine fill first with distilled water. Set the whole in a water-jacket, and bring the temperature to 60 F. Obtain the reading of the hydrometer in the distilled water and determine its error. 2. Clean out the cylinder, dry it thoroughly, and fill with the oil to be tested ; heat in a water-jacket to a temperature of 60 F., and obtain reading of hydrometer ; also obtain reading, at temperatures of 40, 80, 100, 125, and 150, and plot a curve showing relation of temperature and corrected hydrome- ter-reading. Reduce hydrometer-readings to corresponding specific gravities, by table given in Appendix. B. Weigh on a chemical balance the same volume of dis- tilled water at 60 F., and of the oil at the same temperature; and compute the specific gravity. C. Weigh the same metallic body by suspending from the bottom of a scale-pan of a balance: i. In air; 2. In water; 3. In the oil at the required temperature. Carefully clean the body with benzine after immersing in the oil. The ratio of the loss of weight in oil to that in water will be the density. J 35- Viscosity. Viscosity of oil is closely related but not proportional to its density. It is also closely related, and in many cases it is inversely proportional, to its lubricating prop- EXPERIMEN TA L ENGINEERING. [ 136. erties. The relation of the viscosities at ordinary temperatures is not the same as for higher temperatures, and tests for vis- cosity should be made with the temperatures the same as those in use. The less the viscosity, consistent with the pressure to be used, the less the friction. The viscosity test is considered of great value in determin- ing the lubricating qualities of oils, and it is quite probable that by means of it alone we could determine the lubricating qualities to such an extent that a poor oil would not be accepted nor a good oil rejected. It is, however, in the present method of performing it, to be considered rather as giving comparative than absolute results. There are several methods of determining the viscosity It is usual to take the viscosity as inversely proportional to its flow through a standard nozzle while maintained at a constant or constantly diminishing head and constant temperature, a comparison to be made with water or with some well-known oil, as sperm, lard, or rape-seed, under the same conditions of pressure and temperature. 136. Viscosimeter. A pi- pette surrounded by a water- jacket, in which the water can be heated by an auxiliary lamp and maintained at any desired temperature, is generally used as a viscosimeter. Fig. 72 shows the usual, arrangement for this test. E is the heater FIG. ^.-VISCOSITY OF OILS. for the j ac ket-water, BB the jacket, A the pipette, C a thermometer for determining the temperature of the jacket-water. The oil is usually allowed to run partially out from the pipette, in which case the head diminishes. Time for the whole run is noted with a stop-watch. 1 39-] FRICTION TESTING OF LUBRICANTS. 179 ft In the oil-tests made by the Pennsylvania R. R, Co. the pipette is of special form, holding 100 c.c. between two marks, one drawn on the stem, the other some distance from the end of the discharge-nozzle. 137. Tagliabue's Viscosimeter. In Tagliabue's viscosim- eter, shown in Figs. 73 and 74, the oil is supplied in a basin C, and trickles down- ward through a metal coil, being dis- charged at the faucet on the side into a vessel holding 50 c.c. The oil is main- tained at any desired temperature by heating the water in the vessel B sur- rounding the coil ; cold water is supplied from the vessel A, as required to main- tain a uniform temperature. The tem- perature of the oil is taken by the ther- mometer D. 138. Gibbs' Viscosimeter. In the practical use of viscosimeters it is found that the time of flow of 100 c.c. of the same oil, even at the same temperature, ' FIG. 73. TAGLIABUE'S Visco- is not always the same, which is probably due to the change in friction of the oil adhering to the sides of the pipette. To render the conditions which produce flow more constant, Mr. George Gibbs of Chicago surrounds the Viscosimeter, which is of the pipette form, with a jacket of hot oil. A circulation of the jacket-oil is maintained by a force-pump. The oil to be tested is discharged under a constant head, which is insured by air-pressure applied by a pneumatic trough. The tempera- ture of the discharged oil is measured near the point of dis- charge. 139. Perkins' Viscosimeter. The Perkins Viscosimeter consists of a cylindrical vessel of glass, surrounded by a water or oil bath, and fitted with a piston and rod of glass. The edges of this piston are rounded, so as not to be caught by a slight angularity of motion. The diameter is one-thousandth of an i So EXPERIMENTAL ENGINEERING. [ inch less than that of the cylinder. In practice the cylinder is filled nearly full of the oil to be tested, and the piston inserted. FIG. 74. TAGLIABUE'S VISCOSIMETER. The time required for the piston to sink a certain distance into the oil is taken as the measure of the viscosity.* 140. Stillman's Viscosimeter. Prof. Thomas B. Stillman of Stevens Institute uses a conical vessel of copper, 6f inches in length and ij inches greatest diameter, surrounded by a water-bath, and connected to a small branch tube of glass, which is graduated in cubic centimeters ; the time taken for 25 c.c. to flow through a bottom orifice -fy of an inch in diam- eter is taken as the measure of the viscosity, during which time the head changes from 6 to 5 inches. Prof. Stillman makes all comparisons with water, which is the most convenient and uniform standard. The temperature of the oil is taken at about the centre of the viscosimeter. 141. Standard-orifice Viscosimeter. A form of viscosim- eter designed by the author is in the form of a frustum of a cone, with an internal diameter at the bottom of 1.25 inches, and of 1.95 inches at a height of 6 inches from the bottom. * See paper by Prof. Denton, Vol. IX., Transactions of Am. Society of Mechanicaf Engineers. I43-] FRICTION TESTING OF LUBRICANTS. 181 The flow takes place through a sharp-edged orifice in the centre of the bottom -J^- inch in diameter. The whole height is 6 inches. The instrument when made of copper requires a glass oil-gauge, showing the height of the oil in the viscosimeter. This should be connected to the viscosimeter 3 inches from the bottom. The time for the flow of 100 c.c. is taken as the measure of the viscosity, during which time the head changes from 6 to about 3.5 inches, the area of exposed surface dimin- ishes at almost exactly the rate of decrease of velocity of flow, so that the fall of level is very nearly constant. The instru- ment is surrounded with a jacket that can be supplied with water or oil at any required temperature, and is designed to eliminate the friction on the sides of the viscosimeter, and to secure the advantages due to the flow of oil through a standard orifice that can be exactly reproduced. 142. Viscosity Determinations of Oil, by Prof. Thomas B. Stillman. Fluid. Time of Flow in Seconds of 25 c.c. through Orifice as explained. Viscosity compared with water at 20 C. (68 F.). Water 20 C. 68 F. 15 55 70 50 C. 122 F. 100 C. 212 F. 150 C. 302 F. 1.0 3-6 4.6 16.0 4.6 2.2 2.6 3-4 3-8 4.2 4-7 2 9 30 19 18 J 9 15 16 17 27 18 20 18 16 16 360 15 14 15 16 15 15 16 16 No j t < 240 70 33 39 5i 57 7i 63 80 23 22 24 26 27 26 24 " " 2d run .... Sperm-oil Cotton-seed oil winter 143. Method of measuring Viscosity. Apparatus. Stop- watch and viscosimeter. Fill the jacket of the viscosimeter with water and arrange for the maintenance of the same at any desired temperature. This is most conveniently done by cir- culation from a water-bath. Fill the viscosimeter with the oil 1 82 EXPERIMENTAL ENGINEERING. . [ 144- to a point above the upper or initial mark. Allow the oil to run out, noting accurately with the stop-watch the exact time required to discharge a given amount. Make determinations at 60, 1 00, and 150 F., two for each temperature. Clean the apparatus thoroughly at the beginning and end of the test, using benzine or alkali to remove any traces of oil. 143. Gumming or Drying. Gumming or drying is a con- version of the oil into a resin by a process of oxidation, and occurs after exposure of the oils to the air. In linseed and the drying oils it occurs very rapidly, and in the mineral oils very slowly. Methods of Testing. Nasmyttts Apparatus. An iron plate six feet long, four inches wide, one end elevated one inch. Six or less different oils are started by means of brass tubes at the same instant from the upper end : the time taken until the oil reaches the bottom of the plane is a measure of its gum- ming property. Bailey s Apparatus consists of an inclined plane, made of a glass plate, arranged so that it may be heated by boiling water. A scale and thermometer is attached to the plane. Its use is the same as the Nasmyth apparatus. This effect may also be tested in the Standard Oil-testing Machine by applying fresh oil, making a run, and noting the friction ; then exposing the axis to the effect of the air for a time, and noting the increase of friction. In all cases a com- parison must be made with some standard oil. 144. The Flash-test. The effect of heat is in nearly every case to increase the fluidity of oils and to lessen the vis- cosity ; the temperature at which oils ignite, flash, boil, or congeal is often of importance. The Flash-test determines the temperature at which oils discharge by distillation vapors which may be ignited. The test is made in two ways. Firstly. With the open cup. In this case the oil to be tested is placed in an open cup of watch-glass form, which rests on a sand-bath. The cup is so arranged that a thermometer can be kept in it. Heat is applied to the sand-bath, and as the oil 1 44.] FRICTION TESTING OF LUBRICANTS. 183 becomes heated a lighted taper or match is passed at intervals of a few seconds over the surface of the oil, and at a distance of about one half-inch from it. At the instant of flashing the temperature of the water-bath is noted, which is the tempera- ture of the " flash-point." Fig. 75 shows Tagliabue's form of the open cup, in which heat is applied by a spirit-lamp to a water or sand bath sur- rounding the cup containing the oil. The method of applying the match is found to a have great influence on the temperature of the flash-point, and should be distinctly stated in each case. When the vapor is heavier than FIG. 76. CLOSED CUP FOR FLASHING- POINT. air, a lower flash-point will be shown by holding near one edge of the cup. Secondly. With the closed oil-cup. Fig. 76 is a view of Tag- liabue's closed cup for obtaining the flash-point ; in this instru- ment the oil is heated by a sand-bath above a lamp. The thermometer gives the temperature of the oil, and the match 184 EXPERIMENTAL ENGINEERING. [ 146. applied from time to time at the orifice d, which in the inter- vals can be covered \vith a valve, determines the flash-point. The open cup is generally preferred to the closed one as giving more uniform determinations, and it is also more con- venient and less likely to explode than the closed one. Method of Testing. Put some dry sand or water in the outer cup and some of the oil to be tested in the small cup. Light the lamp and heat the oil gently at the rate of about 50 F. in a quarter of an hour. At intervals of half a minute after a temperature of 100 F. is attained, pass a lighted match or taper slowly over the oil at a distance of one half inch at the surface. The reading of the thermometer taken immediately before the vapor ignites is the temperature of the flash-point. With the closed cup the method is essentially the same. The lighted taper is applied to the tube leading from the oil vessel, the valve being opened only long enough for this pur- pose. 145. Method of Determining the Burning-point. The burning-point is determined by heating the oil to such a tem- perature, that when the match is applied as for the flash-test the whole of the oil will take fire. The reading of the ther- mometer just before the match is applied is the burning-point. With Open Cup. Apparatus: Open cup of watch-glass form ; thermometer suspended so that bulb is immersed in cup ; outer vessel filled with sand or water, on which the open vessel rests ; lamp to heat the outer vessel. Method. The burning-point is found in the same manner as the flash-point, with the open cup, the test being continued until the oil takes fire when the match is applied. The last reading of the thermometer before combustion commences is the burning-point. 146. Evaporation. Mineral oil will lose weight by evapo- ration, which may be ascertained by placing a given weight in a watch-glass and exposing to the heat of a water-bath for a given time, as twelve hours. The loss denotes the existence of volatile vapors, and should not exceed 5 per cent in good oil. Other oils often gain weight by absorption of oxygen. I47-] FRICTION TESTING OF LUBRICANTS. I8 5 147. Cold Tests. Cold tests are made to determine the behavior of oils and greases at low temperatures. The method of test is to expose the sample while in a wide-mouthed bottle or test-tube to the action of a freezing mixture, which surrounds the oil to be tested. Freezing mixtures may be made with ice and common salt, with ice alone, or with 15 parts of Glauber's salts, above which is a mixture of 5 parts muriatic acid and 5 parts of cold water. The temperature is read from a thermometer immersed in the oil. The melting- point is to be found by first freezing, then melting. Tagliabue has a special apparatus for the cold test of oils shown in section in Fig. 77. The oil is placed in the glass FIG. 77. TAGLIABUE'S COLD-TEST APPARATUS. vessel, which is surrounded with a freezing mixture. The glass containing the oil can be rocked backward and forward, to insure more thorough freezing. A thermometer is inserted into the oil and another in the surrounding air-chamber ; the oil is frozen, then permitted to melt, and the temperature taken. 1 86 EXPERIMENTAL ENGINEERING. [ I $O. In making this test considerable difficulty may be experi- enced in determining the melting-point, since many of the oils do not suddenly freeze and thaw like water, but gradually soften, until they will finally run, and during this whole change the temperature will continue to rise. This is no doubt due to a mixture of various constituents, with different melting- points. In such a case it is recommended that an arbitrary chill-point be assumed at the temperature that is indicated by a thermometer inserted in the oil, when it has attained suffi- cient fluidity to run slowly from an inverted test-tube. The temperature at the beginning and end of the process of melting is to be observed. 148. Method of Finding the Chill-point. Apparatus. Test-tube thermometer, and dish containing freezing mixture. Method. Pour the sample to be tested in the test-tube, in which insert the thermometer ; surround this with the freezing mixture, which may be composed of small particles of ice mixed with salt, with provision for draining off the water. Allow the sample to congeal, remove the test-tube from the freezing mixture, and while holding it in the hand stir it gently with the thermometer. The temperature indicated when the oil is melted is the chill-point. In case the operation of melting is accompanied with a dis- tinct rise of temperature, note the temperature at the begin- ning and also at the end of the process of melting. In report describe apparatus used and the methods of test- ing. 149. Oleography. An attempt has been made to deter- mine the properties of oil by cohesion-figures, by allowing drops of oil to fall on the surface of water, noting the time re- quired to produce certain characteristic figures, also by noting the peculiar form of these figures. Electrical Conductivity is different for the different oils, and this has been proposed as a test for adulteration. 150. Acid Tests. Tests for acidity may be made by ob- serving the effects on blue litmus-paper ; or better by the fol- lowing method described by Dr. C. B. Dudley : Have ready (i) 151.] FRICTIONTESTING OF LUBRICANTS. 1 87 a quantity of 95 per cent alcohol, to which a few grains of car- bonate of soda have been added, thoroughly shaken and al- lowed to settle ; (2) a small amount of turmeric solution ; (3) caustic-potash solution of such strength that 31^ cubic centi- meters exactly neutralize 5 c.c. of a solution of sulphuric acid and water, containing 40 milligrams H 2 SO 4 per c.c. Now weigh or measure into any suitable closed vessel a four-ounce sample bottle, for example 8.9 grams of the oil to be tested. To this add about two ounces No. I, then add a few drops No. 2, and shake thoroughly. The color becomes yellow. Then add from a burette graduated to c.c., solution No. 3 un- til the color changes to red, and remains so after shaking. The acid is in proportion to the amount of solution (3) re- quired. The best oils will require only from 4 to 30 c.c. to be neutralized and become red. COEFFICIENT OF FRICTION OF LUBRICANTS. 151. Oil-testing Machines. Measurements of the coefficients of friction are made on oil-testing machines, of which various forms have been built. These machines are all species of dynamometers, which provide (i) means of measuring the total work received and that delivered, the difference being the work of friction ; or (2) means of measuring the work of friction directly. Machines of the latter class are the ones commonly employed for this especial purpose. Rankings Oil-testing Machine. Rankine describes two forms of apparatus for testing the lubricating properties of oil and grease. I. Statical Apparatus. This consists of a short cylindrical axle, supported on two bearings and driven by pulleys at each end. In the middle of the axle a plumber-block was rigidly connected to a mass of heavy material, forming a pendulum. The lubricant to be tested was inserted in the plumber-block attached to the pendulum, and the coefficient of friction determined by its deviation from a vertical. In this machine the axle was provided with reversing-gears, so that it 188 EXPERIMENTAL ENGINEERING. [ 151. could be driven first in one direction and then in the opposite. With this class of machine, if r equal the radius of the journal, R the effective arm of the pendulum, P the total force acting on the journal, the angle with the vertical, we shall have the product of the force J^into the arm R sin equal to the moment of resistance Fr. That is, Fr WR sin 0, from which f _F_ WRs'm f '~~P~ ~~Pr * II. Dynamic or Kinetic Apparatus. In this case a loose fly-wheel of the required weight is used instead of the pendu- lum. The bearings of journals and of fly-wheel are lubricated ; then the machine is set in motion at a speed greater than the normal. The driving-power is then disengaged, and the fly- disk rotates on the stationary axis until it comes to rest. The coefficient of friction is obtained by measuring the retardation in a given time. Thus, let W equal the weight of the fly- wheel, k its radius of gyration, so that Wk* -r- g equals its moment of inertia. Let n equal number of revolutions at beginning, and n' at end of period /. Then the retardation in angular velocity per second is 2n(n n') -7- t ; the moment producing retardation, If we neglect the resistance of the air, this must equal the moment of friction fWr. Equating these values, _ 27t(n - n') - FRICTION TESTING OF LUBRICANTS. I8 9 In case the moment of inertia and radius of gyration are un- known, they may be found as in Article 53, page 70. 152. Thurston's Standard Oil-testing Machine. This machine permits variation in speed and in pressure on the journal ; it also affords means of supplying oil at any time, of reading the pressure on the journal, and the friction on grad- uated scales attached to the instrument. ,. 78. SECTION OF THURSTON'S OIL-TESTING MACHINE. FlG. 79. PEKai'liCTIVE VlE\V OF THURSTON'S OIL-TESTING MACHINE. This machine, as shown in the above cuts, Figs. 78 and 79, consists of a cone of pulleys, C, for various speeds carried be- tween two bearings, B, B' , and connected to an overhanging axis, F\ on this overhanging part is a pendulum, //, with plumber-block in which the axis is free to' turn ; the pendulum is supported by brasses which are adjustable and which may be set to exert any given pressure by means of an adjusting screw, AT', acting on a coiled spring within the pendulum. The pressure so exerted can be read directly by the scale M, attached to the pendulum ; a thermometer, Q, in the upper brass gives the temperature of the bearings. The deviation ICp EXPERIMENTAL ENGINEERING. [ 153- of the pendulum is measured by a graduated arc, PP', fastened to the frame of the machine. The graduations of the pendu- lum scale M show on one side the total pressure on the jour- nal P, and on the other the pressure per square inch,/; those on the fixed scale, PP', show the total friction, F\ this divided by the total pressure, P, gives/, the coefficient of friction. From the construction of the machine, it is at once per- ceived that the pressure on the journal is made up of equal pressures due to action of the spring on upper and lower brasses, and of the pressure due to the weight of the pendu- lum, which acts only on the upper brass. This latter weight is often very small, in which case it can be neglected without sensible error. 153. Thurston's Railroad Lubricant-tester. The Thurston machine is made in two sizes ; the larger one, having axles and bearings of the same dimensions as those used in standard-car construction, is termed the " Railroad Lubricant Testing-machine." A form of this machine is shown in the following cut, arranged for testing with a limited supply of lubricant. (See Fig. 80.) Explanation of symbols : T, thermometer, giving temperature of bearings. , 5, rubber tubes for circulation of water through the bearings. N, burette, furnishing supply of oil. M, siphon, controlling supply of oil. P, candle-wicking, for feeding the oil. H, copper rod, for receiving oil from G. The Railroad Testing-machine, which is shown in section in Fig. 8 1, differs from the Standard Oil-testing Machine princi- pally in the construction of the pendulum. This is made by screwing a wrought-iron pipe,/, which is shown by solid black shading in Fig. 81, into the head K, which embraces the jour- nal and holds the bearings aa in their place. In this pipe a loose piece, b, is fitted, which bears against the under journal- bearing, a'. Into the lower end of the pipe /a piece, cc, is screwed, which has a hole drilled in the centre, through which I53-] FRICTION TESTING OF LUBRICANTS 19! a rod, f, passes, the upper end of whicn is screwed into a cap, d\ between this cap and the piece cc a spiral spring is placed. The upper end of the rod bears against the piece b y which in turn bears against the bearing a'. The piece b has a key, /, which passes through it and the pipe J. This key bears FIG, 80. THURSTON'S RAILROAD-LUBRICANT TESTING-MACHINE. against a nut, 0, screwed on the pipe. By turning the nut o the stress on the journal produced by screwing the rod /can be thrown on the key /, and the bearing relieved of pressure, without changing the tension on the spring. A counterbalance above the pendulum is used when accurate readings are de- 192 EXPERIMENTAL ENGINEERING. [ sired. The " brasses " are cast hollow, and when necessary a stream of water can be passed through to take up the heat, and maintain them at an even temperature. The graduations on the machine show on the fixed scale. FIG. 81. SECTION OF RAILROAD LUBRICANT TESTING-MACHINE. as in the standard machine, the total friction ; and on the pendulum, the total pressures (i) on the upper brasses, (2) on the lower brasses, and (3) the sum of these pressures. 154. Theory of the Thurston Oil-testing Machines. The mathematical formulae applying to these machines are as follows : Let P equal the total pressure on the journal ; / the pressure per square inch on projected area of journal ; T the tension of the spring; W the weight of the pendulum; r the radius of the journal ; R the effective arm of the pendulum ; 1 54-] FRICTION TESTING OF LUBRICANTS. IQ3 6 the angle of deviation of the pendulum from a vertical line ; F the total force of friction ; f the coefficient of friction ; / the length of bearing-surface of each brass. Since in this machine both brasses are loaded, the pro- jected area of the journal bearing-surface is 2(2r}l=^lr. We shall evidently have , . ,-.-...... (i) P 2T + W By definition /= F + P. Since the moment of friction is equal to the external mo- ment of forces acting, O.. . . (3) From which F WR sin B P In the machines WR sin -r- r is shown on the fixed scale, and the graduations will evidently vary with sin 6, since WR -i- r is constant. P, the total pressure, is shown on the scale attached to the pendulum. In the standard machine the weight of the pendulum is neglected, and P 2 T\ but in the Railroad Oil-testing Machine the weight must be considered, and P= 2T -\- W, as in equa- tion (i). , Constants of the Machine. As the constants of the machine are likely to change with use, they should be deter- mined before every important test, and the final results cor- rected accordingly. IQ4 EXPERIMENTAL ENGINEERING. [ 155 1. To determine the constant WR, swing the pendulum to a horizontal position, as determined by a spirit-level ; support it in this position by a pointed strut resting on a pair of scales. From the weight, corrected for weight of strut, get the value of WR ; this should be repeated several times, and the average of these products obtained. 2. Obtain the weight cf the pendulum by a number of care- ful weighings. 3. Measure the length and radius of the journal ; compute the projected bearing-surface 2(2/7-). WR 4. Compute the constant , which should equal twice the reading of the arc showing the coefficient of friction when the pendulum is at an angle of 30, since sine of 30 equal \. The following are special directions for obtaining the co- efficient of friction with the Thurston machine. 155. Directions for obtaining Coefficient of Friction with Thurston's Oil-testing Machines. Cleaning. In the testing of oils great care must be taken to prevent the mixing of different samples, and in changing from one oil to another the machine must be thoroughly cleaned by the use of alkali or benzine. In the test for coefficient of friction the loads, velocity, and temperature are kept constant for each run ; the oil-supply is sufficient to keep temperature constant, the journals being generally flooded. The load is changed for each run. The following are the special directions for the test of Coefficient of Friction, as followed in the Sibley College Engi- neering Laboratory. Apparatus. Thurston's Standard Lubricant Testing-ma- chine; thermometer; attached speed-counter. (See Art. 151, page 189.) Method. Remove and thoroughly clean the brasses and the steel' sleeve or journal by the use of benzine. Put the sleeve on the mandrel ; place the brasses in the head of the pendulum and see that the pressure spring is set for zero and pressure as indicated by the pointer on the scale. Slide the 1 5 5-] FRICTION TESTING OF LUBRICANTS. ig$ pendulum carefully over the sleeve, put on the washer, and secure it with the nut. See that the feeding apparatus is in running order. Belt up the machine for the high speed and throw on the power, at the same time supplying the oil at a rate calculated to maintain a free supply. By deflecting the pendulum and using a wrench on the nut at the bottom in- crease the pressure on the brasses gradually until the pointer indicates 50 Ibs. per square inch. Determine the constants of the machine as explained in Article 149, page 194; measure the projected area of journal bearing-surface, and the weight and moment of the pendulum. Ascertain the error, if any, in the graduation of the machine, and correct the results obtained accordingly. Make a run at this pressure, and also for pressures of 100, 150, and 200 Ibs.; but do not in general permit the maximum pressure in pounds per square inch to exceed 44,800 -=- (v -f- 20). Begin by noting the time and the reading of the revolution- counter ; take readings, at intervals of one minute, of the arc and the temperature until both are constant. At the end of the run read the revolution-counter and note the time. The velocity, v, in rubbing surface in feet per minute should be computed from the number of revolutions and circumfer- ence of the journal. Make a second series of runs, with constant pressure and variable speed. In report of the test state clearly the objects, describe apparatus used and method of testing. Tabulate data, and make record of tests on the forms given. Draw a series of curves on the same sheet, showing results of the various tests as follows : 1. With total friction as abscissae, and pressure per square inch as ordinates ; for constant speed. 2. With coefficient of friction as abscissae, and pressure per square inch as ordinates ; for constant speed. 3. With coefficient of friction as abscissae, and velocity of rubbing in feet per minute as ordinates; pressure constant. 196 EXPERIMENTAL ENGINEERING. [ 1$?. 156. Instructions for Use of Thurston's R. R. Lubricant- tester. (See Article 152, page 190.) Follow same directions for coefficient of friction-test as given for the standard machine, applying the pressure as explained in Article 155, page 194. Water or oil of any desired temperature can be forced through the hollow boxes by connecting as shown in Fig. 8o r page 191, and the temperature of the bearings thus maintained at any desired point. With this arrangement the machine may be used for testing cylinder-stocks, as explained in directions for using Boult's machine (see Article 161, page 203). The con- cise directions are : 1. Clean the machine. 2. Obtain the constants of the machine ; do not trust to the graduations. 3. Make run under required conditions, which may be with each rate of speed. a. With flooded bearings, temperature variable. b. With flooded bearings, temperature regulated by forcing oil or water through hollow brasses. c. Feed limited, temperature variable or temperature regulated. In all cases the object will be to ascertain the coefficient of friction. 157. Richie's Oil-testing Machine. This machine con- sists of an axis revolving in two brass boxes, which may be clamped more or less tightly together. The machine as shown in Fig. 82 has two scale-beams, the lower one for the purpose of weighing the pressure put upon the journal by the hand- screw on the opposite side of the machine, the upper one for measuring the tendency of the journal to rotate. The upper scale-beam shows the total friction, or coefficient of friction, as the graduations may be arranged. A thermometer gives the temperature of the journal; a counter the number of revolu- tions. Let P equal the total pressure applied to the bearings. Let B equal the projected area of the journal-bearings,/ equal I 5 7.] FRICTION TESTING OF LUBRICANTS. 197 the pressure per square inch ; F equal the total friction ; /equal FIG. 82. RIEHLE'S OIL-TESTING MACHINE. the coefficient of friction; ;/ equal the arm of the bearing; a the arm of the total pressure. Then do we have Fn = aP = aBp, Bfn = aP, and Bn 198 EXPERIMENTAL ENGINEERING. [ 158. If / be maintained constant, and a -f- n be made the value of the unit of graduation on the scale-beam f= graduation. 158. Durability of Lubricants. In this case the amount of oil supplied is limited, and it is to be used for as long a time as it will continue to cover and lubricate the journal and pre- vent abrasion. To give satisfactory results, this requires a limited supply or a perfectly constant rate of feed, an even dis- tribution of the oil, and the restoration of any oil that is not used to destruction ; these difficulties are serious, and present methods do not give uniform results.* The method at present used is to consider the endurance or durability proportional to the time in which a limited amount, as one fourth c c. will con- tinue to cover and lubricate the journal without assuming a pasty or gummy condition, and without giving a high coefficient of friction. The average of a number of runs is taken as the correct determination. In this test care must be taken not to injure the journal, and it must be put in good condition at the end of the run. The time or number of revolutions required to raise the temperature to a fixed point for instance, 160 F. is in some instances considered proportional to the durability. The Ashcroft (see Article 159, page 199) and the Boult (see Article 160, page 200) machines are especially designed for de- termining the durability of oils from the former by noting the rise in temperature, from the latter by noting the change in the coefficient of friction. The difficulty of properly making this test no doubt lies in the loss of a very slight amount of oil from the journals, which is sufficient, however, to make the results very uncertain. *See paper by Professor Deflton, Vol. XI., p. 1013, Transactions of Ameri- can Society of Mechanical Engineers.. i6o.] FRICTION TESTING OF LUBRICANTS I 99 159. Ashcroft's Oil-testing Machine. This machine (Fig. 83) consists of an axle revolving in two brass boxes ; the pressure on the axle is regulated by the heavy overhanging counterpoise shown in the engraving. The tendency to rotate is resisted by a lever which is connected to the attached gauge. The gauge is graduated to show coefficient of friction. FIG. 83. ASHCROFT'S OIL-TESTING MACHINE. The temperature is taken by an attached thermometer, and the number of revolutions by a counter, as shown in the figure. In this machine the weights and levers are constant, the variables being the temperature and coefficient of friction. It is used exclusively with a limited supply of oil, the value of the oil being supposed to vary with the total number of revolutions required to raise the temperature to a given degree, for instance, to 160 F. 160. Boult's Lubricant-testing Machine. This machine, designed by W. S. Boult of Liverpool, is a modification of 200 EXPERIMENTAL ENGINEERING. [ 160. the Thurston oil-tester, yet it differs in several essential feat- ures. A general view of the machine is shown in Fig. 84, and a section of its boxes and the surrounding bush in Fig. 85. FIG. 84. BOULT'S LUBRICANT-TESTER. The machine is designed to accomplish the following pur- poses: I. Maintaining the testing journal at any desired tem- perature. 2. Complete retention on the rubbing surfaces of the oil under test. 3. Application of suitable pressure to the rubbing surfaces. 4. Measurement of the friction between the rubbing surfaces. i6o.] FRICTION TESTING OF LUBRICANTS. 201 To secure the complete retention of the oil, a complete bush with internal flanges is used instead of the brasses employed in other oil-testing machines. On the inside of the bush is an ex- panding journal, DD, Fig. 85, the parts of which are pressed outward against the surrounding bush by the springs E, or they may be drawn together by the set-screws B B, compressing the springs 5. A limited amount of oil is fed from a pipette or graduated cylinder on the journal, with the bush removed. This oil, it is claimed, will be maintained on the outer surface of the journal and on the interior surface of the metallic bush, so that it may be used to destruction. The bush is hollow, and can be filled with water, oil, or melting ice and brine. The oil to be tested can be FIG. 85. SECTION OF BOULT'S LUBRICANT- TESTER. maintained at any desired tem- perature by a burner, F, which heats the liquid CC in the sur- rounding bush. The temperature of the journal can be read by a thermometer whose bulb is inserted in the liquid CC. . The friction tends to rotate the bush ; this tendency is re- sisted by a lever connected by a chain to an axis carrying a weighted pendulum, G, Fig. 84. The motion of the pendulum is communicated by gearing to a hand, passing over a dial graduated to show the total fric- tion on the rubbing surfaces. The formulae for use of the instrument would be as follows : Let / equal coefficient of friction ; G the weight of the bob on the pendulum, R its lever arm ; a the angle made by the pendulum with the vertical; a the length of the connecting lever; c the radius of the axis to which the pendulum is 202 EXPERIMENTAL ENGINEERING. [ l6l. attached ; r the radius of the journal ; A the projected area of the journal; Pthe total pressure on the journal. Then .<7sin =fAP, from which aGR sin a sin a f = rcAP~ ~P~' ( constant ) In this instrument the total pressure P is usually constant and equal to 68 Ibs., so that the graduations on the dial must be proportional to sin a. If the graduations are correct, the coefficient is found by dividing the readings of the dial by P (68 Ibs.). The work of friction is the product of the total space travelled into the total friction, and this space in the Boult instrument is two thirds of a foot for each revolution, or two thirds of the number of revolutions. The instrument cannot be used with a constant feed of oil, nor can the pressures be varied except by changing the springs E. 161. Directions for Durability Test of Oils with Boult's Oil-testing Machine. To fill cylindrical oil-bath, take out the small thumb-screw in cylindrical bath and insert a bent funnel. Pour in oil any sort of heavy oil may be used until it overflows from the hole in which funnel is inserted, and re- place thumb-screw. I. See that the friction surfaces are perfectly clean. These can be examined by tightening the set-screws in order to de- press the spring. This will enable the cylindrical bath to be lifted away. After seeing that the surfaces are perfectly clean, pour on a measured quantity of the lubricant to be tested, and reset the cylinder-bath in position. Slacken set-screws so as to allow the spring to have full pressure. The set-screws should not be removed entirely when slackening. I6"2.J FRICTION TESTING OF LUBRICANTS. 2O$ 2. Light the Bunsen burner. 3. The thermometer indicates the temperature to which the lubricant has to be subjected in the steam-cylinder, being graduated in degrees Fahrenheit, and their equivalent in pounds pressure. Thus, if the working steam-pressure is 60 Ibs., the thermometer shows that the heat of steam at that pressure is 307 Fahr.; whilst at 100 Ibs. pressure its temperature is 358 Fahr., etc. Run the tester, say, until there is a rise of 50 per cent ; in some cases it is preferable to run the tester until there is a rise of 100 per cent. of the friction' first indicated. There does not appear to be any advantage in going beyond this, as the oil is then practically unfit for further use, and there is danger of roughening the friction surfaces. 4. When it is considered desirable to ascertain the distance travelled by the friction surfaces during a test, read off the counting-indicator before and after the test, and subtract the lesser from the greater total, and the difference will represent the number of revolutions made during the test". As the fric- tion surfaces travel two thirds of a foot during each revolution, the number of feet travelled is arrived at by simply deducting from the number of revolutions made, one third thereof. The value of the oil is proportional to the number of feet travelled by the rubbing surfaces. The speed at which the tester should be run should be about five to six hundred revolutions per minute. For quick- speed engine-oil the speed may be increased to about a thou- sand per minute. 162. Experiment with Limited Feed. The object of this experiment is to ascertain the variation in the coefficient of friction due to a change in the rate of feed, The experiment is to be made with the feeding apparatus arranged so that the supply can be regulated. Different runs are made with different rates of feed, and the variation in the coefficient; of frittjon, determined. Fig. So, p. 191, repre- sents the Thurston R. R, -Lubricant-tester as arranged for the experiment, with a' constantly, diminishing rate of feed, b'y.Pro- fessorG. W. Bissel. In this case oil is obtained by the siphon 204 EXPERIMENTAL ENGINEERING. [ 162. M from the burette N, and conveyed by the candle-wicking P to a copper rod H inserted in the bearings. The rate of flow will depend upon the height of the oil in the burette N above the end of the siphon-tube M, and as the head gradually di- minishes from loss of oil, the rate of flow will decrease. The quantity of oil used is to be determined by gradua- tions on the burette. The increase in coefficient of friction due to the constantly diminishing rate of feed is shown in Fig. 86, the coefficients of friction being shown by the dotted lines, corresponding to a given rate of feed and a given time in minutes. Coefficient of frr'citoit> FIG. 86. The experiment with head and feed maintained constant during each run would represent very closely the usual condi- tions of supplying lubricants. In this case, provided there was no loss of oil from the journals, the experiment might show 1. The laws of friction for ordinary lubrication. 2. The most economical rate of feed for a given lubricant. i6 3 .] FRICTION TESTING OF LUBRICANTS. 205 3. The value of the lubricants on the joint basis of amount consumed and coefficient of friction. A few tables showing coefficients of friction which has been obtained in various trials are given in the Appendix for refer- ence. 163. Forms for Report. The following are the forms used in Sibley College for data and results of lubricant test : REPORT OF LUBRICANT TEST. Name of Lubricant Mark Lab. No Date... Source Observer. Investigation No of feet travelled by rubbing surface Time. Min- utes. Total Revolu- tions. Temper- ature. Read- ing on Arc. Coeffi- cient of Friction. Time. Min- utes. Total Revolu- tions. Temper- ature. 'Read- ing on Arc. Coeffi- cient of Friction. VISCOSITY AND RESULTS OF OIL TEST. Date.. 189.... Kind of oil Received from Color Ash % Specific gravity B. Tar % " Waterloo. Chill-pt F. Flashing pt F. Loss at F. for 3 hrs % Burning-pt F. Acid 206 EXPERIMENTAL ENGINEERING. VISCOSITY TEST. No. Time of Flow of -100 c.c. in Seconds. Temperature Degrees F. Lubricating Value Lard-oil 100. Sample. Lard-oil. Water. RESULTS OF FRICTION TEST. Date. '] I t " I] I. ...180 . Average. Temp. Arc. Temp. Arc. Temp. Arc. Highest reading Lowest reading Average reading Drops per min Time of run, min Speed: Rev. per min Miles per hour Pressure: Total Ibs Per sq. in., Ibs Coefficient of friction. . TEST FOR RESINS. Flow on plane inclined degrees. Kind of plane ,... Tempt, room. Time in hrs., Sample. , Lard-oil...... , Water. CHAPTER VII. MEASUREMENT OF POWER DYNAMOMETERS BELT- TESTING MACHINES. 164. Classes. Dynamometers are instruments for measur- ing power. They are of two classes : I. Absorption; 2. Trans- mission. In the first class the work received is transformed by friction into heat and dissipated ; in the second class the dynamometer absorbs only so much force as is necessary to overcome its own friction, the remainder being transmitted. 165. Absorption Dynamometer. The Prony Brake.* The Prony brake is the most common form of absorption dy- namometer. This brake is so constructed as to absorb the work done by the machine in friction, this friction being pro- duced by some kind of a surface connected to a stationary part, and which rubs on the revolving surface of the wheel with which it is used. The brake usually consists of a por- tion which can be clamped on to a wheel (see Fig. 87, page 211), with more or less pressure, and an arm or its equivalent. The part exerting pressure on the wheel is termed the brake- strap ; the perpendicular distance from the line of action of the weight, G, to the centre of the wheel is termed the arm of the brake. The brake is prevented from turning by a definite load which we term G, applied at a distance equal to the length of the arm (a) from centre of motion. The work of resistance would then evidently be equal to the product of the .weight of resistance, G, into the distance it would pass through *See Engine and Boiler Trials, by R. H. Thurston, page 157; Mechanics of Materials, by I. P. Church, page 269; Du Bois' Weisbach's Mechanics of En- gineering, page 13. 207 2O8 EXPERIMENJ^AL ENGINEERING. [ l6/. if free to move. If n be the number of revolutions per minute, the horse-power shown by the brake would evidently be 2nGan -r- 33000. ....... (i) Brakes are made with various rubbing surfaces, and with various devices to maintain a constant resistance. 166. Stresses on the Brake-strap. Formulas. The strains on the brake-strap are essentially the same as those on a belt, as given in Article 128, page 173. That is, if T, represent the greatest tension, T z the least tension, c the percentage that the arc of contact bears to the whole circumference, N the normal pressure, F the resistance of the brake, /coefficient of friction, T 1 = itf-72Wc = Number whose log is 2.;288/<: = R * (3) 167. Designing a Brake.* The actual process of designing a brake is as follows : There is given the power to be absorbed, number of revolutions, diameter and face of the brake-wheel. In case a special brake-wheel is to be designed, the area of bearing surface is to be taken so that the number obtained by multiplying the width w of the brake in inches by the velocity of the periphery v of the wheel in feet per minute, divided by *See " Engine and Boiler Trials," by R. H. Thurston, pages 260 to 282; also, " Friction and Lubrication." I6/.J MEASUREMENT OF POWER. 2OO, the horse-power H, shall not exceed 500 to 1000.* Call this result K. Then v 400 to 500 is considered a good average value of K. The value of the coefficient of friction f should be taken as the lowest value for the surfaces in contact (see table of co- efficient of friction in Appendix). This coefficient is about 0.2 for wood or leather on metal, and about o. 1 5 for metal on metal. Let H be the work to be transmitted in horse-power, n the number of revolutions of the brake-wheel, D its diameter ; then the resistance F of the brake must be _ -- (4) The arc of contact is known or assumed, and may be expressed as convenient (see Article 128) in circular measure 6, degrees ct t or in percentage of the whole circumference c. Example. Assume the arc of contact as 180 degrees (c = 0.5), the diameter of brake-wheel 4 feet, coefficient of friction (f=o. 15), face of brake-wheel 10 inches, revolutions 90, horse-power 70. Find the safe dimensions of the brake- strap and working parts of the brake. Then, from page 208, B = io 2 - 7288/<: = io - 2046 . That is, B equals the number whose logarithm is 0.2046 ; or. B 1.602. * See also " Engine and Boiler Trials," by R. H. Thurston, pp. 272 and 279. 210 EXPERIMENTAL ENGINEERING. [ l6/. Thus if the brake-wheel is 4 feet diameter revolving at 90 revolutions per minute : from equation (4) (n) (4) (90) Taking B as above, and substituting in equations (2) and (3), we have 7i = 2 43 From the value of T, , the maximum tension, we compute the required area of the brake-straps, using 10,000 pounds as the safe-working strain. Section of brake-straps = 5436-7- 10000 = 0.55 square inch. The assumed width of brake-wheel is 10 inches ; this gives for the value of K, by equation page 209. K = (10) (i 1 32) -r- 70 = 162 ; a low value. If it is proposed in this brake to use 3 straps, each 2 inches wide, the thickness will then be o.J5 -f- 6 = 0.091 inch. To determine a convenient length of the brake-arm, con- sider equation (i) for work delivered in horse-power. H = 27tGan -r- 33000. 169.] MEASUREMENT OF POWER. By dividing both terms by 2?r, H ' Gan -f- 5252; 211 G w 5252 an 168. Brake Horse-power. The following table will often be convenient for determining the delivered horse-power from a brake. HORSE-POWER PER 100 REVOLUTIONS FROM A BRAKE. Length of Brake-arm, feet. Factor to multiply scale-reading to give horse-power, H--G. Ratio of scale-read- ing to horse- power. G-*-H. I O.OIQ 52.52 2 .038 26.26 3 057 17.51 4 .076 ' I3.I3 5 .000 10.50 5-252 .100 IO.OO 6 .114 8.75 7 .133 7.50 8 .152 6.56 9 .172 5.83 10.504 .200 5-00 169. Different Forms of Prony Brakes. Various forms of brakes are made. Fig. 87 shows a very simple form of FIG. 87. PRONY BRAKE. Prony brake, in which the rubbing surfaces are made by two wooden beams clamped together by the bolts C C. Weight is applied to the arm E at the point G ; the stops D D prevent a great range of motion of the arm ; the projection F is used to hang on sufficient counterbalance to prevent the brake from 212 EXPERIMENTAL ENGINEERING. [ 170. revolving by its own arm-weight when the screws C Care very loose. The net load acting on the brake-arm is the difference between the weight at G and that at F, reduced to an equiva- lent weight acting at G. Brakes are usually constructed by fastening blocks of wood, on the inside of flexible bands of iron, so as to encircle a wheel. The inside of the blocks should be fitted to the wheel, and the spaces between the blocks should be at least equal to one third the area of the block. The iron bands are connected to the brake-arm in such a manner that the tension on the wheel can readily be changed. The form of such a brake is shown in Fig. 88 attached to a portable engine. FIG. 88. BRAKE APPLIED TO PORTABLE ENGINE. 170. Strap-brakes. Brakes are sometimes made by taking one or more turns of a rope or strap around a wheel, as shown FIG. 89. STRAP-BRAKE. in Fig. 89. In this case weights must be hung on both sides, and since the arm cf action is equal, the resultant force J 73-] MEASUREMENT OF POWER. 21$ acting is the difference between the two weights : that is, in the figure the resultant force is A B\ the equivalent space passed through is the distance travelled by any point of the circumference of the wheel in a given time. The work done is the product of these quantities. 171. Self-regulating Brakes. Brakes with automatic regulating devices are often made ; in this case the direction of motion of the wheel must be such as to lift the brake-arm. If the tension is too great the brake-arm rises a short distance, and this motion is made to operate a regulating device of some sort, lessening the tension on the brake- wheel ; if the tension is not great enough, the brake-beam falls, producing the oppo- site effect. 172. Brake with oblique Arm. A very simple form of self -regulating brake is shown in Fig. 90: in this case the arm is maintained at an angle with the horizontal. If the friction becomes too great, the weight G rises, and the arm of the brake swings from A to E, thus in- FlG . ^_ creasing the lever-arm from BC to LC\ if BRAKE. the friction diminishes, the lever-arm is correspondingly dimin- ished, thus tending to maintain the brake in equilibrium. 173. Alden Brake. The Alden brake see (Figs. 91 to 94) is an absorption dynamometer in which the rubbing surfaces are separated by a film of oil, and the heat is absorbed by water under pressure, which produces the friction. It is con- structed by fastening a disk of cast-iron, A, Fig. 91, to the. power-shaft ; this disk revolves between two sheets of thin copper E E joined at their outer edges, from which it is sepa- rated by a bath of oil. Outside the copper sheets on either side is a chamber which is connected with the water-supply at G. The water is received at G and discharged at H, thus main- taining a moderate temperature. Any pressure in the chamber causes the copper disks to press against the revolving plate, pro- ducing friction which tends to turn the copper disks. As these 214 EXPERIMENTAL ENGINEERING. [ 174. are rigidly connected to the outside cast-iron casing and brake- arm P, the turning effect can be balanced and measured the same as in the ordinary Prony brake. The pressure of water is automatically regulated by a valve V, Fig. 94, which is par- FIG. 93. SECTION. D FIG. 92. ALDEN'S BRAKE. FIG. 91. SECTION. FIG. 94. VALVE. tially closed if the brake-arm rises above the horizontal, and is partially opened if it falls below ; this brake with a constant head gives exceedingly close regulation. 174. Hydraulic Friction-brake. The author has designed a hydraulic friction-brake that can be applied to the surface of an ordinary brake-wheel. The brake consists of a tube of copper with an oval or rectangular cross-section, which very nearly encircles the brake-wheel, and has both- ends closed. The greatest dimension in its cross-section is equal to the width of the brake-wheel, and its least dimension is one half to three fourths of an inch. One end of the tube is connected with the water-supply, the other to the discharge, which can be throttled as required. Outside is a band of iron completely encircling the tube and the brake-wheel, and held rigidly to- gether by means of bolts. To this band is fastened the brake- arm, and also one end of the copper tube. When water-pres- 3 '*' 1/6.] MEASUREMENT OF POWER. sure is applied to the tube, it tends to assume a round cross- section, the shorter diameter increasing and the greater diameter diminishing. As these changes cannot take place because of the outer band of iron, pressure is exerted on the surface of the brake-wheel, and mo lion of the brake-wheel tends to revolve the tube and band of iron. This is resisted by the weight on the arm of the brake. The water-pressure is regulated automatically by a slight motion of the brake-arm, which closes or opens the supply-valve as is required. The arm may be permitted to act downward on a pair of scales, by interposing a spring of the requisite stiffness between it and the platform of the scales. To prevent wear of the copper tube thin sheets of iron may be interposed. A lubricant is applied by means of lubricators fixed near the ends of the tube. 175. Removal of the Heat generated by the Brake. Various devices have been adopted to secure the removal of the heat. One method is to cast the outer rim of the brake- wheel hollow, and connect this by a tube with a cavity in the centre of the axis, so that water can be received at one end of the axis and discharged at the other. Another way is to leave a deep internal flange on the brake-wheel, and in using the brake, to supply water by means of a crooked pipe on one side and to scoop it out by a pipe with a funnel-shaped mouth bent to meet the current of water near the opposite side of the wheel. Water is sometimes run on to the surface through a hose, but aside from the inconvenience due to flying water, if any of the rubbing surfaces are of wood it is likely to make sudden and irregular variations in the coefficient of friction that are difficult to control. 176. Applying Load. In applying the load, care must be taken that its direction is tangent to the circle that would be described by the brake-arm were it free to move. In other words, the virtual brake-arm must be considered as perpendic- ular to this force. If a vertical load or weight is applied, the brake-arm must be horizontal, and equal in length to the dis- tance from this vertical line to the centre of the motion. 2l6 EXPERIMENTAL ENGINEERING. [ 1/8. It will be found in general safer and more satisfactory to have the motion of the brake-wheel such as to produce a downward force, which may be measured by a pair of scales, rather than the reverse, which requires a weight to be sus- pended on the brake-arm. There should be a knife-edge between the brake-arm and the load ; in case of downward motion, the support upon the scales, should be made the proper length to hold the brake-arm horizontal. 177. Constants of Brake. All brakes with unbalanced arms have a tendency to turn, due to weight of the arm. This amount must be ascertained and added to or taken from the scale or load readings as required by the rotation, in order to give the correct load. To ascertain this amount, the brake may be balanced on a knife-edge, with a bearing point directly over the centre of the wheel, and the correction to the weight obtained by readings on the scale. It is obtained more accu- rately by making the brake loose enough to move easily on the wheel ; then apply a spring-balance at the end of the arm ; first pull the arm upward through an arc of about 3 either side of its central position, moving it very slowly and gradually : the reading will be the weight plus the friction. Then let it back through the same arc very slowly and gradually, and the read- ing will be the weight less the friction. The sum of these two results will be twice the correction for the brake-arm. Repeat this three times for an average result. In case the friction is greater than the weight this second result will be negative, but the method will remain the same. The weight of the brake, as generally mounted, is carried on the main bearings of the wheel, from which the power is obtained, and virtually increases its weight. This may in some instances increase perceptibly the friction of the journals of the wheel, but is generally an imperceptible amount. This weight can be reduced when desired, by a counterbalance con- nected to the brake by means of guide-pulleys. 178. Directions for Using the Prony Brake. i. See that the brake-wheel is rigidly fastened to the main shaft. 2. Provide ample means of lubrication. ISO.] MEASUREMENT OF POWER. 3. If the brake-wheel has an internal rim, provide means for supplying and removing water from this rim. 4. Find the equivalent weight of brake-arm to be taken from or added to the load, depending on the direction of motion of the wheel. 5. In applying the load, tighten the brake-strap very slowly, and give time for the friction to become constant be- fore noting readings of the result. 6. Note the time, number of revolutions, length of brake- arm, corresponding load, and calculate the results. 179. Pump Brakes. A rotary pump which delivers water through an orifice that can be throttled or enlarged at will, has been used with success for absorbing power. If the casing of the pump is mounted so as to be free to revolve, it can be held stationary by a weighted arm, and the absorbed power measured, as in the case of the Prony brake. If the casing of the pump is stationary, the work done can be measured by the weight of water discharged multiplied by the height due to the greatest velocity of its particles multiplied by a coefficient to be determined by trial.* A special form of the pump-brake, with casing mounted so that it is free to revolve, has been used with success on the Owens College experimental engine by Osborne Reynolds. In this case the brake is practically an inverted turbine, the wheel delivering water to the guides so as to produce the maximum resistance. The water forced through the guides at one point is discharged so as to oppose the motion of the wheel at another point. 180. Fan-brakes. A fan or wheel with vanes revolved in water, oil, or air will absorb work, and in many instances forms a valuable absorption-dynamometer. The resistance to be obtained from a fan-brake is expressed by the formula f V* Rl = IKDA ^ * See Rankine, Machinery and Mill-work, page 404. f Ibid., page 406. 218 EXPERIMENTAL ENGINEERING. iSi. in which ^/equals the moment of resistance, V the velocity in feet per second of the centre of vane, A the area of the vane in square feet. / equals the distance from centre of vane to axis in feet, D the weight per cubic foot, of fluid in which the vane moves, K.a coefficient, found by experiment by Pon- celet to have the value = 1.254 . 6244 VA in which s is the distance in feet from the centre of the entire vane to the centre of that half nearest the "axis. When set at an angle i with the direction of motion the value for Rl must be multi- .... 2 sin 3 i plied by : : =-. . * i + sin 3 i 181. Traction-dynamome- ters. Dynamometers for sim- ple traction or pulling are usually constructed as in Fig. 95. Stress is applied at the two ends of the spring, which rotates a hand in proportion to the force exerted. FIG. 95. DYNAMOMETER FOR TRACTION. g 183.] MEASUREMENT OF POWER. 2ig Recording Traction-dynamometers. These are constructed in various forms. Fig. 96 shows a simple form of a recording traction-dynamometer, designed by C. M. Giddings. Paper is placed on the reel A, which is operated by clock-work; a pencil is connected at K to the band, and this draws a diagram, as shown in Fig. 97, the ordinates of which represent pounds Ibs.- - FIG. 97. DIAGRAM FROM TRACTION-DYNAMOMETER. of pull, the abscissa the time. The drum may be arranged to be operated by a wheel in contact with the ground : then the abscissa will be proportional to the space, and the area of the diagram will represent work done. 182. General Types of Transmission-dynamometers.* Transmission-dynamometers are of different types, the ob- ject in each case being to measure the power which is received without absorbing any greater portion than is neces- sary to move the dynamometer. They all consist of a set of pulleys or gear-wheels, so arranged that they may be placed between the prime movers and machinery to be driven, while the power that is transmitted is generally measured by the flexure of springs or by the tendency to rotate a set of gears, which may be resisted by a lever. 183. Morin's Rotation-dynamometer. In Morin's dy- namometer, which is shown in Fig. 97^, the power is trans- mitted through springs, FG, which are thereby flexed an amount proportional to the power. The flexure of the springs is recorded on paper by a pencil z fastened to the rim of the * See Thurston's Engine and Boiler Trials, page 264 ; also Weisbach's Mechanics, Vol. II., pages 39-73; also Rankine's Steam-engine, page 42. 22O EXPERIMENTAL ENGINEERING. [ 183- wheel. A second pencil is stationary with reference to the frame carrying the paper. The paper is made to pass under the pencil by means of clock-work driven by the shafting, which can be engaged or disengaged at any instant by operating the lever R. The springs are fastened at one end rigidly to the main axle, which is in communication with the prime mover, and at the other end to the rim of the pulley, which otherwise is free to turn on the main shaft. The power is taken from this last pulley, and this force acts to bend the H FlG. 97*7. MORIN ROTATION-DYNAM OMETERS. springs as already described. In the figure A is a loose pulley B is fixed to the shaft. The autographic recording apparatus of the Morin dyna- mometer consists essentially of a drum, which is rotated by means of a worm-gear, UK, cut on a sleeve, which is concentric with the main axis. This sleeve slides longitudinally on the axis, and may be engaged with or disengaged from the frame at any instant by means of a lever. When this sleeve is engaged with the frame and made stationary the recording apparatus is put in motion by the concentric motion of the gearing, SV, with respect to the axis. The pencil attached to the spring will at this instant trace a diagram on the paper whose ordi- 184.] MEASUREMENT OF POWER. 221 nates are proportional to the force transmitted. The rate of rotation of the drums carrying the paper, with respect to the main axis, is determined in the same manner as though the gears were at rest by finding the ratios of the radii of the respective wheels, Thus the amount of paper which passe.s off from one drum on to the other can be proportioned to the space passed through, so that the area of the diagram may be proportional to the work transmitted. To find the value of the ordinates in pounds the dyna- mometer must be calibrated ; this may be done by a dead pull of a given weight against the springs, thus obtaining the deflections for a given force ; or, better, connect a Prony brake directly to the rim of the fixed pulley B, and make a series of runs with different loads on the brake, and find the correspond- ing values of the ordinates of the card. 184. Calibration of the Morin Dynamometer. Appara- tus. Speed-indicator, dynamometer-paper, and Prony brake. 1. Fasten paper on the receiving drum, wind off enough to pass over the recording drum, and fasten the end securely to the winding drum. See that the gears for the autographic apparatus are in perfect order, and that both pencils give legible lines. Adjust the pencil fixed to the frame of the clock-work, so that it will draw the same line as the movable pencil, when no load is applied. 2. With the apparatus out of gear apply the power. Take a card with no load. This card will be the friction work of the dynamometer. 3. Apply power and load, take cards at intervals: these cards will represent the total work done. This, less the fric- tion work, will be the power transmitted. The line traced by the pencil affixed to the frame of the clock-work must in all cases be considered the zero-line, or line of no work. 4. To calibrate the dynamometer, attach a Prony brake to the same shaft and absorb the work transmitted. This trans- mitted work must equal that shown by the Prony brake. Find constants of brake as explained Article 177, page 178. 5. Draw a calibration-curve, with pounds on a brake-arm, 222 EXPERIMENTAL ENGINEERING. [ 186. reduced to an equivalent amount acting at a distance equal to the radius of the driving-pulley of the dynamometer, as abscissae, and with ordinate of the diagram as ordinate. Work up the equation of this curve. 6. In report of calibration make record of time, number of revolutions brake-arm, equivalent brake-load for arm equal to radius of dynamometer-pulley, length of ordinate, scale of ordinate. Describe the apparatus. 7. In using it, insert it between the prime mover and re- sistance to be measured. Determine the power transmitted from the calibration. 185. Form of Report. The following form is useful in calibrating this dynamometer: CALIBRATION OF MORIN DYNAMOMETER. Kind of brake used Length of brake-arm ft. Weight of brake-arm Ibs. Zero-reading of scales Ibs. Radius of driving-pulley ft. Observers Date 189.. No. Revolutions per Minute. Effective Brake-load, Ibs. Equivalent Load on Driving- pulley, Ibs. Ordinate, Inches. Brake H. P. Up. Down. Mean. Up. Down. Mean. Remarks: X Equation of Curve, Y-.. 186. Steelyard-dynamometer. In this dynamometei the pressure of the axle of a revolving shaft is determined by shifting the weight G on the graduated scale-beam A C. The power is applied at P, putting in motion the train of gear-wheels, and is delivered at Q. Denote the applied force by P, the delivered force by Q, 1 86.] MEASUREMENT OF POWER. 22$ the radius KM by a, KE by r, LF by r l , NL by b* the force delivered at E by R, that at F by ^. We shall have = Pa, also But and since = FD 9 The resultant force Z=R-\-R l = If we know the number of revolutions, the space passed through by each force can be readily calculated, and the work found by taking the product of the force into the space passed through. FIG. 97*5. HACHETTE'S STEELYARD-DYNAMOMETER. Consideration of Friction. The friction of the axle and gear-teeth will increase the force R and decrease the force R v Let /i be the experimental coefficient expressing this friction, Then Par, - Qbr if Qbr' 224 EXPERIMENTAL ENGINEERING. [ 1 88, II M 187. Pillow-block Dynamometer. The pillow-block dy- namometer operates on the same principle as the steelyard dynamometer, but no intermediate wheel is used. This dynamometer, shown in Fig. 97^, consists of the fixed shaft L, which is rotated by the power Q applied at N. The power rotates the gear-wheel EL y which communicates motion to the wheel KE on the same shaft with the wheel KM. This shaft is sup ported on a pair of weighing-scales so that the downward force Z acting on the bearing can be weighed. Let P equal the force delivered, let a equal the angle this force makes with the horizontal, let KM equal a and KE equal r ; G equal the weight of shaft and wheel. The weight on the pillow-block at K must be FIG. QIC. PILLOW-BLOCK DYNA- MOMETER. a From which Z-G i * sm -J 1 y When the belt is horizontal, y 188. The Lewis Dynamometer.* This transmission-dy- namometer is a modified form of the pillow-block dyna- mometer, arranged in such a manner that the friction of the gearing or journals will not affect the reading on the weighing- scales. This dynamometer is shown in Fig. 97^, and also in Fig. 97/, Article 195, page 237. The dynamometer consists of two * See Vol. VLI., page 276, Trans. Am. Society Mechanical Engineers. 1 88.] MEASUREMENT OF POWER. 22$ gear-wheels A and C, whose pitch-circles are tangent at B\ the gear-wheel A is carried by the fixed frame 7", the wheel Cis carried on the lever BD: the lever BD is connected to the fixed frame T by a thin steel fulcrum, as used in the Eir.ery Testing-machines (Article 67, page 87). The point D, the centre of wheel C, and the fulcrum are in the same right line. The fulcrum B permits vertical motion only of the point D. The point D rests on a pillar, which in turn is supported by a pair of scales. The shaft leading from the wheel C is fur- nished with' a universal joint (see Fig. 9/), so that its weight does not affect that on the journal C. In Fig. 101, A is the FIG. gjd. THE LEWIS DYNAMOMETER. driving and C the driven wheel, the force to be measured being received on a pulley on the shaft a, transmitted through the dynamometer, and delivered from a pulley on the shaft c. From this construction it follows, that no matter how great the friction on the journals of the shaft c, there will be no pressure at the point D except what results from torsion of the shaft c. This will be readily seen by considering : 1. That any downward force acting at B will be resisted by the fixed frame T, and will not increase the pressure at D. 2. A downward force acting on the lever between B and D will produce a pressure proportional to its distance from B. 3. If the driven wheel C were firmly clamped to its frame, no force acting at B would change the pressure at D ; and since 226 EXPERIMENTAL ENGINEERING. [ 1 88. journal-friction would have the effect of partially clamping the wheel to the journal , it would have no effect on the scale- reading at D. Denote the transmitted torsional force by Z; the radius of the driven pulley by r ; the length of lever BD by a ; the scale- reading at D by W. Then from equality of moments 7 Wa Wa Zr, Z = r The effective lever-arm BD is to be obtained experimen- tally as follows : Disconnect the universal joint, shown in Fig. 108, so as to leave the wheel C, free to turn ; block the driving- pulley A ; fasten a horizontal arm, ^/(dotted lines, Fig. 101), to the shaft c, parallel to the line DB and carrying a weight G ; balance the scales in this position, then move the weight out on the lever, until the reading of the scales is increased an amount equal to the weight moved. The distance moved by the weight will equal length of the lever DB. Thus let ef, shown in dotted lines, represent the lever clamped to the axis c\ let e represent the first position of the weight G y and/" the second position; let Wand W represent the corresponding scale-readings, after balancing scales without G on the lever, ef. Then we have 4- G = W = Hence _ W- W _ (fB - eB) ef DB ~ DB ** ' DB ' Then will DB = ef. 189-] MEASUREMENT OF POWER. 22/ 189. The Differential Dynamometer. This is often called the Bachelder, Francis, or Webber dynamometer ; was invented by Samuel White, of England, in 1780, and brought to this country by Mr. Bachelder in 1836. The dynamometer portion consists of four bevel-gears, shown in plan in Fig. g'/e. Power is applied to the pulley M, which carries the bevel- x FIG. 97*. THE DIFFERENTIAL DYNAMOMETER. wheel EE l ; the resistance is overcome by the pulley N, which carries the bevel-wheel /^ . Both wheels run loosely upon the fixed shaft XX l , and are connected by the wheels EF and 1 F l . By the action of the force P and the resistance Q, the pressure of the wheels EE l and FF l is downward at E and F, and upward at E l and F l , tending to swing the lever GG l around the axis XX l , one half as fast as the pulley M. The weight which holds the lever-arm stationary, multiplied by the space it would pass through if free to move, is the measure of the work of the force P. A dashpot is usually attached to the lever GG^ at G l , to lessen vibrations and act as a counterbal- ance. Let Z equal the vertical force acting at B and B l ; R, the vertical pressure between the teeth at each point of con- tact ; b, the distance of B and B l from the centre C\ a, the distance, AC, to the weight. Then we have evidently 2Z = ^.R, or Z = 2R ; also Ga = 2Zb = 228 EXPERIMENTAL ENGINEERING. [ 190. If a' is the radius of the driving-pulley M, and r the radius of each bevel-gear, 2Rr G r a Pa' = 2Rr, or P = - = T -. a' 2 b a' If friction is considered, The mechanical work received is equal to P multiplied by the space passed through in the given time. This instrument has been improved by Mr. S. Webber, as shown in Fig. 9; '/. FIG. g-jf. THE WEBBER DYNAMOMETER. These dynamometers are used in substantially the same way as the Morin dynamometers. 190. Calibration of the Differential Dynamometer. I. See that it is well oiled, in good condition, its axis horizon- tal, and also that the weighing arm is horizontal for no load. 2. Observe constants of the apparatus ; obtain weight of small poise; of large poise; of amount to balance beam W e . Measure the arm of each, and calculate the foot-pounds per 100 revolutions corresponding to weights and graduations. IQO.] MEASUREMENT OF POWER. 2 29 3. Make a preliminary run without load, and note the reading of the poise required to balance the arm. This will determine the friction of the dynamometer without load. Determine the length of the arm, and the value of each sub- division in foot pounds. 4. Attach a strap-brake (see Art. 170, p. 212) to the delivery pulley of the dynamometer, and absorb all the force trans- mitted. Make a series of ten runs, each ten minutes in length, and during each of which the load on the Prony brake-arm is kept as constant as possible, but which is increased by equal increments, in the different runs. Take observations each minute during the run. 5. The difference between the work absorbed by the brake and that shown by the dynamometer should be carefully de- termined. It is the error of the dynamometer. 6. Note whether this error is a constant quantity, or is a percentage of the work delivered. ^7. In your report, describe the apparatus, give the results of the calibration, and draw a curve, using brake foot-pounds as ordinates, and dynamometer foot-pounds as abscissae. 8. To use the dynamometer insert it between the prime mover and the machinery to be run. Special Directions for Calibrating the Webber Differential Dy namometer. Apparatus required : i. Ten small tension-weights. 2. Spring-balance or plat- form-scales. 3. Measuring-scale. 4. Calipers. 5. Stop-watch. Measurements : a. Weight of small tension-weights. b. " " fixed poise-weights. c. " " dynamometer-arm. d. " " sliding poise. e. Length of dynamometer-arm to fixed poise. f. Length of dynamometer-arm to sliding poise. g. Diameter of brake-pulley. h. Thickness of brake-strap. 230 EXPERIMENTAL ENGINEERING. [ I. Friction-run. Remove brake. Find time, in seconds, of 1000 revolutions (10 rings of bell). Balance dynamometer- arm ; the reading is the " zero-reading" by the beam, and must be corrected to get the true friction-reading. II. Test-runs. Put on brake ; hang one weight on its slack side. Time, 1000 revs. Read simultaneously dynamom- eter-arm and platform scales. Repeat the same with succes- sive weights added. III. To Weigh Dynamometer-arm. Run by hand, first for- ward and then backward, weighing in each case the turning effect, with the platform-scale applied at the knife-edge of the dynamometer-arm, and sliding-poise set at the zero-mark. 191. Form of Report. The following blank is used in the exercises with the differential dynamometer in Sibley College : MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL UNI- VERSITY. Calibration of Differential Dynamometer. Kind of Brake used Length of Brake-arm ft. Weight of Brake-arm Ibs. Zero-reading of Brake-scales Ibs. ( Date 189 .. Observers \ Number. Time of 100 Revolutions' Seconds. Brake-tensions, Lbs. Work in ft.-lbs. per 100 Revolutions. Brake Horse-power. Tight Side. Slack Side. Effective Load. Dynamometer-readings. Obtained from Brake. Error of the Dynamometer. Observed on Dynamome- ter-beam. Calculated from Machine Constants. Transmitted as shown by Beam, = \Vt 7*| TI T^TI r+ w c W,-W n W b Wt-W D.H.P. I 2 3 4 6 7 8 9 10 1930 MEASUREMENT OF POWER. CONSTANTS OF MACHINE. 231 Loads at Knife-edge. Moment Arm ft. Data for Beam. Sliding Poise, Weight.... Ibs. Weight, Ibl Value, ft.- Ibs. per 100 Revs. Moment Arm, Feet. Value, ft.- Ibs. per joo Revs. Small Poise First Notch Last Notch Dynamometer-beam ...-We Increase per Notch. = Zero-reading by Beam. ...ft. -Ibs. ^=Frict.ion-reading=. . .ft. -Ibs. 192. Emerson's Power-scale. One of the most complete transmission-dynamometers is shown in Fig. 97^, with attached numbers showing the dimensions of the various sizes manu- factured. In this instrument the wheel C is keyed or fastened to the shaft ; the wheel B is connected with the wheel C near its outer circumference by projecting studs; the amount of pressure on these studs is conveyed by bent levers to a collar, which in turn is connected with weighing-levers. Small weights are read off from the scale D, and larger ones by the weights in the scale-pan N. A dash-pot is used to prevent sudden fluctuations of the weighing-lever. .___! 193. Form of Report. The following forms for report and log of tests on Webber Dynamometer and Emerson's Power-scale are used by the Massachusetts Institute of Tech- nology. REPORT. Test on No. Date. No. of test Ft. -Ibs. per seconds WEBBER DYNAMOMETER. I No. of test Duration of test Revolutions per minute.. Load EMERSON POWER-SCALE. I 232 EXPERIMENTAL ENGINEERING. [ 193- FIG. 97. EMERSON'S PUVVEK-SCALES. I94-] MEASUREMENT OF POWER. 233 BRAKE. i 2 T. T 9 I 2 3 1-2 T 7 2^ H. P. by brake Signed... LOG. Test on, No. Date. be c o O o o Webber Dynamometer. Emerson Power-scale. Brake. i> s H Time of Revolutions. Ft.-lbs. per Revolutions. i H Readings of Counter. Revolutions per Minute. ' V 5 H i 3 O u o 1 1 Pi Revolutions per Minute. Test Number i. Test nu H. P. t H. P. t H. P. b I 2 3 1-2 i-3 2-3 y dynamo y power-s y brake. . . -ale Constants and Remarks. 194. The Van Winkle Power-meter. The Van Winkle Power-meter is shown in Fig. 97^, complete, and with its parts 234 EXPERIMENTAL ENGINEERING. [ 1 94. separated, in Fig. 972'. It consists of a sleeve with attached plate, B, that can be fastened rigidly to the shaft ; and a plate, A t which is revolved by the force communicated through FIG. 97>&. VAN WINKLE POWER-METER. the springs s s. The angular position of the plate A with refer- ence to B will vary with the force transmitted. This angular motion is utilized to operate levers, and move a loose sleeve FIG. 97?'. PARTS OF THE VAN WINKLE POWER-METER. longitudinally on the shaft. The amount of motion of the sleeve, which is proportional to the force transmitted, is indi- cated by a hand moving over a graduated dial. The dial is graduated to show horse-power per 100 revolutions. MEASUREMENT OF POWER. 235 195. Belt-dynamometers. Belts ha-e been used in some instances instead of gearing in transmission-dynamometers, but because of the great loss of power due to stiffness of the belts, and to the uncertainty caused by slipping, they have not been extensively used. The following form, from Church's " Mechanics of Materials," is probably as suc- cessful as any that has been de- vised. It consists of a vertical plate, carrying four pulleys and a scale-pan, as shown in Fig. 97^. The scale-beam is balanced, the belt then adjusted, and power turned on ; a sufficient weight, G, is placed in the scale-pan to balance the plate again. Let b be the arm of the scale-pan, and a that of the forces P and P'. Then, for equilibrium, FIG. 977". A BELT-DYNAMOMETER. Gb-Pa P'a, (0 since P and P f on the right have no leverage about C, as the line of the belts produced intersects C. From (i) a (2) The work transmitted in foot-pounds per minute is equal to (P P'}v, in which v is the velocity of the belt in feet per minute to be obtained by counting. Another form employs two quarter-twist belts to revolve a shaft at right angles to the main shaft. (See Vol. XII., Transactions Am. Soc. Mechan- ical Engineers.) 196. Method of Testing Belts.* The object of this test is to determine the coefficient of friction, and the power trans- mitted by various kinds of belting running under different conditions. 236 EXPERIMENTAL ENGINEERING. [ IQ/. The required formulae are given in Article 128, page 173, as follows: T l , maximum tension; 7" a , minimum tension; F, the force of friction ; c, the percentage of arc of contact to whole circumference ; 0, the arc of contact in circular measure. We have T Common log = 0.434/0 = 2.7288/c. *t From which or /= Napierian log {-j^}^- a' Belt-testing machines must be arranged so that measures of T lt T 2 , 0, and c can be made. To determine loss due to resistance, it is necessary to supply the power by a transmis- sion-dynamometer, and absorb that delivered by a brake. 197. The Sibley College Belt-testing Machine. The belt-testing machine illustrated in Fig. gjk is used in the Mechanical Laboratory of Sibley College. It was designed by Wilfred Lewis of Philadelphia, and used in the tests described in Vol. VII. of Transactions of American Society of Mechanical Engineers. The belt to be tested is placed on the pulleys , F; power is transmitted through the pulleys Pto the Lewis transmitting- * The student is referred to papers in Transactions of American Society of Mechanical Engineers, Vol. VII., by Wilfred Lewis and Prof. G. Lanza ; also to paper in Vol. XII., by Prof. G. Alden ; and to the Holman tests in the Jour- nal of the Franklin Institute, 1885. 197-] MEASUREMENT OF POWER. 237 238 EXPERIMENTAL ENGINEERING. [ 198. dynamometer (see Article 188, page 224), and thence through the shaft J-fto the pulley .. The power transmitted is absorbed by a Prony brake on the shaft M. The slip of the belt is measured by transmitting the motion of the pulley E by gearing to the shaft /, and thence to a disk S, whose edge is graduated. The pulley F is connected to the gear-wheel Z,, shown in a larger scale in centre of Fig. 96. The wheel L is so proportioned that if there is no slip it will revolve at the same rate as the disk 5; if there is slip it will fall behind 5. The amount that it falls behind is read by the scale V, which may be clamped to the hub of L by the screw T. As this device moves only one one-hundredth as fast as the main shafts, the amount of slip can be easily read. The pulley F and the brake M are mounted on a carnage, which can be drawn back by the screw N. The pulley E is mounted in a frame, supported on knife- edges below, R. The shaft H is fitted with a universal joint, to eliminate the effect of transverse strains on the dynamom- eter. Weighing-scales are placed at A, B, and C, respectively, that at A is termed the dynamometer-scales ; that at B, the brake- scales that at C, the tension-scales. The reading on the tension- scales C, multiplied by the horizontal arm K, divided by the height d of the pulley E upon the knife-edge, gives the total tension on the belts 7", + 7^. The reading on brake-scales B, divided by the arm b of the brake, and multiplied by the radius D of the pulley F, gives the difference of tensions, T l T^. The brake-scale reading, multiplied by the brake-arm b, and by 2nn, n being the number of revolutions, gives' the delivered work in foot-pounds. The dynamometer scale-read- ing A, multiplied by the equivalent dynamometer-arm a and by 27tn, gives the work received in foot-pounds. The dyna- mometer-arm a is to be found as described in Article 188. page 225. 198. Directions for Belt-test I. Before starting : (a) Get speed-indicator and log-blanks. (b) Oil all bearings and loose pulley under main belt. 19^.] MEASUREMENT OF 2>OWER. 239 (c] Balance scales A and C, and note their " zero- readings." 2. With test-belt off : (d) Take friction-reading on scales A for driving-shaft, counting its revolutions. (e) Weigh brake-arm (see note below) to get zero- reading of scale B and then remove brake from brake-pulley. 3. With brake off : (/) Put on test-belt (while loose), first moving brake- shaft frame by unscrewing hand-wheel next the floor. Tighten belt to read while at rest 75 Ibs. net, on scales C. . (g) Take friction-reading again on scales A. Count revolutions of driving-shaft and read " per cent of slip," from which the speed of brake-shaft can be calculated. 4. Run I. (/i) For tension of belt : Set scales C to read 50 Ibs. net with belt at rest, by screwing up hand-wheel next the floor, which should not be changed during the run. Take reading of scales C for each load added on brake-scales B. (t) For power given o*it by belt : Set scales B to read 5 Ibs. " net " or effective " load," and balance by tightening brake while running. Feed a light stream of water into rim of brake-pulley. Count its revolutions. (k) For power put into .belt : Read scales A and take speed of driving-shaft. (/) For slip of belt : Read graduated " slip-disk," which has 100 equal divisions. When vernier is set, it turns with the disk, and shows one per cent of slip when falling back one division during one turn of the slip-disk. (m) Thus continue to increase brake-load by 5 Ibs. of increments on scales B. Each time keep it carefully balanced, and take simultaneous readings on scales A, scales B, scales C, slip-disk, and revolution-counter. 5. Runs II., III., and IV. (n) For run II., set tension-scales to read 75 Ibs. net with belt at rest, and proceed as in run I. Increase this initial tension-reading by 25 Ibs. each, for runs III. and IV. 240 EXPERIMENTAL ENGINEERING. [^99 6. Measurement of machine-constants : (o) Get length in feet of (i) brake-arm, (2) dynamom- eter-arm, (3) arms of bell-crank acting on tension-scales, and (4) circumferences of test-belt pulleys, latter with steel tape. Calculate diameters. (/) If the pulleys differ in diameter, the reading on slip-disk, obtained while running " light " (see (g), above), will be the ''zero" of all the slip-readings. N.B. Shut off water at brake-pulley when it stops. Note. To weigh brake-arm : Loosen brake and oil face of pulley. Balance arm on scales while turning pulley first back- ward and again forward. The mean of the two readings will be the weight required. 199. Form of Log and Reports as used in Sibley Col- lege. Test of Belting by 189.. Description of Belt, Material Made by Length feet. Width inches. Thickness inches. Condition umber. u evolutions, Driving pulley. ip, percent. rc of Contact, per cent. Scale-readings, Ibs. 7 1- ension on Belt, Driving side. ension on Belt, Driven side. atio of Ten- sions. oefficient of Friction. ynamometer, Horse-power. cu E ynamom- eter. 3 2 ension. H & C/3 < Q CO H 5 jj H H Pi U Q a n * C A ^ C r,-r a ^i+^a r, T* r^T, f I 2 3 4 5 6 7 3 9 10 ii 12 13 14 15 16 17 18 19 20 Avg I99-] MEASUREMENT OF POWER. CONSTANTS OF MACHINE. 241 Symbol. Results. Arm of transmission-dynamometer Arm of Prony brake , Hor. arm on tension-scales Ver. arm on tension-scales , Diameter driving pulley Diameter driven pulley Face driving pulley Face driven pulley Area of bearings, driving wheel . . . " " " driven wheel. . . . Weight on bearings, driving wheel.. ' " " " driven wheel. . Kind of pulley used sq. in. . Ibs. FORM OF REPORT. Results of Test of Belting. Made by 189. . Average of Results. Test No. I. Test No. II. Test No. III. Test No. IV. D.uration of trial Revolutions driving shaft Revolutions driven shaft Dvnamometer-scales, Ibs Circumference driving pulley Circumference driven pulley Brake, horse-power. . . Horse power per inch in width Minimum tension, T-i 7-, -f 7' 3 CHAPTER VIII. MEASUREMENT OF LIQUIDS AND GASES. 200. Theory of the Flow of Water. General Formula of Disc/large. The theory of the flow of water is fully investigated in Weisbach's Mechanics, Vol. I.; in Church's Mechanics of Engineering; 'and in the article " Hydromechanics," Encyclo- paedia Britannica. A very concise statement of the principles involved and formulae required are given here, preceding the actual methods of measurement of the flow, but students are ad- vised to consult the foregoing works. In the flow of water the particles are urged onward by gravity, or an equivalent force, and move with the same velocity as bodies falling through a height equal to the head of water exerting the pressure. If this head be represented by h, and the corresponding velocity in feet per second by v, we have, neglecting friction losses, v= \2gh .......... (i) If we denote the area in square feet of the discharge ori- fice by Fj the quantity discharged in cubic feet per second by Q, then, neglecting contraction. >';*. . . (2) It is found, however, in the actual discharge of water, that, except in rare cases, I. The actual velocity of discharge is less than the theoretical ; 2. The area of the stream discharged is less than the area of the orifice through which it passes. These losses are corrected by introducing coefficients. The coefficient 242 20O.] MEASUREMENT OF LIQUIDS AND GASES. 243 of velocity is the ratio of the actual to the theoretical velocity, and is represented by c v . The coefficient of contraction is the ratio of the least area of cross-section of the discharged stream to the area of orifice of discharge, and is denoted by^. The coefficient of efflux or discharge is the product of these two quantities, and is represented by c. If v a denotes the actual velocity of discharge, we shall have v a = c, \ / 2g'h (3) The coefficient c v is to be determined by experiment ; it is nearly constant for different heads with well-formed simple orifices. It often has the value 0.97. The difference between the velocity of discharge and that due to the head may be expressed in terms of the equivalent loss of head. Thus the total head producing outflow consists of a part, h a , producing the actual velocity v a ; and a second part, h r , expended in overcoming velocity and friction. Denote the ratio of these parts by c r . Then h r = c r h a .......... v . (4) We also have A = *. + *. = *#,.+ i). ..... (5) Hence Since h a is the head-producing velocity, (7) 244 EXPERIMENTAL ENGINEERING. [ 2OI. By equating (7) and (3) we obtain the relation of c r to c v as follows: ^ = -L-i. ....... (8) ("0 The actual discharge (9) Since c = c v c c , -. . (10) From equation (9), 201. Formulae for Flow of Water over Weirs.* A weir is primarily a dam or obstruction over which the water is made to pass ; but the term is often applied to a notch opening to the air on one side, through which the water flows. In cases where the opening is entirely below the surface, it is spoken of as a submerged weir. The head of water producing the flow is the distance to the surface of still water from the centre of pressure of the issuing stream. The depth of the weir is meas- ured from the surface of still water to the bottom or sill of the notch. Rectangular Notch. Denote the coefficient of efflux bye, the depth of the weir in feet by /z, the area in sq. feet enclosed by the wetted perimeter by F, and the number of cubic feet per second by Q. We have, as a formula applicable to open rectangular notches, Q = %FcV^h ....... (ii) * See Church's Mechanics, page 684; Rankine's Steam-engine, p. 90; Encyc. Britannica, Vol. XII. p. 470; Bulletin on Irrigation and Use of Weirs, by Prof. L. G. Carpenter, Fort Collins, Colorado. 201.] MEASUREMENT OF LIQUIDS AND GASES. 245 With most areas c increases slightly with the length and diminishes with the head ; it probably depends on the ratio of wetted perimeter to area, although it is not quite constant for triangular notches, in which this ratio is a constant one. Very complete and extensive experiments were conducted by J. B. Francis at Lowell, Mass., and from these experiments he de- duced the value of the coefficient of contraction to equal one tenth the head, and consequently for rectangular weirs Q = $c(b (12) in which n = number of contractions. Applying this correc tion to an ordinary rectangular notch with two contractions we have the well-known Francis formula for rectangular weirs, Q o.2h)/i .(13) For heads ranging from three inches to two feet it has been found by experiment that c = 0.62 and Q = g-(b o.2h)k*. Triangular Notch. For the triangular notch in which apex is down, b the base at water-level, h the depth, (14) Q = (4 -T- ifybk V~2gh = 4. If the angle is 60, b = 2h tan 30 = 1.1547^5 and Q = 2.47^. If the angle is 90, b = 2h and = Trapezoidal Notch. To avoid the corrections for contrac- tions, Cippoletti of Milan in, 1886 proposed to use a trape- 246 EXPERIMENTAL ENGINEERING. [ zoidal notch of such dimensions that the area of the stream flowing through the triangular portion should be just sufficient to correct for the contraction of the stream in a rectangular weir. The proportions of such a weir, in terms of the length at bottom of the notch, is as follows : height equal to six tenths the bottom length, width of top equal to the bottom plus one fourth the height added to either side ; the tangent of the angle of inclination of the sides equal to 0.25. It is asserted that such a weir will give the discharge with an error less than one half of one per cent. The formula for the use of such a notch would be simply = 1^^^ = 3.33^ (15) Submerged orifices, rectangular or circular, are sometimes used for the measurement of water. The required formulae are given in the table following. From table in Weisbach's Mechanics, c on the average O.6. For small areas it diminishes with increase of head from 0.7 to 0.6, and for large areas it increases with increase of head from 0.57 to 0.60. These formulae are conveniently tabulated as follows : 202. Table of Formulae for Flow over Weirs. &d N *, i Scjj > if; 13 g|| Form of Notch. cl 5 \ J3 * Formula for discharge in cubic feet per second. ! ||S |H ^""o Rectangular: Usual form . . . h b .63 to .58 $cbh \/^gh h o b .622 / A/ 7/i i\ Submerged.. . h b f^f^ 1 -*' 1 ) r h h' b .62 ^(/6 - ^') V>(>4 -h *') Triangular: \ h o b' .617 iV^'yJ |/2^ I h o 2h tan a .617 -i^ebh? tan a -f/2^ Ang. at b. 120 h I.I547* .617 2.47^2 Ang. at b. 90 h o 24 .617 y 8 gM 2 tflgh Trapezoidal: Cippoletti's. . . h o * + P 0.62 %cbh ^"2gh 204-] MEASUREMENT OF LIQUIDS AND GASES. When still water cannot be found above the weir, and we have a velocity of approach that can be measured and is equal v 1 = V2gk', we can compute k ' . Then (16) In above formula Q = discharge in cubic feet per second, b the length of sill at bottom of notch. 203. Efflux of Water through Nozzles, or Conical Con- verging Orifices. In this case, if we denote least area in square feet by F, in which c" is the coefficient of contraction, c' that of velocity, and c that of discharge, Q = c'c"FV~2gh = cF V~2gh. (17) In this case the head is to be measured by a pressure-gauge attached close to the nozzle. The value of c is a maximum when the sides of the nozzle make an angle of 13 24', attaining a value of 0.946. When the angle of the nozzle is 3 io r , c = 0.895, and when 49, c = 0.895. (See Church's Mechanics, page 692 ; " Hydromechanics," Encyc. Brit., page 475.) 204. Efflux of Water through Venturi Tubes or Bell- mouthed Orifices. A conically divergent orifice, with rounded entrance to conform to the shape of the contracted vein, is now termed, from the first experimenter, Ventures tube. The dimensions of such a tube, as given in Encyc. Britannica, Vol. XII., page 463, are as follows, in terms of the small diameter (d). Large diameter (D) at opening equals 1.25^; length equals .625^, or .$D. The sides are in section a circular arc, struck with a radius of 1.625^, from a centre in the line of (a) produced. * Rankine's Steam-engine. 248 EXPERIMENTAL ENGINEERING. [ 205. The formula of discharge is ....... (18) in which /MS the least area, // the head to be measured by a pressure-gauge attached to the pipe before the area of cross- section is reduced, c' the coefficient of velocity. The coeffi- cient of contraction in this case is equal to one. Weisbach gives the value of c' as .959, -975, and .994 for heads respec* tively 2 feet, 40 feet, and 160 to 1000 feet. Prof. Church, in his Mechanics, page 694, describes an ex- periment on a conically divergent tube 3 inches long, .8 inch diameter at least section. Coefficient of discharge with heads from 2 to 4 feet varied from .901 to .914. 205. Flow of Water under Pressure. The pressure ex- erted by flowing water in pipes is very different from that due to still water under the same head. The pressure follows more or less closely the law enunciated in the theorem of Bernouilli, which may be stated in a general form as follows : " The exter- nal and internal work done on a mass is equal to the change of kinetic energy produced '/" that is, the total energy of a flowing stream remains constant except for losses due to friction. In the flow of water through a pipe with varying cross- section the velocity of flow will be very nearly inversely as the area of cross-section. Since the energy or product of pressure and velocity is nearly constant by Bernouilli's theorem, as the velocity increases the pressure must diminish, and we shall find least pressure at the points where the cross-sections are least. From some experiments made by the author, the same law of varying pressure with varying cross-section applies in a less degree to the flow of steam through a pipe.* The formula expressing Bernouilli's theorem, neglecting friction, is v* p _+_ + * = constant; *See "Hydromechanics," Encyc. Britannica, page 468. 206.] MEASUREMENT OF LIQUIDS AND GASES. 249 in which i? -f- 2g is the velocity-head, p is the pressure per square foot, y the weight per cubic foot ; so that p -^ y is the pressure-head, and z the potential head, or vertical distance from any horizontal reference line. 206. Flow of Water in Circular Pipes.* In this case there is a loss of head, h' , due to friction. Denote the sine of the angle of inclination by i, diameter by d, length by Z, loss of head by h p ' , all in feet coefficient of loss of head by C. From experiments of Darcy, C = 0.005^1 + -J for clean pipes; = o.oi \i -] -- -J for incrusted pipes ; C = O.a( I -| -- ^J in general ; ... ^.:^. . (21) of Head at Elbows. In this case the loss is principally due to contraction. Weisbach gives the following formulae: (22) See "Hydromechanics." Encyc. Britannica. 2$0 EXPERIMENTAL ENGINEERING. If equal the exterior angle, [206. , = 0.945 7 sin 2 + 2.047 sin 4 --. - ( 2 3) From this are deduced the following values : 20 0.046 4 0.139 60 0.364 80 0.740 90 0.984 100 1.26 IIO 1-556 1 20 1.861 130 2.158 For pipes neatly bent the value of C* is much less. By equating /// and h e r in equations (19) and (22), a length of pipe can be found which will produce a loss of head equiva- lent to that produced by any given elbow. We shall have this additional length : . 4? (24) On substituting the values of C* as above, and as equal to 0.006, this additional length will be found not to vary much from 40 diameters for each 90 elbow, and 7 diameters for each 45 elbow. Loss of Head on entering a Pipe. This loss is very small when a special bell-mouthed entrance is used, but is great in other cases. The loss of head in entering a straight tube is expressed by the formula (25) 20/.] MEASUREMENT OF LIQUIDS AND GASES. 251 Weisbach found c = 0.505. By making hp of equation (19) equal to h^ and reducing, we find the additional length, Z,, of straight pipe producing the same loss of head. Assuming C has an average value of 0.006, and C c as above, L = 20d. Loss of Head by abrupt Contraction of Pipe. In this case Weisbach found which would correspond to an additional length of pipe equal to about 13 diameters. When the mouth of the contracted pipe is .reduced by an aperture smaller than the pipe, Weis- bach found the following values of C,. In the table, F^ is area of orifice, F t that of pipe into which the flow takes place. K + F* . . . . O.I 0.016 0.2 0.614 0-3 O.6t2 0.4 0.610 0.5 0.607 0.6 0.605 0.8 0.601 I.O 0.596 t c , . . . 231.7 50.99 19.78 9.612 5.256 3-077 1.169 0.480 95O*/ 2I2(t 82^ 40^ 22d 13^ 5^ 2d Globe valves produce about one half more resistance than a right-angled elbow, or an amount equal to an additional length of about 60 diameters. 207. Loss of Head in flowing through a Perforated Diaphragm in a Tube of Uniform Section. Let F l be the area of the orifice, F that of the pipe in square feet, C the co- efficient of discharge, c the coefficient of contraction. 25 2 EXPERIMENTAL ENGINEERING. The loss of head in feet [ 208. (26) Weisbach gives the following values as the results of ex- periments : F\ F O.I 0.2 0-3 0.4 0-5 0.6 0.7 0.8 0.9 I.O C C 0.624 0.632 0.643 0.659 0.681 0.712 0-755 0.813 0.892 I.O - c 225.9 47-77 30.83 7.801 1-753 1.796 0.797 0.290 0.060 o.o 2o8. Volume flowing through a Perforated Diaphragm. Let H a represent the head in feet on side of greatest press- ure, and H b that on the opposite side. The loss of head From equation (26), by transposing and substituting, v = - ff *>- (27) The quantity discharged in cubic feet per second, .. (28) From this (28) 2IO.] MEASUREMENT OF LIQUIDS AND GASES. 253 209. Measurements of the Flow of Water. General Methods. The measurement of the flow of water is of import- ance in connection with efficiency-tests of pumps, water-meters, and steam-engines, as well as in determining the amount of water that can be obtained from, a given stream. The methods used for measurement of the flow usually con- sist in making the water pass through open notches over weirs, through standard orifices or nozzles, or through meters. The coefficients that have been given are in every case to be considered approximations only, and should be tested by actual measurement under the conditions of use. The head of water is the distance from -the centre of press- ure to the surface of still water under atmospheric pressure. In case the water is under pressure and at rest, this head can be measured by a calibrated pressure-gauge. The gauge is usually graduated to show pressure in pounds per square inch, each pound being equivalent to a head of 2.307 feet of water at a temperature of 70 Fahr., or to 2.037 inches of mercury. In case the water-pressure is read in inches of mercury, one inch of mercury corresponds to a head equal to 1.113 feet. A convenient table, showing relation of pounds of pressure- head in feet of water or inches of mercury, will be found in Article 260. 210. Flow of Water over Weirs. Methods of measuring the Head. The head is measured most accurately by the use of the hook-gauge, used first by Mr. U. Boyden of Boston in 1840, Many of the English engineers still depend on the use of floats. The head in all cases is to be measured at a distance sufficiently back from the weir to insure a surface which is un- affected by the flow. The channel above the weir must be of sufficient depth and width to secure comparatively still water. The addition of baffle-plates, some near the surface and some near the bottom, under or over which the water must flow, or the introduction of screens of wire-netting, serves to check the current to great extent. Such an arrangement is sometimes called a tumbling-bay. The object of the baffle-plates is to secure still water for the 254 EXPERIMENTAL ENGINEERING. accurate measurement of height of the surface above the sill of the weir. The same object can be accomplished by connecting a box or vessel to the water above the weir by a small pipe entering near the bottom of the vessel ; the water will stand in this vessel at the same height as that above the weir, and will be disturbed but little by waves or eddies in the main channel. The height of water is then obtained from that in the vessel. Prof. I. P. Church has the connecting-pipe pass over the top of the vessel and arranged so as to act as a siphon. The Hook-gauge. This consists of a sharp- pointed hook attached to a vernier scale, as shown in Fig. 98, in such a manner that the amount it is raised or lowered can be accurately measured. To use it, the hook is submerged, then slowly raised to break the surface. The correct height is the read- ing the instant the hook pierces the surface. To obtain the head of water flowing over the weir, set the point of the hook at the same level as the sill of the weir. The reading taken in this position will correspond to the zero-head, and is to be sub- tracted from all other readings to give the head of the water flowing over the weir. In some forms of the hook-gauge the zero. of FIG 98 HOOK- the main scale can be adjusted to correspond to GAUGE. t ^ e zero _head, or level of the sill of the weir. Floats. Floats are sometimes used : they are made of hol- low metallic vessels, or painted blocks of wood or cork, and carry a vertical stem ; on the stem is an index-hand or pointer that moves over a graduated scale. 211. Conditions affecting the Accuracy of Weirs. I. The weir must be preceded by a straight channel of con- stant cross-section, with its axis passing through the middle of the weir and perpendicular to it, of sufficient length to secure uniform velocity without internal agitation or eddies. 2. The opening itself must have a sharp edge on the up- 213-] MEASUREMENT OF LIQUIDS AND GASES. stream face, and the walls cut away so that the thickness shall not exceed one tenth the depth of the overflow. 3. The distance of the sill or bottom of the weir from the bottom of the canal shall be at least three times the depth on the weir, and the ends of the sill must be at least twice the depth on the weir from the sides of the canal. 4. The length of the weir perpendicular to the current shall be three or four times the depth of the water. 5. The velocity of approach must be small; for small weirs it should be less than 6 inches per second. This requires the channel of approach to be much longer than the weir opening. 4. The layer of falling water should be perfectly free from the walls below the weir, in order that air may freely circulate underneath. 5. The depth of the water should be measured with accuracy, at a point back from the weir unaffected by the suction of the flow and by the action of waves or winds. 6. The sill should be horizontal, the plane of the notch vertical. 212. Effect of Disturbing Causes and Error in Weir Measurements. I. Incorrect measurement of head. This may increase or decrease the computed flow, as the error is a positive or negative quantity. ; : " 4 2. Obliquity of weir ; the effect of this or of eddies is to retard the flow. 3. Velocity of approach too great, sides and bottom too near the crest, contraction incomplete, crest not perfectly sharp, or water clinging to the outside of the weir, tend in each case to increase the discharge. The causes tending to increase the discharge evidently out- number those decreasing it, and are, all things being taken into account, more difficult to overcome. 213. Water-meters. The water-meter is an instrument for measuring^ the amount of water flowing through a pipe. Knight makes seven distinct classes of water-meters, as follows:* * Knight's Mechanical Dictionary, Vol. III. 256 EXPERIMENTAL ENGINEERING. [ 2I 4 1. Those in which the water rotates a horizontal case, or a horizontal wheel in a fixed case, delivering a definite amount at each rotation. 2. A piston or wheel made to rotate by the pressure of the water, the meter in this case being the converse of the rotary engine or pump. 3. A screw made to rotate by the motion of the water. 4. A reciprocating piston in a cylinder of known capacity driven backward and forward by the pressure of the water. 5. The pulsating diaphragm, in a vessel of known capacity, which is moved alternately as the side chambers are filled and emptied. 6. The bucket and balance-beam, in which the buckets of known capacity on the ends of the beam, are alternately pre- sented to catch the water and are depressed and emptied as they become filled. 7. The meter-wheel, in which chambers of known capacity are alternately filled and discharged as the wheel rotates. Besides these seven classes, it is evident that any machine may be used in which the motion is proportional to the velocity of flow of water. These classes can be united into two general classes : I. Posi- tive; II. Inferential. In class I. the water cannot pass without moving the mechanism, and meters of this kind are considered more delicate and accurate than those in class II. Each class of meter has a registering apparatus, which in general consists of a series of gear-wheels, so arranged as to move a hand continuously around a graduated dial, from which the volume can be read. 214. Errors of Water-meters. In addition to the constant errors of graduation, meters are liable to be clogged by dirt, to be affected by air in the water, and by change in the tempera- ture, head, or quantity of discharge of the water passing through. While the rneter is no doubt of sufficient accuracy for com- mercial purposes, it should be used with caution in the measure- ment of water for tests or for purposes of scientific investiga- 21 5-] MEASUREMENT OF LIQUIDS AND GASES. tion. Before and after such tests a careful calibration of the meter should be made under the exact conditions of the test. The following directions explain the method of calibrating the weir notch and meter, arranged in series. In this experi- ment the water is to be weighed. Either instrument may be calibrated separately. In case the weir has been calibrated, the meter could be calibrated by direct comparison, without the use of weighing-scales. 215. Directions for Calibrating the Weir Notch and Meter. The object of this experiment is to determine the coefficient c of formula (9), Article 200, page 201, and the ac- curacy of previous determinations. Apparatus needed. Hook-gauge, pair of scales, thermom- eter, spirit-level, pressure-gauge, weir, and meter. 1. Accurately level the sill of the weir, and see that the notch is in a truly vertical plane. 2. Take the zero-reading of the^ hook-gauge, by setting the point of the hook with a spirit-level, at the same height as the sill of the notch. In case the form of the notch is such as to prevent the use of the spirit-level, grease the edge of the notch and set the hook by the water-level ; being sure that the water surface does not, through capillary action, rise above the lower edge of the notch. 3. Start the water flowing, and after it has obtained a con- stant rate, take measurements of weights and of head. The commencement of the experiment to be determined by the rising of the poise on the scale-beam, which previously must be set at a given weight. Note the time, scale reading, thermom- eter-reading, reading of the hook-gauge at the beginning and once in five minutes during the run. As the experiment ap- proaches the end set the poise of the scale-beam in advance of the weight, terminate the run when the beam rises, accurately noting the time, weight, thermometer-reading, and reading of the hook-gauge. Make direct measurements of the coefficient of contraction. Calculate coefficient of discharge. 4. If the water to the weir first passes through a meter, take corresponding readings of the. meter-dial. Note the pressure 2 5 8 EXPERIMENTAL ENGINEERING. [ 216. and temperature at the meter. Calculate the number of cubic feet. 5. Draw on cross-section paper a curve of discharge, in which cubic feet per second are taken as abscissae and the cor- responding heads as ordinates. Also draw in dotted lines on the same sheet a curve of coefficients, of discharge in which co- efficients are taken as abscissas, and corresponding heads as ordinates. Also, draw a curve showing error of meter for each head. 216. Form of Report. The following form has been used by the author for calibration of the weir notch and meter : CALIBRATION OF WEIR NOTCH AND METER. Made by. at.. Date. Number of Run. I. II. III. IV. V. Duration, minutes Temperature discharge, deg. F Max ft. ' " " Min ft. Av ft. * " Total Ibs Cubic feet per second Q. " End ft End Error per cent Constants of Weir, Form ....... Length ....... ft. Angle of sides. .. .... Remarks .............................................................. Meter, manf . by ................. General class ................. No . . . Remarks. Formulae: c 2 1 8.] MEASUREMENT OF LIQUIDS AND GASES. 2$$ 217. Calibration of Nozzles and Venturi Tubes. These are often more convenient to use than weir-notches, in the measurement of the efflux of water. Before using these they should be carefully calibrated by measurements of the head and discharge. The Venturi tube is sometimes inserted in a length of pipe ; in this case the pressure should be observed on either side of the tube, and the discharge measured. The special directions for calibrating when discharging into the air would be as follows : 1. Arrange the nozzle or Venturi tube, so that the discharge can be caught in tanks and measured or weighed. 2. Attach a pressure-gauge, which has been previously cali brated, to the pipe near the nozzle. Since the pressure is a function of the area of cross-section, the position of the gauge should be described and the area of the cross-section at that point measured. 3. Make careful measurements of least and greatest inter- nal diameters of nozzles, of length of nozzle, and note condition of interior surface. Make sketch showing the form. 4. Make five runs, as explained in directions for calibrating weir-notches, Article 215, page 258, obtaining weight of water by the same method. In case it is not convenient to weigh the water, discharge into tanks which have been carefully calibrated by weighing, arranged so that one is emptying while the other is filling. 5. Observe during run, reading of pressure-gauge, temper- ature of discharge-water, weight of discharged water. Com- pute corresponding head producing flow, volume of discharged water, and the coefficient of discharge in the formula 6. Draw a curve showing relation of discharge in cubic feet to head, as explained for weir-notches, page 258 ; also one showing relation of coefficient to head. 218. Measurement of Efflux of Water through an Ori- fice in End of Tube of Uniform Section. A cap can often 26O EXPERIMENTAL ENGINEERING. [ 2 1 9. be arranged over the end of a tube, and an orifice made in this cap with a sharp edge on the side toward the current, This will be found to give very uniform coefficients of dis- charge. The special method of calibrating this orifice would be as follows : 1. Arrange the tube with a cap in which is an orifice, the area of which is one third that of the pipe. Ream the sides of the orifice so that a sharp edge will be presented to the out- flowing water. Attach a calibrated gauge at a distance of two diameters of the pipe back from the orifice. Arrange to weigh or measure the discharged water.- Measure the orifice. 2. Make runs as explained for other calibrations with five different heads, and note reading of pressure-gauge, temperature of discharged water, weight or volume of discharged water, and least diameter of stream discharged. The least diameter of the discharged 1 stream can be measured by arranging two sharp- pointed set-screws in a frame, so that they can be screwed toward each other. These screws can be made to touch the outflowing stream, and the distance between their points meas- ured. 3. Compute head producing the flow, coefficient of con- traction, which is ratio of area of stream to area of orifice, coefficient of discharge, and loss of head. See equations (i) to (10), Article 200, page 201. 4. Draw curves on cross-section paper showing the relations of these various quantities. 5. Repeat the experiment with orifices of different sizes. 219. Measurement of the Flow of Water in Pipes by use of a Perforated Diaphragm or of a Venturi Tube. In this case the loss of head flowing through the orifice in the diaphragm or the Venturi tube must be measured ; then, know- ing the coefficient of efflux and area of cross-section, the vol- ume discharged can be computed by equation (28), Article 208, page 252. (28) 22O.] MEASUREMENT OF LIQUIDS AND GASES. 26 1 The difference of head is measured accurately by inserting tubes at a distance of two diameters on each side of the orifice, connecting each of these tubes to a U-shaped glass tube partly filled with water, very much as shown jn Fig. 104, page 266, except that the ends of the tubes A and B are in each case perpendicular to the pipe, and are on opposite sides of the diaphragm. The difference in the height of the water in the two branches of the U-shaped tube will be the loss of head (H a H b ) caused by the orifice. It is essential that the tubes be connected into pipes having equal areas of cross-section, since the pressure, even in the same line of pipe, increases with the area (see Article 205). The coefficient should be deter- mined by calibration, following essentially the same method as that prescribed for nozzles and Venturi tubes in Article 217. 220. Measurement of the Flow of Water in Streams.* This is done by (i) Floating bodies ; (2) Tachometer ; (3) Pitot's tube ; (4) Hydrometric pendulum. Floating bodies, when used, should be small, and about the density of the water. A floating body with a volume about one tenth of a cubic foot is better than larger. They can be made of wood and weighted, or of hollow metal and partially filled with water. A coat of paint will serve to render them visible. To obtain the velocity for different depths, the sur- face velocity is first found, the float is then connected with a weighted ball that can be adjusted to float at any depth, and the joint velocity observed. Call the surface velocity V Q , the joint velocity v m ; then will the velocity of the submerged ball be v, 2v m v . A floating staff that remains vertical in still water is some- times used. In case floats are used, the velocity is obtained by noting the time of passing over a measured distance. The measured distance should be marked by sights, so that the line of begin- * See Weisbach's Mechanics, Vol. I. 262 EXPERIMENTAL ENGINEERING. [ 221. ning and ending can be accurately determined. The float is put in above the initial point, and the instant of passing the FIG. 99. THE TACHOMETER. first and last lines of the course is to be determined by a stop- watch. 221. The Tachometer, or Woltman's Mill, consists of a small water-wheel connected to gearing so as to register the 221.] MEASUREMENT OF LIQUIDS AND GASES. 263 number of revolutions. The wheel is anchored at the required depth in the stream, and at a given instant, the time of which is noted on a stop-watch, the gearing is set in motion by pull- ing on a lever ; at the instant of stopping the experiment, the gears are stopped by a trip. The machine is removed, and the number of revolutions multiplied by a constant factor gives the total space moved by the water; this divided by the time gives the velocity. The shape of the vanes of the revolving wheel are varied by different makers, an.d the wheel is made to revolve either in a horizontal or a vertical plane. Fig. 99 shows a form used extensively, in which the gearing for registering the number of revolutions is operated by an electric current, and can be seen at any instant. The electric register shown in Fig. IOO can be located at any distance from the tachometer convenient to the observer. Calibration. The constant factor, which multiplied into the dial-reading gives the velocity, is obtained by calibration. The calibration is performed by attaching the instrument to a float or a boat, and towing it past fixed marks at a known dis- tance from each other. The velocity is obtained as for floating bodies, and the constant is found by comparing this with the readings of the instrument. One method of calibrating the FIG. ioi . instrument is as follows (see Fig. ioi) : The instrument is attached to the bow of a boat, so as to remain in a vertical position ; the water being still, and little or no current. The boat is propelled by a cord, which may be wound up by a windlass ; the motion must be in a right line, and over a known 264 EXPERIMEN TA L ENGINEERING. [ 222. distance. Several trials are to be made, and the average results taken, and reduced by the method of Least Squares, as ex- plained in Chapter I. The tachometer is the most convenient, and if properly constructed the most accurate, method of measuring the ve- locity of running water. 222. Pilot's Tube. This is a bent glass tube, held in the water in such a manner that the lower part is horizontal and opposite the motion of the current. By the impulse of the current a column of the water will be forced into the tube and held above the level of the water in the stream ; this rise, DE (see Fig. 102) is proportional to the impulse or to the velocity of the water that produces it. If the height DE above the surface of the water equal h and the velocity of the water equal v, we have in which c equals the coefficient to be determined by experiment. To determine the coefficient c, the instrument is either to be held in moving water whose velocity is known, or else moved through the water at a constant velocity. From the known value of v and the observed value of h the coefficient c can be calculated. Weisbach found that with fine instruments, when the velocities were between 0.32 and 1.24 meters (1.04 and 4.068 feet) per second, that v = 3-545 Vh meters per second, or, in English measures, v 6.43 Vh feet per second. 222.] MEASUREMENT OF LIQUIDS AND CASES. 265 Pitofs tube, as ordinarily used, is shown in the diagram Fig. 103. It consists of two tubes, one, AB, bent as in Fig. 102, the other, CD, vertical. The mouth-pieces of both tubes are slightly convergent, to prevent rapid fluctuation in the FIG. 103. SKETCH OF PITOT'S TUBE. tubes. These tubes are so arranged that both can be closed at any instant by pulling on the cord ~ss leading to the cock R. Between the glass tubes dD and bB is a scale which can be read closely by means of the sliding verniers m and ;/. The tubes are connected at the top, and a rubber tube with a mouth-piece O is attached. In using the instrument it is fastened to a stake or post by the thumb-screws EF\ the bent tube is placed to oppose the current of water, the cocks K and R opened. The difference in height of the water in the tubes will be that due to the velocity of the current. The water in the column dD will not rise above the surface of the surrounding water, and the instru- ment may be inconvenient to read. In that case some of the air may be sucked out at the mouth-piece O, and the cock K closed ; this will have the effect to raise the water in both 266 EXPERIMENTAL ENGINEERING. [ columns without changing the difference of level, so that the readings can be taken in a more convenient position ; or by clos- ing the cock K, by pulling on the strings ss, the instrument may be withdrawn, and the readings made at any convenient place. 223. Pitot's Tube for High Pressures. A modified form, as shown in Fig. 104, of Pitot's tube is useful for obtain- ing the velocity of liquids or gases flowing under pressure. The arrangement is readily understood from the drawing. The difference of pressure is shown by the difference in heights FIG. 104. SKETCH OF PITOT'S TUBE FOR GREAT PRESSURES. of the liquid in the branches of the U-shaped tube eGH', this difference is due entirely to the velocity, since both branches are under equal pressure. Thus, if the liquid stand at m on one side and at n on the other, the velocity is that due to the height of a column of liquid equal to the distance that m is above n. Call this distance h ; then v = c The coefficient c is to be determined by experiments made on a tube in which the velocity of flow is known. 225-] MEASUREMENT OF LIQUIDS AND GASES. 26/ 224. Hydrometric Pendulum. This instrument consists of a ball, two or three inches in diameter, attached to a string. The ball is suspended in the water and carried downward by the current ; the angle of deviation with a vertical may be measured by a graduated arc supported so that the initial or zero-point is in a vertical line through the point of suspension. If the current is less than 4 feet per second an ivory ball can be used, but for greater velocities an iron ball will be required. The instrument cannot give accurate determinations, because of the fluctuations of the ball and consequent variations in the angle. The formulae for use are as follows: Let G equal the. weight of the ball, D equal the weight of an equal volume of water ; then G D is the resultant vertical force. Let F equal area of cross-section of the body, v the velocity of the current, c a coefficient to be determined by experiment ; then we have the horizontal force P = cFv*. Let angle of deviation be d ; then P cFv* --G=~D-~G~^D> from, which (-/?) tan d ^F The best results with this instrument will be only approxi- mations. 225. Flow of Compressible Fluids through an Orifice. General Case. In this case, as heat is neither given nor taken up, the flow is adiabatic. The formulae are deduced by prin- ciples of thermodynamics, and their derivation can be studied in treatises devoted to those subjects.* Denote the velocity by v, the weight per cubic foot by G, the pressure per square foot in the vessel from which the flow * See Peabody's Thermodynamics, p. 132; also, art. "Hydromechanics," Encyc. Britannica. 268 EXPERIMENTAL ENGINEERING. [ 226. takes place by / lt the pressure against which the flow takes place by/ 2 , the volume of one pound in cubic feet by C, the absolute temperature corresponding to pressure / t by T lt the ratio of specific heats by y. 7' 2 / V * A **' ' ~ P 2,~ also, 7 , A ~ 226. Flow of Air. For air, / = 2116.8, ^ = 0.08075, T = 492.6 at 32 Fahr., y = 1.405. Inserting these numerical values, we have the following equation for the theoretical velocity of flow of air through an orifice: 2,2 f / ^\o.2Q ) * 1^83.67; {'i -(|| }. . . (31 Volume of Air discharged. The volume of air discharged, in cubic feet per second at pressure of discharge, is to be com- puted by multiplying the area of the orifice F l in square feet, by the velocity 7;,, by a coefficient of discharge c. Then Substituting numerical values for the ratio of / 2 to/j, we have &= 108.7^1/0.16957; (33) * See article " Hydromechanics," Encyc. Britannica, Vol. XII, page 481. 22;.] MEASUREMENT OF LIQUIDS AND CASES. 269 To express this in terms of the volume discharged from the reservoir <2, , in which p l is reservoir pressure and / a pressure of discharge, we have Substituting numerical values for free flow, i G, = (0.527)^0, = 0.63390,5 Substituting values of/ 2 -:-/,, , = 68.8^ Vo. 1 6957;. (35) 227. Velocity of Flow of Air through an Orifice. The velocity of flow is obtained by substituting numerical values in the preceding equations. We have, denoting by T l the abso- lute temperature in the reservoir as the greatest velocity of flow of air, = 183.6 r,(i- 0.8305). (36) Solving equation (36), we have the following theoretical results : Temperature of Air in Reservoir. Velocity of Flow in Feet Degrees Fahr. Absolute. per Sec. 32 492.6 991 70 530.6 1030 100 560.6 1058 150 610.6 1105 200 660.6 1148 300 760.6 1233 400 860.6 I 3 I2 5OO 960.6 1386 270 EXPERIMENTAL ENGINEERING. [ 228. 228. The Weight of Air discharged. This is to be com- puted by multiplying the volume of discharge by the specific weight. Thus the weight of air is G l = - ^F pounds per cubic foot, when p } and T l are, respectively, pressure and absolute tem- perature in the reservoir. Hence the weight of air dis- charged is *: Q^- a-^.gJV^'-K) (37) Weisbach has found the following values of c, the coefficient of discharge : Conoidal mouth-piece of the form of the con- tracted vein, with effective pressures of 0.23 to i.i atmospheres 0.97 to 0.99 Circular sharp-edged orifices 0.563 to 0.788 Short cylindrical mouth-pieces 0.8 1 to 0.84 The same rounded at the inner end 0.92 to 0.93 Conical converging mouth-pieces 0.90 to 0.99 In the general formula for the flow of air, the weight de- livered becomes a maximum when /. v + This equals 0.527 for air and 0.58 for dry steam. This has been verified by experiment, and tends to prove that the press- ure of the orifice of discharge is independent of the back- pressure. In the flow of. air from a higher to a lower pressure 229.] MEASUREMENT OF LIQUIDS AND GASES. 2/1 through a small tube or orifice, the pressure in the orifice may be less than the back-pressure. 229. Flow of Air in Pipes. When air flows through a long pipe, a great part of the work is expended in overcoming fric- tional resistances. This friction generates heat, which is largely used in increasing the pressure in the pipes, the only loss being from radiation, which is small. The expansion then is isothermal, the heat generated by friction exactly neutralizing the heat due to work. For pipes of circular section, when d is the diameter, /the length, p 9 the greater and p^ the less pressure, T the absolute temperature, C the coefficient of discharge, c p (= 53.15 foot-lbs.) the specific heat, we have the velocity (38) This may be reduced to 4V It has been found from recent experiments that fair values of the coefficient are as follows: * in ordinary pipes for velocities of 100 feet per second ; , , /...._,, c = - 0028 ( I + ii) for pipes as smooth as those at the St. Gothard Tunnel. See " Hydromechanics," Encyc. Britannica, Vol. XII, p. 491. 2/2 EXPERIMENTAL ENGINEERING. [ 230. Weight of air flowing per second in circular pipes in pounds is given by the equation Approximately, W =(0.69 1 6A- 0.4438A) - (39) 230. Flow of Steam through an Orifice. Velocity. In this case, as in Article 226, the expansion is supposed to be adiabatic. Denote by A the reciprocal of the mechanical equivalent of one B. T. U. corresponding to the quantity 778 ; by x l the quality or percentage of dry vapor in the reservoir, corre- sponding to the pressure per sq. foot/! , and by jr 2 the quality in the tube, corresponding to pressure / ; by r l the latent heat per pound in reservoir, ?\ the same in the tube ; 7^ and T^ the respective absolute temperatures, B l and a the respective entropies of the liquids, c the specific heat of the liquid, q l and q^ the sensible heat of the liquid in reservoir and tube ; the reciprocal of the weight of a cubic foot of the liquid by 0\ Then Av* - = x^ - *S, J r q i -q^A C, and is received by the curved buckets FF, and finally discharged on the inside of the wheel. In the figure G, G is the outer casing of the wheel, N the support. FIG. 113. HORIZONTAL IMPULSE- WHEEL. Most of the small motors are of this class ; the Backus motor using a jet at the top of the wheel and small curved buckets, the Pelton using a jet at the bottom of the wheel and a hemispherical bucket, with a centre partition which divides the jet into two portions, The efficiency of the Pelton wheel, which is also made in large sizes, has exceeded in some in- stances 0.92. 245. Turbines. The turbine-wheels receive water con- stantly and uniformly, and usually in each bucket simultane- ously. The buckets are usually curved, and the water is guided into the buckets by fixed plates. The name was originally applied in France to any wheel rotating in a horizontal plane, but the wheels are now frequently erected so as to revolve in vertical planes. The turbine was invented by Fourneyron in 1823, the original wheel being constructed to receive water near 288 EXPERIMENTAL ENGINEERING. [ 246. the axis, and to deliver it by flow outward at the circumfer- ence. Turbines are now built for water flowing parallel to the axis, and also inward from the circumference toward the centre ; they are also constructed double and compound. In some of the turbines the wheel-passages or buckets are com pletely filled with water, in others the passages are only partly filled. The following classes are usually recognized : I. Impulse Turbines. II. Reaction Turbines. In both these classes the flow may be axial outward, in- ward, or mixed, and the turbine may be in each case simple, double, or compound. In the Impulse turbines the whole available energy of the water is converted into kinetic energy before it acts on the mov- ing part of the turbine. In these wheels the passages are never entirely filled with water. To insure this condition they must be placed a little above the tail-water and discharge into free air. In the Reaction turbines a part only of the available energy of the water is converted into kinetic energy before it acts on the turbine. In this class of wheels the pressure is greater at the inlet than at the outlet end of the wheel-passages. The wheel-passages are entirely filled with water, and the wheel may be, and is generally, placed below the water-level in the tail-race. 246. Theory of the Turbine. * The water flowing through a turbine enters at the admission-surface and leaves at the dis- charge-surface of the wheel, with its angular momentum rela- tive to the wheel changed. It must exert a couple M, tend- ing to rotate the wheel, and equal and opposite to the couple M which the wheel exerts on the water. Let Q cubic feet enter and leave the wheel per second, c l , c^ be the tangential com- ponents of the velocity of the water at the receiving and dis- charging surfaces of the wheel, r 1 , r^ the radii of these surfaces. Then -M= ( ^(c,r,-c l r l }. . . ; ,: : .'.; (I) * See "Hydromechanics," Encyc. Britannica. 246.] HYDRAULIC MACHINERY. 2%g If a is the angular velocity of the wheel, the work done on the wheel is CO T = Ma = - (c^r l CJ^OL foot-pounds per second. (2) g The total head of the water h t is reduced by friction and resistances h p in the channels leading to the wheel, so that the effective head h which should be used in calculating the efficiency is h=.h t -h p (3) In case the construction of the turbine requires that it set above tail-race d feet, the velocity of water in the turbine should be calculated for a head of h d, but the efficiency for a head of h feet. The work of the turbine is partially absorbed in friction. Let T equal the total work, T d the useful work, and T t the work used in friction. Then T=T d +T t . . ._.. .; ,, : ; . . (4) The gross efficiency / J- H The hydraulic efficiency r The hydraulic efficiency is of principal importance in th< theory of turbines. Substituting this value of T in equation (2] which is the fundamental equation in the theory of turbines. 2QO EXPERIMENTAL ENGINEERING. [ 247. For greatest efficiency the velocity of the water leaving should be o, in which case c^ = o and But r^a is the lineal velocity of the wheel at the inlet surface ; if we call this V l , The efficiency of the best turbines is 0.80 to 0.90. Speed of the Wheel. The' best speed of the wheel depends on frictional losses which have been neglected in the preced- ing formulae. The best values are the ones obtained by ex- periment. Let V Q equal the peripheral velocity at outlet, V t at inlet, r and r i the corresponding radii of outlet and inlet surfaces. Then we shall have as best speeds* for axial-flow turbine F V { = 0.6 V'2gk to 0.66 V2gh ; radial outward-flow turbine <. = 0.56 V2gh ; V = J/ t - ; r. r. radial inward-flow turbine V t = 0.66 \/2gh ; F V i - . f\ 247. Forms of Turbines. Fourneyrons Turbine. This is an outward flow turbine, with a horizontal section as shown in Fig. 114. C is the axis of the wheel, which is protected from the water by vertical concentric tubes shown in section. On the same level with the wheel and supported by these tubes is a fixed cylinder, with a bottom but no top, contain- ing the curved guides F F. The wheel AA is supplied with curved buckets bd, b l d l , so arranged as to absorb most of the energy of the -water ; the water enters the wheel at the inner edges of the buckets and is discharged at the outer circum- * " Hydromechanics," Encyc. Britannica. 248.] // YDKA ULIC MA CHINE R Y. 291 ference. Gates for regulating the supply of water are shown in section between the ends of the guides and the wheel. FIG. 114. OUTWARD-FLOW TURBINE. 248. Reaction -wheels. The simple reaction-wheel is shown in Fig. 115, from which it is seen to consist of a vertical cylinder, CB, which receives the water, and two cylindric arms, G and F\ on opposite sides of each arm is a circular orifice through which the water is discharged. The effect of this arrangement is to reduce the pressure on the sides toward the ori- fices, thus producing an unbalanced pressure which tends to make the wheel revolve. If we denote by Ji the available fall measured from the level of the water in the vertical pipe to the centre of the orifices, r the radius of rotation measured from the axis to the FlG - "S--THE REACTION-WHEEL. centre of each orifice, v the velocity of discharge, a the angular velocity of the machine, F the area of the orifices, when at rest the velocity would equal V2gk, but when in motion the water in the arms moves with a velocity ar, which corresponds to an increased head due to centrifugal force of arV 2 ~ 2g. 2Q2 EXPERIMENTAL ENGINEERING. [ 248. Hence the velocity of discharge through the orifices is v = \/2gh the quantity discharged Since the orifices move with a velocity cxr, the velocity with reference to a fixed point is v cxr. If G be the weight per cubic foot, the momentum or mass times the velocity is ~(v-ar) This mass moves with an angular velocity a and arm r, hence the work done per second in rotating the wheel is -(v ar)ar foot-pounds. <5 The work expended by the water-fall is GQh. Hence the efficiency (v ar)otr This increases as cxr increases, or the maximum efficiency is reached when the velocity is infinite. The friction considera- bly reduces these results, and experiment indicates the greatest efficiency when cxr \/2gh. In which case, by substitution, we should have " = 0.828. The best efficiency realized in prac- tice with these wheels is about 0.60. The Scottish turbine, shown in Fig. 1 16 in section, is a reaction-wheel with FIG. xi6. SCOTTISH TURBINE, three discharge-jets, the water being Supplied from a tube filled with water under pressure beneath the wheel. 2 49 .] HYDRAULIC MACHINERY. 293 249. The Hydraulic Ram. The hydraulic ram is a ma- chine so arranged that a quantity of water falling a height h forces a smaller quantity through a greater height k f . FIG. 117. HYDRAULIC RAM. The essential parts of the hydraulic ram are: I. The air- chamber C, connected with the discharge-pipe eD, and pro- vided with a clack or check-valve Revolutions of pump per minute Water pumped in lb s Duration of test mins. ( Depth of water on weir ft. ^ ( Temperature at weir (corrected) C. F. ( Suction-gauge (corrected) ins. .ft. a Discharge-gauge (corrected) lbs. ft. rt J I Actual suction ft. [_ Actual head .%:. ft. ( cu . ( Scale-reading ..lbs. 3 6 ^ - M I 3.5 ( Revolutions per minute.. ? j 4J ( Scale-reading , lbs. CL, L H ( Revolutions per minute Water pumped in minutes , lbs. Capacity in gallons per minute Total work by power-scale (pumping) H. P. Tare H. P. Work given to pump H. P. Work delivered by pump H. P. Efficiency per cent. Duty (ft. -lbs. per 1,000,000 B. T. U.) Signed LOG OF TEST ON ROTARY PUMP. No.. Date.. No. of Gong. Time. Total. Av Cor. Power-scale. Pumping. Counter Revolu- Weight. Tare. C. R. W Gauges. SucLion, inches mercury Deliv- ery, lbs. per sq. in. Orifices. Head, in feet. Temper- 306 EXPERIMENTAL ENGINEERING. [258 RESULTS OF TEST ON ROTARY PUMP. Duration of test min. Power-scale, pumping, revolutions per minute " " weight Ibs. tare, revolutions per minute " " weight Ibs. Suction-head by gauge, ...... .inches mercury ft. H 2 O Discharge-head by gauge Ibs. per sq. in " Head on orifices " Temperature C F. Revolutions of pump per minute Area of discharge at gauge sq. ft. Vertical distance between gauges ft. Diameter of orifices, a. . . . , b. . . ., c d. . . ., e. . . ., f . . ., g. . . ., h. . . ., i. . . . Coefficients, a. . . ., b. . . ., c. . . ., d. . . ., e. . . ,/"...., g. . . ., h. . . ., i. . . . Constant for power-scale ft. Power-pumping, by scale H. P. Tare.. H. P. Power given to pump H. P. Velocity-head of discharge ft. Total head press, heads -|- vel. head -f- vert. dist. bet. gauges ft. Water pumped .Ibs. per sec. "Work done by pump .... H. P. Efficiency of pump , per cent. Capacity of pump in gallons per minute .Duty of pump (ft. -Ibs. per 1,000,000 B. T. U.) Signed , II. METHODS OF TESTING THE STEAM-ENGINE. CHAPTER X. DEFINITIONS OF THERMODYNAMIC TERMS. 259. General Remarks. The methods of testing the steam-engine which are given here presume an accurate knowledge of the principles of action of the engine, an ac- quaintance with the details of its mechanism, and a knowledge of the thermodynamic principles which relate to the transfor- mation of heat energy into work. In connection with the methods of testing, the student is advised to read one or more of the following books : Manual of the Steam-engine, by R. H. Thurston. 2 vols. N. Y., J. Wiley & Sons. Manual of Steam-boilers. Ibid. Engine and Boiler Trials. Ibid. Etude Experimental Calorimetrique de la Machine a Vapeur, par V. Dwelshauvers-Dery. Paris, Gauthier-Villars et Fils. Steam-engine, by D. K. Clark. 2 vols. N. Y., Blackie & Co. Steam-engine, by C. V. Holmes. I vol. London, Longmans, Green & Co. Steam-engine, by J. M. Rankine. I vol. London, Chas. Griffin & Co. Steam-making, by C. A. Smith, i vol. Chicago, American Engineer. Steam-using. Ibid. 307 308 EXPER1MEN TAL ENGINEERING. [ 260. Steam-engine, by James H. Cotterill. London, E. & F. N. Spoil. Thermodynamics, by C. H. Peabody. N. Y., J. Wiley & Sons. Thermodynamics, by De Volson Wood. N. Y., J. Wiley & Sons. Thermodynamics, by R. Clausius. N. Y., Macmillan. Steam-tables, by C. H. Peabody. N. Y., J. Wiley & Sons. Handy Tables, by R. H. Thurston. N. Y., J. Wiley & Sons. 260. Relations of Units of Pressure. The term pressure, as employed in engineering, refers to the force tending to com- press a body, and. is expressed as follows : (i) In pounds per square inch; (2) In pounds per square foot; (3) In inches of mercury ; (4) In feet or inches of water. The value of these different units of pressure are as follows: TABLE SHOWING RELATION BETWEEN PRESSURE EXPRESSED IN POUNDS, AND THAT EXPRESSED IN INCHES OF MERCURY, OR FEET OF WATER. 70 Fah. Pressure in Pressure in pounds per sq. inch. pounds per sq. foot. Inches of mer- cury. Feet of water. Inches of water. I 144 2.0378 2.307 27.68 2 288 4.0756 4.614 55-36 3 432 6.1134 6.921 83.04 4 576 8.0512 9-23 110.72 5 720 10. 1890 11-54 138-40 6 864 12.2268 13-85 166.08 7 1008 14.2646 16.15 103.76 8 1152 16.3024 18.46 221.44 9 1296 18.3402 20.76 24Q.I2 10 1440 20.3781 23.07 276.80 The barometer presstire is that of the atmosphere in inches of mercury reckoned from a vacuum. At the sea-level, latitude of Paris, the normal reading of the barometer is 29.92 inches, corresponding to a pressure of 14.7 pounds per square inch. Gauge or Manometer pressure is reckoned from the atmos- pheric pressure. Absolute pressure is measured from a vacuum, and is equal to the sum of gauge-pressure and barometer readings expressed 26 1.] DEFINITIONS OF THERMODYNAMIC TERMS. 309 in the same units. Absolute pressure is always meant unless otherwise specified. Pressure below the atmosphere is usually reckoned in inches of mercury from the atmospheric pressure, so that 29.92 inches would correspond to a perfect vacuum at sea-level, latitude 49. 261. Heat and Temperature. The term heat is used sometimes as referring to a familiar sensation, and again as applying to a certain form of energy which is capable of pro- ducing the sensation. In this treatise it is used in the latter sense only. Temperature is essentially different from heat, and is merely one of its qualities ; it is difficult to define, but two bodies are of equal temperature when there is no tendency to the trans- fer of heat from one to the other. Temperature is measured by the expansion of some substance in an instrument termed a thermometer. Two points, that of melting ice and of steam from water boiling at atmospheric pressure, are fixed tempera- tures on all scales of thermometry. The expansion between the'se points is divided into various parts according to the scale adopted, and each part is termed a degree. The following thermometric scales are in use in different portions of the world : Fixed Points, Temperature of Water. Fahrenheit. Centigrade. Rdaumur. Degrees between freezing and boil- \ ' 180 100 80 Temperature at freezing point 2,2 o o I 9 5 I I < ( 1 4 I Degrees of temperature taken on one scale can easily be reduced to any other; thus, let t f be the temperature of a body on the Fahrenheit scale, t c on the Centigrade scale, and t r on the Re"amur scale. We shall have, from the preceding table, t f = |4 + 32 I t e = -!('/ - 32) ; tf = K + 32. 3 io EXPER1MEN TA L ENGINEERING. [' 262. The Fahrenheit thermometer is used principally by English- speaking people, and unless otherwise mentioned is the one us id in this treatise. The Thermometric Substances principally used are mercury, alcohol, and air, from the expansion of which the temperature is obtained. Absolute Zero. This quantity is fixed by reasoning as the point where gaseous elasticity or expansion would be zero. This is 492, more exactly 491.8, of the Fahrenheit scale or 273 + * of the Centigrade scale below the freezing-point of water, so that in the Fahrenheit scale the absolute tempera- ture is 460 -|- tne reading of the thermometer, and on the Centigrade scale 273 + the reading of the thermometer. Absolute Temperature, on any scale, is temperature reckoned from absolute zero. 262. Specific Heat. Specific heat is the ratio of that re- quired to raise a pound one degree in temperature compared with that required to raise one pound of water from 60 to 61 Fahr. Specific heat of water is not quite constant, but varies as follows : f Centigrade. Fahrenheit. Specific Heat. Centigrade. Fahrenheit. Specific Heat. O 32 1.0072 30 86 0.9954 5 41 1.0044 35 95 0.9982 10 50 I.OOI6 40 104 I. 0000 15 59 I .OOOO 45 113 1. 008 20 68 0.9984 155 3H 1.046 25 77. 0.9948 200 392 1.046 Specific heat of saturated steam at atmospheric pressure was found by Regnault to equal 0.478. Investigations made at Sibley College would seem to indicate that the specific heat of steam increases with the pressure and temperature. The heat contained in different bodies of the same tempera- * Encyc. Brit., Vol. XI. p. 573. f See Peabody's Steam-tables. .264.] DEFINITIONS OF THERMO DYNAMIC TERMS. 311 ture, or in the same body in its liquid and gaseous condition, is quite different and cannot be measured by the thermometer. Thus in equal weights of water and iron at the same tempera- ture, the heat in the water is several times that in the iron. This is known because in cooling a degree in temperature, water will heat a much greater weight of some other substance. 263. Mechanical Equivalent of Heat. The experiments made by Rumford and Joule established the fact that heat- energy could be transformed into work, or vice versa. The re- sults of Joule's latest determination gave the mechanical work equivalent to the heating of one pound of water one degree Fahr. in temperature as 774 foot-pounds, while the later and more refined determinations of Rowland, reduced to 45 of latitude and to the sea-level, make the mechanical work equivalent to the raising the temperature of one pound of water from 62 to 63 Fahr. to be 778 foot-pounds. The heating of one pound of water one degree, from 39 to 40 Fahr., is termed a British thermal unit, B. T. U., and this is equivalent in me- chanical work to 778 foot-pounds. This number is represented by J and its reciprocal by A throughout this work. The heat needed for raising one kilogram of water one de- gree Centigrade is termed a calorie, and this is equivalent to 426.9 foot-pounds. In some treatises a British thermal unit is the heat required to raise one pound of water from 62 to 63 Fahr., which differs little from that defined above. 264. Relations of Pressure and Temperature of Steam. There is a definite relation between the temperature and pressure of steam in its normal or saturated condition. This relation was very carefully investigated 1836-42 by M. V. Reg- nault in Paris by a series of careful experiments made on a large scale. These experiments form the basis of our experimental knowledge of the properties of steam. The properties of steam are also shown by the thermody- namic laws, and are given in tables of Rankine, Clausius, M. V. Dwelshauvers-Dery, Peabody, and Buel. The following empirical formula, deduced from Regnault's 312 EXPERIMENTAL ENGINEERING. [ 265. experiments, gives the relation between the temperature and pressure of steam at a latitude of 45 : For steam* from 32 to 212 Fahr. pressure in pounds per square inch, in which a = 3.025908, log b 0.61174, log c 8.13204 10, log;* = 9.998181015 10, log B = 0.0038134, T=t 32. For steam from 212 to 428 Fahr., in which a, = 3-74397 6 > log ^ = 04120021, log c, = 7.74168 - 10, logtf, =9.998561831 10, log ^ = 0.0042454, T= t 212'. 265. Properties of Steam. Definitions. Steam occurs in two different conditions: i, saturated ; 2, superheated. 1. Saturated Steam. This can exist only in contact with the water from which it was generated, although the quantity of water present may be very small. Saturated steam of any pressure is at the lowest tempera- ture and possesses the least specific volume and the greatest density consistent with that pressure. The slightest decrease in temperature results in partial condensation, forming what is termed moist or wet steam, in distinction from dry steam. Thus saturated steam may be either wet or dry. The percentage of dry steam in a mass of wet steam is termed its quality. 2. Superheated steam cannot exist in contact with the water from which it was generated. Its temperature is higher, its specific volume greater and its density less than saturated steam of the same pressure. Steam-tables give the properties of dry saturated steam only and usually arranged with absolute pressure as the argument or given quantity. The important properties are as follows : (a) Total Heat (symbol, A). This is the amount of heat required to convert one pound of water from 32 into saturated * Steam-tables, by Prof. Cecil H. Peabody. 265.] DEFINITIONS OF THERMOD YNAMIC TERMS. 313 steam at a pressure P. If t is the temperature of the steam, the total heat, A, is calculated by an empirical formula based on the experiments of Regnault. Expressed in English units, A 1081.4 + 0.305/. (b] Heat of the Liquid (q) is the number of thermal units used in heating one pound of water from 32 Fahr. to the tem- perature required to generate steam. According to Regnault, q = t -|- O.OOOO2/ 2 -f- O.OOOOOO3/ 2 for Centigrade units. And according to Rankine for English units when t l is the initial and t the final temperature, q = t - t, + o.ooooooio3[(/ - 39.i) 3 - (/, - 39- 0']- (c] Internal Latent Heat (/>). This is the work done, measured in thermal units, in separating the molecules of the steam beyond the range of mutual attraction. It is calculated from the formula p = 1 06 1 0.79 it. (d) External Latent Heat (APu). This is the work, ex- pressed in heat-units, of expanding the steam against an external pressure which is equal to that of the steam generated. Thus, let u = s cr be the difference in volume of a pound of steam, s, and a pound of water, By opening the cock and elevating the bottle, mercury will FIG. 138. PRESTON AIR-THERMOMETER. pass into the tubes : when it reaches the height of the mark a, the connecting cock B is closed, and the amount that the col- umn BE extends above the level of this mark, or fails of reaching this level, is read on the scale. Hoadley Air-thermometer. The Hoadley air-thermome- ter, as described in the Transactions of the American Society of Mechanical Engineers, Vol. VI., page 282, is shown in Fig. 139, with all the dimensions marked. It differs from the preceding one in having no means provided for introducing or removing mercury to maintain the volume of air constant. The tube con- nected to the air-bulb, instead of being capillary, is about inch diameter. The instrument consists of a U-tube about 288.] MEASUREMENT OF TEMPERATURE. 345 f inch external diameter, y 1 ^- bore, having a short leg about 39 inches long, and the other leg longer by 12 inches or more, the latter sur- mounted by a bulb blown out of the tube if inches in diameter, 6f inches in extreme length. The branches of the U-tube are 2 inches apart and vertical ; these are separate tubes, each one bent to a right angle by a curve of short radius, ground square and true at the ends and united by a short coupling of rubber tubing, eaj firmly bound on each branch with wire. After it is filled with dry air according to the directions in Article 290, page 348, it is fastened on a piece of board by annealed wire staples, and paper scales affixed as shown in the figure. The difference in height of the two columns of mercury is taken as the read- ing of the thermometer, and no correction is made for slight variations in the volume of air, as shown by variation in the position of the height of the mercury column in the branch BC. The error caused in this way is very small and amounts to only 0.0030 inch per inch of height. This is equivalent to an error of about five degrees in a range of temperature of 600 degrees F. The. Jolly Air-thermometer. An exceedingly simple form of the air-thermometer, and one also very accurate, consists of the air-bulb C, and a capillary stem attached to three or four feet of rubber tubing, which replaces the U-tube in Fig. 139; in the other end of the rubber tubing is inserted a piece of glass tube 8 to 12 inches long and about -^ inch bore ; on this glass tube, and also on the capillary tube, is etched a single mark ; the rubber tube is filled with mercury, which extends up the glass tube FlG . I39 ._T H B HOAJ>- on the other branch. A fixed scale, similar to DE 139-- LEY AIR-THERMOM- ETER. 34-6 EXPERIMENTAL ENGINEERING. [ 289. in Fig. 139, is located near the instrument. To use the instru- ment the tube is manipulated until the air is brought to its limit of volume, then the other end of the tube is held oppo- site the scale, and the reading corresponding to the height of the mercury is taken. This is repeated for several tempera- tures, and, if the constant of the instrument is known, gives the data for computing the temperature. 289. Formulae for the Air-thermometer of Constant Vol- ume. The pressure exerted by the confined air, added to the weight of mercury, in the branch Bt 1 , Fig. 138, will equal the weight of mercury in the other branch plus the weight of the atmosphere. Thus let p equal the pressure expressed in inches of mercury of the confined air, v its volume, m the height of the mercury in the branch of the tube on the side of the air- bulb, m' the height in the other branch, b the pressure of the atmosphere expressed in inches of mercury, T the absolute temperature, t the thermometer-reading, h the height of mer- cury in the tube BE above the mark cr Internal latent heat " r p or j Quality of steam . . . X External latent heat. . . . APuor E Per cent of moisture I X r or L Degree of superheat 2) * Mathematical Papers, XLVIII., p. 194. 3I2-] THE AMOUNT OF MOISTURE IN STEAM. 363 The quantities q, p, APu, r, and A are given in B. T. U. per pound of saturated steam reckoned from 32 Fahr. 311. General Formula for the Heat in One Pound of Steam. The heat existing in one pound of steam with any quality x can be expressed by the formula (i) The heat, however, which is required to raise water from 32 F. and convert it into steam at a given temperature will include the external latent heat, and will be expressed by the formula xr + q = h'. ....... (2) The heat that may be given out by condensation or change of pressure is expressed in equation (2) ; that which exists in the steam without change of pressure or external work, by equation (i). Since in all calorimetric processes the steam is condensed, or at least the pressure changed, equation (2) is to be employed to represent the available heat. If the pressure of the steam is known, r and q can be found from the steam-tables: If the heat h in B. T. U. above 32 can be found for the sample steam, all the quantities in the above equation with the exception of x are known, and we shall find 0) In case x is greater than unity, the steam is superheated, and the degree of superheat / \ ....... (4) when 0.48 equals the specific heat of steam, c p . 312. Methods of Determining the Heat in a given Sample of Steam. There are two methods of determining the heat // in a given sample of steam. 364 EXPERIMENTAL ENGINEERING. [ 312. I. Condensing the Steam at Atmospheric Pressure. In this case the weight of the steam is obtained by weighing the con- densing water before and after condensation has taken place and determining the corresponding temperatures. Thus let the weight of condensing water be represented by -W, that of the condensed steam by w\ the temperature of the condensing water cold by /, , the condensing water warm by t^ ; the original temperature of the steam by /, that of the condensed steam by /,.. Suppose that the calorimeter absorb heat to the same extent as 'pound's of water; then the heat added by con- densing one pound of steam is equal to The original heat above 32 from equation (2), page 363, is xr-\-q. Since in equation (5) the temperature is reck- oned above zero, it will be more convenient to use, instead of xr-\- q-\- 32, xr -\- 1, which is very nearly identical. Since the heat lost in condensing one pound of steam is equal to that gained by the water, we shall evidently have from which (,) \ ~~~"*t) f \ - r 2 - ( 6 ) w If the temperature of condensed steam equal that of the warm condensing water, t 3 = t^, which is the usual condition of condensation. 2. Superheating the Steam. If the pressure and tempera- ture of superheated steam is known, the degree of superheat D can be found by deducting the normal temperature, as given in the steam-table for that pressure, from the observed tem- perature. The total heat in a pound of the superheated steam 3I3-] THE AMOUNT OF MOISTURE IN STEAM. 365 is equal to that in a pound of saturated steam, as given by the steam-tables, plus the product of the degree of superheat into the specific heat c p of the steam ; that is, H = A + c p D. The superheating may be done by extraneous means, as in the Barrus superheating calorimeter, or by throttling, as in the throttling calorimeter. In the latter the heat required for superheating is obtained by reducing the pressure, which, being accompanied by a corresponding reduction of boiling point, liberates heat sufficient to evaporate a small percentage of moisture only. In the case of the superheating calorimeter, the heat re- quired to evaporate the moisture and superheat the steam is measured by the loss of temperature n in an equal weight of superheated steam, so that cn = In the case of the throttling calorimeter there is no change in the total amount of heat, but there is a change of pressure, so that the quantities in the first member of (8) correspond to the original pressures of steam before throttling, and those in the second member to the calorimeter pressures after throttling, and (8) 313- Condensing Calorimeters. Condensing calorimeters are of two general classes : I. The jet of steam is received by the condensing" water, and the condensed steam intermingles directly with the condensing water. 2. The jet of steam is condensed in a coil or pipe arranged as in a surface condenser, 366 EXPERIMENTAL ENGINEERING. [3H- and the condensed steam is maintained separate from the con- densing water. The principle of action of both classes of condensing calo- rimeter is essentially the same, and is expressed by equation (6): w In the first class / 3 = / a , and w Both forms of condensing calorimeter can be made to act con- tinuously or at intervals, and there are several distinct types of each. The most common type of condensing calorimeter is one in which the condensing water is received in a barrel or tank, and hence is termed a barrel calorimeter. The special forms will be described later. 314. Effect of Errors in Calorimeter Determinations. First. Condensing Calorimeters. To determine the effect of error, suppose in each case the quantity under discussion to be a variable and differentiate the equation r We have Ax ~ A W (/ /,) -r- wr Ax -7- At^ = W -f- wr. 3 r 4-] THE AMOUNT OF MOISTURE IN STEAM. Since Ar At, nearly, for ordinary pressures of steam, and further is a function of the pressure, we have approximately Ap = Ap = Ar ; [W (',-0 -'- The weight of condensing water usually held by the barrel- calorimeters is from 300 to 400 Ibs., while the weight of the steam condensed varies from 1 6 to 20 Ibs., and the correspond- ing temperatures have a range of 50 to 70 F. For these cases it will be found that the percentage of error in quality, sup- posing other data correct, is approximately the same as the percentage of error in the weights. The error in thermometer- determination has nearly the same effect, whether made before or after the steam has been condensed. For the amounts usu- ally employed the error of one fifth of one degree in tempera ture has about the same^effect as one half of one per cent error in weight ; that is, it makes an error of about the same amount in the quality of steam. The following shows in tabular form the effect of errors with condensing calorimeters in which the ordinary weights of water and of steam are used : TABULATION OF ERRORS. Error in Condensing Water. Error in Condensed Steam. Error in Temperature, Cold Water. Error in Temperature, Warm Water. Error in Steam- pressure. Resulting Error in Quality. Per cent. | Lbs. Per ct. Lbs. Per ct. Degs. Per ct. Degs. Per ct. Lbs. Per c. Total wt. = 360 Ibs. Total wt. 20 Ibs. Temp. = 50 F. Temp. =no F. Pr. = 88 Ibs. 3.6 1.8 I -5 0.3 i .0 0.5 0.40 0.08 0.2 O. I 0.08 0.016 i .0 o-5 0.4 0.08 -53 0.27 0.18 0.045 I .2 0.6 o-S O.I 0.65 0.30 0.25 0.05 0.60 0.30 2 5 0.50 7.0 3-5 3- 0.6 8.0 4.0 3-5 0.7 1 .2 0.6 o-S O.I Total wt. = 300 Ibs. Total wt. = 20 Ibs. 0.25 i-5 0.5 O.I o-5 O.2 2.2 0-5 368 EXPERIMENTAL ENGINEERING. [ 314. In the table, the errors in the various observations ex~ pressed in the same horizontal line have the same effect on the result. From the table it is seen, for the given weights, that an error of 3.6 pounds in condensing water, of 0.2 pound in con- densed steam, of 0.53 F. in temperature of cold water, of 0.65 F. in warm water, or of 7 pounds in steam-pressure will sever- ally make an error in the result of 1.2 per cent. Expressed in percentages, an error of I per cent in weight or 1.2 and 0.6 per cent in thermometer-readings makes an error in the quality of 1.2 per cent. The conditions for determination of moisture within one half of one per cent require 1. Scales that weigh accurately to half of one per cent of the quantity to be weighed. 2. Thermometers that give accurate determinations to about one fifth of one degree F. 3. An accurate pressure-gauge. 4. Correct observations of the resulting quantities. 5. Determination of loss caused by calorimeter. Secondly. Superheating Calorimeters. The Barrus Suptr- heating Calorimeter. In this, if / 3 t is the gain of tempera- ture of the sample steam, and t^t^ is the loss of temperature in the superheated steam, we have, neglecting radiation, i - x = o. 4 8[/ 2 - /, - (/, - /)] + r. In the Throttling Calorimeter, where the steam is super- heated by expanding, we have by equation (7), making c p = 0.48, _ \ + 0.48> q In either form of superheating calorimeter the effect of an error of one degree in temperature is to make an error in x of 0.06 of one per cent, while an error of 9 in temperature will affect the value of x but 0.5 per cent. The boiling-point 315-] THE AMOUNT OF MOISTURE IN STEAM. 369 should be correctly determined, however, especially if the amount of superheating is small. An error in gauge-reading has about one half the effect on the quality of the steam as in the other class of calorimeters. 315. Method of Obtaining a Sample of Steam. It is usually arranged so as to pass only a very small percentage of the total steam through the calorimeter, and it is important that this sample shall fairly represent the entire quantity of steam. From experiments made by the author, it is quite cer- tain that the quality varies greatly in different portions of the same pipe, and that it differs more in horizontal than in verti- cal pipes. Steam drawn from the surface of the pipe is likely to contain more than the average amount of moisture ; that from the centre of the pipe to contain less. The better method for obtaining a sample of steam is to cut a long threaded nipple into which a series of holes may be drilled, and screw this well into the pipe. Half-inch pipe is gen- erally used for calorimeter connections, and it may be screwed into the main pipe one half or three quarters of the distance to the centre, with the end left open and without side-perfora- tions, as shown in Fig. 143, or screwed three fourths the FIG. 143. COLLECTING-NIPPLES. FIG. 144. distance across the pipe, a series of holes drilled through the sides, and the end left open or stopped, as shown in Fig. 144. A lock-nut on the nipple, which can be screwed against the pipe when the nipple is in place, will serve to make a tight joint. Since it is very easy to separate a portion of the water from the steam mechanically, the holes drilled in the nipples should be large, otherwise the sample of steam is likely to be too dry. It has been the recent practice of the author to use 370 EXPERIMENTAL ENGINEERING. [ 316. a nipple of sufficient length to reach three quarters across the main steam-pipe, and provided with several holes, each one- fourth inch in diameter. The collecting-nipple is placed preferably in a vertical pipe a short distance below a bend from the horizontal, and the calo- rimeter is located as close as possible to the main steam-pipe. 316. Method of Inserting Thermometers. In the use of calorimeters it is frequently necessary to insert thermometers FIG. 145. STEAM-THERMOMETER. FIG. 746. THERMOMETER-CUP. into the steam in order to correctly measure the temperature. For this purpose thermometers can be had mounted in a brass case, as shown in Fig. 145, which will screw into a threaded opening in the main pipe. The author prefers to use instead a thermometer-cup of the form shown in Fig. 146, which is screwed into a tapped open- 3 1 /-] THE AMOUNT OF MOISTURE IN STEAM. 3/1 ing in the pipe. Cylinder-oil or mercury is then poured into the cup, and a thermometer with graduations cut on the glass inserted. The thermometer-cups are usually made of a solid brass casting, the outside being turned down to the proper di- mensions and threaded to fit a f-inch pipe-fitting. The inside hole is drilled ^ inch in diameter, and the walls are left ^ inch thick. The total length varies from 4^- to 6 inches depending on the place where it must be used. In either case it is essen- tial that the thermometer be inserted deep into the current of steam or water, and that no air-pocket forms around the bulb of the thermometer. The thermometer should be nearly ver- tical, and as much of the stem as possible should be protected from radiating influence. If the thermometer is to be inserted into steam of very little pressure, the stem of the thermometer can be crowded into a hole cut in a rubber cork which fits the opening in the pipe. In case the thermometer cannot be inserted in the pipe it is sometimes bound on the outside, being well protected from radiation by hair-felting ; but this practice cannot be recom- mended, as the reading is often much less than is shown by a thermometer inserted in the current of flowing steam. In the use of thermometers, breakages will be lessened by carefully observing the directions as given in Article 286, p. 342. 317. Determination of the Water-equivalent of the Calorimeter. The calorimeters exert some effect on the heating of the liquid contained in them, since the inner sub- stance of the calorimeter must also be heated. This effect is best expressed by considering the calorimeter as equivalent to a certain number of pounds of water producing the same result. This number is termed the water-equivalent of the calorimeter. The water-equivalent, k, can be found in three ways : I. By computing from the known weight and specific heat of the materials composing the calorimeter. Thus let c be the specific heat, W c the weight ; then 372 EXPERIMENTAL ENGINEERING. [3 l8 * 2. By drawing into the calorimeter, when it is cooled down to a low temperature, a weighed quantity of water of higher temperature and observing the resulting temperature. Thus let W equal the weight of water, t l the first and t^ the final temperatures, and k the water-equivalent sought. Since the heat before and after this operation is the same, (W+k)t, = Wt,. From which __ W(l, - t,) rC - -- 3. By condensing steam drawn from a quiescent boiler, and thus known to be dry and saturated, with a weighed quantity of water of known temperature in the calorimeter ; the tempera- ture, pressure, and weight of the steam being known. The con- ditions are the same as for equation (6), page 364, all the quantities being known excepting k. By solving equation (6), For the barrel and jet condensing calorimeters generally, / 3 = / a , and we have k = w ( rx + /-*.) ' - 'i . The cooling effect of superheating calorimeters is generally .expressed in degrees of temperature in the reading of one of the thermometers. \ SPECIAL FORMS OF CALORIMETERS. 318. Barrel or Tank Calorimeter. The barrel calorim- eter belongs to that class of condensing calorimeters in which a jet of steam intermingles directly with the water of conden- sation. It is made in various ways ; in some instances the 3 l8 -J THE AMOUNT OF MOISTURE IN STEAM. 373 walls are made double and packed with a non-condensing substance, as down or hair-felting, to prevent radiation, and the instrument is provided with an agitator consisting of paddles fastened to a vertical axis that can be revolved and the water thoroughly mixed ; but it usually consists of an ordi- nary wooden tank or barrel resting on a pair of scales, as shown in Fig. 147. FIG. 147 THE BARREL CALORIMETER. A sample of steam is drawn from the main steam-pipe by connections, as explained in Article 315, page 369, and con- veyed by hose, or partly by iron pipe and partly by hose, to the calorimeter. In the use of the instrument, water is first admitted to the barrel and the weight accurately determined. The pipe is then heated by permitting steam to blow through it into the air ; steam is then shut off, the end of the pipe is submerged in the water of the calorimeter, and steam turned on until the temperature of the condensing water is about 110 F. The pipe is then removed, the water vigorously stirred, the temperature and the final weight taken. If the effect of the calorimeter, k, expressed as additional weight of water, is known, the quality can be computed as in equation (6), page 364. (t - 1.) wr 374 EXPERIMENTAL ENGINEERING. [ A tee screwed crosswise of the pipe, as shown in Fig. 147, forms an efficient agitator, provided the temperature be taken immediately after the steam is turned off. The pipe may remain in the calorimeter during the final weighing if supported externally, and if air be admitted so that it will not keep full of water ; in such a case, however, it should also be in the barrel during the first weighing, or else the final weight must be corrected for displacement of water by the pipe. The effect of displacement is readily determined by weighing with and without the pipe in the water of the calo- rimeter. The determination of the water-equivalent of the barrel calorimeter will be found very difficult in. practice, and it is usually customary to heat the barrel previous to using it, and then neglect any effect of the calorimeter. This nearly elimi- nates the effect of the calorimeter. The accuracy of this instrument, as shown in Article 314, page 367, depends prin- cipally on the accuracy with which the temperature and the weight of the condensed steam are obtained. The conditions for obtaining the temperature of the water accurately are seldom favorable, as it is nearly impossible to secure a uniform mixture of the hot and cold water; the result is that deter- minations made with this instrument on the same quality of steam often vary 3 to 6 per cent. From an extended use in comparison with more accurate calorimeters, the author would place the average error resulting from the use of the barrel calorimeter at from 2 to 4 per cent. Example. Temperature of condensing water, cold, /, , is 52. 8 F.; warm, , , IO9.6 F. Steam-pressure by gauge, 79.7; absolute, 94.4. Entering steam, normal temperature, from steam-table, /, 323.5 F. Latent heat, r, 888.2 B. T. IL Weight of condensing water cold, W, 360 pounds ; warm, W-\-w, 379.1 pounds, wet steam, w, 19.1 pounds. Calorim- eter-equivalent eliminated by heating. The quality = ^60 (1096- 52.8) _ 323.5 - 109-6 19.1 888.2 888.2 320.] THE AMOUNT OF MOISTURE IN STEAM. 3/5 319. Directions for Use of the Barrel Calorimeter. Apparatus. Thermometer reading to \ degree F., range 32 to 212 ; scales reading to -fa of a pound ; barrel provided with means of filling with water and emptying ; proper steam con- nections ; steam-gauge or thermometer in main steam-pipe. 1. Calibrate all apparatus. 2. Fill barrel with 360 pounds of water, and heat to 130 degrees by steam ; waste this and make no determinations for moisture. This is to warm up the barrel. 3. Empty the barrel, take its weight, add quickly 360 pounds of water, and take its temperature. 4. Remove steam-pipe from barrel ; blow steam through it to warm and dry it ; hang on bracket so as not to be in contact with barrel ; turn on steam, and leave it on until temperature of resulting water rises to 110 F. Turn off steam; open air- cock at steam-pipe as explained. 5. Take the final weights with pipe in barrel, in same po- sition as -in previous weighings ; also take weights with the pipe removed : calculate from this the displacement due to pipe, and correct for same. Alternative for fourtJi and fifth operations. Supply steam through a hose, which is removed as soon as water rises to a temperature of 110 F. Weigh with the hose removed from the barrel. Stir the water while taking temperatures. 6. Take five determinations, and compute results as ex- plained. Fill out and file blank containing data and results. 7. Compute the value of the water-equivalent, k, in pounds by comparing the different sets of observations. 320. The Continuous-jet Condensing Calorimeter. A calorimeter may be made by condensing the jet of steam in a stream of water passing through a small injector or an equiva- lent instrument. The method is well shown in Fig. 148. A tank of cold water, B, placed upon the scales R, is connected to the small injector by the pipe C] the injector is supplied with steam by the pipe S, the pressure of which is taken by the gauge P\ the temperature of the cold water is taken at e, that of the warm water at g. Water is discharged into the 376 EXPERIMENTAL ENGINEERING. [ 320. weighing-tank A. The amount taken from the tank B is the weight of cold water W\ the difference in the respective weights of the water in tanks A and B is the weight of the steam w. The quality is computed exactly as for the barrel calorim- eter. In case an injector is used, as shown in Fig. 148, the tank B is not needed : water can be raised by suction from the tank A through the pipe d. The original weight of A will be that FIG. 148. THE INJECTOR CALORIMETER. of the cold water; the final weight will be that of steam added to the cold water. In case an injector is not convenient, and the water is sup- plied under a small head, a very satisfactory substitute can be made of pipe-fittings, as shown in Fig. 149. In this case, steam of known pressure and temperature is supplied by the pipe A cold water is received at S', and the warm water is discharged at 5. The temperature of the entering water is taken by a thermometer in the thermometer-cup 7 1 ', that of the discharge by a thermometer at T. The steam is condensed in front of the nozzle C. This class of instruments present much better opportunities of measuring the temperatures accurately than the barrel calorimeter, and the results are somewhat more reliable. 321.] THE AMOUNT OF MOISTURE IN STEAM. 377 In the use of continuous calorimeters of any class, the in- strument should be put in operation before the thermometers are put in place or any observations taken. The poise on the weighing-scale can be set somewhat in advance of its bal- ancing position, and when sufficient water has been pumped out the scale-beam will rise ; this may be taken as the signal ;r FIG. 149. JET CONTINUOUS CALORIMETER. for saving the water which has been previously wasted, and of commencing the run. The water equivalent of the calorimeter, k, will be small, and due principally to radiation. It can be found by passing hot water through the calorimeter and noting the loss in tem- perature. 321. The Hoadley Calorimeter. This instrument be- to the class of non-continuous surface calorimeters. The 378 EXPERIMENTAL ENGINEERING. [321- instrument is described in Transactions of the American So- ciety of Mechanical Engineers, Vol. VI., page 716, and consisted of a condensing coil for the steam, situated in the bottom of a tank-calorimeter, very carefully made to prevent radiation- losses. The dimensions were 17 inches diameter by 32 inches deep, with a capacity of about 200 pounds of water. The FIG. 150. HOADLEY'S CALORIMETER. calorimeter was made of three concentric vessels of galvanized iron, the spaces being filled with hair-felt and eider-down. The condenser consisted of a drum through which passed a large number of half-inch copper tubes, the steam being on the outside, the water on the inside, of these tubes ; the agitator consisting of a propeller-wheel attached to an axis that could be rotated by turning the external crank K, effectu- ally stirring the water. The thermometer for measuring the temperature was inserted in the axis of the agitator at 71 322,] THE AMOUNT OF MOISTURE IN STEAM. 379 In the hands of Mr. Hoadley the instrument gave accurate determinations. In practice the instrument was arranged as in Fig. 151 ; the calorimeter E was placed on the scales F, and supplied by cold water from the elevated barrel A. The temperature of the entering water was taken at C. Steam was admitted to the condensing-coil until the temperature of the condensing water reached, say, 110 F. The weights before and after FIG. 151. HOADLEY'S CALORIMETER ARRANGED FOR USB. adding steam were taken by the scales F; the temperature of the warm condensing water was taken by a thermometer, G, inserted in the axis of the agitator. The water-equivalent was determined as explained in Article 317, page 371, and the quality computed by equation (6), page 364. The rate of cooling was determined, and an equivalent amount added as a correction for any loss of heat by radiation. 322. The Kent Calorimeter. This instrument differs from the Hoadley instrument principally in the arrangement of the condensing coil. This when filled with steam could be removed from the calorimeter, so as to enable the weight of 380 EXPERIMEN TA L ENGINEERING. [ 323. steam to be taken on a smaller and more delicate pair of scales than those required for the condensing water, thus giving more accurate determinations of the weight of the steam con- densed. 323. The Barrus Continuous Calorimeter. This calo- rimeter is shown in Fig. 152 in section and in Fig. 153 in per- spective. It consists of a steam-pipe, aj, surrounded by a Condensed Steam FIG. 152. BARRUS CONTINUOUS CALORIMETER. tub or bucket, 0, into which cold water flows; the condensing water is received as it enters the bucket in a small brass tube, k, surrounding the pipe a, and is conveyed over and under baffle-plates, m, so as to be thoroughly mixed with the water in the vessel, and is finally discharged at c. Thermometers are placed at /and at g to take the temperature of the water as it 3 2 3] THE AMOUNT OF MOISTURE IN STEAM. 38! enters and leaves, and finally the condensing water is caught from the overflow and weighed. The condensed steam falls below the calorimeter ; by means of the water gauge glass at e FIG. 153. THE BARKUS CONTINUOUS AND SUPERHEATING CALORIMETERS. it may be seen and kept at a constant height. The temperature of the condensed steam while it is still under pressure is shown by a thermometer at h. In order to use the calorimeter it is necessary to weigh the condensed steam ; this cannot be done without further cooling, as it would be converted into steam were the pressure removed. For this purpose it is passed through a coil of pipe immersed in a bucket filled with water, 382 EXPERIMENTAL ENGINEERING. [ 324. shown at 5 in Fig. 153. The water used in the cooling bucket 5 has no effect on the quality of the steam and is not con- sidered in the results ; it is allowed to waste, but the condensed steam is caught at W, Fig. 153, and weighed. The quality of steam is computed by omitting k in for- mula (6), page 364. Hence w w is the weight of condensed steam after correction for radia- tion-loss as explained in Article 324 ; w being equal .to w' u. 324. Directions for Using the Barrus Continuous Calo- rimeter. Apparatus needed. Thermometers ; pail for receiv- ing condensed steam ; tank and scales for the condensing water. Directions. I. Fill the thermometer-cups with cylinder- oil. (Do not put thermometers in place until apparatus is working.) 2. Turn on condensing water and steam ; regulate the flow of condensing water so as to keep the bucket O nearly full, and the temperature of the discharge-water as much above tem- perature of the room as injection is below : this should be about 110 F. Regulate the flow of condensed steam so as to keep the water in the glass e at a constant level. Turn water on to the cooling coil in the bucket 5, and reduce the con- densed steam to a temperature of about 120. 3. After the apparatus is working under uniform condi- tions, put the thermometers in the cups for temperature of injection and discharge water, and having previously weighed the vessels, at a given signal, note time and commence to catch the condensed steam and the condensing water. Con- tinue the run until about 360 or 400 pounds of condensing water has run into the receiving tank. Without disturbing the condition of the apparatus, commence simultaneously to waste the discharge from both pipes. Find the weights of 3 2 4-] THE AMOUNT OF MOISTURE IN STEAM. 383 condensed steam (w r ) and condensing water (W) ; note time of ending run. 4. Make three more runs similar to the first. 5. To find the radiation-correction of the instrument: Empty the bucket O of condensing water, and surround the condensing tube a with hair-felting ; make a run of the same length, and with steam of same pressure as in the previous runs. The weight of steam condensed will be the radiation- loss, which we call u, and is to be deducted from the weight of condensed steam obtained in the previous runs of the same length. Find the condensation per hour. 6. Work up quality of steam by the formula Make report as described for other calorimeters. Example. The following is the result of a trial with the Barrus continuous calorimeter: Temperature of injection-water, /, = 37. 5 Fahr. ; temperature of discharge-water, t^ = 83. 8 Fahr. ; temperature of condensed steam, / 3 = 304.9 Fahr. ; steam-pressure by gauge, 72.4 Ibs. ; temperature of entering steam, / = 3i7.9 ; length of test, 40 minutes ; weight of cool- ing water, W = 573.5 Ibs.; weight of condensed steam, w' = 29.89 Ibs. ; radiation-loss u 0.13 Ib. Neglecting value of u, _ 573-5 (83.8 - 37-5) _ (317.9- 304.9) ~ 29.89 891 891 _ 19.21 X 46.3- 130 _ 8 7 6 -4 _ 8 891 " 891 x = 98.4 if not corrected for radiation-loss. If corrected, *=gg!*3- '30)^89. = 9 8. 9 . . _ ?i;: 384 EXPERIMENTAL ENGINEERING. [ 325. 325. Forms for Use with Condensing Calorimeters. MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL UNIVERSITY. PRIMING TEST WITH CONDENSING CALORIMETER. Made by 1 89 . . Test of Steam at , N. Y. Kind of calorimeter I. II. III. IV. v. Duration of run, minutes Symbols. Gauge-pressure Ibs P Scale-readings tare Ibs v Tare and cold water Ibs W '->- V Quantities : Condensing water Ibs . . w Condensed steam Ibs w Temperatures, deg. Fahr. : Condensing water, cold t\ Condensing water warm ti / 3 Steam at pressure P t W - iu Decree of suoer-heat. . D Correction due to displacement of water by hose Ibs. Calorimeter-equivalent Ibs. How found Temp, room deg. Fahr. Barometer-reading inches. Quali Degree of super-heat D = (x i}r -*- 0.48. lity x = . Weigh, ? Hot Cold. ||| j* || Total . Aver. Cor.. Duration of test min. Weight of steam condensed Ibs. Weight of condensing water ' Average temperature of hot condensing water. . . .C.; . . . .Fahr. ; . . . .B.T.U. " cold " " .... " .... " .... " " " " condensed steam " " .... " " "room ....deg.C. pressure of air Ibs. per sq. in. " absolute pressure of the steam Thermal units in water corresponding to absolute pressure of steam. . . .B.T.U. Heat acquired by condensing water Heat given up by condensed steam in cooling to temperature of ther- tf mometer in same. Weight of water condensed by radiation Ibs. Heat given up by each pound of steam in condensing B.T.U. Latent heat of one pound of steam at average absolute pressure Per cent of * Signed 3 86 EXPERIMENTAL ENGINEERING. [ 326. TO BE TESTED V2 PIPE 326. Barrus Superheating Calorimeters. In the Barrus Superheating Calorimeter, Fig. 1 54, the steam-pipe leading from the main is bifurcated, one branch, E, passing over the flames of a large Bunsen burner, the other passing up- ward, and finally downward, when it is jacketed by the enlargement of the first branch. The branches discharge separately, each through equal orifices, about one-eighth inch in diameter. This instrument is shown in Fig. 154 in elevation, and on the left-hand side of Fig. 153 in perspective. The steam in one branch is superheated at G\ that in its normal condition is received at H, and is discharged at N. The superheated steam forms a jacket from / to K outside the sample to be tested, and is discharged at the orifice M. The temperature of the jacket steam is taken at A and at B ; that of the normal steam is measured at C, as it is discharged ; it is found as it enters from its pressure taken at H, by reference to the steam-table. The theory of this calorimeter is as follows: FIG. 154. BARRUS SUPER- HEATING CALORIMETER. 326.] THE AMOUNT OF MOISTURE IN STEAM. 387 1. An equal weight of steam flows through each branch of the pipe. 2. The steam, superheated by the gas-flame, is used as a jacket for the other branch, and parts with as much heat, ex- cept for radiation, as the other gains. 3. This amount may be measured provided the steam dis- charged from the central tube is superheated. To measure this gain or loss of heat, thermometers are placed to take the temperature of steam as it enters and leaves the jacket, and on the central pipe near the same places. Formula. Let (i x) be the amount of water to be evap- orated ; in so doing it will take up from the jacket-steam r(i x] heat-units. Let / be the normal temperature of the steam at the gauge pressure ; let 7^ be the temperature of the superheated jacket-steam at entering, and 7 1 , as it leaves ; let 7*3 be the temperature of the superheated steam discharged from the sample pipe, and let radiation-loss in degrees F. be /. If the specific heat of steam be 0.48, since gain and loss of heat are equal, we have 0.48(7; - T; - /) - r(i -x) + 0.48(7; - t). .-. i - x - o. 4 8[7; - r s - /- (7; - /)] -r r; from which x may be found. To find /, the radiation-loss in degrees, shut off steam in the branch leading to the centre steam-pipe, and find reading of thermometers T l and 7 1 , . After a run of same length as in test, take / = T, T, . Directions for using Barrus Superheating Calorimeter. Ap- paratus needed. Three thermometers reading 400 F. each, and pressure-gauge, superheating lamps, etc. First. Calibrate instruments, and ascertain by a run of twenty minutes that equal amounts of steam are discharged from each orifice. This may be done by condensing the steam, Second. Put cylinder-oil in oil-cups ; attach gauge. 388 EXPERIMENTAL ENGINEERING. [ 328. Third. Put in working order ; after thermometer at end of sample-steam-pipe shows superheat, commence the run. Fourth. Take readings once in two minutes for twenty minutes. Fifth. Obtain radiation-loss / as explained. Sixth. Work up results as explained, and make report as in previous cases. 327. Form for Determination with Barrus Superheat- ing Calorimeter. No. BARRUS SUPERHEATING CALORIMETER. DATE. . Time. Temp. Jacket-steam Entering. Temp. Jacket steam at Exit. Temp Sample Steam at Exit. Steam- pressure by Gaue. Barometer. Total . Average . . Corrected . Duration of test rain. Barometer. in.; Ibs. per sq. in. Sample steam, gauge pressure Ibs. per sq. in. " absolute " Ibs. per sq. in. " " temperature at absolute pressure. C.; F. " outlet .C.; F. Superheated steam, temperature at inlet C.; F, " " " " outlet C.; F. Latent heat of steam at absolute pressure B. T. U. Specific heat of superheated steam B. T. U, Correction for condensation , " radiation Per cent of moisture in steam ". 328. The Throttling Calorimeter. This instrument was designed in 1888 by Prof. C. H. Peabody of Boston, and rep- 328.] THE AMOUNT OF MOISTURE Iff STEAM. 389 resents a greater advance than any previously made in practical calorimetry. The equations for its use and limitations of the same were given by Prof. Peabody in Vol. IX., Transactions Am. Society Mechanical Engineers. As designed originally, it consisted of a small vessel four inches in diameter by six to eight inches long, and connected to the steam-supply with a pipe containing a valve, b, used to throttle the steam supplied the calorimeter. Fig. 155 shows the original form of the calorimeter, which is arranged so that any de- sired pressure less than that in the main steam-pipe can be maintained in the calorimeter A. The press- ure in the calorimeter is shown by a steam-gauge at g, and the tem- perature by a thermometer at D\ the main steam-pipe is provided with a drip at f, to drain the pipe before making calorimetric tests. In using the calorimeter, any desired pressure can be main- tained in the vessel A by regulating the opening of the ad- mission and exhaust valves. The effect of this operation will be to admit the heat due to high-pressure steam into a vessel filled with steam of lower pressure. The excess of heat is utilized firstly in evaporating- moisture in the original steam ; secondly, if there is sufficient heat remaining, in raising the temperature in the vessel A above that due to its pressure, thus superheating the steam. Unless the steam in the chamber A is superheated, no deter- minations can be made with the instrument. The equation for its use is obtained as follows: the heat in one pound of high- pressure steam before reaching the calorimeter is expressed as in formula (2), Article 311, page 363, by xr + q. After reaching the calorimeter the heat is that due to the press- FIG. 155. PEABODY'S THROTTLING CALORIMETER. 390 EXPERIMENTAL ENGINEERING. [ 328. ure in the calorimeter added to that due to the superheat, or A, -4-0.48(7^ T c ). Since these quantities are equal, = A, + 0.48(7; -T;); = [*,- + 0.48(7;- 7;)]^r; ., . . (ii) from which in which r equals latent heat, and q heat of liquid due to pressure in main pipe as given in the steam-table. \ c total heat in one pound of dry steam at calorimeter pressure ; T l = reading of thermometer in calorimeter, and T c = normal temperature of steam in calorimeter due to calo- rimeter pressure. Care must be taken that both X c and q are given in the same units. Example. Suppose that the gauge pressure on the main steam-pipe is 80 pounds, that on the calorimeter 8 pounds atmospheric pressure 14 pounds, as reduced from the barom- eter-reading, and that the thermometer in the calorimeter reads 274. 2 F. Required the quality of the steam. In this case we obtain the following quantities from the steam-table : P Absolute Pressure. T Temperature Deg. F. q Heat of Liquid, B. T. U. * Total Heal. B. T. U. r Latent Heat. B. T. U. Entering steam .... 04 q27 I 2QT 2 887.1 In calorimeter 22 211- 1 2O2.O i im.o Q?I .O From which * = [i 1 53 293-2 + 0.48(274.2 - 233.1)] -*- 887.3 ; Per cent of moisture, TOO x = 0.9. 3 2 9-] AMOUNT OF MOISTURE IN STEAM 391 329. Heisler's Throttling: Calorimeter. This instrument differs from Peabody's principally in size and form. It is shown complete and ready for use in Fig. 156, and full size in the sectional view, Fig. 157. FIG 156. HEISLER'S THROTTLING CALORIMETER. The chief difference between this and Peabody's calorim- eter is in the use of a standard orifice placed between two non-conducting washers. The steam is throttled in passing through this orifice, and reduced to a low pressure in the calo- rimeter. The form, as shown in Fig. 157, it is claimed, is such as to bring the steam intimately in contact with the thermom- eter-tube in its passage through the calorimeter. The instrument, as shown in Fig. 156, is connected to an attached mercury-manometer which is used for measuring the pressure in the calorimeter. 39^ EXPERIMENTAL ENGINEERING. [ 330. YC Manometer FIG. 157. HEISLER'S CALORIMETER. (SECTION; FULL SIZE.) 330. Throttling Calorimeter of Pipe-fittings. A very satisfactory calorimeter can be made of pipe-fittings, as shown o Jl FIG. 158. THROTTLING CALORIMETER OF PIPE-FITTINGS. in Fig. 158. Connection is made to the main steam pipe, as explained in Article 315, page 369. The calorimeter is made 33 !! THE AMOUNT OF MOISTURE IN STEAM. 39? of f-inch fittings arranged as shown ; the steam-pipe W is of J-inch pipe, and the throttling orifice is made by screwing on a cap, in which is drilled a hole \ or -fa inch in diameter. A thermometer-cup, Fig. 146, page 370, is screwed into the top, and an air-cock inserted opposite the supply of steam. A manometer, B, for measuring the pressure is attached by a piece of rubber tubing as shown. The exhaust steam is dis- charged at E. The back-pressure on the calorimeter can be increased any desired amount by a valve on the exhaust-pipe ; when no valve is used the pressure is so nearly atmospheric that a manometer is seldom required. 331. Method of finding Normal Temperature in the Calorimeter. It is essential to know the normal temperature within the calorimeter ; this will vary with the pressure on the calorimeter, which pressure is equal to the barometer-reading plus the manometer-reading. The following table gives the normal temperature corre- TABLE OF BOILING-POINTS. Normal Temperature. Degrees F. Total Pressure on Calorimeter. Inches Hg. Normal Temperature. Degrees F. Total Pressure on Calorimeter. Inches Hg. 209.5 28.466 7 744 .6 523 .8 .803 7 .580 9 .863 .8 637 212.0 .922 9 695 .1 .982 210. O 752 .2 30.041 . I .810 3 .101 .2 .867 .4 .161 3 .925 5 .221 4 .933 .6 .281 5 29.041 7 341 .6 - .099 .8 .401 7 157 9 .462 .8 .215 213.0 .522 9 .274 .8 31.004 211 .O 332 214.0 .107 .1 .391 215.0 .692 .2 449 216.0 32.277 3 .508 217.0 .862 4 .567 218.0 33-447 5 .626 219.0 34-032 .6 .685 220.0 .617 i Difference i F = 0.585 inch. Difference I inch = i.7O9. 394 EXPERIMENTAL ENGINEERING. [ 332. spending to various absolute pressures nearly atmospheric, ex- pressed in inches of mercury: In the use of the instrument the total pressure in the calorimeter is to be taken as the sum of the barometer-reading and the attached manometer. The degree of superheat of the steam in the calorimeter is the difference between the tempera- ture as shown by the pressure and that shown by the inserted thermometer. 332. Graphical Solution for Throttling-Calorimeter Determinations. In the practical use of this instrument it is customary to exhaust at atmospheric pressure, so that the normal temperature in the calorimeter is the boiling-point at atmospheric pressure, and A c is 1146.6; in which case formula (u) becomes _ 1*46.6-+ 0,48(7; 212) q r _ 1146.6 ^0.48(7", 212) If in this form we suppose the steam-pressure constant, and the degree of superheat and quality of steam alone to vary, r and q will both be constant, and we shall have the equation 1 146.6 q of a right line, in which is the distance above the origin that the line cuts the axis of ordinates, and 0.48 -r- r is the tangent of the angle that the line makes with the axis of abscissae. Drawing lines corresponding to the different gauge or absolute pressures, a chart may be formed from which the values of x may be obtained without calculation. Using degrees of superheat in the calorimeter as abscissae and absolute steam-pressure as ordinates, and drawing lines corresponding to various percentages of moisture, we have a diagram shown in Fig. 159, from which the results of observa- tions made with the throttling calorimeter may be taken at once without further calculation. FIG. 159. DIAGRAM GIVING RESULTS FROM THROTTLING CALORIMETER WITHOUT COMPUTATION. 396 EXPERIMENTAL ENGINEERING, [333- Use of tne Diagram. To find the percentage of moisture in the steam from the diagram, pass in a horizontal direction along the base-line until you arrive at the number corresponding to the degree of superheat in the calorimeter; then pass in a ver- tical direction until you reach the required absolute pressure of steam. The position with reference to the curved lines shows at once the percentage of moisture, and can be read easily to one tenth of one per cent. Thus, for example, sup- pose that we have the following readings : Barometer, 29.8 inches; attached manometer, 1.5 inches making a total press- ure in the calorimeter of 31.3 inches, corresponding to a tem- perature of 214. 27 Fahr. Steam-gauge, 80 pounds; absolute pressure, 94.7 pounds ; thermometer-reading in calorimeter, 254 Fahr. From which the degree of superheat is found to Following the directions as given, the percentage of moist- ure is seen from the diagram to be 1.66 per cent. The quality would be i .00 1.66 = 98.34 per cent. While the diagram is especially computed for determinations when the pressure in the calorimeter is atmospheric or but slightly above, it will be found to give quite accurate results when the calorimeter is under pressure, by considering that the ordinates represent the difference of pressures on the steam and in the calorimeter. Thus, in the example, Article 328, page 390, the steam-pressure was 80 pounds, calorimeter-pressure 8 pounds ; degree of super- heat 274.2 233.1 41.1 ; resulting quality by calculation 99.1, indicating 0.9 per cent of moisture. Using difference of press- ure 80 8 = 72 as ordinate, and 41.1 as abscissa, we find from the chart that the percentage of moisture is 0.92 ; from which x = 99.08. 333. Limits of the Throttling- Calorimeter. To deter- mine the amount of moisture that can be evaporated by throttling, make T t = T c in formula (11) ; then # = (A, q) ^r ....... (12) The amount of moisture that can be determined by the ? 335-] THE AMOUNT OF MOISTURE IN STEAM. 397 throttling calorimeter in expanding from the given pressure to atmospheric, as computed by substituting in formula (12), is as follows : LIMITS OF THE THROTTLING CALORIMETER. Pressure, pounds per square in. Maximum per cent of prim- ing. Quality of the steam, per cent. Absolute. Gauge. 300 285-3 07.7 9 2 -3 250 235-3 7.0 93-o 200 185.3 6.1 93-9 175 160.3 5-8 94-2 150 135-3 5-2 94.8 125 110.3 4.6 95-4 100 85.3 4.0 96.0 75 60.3 3-2 96.8 50 35-3 2-3 97-7 By reducing the pressure below the atmosphere, the limits of the instrument may be somewhat increased. 334. Directions for Use of Throttling Calorimeter. Apparatus. Steam-thermometer; pressure-gauge; manometer for measuring pressure in calorimeter in inches of mercury. 1. Attach the calorimeter to a perforated pipe extending well into the main steam-pipe to secure a fair sample of steam. Calibrate all the apparatus. 2. Fill thermometer-cup with cylinder-oil, having first care- fully removed any moisture from the cup. Place thermometer in the cup, and after it has reached its maximum commence to take observations. 3. Read steam-pressure, attached manometer, and tempera- ture at frequent intervals. 4. Compute the quality of the steam for each observation. 335. Forms for Throttling-Calorimeter Determinations. Priming tests of. Made by at, N. Y. 189. with Throttling Calorimeter. Barometer-reading inches. Steam used during run Ibs. 393 EXPERIMENTAL ENGINEERING. [ 336. Number f, R "5 Time .... 1 >r Steam-pressure, main pipe 00 J < k M Manometer reading calo- rimeter -f 7 5- /I Observed temperature calorimeter > Heat at steam-pressure P < ^'^ fc Normal temperature in calorimeter H II Q J Absolute . pressure in main o 48(/ t'\ Ej 1 Ac Total heat, pressure tn, . . rt V E 1 r Latent heat for pressure p \ c _ q -f .48(/! /c) > ^ | i jr Per cent of entrained water 3 w jr Quality of steam Ul Q D Degrees of superheat . . AVERAGE RESULTS OF CALORIMETER TEST. Date , Duration of test min. Barometer in. ; . . Ibs. per sq. in. Boiler-pressure by gauge " " " " absolute " " Calorimeter-pressure by gauge " " " absolute " ' Calorimeter-temperature C.; F. Per cent of moisture in steam Signed 336. The Separator Calorimeter. The separator calorim- eter, as designed by the author, consists of a chamber A into which leads the steam-pipe SB, Fig. 160, perforated in its lower portion with a large number of holes, each % inch in diameter. From the top of the chamber an exhaust-pipe S' is connected, across which extends a diaphram with a centre orifice O, T \ inch in diameter. In the use of the instrument steam is supplied at S, the water is deposited in the chamber A, and dry steam escapes through the orifice at O. A steam-gauge can be attached at G if desired, but neither gauge-readings nor temperatures are required. 336-] THE AMOUNT* OF MOISTURE IN STEAM. 399 The later forms of the instrument consist of two chambers, each made as shown in Fig. 160, the instrument being so con- structed that the exhaust S' from the first chamber is made to FIG. 160. THE SEPARATOR CALORIMETER. supply the steam for the second chamber; but one orifice is used, and that is placed in the discharge from the second chamber. In this case perfectly dry steam will be received in the second chamber, and any moisture deposited there will be 400 EXPERIMENTAL ENGINEERING. [ 336. due to radiation-loss. Since the chambers are of the same size, this quantity is to be used as a correction to the amount de- posited in the first chamber. The later forms of the instrument are provided with a graduated scale for determining the weight of water deposited in each chamber, an arrangement not shown in Fig. 160. The accuracy of this instrument depends on the complete- ness of the separation of the water from the steam, and on the condition that the exhaust steam is in each case dry and saturated. To determine this a series of tests were conducted for the author by Messrs. Brill and Meeker with steam of varying degrees of quality. The range in moisture was from 33 to i per cent, yet in every case the throttling calorimeter attached to the exhaust gave dry steam within limits of error of obser- vation. The following were the results of this examination : SEPARATING CALORIMETER. Examination of Exhaust Observations on Entering Steam. Steam from Calorimeter by Throttling Calorimeter. T P w IV X t X XT _ ~ Calori- meter. Duration Run, minutes. Gauge Pressure, pounds. Pounds Separated Water in Run. Pounds Condensed Steam in Run. Quality Steam, per cent. Temp, in Calori- meter. Quality Steam in Exhaust. i\ O . O I Obser- vations A 25 81.5 I-I5 4-45 79.46 2Sl 99-95 6 B' 25 7 8.2 0.15 5-20 97.2 281.3 IOO.OO 6 A\ 25 80.8 0.525 4.25 89.005 286.5 IOO.OO 6 B\ 25 79-5 0.150 4-75 96.94 281.8 99-95 6 A\ 25 78-5 0.300 5.000 94-34 282.8 IOO.OO 6 B\ 25 77.6 .150 5-45 97.32 282.3 IOO.OO 6 A 24 79-5 1.8 4-55 71.65 280. I 99-94 6 B 24 78.5 1.4 4.90 77-77 279-5 99-9 6 A 20 83-5 1.15 4.1 77.67 286.5 100.00 5 B' 2O 81.6 1.70 4-75 73.64 282.7 99.98 5 20 74-8 0.65 3-95 85.87 283.7 100.05 5 2O 82.0 0.85 3-95 82.29 286.8 100.05 5 20 82.6 0-35 4-15 92.22 285.6 IOO.O 5 20 81.5 0.20 3-95 95-^5 285.2 100.05 5 A ( 20 81.4 2.20 4-325 66.28 283.1 IOO.O 5 &( 20 80.3 O.3O 4-55 93-8i 282.8 IOO.O 5 A \ 2O 82.0 0.20 4-65 95.8 282.8 99.98 5 B' 20 Bi.i O.2O 4-4 95-7 284.0 IOO.O 5 Average of 18 trials, involving 98 observati ons . . 99.998 338-] THE AMOUNT OF MOISTURE IN STEAM. 4 throttling; separating ; Barrus superheating; Hoadley ; con- tinuous condensing; chemical; and lastly the barrel. The ease with which the throttling and separating instru- ments can be used, their small bulk, and great accuracy, render them of chief practical importance. The throttling calorimeter can be used only for steam with a small amount of moisture, as explained in Article 333 ; but the separating instrument is not limited by the amount of moisture entrained in the steam. It is not, however, as well adapted for superheated steam, nor can the results be deter- mined as quickly as with the throttling instrument ; when carefully handled the accuracy is, however, substantially the same. CHAPTER XIV. DETERMINATION OF THE HEATING VALUE OF FUELS FLUE-GAS ANALYSIS. 343* Combustion. Combustion or burning is a rapid chemical combination. The only kind of combustion which is used to produce heat for engineering purposes is the combina- tion of fuel of different kinds with oxygen. In the ordinary sense the word combustible implies a capacity of combining rapidly with oxygen so as to produce heat. The chief elemen- tary constituents of ordinary fuel are carbon and hydrogen. Sulphur is another combustible constituent of ordinary fuel, but its quantity and its heat-producing power are so small that it is of no appreciable value. The chemical elements are those which have not been de- composed ; these unite with each other in various definite proportions, which may be represented by certain numbers termed chemical equivalents or atomic weights. These for gaseous bodies are very nearly proportional to their densities at the same pressure and temperature. The atomic weight of a chemical compound equals the sum of the atomic weights of all the elements entering into the com- bination. Air is not a chemical compound, but a mechanical mixture of nitrogen and oxygen. The following table gives the properties of the principal elementary and compound substances that enter into the com- position of ordinary fuels : 408 EXPERIMENTAL ENGINEERING. [344- Substance. Symbol. Chemical Equivalent by Weight. Chemical Equivalent by Volume. Properties of Elements by Volume. O 16 I N 14 I H I I c ] 2 ? Phosphorus P TI s 32 ? Si I A Air 77N -1- 23O IOO TOO 7Q N 4- 2lO Water H 2 O 18 2 H H- O NH 3 I 7 2 H -j- N CO 28 2 C H- O Carbonic acid CO 2 4-1 2 C -j- O 2 Olefiant gas CH 2 4- 2 C -f H 2 CH 4 16 2 C 4- H* Sulphurous acid SO 2 64 2 S -f- O 3 Sulphuretted hydrogen Bisulphuret of carbon SH 2 S 2 C 34 76 2 2 S +H a C 4- So 344. Calorific Power or Heat of Combustion. The calorific value of a fuel is expressed in British thermal units or in calories, according as Fahrenheit or Centigrade thermo- metric scales are used. The calorific value may be deter- mined by direct experiment, or it may be computed from a chemical analysis as follows : The carbon is credited with its full heating power, due to its complete oxidation as determined by a calorimeter ex- periment. The hydrogen is credited with its full heating power, after deducting sufficient to form water with the oxygen present in the compound ; since when hydrogen and oxygen exist in a compound in the proper proportion to form water, the combination of these constituents has no effect on the total heat of combustion. The calorimetric value, determined experimentally, of one pound of hydrogen is 62,032 B. T. U. ; that of one pound of carbon, 14,500 B. T. U. Hence the combustion of one pound of hydrogen is equivalent to that of 4.28 pounds of carbon. A formula for the total heat, h, of combustion in B. T. U. 344-] THE HEATING VALUE OF FUELS 409 for each pound of the compound containing hydrogen and carbon would be (0 For theoretical evaporative power, in pounds of water from and at 212 F., The number of pounds of air required to supply the oxygen necessary for the combustion of one pound of fuel to CO, can be computed from the formula (3) and the corresponding volume in cubic feet can be found by mul- tiplying by the specific volume of one pound at 70 degrees Fr. In which case the volume in cubic feet is (4) In the above formulae, C, H, and O represent the number of pounds respectively of carbon, hydrogen, and oxygen in the product of combustion. When in the combustion of hydro-carbon fuels in an ordi- nary furnace hydrogen is consumed, the water formed passes off in the state of vapor, hence the latent heat of evaporation is not available. One pound of hydrogen burns to 9 pounds of water, the latent heat of which at 212 is 966 units; hence we must deduct 966 X 9 = 8694 units from the tabular value 4io EXPERIMEN TA L ENGINEERING. [ 345- of the heat due to the. combustion of hydrogen. This leaves 53,338 units available. Therefore the actual value in terms of carbon is H = 3.670, instead of 4.28C as stated in (i), and the heat of combustion actually available is *=i4,5a>[c+ 3.67(11 - (5) The following table gives the heat of combustion of the principal combustible substances: TOTAL HEAT OF COMBUSTION WITH OXYGEN. Substance. Pounds of Oxygen required per Pound of Combustible. Pounds of Air re- quired per Pound of Combustible (nearly). H Eo ~PLH m & a . O o Product of Combustion. 8 36 62,O32 62 6 H 2 O 6 44OO 4 5o CO Carbon burned to CO 2 . . 2.67 12 14 4CQ 14 67 CO 2 3.43 21 ,344 22 I CO 2 and H 2 O Liquid hydro-carbon ** >Jt-f j 19,000 20 1 i 4. e i 21,700 q 740 22.5 f 4OQ SO 2 2.20 IO. 2 I4,OOO 14.24 SiO 2 I .44 6.5 IO,25O P 2 O 6 Marsh gas C 2 H 4 . 3. 5 5 16 2 26 4OO 26 68 CO 2 and H 2 O 2.8 15 .O l8,6OO 18.53 I9,2OO IQ. 7-2 Wax ... 18 800 IQ 04 Ether 1 6, i o > 16 41 Tallow 16,000 16.37 Alcoho' . 12 700 13 06 Q 2OO 0.6^ Bisulphide of carbon CS 2 i 28 r 7 57CO 6 18 CO 2 and SO 2 1 . 33 6 IO IOO IO 4 CO 2 345. Determination of the Heating Value by the Oxygen required. It was observed by Welter* that those * Chemical Technology, Vol. I., p. 336 : Graves and Thorp. 345-] THE HEATING VALUE OF FUELS. 411 constituents of a compound which require an equal amount of oxygen for combustion evolve also equal quantities of heat; from which he concluded that since the oxygen required for the combustion of a body is in the same relation as the quan- tity of heat evolved, it might fairly be made the measure of the heating power. When, therefore, oxygen is consumed by the burning of carbon, wood, hydrogen, etc., the heat which is evolved must increase with the quantity that is consumed ; or the same amount of heat is generated by a certain given .weight of oxygen, whether that quantity be employed in con- verting carbon into carbonic acid, or hydrogen into water. The oxygen required is 2f for one part of carbon ; 8 for one part of hydrogen. One part by weight of carbon will raise the temperature of 80.5 parts of water from freezing to boiling. One part by weight of hydrogen will raise 234 parts of water from freezing to boiling. One part by weight of oxygen in burning carbon will heat 80.5 -- = 29. 1 parts of water. One part by weight of oxygen in burning hydrogen will heat -2.f4. = 29.3 parts of water from the freezing to the boiling point. In round numbers, therefore, the heating effect of oxygen may be assumed as sufficient to raise 29.2 parts of water from the freezing to the boiling point. This is equivalent to 2920 Centigrade heat-units, or to 5230 B. T. U. Calorific Value. The calorific value of the fuel would therefore be the product of this number by the number of parts of oxygen required. Thus let a equal the number of parts of oxygen required for each combustible ; then the heat produced by the combustion is h = 29200: in Centigrade units ; h 52300: in B. T. U. Thus, for example, in the combustion of carbon to CO 9 , 412 EXPERIMENTAL ENGINEERING. [ 346, 2| parts by weight of oxygen are required for each one of carbon ; hence for this case a = 2f , and h = 5230 X 2f = 14,100. In the combustion of hydrogen to water 8 parts by weight of oxygen are required, and in this case a 8 ; hence h = 5230 X 8 == 41,840. This is about two thirds of the actual value of the calorific power of hydrogen, but does not differ much from the heat available in ordinary combustion. In case of a compound body, let a fuel contain a, b, c, and d parts by weight of different combustible ingredients ; and let , 01 1 , o 70 o o^ o 20 Peat dry o s8 o 06 O "31 5 tO I H J u 7 68 \Vood dry . . O ^ J O CK7 42 o O OI air-dried, 20% H 2 O. M neral oil 39- 6 0.85 4.8 0. 1 5 34-8 0.01 6.00 I e 7 348. Principle of Fuel-calorimeters. The caloric value of a fuel is determined by its perfect combustion under such conditions that the heat evolved can be absorbed and measured. It is essential in such cases that (i) the combustion be perfect, and that (2) the heat evolved be absorbed and measured. The combustion may take place in atmospheric air, in oxy- gen gas, or in combination with a chemical that supplies the oxygen required. It is essential in all cases that the supply of oxygen be adequate for perfect combustion. The heat evolved by combustion is determined by the rise in temperature of a given weight of water in a calorimeter of which the cooling effect, K, has been carefully determined, and in which the escaping gases are reduced to the temperature of the room. Let w equal the weight of fuel, E the heat evolved in heat-units by the combustion of one part, ^Fthe number of parts by weight of water heated from a temperature t' to /. Then if the escaping gases be reduced in temperature to that of the room, 4 1 6 EXPERIMENTA L ENGINEERING. [ 3 5 I . from which w 349. Method of Obtaining Sample of the Fuel. The calorimetric determination is made only on a very small portion of the fuel, and care should be exercised to have the se- lected sample fairly represent the fuel to be tested. To select a sample of coal for calorimetric examination several lots of ten pounds each should be chosen from different por- tions of the coal to be tested. These should be put in one pile, thoroughly mixed, and from the mixture several lots of one pound each taken. These latter quantities are to be pulver- ized, thoroughly mixed into one pile, and from this the required sample selected. It is recommended that the sample be sub- jected to a considerable pressure by placing it in a cylinder and compressing it by means of a piston moved by hydraulic pressure or by a screw : this is of especial importance if the fuel is to be burned in oxygen gas, since small particles are likely to form an explosive mixture; and further, soot and tarry masses, which under the most favorable circumstances might be burned, will be found in the residue. 350. Heat-equivalent of the Calorimeter. The effect of the calorimeter is most conveniently expressed as equivalent to a given weight of water; this is obtained, as for calorimeters used in determining the quality of steam (see Article 317, page 371), either by finding the sum of the products of the weights and specific heats of the various constituents of the calorimeter, or by comparing the results obtained with those which should have been found by the combustion of some fuel whose calo- rific power is known as for instance pure carbon in oxygen gas or again by its cooling effect on steam of known pressure and weight, or on warm water as explained on page 372. 351. Method of Determining Perfect Combustion. The quality of the combustion is only to be determined by an analysis of the resulting gases and of the products of combus- tion. In case of perfect combustion all carbon is reduced to 35 2 -] THE HEATING VALUE OF FUELS. 417 CO 9 , all available hydrogen to water, sulphur to sulphuric acid; and further, the sum of the weights of all the products of com- bustion should, after deducting the air and oxygen obtained from the atmosphere, equal the original weight of the coal. The method adopted by Favre and Silbermann * of ascer taining the weight of the substances consumed by calculation from the weight of the products of combustion was as follows : Carbonic acid was absorbed by caustic potash, carbonic oxide was first oxidized to carbonic acid by heated oxide of copper and then absorbed by caustic potash ; water vapor was absorbed by sulphuric acid. This system showed that it was necessary to analyze the products of combustion in order to detect im- perfect action. Thus in the case of substances containing car- bon, CO was always present to a variable extent with CO a , and corrections were necessary in order to determine the total heat due to the complete combination with oxygen. The conclusion arrived at by these experimenters was that in gen- eral there was an equality in the heat disengaged or absorbed in the respective acts of chemical combination or of decom- position of the same elements ; that is, the heat evolved during the combination of two simple elements is equal to the heat absorbed at the time of the chemical separation, and the quan- tity of heat evolved is the measure of the sum of the chemical and mechanical work accomplished in the reaction. 352, Favre and Silbermann's Fuel-calorimeter. This apparatus, as shown in Fig. 161, consisted of a combustion- chamber, A, formed of thin copper, gilt internally, and fitted with a cover through which solid combustibles could be intro- duced into the cage C. The cover was traversed by a tube, E y connected by means of a suitable pipe to a reservoir of the gas to be used in combustion, and by a second tube, D, the lower end of which was closed with alum and glass, transparent but adiathermic substances -which permitted a view of the process of combustion without any loss of heat. For convenience of observation a small inclined mirror was placed above the peep tube D. *See Conversion of Heait into Work : Anderson, EXPERIMEN TA L ENGINEERING. [352. The products of combustion were carried off by a pipe, F, the" lower portion of which constituted a thin copper coil, and the upper part was connected to the apparatus in which the non-condensible products were collected and examined. The whole of this portion of the calorimeter was plunged into a thin copper vessel, G, silvered internally and filled with water, which FIG. 161. FAVRE AND Sn. HERMANN'S FUEL-CALORIMETER. was kept thoroughly mixed by means of agitators, H. The second vessel stood on wooden blocks inside a third one, /, the sides and bottoms of which were covered with swan-skins with the down on, and the whole was immersed in a fourth vessel, y, filled with water kept at the average temperature of the laboratory. Thermometers, K, K, of great delicacy were 353-] THE HEATING VALUE OF FUELS. 419 used to measure the increase of temperature in the water sur- rounding the combustion-chamber. The quantity of heat developed by the combustion of a known weight of fuel was determined by the increase of temperature of the water con- tained in the vessel G. For finding the calorific value of gases only, the cage C was removed and a compound jet, NO, sub- stituted for the single gas-pipe, ignition being produced by an electric spark or by some spongy platinum fixed at the end of the jet. 353. Thompson's Calorimeter. Thompson's Calorimeter* is often employed for determination of the heating values of fuels. It consists of a glass jar graduated to contain 1934 grams of water; in this are inserted (i) a thermometer to indi- cate elevation of temperature, and (2) a cylindrical combustion- chamber with a capacity of about 200 grams of water. This chamber is capped at the top, and a small tube furnished with a valve is screwed into it, to hold the fuel. The combustible to be examined, 2 grams, is mixed as intimately as possible with 22 grams of a very dry mixture of 3 parts of potassic chlorate and i part of potassic nitrate, and introduced into the combus- tion-tube ; a nitrate of-lead fuse is added and lighted. This tube is introduced into the combustion-chamber, the cap screwed on, and the whole placed without delay in the water of the calorimeter. The combustion takes place directly in the water, and the gases disengaged rise to the surface. The water is proportioned to the fuel as 966 is to i, so that the rise in temperature in degrees F. is proportional to the evaporative power. The oxygen required for the combustion is supplied by the chemicals added. The water-equivalent of the calorim- eter as above described is about ten per cent. When com- bustion has ceased, the rise in temperature of the water is observed ; to this one tenth is added for the water value of the calorimeter. The corrected number gives the number of grams of water which a gram of the combustible can evaporate. *See Chemical Technology, Vol. I. 420 EXPERIMENTAL ENGINEERING, [ 355. 354. The Berthier Calorimeter.* This calorimeter is based on the reduction of oxide of lead by the carbon and hydrogen of the coal, the amount of lead reduced affording a measure of the oxygen expended, whence the heating power may be calculated by Welter's law, Article 345. One part of pure carbon being capable of reducing 34^ times its weight in lead. The operation is performed by mixing intimately the weighed sample (10 grams) with a large excess of pure litharge (400 grains). The mixture, placed in a crucible sufficiently capacious to contain three times its bulk, and rendered im- pervious to the gases of the furnace by a coating of fire-clay or by a glaze, is covered with an equal quantity of pure litharge (protoxide of lead). The crucible, being closed with a lid and placed on a support in the furnace, is slowly heated to redness, and when the gases which cause the mixture to swell considerably have escaped, it is covered with fuel and strongly heated for about ten minutes, in order to collect the globules of lead in a single button. The oxygen from the litharge com- bines with and burns the combustible ingredients of the fuel, leaving for every equivalent of oxygen consumed an equiva- lent of reduced metallic lead. The heating power is calculated as follows: I part of pure car- bon requires 2.666 parts of oxygen by weight, which taken from litharge leaves 34.5 parts of metallic lead. The same weight of carbon is sufficient to heat 80 parts of water from 32 to 212. Hence every unit of lead reduced by any kind of fuel corre- sponds by Welter's law with = 2.23 parts of water raised from the freezing to the boiling point. 355. The Berthelot Calorimeter. This calorimeter, as modified by Hempel, consists of a very strong vessel with a capacity of about 250 c.c., into which the fuel is placed after being compressed into a solid form ; the combustion is per- * Chemical Technology, Vol. I., page 337. 3 5 ^.] THE HEATING VALUE .OF FUELS. 421 formed in an atmosphere of oxygen gas under a pressure of 10 to 12 atmospheres.* The fuel is ignited by an electric spark, and the heat gen- erated is known by measuring the rise in temperature in the sur- rounding water, as in the Favre and Silbermann calorimeter. The oxygen gas is generated in a tube about one inch in diameter connected to the calorimeter by an intervening tube about .J inch in diameter. To this latter tube is attached a pressure-gauge to indicate the pressure, and a safety-gauge to prevent damage from explosion or excessive pressure. A stop-cock is also inserted close to the calorimeter. For gen- erating the oxygen the tube is filled with 40 grams of a mix^ ture of equal parts of manganese dioxide and potassium chlorate. It is then heated by the full, flame of a Bunsen burner applied first at the end nearest the calorimeter and gradually moved to the farther end. To use the instrument, the fuel, connected to platinum wires for electrical ignition, is introduced and suspended in the calorimeter, the top of which is firmly screwed on and the valve closed. Oxygen gas is then generated until the pressure reaches 90 pounds, and exhausted into the air to remove other gases from the calorimeter. The escape-valve from the calo- rimeter is closed and oxygen gas generated until the pressure- gauge shows 150 to 175 pounds pressure per square inch ; then the connecting stop-valve is closed and the electric current ap- plied. After the heat of combustion has been absorbed the determination is made as with the Favre and Silbermann calo- rimeter. 356. Continuous Coal-calorimeter. A continuous coal- calorimeter, designed chiefly by Wm. Kent of New York, was employed in the recent investigations of Hoyt and Mc- Gregor at Sibley College in determining the heating values of various American coals. This calorimeter differs from that used by Favre and Silbermann principally in size and form. The fuel is introduced, by means of a piston working in a tube, to a chamber surrounded with fire-clay, and the combustion * See Hempel's Gas Analysis, translated by Dennis. 422 EXPERIMENTAL ENGINEERING. [357* arranged to take place either in an atmosphere of oxygen gas, or in air at any pressure. The coal is ignited by an electric spark or by a jet of illuminating-gas; the products of combus- tion are carried through a coiled pipe immersed in a vessel of water. Cold water is continuously supplied at one point and the heated water removed at another, the product of the weight of water by the gain in temperature, corrected by the calorim- eter equivalent, being the calorific power of the coal. The products of combustion and the ash in each case being ana- lyzed, to determine the character of the combustion. In using the instrument, the same precautions are to be observed as in using the continuous calorimeters for steam, Article 324, page 382. No observations are to be taken until the instrument is in full operation and the working conditions are uniform. 357. Value of Coal determined by a Boiler-trial. The calorific value of a coal is sometimes determined by the amount of water evaporated into dry steam under the con- ditions of use in a steam-boiler. This method is fully ex- plained in the latter part of the present work in the chapter on the methods of testing steam-boilers. The calorific values obtained in actual boiler-trials are much less than those ob- tained in the calorimeters, because of loss of heat by radiation into the air and by discharge of hot gases into the chim- ney. The results obtained by such a trial by Prof. W. R. Johnson at the Navy Yard, Washington, in 1843, w ^ tn a small cylindrical boiler, were as follows : Coal per Hour. Water evaporated per Hour. Water Coal. Fire- evaporated from grate, Sq. Ft. Total. Per Sq. Ft. of Total. Per Sq. Ft. of 212 F. par ib. of Coal. Grate. Grate. Anthracite (7 samples). . . 14.30 94-94 6.64 12.37 0.87 9- 6 3 Bituminous coals, free burning (it samples). . . 14.14 99.16 7.01 13-73 0.97 9.68 Bituminous coking coals, Virginian (10 samples).. 14.15 105.02 7.42 12. l6 0.86 8.48 Average 14.20 99.71 7.O2 12-75 0.90 9.26 35 8 -] THE HEATING VALUE OF FUELS. 423 358. Object of Analysis of the Products of Combustion. The products resulting from the combustion of ordinary fuel contain principally a mixture of air, CO 2 , and some combus- tible gases, as CO and H. To determine whether or not the combustion is perfect, it is necessary to know the percentage that the combustible gases escaping bear to the total products of combustion. It is also important to know whether the air supplied is sufficient for the purposes of combustion, and also whether it is in excess of the amount actually required. As shown in Article 346, page 412, the presence of an excess of air over that required has the effect of lowering the tempera- ture of the furnace ; steam would have the same effect even in a greater degree, as can readily be shown by calculation. From a careful examination of the products of combustion we should be able to ascertain its character and make the necessary corrections for such losses as may be due to imper- fect combustion. The methods to be employed must be such as any en- gineer can fully comprehend, and the apparatus portable and convenient. The degree of accuracy sought need not be such as would be required in a chemical laboratory where every convenience for accurate work is to be found. Indeed, considering the approximations to be made in its ap- plication, it is very doubtful if determinations nearer than one per cent in volume are required, or even of any value. Such determinations are obtained readily with simple instruments, and serve to show the approximate condition of the gaseous products of combustion. The student is referred to " Hand- book of Technical Gas Analysis," by Clemens Winkler (London, John Van Voorst), and to " Methods of Gas Analysis," by Dr. W. Hempel, translated by L. M. Dennis (Macmillan & Co.) ; also to a paper on tests of a hot-blast apparatus by J. C. Hoad- ley, Vol. VI. Transactions of the American Society of Mechani- cal Engineers. In a thorough examination of the value of fuel, the ashes should also be analyzed, since if they contain any combustible, 424 EXPERIMENTAL ENGINEERING. [ 359- or partly burned combustible, the heating value must be de- termined, and proper allowance made for the same. 359. General Methods of Flue-gas Analysis. The gases to be sought for are CO 2 , CO, O, and H. Unless the temperature is very high, CO is found only in very small quantities, and rarely exceeds one per cent. Prof. L. M. Dennis, of Cornell University, makes the statement that Dr. W. Hempel, of Dresden, whose principal work has been the analysis of gases, states that rarely ever is more than a trace of carbonic oxide (CO) to be found in the products resulting from ordinary combustion. Considering the difficulty of ab- sorbing CO, and the consequent errors that are likely to arise, it may be in general better to neglect it. The hydrogen, H, present js also a very small quantity, unless the temperature js r abnormally low, and can be neglected without sensible error. -: THe analysis may be of two kinds, gravimetrical and volumetric. The former is seldom used, but will be found described in an article by J. C. Hoadley, Transactions of the American Society of Mechanical Engineers, Vol. VI., page 786.^ In this case the various gases are passed through 'solid absorbents, and. the several constituents successively absorbed and weighed. The method of analysis usually adopted is a volumetric one, and consists of the following steps, which will be described in detail later on. A. The sample is first collected and then introduced into a measuring-tube; 100 c.c. of the gas is retained, the remainder wasted. B. The constituents of the gas are then absorbed by suc- cessive operations, in the following order : carbonic acid (CO 2 ), free oxygen (O), carbonic oxide (CO), and hydrogen (H). The absorption is accomplished by causing the gas to flow over the reagent in the liquid or solid form, which is introduced into the gas or remains permanently in a separate treating- tube. It is then made to flow back to the measuring-tube and the loss of volume measured. The loss is due to absorp- tion, the various absorbents used being as follows : 360.] THE HEATING VALUE OF FUELS. 425 For carbonic acid, CO 9 , either potassium hydroxide (caustic potash KOH), or barium hydroxide. For oxygen, O, either (i) a strong alkaline solution of pyrogallic acid, (2) chromous chloride, (3) phosphorus, (4) metallic copper. For carbon monoxide, CO, either an ammoniacal or a hydro- chloric-acid solution of cuprous chloride. For hydrogen, H, an explosion or rapid combustion in the presence of oxygen, or absorption by metallic potassium, sodium, or palladium. The reagent usually employed as an absorbent is the one first mentioned in each case. 360. Preparation of the Reagents. Absorbents of Oxy- gen. i. Potassium pyrogallate. This is prepared by mixing together, either directly in the absorption pipette or in the apparatus, 5 grams of pyrogallic acid dissolved in 15 c.c. of water, and 120 grams of caustic potash (KOH) dissolved in 80 c.c. of water. Caustic potash purified with alcohol should not be used for analysis. The absorption of the gas should not be carried on at a temperature under I5-C. (55 Fahr.) ; it may be completed with certainty in three minutes by shaking the "gas in contact with the solution. 2. .Chromous chloride will absorb oxygen alone in a mi-xture of oxygen and hydrogen sulphide ; it is prepared with difficulty, and not much used. 3. Phosphorus is one of the most convenient absorbents: it is to be kept in the solid form under water and in the dark; the gas is to be passed, over the reagent, displacing the water, and kept in contact with it for about three minutes. The end of the absorption is shown by a disappearance of a light glow, which characterizes the process of absorption. The phosphorus will remain in serviceable condition for a long time. 4. Copper, at a red heat or in the form of little rolls of wire- gauze immersed in a solution of ammonia and ammonium car- bonate, is a very active absorbent for oxygen. Absorbents of Carbonic Acid (CO 2 ). i. Caustic potash. This solution may be used in varying strengths, depending on the method of gas analysis. With the Elliot apparatus, a solu- 426 EXPERIMENTAL ENGINEERING. [ 360. tion of 3 to 5 per cent of KOH in distilled water is sufficiently strong, the gas being kept in contact with it for several min- utes. When a separate treating-tube is used for each reagent, a solution of one part of commercial caustic potash to two parts of water is employed. The absorption is accomplished very quickly in the latter case, and often bypassing the gas but once through the treating-tube. The process is more quickly and thoroughly performed by f introducing into the treating- tubes as many rolls of fine iron-wire gauze as it will hold. 2. Barium hydroxide in solution is the best absorbent in case the quantity of CO 2 is very small ; in this case titration with oxalic acid will be required. Absorbents of Carbon Monoxide (CO). i. (a) Hydrochlo- ric-acid solution of cuprous chloride is prepared by dissolving 10.3 grams of copper oxide in 100 to 200 c.c. of concentrated hydro- chloric acid, and then allowing the solution to stand in a flask of suitable size, filled as full as possible with copper wire, until the cupric chloride is reduced to cuprous chloride, and the solution is completely colorless. (b) Winkler directs that 86 grams of copper scale be mixed with 17 grams of copper powder, prepared by reducing copper oxide with hydrogen, and that this mixture be brought slowly and with shaking into 1086 grams of hydrochloric acid of 1.124 specific gravity. A spiral of copper wire is then placed in the solution, and the bottle closed with a soft rubber stopper. It is dark at first, then becomes colorless, but in contact with the air becomes brown. The absorbing power is 4 c.c. of CO. The ammoniacial solution is to be used in case hydrogen is to be absorbed by palladium. This is prepared from the colorless solution (a) as follows : Pour the clear hydrochloric acid solution into a large beaker-glass containing i^ to 2 litres of water, to precipitate the cuprous chloride. After the pre- cipitate has settled, pour off the dilute acid as completely as of possible, then wash the cuprous chloride with 100 to 150 c.c. distilled water, and add ammonia to the solution until the liquid takes a pale-blue color. The solutions of cupric chloride de- compose readily, and in general should be used when fresh, or THE HEATING VALUE OF FUELS. 427 preserved under a layer of petroleum. The treating-tube con- taining the reagent is frequently supplied with spirals of small copper wire which tend to preserve and increase the absorb- ing capacity of this reagent. 361. Method of obtaining a Sample of the Gas. In order to take a sample of the gas for analysis from any place, such as a furnace, flue, or chimney, an aspirating-tube is intro- duced into the flue : this consists of a tube open at both ends, the outside end being provided with a stop-cock and connected with the collecting apparatus by an india-rubber tube. There FIG. 162. HOADLEY'S FLUE-GAS SAMPLER. is probably a great diversity in the composition of gases from various parts of the flue. For obtaining an average sample, J. C. Hoadley employed a mixing-box B* provided with a large number of J-inch pipes, ending in various parts of the cross-section of the flue A. An elevation of the mixing-box is shown at B'. From the mix- ing-box four tubes CC lead downward from various parts to a mixing-chamber D, from which a pipe E leads to the collecting apparatus. Two of these mixing-boxes were used, one placed in the flue a short distance above the other, and an agreement of the samples obtained from each was regarded as proof of the substantial accuracy of the sample. * Trans. Am. Soc, M. E., Vol. VI. 428 EXPERIMENTAL ENGINEERING. [ 361. It is hardly probable that a tube furnished with various branches or a long slit will give a fair sample, since the velocity of gases in the aspirating-tube is such that most of the gas will be collected at the openings nearest the collecting appa- ratus ; the author has often employed a branch-tube with holes opening in different portions of the chimney. The material for the aspirating-tube is preferably porcelain or glass, but iron has no especial absorptive action on the gases usually to be found in the flue, and may be used with satisfaction. A long length of rubber tubing may, however, sensibly affect the results. The gas should be collected as closely as possible to the furnace, since it is liable to be diluted to a considerable extent by infiltration of air through the brick-work. beyond the furnace. In order to induce the gas to flow outward and into the collecting apparatus, pressure in the collecting vessel, termed an aspirator, must be reduced below that in the flue. This is accomplished by using for an aspirator two large bottles con- nected together by rubber tubing near the bottom, or better still, two galvanized iron tanks, about 6 inches diameter and 2 feet high, connected near the bottom by a rubber tube, in which is a stop-cock; one of the bottles or tanks has a closed top and a connection for rubber tubing provided with stop- cock at the top ; the other bottle or tank is open to the atmos- phere. To use the aspirator, the vessel with the closed top is filled with water by elevating the other vessel ; it is then con- nected to the aspirating-tube, the open vessel being held so high that it will remain nearly empty. After the connection is made, and the stop-cocks opened, the empty vessel is brought below the level of the full one, and the water passing from the one connected to the aspirating-tube lessens the pres- sure to such an extent that it will be filled with gas. This process should be repeated several times in order to in- sure the thorough removal of all air from the aspirating- tubes. The liquid used for this purpose is generally water, which is an absorbent to a considerable extent of the gases 363.] THE HEATING VALUE OF FUELS. 429 contained in the flues. To lessen its absorbent power, the water used should be shaken intimately with the gas in order to saturate it before the sample for analysis is taken. When mercury is used as the liquid this precaution is not necessary. A small instrument, on the principle of an injector, in which a small stream of water or mercury is constantly delivered, is an efficient aspirator, and is extremely convenient for continu- ous analysis. 362. General Forms of Apparatus employed for Volu- metric Gas Analysis. The apparatus employed for volumetric gas analysis consists of a measuring-tube, in which the volume of gas can be drawn and accurately measured at a given press- ure, and a treating tube into which the gases are introduced and then brought in contact with the various reagents already described. The apparatus employed may be divided into two classes: (i) those in which there is but one treating-tube, the different reagents being successively introduced into the same tube ; (2) those in which there are as many treating-tubes as there are reagents to be employed, the reagents being used in a concentrated form, and the gases brought into contact with the required reagent by passing them into the special treating tube. In either case the steps are, as explained in Article 358: (a) Obtain 100 c.c. by measurement; (b) to absorb the CO 3 , bring the gas in contact with KOH, and measure the reduction of volume so caused ; this is equivalent to the percentage of CO 2 ; (c) bring the gas in contact with pyrogallic acid and KOH, and absorb the free oxygen. Measure the reduction of volume so caused ; this is equivalent to the percentage of free oxygen ; (d) determine the other constituents in a similar manner. In performing these various operations it is essential that the tubes be kept clean and that the reagents be kept entirely separate from each other. This is accomplished by washing or causing some water to pass up and down the tubes or pipettes several times after each operation. 363. Elliot's Apparatus. This is one of the most simple outfits for gas analysis, and consists of a treating-tube AB and 430 EXPERIMENTAL ENGINEERING. [ 363. FIG. 163. ELLIOT'S APPARATUS. a measuring-tube A'B', Fig. 163, connected by a capillary tube at the top, in which is a stop-cock, G. The tubes shown in Fig. 163 are set in a frame-work having an upper and a lower shelf, on which the bottles L and K can be placed. In using the apparatus, it is first washed, which is done by filling the bottles with water, opening the stop-cocks F and G, and alternately raising and lowering the bottles K and L. The bottles are then filled with clean distilled water, raised to the positions shown, and the stop-cocks G and F closed. The gas is then introduced by connecting the discharge from the aspirator to the stem of the three-way- cock F, and turning it so that its hollow stem is in connection with the interior of the tube AB ; lowering the bottle L, the water will flow out from the tube AB and the gas will flow in. When the tube AB is full of gas the cock F is closed, the aspirator is disconnected, and the gas is measured. The gas must be measured at atmos- pheric pressure. That may be done by holding the bottle in such a position that the surface of the water in the bottle shall be of the same height as that in the tube. A distinct meniscus will be formed by the surface of the water in the tube ; the reading must in each case be made to the bottom of the meniscus. To measure the gas, which will be considerably in excess of that needed, the cock G is opened, the bottle K de- pressed, the bottle L elevated ; the gas will then pass over into the measuring-tube A'B' ; the bottle K is then held so that the surface of the water shall be at the same level as in the measuring- tube, and the bottle L manipulated until exactly 100 c. c. are in the measuring-tube ; then the cock G is closed, the cock F opened, the bottle L raised, and the remaining gas wasted, causing a little water to flow out each time to clean the con- necting tubes. The measuring-tube A' B' is surrounded with a jacket of water to maintain the gas at the uniform temperature of the room. After measuring the sample it is then run over into the treating-tube AB, and the reagent introduced through 365.] THE HEATING VALUE OF FUELS. 431 the funnel above F by letting it drip very slowly into the tube AB. After there is no farther absorption in the tube AB y the cock Fis closed and the gas again passed over to the measur- ing-tube ^Z?', and its loss of volume measured. This operation is repeated until all the reagents have been used ; in each case, when the gas is run back from the measuring-tube, pass over a little water to wash out the connections ; exercise great care that in manipulating the cocks K or G no gas be allowed to escape or air to enter. 364. Wilson's Apparatus.* This apparatus is illustrated in Fig. 164. It is used in essentially the same manner as the Elliot apparatus, mercury being used as the displacing liquid in place of water. It consists of a treating-tube d, a measuring- tube a, connected at the top by a capillary tube f. The measuring- tube ends in a vessel rilled with mercury, and in this case the press- ure on the tubes can be regulated by lowering and raising the single bottle filled with mercury, and the gas can be manipulated as in the Elliot apparatus, using one bottle instead of two. Reagents are in- troduced into the funnel e, and come in contact with the gas in the treating-tube d. The collecting-tube used with this apparatus is shown at B, and consists of a vessel filled with mer- cury. One side is connected to the aspirator-tube ; some of the mercury is allowed to run out through a cock, and the space is filled by the gas. mercury is retained to form a seal. 365. Fisher's Modification of Orsat's Apparatus. This * Thurston's Engine and Boiler Trials, p. 107. FIG. 164. API \NALYSIS. Sufficient 432 EXPERIMENTAL ENGINEERING. [3^5- apparatus, shown in Fig. 165, belongs to the class in which 'each reagent is introduced in a concentrated form into a special treating-tube. The apparatus consists of a measuring-tube surrounded by a water-jacket, into which the gas can be intro- duced substantially as explained for the Elliot apparatus. Each FIG. 165. FISHER'S GAS-ANALYSIS APPARATUS. reagent is introduced in a concentrated form into a pair of burettes connected at the bottom by a U-shaped tube. In making an analysis the gas is first drawn into the measuring-tube and 100 c.c. retained ; the cock in the tube leading to one of the treating-tubes is then opened, the bottle raised, and the gas driven over into the treating-tube. This 3^6.] THE HEATING VALUE OF FUELS. 433 operation is facilitated by connecting a soft rubber bag to the opposite side of the treating-tube, by means of which alternate pressure and suction can be applied, and the reagent protected from the atmosphere. After the absorption is com- plete, which will take from one to three minutes in each tube, the gas is returned to the measuring-tube by lowering the bottle and exerting pressure on the attached rubber bag. The rubber bag is not shown in Fig. 165, and is not required, pro- vided the treating-tube is completely filled with the reagent on the side toward the measuring-tube. The treating-tubes are filled in order from the measuring- tube with the following reagents: (i) with 50 per cent solution of KOH ; (2) with a solution of pyrogallic acid and KOH, or with sticks of phosphorus (see Article 359); (3) with a hydrochloric. acid or an ammoniacal solution of cuprous chloride in contact with copper wire (see Article 359). In the first treating-tube is absorbed CO 3 , in the second O, and in the third CO. A modification of the Fisher apparatus has a fourth tube in which hydrogen can be exploded; the reduction in volume, due to the explosion, gives the amount of hydrogen present. Fisher's apparatus can be used with water or mercury for obtaining the required pressure to move the gases. It is ex- tremely portable, accurate, and convenient for use. For engineering uses, when an apparatus must be carried from place to place for determinations, it is the most valuable form which has been devised. 366. Hempel's Apparatus for Gas Analysis.* This ap- paratus, shown in Figs. 166 to 170, is especially designed for the accurate analysis of the constituents of various gases ; for laboratory use it presents many advantages over the other apparatus described. The apparatus consists of the following parts: I. The measuring burette, shown in Fig. i66a, which is constructed and used as follows: It is furnished with an iron * See Hempel's Gas Analysis, by L. M. Dennis. Catalogue of Eimer & Amend, New York. 434 EXPERIMENTAL ENGINEERING. [ 366. base, which 'is connected by a rubber tube to an open tube a (see Fig. 166) with a similar base. The stop-cock d is opened, the tube a elevated, and water or mercury, whichever may be FIG. 166. FIG. i66a. used, flows from a over to b. Gas is introduced as follows : The measuring-tube b is filled with liquid, the cocks d and c closed, and connection made at e to the vessel containing the gas to be measured ; the cocks d and c are then opened, the 366.] THE HEATING VALUE OF FUELS. 435 tube a lowered ; the liquid will then flow from the measuring- tube b to a, and the gas will fill the measuring-tube. To meas- ure the volume of gas, hold the tube a as shown in Fig. 165, so that the water-level shall be the same in both tubes, thus bringing the gas under atmospheric pressure. Read the vol- FlG. 167. FIG. 168. FIGS. 169-170. HEMPEL'S ABSORPTION BURETTES. ume directly by the graduation corresponding to the lower edge of the meniscus. The absorption-pipettes are different in form from those used in the Fisher apparatus, and are connected only as required to the measuring-burette, but are used in essentially the same way. Several forms of these are employed as shown in Figs. 167 to 170. The forms shown in Fig. 168 and Fig. 170 are EXPERIMENTAL ENGINEERING. [ 367 ordinarily used for reagents in solution. In such a case the measuring-tube is connected at e, Fig. 168, the reagent occupy- ing -the bulbs a and b. The top of the measuring-burette ^, Fig. 165, is connected to the absorption-pipette, and the gas moved alternately forward and backward as required by raising or lowering the tube a. In case reagents in the solid form are to be used, the absorption-pipette is made of the form shown in Fig. 169, in case regents which decompose very easily are used a pipette of the form shown in Fig. 167 is employed. The general methods employed are the same as those pre- viously described. 367. Deductions ancj Computations from Flue-gas Analysis. The determinations give the percentage of volume of CO 2 , O, and CO existing in the products of combustion. Of these constituents the carbon is derived entirely from the fuel and the oxygen in great part from the atmosphere. Every part of oxygen drawn in from the atmosphere brings with it nitrogen, which passes through the furnace unchanged. The nitrogen is calculated as follows : The proportion of nitrogen to oxygen existing in the atmosphere is 79 to 21 by volume; call this ratio 5; denote the percentage of volume of the gases existing in the sample as follows: CO 2 by K', oxygen by O\ CO by U', nitrogen by N 1 '. Then we shall have K'+ O' + U' + N' = 100 per cent, . . . (i) from which N' = 100 - (K f + O' + U') (2) If the oxygen were all derived from the atmosphere, both the amount of nitrogen N' and of carbonic oxide U' could be computed, since in such a case the volume occupied by the free oxygen before combining would equal 2 K'+0' + U f . Hence the nitrogen N" = S(2K' + 0'+ U') (3) 367.] THE HEATING VALUE OF FUELS. 437 Substituting this latter value in equation (i), K' + O' + U' + S(2K' + 0'+ U') = 100, from which (4) Since there is to be found from 2 to 5 per cent of oxygen in the fuel, equation (4) will generally give negative values for the CO, and shouJ^Lnot be used. In practice, if the CO cannot be determined it can be con- sidered zero without sensible error, since it seldom exceeds one half of one per cent. The amount of oxygen found in the coal can be computed as follows : The value of the nitrogen in the sample is given in equa- tion (2). The oxygen O" drawn from the air with the nitrogen is N f .. - ., ... . (5) Hence that obtained from the fuel must be 2 K f +0' -O". In equation (2) the nitrogen is calculated on the assumption that the flue-gas contains only oxygen and carbon ; in case hydrogen, H ', is present, then the value of the nitrogen would be N' = ioo-(K' + 0'+U' + H'}. ... (6) The principal object of the flue-gas analysis may be con- sidered as accomplished when the percentage of uncombined 43 8 EXPERIMENTAL ENGINEERING. [ oxygen and of CO a is determined, since in every case the amount of the ether gases present will be very small. From these we can find the ratio of the total oxygen supplied to that used. This ratio, which is called the dilution coefficient X> shows the volume of air supplied to that required to furnish the oxygen for the combustion. It may be computed by comparing the total volume, of nitrogen with that required to unite with the combined oxygen, from which N ' The analysis and the computations considered relate to volumes of the various gases. They may be reduced to pro- portional weights by multiplying the volume of each gas by its atomic weight and dividing by the total weights. Knowing the proportional weights for each gas and the total carbon consumed, the total air passing through the furnace can be computed. Thus for the perfect combustion of a pound of carbon will be required 2.67 pounds of oxygen, for which will be required 11.7 pounds of air. If the ratio of air used to that required be X, then the weight of air per pound of fuel equal \\.'jX. One pound of air at 32 Fahr. occupies 12.5 cubic feet. Knowing which, the volume of air per pound of coal can be computed as equal 12.5 X 11.7^ 14-6.2X. The maximum temperature T m , that can possibly be attained in the furnace, is to be calculated as in Article 346, page 413. T I45QQ (3.67X0.216) + (8.88)(o.2 4 ) + (X - i)(i 1.7X0.238) = 2.91 + 2 4 8%T- ^^approximately. . . (8) 368.] THE HEATING VALUE OF FUELS. 439 Having the maximum temperature of the furnace and the temperature of the escaping gases, the efficiency, E, of the furnace may be calculated by an application of Carnot's law as Z? , ^ (9) in which T m f is the absolute temperature of the furnace and T' the absolute temperature of the escaping gases. The absolute temperature in degrees Fahr. is found by adding 460 to the thermometer-reading. That is, T m f = T m + 460. Rankine, in his work on the steam-engine, pages 287 and 288, gives formulae for computing velocity of flow in flues, the head required to produce a given reading of the draught- gauge, and the required height of chimney. These formulae are developed from the experimental wo^k of Pecle"t, and while they do not agree well with modern practice, still give interesting results for comparison. The practical application is shown in the following example of an analysis made at Cornell University, the coal burned being that obtained after deducting ashes and clinkers. 368. Form for Data and Computations in Flue-gas Analysis. Test made Nov. 3, 1890. Determinations made by F. Land, H. B. Clarke, and O. G. Heilman. Location of plant, Ithaca, N. Y. Owners, Cornell University. Area of grate, sq. ft .............................................. l8l Area of chimney, sq. ft. (symbol A) ............................... 12.5 Height of chimney, in feet (symbol ff') .............. . .............. loo Length of heated flue (symbol /), feet ................ . ............. 13 Inside perimeter of chimney, feet ................................... 14 Number of boilers ................................................ 3 Size of boilers: one of 61 H. P., two of 250 H. P. Kind of boilers : Water-tube, made by Babcock & Wilcox. Character of draught, forced by steam-blowers. 440 EXPERIMENTAL ENGINEERING. [ 368. c - -1- ^ O C^ CO O W O o o o ""* r^ o c^ O c^ O O N 1-1 00 w r -^- m CO r>. M ^- c -H co oo u r ^ Q. N rj- O OO ;terminatio . i^ do o o ^vdvdddw' S rl N Tn ~ "" CO "* ? c nj H \O O^ fj tn u r a; o. r^ o S' Q - CO J ^ * O^ u^ vO O *^" J O O C^ "~ * - oo CO *< <- ^ c _ w " l^r ^ i r- m ID 00 ^ |M '. ^^ 5 ^ E ' f'fc P 00 7+|j^ | N 3 f C :> 4- U V I 1 ::::::::: 8 i *S i O I sl * ' ll \ r ^^^x>^ O^^; ^ i * J3 D _ 2 : : : g > J c OT <*- g i'll^lss.^s^ 1 ^|'33^o .^S " C 1 I '* d "H * d J 1 Proportional weight Per cent free O. by Weight. . . Per cent total O hv wpio-Vit bO '5 1 ' ? fljj c V (J 3 68.] THE HEATING VALUE OF FUELS. 441 NO v o D 8? ^ r^ co O CT* oc t>- m O H- CO N w > O^ f 3 en r i < c 1 5 cT 3 1 CO a ON OC CO 8 i rj vO O^ O f""* C N C > CO K > ( Bin *^ 4 ft co m r i- I ^ CO f* c N ^ ^o in rf co 8 3 d M co O m r^ ^ r co oc < ? N M gs co M m M v ) co r- I 5 N CO M o a C ^* "" w "1^ M o" oo " T ^ ^ + q ^ EN ^ ^ W CO J 1 Js J "a O "fr H L 2Q m "^ \o c^ + I rt *a c rt H s* ^ * SL , - *" J 'L. ^^- ^ S 3 d ^ \ ^ 2 N OT |y ^ ^ V & s i oq k , ^^ * \ ^ ^ 5 i i 1 'So d s w S 43 bi) S 2- rt c C CO fe * I -3 ^M I ^ & JM **!) en " : g : 't c 1 i y c bfl J "o bo "* rt i 3 ! a. 1 fil c: i HH c Z. * i i Jlr E c c. *o o v i O "" a E \ 6 c3 V I 3 - c u o u > rt ^ ' * H ,, - v- II *o ' T3 1 O "rt 3 a 8 c 1 *. i b o -a 1 V Co t/) S a 3 C ' ! 2 ' S k & Q. B = 8 E o a. :u *-> . I S. " 1 . ^ I J , s ^ t> ' a; ^ i 1 | ) T3 C g c^ >- 3 c 1 2 I : ; rt ^ ^ i "= s ' - s = 2 r * a- :& * 'x 3 C 1 1 : c ^ *" ' ' 4, ' ' 2 1 "O 3 V QJ J "5 ' 1 M I 78 S a, I| 5 HE J- 03 "o 1 Hp ^C "^ u r; E x S > > * IT * < H h CHAPTER XV. METHODS OF TESTING STEAM-BOILERS. 369. Object of Testing Steam-boilers. The object of the test must be clearly perceived in the outset ; it may be to determine the efficiency of a given boiler under given condi- tions; the comparative value of various fuels, or of different boilers working under the same conditions; or the quantity of coal consumed and water used in providing steam for a given engine. The results of .the test are usually expressed in pounds of v/ater evaporated for one pound of the fuel used. The conditions of temperature and pressure between which boilers work vary within wide limits, the amount of heat ab- sorbed per pound of steam produced is not constant, and a standard of reference is necessary. Thus to convert a pound of steam from feed-water at a temperature of 70 degrees Fahr. into steam at 80 pounds absolute pressure per square inch will require, per pound of steam, (1174.3 70 + 32) = 1036.3 B. T. U. ; but to convert a pound of water at a temperature of 212 into steam at atmospheric pressure will require only 967 B. T. U. To compare the work done with a standard con- dition it is customary to express the results of the test as equivalent to the evaporation per pound of fuel from water at 212 Fahr. to steam at atmospheric pressure, or, in other words, " from and at 212." The fuel also varies greatly in its evaporative power, as shown in the preceding chapter, and, moreover, a certain propor- tion is likely to drop through the grates unconsumed, so that 442 37 1 -] METHODS OF TESTING STEAM-BOILERS. 443 it is customary to reduce the results still further, and to find the evaporation per pound of the combustible part. 370. Definitions. The following terms are frequently used : Actual evaporation. This is the evaporation per pound of fuel or of combustible under the actual conditions of the test, uncorrected for temperature of feed-water and for moisture. Equivalent evaporation from and at 212 is the amount of water that would have been evaporated had the temperature of feed-water been 212, the steam dry and at atmospheric pressure. If x represent the quality of steam, e the factor of evaporation, the equivalent evaporation is equal to the actual multiplied by xe. Factor of evaporation is the ratio that the heat, A, existing in one pound of steam at the given pressure and reckoned from the temperature, /, of feed-water, bears to the total heat of evaporation at 212, r. That is, _ A table of the factors of evaporation is given in the Appendix. The ash is the actual incombustible part of the coal; it is the residue which falls through the grates, less any combustible particles. The combustible is the fuel less the residue which falls through the grates ; it is the weight of that portion actually burned. In the absence of any determinations whatever, the combustible is frequently assumed as $ of that of the coal. The quality of the steam is the percentage by weight of dry saturated steam in a mixture of steam and water. It is to be found by a throttling or separating calorimeter attached very near the boiler (see Articles 334 to 338). 371. The Efficiency of a Boiler. The efficiency is the ratio of the heat supplied to that utilized. The heat supplied is measured by the coal consumed, less the heat discharged into the chimney ; it is assumed that it is all converted into 444 EXPERIMENTAL ENGINEERING. [373- CO and CO 2 , and that each pound of carbon converted into CO 2 gives off 14,500 B. T. U., and each pound converted into CO generates 4400 B. T. U. The amount of coal consumed is obtained by carefully measuring and deducting all ash and un- consumed portions. The relative proportions of CO 2 and CO are obtained by a flue-gas analysis (see Articles 363 to 367). The heat utilized is obtained by weighing the water evap- orated into dry steam and multiplying by the heat required, as given in a steam-table, to convert one pound from the tem- perature of feed-water into steam of the given pressure, reduc- ing this result if necessary for any moisture in the steam. The moisture is to be found as explained in Article 334 or 337- 372. Efficiency of the Furnace. This is not usually con- sidered separately from the boiler. It can be obtained (see Article 367) by finding the temperature of the furnace with a pyrometer as explained in Article 304, page 358, or by compu- tation as explained in Article 346, page 412, and by measure- ment of the temperature of the entering and discharged gases. Thus let T f be the temperature of the furnace, t d that of the discharged gas. t r that of the boiler-room. Then the efficiency is, by application of Carnot's cycle (see Article 368), 7} +460 The heat discharged from the furnace is in part utilized in converting water into steam, in part dissipated in radiation, and in part discharged into the flue. These losses should, if possible, be separately determined. It is recommended that the temperature of the furnace and of the flue be measured in each boiler test. 373. Horse-power of a Boiler. The horse-power of a boiler is a conventional definition of capacity, since the boiler of itself does no work. As the weight of steam required for different engines varies within wide limits, an arbitrary rating was adopted by the judges of the Centennial Exhibition in 375-] METHODS OF TESTING STEAM-BOILERS. 445 1876 as a standard nominal horse-power for boilers. This standard, which is now generally used, fixed one horse-power as equivalent to 30 pounds of water evaporated into dry steam per hour from feed-vvater at 100 Fahr., and under a pressure of seventy pounds per square inch above the atmosphere. This is equal to an evaporation of 34.488 pounds from and at 212 F. The " unit of evaporation " being 966.7 B. T. U., the commer- cial horse-power is 34.488 X 966.7 = 33,600 B. T. U. 374. Graphical Log. The results of a boiler-test can be represented graphically by considering intervals of time as proportional to the abscissae, and ordinates as proportional to the various pressures and temperatures measured. The graph- (9216.1) 10.30 10.50 11.10 11.30 11.50 12.10 12.30 12.50 1.10 1.30 1.50 .10 2.JO 2JO 3.W 8UJO OM 4.10 4.30 FIG. 171. ical representation is valuable as showing variations in any of these quantities. The boiler-test is usually made in connection with that of an engine, and the complete log is represented on one sheet, as shown in Fig. 171 (from Thurston's Engine and Boiler Trials). 375. Method of Making a Boiler-test.- A standard method of making a boiler-test was adopted by the American Society of Mechanical Engineers, and is published in Vol. VI. 446 EXPERIMENTAL ENGINEERING. [ 375- of the Transactions. This method is complete and should be followed in every case. The method is as follows. PRELIMINARIES OF A TEST. I. In preparing for and conducting trials of steam-boilers, the specific object of the proposed trial should be clearly defined and steadily kept in view. II. Measure and record the dimensions, position, etc., of grate and heating surfaces, flues and chimneys, proportion of air-space in the grate-surface, kind of draught, natural or forced. III. Put the Boiler in good condition. Have heating-surface clean inside and out, grate-bars and sides of furnace free from clinkers, dust and ashes removed from back connections, leaks in masonry stopped, and all obstructions to draught removed. See that the damper will open to full extent, and that it may be closed when desired. Test for leaks in masonry by firing a little smoky fuel and immediately closing damper. The smoke will then escape through the leaks. IV. Have an understanding with the parties in whose inter- est the test is to be made as to the character of the coal to be used. The coal must be dry, or, if wet, a sample must be dried carefully and a determination of the amount of moisture in the coal made, and the calculation of the results of the test corrected accordingly. Wherever possible, the test should be made with standard coal of a known quality. For that portion of the country east of the Alleghany Mountains good anthracite egg coal or Cumberland semi-bituminous coal may be taken as the stand- ard for making tests. West of the Alleghany Mountains and east of the Missouri River, Pittsburg lump coal may be used.* V. In all important tests a sample of coal should be selected for chemical analysis. * These coals are selected because they are almost the only coals which con- tain the essentials of excellence of quality, adaptability to various kinds of fur- naces, grates, boilers, and methods of firing, and wide distribution and general accessibility in the markets. 375-] METHODS OF TESTING STEAM-BOILERS. 447 VI. Establish the correctness of all apparatus used in the test for weighing and measuring. These are : 1. Scales for weighing coal, ashes, and water. 2. Tanks, or water-meters f or measuring water. Water- meters, as a rule, should only be used as a check on other meas- urements. For accurate work, the water should be weighed or measured in a tank. 3. Thermometers and pyrometers for taking temperatures of air, steam, feed-water, waste gases, etc. 4. Pressure-gauges, draught-gauges, etc. VII. Before beginning a test, the boiler and chimney should be thoroughly heated to their usual working temperature. If the boiler is new, it should be in continuous use at least a week before testing, so as to dry the mortar thoroughly and heat the walls. VIII. Before beginning a test, the boiler and connections should be free from leaks, anb! all water-connections, including blow and extra-feed pipes, should be disconnected or stopped with blank flanges, except the particular pipe through which water is to be fed to the boiler during the trial. In locations where the reliability of the power is so important that an extra feed-pipe must be kept in position, and in general when for any other reason water-pipes other than the feed-pipes cannot be disconnected, such pipes may be drilled so as to leave openings in their lower sides, which should be kept open throughout the test as a means of detecting leaks, or accidental or unauthorized opening of valves. During the test the blow-off pipe should remain exposed. If an injector is used, it must receive steam directly from the boiler being tested, and not from a steam-pipe, or from any other boiler. See that the steam-pipe is so arranged that water of con- densation cannot run back into the boiler. If the steam-pipe has such an inclination that the water of condensation from any portion of the steam-pipe system may run back into the boiler, it must be trapped so as to prevent this water getting into the boiler without being measured. 448 EXPERIMENTAL ENGINEERING. [ 375. STARTING AND STOPPING A TEST. A test should last at least ten hours of continuous running, and twenty-four hours whenever practicable. The conditions of the boiler and furnace in alf respects should be, as nearly as possible, the same at the end as at the beginning of the test. The steam-pressure should be the same, the water-level the same, the fire upon the grates should be the same in quantity and condition, and the walls, flues, etc., should be of the same temperature. To secure as near an approximation to exact uniformity as possible in conditions of the fire and in tempera- tures of the walls and flues, the following method of starting and stopping a test should be adopted : X. Standard Method. Steam being raised to the working pressure, remove rapidly all the fire from the grate, close the damper, clean the ash-pit, and as quickly as possible start a new fire with weighed wood and coal, noting the time of starting the test and the height of the water-level while the water is in a quiescent state, just before lighting the fire. At the end of the test, remove the whole fire, clean the grates and ash-pit, and note the water-level when the water is in a quiescent state ; record the time of hauling the fire as the end of the test. The water-level should be as nearly as pos- sible the. same as at the beginning of the test. If it is not the same, a correction should be made by computation, and not by operating pump after test is completed. It will generally be necessary to regulate the discharge of steam from the boiler tested by means of the stop-valve for a time while fires are being hauled at the beginning and at the end of the test, in order to keep the steam-pressure in the boiler at those times up to the average during the test. XL Alternate Method. Instead of the Standard Method above described, the following may be employed where local conditions render it necessary : At the regular time for slicing and cleaning fires have them burned rather low, as is usual before cleaning, and then thoroughly cleaned ; note the amount of coal left on the grate as nearly as it can be estimated ; note the pressure of 375-] METHODS OF TESTING STEAM-BOILERS. 449 steam and the height of the water-level which should be at the medium height to be carried throughout the test at the same time ; and note this time as the time of starting the test. Fresh coal, which has been weighed, should now be fired. The ash-pits should be thoroughly cleaned at once after starting. Before the end of the test the fires should be burned low, just as before the start, and the fires cleaned in such a manner as to leave the same amount of fire, and in the same condition, on the grates as at the start. The water-level and steam-pressure should be brought to the same point as at the start, and the time of the ending of the test should be noted just before fresh coal is fired. DURING THE TEST. XII. Keep the Conditions Uniform. The boiler should be run continuously, without stopping for meal-times or for rise or fall of pressure of steam due to change of demand for steam. The draught being adjusted to the rate of evaporation or com- bustion desired before the test is begun, it should be retained constant during the test by means of the damper. If the boiler is not connected to the same steam-pipe with other boilers, an extra outlet for steam with valve in same should be provided, so that in case the pressure should rise to that at which the safety-valve is set, it may be reduced to the desired point by opening the extra outlet, without checking the fires. If the boiler is connected to a main steam-pipe with other boilers, the safety-valve on the boiler being tested should be set a few pounds higher than those of the other boilers, so that in case of a rise in pressure the other boilers may blow off, and the pressure be reduced by closing their dampers, allowing the damper of the boiler being tested to remain open, and firing as usual. All the conditions should be kept as nearly uniform as pos- sible, such as force of draught, pressure of steam, and height of water. The time of cleaning the fires will depend upon the character of the fuel, the rapidity of combustion, and the kind of grates. When very good coal is used, and the combustion not too rapid, a ten-hour test may be run without any cleaning 45 EXPERIMENTAL ENGINEERING. [ 375. of the grates, other than just before the beginning and just be- fore the end of the test. But in case the grates have to be cleaned during the test, the intervals between one cleaning and another should be uniform. XIII. Keeping the Records. The coal should be weighed and delivered to the firemen in equal portions, each sufficient for about one hour's run, and a fresh portion should not be de- livered until the previous one has all been fired. The time required to consume each portion should be noted, the time be- ing recorded at the instant of firing the first of each new por- tion. It is desirable that at the same time the amount of water fed into the boiler should be accurately noted and recorded, in- cluding the height of the water in the boiler, and the average pressure of steam and temperature of feed during the time. By thus recording the amount of water evaporated by successive portions of coal, the record of the test may be divided into sev- eral divisions, if desired, at the end of the test, to discover the degree of uniformity of combustion, evaporation, and economy at different stages of the test. XIV. Priming Tests. In all tests in which accuracy of re- sults is important, calorimeter tests should be made of the per- centage of moisture in the steam, or of the degree of super- heating. At least ten such tests should be made during the trial of the boiler, or so many as to reduce the probable average error to less than one per cent, and the final records of the boiler test corrected according to the average results of the calorimeter tests. On account of the difficulty of securing accuracy in these tests the greatest care should be taken in the measurements of weights and temperatures. The thermometers should be ac- curate to within a tenth of a degree, and the scales on which the water is weighed to within one hundredth of a pound. ANALYSES OF GASES. MEASUREMENT OF AIR-SUPPLY, ETC. XV. In tests for purposes of scientific research, in which the determination of all the variables entering into the test is de- sired, certain observations should be made which are in general not necessary in tests for commercial purposes. These are the measurement of the air-supply, the determination of its con- 375.] METHODS OF TESTING STEAM-BOILERS. 451 tained moisture, the measurement and analysis of the flue- gases, the determination of the amount of heat lost by radiation, of the amount of infiltration of air through the setting, the direct determination by calorimeter experiments of the absolute heating value of the fuel, and (by condensation of all the steam made by the boiler) of the total heat imparted to the water. The analysis of the flue-gases is an especially valuable method of determining the relative value of different methods of firing, or of different kinds of furnaces. In making these analyses great care should be taken to procure average samples, since the composition is apt to vary at different points of the flue, and the analyses should be intrusted only to a thoroughly competent chemist, who is provided with complete and accurate apparatus. As the determination of the other variables mentioned above are not likely to be undertaken except by engineers of high scientific attainments, and as apparatus for making them is likely to be improved in the course of scientific research, it is not deemed advisable to include in this code any specific direc- tions for making them. RECORD OF THE TEST. XVI. A " log" of the test should be kept on properly pre- pared blanks, containing headings as follows : TIME. PRESSURES. TEMPERATURES. FUEL. FEED- WATER. Barometer. i c CSC g rt z Draught- gauge. External Air. Boiler-room. if 3 E Feed-water. 1 i H Pounds. g H Pounds or c. ft. 452 EXPERIMEN TA L ENGINEERING. [ 375- REPORTING THE TRIAL. XVII. The final results should be recorded upon a properly prepared blank, and should include as many of the following items as are adapted for the specific object for which the trial is made. The items marked with a * may be omitted for or- dinary trials, but are desirable for comparison with similar data from other sources. Results of the trials of a. Boiler at , , To determine j Date of trial hours. DIMENSIONS AND PROPORTIONS. Leave space for complete description. See Ap pendix XXIII. 3. Grate surface. . . wide. . . .long. . . .Area. . . . 4 Water-heating surface sq. ft. sq. ft. 5 Superheating-surface sq. ft. 6. Ratio of water heating surface to grate-sur- face AVERAGE PRESSURES. 7. Steam-pressure in boiler, by gauge Ibs. Ibs. *g. Atmospheric pressure per barometer in. 10. Force of draught in inches of water in. AVERAGE TEMPERATURES. *I2. Of fire-room ucg. *I3. Of steam deer 14. Of escaping gases 15. Of feed- water ueg. Hppr FUEL. 16. Total amount of coal consumed f Ibs 17. Moisture in coal per cent 18. Dry coal consumed , Ibs 19. Total refuse, drv pounds per cent 20. Total combustible (dry weight of coal, Item 18, less refuse, Item 19) *2i. Drv coal consumed per hour Ibs. Ibs *22. Combustible consumed per hour. . Ibs. * See reference in paragraph preceding table. f Including equivalent of wood used in lighting fire. equals 0.4 pound coal, of test. i pound of wood Not including unburnt coal withdrawn from fire at end 375-] METHODS OF TESTING STEAM-BOILERS. 453 RESULTS OF CALORIMETRIC TESTS. 23. Quality of steam, dry steam being taken as unity 24. Percentage of moisture in steam per cent. 25. Number of degrees superheated deg. WATER. 26. Total weight of water pumped into boiler and apparently evaporated * Ibs. 27. Water actually evaporated, corrected for quality of steam f Ibs. 28. Equivalent water evaporated into dry steam from and at 212 F.f Ibs. 2g. Equivalent total heat derived from fuel in British thermal units f B. T. u. 30. Equivalent water evaporated into dry steam from and at 212 F. per hour Ibs. ECONOMIC EVAPORATION. 31. Water actually evaporated per pound of dry coal, from actual pressure and tempera- ture \ Ibs. 32. Equivalent water evaporated per pound of dry coal from and at 212 F.f Ibs. 33. Equivalent water evaporated per pound of combustible from and at 212 F.f Ibs. * Corrected for inequality of water-level and of steam-pressure at beginning and end of test. f The following shows how some of the items in the above table are de- rived from others: Item 27 = Item 26 X Item 23. Item 28 = Item 27 X Factor of evaporation. rr r Factor of evaporation = -: , H and h being respectively the total heat- 95-7 units in steam of the average observed pressure and in water of the average observed temperature of feed, as obtained from tables of the properties of steam and water. Item 29 = Item 27 X (H X). Item 31 = Item 27 -f- Item 18. Item 32 = Item 28 4- Item 18 or = Item 31 X Factor of evaporation. Item 33 = Item 28 -f- Item 20 or = Item 32 *- (per cent 100 Item 19). Items 36 to 38. First term = Item 20 X 7 5 Items 40 to 42. First term = Item 39 X 0.8698. Item 43 = Item 29 X 0.00003 or = Difference of Items 43 and 44 Item 45 = - i tem 44. ~~' Item 30 34* ' 454 EXPERIMENTAL ENGINEERING. [ 375- COMMERCIAL EVAPORATION. 34. Equivalent water evaporated per pound o dry coal with one sixth refuse, at 70 pounds gauge-pressure, from temperature of ioo c F. = Item 33 multiplied by 0.7249 Ibs, RATE OF COMBUSTION. 35. Dry coal actually burned per square foot ol grate-surface per hour Ibs. (] Per sq. ft. of grate- Consumption of | surface. Ibs. dry coal per hour. I Per sq. ft. of water- Coal assumed with | heating surface.. .. Ibs, one sixth refuse, f Per sq. ft. of least J area for draught. . . Ibs. RATE OF EVAPORATION. 39. Water evaporated from and at 212 F. per square foot of heating-surface per hour. . . Ibs. f Water evaporated ] Per sq. ft. of grate* *dO per hour * rom lem " ' surface Ibs. *4i 4 P erature f I00 F - I Per sq. ft. of water- #2 2 I mto steam of 70 J heating surface. . Ibs. I pounds gauge-pres- Per sq. ft. of least [sure. f J area for draught. Ibs. COMMERCIAL HORSE POWER. 43. On basis of thirty pounds of water per hour evaporated from temperature of 100 F. into steam of 70 pounds gauge pressure, ( = 34i Ibs. from and at 212) f H. p. 44. Horse-power, builders' rating, at square feet per horse-power H. p. 45. Per cent developed above, or below, rat- ing f Per cent. Precautions are to be taken in every possible way to prevent and avoid irregularities in the conduct of the trial and errors of observation.* In preparing for and conducting trials of steam-boilers the specific object of the proposed trial should be clearly defined and steadily kept in view, and as suggested by Mr. Hoadley (i) If it be to determine the efficiency of a given style of boiler or of boiler-setting under normal conditions, the boiler brickwork, grates, dampers, flues, pipes, in short, the whole ap- paratus, should be carefully examined and accurately described, * The appendix to the report above quoted should be read in this connection. 375-1 METHODS OF TESTING STEAM-BOILERS. 455 and any variation from a normal condition should be remedied, if possible, and if irremediable, clearly described and pointed out. (2) If it be to ascertain the condition of a given boiler or set of boilers with a view to the improvement of whatever may be faulty, the conditions actually existing should be accurately observed and clearly described. (3) If the object be to determine the relative value of two or more kinds of coal, or the actual value of any kind, exact equality of conditions should be maintained if possible, or, where that is not practicable, all variations should be duly al- lowed for. (4) Only one variable should be allowed to enter into the problem ; or, since the entire exclusion of disturbing variations cannot usually be effected, they should be kept as closely as possible within narrow limits, and allowed for with all possible accuracy. Blanks should be provided in advance, in which to enter all data observed during the test. The preceding instructions contain the form used in presenting the general results. Rec- ords should be, as far as possible, made in a standard form, in order that all may be comparable. The observations must be made by the engineer conduct- ing the trial, or by his assistants, with this object distinctly in mind ; and each should have a well-defined part of the work assigned him, and should assume responsibility for that part, having a distinct understanding in regard to the extent of his responsibility, and a good idea of the extent and nature of the work done by his colleagues, and the relations of each part to his own. No observations should be permitted to be made by unauthorized persons for entrance upon the log ; and no duties should be permitted to be delegated by one as- sistant to another, without consultation and distinct under- standing with the engineer in charge. The trial should, wher- ever possible, be so conducted that any error that may occur in the record may be detected, checked, or, if advisable, removed, by some process of mutual verification of related observations. It is in this direction that the use of graphical methods of rec- ord and automatic instruments have greatest value. 456 EXPERIMENTAL ENGINEERING. [ 375. Several methods of weighing fuel have been found very satis- factory, but it should be an essential feature that the weights shall be made by one observer and checked by another, at as distant a point as is convenient. The weighing of the fuel by one observer at the point of storage, and the record at that point of times of delivery, as well as of weights of each lot, and the tallying of the number and record of the time of receipt at the furnace-door, will be usually found a safe system. The fail- ure to record any one weight leads to similar error, and can only be certainly prevented by an effective method of double observation and check. The same remarks apply, to a considerable extent, to the weighing of the water fed to the boiler. A careful arrangement of weighing apparatus, a double set of observations, where pos- sible, and thus safe checks on the figures obtained, are essential to certainty of results. With good observers at the tank, and with small demand for water, a single tank can be used ; but two are preferable in all cases, and three should be used if the work demands very large amounts of feed-water, as at trials of very large boilers, or of " batteries." The more uniform the water supply, as well as the more steady the firing, the less the liability to mistake in making the record. The two blanks which follow were prepared by the Author for use in laboratory as well as professional work. Such blanks are always desirable, and are sometimes even more elaborate than those here illustrated.* For ordinary purposes, a less complete tabulation may be sufficient ; while, for special purposes and for scientific investigations and the work of research, considerable more elaboration may be found desirable, or even necessary. Graphical methods of representation of the data and con- ditions and of the progress of the trial, as elsewhere illustrated, are also often found exceedingly useful and convenient. 376. Additional Forms for Log and Report. The fol- lowing forms are somewhat more complete than those given in Article 375 : *Vide "Stevens Indicator," Nov. '89. 376-] METHODS OF TESTING STEAM-BOILERS. 457 MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL UNIVERSITY. LOG OF BOILER-TRIAL. Made at n j Date i8 9 .. B y \ ;.. Fireman REPORT OF BOILER-TEST. Made by N. Y 189.. Kind of Boiler Manufactured bv. . Duration of Trial Hours. Grate-surf., length ft., width ft Sq. ft. Water-heating surface " Superheating surface " Area for draught (calorimeter). " Area, chimney " Height, chimney Ft. Ratio heating to grate surface Ratio air-space to grate-surface Barometer Inches mercury. Steam-gauge Pounds. Draught-gauge Inches water. Absolute steam-pressure Pounds. External air Degrees F. Boiler-room " Flue Furnace " Feed-water " Steam Total coal consumed . ... Pounds. Moisture in coal Per cent. Dry coal consumed Pounds. Total refuse, dry Total refuse, dry Percent. Total combustible Pounds. Dry coal per hour Combustible per hour Dry coal per square foot of grate " Combustible per square foot of grate Dry coal per square foot of grate Heating-surface. Combustible per square foot of grate. Heating-surface. Quality of steam Percent. Superheat Degrees. Total weight water used . . Pounds, (by meter)... Cu. ft. Total evap., dry steam Pounds. Factor of evaporation. Total from and at 212 Pounds. Amount used Pounds. Evaporated, dry steam " Evap. from and at 212 " Per Pound of Fuel. Actual Pounds. Equiv.^from and at 2t2 " Per Pound of Combustible. Actual Pounds. Equiv. from and at 212 " Per Sq. Ft. Heating-surface per Hr. Actual Pounds. Equiv. from and at 212 " From 100 F. to 70 Pounds by Gauge. Per Pound of Fuel Pounds. Per Pound of Combustible. . . " Per f-pound of Fuel " Per Square Foot of Grate. Actual, from feed -water tem- perature Pounds. Equiv. from and at 212. ... " Per Sq. Ft. of Water-heating Surface. Actual Pounds. Equiv. from and at 212 " Per Sq. Ft. of Least Draught-area. Actual Pounds. Equiv. from and at 212 " *On basis 34^ Ibs. equiv. evap. per hour H. P. Builders' rating Ratio of commercial to builders' rat- ing Heat generated per hour. . . B. T. U. Heat absorbed per hour Efficiency 1 of boiler Per cent. Efficiency of furnace " NOTE Actual evaporation signifies the evaporation from feed-water temperature to dry steam at gauge-pressure It is apparent evaporation corrected for calorimeter-determination. *. Standard Commercial H. 1'. 458 EXPERIMENTAL ENGINEERING. [ 3/7. 377. Abbreviated Directions for Boiler-testing. Ap- paratus. As in standard tests : tanks and scales for weighing water; meter for measuring water; apparatus for flue-^as analysis ; barometer and pyrometer. Directions. Calibrate all apparatus, meters, scales, ther- mometers, and gauges ; arrange throttling or separator calo- rimeter to obtain quality of steam delivered. Note condition of Boiler and Furnace Rules, VII-IX. Start and close the test either by standard or alternative method, Rules X and XL During test proceed as in Rules XIII and XIV. Continue the test as long as time will permit, at least four hours, taking simultaneous observations each 15 minutes at a signal given by a whistle ; keep record so that coal and water consumption can be computed for each hour. Put 100 pounds of coal in a box and dry in a hot place for 24 hours ; if ashes are damp from use of a steam-blower, dry a sample of 100 pounds in same manner. In general, ashes may be removed at once and weighed. Report and Computation. Make report on standard forms submitted and compute the required quantities. Submit with report & graphical log, in which tirtie is taken as abscissa, and the various observed quantities as ordinates. CHAPTER XVI. THE STEAM-ENGINE INDICATOR. 378. Uses of the Steam-engine Indicator. The steam- engine indicator is an instrument for drawing a diagram on paper which shall accurately represent the various changes of pressure on one side of the piston of the steam-engine during both the forward and return stroke. FIG. 172. THE INDICATOR-DIAGRAM. The general form of the indicator-diagram is shown in Fig. f/2; the ordinates of the diagram, measured from the line GG, are proportional to the pressure per square inch above the atmosphere ; measured from the line HH, are proportional to the absolute pressure per square inch acting on the piston. The abscissa corresponding to any ordinate is proportional to the distance moved by the piston. ABCDE is the line drawn during the forward stroke of the engine, EFA that drawn dur- ing the return stroke. The ordinates to the line ABCDE rep- resent the pressures acting to move the piston forward ; those to the line EFA represent the pressures acting to retard or 459 460 EXPERIMENTAL ENGINEERING. [ 3/9. stop the motion of the piston on its back stroke. The ordi- nates intercepted between the lines represent the effective pressure acting to urge the piston forward. Since the abscissae of the diagram are proportional to the space passed through by the piston, and the intercepted ordinate to the effective pressure acting on the piston, the area of the diagram must be proportional to the work done by the steam on one side of the piston, acting on a unit of area and during both forward and return stroke. (See Article 21, page i^.) From this diagram can be obtained, by processes to be ex- plained later: i. The quantity of power developed in the cylinder, and the quantity lost in various ways, by wire-draw- ing, by back pressure, by premature release, by mal-adjustment of valves, leakage, etc. 2. The redistribution of horizontal pressures at the crank- pin, through the momentum and inertia of the reciprocating parts, and the angular distribution of the tangential component of the horizontal pressure ; in other words, the rotative effect around the path of the crank. 3. Taken in combination with measurements of feed-water or of the exhaust steam, with the amount and temperatures of condensing water, the indicator furnishes opportunities for measuring the h'eat losses which occur at different points during the stroke. 4. The indicator-diagram also shows the position of the piston at times when the valve-motion opens or closes the steam and exhaust ports of the engine. It also furnishes in- formation regarding the general condition of the engine, and the arrangement of the valves, adequacy of the ports and pas- sages, and of the steam or the exhaust pipes. 379. Indicated and Dynamometric Power. The steam, engine indicator is used in all steam-engine tests to measure the force of the steam acting on a unit of area cf the piston. A dynamometer of the absorbing or transmission type (see pages 216 to 228) is used to measure the work delivered by the steam- engine. The work of the engine is usually expressed in horse- power; one horse-power being equivalent to 33,000 foot-pounds 38o.] THE STEAM-ENGINE INDICATOR. 4 6l per minute. The work shown by the steam-engine indicator- diagram is termed the Indicated horse-power (I.H.P.); that shown by the dynamometer, Dynamometric horse-power (D.H.P.). The mean effective pressure per unit of area acting on the piston is obtained from the indicator-diagram ; this quantity, multiplied by the area of the piston and the distance travelled by the piston in feet per minute, will give the work in foot- pounds. Thus let / equal the mean effective pressure, / the length of stroke of the engine in feet, n the number of revolu- tions, a the area of the piston in square inches. Then the work done per minute by the steam acting on one side of the piston, in horse-power, is plan -r- 33,000. 380. Early Forms of the Steam-engine Indicator. Watt and McNanght. The steam-engine indicator was in- vented by James Watt, and was extensive- ly used by him in perfecting his engine. The indicator of Watt,* as used in 1814, consisted of a small steam-cylinder AA, as shown in Fig. 173, in which a piston was moved by the steam-pressure, against the resistance of a spring FC. The end of the piston-rod carried a pencil, which was made to press against a sheet of paper DD, moved backward and forward in conformity to the motion of the piston. By this method a diagram was produced similar to that shown in Fig. 172. McNaught's indicator, which succeeded that of Watt and was in general use until about 1860, differed from the form used by Watt principally in the use of a verti- cal cylinder instead of the sliding panel, which was turned backward and forward on a vertical axis, in conformity to the motion of the piston. FIG. 173. THE WATT INDICATOR. * See Thurston's Engine and Boiler Trials, page 130. 462 EXPERIMENTAL ENGINEERING. 381. The Richards Indicator.* The Richards indicator was invented by Professor C. B. Richards about 1860; it con- tains every essential constructive feature found in recent indi- cators, and may be considered the prototype from which all other indicators differ simply in details of .workmanship, form, and size of parts. The construction of this indicator is well shown in Fig. 174, FIG. 174. THE RICHARDS INDICATOR. from which it is seen to consist of a steam-cylinder AA, in which is a piston B, connected by a rigid rod with the cap F. The movement of the piston is resisted by the spring CD in such a manner that its motion in either direction is proportional to the pressure. The motion of the piston-rod is transferred to a pencil at K, by links which are so arranged that the pencil * See the Richards Indicator, by C. B. Porter; New York, D. Van Nostrand. 382.] 1 THE STEAM-ENGINE INDICATOR. 463 moves parallel to the piston B, but through a considerably greater range. The indicator-spring can be taken out by unscrewing the cap E, removing the top of the instrument and unscrewing the piston B, and another spring with a different tension can be substituted. The drum OR is made of light metal, mounted on a vertical axis, and provided with a spring arranged to resist rotation. The drum is connected to the cross- head or reducing motion by a cord, and is given a motion in one direction by the tension transmitted through the cord and in a reverse direction by the indicator drum-spring. The paper on which the diagram is to be drawn is wrapped smoothly around the drum OQ, being held in place by the clips PQ. The indicator is connected to the steam-cylinder by a pipe leading to the clearance-space of the engine ; a cock, T, being screwed into this pipe, and the indicator connected to the cock by the coupling U. 382. The Thompson Indicator. This indicator is shown in Figs. 175 and 176. It differs from the Richards indicator FIG. 175. THE THOMPSON INDICATOR. FIG. 176. SECTION OF THOMPSON INDICATOR. principally in the form of the parallel motion, form of indicator- spring, and details of workmanship. The parts of the instru- 464 EXPERIMEN TA L ENGINEERING, [ 3*3- ment are much lighter, and it is better adapted for use on high- speed engines. The use is essentially the same as the Richards ; the method of changing springs should be thoroughly understood, and is as follows : Unscrew the miiled-edged cap at the top of steam- cylinder; then take out piston, with arm and connections; dis- connect pencil-lever and piston by unscrewing the small milled- headed screw which connects them ; remove the spring from the piston, substitute the one desired, and put together in same manner, being careful, of course, to screw the spring up firmly against cap and well down to the piston-head. The method of changing springs is simple, easy, and convenient, and does not require the use of any wrench or pin of any kind. 383. The Tabor Indicator. The Tabor indicator, shown in Figs. 177 and 178, in the form now manufactured differs from other indicators principally in producing the parallel FIG. 177. THE TABOR INDICATOR. motion of the pencil by a pin moving in a peculiarly-shaped slot. It also differs in details of construction and in form of the indicator-spring; the pencil-point being arranged to move not only parallel to the piston, but uniformly five times as fast as the piston at every part of the range. 3840 THE STEAM-ENGINE INDICATOR. 465 The method of changing springs in the Tabor indicator is as follows : Remove the cover of the cylinder, remove the screw beneath the piston, unscrew the piston from the spring and the spring from the cover, and replace the spring desired. When the lower end of the piston-rod is introduced into the square hole in the centre of the piston, care must be taken ihat it sets fairly in the hole be- fore the screw is applied. Unless such care is observed, the corners may catch and cause derangement. The tension on the drum-spring . . . FIG. 178. SECTION OF TABOR INDICATOR. may be varied by removing the paper drum, loosening the thumb-screw which encircles the central shaft, lifting the drum-carriage so as to clear the stop ; and then winding the carriage in the direction desired. 384. The Crosby Indicator. The Crosby indicator as at present constructed is shown in Figs. 179 and 180. It differs from those already described in the form of piston- and drum- springs and in the arrangement for producing accurate parallel motion. The special directions for this instrument are given by the manufacturers as follows: To remove the piston, spring, etc., unscrew the cap, then, by the sleeve, lift all the connected parts free. This gives full access to the parts to clean and oil them. To detach the spring, unscrew the cap from spring-head, then unscrew piston-rod from swivel-head, then, with the hol- low slotted wrench, unscrew the piston-rod from the piston. To attach a spring, simply reverse this process. Before setting the foot of the spring unscrew G slightly, then, after the piston- rod has been firmly screwed down to its shoulder, set G up firmly against the bead, and thereby take up all lost motion. It is often desirable to change the position of the atmospheric 466 EXPERIMENTAL ENGINEERING. [ 384. line on the paper. This can easily be done by unscrewing the cap from the cylinder and raising the sleeve BB which carries the pencil-movement. Then turn the cap to the right or left, FIG. 179. THE CROSBY INDICATOR. and the piston-rod will be screwed off or on the swivel , and the position of the atmospheric line will be raised or lowered. Never remove the pins or screws from the joints K, /, Z, M, but keep them well oiled with refined porpoise-jaw oil, which is furnished with each instrument. The tension on the drum-spring should be increased or diminished according to the speed at which the instrument is used, by means of the thumb-nut on top of the drum-spindle. Use a spring of such a number that the diagram will not be 385-] THE STEAM-ENGINE INDICATOR. 467 over one and three-quarter inches high ; as, for instance, a No. 40 spring should not be used for pressures above 70 Ibs. FIG. 180. SECTION OF THE CROSBY INDICATOR. 385. The Calkins Indicator. The Calkins indicator is one of the recent forms, worthy of notice. It possesses, as shown in Fig. 181, the usual features of steam-engine indicators, modified by details of construction in its moving parts and form of indicator-spring. The parallel motion is produced partly by cams, partly by links, and gives a good diagram 2j inches in height. The spring is inserted by screwing it first into the cap and afterward screwing on the piston to the squared shank. The drum-spring is adjusted by simply turning a ratchet- wheel placed beneath the paper-drum. 468 EXPERIMEN TA L ENGINEERING. [ 386. 386. The Straight Lyne and the Perfection Indicators. The straight Lyne indicator, as shown in Fig. 182, was de- FIG. 181. SECTIONAL VIEW, ONE-HALF SIZE, CALKINS STEAM-ENGINE INDICATOR. signed by Mr. L. F. Lyne. Its principal peculiarity is the guide near the paper drum for securing the parallel motion. The Perfection indicator, shown in Fig. 183, differs from those described in. the form of the spring and in the arrange- ment of the levers for the parallel motion. This instrument is made with jewelled bearings and with aluminium drum. THE STEAM-ENGINE INDICATOR. 469 387. The Bachelder, Straight Line, and Arc Indicators. The Bachelder indicator, as shown in Fig. 184, differs radi- FIG. 182. THE STRAIGHT LYNE INDICATOR. FIG. 183. THE PERFECTION INDICATOR. cally from the indicators described in the form of springs em- ployed ; the indicator-spring is flat and arranged with a 'Fie. 184. THE BACHELDER INDICATOR. movable fulcrum, so that the scale of the spring can be easily and quickly changed, and the drum-spring is conical in form. The straight-line indicator, as shown in Fig. 185, differs 470 EXPERIMENTAL ENGINEERING. [ 388. from the ones described principally in the form of its parallel motion. The instrument shown in the figure has a reducing motion attached as a part of the indicator, which the author re- gards as a desirable improvement. FIG. 185. THE STRAIGHT-I INE INDICATOR. The arc indicator is similar to the straight-line indicator as shown above, but the pencil part is pivoted to a fixed point, and the pencil rises in an arc of a circle instead of a straight line. 388. Parts of the Steam-engine Indicator. The parts of the steam-engine indicator must be constructed essentially as follows : 1. The Steam-cylinder. This contains the piston, the indi- cator-spring, and attachments for the pencil mechanism. In the upper portions of the walls relief-holes are bored to insure atmospheric pressure above the piston. 2. The Piston. This is usually solid, with grooves or holes in its outer edge ; it is made to fit loosely in the cylinder to reduce friction, and is not steam-tight. When in use it must be lubricated with cylinder-oil of best quality ; it is connected to the pencil mechanism by a piston-rod. 3. The Pencil Mechanism. This receives the motion from the piston-rod, increases its amplitude, and transfers it to a pencil by means of guides or parallel-motion links, so that the 388.] THE -STEAM-ENGINE INDICATOR. 471 pencil moves in a right line and usually four to six times the distance of the piston. The height of the atmospheric line, or line of no pressure, on the drum, can often be adjusted by means of a threaded sleeve fitting on the piston-rod. In the arc indicator the pencil swings in an arc of a circle. 4. The Indicator- spring. This is usually a helical spring; when in use it has one end screwed to the upper head of the cylinder, and the other screwed to the piston. To insure accu- rate results the spring must be accurate, and there must be no play or lost motion between the piston and the cylinder-head, and the spring must receive and deliver the force axially. The number of pounds pressure on the square inch required to move the pencil one inch is stamped on the spring, and the springs are designated by that number. It is essential to know the error, if any, in this number. A spring can be readily removed and another substituted when desired ; the maximum compres- sion probably should not exceed one third of an inch. The spring is in many respects the most important part of the indicator, as the form of the diagram is directly affected by any error. The following cuts show some of the principal FIG. 186. CROSBY SPRING. FIG. 187. TABOR SPRING. forms adopted by a few of the makers, and it may perhaps be sufficient to state that within the range of action of the indi- cator any of these forms can be made practically perfect. 472 EXPERIMENTAL ENGINEERING. [ C/3 8 o * 0^ co .d K C#T ^* to f-x CM ^ in c^ rf o" ^o u 55 E c OS !/3 Q E 6 c C/i 8 M in R o f 8 3 "8 43 rf 1 U c 3 1 CO CO o c- o s 6 (5 < O ft. to w C * ^ 3 M U o 1! H 8 f O 1 m O in co 6 15 a. C/) c o 03 PQ J20Q V) t/j 06 z -M- q 1 1: I m CO co co 1 o > H 1 M ' o" Ou CO o . c o 8 M co ^c3 55 < * *tn PS in M in O o" "? CO O il 'i ^ w <& S 2 d X bo CQ o c 2 M J> PRINC ^yj !* H U to 03 \J 8 f CO 6 8 o S 6 c^ O E c OJ X 'd 2 (^ o gco s Jo > v 8 8 xn o co CO co O ^3 rf ct tu U In w J: i ^~ 5 2 03 IU r 8 8 CO t o m 3 O X 1 - s ? 15 ^ f2 ^ bi) to o* CO >> B4 U U o M ' o o M O C/) ^ ) ' -5. : > O O g c C t Sj E id o s 1 t/5 C 1 c c" d* c c 6 C o E a C KM s H 1 !.* 3 fcj "o 1 Maker. . Address. ^ * 39-] THE STEAM-ENGINE INDICATOR. 473 The Bachelder indicator (see Fig. 184) is made with a flat spring, and to a certain extent the tension is regulated by changing its fulcrum. 5. The Paper-drum, to which the card is attached, consists of a brass cylinder attached to a spindle which is connected to the drum-spring, the action of which has been described. The drum can be removed readily, and the tension on the spring changed at pleasure. Two clips or fingers serve to hold the paper in position. 6. The Cord used, although not a part of the indicator, must be selected with great care; it must be of a character not to be stretched by the forces acting on the indicator. Steel wire is sometimes used for this purpose. Any variation in length of the connecting cord affects the abscissa in the diagram. 7. The Reducing-motions, also not a part of the indicator, must give an exact reproduction, on a smaller scale, of the motion of the piston ; otherwise the length of the indicator- diagram will either not be accurately reduced, or the events will not be properly timed. 389. The table opposite gives the actual dimensions of the principal indicators described, as obtained by careful measure- ment of those owned by Sibley College. 390. Reducing-motions for Indicators. The maximum motion of the indicator-drum is usually less than four inches; consequently it can seldom be connected directly to the cross- head of the engine, but must be connected to some apparatus which has a motion less in amplitude but corresponding exactly in all its phases 'to that of the cross-head. This apparatus is termed a reducing-motion. Since the horizontal components" of the indicator-diagram and consequently its area and form depend upon the motion of the piston, it is evident that the accuracy of the diagram depends upon the accuracy of the reducing-motion. Various combinations of levers and pulleys have been used * for reducing-motions, a few of which will be * See Thurston's Engine and Boiler Trials. 474 EXPERIMENTAL ENGINEERING. [ 390. described. Several simple forms of reducing-motion are given here as suggestions, but it is expected that the student will devise other motions if required, and ascertain the amount of error, if any, in the motion used. H f FIG. 188. THE SIMPLE PENDULUM REDUCING-MOTION. The cheaper and more easily arranged reducing-motions consist usually of some form of swinging lever or pendulum (see Fig. 188) pivoted at one point, and connected at its lower end to the cross-head by a lever. The indicator-cord is attached to the swinging lever at some point having the proper motion. These motions never give an exact reproduc- 390.] THE STEAM-ENGINE INDICATOR. 4/5 tion of the motion of the piston ; but if the pendulum and cross-head are simultaneously at the centre of the stroke, the error is very small. FIG. 189. THE BRUMBO PULLEY. A form of the pendulum-motion, called the Brumbo pulley, is frequently used as shown in Fig. 189. The pendulum is some- times modified, so that its lower end is pivoted directly to a FIG. 190. THE PANTOGRAPH. point in the cross-head, its upper half moving vertically in a swinging tube. The cord is attached to an arc on this tube as 1 88. in Fig. 476 EXPERIMENTAL ENGINEERING. [ 391 The pantograph, or lazy-tongs, as shown in Fig. 190, with plan of method of attachment shown in Fig. 191, is a perfect reducing motion, but because of its numerous joints it is not adapted to high-speed engines. FIG. 191. METHOD OF ATTACHING THE PANTOGRAPH. A form of pantograph with four joints only, shown in Fig. 192, is much better adapted to high-speed engines than the one with more numerous joints shown above. FIG. iQ2. METHOD OF USING THE PANTOGRAPH. Reducing-wheels Reducing wheels, which consist of a large and a small pulley (see Fig. 193) attached to the same axis, are extensively used by engineers. The method of attach- ing this reducing-motion to an engine is shown in Fig. 194. 391. The Indicator-cord. The indicator-cord should be as nearly as possible inextensible, since any stretch of the cord causes a corresponding error in the motion of the indicator- drum. As it is nearly impossible to secure a cord that will not 39i.] THE STEAM-ENGINE INDICATOR. 477 stretch, it should be made as short as possible, and a fine wire of steel or iron or of hard-drawn brass should be used if practicable. FlG. 193. SCHAkFFER AND BuDKNBEKG Rl.ULXlNG-MOTION. FIG. 194.- WEBSTER AND PERKS REDUCING MOTION. The indicator-cord supplied by makers of indicators is a braided hard cotton cord, stretching but little under the required stress. 478 EXPERIMENTAL ENGINEERING. [ 39 2 - If a " rig" is to be permanently erected, it is recommended that the motion be taken from a sliding bar attached to the cross- head and extending to or beyond the indicators. The angle of the cord with the path of motion of the cross-head should be as nearly constant as possible, since any variation in this angle will cause a distortion in the motion of the drum. In Figs. 189, 192, and 194 will be seen devices to over- come the effect of angularity of the indicator-cord. The indicator-cord is usually hooked and unhooked into a loop in a cord fastened to the reducing-motion. A very con- venient form for such a loop, and one that can readily be ad- justed, is shown in Fig. 195. The indicator-cord is usually FIG. 195. THE LOOP. provided with a hook fastened as shown in Fig. 182, which is hooked when diagrams are needed into the loop attached to the reducing-motion. The author would strongly urge that the indicator-cord be arranged so as to avoid the necessity of frequent hooking and unhooking, thus throwing severe and unnecessary strains on. the indicator-drum and cord : this can be done by connecting a point on the cord near the indicator with a spiral spring fastened to a fixed point in the line of the cord produced. This spring should be strong enough to keep the slack out of the cord. When it is desired to stop the motion, the drum-cord is pulled toward the reducing-motion to the extent of its travel, and held or tied until another diagram is needed. Some of the indicator-drums are provided with ratchets or detents that serve the same purpose. When several indicators are in use and simultaneous diagrams are required, a detent-motion worked by an electric current will prove very satisfactory. In case of compound engines when numerous indicators are re- quired these suggestions become of even greater importance. 392. Standardization of the Indicator. The accuracy of 393-] THE STEAM-ENGINE INDICA TOR. 479 the indicator-diagram depends upon the following features, all of which should be the subject of careful examination : (1) Uniformity of the indicator-spring. (2) Accuracy of the drum-motion. (3) Parallelism of the piston-movement to the cylinder. (4) Parallelism of the pencil-movement to the axis of the drum. (5) Friction of the piston and pencil-movements. (6) Lost motion. The calibration of these parts should be made as nearly as possible under the conditions of actual use and as described in the following articles. 393. Calibration of the Indicator-spring. The accuracy of the indicator-spring is only to be determined by comparison with standardized apparatus. This may be done as follows : Firstly : with the open mercury column. This can be done with steam only, as the leakage of water past the loosely- fitting piston would render it impossible to maintain the pressure. Insert the spring; see that the indicator is oiled and in good condition. Attach the indicator as previously explained for the calibration of steam-gauges, page 338 ; put paper on the drum ; turn on steam-pressure until the instrument is warm; turn off the steam, and pressing the pencil lightly against the paper, turn the drum by hand, thus drawing the atmospheric line. Apply pressure by increments equal to one fifth that marked on the spring, keeping the motion continually upward, stopping only long enough to draw the line for the required pressure. Take ten increments first up then down ; the average position of any line will give the ordinate corresponding to that pressure ; the difference between any two lines (see Fig. 196) will be twice the friction of indicator-piston at that point. Second : with the standard scales. This method was devised by Professor M. E. Cooley, of Ann Arbor. In this case the indicator is supported on a bracket above the platform of the scales. Force is applied to the indicator-piston by means of a rod which can be raised or lowered by turning a hand-wheel ; this rod terminates above in a cap nicely fitted to the under 480 EXPERIMEN TA L ENGINEERING. [ 393- side of the piston, and below it rests on a pedestal standing on the platform of the scales. Any force applied to compress the spring is registered on the scale beam. The reading of the scale-beam is that force acting on one-half square inch, as the piston is usually one-half square inch in area ; this is to be multi- plied by 2 to correspond with the reading given by the indica- tor-spring. The indicator can be heated by wrapping rubber tubing around the cylinder and passing steam through the tube. A Up. Down. ) Up. Down. FIG. 196. INDICATOR-SPRING CALIBRATION. FORM FOR CALIBRATION OF INDICATOR-SPRING. By comparison with , Make of indicator Mark and No. of spring. . . . Date.. Observers No. Gauge. Actual Pressure. Ordinates. Actual Pressure. Error. Per cent. Inches Lbs. Inches. Pounds. Up. Down. Mean. 395-1 THE STEAM-ENGINE INDICATOR. 481 394. Test for Parallelism of the Pencil-movement to the Axis of the Drum. This is tested by removing the spring from the indicator, rotating the drum, and drawing an atmos- pheric line ; then hold the drum stationary in various positions and press the piston of the indicator upward throughout its full stroke, while the pencil is in contact with the paper. The lines thus drawn should be parallel to each other and perpen- dicular to the atmospheric line. I^arallelism of the piston-movement to the cylinder axis is shown when the increments for equal pressure are the same in all positions of the diagram. It is important that the piston is not cramped or pushed over by the spring, in any part of its stroke. Friction of the piston and pencil-movement can be determined in the calibration of the indicator-spring as explained. When the spring is removed from the indicator, the parts should work easily and freely but without lost motion. 395. Accuracy of the Drum-motion. The accuracy of the drum-motion depends on the form of the drum-spring, the mass moved, the length of the diagram, and the elasticity of the connecting cord. Indicator-drums would revolve in a harmonic motion if the inertia of the mass could be neglected. The speed of ro- tation is greatest near the half-stroke of the piston ; therefore, if the drum-spring tension can be adjusted so as to exactly counterbalance the effect of the inertia of the moving parts, the theoretical harmonic motion will be nearly realized. In most indicator drum-springs the tension increases directly in proportion to the extension. Since the speed of the drum is greatest at half stroke, at this point the drum will run ahead of its theoretic motion if the spring tension is not suffi- cient to counteract the effect of the inertia of the moving parts. Therefore if the tension of the drum-spring is adjusted to exactly balance the effect of inertia at half-stroke, the card should be as nearly as possible theoretically correct. To ob- tain the value of this tension, use is made of the formulae for the harmonic motion of a body as follows. Let 482 EXPEKIMEN TA L ENGINEERING, [ 395- / = time of i length of card = J of a revolution ; s = length of card ; / = - -= ; (see Church's Mechanics.) 2 \ a P = pM = T, where T is the tension in the spring at J the length of the card. p = - sa\ a = P-\ W T M = mass of rotating parts ; a = . T = T 41 n/r,. The foot, pound, second system is used in the formulae. The results are shown in the following table. TABLE FOR TENSION ON INDICATOR DRUM OF i.o LB. WEIGHT. Revolutions per Minute. Pounds of Force to pull Drum 1.75 in. Revolutions per Minute. Pounds of Force to pull Drum 1.75 in. 50 O IO 225 2-5 75 0.25 250 3-15 100 0.50 275 3 .8 125 150 0.8 I-I5 300 350 4-55 6.15 i?5 1-55 375 7.0 200 2.O 400 8.0 The total error introduced by inertia can be determined as follows : Attaching the indicator to an engine, permit: it to run sufficiently long to harden the cord and the knots, then stop the engine, turn it over by hand and find the length of the diagram with the speed so small as to eliminate the inertia ; leaving the cords connected, run the engine at full speed : any 395-] THE STEAM-ENGINE INDICATOR. 483 inertia effect will be shown by an increase in the length of the diagram. This increase in length may be partly due to stretch in the indicator-cord caused by inertia of the rotating parts, as even with the best tension on the springs, determined as ex- plained, it may be sensibly lessened by the use of wire. A simple arrangement, consisting of a pin and connecting-rod leading to the face-plate of a lathe, the tool-rest being utilized as a guide, may be used instead of an engine for obtaining complete determination of this error. The amount of error caused by over-travel of the drum has been found by experi- ment to be from 0.5 to 1.5 per cent at 250 revolutions, with the best tension on the drum spring. Uniform Tension on the Indicator-cord. It is often impor- tant to determine whether the drum-spring maintains a uniform tension on the cord, or whether it alternately exerts a greater FIG. 197 BROWN DRUM-SPRING TESTING-DEVICE. or less stress ; this may be determined by the instrument shown in Fig. 197. The testing instrument consists of a wooden plate, A, on one end of which is fastened the brass frame, BB, carrying the slide, C, with its cross-head, D. The head of the spring, F, is screwed to the cross-head, while the other end is connected with the bent lever, , carrying the pencil The connecting-rod, E, which moves the slide, C, receives its motion from a crank not shown in the figure, swinging leaf holds the paper on which the diagram is to be taken. The indicator to be tested is clamped to the plate as shown, and the drum-cord connected with the free end of the spring The crank is made to move at the speed at which it is desired to test the drum-spring. The paper is then pressed up to the pencil and the diagram taken. If the tension 484 EXPERIMENTAL ENGINEERING. [ 396. on the cord is constant, the lines which represent the forward and return strokes will be parallel to the motion of the slide ; but, if the stress is not constant, the pencil will rise and fall as the stress is greater or less. The line drawn when the cord has been detached from the indicator (Fig. 198) is the line of no stress. In the diagram, horizontal distance represents the position of the drum, and vertical distance represents strain on the cord. The perfect diagram would be two lines near together and parallel to the line of no stress, and would repre- sent a constant stress, and consequently a constant stretch of the cord, from which no error would result. When the length of the cord and the amount it will stretch under varying stresses is known, the errors in the diagram due to stretch of cord caused by irregular stresses applied by the drum-spring can be calculated. Indicator. 250 revolutions Indicator. 250 revolutions A B Indicator. 400 revolutions Indicator. 40 J revolutions c FIG. 198. DIAGRAMS SHOWING VARIATION IN DRUM-SPRING STRESS. 396. To Adjust and Calibrate a Drum-spring. 1. Find the weight of the moving parts, and compute the theoretic stress on the indicator-cord. (See Article 395.) 2. Attach to the face-plate of a lathe in such a manner that the speed can be varied within wide limits. 3. Draw diagrams at various rates of speed, various lengths of stroke, and various tensions on the drum-spring. 4. Find the error in the diagram for each condition. Plot the results, and deduce from the curve shown the best length of diagram and. best tension for each speed. 3970 THE STEAM-ENGINE INDICATOR. 485 5. Repeat the fame operations with the Brown spring test- ing-device, and compare the results. 397. Method of Attaching the Indicator to the Cylinder. Holes for the indicator are drilled in the clearance-spaces at the ends of the cylinders, in such a position that they are not even partially choked by any motion of the piston. These holes are fitted for connection to half-inch pipe : they are located preferably in horizontal cylinders at the top of the cylinder ; but if the clearance-spaces are not sufficiently great they may be drilled in the heads of the cylinder, and connec- tions to the indicators made by elbows. The holes for the in- W/////7/ \ Awm^mmN^^^^ FIG. 199. SECTION OF CROSBY THREE-WAY COCK. FIG. 200. ELEVATION OF CROSBY THREE-WAY COCK. dicator-cocks are usually put in the cylinders by the makers of the engine, but in case they have to be drilled great care must be exercised that no drill-chips get into the cylinder. This may be entire-ly prevented by blocking the piston and admitting twenty or thirty pounds of steam-pressure to the cylinder. The connections for the indicator are to be made as short and direct as possible. Usually the indicator-cock can be screwed directly into the holes in the cylinder, and an indicator attached at each end. In case a single indicator is used to take dia- grams from both ends of the- cylinder, half-inch piping with as easy bends as possible is carried to a three-way cock, as in Fig. 486 EXPERIMENTAL ENGINEERING. [ 398. 194, to which the indicator is attached. The cock is located as nearly as possible equidistant from the two ends of the cylinder. The form of the three-way cock is shown in Figs. 199 and 2OO ; and the method of connecting in Fig. 194. In connecting an indicator-cock, use a wrench very care- fully ; but on no account use lead in the connections, as it is likely to get in the indicator and prevent the free motion of the piston. 398. Directions for Taking Indicator-diagrams. Firstly, provide a perfect reducing-motion, and make ar- rangements so that the indicator-drum can be stopped or started at full speed of the engine. (See Article 391.) Secondly, clean and oil the indicator, and attach it to 'the engine as previously explained. Insert proper spring ; oil piston with cylinder-oil. Thirdly, put proper tension on the drum-spring (see Article 395) ; see that the pencil-point is sharp and will draw a fine line. Fourthly, connect the indicator-cord to the reducing-motion; turn the engine over and adjust the cord so that the indicator- drum has the proper movement and does not hit the stops. Fifthly, put the paper on the drum ; turn on steam, allow it to blow through the relief-hole in the side of the cock ; then admit steam to the indicator-cylinder, close the indicator-cock, start the drum in motion, and draw the atmospheric line with engine and drum in motion ; open the cock, press the pencil lightly and take the diagram ; close the cock and draw a second atmospheric line. Do not try to obtain a heavy diagram, as all pressure on the card increases the indicator friction and causes more or less error. Take as light a card as can be seen ; brass point and metallic paper are to be used when especially fine diagrams are required. When the load is varying, and the average horse-power is required, it is better to allow the pencil to remain during a number of revolutions, and to take the mean effective pressure from the several diagrams drawn. 399-] THE STEAM-ENGINE INDICATOR. 487 Remove card after diagram has been taken, and on the back of card make note of the following particulars, as far as conveniently obtainable : No Time. . Diagram from M Diameter of cylinder Built by Length of stroke Revolutions per minute Barometer reads Pressure of steam, in Ibs., in boiler. . . Position of throttle-valve. ...... Vacuum per gauge, in inches Remarks Temperature of hot-well -... Inside diameter of feed-pipe " " exhaust-pipe ..Valves.. Sixthly, after a sufficient number of diagrams has been taken, remove the piston, spring, etc., from the indicator while it is still upon the cylinder ; allow the steam to blow for a moment through the indicator-cylinder, and then turn attention to the piston, spring, and all movable parts, which must be thoroughly wiped, oiled, and cleaned. Particular attention should be paid to the springs, as their accuracy will be impaired if they are al- lowed to rust ; and great care should be exercised that no gritty substance be introduced to cut the cylinder or scratch the piston. Be careful never to bend the steel bars or rods. 399. Care of the Indicator. The steam-engine indicator is a delicate instrument, and its accuracy is liable to be im- paired by rough usage. It must be handled with care, kept clean and bright ; its journals must be kept oiled with suitable oil. It must be kept in adjustment. In general, all screws can be turned by hand sufficiently tight, and no wrench should be used to connect or disconnect it. Never use lead on the con- nections. Before using it, take it apart, clean and oil it. Try each part separately. See if it works smoothly; if so, put it together without the spring. Lift the pencil-lever, and let it 488 EXPERIMENTAL ENGINEERING. [ 39Q. fall ; if perfectly free, insert the spring as explained, and see that there is no lost motion ; oil the piston with cylinder-oil, and all the bearings with nut- or best sperm-oil. Give it steam, but do not attempt to take a card until it blows dry steam through the relief. If the oil from the engine gums the indicator, always take it off and clean i.t. After using it remove the spring, dry it and all parts of the indicator, then wipe off with oily waste. Fasten the indicator in its box, in which it will go, as a rule, only one way, but it requires no pounding to get it properly in place ; carefully close the box to protect it from dust. CHAPTER XVII. THE INDICATOR-DIAGRAM. 400. Definitions. The indicator-diagram is the diagram taken by the indicator, as explained in Article 378, page 459. In the diagram the ordinates correspond to the pressures per square inch acting on the piston, the abscissa to the travel FIG. 201. DIAGRAM FROM AN IMPROVED GREENE ENGINE. CYLINDER, 16 INCHES IN DIAMETER, 36 INCHES STROKE. BOILER-PRESSURE, 100 LBS. 80 REVOLUTIONS PER MINUTE. SCALE, 50. of the piston. During a complete revolution of an engine occur four phases of valve-motion which are shown on the indi- cator-diagram, viz. : admission, CDE, when the valve is open, and the steam is passing into the cylinder; expansion, EF y when steam is neither admitted nor released and acts by its 4 S 9 490 EXPERIMENTAL ENGINEERING. [ 4-OO. expansive force to move the piston ; exhaust, FGH, when the admission-port is closed and the exhaust opened so that steam is escaping from the cylinder; and compression, HC, when all the ports are closed and the steam remaining in the cylinder acts to bring the piston to rest. The Atmospheric Line, AB, is a line drawn by the pencil of the indicator when the connections with the engine are closed and both sides of the piston are open to the atmosphere. This line represents on the diagram the pressure of the atmosphere, or zero gauge-pressure. The Vacuum Line, OK, is a reference-line drawn a distance corresponding to the barometer-pressure (usually about 14.7 pounds) by scale below the atmospheric line. It represents a perfect vacuum, or absence of all pressure. The Clearance Line, OY, is a reference-line drawn at a dis- tance from the end of the diagram equal to the same per cent of its length as the clearance or volume not swept through by the piston is of the piston-displacement. The distance between the clearance line and the end of the diagram represents the volume of the clearance of the ports and passages at the end of the cylinder. The Line of Boiler-pressure, JK, is drawn parallel to the atmospheric line, and at a distance from it by scale equal to the boiler-pressure shown by the gauge. The difference in pounds between it and DE shows the loss of pressure due to the steam-pipe and the ports and passages in the engine. The Admission Line, CD, shows the rise of pressure due to the admission of steam to the cylinder by opening the steam- valve. If the steam is admitted quickly when the engine is about on the dead-centre, this line will be nearly vertical. The Point of Admission, C, indicates the pressure when the admission of steam begins at the opening of the valve. The Steam Line, DE, is drawn when the steam-valve is open and steam is being admitted to the cylinder. The Point of Cut-off, E, is the point where the admission of steam is stopped by the closing of the valve. It is difficult to determine the exact point at which the cut-off takes place. 400.] THE INDICATOR DIAGRAM. 49! It is usually located where the outline of the diagram changes its curvature from convex to concave. It is most accurately determined by extending the expansion line and steam line so that- they meet at a point. The Expansion Curve, EF, shows the fall in pressure as the steam in the cylinder expands doing work. The Point of Release, F, shows when the exhaust-valve opens. The Exliaust Line, FG, represents the change in pressure that takes place when the exhaust-valve opens. The Backpressure Line, GH, shows the pressure against which the piston acts during its return stroke. On diagrams taken from non-condensing engines it is either coincident with or above the atmospheric line, as in Fig. 201. On cards taken from condensing engines it is found below the atmospheric line, and at a distance greater or less according to the vacuum obtained in the cylinder. The Point of Exhaust Closure, H, is the point where the exhaust-valve closes. It cannot be located very definitely, as the first slight change in pressure is due to the gradual closing of the valve. The Point of Compression, H, is where the exhaust-valve closes and the compression begins. The Compression Curve, HC y shows the rise in pressure due to the compression of the steam remaining in the cylinder after the exhaust-valve has closed. The Initial Pressure is the pressure acting on the piston at the beginning of the stroke. The Terminal Pressure is the pressure above the line of perfect vacuum that would exist at the end of the stroke if the steam had not been already released. It is found by con- tinuing the expansion curve to the end of the diagram, as in Fig. 201. This pressure is always measured from the line of perfect vacuum, hence it is the absolute terminal pressure. Admission Pressure is the pressure acting on the piston at end of compression, and is usually less than initial pressure. 49 2 EXPERIMENTAL ENGINEERING. [ 4OO. Compression Pressure is the pressure acting on the piston at beginning of compression ; this is also the least back pressure. Cut-off Pressure is the pressure acting on the piston at beginning of expansion. Release Pressure is the pressure acting on the piston at end of expansion. Mean Forward Pressure is the average height of that part of the diagram traced on the forward stroke. Mean Back Pressure is the average height of that part traced on the return stroke. Mean Effective Pressure (M. E. P.) is the difference between mean forward and mean back pressure during a forward and return stroke. It is the length of the mean ordinate inter- cepted between the top and bottom lines of the diagram mul- tiplied by the scale of the diagram. It is obtained without regard to atmospheric or vacuum lines. Ratio of Expansion is the ratio of the volume of steam in t'.ie cylinder at end of the stroke, compared with that at cut- off. In computations for this quantity the volume of clear- ance must be taken into account. Ratio of expansion is denoted by r. For hyperbolic expansion,/ being pressure in pounds per square foot at cut-off, and v the corresponding total volumes, the work done per stroke and per square inch of area = pv(y^\- Hy log r). The volume may be expressed as proportional to linear feet, with an additional length equal to the per cent of clear- ance, since the area of the cylinder is constant. The product of pressure per square foot into total volume is a constant quantity for hyperbolic expansion. The ratio of expansion is the reciprocal of the cut-off measured from the clearance line. This cut-off is distinguished from that shown directly on the card by designating it as the absolute cut-off. Initial Expansion is the fall of pressure during admission, due to an imperfect supply of steam. Wire-drawing is the fall of pressure between the boiler and cylinder; it is usually indicated by initial expansion. 401.] THE INDICATOR-DIAGRAM. 493 401. Measurement of Diagrams. The diagrams taken are on a small scale, they are often irregular, and the boundary lines are frequently obscure, so that the measurement must be made with great care. The diagrams may be taken from each end of the cylinder on a separate card, as shown in Fig. 201 ; or by the use of the three-way cock (see Article 398), in which case the two dia- grams will be drawn on the same card as shown in Fig. 202. In the latter case each diagram is to be considered separately; that is, the area of each diagram, as CDEBFC and GHIJKG, is to M FlG. 202. be determined as though on a separate card. The object of diagram-measurements is principally to obtain the mean effect- ive pressure (M. E. P.). Two methods are practised. First, the method of ordinates. In this case the atmos- pheric line AB is divided into ten equal spaces, and ordinates are erected from the centre of each space. The sum of the length of these various ordi-nates divided by the number gives the mean ordinate. This multiplied by the scale of the dia- gram gives the mean effective pressure. The sum of the ordinates is expeditiously obtained by successively transferring the length of each ordinate to a strip of paper and measuring its length. Secondly, with the planimeter. The planimeter gives t 'mean ordinate much more accurately and quickly than the 494 EXPERIMEN TA L ENGINEERING. [ 402, method of ordinates. The various planimeters are fully described, pages 26 to 49. With any planimeter the area of the diagram can be ob- tained, in which case the mean ordinate is to be found by dividing by the length of the diagram. Several of the pla- nimeters give the value of the mean ordinate, or M. E. P., directly. In some instances the indicator-diagram has a loop, as in Fig. 203, caused by expanding below the back-pressure line; in this case the ordinates to the loop are negative and should be FIG. 203. subtracted from the lengths of the ordinates above. In case of measurement by the planimeter, if the tracing-point be made to follow the expansion-line in the order it was drawn by the indicator-pencil, the part within the loop will be circum- scribed by a reverse motion, and will be deducted automatically by the instrument, so that the reading of the planimeter will be the result sought. 402. Indicated Horse-power. Indicated horse-power is the horse-power computed from the indicator-diagram, being obtained by the product of M. E. P. (/), length of stroke in feet (/),area of piston in square inches (a), and number of revolu- tions (n), as represented in the formula plan -r- 33,000. In this computation the area on the crank side of the piston is to be corrected for area of piston-rod, and the two ends of the cylin- ders computed as separate engines. Further, in this computa- tion, it will not in general answer to multiply the average M.E.P. of a number of cards by the length of stroke and by the 403-] THE INDICATOR-DIAGRAM. 495 average of the number of revolutions, but each card must be subjected to a separate computation and the results averaged. This can be readily done for each engine by computing a table made up of the products of the average value of n by length of stroke and area of piston, and for different values of M. E. P. from i to 10. Take from this table the values corresponding to the given M. E. P., increase or diminish this as required by the per cent of change of speed from the average. A very convenient table for this purpose, entitled " Horse-power per Pound, Mean Pressure," is given in the Appendix to this work, arranged with reference to diameter of cylinder in inches and piston-speed in feet per minute. 403. Form of the Indicator-diagram. The form of the indicator-diagram has been carefully worked out for the ideal case by Rankine and CotterelL* In the ideal case the steam works in a non-conducting cylinder, and all loss of heat is due to transformation into work, the expansion in such a case being adiabatic. In the actual case the problem is much more com- plicated, since a large portion of the heat is utilized in heating the cylinder, and is returned to the steam at or near the time of exhaust, doing little work. It is found, however, in the best engines working with quick-acting valve-gear, that the steam and back-pressure lines are straight and parallel to the atmos- pheric line, and that the expansion and compression lines are very nearly hyperbolae, asymptotic to the clearance line and to the vacuum line. If we denote by p the pressure measured from the vacuum line, and by v the volume corresponding to a distance meas- ured from the clearance line, so that/z; shall be the co-ordinates of any point, we shall have as characteristic of the hyperbola pv = constant. This is the same as Mariotte's law for the expansion of non- condensible gases, since, according to that law, the pressure varies inversely as the volume. * Steam-engine, by James H. Cotterell. 49 6 EXPERIMEN TA L ENGINEERING. [ 404. Rankine found by examination of a great many actual cases that the expression pi& = constant agrees very nearly with the ideal case of adiabatic expansion. The variation from the ideal expansion line in any given case may be considerable, and the hyperbola drawn from the same origin is considered as good a reference-line as any that can be used, and the student should become familiar with the best methods of constructing it. 404. Methods of Drawing an Hyperbola. The methods of drawing an hyperbola, the clearance and vacuum lines being given, are as follows : First Method. (See Fig. 204.) CB, the clearance line, and CD, the vacuum line, being given, draw a line parallel to the FIG. 204 METHOD OF DRAWING AN HYPERBOLA. atmospheric line through B\ find by producing the steam and expansion lines the point of cut-off, c. Draw a series of radiating lines from the point C to the points E, F, G, H, and A, taken at random, and a line cb intersecting these lines, drawn from c parallel to BC. From the points of the inter- section of cb with -these radiating lines draw horizontal lines to meet vertical lines drawn from the points , F, G, H, and 4 o 5 .] THE IN DIC A 7 'OR- L > I A GA'.l A ; the intersections of these lines at e, f, g, h, and a are points in the hyperbola passing through the point c. If it is desired to produce the hyperbola from a upward, the same method is used, but the line AB is drawn through the point #, and the vertical lines are extended above AB instead of below. Second Method. (See Fig. 205.) The hyperbola may be drawn by a method founded on the principle that the inter- cepts made by a straight line intersecting an hyperbola and its asymptotes are equal. Thus if abed represent an hyperbola, BC and CD its asymptotes, then the intercepts a a' and bb' made by the straight line a'b' are equal. To draw the hyperbola : Beginning at any point, as a, draw ^4 6' ? A^V can ^ e drawn as follows : From the above expression n log 7' + log/ n log v l + log/, , from which log/ - n log z\ -f- log p l n log v ; from which, if ;/, v l , and v are known,/ may be determined. The values of n are as follows : Equilateral hyperbola, n I ; Saturation curve steam, n = -J--J = 1.0646; Adiabatic curve steam, n = 1.035 +0.14; " " gas, ;/ = 1.408 ; Isothermal " " n = i.o. These three expansion curvesf are represented in Fig. 206 ; the pressures from o to 90 pounds per square inch are repre- sented by the ordinates, and the volumes in cubic feet corre- sponding to one pound in weight are represented by abscissae. * Rankine's Steam-engine, page 385. f See Thurston's Engine and Boiler Trials, page 251. 406.] THE INDICATOR-DIAGRAM. 499 In the figure the curve A to G is the hyperbola. A to / the saturation curve, and A to L the adiabatic curve. ON is the axis of the hyperbola, of which OB and OH are asymptotes. It is to be noticed that the saturation curve corresponds to a uniform quality of steam, the adiabatic curve to a condition in which the moisture is increasing, and the hyperbolic curve H-IIM 1800 1700 1600 1300 1400 1300 1200 1100 1000 900 800 700 600 500 400 Fio. 206. THE THREE EXPANSION CURVES. 800 auo loo to a condition in which the moisture is decreasing, the latter agreeing more closely with the actual condition. 406. Weight of Steam from the Indicator-diagram. The diagram shows by direct measurement the pressure and volume at any point in the stroke of the piston ; the weight per cubic foot for any given pressure may be taken directly from a steam-table. The method, then, of finding the weight of steam for any point in the stroke is to find the volume in cubic feet, including the clearance and piston displacement to the given point, which must be taken at cut-off or later, and multiply this by the weight per cubic foot corresponding to the pressure at the given point as measured on the diagram. This will give the weight of steam in the cylinder accounted for by the indicator-diagram, per stroke. In an engine work- ing with compression, the weight of steam at terminal pressure 500 EXPERIMENTAL ENGINEERING. [\ filling the clearance-space is not exhausted ; this weight, com- puted for a volume equal to clearance and with weight per cubic foot corresponding to admission pressure, should be subtracted from the above. This may be reduced to pounds of steam per I. H. P. per hour, by multiplying by the number of strokes required to develop one horse-power per hour of time. The method of computing would then be : Find the weight per cubic foot, from a steam-table corresponding to the abso- lute pressure, at the given point, multiply this by the corre- sponding volume in cubic feet, including clearance, and this by the number of strokes per hour. The result will be the weight of steam per hour. Divide this by the horse-power developed, and we shall have the consumption in pounds of dry steam per I. H. P. Thus let A area of piston in square feet ; a= " " " " " inches; A r = number of strokes per hour; n = " " " " minute ; w = weight of cubic foot of steam at the given pressure : / = total length of stroke in feet ; 4 = length of stroke in feet to point under consideration ; c = per cent of clearance ; I' = l a + cl. Then the consumption of dry steam in pounds per hour per horse-power, 6on (L-\-cl}w f , . K I y A A \ # I / /7/7 / / I / /\ H, P. plan 33.000 Some of the steam may be restored by compression, reduc- ing the results given in equation (i). As an example : Compute the steam consumption as shown in. Fig. 20 1 at point of cut-off E and at terminal pressure. 406.] THE INDICATOR-DIAGRAM. 50! The absolute pressure shown by the diagram is 7 pounds at cut-off and 37 at end of the stroke. The length of stroke total is 3 feet, at cut-off is J foot. Clearance is 3.2 per cent. M. E. P. (/) is 50 pounds. Steam- consumption at Cut-off. -From steam-table ?f/=o.22o8. (o. 2 208) (0.754-0.09) 5 = I3,750 V *3p -=17-15 Ibs. per I.H.P. per hour. ' 'i : "'"* ''}'' 'i *',''' '.I~J I '.',' 1 Steam- consumption at End of Stroke. From steam-table w = 0.0896. 5 = , 3,750 <1^3) = 20.5 Ibs. per I. H. P. per hour. This, it should be noticed, is not the actual weight of steam used per horse-power by the engine, but is that part which is shown from the amount of dry steam remaining in the cylin- der at the points under consideration. The amount is usually less when computed at cut-off than at the end of the stroke, since some of the steam which was condensed when the steam first entered the cylinder is restored by evaporation during the latter portion of the period of expansion. The correction factor for the steam restored by compression can be calculated graphically by drawing a line parallel to the atmospheric line, through the point for which the steam-consumption was cal- culated, to an ordinate through the point of admission. The ratio of the part between expansion and compression curves to the whole line is the factor which is to be multiplied by the previous results to give the consumption of steam per I. H. P. per hour. In the examples considered above this fac- tor is unity. If we consider the steam-consumption only for the end of the stroke, 4 of equation (i) becomes equal to /, and the equation reduces to the following form : 5 = 13,750^(1+4 ..'*... (2) 5O2 EXPERIMENTAL ENGINEERING. [ 407. Neglecting the clearance, S;= I3>750 jl (3) in which / = the M. E. P. of the diagram, and w the weight per cubic foot corresponding to the terminal pressure. For- mula (3) has been tabulated as follows : Thompson's tables, given in the Appendix, give values of 13,750^, and the tabular values must be divided by the M. E. P. to give the steam-consumption per I. H. P. per hour. Tabor's tables give values of -^- , and the tabular values must be multiplied by the weight of a pound of steam corre- sponding to the terminal pressure, to give the steam-consump- tion. 4 Williams's tables, published in the Crosby catalogue, give values of , and the results in each case have to be multi- 42543 plied by 32. $2w to give the steam-consumption. A graphical correction is made in all cases for compression by drawing a horizontal line through the terminal pressure to compression line of diagram, and multiplying the result given in the table by the ratio of the portion of this line intercepted between terminal point and compression, to the whole stroke. 407. Clearance Determined by the Diagram. The clearance is usually to be determined by actual measurement of the volume of the spaces not swept through by the piston, and comparing this result with the volume of piston-displace- ment, the ratio being the clearance. Since the expansion and compression lines of the diagram are nearly hyperbolae, the clearance line can be drawn by a method nearly the reverse of that used in constructing an hyperbola (Article 404). In this case proceed as follows : Lay off the vacuum line CD (Fig. 207) parallel to the atmospheric line FT, and at a distance corresponding to the atmospheric pressure. The position of the clearance line can be determined by two methods, corresponding to those used in di awing the hyperbola. First 408.1 THE INDICATOR-DIAGRAM. 503 method: Take two points, a and b in the expansion curve and c and d in the compression line, and draw horizontal and vertical lines through these points, forming rectangles aa'bV and cc'dd. Draw the diagonal of either rectangle, as a'V, to meet the vacuum line CD-, the point of intersection C will' be I a po|it : CN~F FIG. 207. METHODS OF FINDING THE CLEARANCE. in the clearance line CB, and the clearance will equal FT. Second method: Draw a straight line through either curve, as mn through the compression curve or ef through the expansion curve, and extend it in both direc- tions. On the line m'n' lay off nn' equal to mm' , or on the line e'f lay off ee' equal to ff'\ then will either of the points e' or n' be in the clearance line and the line drawn perpendicular to the vacuum line through either of these points is the clear- ance line. In an engine working with much compression the clearance will be given more accurately from the compression curve than from the expansion curve, since it is more nearly an hyperbola. 408. Re-evaporation and Cylinder Condensation. By considering the hyperbolic curve as a standard, an idea can be obtained of the restoration by re-evaporation and the loss by 504 EXPERIMENTAL ENGINEERING. [ 409. cylinder condensation. Thus in Fig. 208, suppose that a is the point of cut-off at boiler-pressure, construct an hyperbola as explained ; in the example considered it is seen to lie above the expansion line for a short distance after cut-off, then to cross the line at b, and remain below it nearly to the end of the stroke. The amount by which the expansion line rises above the hyperbola may be considered as due to re-evaporation. The area of the diagram lying above would represent the work added by heat returned to the steam from the cylinder. The methods for determining the cylinder condensation are C V 4 6' d' FIG. 208. WORK RESTORED BY RE-EVAPORATIOX. similar to this process, except that the hyperbola is usually drawn upward from the point corresponding to the terminal pressure, to meet a horizontal line drawn to represent the boiler- pressure, as follows : This construction is shown by the dotted lines in the diagrams in Fig. 209. The area of the figure enclosed by the dotted lines, compared with that of the diagram, is the ratio that the ideal diagram bears to the real ; the difference is the loss by cylinder condensation. The student should understand that both these methods are approximations which may vary much from the truth. 409. Discussion of Diagrams. Diagrams are often taken 409-] THE INDICATOR-DIAGRAM. 505 where some portion of the engine is out of adjustment, or the indicator or reducing motion is not in perfect order. It is often 91 per cent of ideal. 40.0 Horse Power DO per cent of Ideal. 62.4 Horse Power 65 Ib&Boiler Press. Fio. 209. Loss BY CYLINDER-CONDENSATION. possible in such cases to determine the defect from the dia- gram, and to suggest the proper remedy. A few examples are submitted. Such examples could be multiplied indefinitely, and skill and experience will, in general, be required to prop- Top of cylinder Steam side. Bottom of cyfinder Steam side. Vacuum side. FIG. 210. UNSYMMETRICAL VALVE-SETTING. erly interpret them. Thus Fig. 210 is an illustration of a dia- gram taken when the valves were set unsymmetrically. Curves or waves in the expansion or compression lines indicate inertia- 5 o6 EXPERIMENTAL ENGINEERING. [409. effects in the drum-motion, which is sometimes sufficient to make the compression line concave when it should be convex, as shown in the lower diagram of Fig. 211. Vertical curves are due in large measure to vibrations in the pencil-lever and indicator-spring ; they are usually excessive with a light spring and high speed. In the case of an automatic engine running under variable loads, each revolution will show a different dia- gram, as shown in Fig. 211. FIG. 211. VARIATION OF LOAD. Different Forms of Admission-lines. The form of the ad- mission-line is changed* according to the relative time of valve- opening and position of piston in its stroke. The normal form is shown at A. In B CD and E the valve opens late, and after the piston has started on its return stroke. In .Fand G the exhaust-valve closes late, so that live steam escapes. H and / are familiar examples of extreme compres- sion, produced on high-speed automatic engines working with a light load. J shows a sharp corner above the compression * Power, September 1891. 4io.] THE INDICATOR-DIAGRAM. SO/ line, and in general indicates too much lead. In case the valve opens too early, the admission-line leans as at K. 410. Diagrams from Compound and Triple-expansion Engines. The diagram from any cylinder of a compound or triple-expansion engine is not likely to differ in any noticeable FIG. 212. TYPICAL ADMISSION-LINKS. particular from those taken from a simple engine as already described. They are usually taken with different springs for the different cylinders, but may have very nearly or exactly the same lengths. The diagrams from a compound engine may be reduced to an equivalent diagram, taken from a single cylinder by the fol- lowing method : Lay off a vertical line OB, and a horizontal line PQ. Let PQ be the vacuum line, and BC the line of 508 EXPERIMENTAL ENGINEERING. [ 410. highest steam-pressure acting in the small cylinder. Lay off ON proportional to the volume of the small cylinder, and OP proportional to the volume of the large cylinder. Let FA be the line of back pressure of the large cylinder, AD that of the small cylinder: then BCD A is the diagram from the small cylinder, EKFA that from the large cylinder. To combine them into one diagram, draw a line KGHpzr- allel to POQ, intersecting both diagrams, and lay off upon it HL = KG ; and GL GH ' -\- KG represents the total volume B C " P -*A " M ON Q FIG. 21,,. in both cylinders when the pressure is OG, and L is a point in the expansion line the same as though the action took place in the large cylinder only. In the same way other points may be found, and the line CDLM drawn. This diagram may be discussed as if it represented the steam acting in the large cylinder only. Fig. 214 is a combined diagram from a triple-expansion engine,* in which the cylinders have the ratio of I : 2.25 : 2.42, and the total ratio of expansion is 8. The length of each dia- gram is made proportional to the total volume of the cylinder from which it was taken ; the diagrams are all drawn to the same scale of pressures, and each is located at a distance from a vertical line proportional to the volume of its clearance. From the point of cut-off corresponding to boiler-pressure an hyperbola is drawn as has been explained, and the area sur- rounding the diagrams is shaded. The work done in the three cylinders can be computed from the diagram as though done in one only. * See Thurston's Engine and Boiler Trials, page 202. i-A.ti: THE IND 1C A TOR-DIA GRA M. 509 411. Crank-shaft and Steam-chest Diagrams. Dia- grams may be taken with the motion of the indicator-drum proportional to any moving part of the engine, as for instance the crank-shaft. FIG. 214. COMBINED DIAGRAM FROM TRIPLE-EXPANSION ENGINE. In such a case, shown by Fig. 215, the ordinates will be as before proportional to the pressures per square inch acting on the piston, but the abscissae will correspond to distances moved FIG. 215. SHAFT-DIAGRAM. through by the crank-pin. In Fig. 215 A to B is the exhaust, from B to C compression, D to E steam line, E to A expan- sion. Diagrams may also be taken with the indicator mounted on the valve-chest ; in this case the indicator would show vari- ation in pressure in the steam-chest. 5io EXPERIMENTAL ENGINEERING. CHAPTER XVIII. METHODS OF TESTING THE STEAM-ENGINE. 412. Various Efficiencies of the Steam-engine.* The efficiency of the steam-engine is frequently expressed in vari- ous manners, as follows: 1. Thernwdynamic efficiency. This is the ratio of work done by the working substance to the mechanical equivalent of the heat expended on it to do that work. In the perfect engine-cycle this efficiency is measured by the quantity T T --^ * , the range of temperature worked through divided by * i the maximum initial absolute temperature of the fluid enter- ing the cylinder of the engine. 2. Actual efficiency of working substance. This is here con- sidered to be the ratio of the heat transformed into work to the total available heat entering the system. If there were no losses of heat except those due to work, the efficiency of the working substance would be i.oo, but radiation, the cooling effect of the cylinder, etc., cause losses which vary with dif- ferent working substances and in different cylinders. 3. Mechanical efficiency. This is the ratio of the work done on the piston to that delivered, or that of I.H.P. to D.H.P. 4. Efficiency of the engine. This is the ratio of the work actually done to the mechanical equivalent of the heat ex- pended ; it should equal the product of the efficiencies of the various parts. 5. Plant efficiency. This is the product of the several * See " Manual of the Steam-engine," by R. H. Thurston, Vol. I., page 706. 5" 5 1 2 EXPERIMEN TA L ENGINEERING. [ 4 1 3 efficiencies of the various parts or machines which compose the plant. Fuel and Water Consumption of Ideal and Real Engines. The ordinary standard of comparison of the work done by dif- ferent engines is the fuel and water consumed for each horse- power per hour. The horse-power is equal to 33,000 foot- pounds per minute, or 1,980,000 per hour, which is equivalent to 42.4 B. T. U. per minute, or 2544 units per hour. Since in steam of ordinary pressure there are about 1 150 B. T. U. per pound above 32 Fahr. in a perfect engine, with efficiency equal to I, the water-consumption would be 2.2 to 2.25 pounds per horse-power per hour. The weight of coal under the best conditions would be about one tenth the water-con- sumption, or from 0.2 to 0.22 pound per horse-power per hour. The several efficiencies of the real engine are much less than unity in each case. Thus in the best engine the thermo- dynamic efficiency is about 0.2, the efficiency of the working- substance from 0.9 to 0.75, and of the machine about 0.95. So that the total efficiency of the best real engine would be E 0.20 X 0.90 X 0.95 = 0.17. This wouid mean a consumption per I.H.P. per hour of - = 14,940 B. T. U. ; 2.2 0.17 0.22 = 12.94 pounds of water; = 1.29 pounds of fuel. 413. Objects of the Engine-test. The test may be made : I. To adjust the valves or working parts of the engine. 2. To determine the indicated or dynamometric horse-power. 3. To ascertain the friction for different speeds or conditions. 4. To determine the consumption of fuel or steam per horse- power per hour. 5. To investigate the heat-changes which 4H-] METHODS OF TESTING THE STEAM-ENGINE. 513 characterize the passage of the steam through the engine. The general method of the test will depend largely on the ob- ject for which the test is made; in any event the apparatus to be used should be carefully calibrated, the dimensions of the engine obtained, and the test conducted with care. 414. Measurements of Speed. The various instruments employed for measurement of speed are speed-indicators, ta- chometers, continuous counters, and chronographs. Where the number of revolutions only is required, it is usually obtained either by counting or by the hand speed- indicator. Counting can be done quite accurately without an KIG. 217. DOUBLE-ENDED SPEED-INDICATOR. instrument, by holding a stick in the hand in such a position that it is struck by some moving part, as the cross-head of an engine, once in each revolution. The Jiand speed-indicator, of which one form is shown in Fig. 217, consists of a counter operated by holding the pointed end of the instrument in the end of the rotating shaft. In using the instrument, the time is noted by a watch at the instant the counting gears are put in operation or are stopped. A stop-watch is very convenient for obtaining the time. The errors to be corrected are princi- pally those due to slipping of the point on the shaft, and to the slip of the gears in the counting device in putting in and out of operation. The best counters have a stop device to prevent this latter error, and the gears are engaged or disengaged with WVBR3ITY EXPERTMENTA L ENGINEERING. [ 4H. the point in contact with the shaft. To prevent slipping of the point, the end of the instrument is sometimes threaded and screwed into a hole in the end of the shaft. The continuous counter consists of a series of gears arranged to work a set of dials which show the number of revolutions. The arrangement of gearing in such an instrument is shown in Fig. 218. The instrument can usually be made to register by either rotary or reciprocating motion, and can be had in a FIG. 218. square or round case. The reading of the counter is taken at stated intervals and the rate of rotation calculated. Tachometers (see Fig. 2 19) are instruments which utilize the centrifugal force in throwing outward either heavy balls or a liquid. The motion so caused moves a needle a distance pro- portional to the speed, so that the number of revolutions is read directly from the position of the needle on the graduated dial. The tachometer is arranged with a pointed end to hold against the shaft whose speed is to be determined, or with a pulley so that it may be driven by a belt. 4150 METHODS OF TESTING THE STEAM-ENGINE. 515 Browns Speed-indicator consists of a U-shaped tube joined to a straight tube in the centre. The revolution of the U-tube around the centre tube induces a centrifugal force which ele- FlG. 219. SCHAEFFER AND BUDENBERG HAND TACHOMETER. vates mercury in the revolving arms and depresses it in the centre tube. A calibrated scale gives the number of revolu- tions corresponding to a given depression. 415. The Chronograph. The chronograph,* Fig. 220, con- sists of a drum revolved by clock-work so as to make a FIG. 220. definite number of revolutions per minute. A carnage hav- ing one or two pens, //, g, as may be required is moved parallel * See Thurston's Engine and Boiler Trials, page 226. 5 1 6 EXPE KIM EN TA L ENGINEERING. [ 4 1 5 to the axis of the cylinder by a screw which is connected with the chronograph-drum A by gearing. The pen in its normal condition is in contact with the paper, and it is so connected to an electro-magnet that it is moved axially on the paper whenever the circuit is broken. The cir- cuit may be broken automatically by the motion of a clock, or by hand with a special key, or by any moving mechanism. Two pens are usually employed, one of which registers auto- matically the beats of a standard clock; the other may be ar- ranged to note each revolution or fraction of a revolution of a revolving shaft. The distance between the marks made by the clock gives the distance corresponding to one second of time ; the distance between the marks made by breaking the circuit at other intervals represents the required time which is to be measured on the same scale. This instrument has been in use by astronomers for a long time for minute measurements of time, and by its use intervals as short as one one-hundredth (.01) part of a second can be measured accurately. Timing-fork Chronograph. A tuning-fork emitting a musi- cal note makes a constant and known number of vibrations. The number of vibrations of the fork corresponding to the musical tones are as follows : Note C D E F G A B C 2 Vibrations ) per second. } I28 '44 160 I/of 192 213! 240 256 If now a small point or stylus be attached to one of the arms of a tuning-fork, as shown in Fig. 221,* in which /MS one of the arms of the tuning-fork, and CAED a piece of elastic metal to which the stylus, AP, is attached, and if the fork be put in vibration and the stylus permitted to come in contact with any surface that can be marked, as a smoked and var- nished cylinder moved at a uniform rate, the vibrations of the tuning-fork will be recorded on the cylinder by a series of wavy lines, as shown in Fig. 223 ; the distance between the * See Thurston's Engine and Boiler Trials, page 233. 415-] METHODS OF TESTING THE STEAM-ENGINE. 517 waves corresponding to known increments of time. If each revolution or portion of a revolution of the shaft whose speed is required be marked on the cylin- der, the distance between such marks, measured to the same scale as the wavy lines made by the tuning-fork, would represent the time of revolu- tion. Fig. 222 (from Thurston's Engine and Boiler Trials) represents the Ran- son chronograph ; in this case the tun- ing-fork is moved axially_by a carriage operated by gears, and is kept in vibration by an electro-magnet. The operation of the instru- ment is the same as already described. The form of the record being shown in Fig. 223 ; the wavy marks being those FIG. 221. STYLUS FOR TUNING- FORK. FIG. 222. TUNING-FORK CHRONOGRAPH. made by the tuning-forks, those at right angles being made at the end of a revolution of the shaft whose speed is required. The tuning-fork with stylus attached,* as in Fig. 222, can be made to draw a diagram on a revolving cylinder connected * See Engine and Boiler Trials, page 234. 518 EXPERIMENTAL ENGINEERING. [ directly to the main shaft of the engine, or the shaft itself may be smoked and afterward varnished. If the fork be moved axially at a perfectly uniform rate, the development of the lines drawn will be for uniform motion, straight and of uniform pitch; but for variations in speed these lines will be FIG. 223. SPEED-RECORD FROM CHKONOGRAPH. curved and at a varying distance apart. From such a diagram the variation in speed during a single revolution can be.deter- mined. 416. Autographic Speed-recorder. Variations in speed are shown autographically in several instruments by recording on a strip of paper moved by clock-work the variation in cen- trifugal force of revolving weights. In the Moscrop speed- recorder, shown in Fig. 224, the shaft B is connected with the shaft whose speed is to be measured. The variation in the height of the balls near B, caused by variation in speed, gives the arm C a reciprocating motion, so that an attached pencil makes a diagram, FED, on the strip of paper moved by clock- work. The ordinates of this diagram are proportional to the speed. 417. The Surface Condenser. In the measurement of the steam used by the engine the surface condenser is fre- quently employed. The surface condenser usually consists of a vessel in which are a great many brass tubes. It is usually arranged so that the exhaust steam comes in contact with the outer surface of these tubes, and the condensing water flows through the tubes. The condensed steam falls to the bottom of the condenser and is removed by an air-pump ; the heat of the steam being taken up by the condensing water. If the condenser is free from leaks, the air-pump of ample size and with little clearance, and if the proper temperatures are main- 417-] METHODS OF TESTING THE STEAM-ENGINE. $19 tained, nearly all the atmospheric pressure can be removed from the condenser and the back-pressure on the engine cor- respondingly reduced. The surface condenser affords more accurate means of FIG. 224 .-THE MOSCROP SPEED-RECO 520 EXPERIMENTAL ENGINEERING. '[ 418. long a given reading of the vacuum-gauge can be maintained when all the connecting valves are closed, or by turning on steam when the water-pipes are empty, or vice versa, and noting whether there is any leakage. FORM FOR TEST ON CONDENSER. Date Duration of test . . .min. Barometer inches. Ibs. per sq. in. Temperature, entering steam C. F. Temperature, condensed steam C F. Temperature, cold condensing water C F. Temperature, hot condensing water C F. Hook-gauge reading (corrected) inches. (Hook-gauge reading) * Temperature at weir C F. Weight of condensed steam Ibs. Breadth of weir inches. End area of tubes. sq. ft. Area steam surface sq. ft. Area water surface sq. f t. Weight steam condensed per hour Ibs. Weight condensing water used per hour ibs. Weight steam condensed per pound of water Ibs. Weight steam condensed per sq. ft. steam surface per hour Ibs. Weight steam condensed per sq. ft. water surface per hour Ibs. Velocity of water through tubes ft. per sec. Heat acquired by condensing water used per hour B. T. U. Heat given up by steam condensed per hour B. T. U. Signed , 418. Calibration of Apparatus for Engine-testing. Before commencing any important test, all instruments and apparatus to be used should be adjusted and carefully com- pared with standards, under the same conditions as in actual practice. The errors or constants of all instruments should be 4 ! 8.] METHODS OF TESTING THE STEAM-ENGINE. $21 noted in the report of the test, and corresponding corrections made to the data obtained. The instruments to be calibrated are : 1. Steam-gauge. Compare with mercury column, or with standard square-inch gauge, for each five pounds of pressure, reading both up and down throughout the range of pressures likely to be used in the test. (See Article 282, page 338.) 2. Steam-engine Indie at or -springs. Put the indicator under actual steam-pressure (see Art. 393, p. 479) and compare the length of ordinate of the card with the reading of the mercury column or a standard gauge for the same pressure. Take ten readings, both up and down, through an extreme range equal to two and one-half times the number on the spring. The steam-pressure may be varied by throttling the supply and exhaust. The ordinate may also be compared by a special method with readings of a standard scale ; the indicator being heated by the flow of steam through a rubber tube wound around it. 3. Speed-indicators. The accuracy can be checked by hand counting. For the best work chronographs should be used. Continuous counters are necessary for accuracy in a long run. (See Articles 414 and 415.) 4. Indicator Reducing-motion. This may be tested by divid- ing the stroke of the engine on the guides into twelve equal parts and noting whether the card is similarly divided. It should be tested for both return and forward stroke. When the form of the card is considered, this is an important matter, as many reducing-motions distort its shape. (See Article 390, page 472.) 5. Indicator-cords and Connections. See that the connecting cords do not stretch at high speeds, and that the drum-spring of the indicator has a proper tension and gives a correct motion of the drum. This is important. (See Article 395.) 6. Weighing-scales. Compare the readings with standard weights. 7. Water-meters. Calibrate by actually weighing the dis- charge under conditions of use as regards pressure and flow. 522 EXPERIMEN TA L ENGINEERING. [418. In case meters are used, temperatures of the water must be taken in order to obtain the weight. (See Article 213, page 255.) 8. Thermometers. Test the thermometer for freezing-point by comparison with water containing ice or snow ; test for boil- ing-point by comparison with steam at atmospheric pressure in the special apparatus described on page 352, the correct boiling- point being determined by readings of the standard barometer. The other tests of the thermometer can in general be left to the makers of the instrument. In cases where great accuracy is required the readings should be compared throughout the whole scale with a standard air-thermometer, as described on page 350. 9. Pyrometer. Compare with a standard thermometer while immersed in steam for the lower ranges of temperature, and with known melting-points of metals for higher. The correction may also be determined by cooling heated masses of metals in large bodies of water and calculating the temper- ature from the known relations of specific heats. (See Articles 298 to 304). 10. The Planimeter, which is used for measuring the indi- cator-diagram, should be calibrated by making a comparison with a standard area, as explained in Article 38, page 44. The following form is useful to record the results of calibrations : BLANK FORM FOR CALIBRATION OF INSTRUMENTS. STEAM-ENGINE INDICATOR-SPRINGS. Used on Head. Crank. Maker's number. Number of spring . . When tested. . . . Per cent error .... 4I9-] METHODS OF TESTING THE STEAM-ENGINE. 523 STEAM-GAUGES. Maker. Position. Number. Error, Ibs. When Tested. How Tested. THERMOMETERS. Position. Registered Number. Boiling-point. Freezing-point. Barometer. Read- ing. Per Ba- rometer. Error. Read- ing. Error. 419. Preparations for Testing". The preparations re- quired will depend largely on the object of the test. They should always be carefully made, and in general are to include the following operations : 1, Weighing of Steam. Prepare to weigh all the steam supplied the engine. This may be done by weighing or meas- uring all the feed-water supplied the boiler (see Article 375), provided there i-s no waste nor other use of steam ; or it may be done by condensing (see Article 417) and weighing all the exhaust from the engine. In the first case especial precaution must be taken to prevent leaks, and in the latter to reduce the temperature of the condensed steam to 110 F. before weigh- ing. The weights may in some cases be determined from a meter- reading (see Article 214). 2. Quality of Steam. Attach a calorimeter (see Articles to 336), which may be of the throttling or separator kind, to the main steam-pipe, near the engine. This attachment may be made by a half-inch pipe, cut with a long thread and ex- tending three fourths across the main steam-pipe. This pipe $24 EXPERIMENTAL ENGINEERING. [ 4 I 9- should be provided with large holes so that steam will be drawn from all parts of the main steam-pipe (see page 370). 3. Leaks. The engine should be tested for piston-leaks by turning on steam with the piston blocked and cylinder-cocks opened on the end opposite that at which steam is supplied. If leaks are found, they should be stopped before beginning the test. 4. Indicator Attachments. Arrange a perfect reducing-mo- tion. The kind to be used will depend entirely upon circum- stances. The lazy-tongs or pantograph is reliable for speeds less than 125, and can be easily applied. The pendulum piv- oted above and furnished with an arc, although not perfectly accurate, is much used. Make yourself familiar with the vari- ous devices in use. (See Article 390). 5. An Absorption Dynamometer may be required ; if so, ar- range a Prony brake to absorb the power of the engine, and make provision for lubricating it and removing the heat gen- erated (see Article 178, page 4^2)'. In many commercial tests : the power is absorbed by machinery or in useful work, and the efficiency is wholly determined by measurements of the amount and quality of steam and from the indicator-diagram. 6. Weight of Coal. This is generally taken during an engine- test, but will be treated here as pertaining to boiler-testing ; the methods of weighing are fully described under that head (see Article 375). An engine fitted completely for a test is shown in Fig. 216, from Thurston's Engine and Boiler Trials. In this case two indicators are employed, the drum-motion being derived from a pendulum reducing-motion; a Prony brake is attached to absorb 'and measure the power delivered, water for keeping the brake cool being delivered near the bottom and on the inside of the flanged brake-wheel by a curved pipe, and drawn out by an- other pipe the end of which is funnel-shaped and bent so as to meet the current of water in the wheel. The speed is taken by a Brown speed-indicator mounted on top of the brake, and also by a hand speed-indicator. The steam-pressure is measured 421-] METHODS OF TESTING THE STEAM-ENGINE. 525 near the engine ; the quality of steam is determined by a sam- pie drawn from the vertical pipe near the engine. 420. Measurement of Dimensions of Engine. Make careful measurements of the dimensions of engine ; the diam- eter of piston, length of stroke, and diameter of piston-rod, as may be required. Piston-displacement. This is the space swept through by the piston ; it is obtained by multiplying the area of the piston by the length of stroke. For the crank end of the cylinder the area of the piston-rod is to be deducted from the area of the piston. Clearance is the space at the end of cylinder and between valve and piston, filled with steam, but not swept through by the piston. To measure the clearance, put the piston at end of its stroke and fill the space with a known weight of water, ascertaining that no leaks occur by watching with valve-chest cover and cylinder-head removed. Make this determination for both ends of the cylinder, and from the known weight of water compute the volume required. This is usually reduced to percentage, by dividing by the volume of piston-displacement. This last reduction may be obviated, as suggested by Prof. Sweet, by finding, after the clearance-spaces are full of water, how far the piston will have to move in order to make room for an equal amount of water ; this distance divided by the full stroke is the percentage required. Another approximate way sometimes necessary is to fill the whole cylinder and clearance- spaces with water; from this volume deduct the piston-dis- placement and divide by 2. Preliminary Run. It will be found advisable to make a pre- liminary run of several hours before beginning the regular test, to ascertain if all the arrangements are perfect. 421. Quantities to be observed. The observations to be taken on a complete engine-test are given in the following list. Fill out the following blank spaces. 5 20 EXPERIMENTAL ENGINEERING. [ 422, Kind of engine Maker's name Brake-arm feet. Diameter cylinder inches. Length stroke feet. Diameter piston-rod inches. Diameter crank-pin " Length crank-pin " Diameter wrist-pin " Travel valve " DESCRIPTION OF ENGINE. Lap of valve , inches. Scale indicator-spring Piston area sq. in. Steam-port area " Exhaust-port area " Diameter fly-wheel inches. Clearance, head Ibs. water. " crank " " per cent P.D. head " " " crank,.. Number Time Revolutions : Continuous counter Speed-indicator Gauge-readings : Boiler Ibs. Steam-pipe " Steam-chest " Exhaust inches hg. Condenser " " Barometer " " Temperatures : External air LOG OF TEST. Temperatures : Engine-room Condensed steam. Feed-water Injection-water.. . Discharge-water. . Calorimeter : Steam-pipe Steam-chest Weights : Condensed steam. Feed-water .Injection-water. . . Calorimeter. . 422. Special Engine-tests. Preliminary Indicator Prac- tice. A simple test with the indicator will be found a useful exercise in rendering the student familiar with the methods of handling the indicator and of reducing and com- puting the data to be obtained from the indicator-diagrams. The directions are as follows: Apparatus. Throttling calorimeter ; steam-gauge ; two indi- cators ; reducing-motion, and indicator-cord. I. Obtain dimensions of engines. Measure the clearance ; see that indicators are oiled and in good condition, and that 422.] METHODS OF TESTING THE STEAM-ENGINE. $2? the reducing^motion gives a perfect diagram. Adjust the length of cord so that the indicator will not hit the stops. Pre- pare to take cards as explained in Article 398, page 486. 2. Take diagrams once in each five minutes, simultaneously from head and crank end of cylinder ; take reading of boiler- gauge, barometer, gauge on steam-pipe or on steam-chest, vacuum-gauge if condenser is used, temperature or pressure of entering steam, temperature of room, and number of revolu- tions. 3. Measure or weigh the condensed steam during run. 4. From the cards taken compute the M. E. P. and I. H. P. for each card as required by the log. 5. Take a sample pair of diagrams, one from head and one from crank end. (a) Find clearance from diagrams (see Article 407, page 503); (b) draw hyperbolae respectively from cut-off and release and find re-evaporation and cylinder condensation (see Article 408) ; (c) produce hyperbola from release to meet hori- zontal line representing boiler-pressure ; complete the diagram with hyperbola from point of admission. Compute the work (I. H. P.) from this new diagram, Draw conclusions from the form of card (see Article 409). 6. Compute the steam-consumption per stroke and per I. H. P. at cut-off and at end of stroke from the diagram (see Article 406). Compare this with the actual amount as deter- mined by the test. 7. From the weight of dry steam as shown by the indicator- diagram, and the actual weight as determined by the amount of condensed steam, determine the quality at cut-off and re- lease. 8. Make report of test on the following form: REPORT OF TEST ON ENGINE. Date Duration of test rain> Revolutions per min Steam used per min '" Sl Barometer m. 528 EXPERIMENTAL ENGINEERING. [ 423. Crank End. CU. ft. Head End. cu. ft. ent of P D ) .... >ff Ibs. Ibs. it (( l( ressure. . . ft K Piston -displacement Clearance (per c Engine constant Cut-off (per cent Release (per cen Compression (p Pressure at cut-off Pressure at release Pressure at compre Mean effective pres Revolutions per minute Horse-power C. E. ; H.E Total. Per S C. E. Lroke. H.E. Per Revo- lution. Per I.H.P. mpression. . . .Ibs. Weight of steam at cut-off. Weight of steam at release. . Weight of steam during com] Re-evaporation per H. P. per hour. Weight of water per revolution, actual " W T eight of mixture in cylinder per revolution " Per cent of mixture accounted for as steam at cut-off Per cent of mixture accounted for as steam at release Weight of water per H. P. per hour, actual Ibs. Weight of water per H. P. per hour, by indicator. . , " Signed 423. Valve-setting. This exercise will consist, first, in obtaining dimensions of ports and valves, and in drawing the valve-diagram corresponding to a given lead and angular ad- vance, and setting the valve by measurement with a lead cor- responding to that shown on the diagram. The valve-diagram may be drawn by Zeuner's * or Bilgram's method, as may be convenient ;f from the valve-diagram draw .the probable in- dicator-diagram and compute its area, and from that figure the indicated horse-power.^; * See Valve-gears, by Halsey. D. Van Nostrand Co., N. Y. f Valve-gears, by Peabody. J. Wiley & Sons, N. Y. \ Valve-gears, by Spangler. J. Wiley & Sons, N. Y. 423-] METHODS OF TESTING THE STEAM-ENGINE. 529 The method of drawing the indicator-diagram by projection from the valve-diagram is well shown in Fig. 225, from Thurs ton's Manual of the Steam-engine. The steam-pressure and back-pressure lines being assumed, the various events as shown on the valve-diagram are projected upon these lines, and the indicator-diagram completed as shown. Secondly, in attaching the indicators and taking diagrams lease. Indicator Diagram ' Exhaust FIG. 225. INDICATOR-DIAGRAM CONSTRUCTED FROM VALVE-DIAGRAM. from which the error in the position of the valve is determined. Its position is corrected as required, to equalize the indicator- diagrams taken from each end of the cylinder. The special directions are as follows: Apparatus. Scale, dividers, and trammel-point, the latter consisting of a rod the pointed end of which can be set on a mark on the floor and which carries a marking point at the other end. i. Measure dimensions of valves and ports, throw of ec- centric, and other dimensions called for by engine-log. 53 EXPERIMENTAL ENGINEERING. [ 4 2 3- 2. From these data, with a definite lead assumed, draw valve-diagram, and note position of piston for cut-off, release, compression, and admission. 3. Set the valve to the assumed lead, and with angular ad- vance as indicated by the valve-diagram. Turn the engine over and see that the lead is the same at both ends of the pis- ton. This requires the engine to be set on its centre ; this is done by bringing the piston to the extreme end of the stroke at either cylinder-end, so that the piston- and connecting-rods form one straight line. As the motion of the piston is very slow near the end of the stroke, this position is determined most accurately as follows : Mark a coincident line on cross- head and guides corresponding to the position of the crank when at an angle of about 20 measured from its horizontal position ; then, from a fixed point on the floor, swing the trammel-point as a radius, and mark a line on the circumference of the fly-wheel ; turn the engine over until the marks again coincide with the piston on the other side of the centre and make a second mark on the fly-wheel with the trammel-point; bisect the distance on the wheel between these marks and ob- tain a third line ; turn the wheel until this line is shown by the trammel to be at the same distance from the reference-point, on the floor, as the other marks: the engine will then be on its centre. Move the valve the proper amount to make its position correspond with that shown on the diagram. In set- ting the valve remember that to change angular advance, the eccentric must be rotated on the shaft ; and to equalize events for both ends of cylinder, the valve must be moved on the stem. These adjustments must be made together, as they are to some extent mutually dependent. 4. From the valve-diagram draw an ideal indicator-diagram as explained, assuming initial steam-pressure to be 100 pounds per square inch, absolute back pressure 5 pounds absolute, and that expansion and compression curves are true hyperbolae. Calculate its area by formula. Area = PV(i + \og e r) - P F (i + log e r'), 4 2 5] METHODS OF TESTING THE STEAM-ENGINE. 531 in which V ~ volume at cut-off, and P corresponding pres- sure ; F = clearance volume, and P 9 = clearance pressure; r = number of expansions, and r' = number of compressions. 5. Compute the horse-power of the diagram so drawn, and compare with that shown by the diagram taken. 424. Friction-test. For this test the engine should be fitted with a Prony brake (see Article 178, page 216), to absorb and measure the power developed. Indicator-diagrams are to be taken and the indicated horse-power computed (see Article 402, page 494). The indicated horse-power being the work done by the steam on the piston of the engine, the dyna- mometer horse-power, that delivered by the engine, the dif- ference will be the power absorbed by the engine in friction, or the friction horse-power. It is customary to reduce this amount to equivalent mean pressure acting on the piston by dividing by product of area of piston in square inches and speed in feet per minute. In making the test for friction of the engine the loads on the brake-arm should be varied, with the speed uniform, or the load on the brake-arm should be constant with varied speed, noting in each case the effect on the frictional work. It has been shown by an extended series of experiments * that the friction of engines is practically constant regardless of the work performed, and that the work shown by the indicator-diagram, when the engine is running light or not attached to machinery, is practically equal to the engine-friction in case the speed is maintained uniform. In the case of variation in speed the friction work increases nearly in proportion to increase of speed. Detailed directions for this test are not considered neces- sary. 425. Simple Efficiency-test Engines are frequently sold on a guarantee as to coal or water consumption per in- dicated horse-power (I. H. P.), or in some instances per dyna- mometer horse-power (D. H. P.); in such a case a test is to be made showing the I. H. P. or the D. H. P. as may be required, and the water and coal consumed. *See Transactions Am. Soc. Mech. Engineers, Vol. VIII., page 86. 532 EXPERIMENTAL ENGINEERING. [ 426. The I. H. P. is to be obtained as already explained in Article 402 ; the D. H. P. by readings from a Prony brake, Article 178. The coal-consumption is to be obtained by a boiler-test, Article 375 ; the total water consumed, by the feed water used in the boiler-test, corrected for leaks and quality ; or by condensing the steam in a surface condenser, Article 417. The quality of the steam should be taken near the engine, as explained in Article 336, page 400. The principal quantities to be observed are quantities required for a boiler-test, quality of steam near engine, number of revolutions of engine per minute, and weight of feed-water or weight of condensed steam. These observations should be taken regularly and simultaneously once in ten or fifteen minutes, and at the same instant an in- dicator-diagram should be taken. From these data are com- puted the quantities required. 426. The Calorimetric Method of Engine-testing. Hirris Analysis. The calorimetric method of testing engines as developed from Hirn's theory by Professor V. Dwelshauvers- Dery of Liege enables the experimenter to determine the amount of heat lost and restored and that transformed into work in the passage of the steam through the cylinder.* The principle on which the method is founded is as follows: The amount of heat supplied the engine is determined by measuring the pressure, quality, and weight of the steam ; that removed from the engine is obtained by measuring the heat in the condensed steam and that given to the condensing water. The amount of heat remaining in the cylinder per pound of steam at any point after cut-off can be calculated from the data obtained from the indicator-diagram ; this multiplied by the known weight gives the total heat. The heat supplied to the engine added to that already existing in the clearance-spaces gives the total amount of heat available ; if from this sum there be taken the heat existing at cut-off and the heat equivalent of the work done during admission, the difference will be the loss during admission, due * See Table Properiies of Steam, V. Dvvelshauvers-Dery, Trans. Am. Soc. M. E., Vol. XI. 426.] METHODS OF TESTING THE STEAM-ENGINE. 533 principally to cylinder-condensation. The difference between the heat in the cylinder at cut-off and that at release after de- ducting the work equivalent is that lost or restored during expansion. This method applied to all the events of the stroke, and at as many places as required, gives full informa- tion of the transfer of heat to and from the metal. In the fundamental equations of this analysis which follow, the following symbols are used : Quantity. Symbol. Quantity. Symbol. Heat admitted per stroke. . . . Weight of steam per stroke. . . Absolute pressure of entering steam, per sq. inch Temperature, degrees Fahr. Heat of the liquid Internal latent heat Total latent heat Quality of the steam Degree of superheat Per cent of moisture Specific heat of steam of con- stant pressure Q M P t P r x D I x Heat equivalent of energy of steam in the cylinder at any instant Joule's equivalent Reciprocal of Joule's equiva- lent Weight of I cu. foot of steam. Vol. of i Ib. of steam, cu. ft. . Volume of cylinder to any point under consideration moved through by the piston, cu. ft Volume of clearance, cu. ft. . . External work in foot-pounds. Vol. of i Ib. of water in cu. ft V Vc W a The value of the quantity at any point under discussion is denoted by the following subscripts : clearance,*:; beginning of admission, o; cut-off, I ; release, 2; beginning of compression, 3- The equations are as follows : Heat in the Entering Steam II the steam is moist, Q=M(q+xr); . . . .. (0 if the steam is superheated D degrees, Q = M(q+r+c p D) (2) 534 EXPERIMENTAL ENGINEERING. [ 426. Heat in the Cylinder. Since the steam in this case is in- variably moist, we have the following equations : In the clearance spaces, h c = M^q c -f- x c p c ) ; ... (3) At admission, /* = M G (q, + * p ) ; . . (4) At cut-off, h, = (M + M )(^ + * lPl ) ; . (5) At release, // = (M + M u )(g, + ^ a p a ) ; . (6j At compression, _ Jfc, =_(M.+.M 9 )(g 9 + x,p^). . _(;) 'The external work is to be determined from the indicator- diagram. Let the heat equivalent of this work be represented as follows : During admission, AW a \ . . < . . . . (8) During expansion, AW b \ . -. - i -v ' V \; - . (9) During exhaust, AW C \ . /-.-.- . . . . (10) During compression, AW d . . . . . . .'.V. .-. (11) The volume in cubic feet, F, of a given weight of steam, M, can always be expressed by the formula (12) in which u equal the excess of volume of one pound of steam over that of one pound of water ; u v cr. Substituting the value of u in the above equation, (13) As cr is a very small quantity, (i x}cr can be safely dropped as less than the errors of observation, and in all prac- tical applications the formula used is V Mxv. ". ...... (141 426.] METHODS OF TESTING THE STEAM-ENGINE. 535 In the exact equation (13) or the approximate equation (14), if the pressure, weight, and volume of steam are known, its specific volume, z>, can be found, and x may be computed. At any point in the stroke after the steam-valve is closed, the volume and pressure of steam in the cylinder can be determined from the indicator-diagram if the dimensions of the engine and its clearance are known. If the weight of steam used is known from an engine-test, there can be determined from the indicator-diagram both the quality and amount of heat in the cylinder at any point, with the single exception of the steam remaining in the clearance spaces. Thus let V c equal volume of clearance; V Q -f- V c , volume at admission, usually equal to V c ; V^-\-V c , volume at cut-off ; F a + V c , at release ; F 3 + V c , at compression ; M, the weight of steam used; M , the weight of steam caught and retained in the clearance spaces. Then, by method used in equation (12), (15) 1 4-)l >' 07) V c = (M + M)(x,u, + .... (21) H^x.pM; ... ., . ..; ,'i . . (22) and in equation (5), Jf^fUM. + M), . . . , V".'' v . ."'(23) H,' = ( XlPl )(M a -\-M). . . ,-. . , . (24) From equation (17), M. + M = L* = -%y|i * %Z. neariy. (25) *i, + 0-, ^^+07(1-^) w By substituting in (24), which form is used in the computations that follow. The analysis determines the loss of heat during a given period, by finding the difference between the heat in the cylin- der at the beginning of the period and the sum of that utilized in work during the period and that remaining at the end of the period. The following directions and example should make the metnod clearly understood. 4 2 7-] METHODS OF TESTING THE STEAM-ENGINE. 537 427. Directions for Engine-testing by Hirn's Analysis. Directions. f. Make a complete engine-test with a constant load, weigh the condensing water, and measure its temperature before and after condensing the steam. Obtain the quality of the entering steam either in the steam-pipe or steam-chest ; li convenient, make calorimetric determinations of the quality c 538 EXPERIMENTAL ENGINEERING. [ 427. the steam in the exhaust, which may be used as a check on the results, but which is necessary in case the exhaust steam is not condensed. 2. Calibrate all the instruments used, and correct all obser- vations where required. 3. From the average quantities on the log, corrected as shown by the calibration, fill out form I, of data and results. The steam and condensing water used per revolution to be di- vided between the forward and backward strokes of the piston in proportion to the M. E. P. of these respective strokes, as shown on the log. 4. Draw on each diagram as explained lines corresponding to zero volume and to zero pressure, and divide the diagrams as shown in Fig. 226 into sections, by drawing lines to points of admission W, cut-off en, release Oe, and compression od. Measure for each diagram the percentages of cut-off, release, and compression, calling the original length of the diagram without clearance 100 per cent. 5. Measure the absolute pressure from each card and enter the averages in blank form No II, using subscripts as follows: o, admission ; I, cut-off ; 2, release ; 3, compression ; c, clearance. Take from a steam-table the heat of liquid, internal latent heat, total latent heat, total heat, and specific volume, corre- sponding to each of the above pressures. 6. Compute the volumes in cubic feet for clearance, total volumes, including clearance, at admission, cut-off, release, and compression, and place the average results in the proper columns. 7. Compute the area corresponding to each period into which the diagram is divided and find the mean pressure for that period. Also find the work done in each period, expressed in foot-pounds and also in B. T. U. (It is to be noted that the work done during the return stroke is negative.) Enter the average of these results in the proper place, noting the use of the subscripts a, b, c, and d. 8. Calculate the heat-losses as indicated on Form III, which is an account of the heat used during 100 strokes of the engine. 42/.] METHODS OF TESTING THE STEAM-ENGINE. 539 The weight of steam, M, in pounds is 100 times the amount used for one stroke as given on Form I. The weight of steam in clearance is to be calculated for admission, pressure, and volume, and with x equal i>oo. M t - to be calculated in the same manner. Calculate from known weights. And temperatures the heat ex- hausted from the engine in the condensed steam K' and in the condensing water K. Calculate by the formulae, as explained, the heat supplied the engine, and the sensible and internal heat, at each event in the stroke of the engine;' 9. Calculate the cylinder-loss at admission as the difference between that supplied added to that already in the clearance, and that remaining^ at ..cut-off. .added to that used in work. If the heat is flowing from the metal, the sign will be negative, otherwise positive. 10. Perform the same operation for each period of the engine; the difference between the heat "at the beginning of each period and that at the end, taking into account the work done, is the loss. 11. Take the algebraic sum of these losses and of the heat equivalent of the external work, and if no error-has been made in the calculations, this sum, which is the total transformation, will equal the difference between the heat supplied and that exhausted. That is,, using the symbols of the analysis, D = D' It is also evident that this quantity is the loss by radiation. The importance of this check on the accuracy of the com- putations should not be overlooked. If no errors of computa- tion are made, in each case the value of D will equal that of D f . 12. Make the remaining calculations as on Form IV; these give the quality which the. steam must have at various portions of the stroke to correspond with the foregoing calculations. The quality is calculated from the volume remaining in the cylinder. Compute 'the' various efficiencies. Note that the heat lost d unrig admission is in some respects a measure of the initial- cylinder-condensation. The following forms are given partially filled out with the results of a test made by application of Hirn's analysis. 540 EXPERIMENTAL ENGINEERING. [ 428- 428. Forms for Kirn's Analysis. SuudS JO 3[BOS ^ : ON CO & 'd 'H 'a ^ ^ t PC pBoq -> tB;o X - d -H 'I CN > c 'd'H "I on 5 u 'd '3 'IV w K-* * a 'd'H 'I x E 'd '3 'IM s 1 j ! * S J "S cr w j w 2 ^BM-uopDafai .s ^ .s K 06 ^ J3) BM- P33J I -' jsneqxg o c i S * 2 1 J B w j t5 s J3P u.,X D c on u T: E ' H .' <5 o | 1 "rt IsgqD-uiBais .^^ v^ ^ u H U 9dld UIH31S ". > & W o *J o D J91'BM.-93jEqDSIQ *N B f j : C2 C c/: i c. 6 J35BAV-UOI}D9fui 1 1 1 ; 1 1 j >" v H J3 ,HM- P 99J I c -5 'I- ' S . 1 ft! UB9JS p3SU3pUO3 } ? - O. c U .5 ^ _A '. > . S * "e ~ ci w H < uiooj-3urSug S 2 ! " '5, b " & *C > O ( jiy i^uJ9;xg E E t E "i | < J U u^uio^g <9 rt rt c a3 rt O. C Q Jj Q H J J < Sc A 'J9SU9pUO^) . . . u "2 c 'jsn^qxg QL ' ^ 5K o z -5> < ^ 4 ?S3 qD-ui^:s -r - t3 - ; u 1 a '9dld-UJ'B9}S . ^ "5 C *-] fi M31FOH . JD - "S -~ c o" ^ I ig J01BOIpUI-p99dS C . " 1 g 1 5 s? * ino3 snonuijuo3 S J E ~ <-> >->%( OOJ.JL C rt u _ : ^ E ^qmntf J 2 .2 U ff C Jj 428.] METHODS OF TESTING THE STEAM-ENGINE. 541 FORM No. I. APPLICATION OF HIRN'S ANALYSIS TO SIMPLE CONDENSING ENGINE. DATA AND RESULTS. Test of steam-engine made by at Cornell University, Kind of engine, slide-valve throttling. Diameter cylinder. . . . 6.06 inches. Length stroke 8 inches. Diameter piston-rod. . i|f " Volume cylinder .crank end, o. 12921 cu. ft. ; head end, o. 13354 cu. ft. Volume clearance, cubic foot, head ,', 0.01744 Clearance in per cent of stroke 13.06 Volume clearance, cubic foot, crank 0.01616 Clearance in per cent of stroke 12.51 Boiler-pressure by gauge 69.4. Barometer 29.276 Boiler pressure absolute, pounds 83.7 Boiling temperature, atmospheric pressure, deg. F 210.7 Revolutions per hour 11898 Steam used during run, pounds 716.424 Quality of steam in steam-pipe , 0.99 Quality of steam in steam-chest 0.9941 Quality of steam in compression i.ooi Quality of steam in exhaust 0.9021 Weight of condensed steam per hour 259.92 Pounds of wet steam* per stroke head, 0.0109707; crank, 0.0109383 Temperatures condensed steam 103.47 deg. F. Temperatures condensing water cold, 42.758 deg. F.; hot, 92.219 Pounds of condensing water, per hour 5044.878 " ' " " " revolution 0.42429 " " " " " stroke-head 0.212016 " " " " " crank 0.212274 SYMBOLS. To denote different portions of the stroke, the following subscripts are used- Admission, a; expansion, b; exhaust, c; compression, d. To denote different events of the stroke, the following sub-numbers are used : Cut-off, i; release, 2; compression, beginning of, 3; admission, .beginning of, o; in exhaust, 5. Quality of steam denoted by X. Cut-off, crank end, per cent of stroke. .. 20.544. Release, crank end. . 93.958 Cut-off, head end, per cent of stroke... . 18.963. Release, head end. . . 94.97'! Compression, crank end, per cent of stroke 52.341 Compression, head end, per cent of stroke 39-77O Pounds of steam per I. H. P 39-35' Pounds of steam per brake H. P 55-3M I. H. P.- Head. 3.3152. Crank 3-3O54- Total 6.6206 Brake horse-power 4'? ] * Wet steam is the steam uncorrected for calorimetric determinations. 542 EXPERIMENTA L ENGINEERING. FORM No. II. [ 428 ABSOLUTE PRESSURES FROM INDICATOR-DIAGRAMS AND CORRESPONDING PROPERTIES OF SATURATED STEAM. Cut-off. Release. Beginning Symbols. Com- pression. Of Ad- mission. Ran- kine. Clau- sius. Subscripts used . ..... i 2 3 o P s I L H C P q p r A Absolute pressure. . j Q^m^ , ,. . , ( Head Heat of liquid \ Crank Internal latent heat. -J c e a a nk Latent-heat evapo- j Head ration ( Crank Totalheat \ Crank Vol.,lb.cu.f t ....te k ^4->i r c +K ^C+^3 Fo+F c Volumes crank cu ft ( . MEAN PRESSURES AND HEAT EQUIVALENTS OF EXTERNAL WORK. 1 tfead End. < >ank End. 1 *U % Mean Externa \ Work. Mean Externa 1 Work. 1 Foot-lbs. B. T. U. Pressures. Foot-lbs. B. T. U. Symbols MP W A W* MP W A W* Expansion . . fi Exhaust f Compression d Total * A = 7 { F . V = volume in clearance-spates. 428.] METHODS OF TESTING THE STEAM-ENGINE. 543 rt ?? i. ^".C'T3-' a 'O *O 3 3 u w bXfcC'C-j-, ~ 1.1 j J 1 8;?.| SSSSU- 2 . *> ? 1 = - liirfiJ 1 1 11 IlMv"! ll^liti 1 ill If I J...1,, '~j- llllllll 11 11 II II =^ 544 EX PERI MEN TA L ENGINEERING. o vo vo y?^s!E?- N 00 O OO 10 M 00 c S3 OVtnlO t- W O WNN O 10 VO t^ ON - >H N M lOVOMt^OlOOO U 1 ^ ro s ^ si vf 1 co = ^8 2 - oo 1 (>N lO ' N O C) O M j>iO VO Cv O O\ t- M N N .0 vo' - r; j ^ jj. s * 1 "3 V? k o 1- Q b 5 I'sT tf t^? T VO "tl-h J + i JST5.^ (-vrs ^ OJ -5 <^j c^ ^ 1^" is 1 cj -4- "^ ^^ ^^ ^^ ** , Q g g -4? , 1 r f ^4^ 3kftqi!Uf jf 1 ^ H - 4- ^ if C ' A < *. ^ [^ ^ V) i ' : 1 5 i o I ill. I ! I 1 1 1 s 53 S 8 "S S fl 1 1 -_i >^ *j *-* e ( S3 rt u rt d rt - 2 -s9--5 as a s sa.sSS S3 * ' 1 1 i i > 111 ! S 3 J 1 1 ' 1 1 ? . Is^l r 1 8 1 2 I -S g S "0*0 o *o o*^'5). a; >,>, > >,>v>,0W > T-j -^ >, jg ^ s s s 2 u | | 1313 rt IS'rt'rt^rtrt 33 3 3 SS^^W ac a o aaKKs; : 2 z o' o g g -g rt rS rt 'S 'S u i tS y ifi C B BftJoir" < W [ 423. S i 6 1w I 430-] METHODS OF TESTING THE STEAM-ENGINE. $45 429. Hirn's Analysis applied to Non-condensing En- gines. In this case : I. Determine the weight of water used by weighing that supplied the boiler, taking precautions to prevent loss of steam between the engine and the boiler by leaks. Apply the calorimeter and ascertain the quality near the engine. The heat in one pound of steam above 32 Fahr. will be represented by the formula xr + q, as previously explained. This quantity multiplied by the weight, M, is the heat supplied. M may be taken for i or for 100 strokes, as convenient. 2. Determine the quality of the exhaust-steam by attaching a calorimeter in the exhaust-pipe, close to the engine. The heat discharged by one pound will be, as explained in Article 311, x e r e -j- q e \ in which the symbols denote quantities taken at exhaust-steam pressure. This quantity multiplied by the weight, M, is the heat discharged, and is equal to K -\- K' in the Form III, page 543. 3. With these exceptions, the method is exactly as explained for the condensing engine, and the same forms are to be used. In obtaining the quality of the exhaust-steam, a separating calorimeter (see page 399) with two chambers arranged in series can be used with success. 430. Application of Hirn's Analysis to Compound Engines. Compound engines are usually run condensing, and the special directions are for that case ; but in case the engine is run non-condensing the method of Article 429 can be applied. Directions. With calorimeter between the cylinders : 1. Attach a calorimeter in the exhaust of the high-pressure cylinder, and determine the heat exhausted from the high- pressure cylinder as explained for non-condensing engines. Treat the high pressure cylinder as a simple non-condensing engine, as explained in Article 429. 2. Determine by the calorimeter between the cylinders the heat supplied to the low-pressure engine. This quantity will be the same as that exhausted from the high-pressure, corrected for steam used by the calorimeter and for radiation from the connecting pipes. EXPERIMENTAL ENGINEERING. [ 431. 3. Fill out the forms for each cylinder as a separate .engine. By using two calorimeters between cylinders the same method can be applied to a triple-expansion engine. " In case the pressure of the steam between the cylinders is 'ess than atmospheric a calorimeter can be used by attaching a special air-pump and condenser, so as to secure a flow of steam through the calorimeter. Without calorimeter between the cylinders : 1. Determine the weight of steam, M, for both cylinders from the condensed steam of the low-pressure cylinder. This will give the quantity M. 2. For the high-pressure cylinder compute the quantities as in Form III, omitting those terms containing K and K' t the heat exhausted. 3. Determine K and K' as follows: K -|- K' is evidently equal to the heat supplied the high-pressure engine, less the heat transformed into work, expressed in B. T. U.,less the loss by radiation. The total loss by radiation in the whole engine is equal to the heat supplied the first cylinder, less the work done by all the cylinders, less the heat discharged from the last one. As an approximation, divide this total radiation-loss equally between the cylinders, assuming that the lower tem- perature of the low-pressure cylinder will offset its increased size. This will give us in Form III the value of D = Q B. Compute B, substitute this value in the equation B = K -\- K' -f- A W. Compute A' -j- A! 7 and complete the analysis for the high-pressure cylinder. 4. For the low-pressure cylinder, determine the entering heat as that discharged from the high-pressure cylinder, K-\-K ', plus the assumed radiation as given above. Make a complete analysis for each cylinder as explained for a simple engine. 431. Hirn's Analysis applied to a Triple-expansion En- gine. When the quality of the steam between the cylinders can be determined, treat the engine as three separate engines as explained. 43 1 -] METHODS OF TESTING THE STEAM-ENGINE. 547 When the quality cannot be determined, treat the case as explained for a compound engine, as follows : 1. Find the entire loss as equal to the difference between that supplied to the first cylinder and that discharged from the last, increased by the work done in the whole system reduced to thermal units. Divide this by the number of cylinders to find the assumed radiation-loss from each. 2. Take the cylinders in series, and assume the discharged heat to equal the heat supplied, diminished by that transformed into external work, and make a separate analysis for each cylinder as explained for a simple engine. The following is an application of Hirn's analysis to a triple-expansion engine by Prof. C. H. Peabody at the Massa- chusetts Institute of Technology. The main dimensions of the engine are as follows : Diameter of the high-pressure cylinder .............. 9 inches. Diameter of the intermediate cylinder ........... ... 16 Diameter of the low-pressure cylinder .............. 24 Diameter of the piston-rods ..... . ................. 2& Stroke ......................................... 3<> Clearance in per cent of the piston displacements : High-pressure cylinder, headend, 8.83; crank end, 9.76 Intermediate " 10.4 10.9 Low-pressure " 11.25 8.84 The following table gives the data and results of a test with Hirn's analysis, made by the graduating class: Duration of test, minutes . , ..................................... Total number of revolutions ............................. ...... . 00. Revolutions per minute ..... .......... Steam-consumption during test, pounds: Passing through cylinders .................................. Condensation in high-pressure jacket ................... " in first receiver jacket ........................ in intermediate jacket .......................... " in second receiver jacket ....................... " 'in low-pressure jacket ............... ......... .............. 1538 Total ---- .................... 548 EXPERIMENTAL ENGINEERING. [43!- Condensing water for test, pounds 22847 Priming, by calorimeter , 0,013 Temperatures, Fahrenheit: Condensed steam 95.4 Condensing water, cold 41.9 Condensing water, hot 96.1 Pressure of the atmosphere, by the barometer, Ibs. per sq. in 14.8 Boiler-pressure, Ibs. per sq. inch, absolute 155-3 Vacuum in condenser, inches of mercury , 25.0 Events of the stroke: High-pressure cylinder Cut-off, crank end o. 192 " headend 0.215 Release, both ends i .00 Compression, crank end 0.05 ' ' head end , , 0.05 Intermediate cylinder Cut-off, both ends. o. 29 Release, both ends i.oo Compression, crank end 0.03 head end 0.04 Low-pressure cylinder Cut-off, crank end 0.38 " headend 0.39 Release, both ends , i.oo Quality of the steam in the cylinder (at admission and at compression the steam was assumed to be dry and saturated:) High-pressure cylinder At cut-off oc\ 0.785 At release x 2 0.899 Intermediate cylinder At cut-off xi 0.899 At release x-t 0.994 Low-pressure cylinder At cut-off , xi 0.978 Interchanges of heat between the steam and the walls of the cylinders, in B. T. U. Quantities affected by the positive sign are absorbed by the cylinder-walls; quantities affected by the negative sign are yielded by the walls. High-pressure cylinder Brought in by steam Q 132.92 During admission Q a 23.54 During expansion QJ, 18.69 During exhaust Q c 8. 36 43 1 -] METHODS OF TESTING THE STEAM-ENGINE. 549 During compression Q d o ,- Supplied by jacket QJ 4.56 Lost by radiation Q e l ^ o First intermediate receiver Supplied by jacket QJR 4.92 Lost by radiation Q eR o 5 g Intermediate cylinder Brought in by steam (X 131.89 During admission Q a ' 13.62 During expansion Q b ' 18.65 During exhaust * ... Q c ' 0.22 During compression Q d ' 0.44 Supplied by jacket QJ' 6.82 Lost by radiation Q e ' 2.45 Second intermediate receiver Supplied by jacket QJR 4.20 Lost by radiation Q e R 1.20 Low-pressure cylinder Brought in by steam , Q' 132.14 During admission Q t " 5.85 During expansion Qt>" 9.51 During exhaust Qc" 2.53 During compression Qd" o.oo Supplied by jacket Q" 7-oS Lost by radiation Q' 4-34 Total loss by radiation : By preliminary test ^Qe 10.07 By equation (49) JI - 68 Absolute pressures in the cylinder, Ibs. per sq. inch : High-pressure cylinder Cut-off, crank end *45'9 headend..... *43-2 Release, crank end 4''3 " headend 4'-5 Compression, crank end 43-7 headend 48-7 Admission, crank end " headend 75-3 Intermediate cylinder Cut-off, crank end " headend Release, crank end headend Compression, crank end headend J 7-9 550 EXPERIMEN TA L ENGINEERING. Admission, crank end 20.4 " headend 21.1 Low-pressure cylinder Cut-off, crank end 12. i " headend 12.0 Release, crank end 5.6 " headend 5.4 Compression and admission, crank end 3.7 " " " headend 4.3 Heat equivalents of external work, B. T. U., from areas on indicator- diagram to line of absolute vacuum : High-pressure cylinder During admission, A W a , crank end 5.71 headend 6.61 During expansion, A Wb , crank end 10.65 " " headend 10.81 During exhaust, A W c , crank end 7.73 " " headend 8.08 During compression, A Wd , crank end 0.48 " " headend 0.62 Intermediate cylinder During admission, A W a , crank end 7. 58 " " headend 7.43 During expansion, A Wb , crank end 9. 54 " " headend 9.22 During exhaust, A W c , crank end 9.27 " headend 9.27 During compression, A Wd , crank end 0.39 " " headend 0.60 Low-pressure cylinder During admission, A W a , crank end 7.75 " " headend 7.99 During expansion, A Wb, crank end 6.83 " " headend 6.87 During exhaust, A W c , crank end 5.08 " " headend 5.08 During compression, A Wd, crank end o.oo " " headend o.oo Power and economy : Heat equivalents of work per stroke High-pressure cylinder A W 8.44 Intermediate cylinder A W' 7. 12 Low-pressure cylinder .A W" 9.64 Total 25.20 Total heat furnished by jackets .... 27.58 43 I -1 METHODS OF TESTING THE STEAM-ENGINE. 551 Distribution of work : High-pressure cylinder i.oo Intermediate cylinder 0.84 Low-pressure cylinder 1.14 Horse-power 104.9 Steam per horse-power per hour 14.65 B. T. U. per horse-power per minute 258.3 CHAPTER XIX. METHODS OF TESTING ENGINES OF SPECIAL CONSTRUCTION. 432. Special Methods of Engine-testing. Engines em- ployed for certain specific purposes, as for pumping water or for locomotive service, are constructed with peculiar features rendered necessary by the work to be accomplished. In such cases it is frequently difficult to arrange to make all the measurements in the manner prescribed for the tests of the general type of the steam-engine ; further, it is often of impor- tance that the amount and character of the work accomplished be taken into consideration. To secure results that can safely be compared, it is essential that certain methods of testing be adopted and that the results be expressed in the same form and referred to the same standards. 433. Method of Testing Steam Pumping-engines. A standard method of testing steam pumping-engtnes has been adopted by the American Society of Mechanical Engineers (see Vol. XL of the Transactions). The method is as follows : (l) TEST OF FEED-WATER TEMPERATURES. The plant is subjected to a preliminary run, under the con- ditions determined upon for the test, for a period of three hours, or such a time as is necessary to find the temperature of the feed-water (or the several temperatures, if there is more than one supply) for use in the calculation of the duty. During this test observations of the temperature are made every fifteen minutes. Frequent observations are also made of the speed, length of stroke, indication of water-pressure gauges, and other 552 432.] TESTING SPECIAL ENGINES. 553 instruments, so as to have a record of the general conditions under which this test is made. Directions for obtaining Feed-water Temperatures. When the feed-water is all supplied by one feeding instrument, the temperature to be found is that of the water in the feed-pipe near the point where it enters the boiler. If the water is fed by an injector this temperature is to be corrected for the heat added to the water by the injector, and for this purpose the temperature of the water entering and of that leaving the injector are both observed. If the water does not pass through a heater on its way to the boiler (that is, that form of heater which depends upon the rejected heat of the engine, such as that contained in the exhaust-steam either of the main cylin- ders or of the auxiliary pumps), it is sufficient, for practical purposes, to take the temperature of the water at the source of supply, whether the feeding instrument is a pump or an injector. When there are two independent sources of feed-water supply, one the main supply from the hot-well, or from some other source, and the other an auxiliary supply derived from the water condensed in the jackets of the main engine and in the live-steam reheater, if one be used, they are to be treated independently. The remarks already made apply to the first, or main, supply. The temperature of the auxiliary supply, if carried by an independent pipe either direct to the boiler or to the main feed-pipe near the boiler, is to be taken at convenient points in the independent pipe. When a separator is used in the main steam-pipe, arranged so as to discharge the entrained water back into the boiler by gravity, no account need be made of the temperature of the water thus returned. Should it discharge either into the atmosphere to waste, to the hot-well, or to the jacket-tank, its temperature is to be determined at the point where the water leaves the separator before its pressure is reduced. When a separator is used, and it drains by gravity into the jacket-tank, this tank being subjected to boiler-pressure, the 554 EXPERIMENTAL ENGINEERING. [ 43 2 * temperature of the separator-water and jacket-water are each to be taken before their entrance to the tank. Should there be any other independent supply of water, the temperature of that is also to be taken on this preliminary test. Directions for Measurement of Feed-water. As soon as the feed-water temperatures have been obtained the engine is stopped, and the necessary apparatus arranged for determin- ing the weight of the feed-water consumed, or of the various supplies of feed-water if there is more than one. In order that the main supply of feed-water may be meas- ured, it will generally be found desirable to draw it from the cold-water service-main. The best form of apparatus for weighing the water consists of two tanks, one of which rests upon a platform-scale supported by staging, wlyle the other is placed underneath. The water is drawn from the service-main into the upper tank, where it is weighed, and it is then emptied into the lower tank. The lower tank serves as a reservoir, and to this the suction-pipe of the feeding apparatus is connected. The jacket-water may be measured by using a pair of small barrels, one being filled while the other is being weighed and emptied. This water, after being measured, may be thrown away, the loss being made up by the main feed-pump. To prevent evaporation from the water, and consequent loss on account of its highly heated condition, each barrel should be partially filled with cold water previous to using it for collect- ing the jacket-water, and the weight of this water treated as tare. When the jacket-water drains back by gravity to the boiler, waste of live steam during the weighing should be prevented by providing a small vertical chamber, and conducting the water into this receptacle before its escape. A glass water- gauge is attached, so as to show the height of water inside the chamber, and this serves as a guide in regulating the discharge- valve. When the jacket-water is returned to the boiler by means of a pump, the discharge-valve should be throttled during the test, so that the pump may work against its usual pressure. 432.] TESTING SPECIAL ENGINES. 5$$ that is, the boiler-pressure as nearly as may be, a gauge being attached to the discharge-pipe for this purpose. When a separator is used and the entrained water dis- charges either to waste, to the hot well, or to the jacket-tank, the weight of this water is to be determined, the water being drawn into barrels in the manner pointed out for measuring the jacket-water. Except in the case where the separator dis- charges into the jacket-tank, the entrained water thus found is treated, in the calculations, in the same manner as moisture shown by the calorimeter-test. When it discharges into the jacket-tank, its weight is simply subtracted from the total weight of water fed, and allowance made for heat of this water lost by radiation between separator and tank. When the jackets are drained by a trap, and the condensed water goes either to waste or to the hot-well, the determination of the quantity used is not necessary to the main object of the duty trial, because the main feed-pump in such cases supplies all the feed-water. For the sake of having complete data, how- ever, it is desirable that this water be measured, whatever the use to which it is applied. Should live steam be used for reheating the steam in the intermediate receiver, it is desirable to separate this from the jacket-steam, if it drain into the same tank, and measure it independently. This, likewise, is not essential to the main object of the duty trial, though useful for purposes of in- formation. The remarks as to the manner of preventing losses of live steam and of evaporation, in the measurement of jacket-water, apply to the measurement of any other hot water under press- ure, which may be used foi feed-water. Should there be any other independent supply of water to the boiler, besides those named, its quantity is to be deter- mined independently, apparatus for all these measurements being set up during the interval between the preliminary run and the main trial, when the plant is idle. 556 EXPERIMENTAL ENGINEERING. [ 432. (2) THE MAIN DUTY-TRIAL. The duty-trial is here assumed to apply to a complete plant, embracing a test of the performance of the boiler as well as that of the engine. The test of the two will go on simultaneously after both are started, but the boiler-test will begin a short time in advance of the commencement of the o engine-test, and continue a short time after the engine-test is finished. The mode of procedure is as follows: The plant having been worked for a suitable time under normal conditions, the fire is burned down to a low point and the engine brought to rest. The fire remaining on the grate is then quickly hauled, the furnace cleaned, and the refuse with- drawn from the ash-pit. The boiler-test is now started, and this test is made in accordance with the rules for a standard method recommended by the Committee on Boiler Tests of the American Society of Mechanical Engineers. This method, briefly described, consists in starting the test with a new fire lighted with wood, the boiler having previously been heated to its normal working degree ; operating the boiler in accordance with the conditions determined upon ; weighing coal, ashes, and feed-water ; observing the draught, temperatures of feed- water and escaping gases, and such other data as may be inci- dentally desired ; determining the quantity of moisture in the coal and in the steam ; and at the close of the test hauling the fire, and deducting from the weight of coal fired whatever unburned coal is contained in the refuse withdrawn from the furnace, the quantity of water in the boiler and the steam-press- ure being the same as at the time of lighting the fire at the beginning of the test. Previous to the close of the test it is desirable that the fire should be burned down to a low point, so that the unburned coal withdrawn may be in a nearly consumed state. The tem- perature of the feed-water is observed at the point where the water leaves the engine heater, if this be used, or at the point where it enters the flue-heater, if that apparatus be employed. Where an injector is used for supplying the water, a deduction 43 2 -] TESTING SPECIAL ENGINES. 557 is to be made in either case for the increased temperature of the water derived from the steam which it consumes. As soon after the beginning of the boiler-test as practicable the engine is started and preparations are made for the begin- ning of the engine-test. The formal commencement of this test is delayed till the plant is again in normal working con- dition, which should not be over one hour after the time of lighting the fire. When the time for commencement arrives the feed-water is momentarily shut off, and the water in the lower tank is brought to a mark. Observations are then made of the number of tanks of water thus far supplied, the height of water in the gauge-glass of the boiler, the indication of the counter on the engine, and the time of day; after which the supply of feed-water is renewed, and the regular observations of the test, including the measurement of the auxiliary supplies of feed-water, are commenced. The engine-test is to continue at least ten hours. At its expiration the feed-pump is again momentarily stopped, care having been taken to have the water slightly higher than at the start, and the water in the lower tank is brought to the mark. When the water in the gauge-glass has settled to the point which it occupied at the beginning, the time of day and the indication of the counter are observed, together with the number of tanks of water thus far supplied, and the engine-test is held to be finished. The engine continues to run after this time till the fire reaches a condition for hauling, and completing the boiler-test. It is then stopped, and the final observations relating to the boiler- test are taken. The observations to be made and data obtained for the purposes of the engine-test, or duty-trial proper, embrace the weight of feed-water supplied by the main feeding apparatus, that of the water drained from the jackets, and any other water which is ordinarily supplied to the boiler, determined in the manner pointed out. They also embrace the number of hours' duration, and number of single strokes of the pump during the test ; and, in direct-acting engines, the length of the stroke, together with the indications of the gauges attached to the 558 EXPERIMENTAL ENGINEERING. [ 432* force and suction mains, and indicator-diagrams from the steam- cylinders. It is desirable that pump-diagrams also be obtained. Observations of the length of stroke, in the case of direct- acting engines, should be made every five minutes; observa- tions of the water-pressure gauges every fifteen ' minutes ; observations of the remaining instruments such as steam- gauge, vacuum-gauge, thermometer in pump-well, thermome- ter in feed-pipe ; thermometer showing temperature of engine- room, boiler-room, and outside air ; thermometer in flue, ther- mometer in steam-pipe, if the boiler has steam-heating surface, barometer, and other instruments which may be used every half-hour. Indicator-diagrams should be taken every half-hour. When the duty-trial embraces simply a test of the engine, apart from the boiler, the course of procedure will be the same as that described, excepting that the fires will not be hauled, and the special observations relating to the performance of the boiler will not be taken. Directions regarding Arrangement and Use of Instruments, and other Provisions for the Test. The gauge attached to the force-main is liable to a considerable amount of fluctuation unless the gauge-cock is nearly closed. The practice of choking the cock is objectionable. The difficulty may be satisfactorily overcome, and a nearly steady indication se- cured, with cock wide open, if a small reservoir having an air- chamber is interposed between the gauge and the force-main. By means of a gauge-glass on the side of the chamber and an air-valve, the average water-level may be adjusted to the height of the centre of the gauge, and correction for this element of variation is avoided. If not thus adjusted, the reading is to be referred to the level shown, whatever this may be. To determine the length of stroke in the case of direct act- ing engines, a scale should be securely fastened to the frame which connects the steam and water cylinders, in a position parallel to the piston-rod, and a pointer attached to the rod so as to move back and forth over the graduations on the scale. The marks on the scale, which the pointer reaches at the two 43 2 -] TESTING SPECIAL ENGINES. 559 ends of the stroke, are thus readily observed, and the distance moved over computed. If the length of the stroke can be de- termined by the use of some form of registering apparatus, such a method of measurement is preferred. The personal errors in observing the exact scale-marks, which are liable to creep in, may thereby be avoided. The form of calorimeter to be used for testing the quality of the steam is left to the decision of the person who conducts the trial. It is preferred that some form of continuous calo- rimeter be used, which acts directly on the moisture tested. If either the superheating calorimeter* or the wire-drawing f instrument be employed, the steam which it discharges is to be measured either by numerous short trials, made by condensing it in a barrel of water previously weighed, thereby obtaining the rate by which it is discharged, or by passing it through a sur- face-condenser of some simple construction, and measuring the whole quantity consumed. When neither of these instruments is at hand, and dependence must be placed upon the barrel calorimeter, scales should be used which are sensitive to a change in weight of a small fraction of a pound, and thermom- eters which may be read to tenths of a degree. The pipe which supplies the calorimeter should be thoroughly warmed and drained just previous to each test. In making the calcu- lations the specific heat of the material of the barrel or tank should be taken into account, whether this be of metal or of wood. If the steam is superheated, or if the boiler is provided with steam-heating surface, the temperature of the steam is to be taken by means of a high-grade thermometer resting in a cup holding oil or mercury, which is screwed into the steam- pipe so as to be surrounded by the current of steam. The temperature of the feed-water is preferably taken by means of a cup screwed into the feed-pipe in the same manner. Indicator-pipes and connections used for the water-cylin- * Vol. vn, p. 178, 1886, Transactions A. S. M. E. See page 386 of this volume. f Vol. xi, 1890, p. 193, Transactions A. S. M. E. See page 388 of this volume. 560 EXPERIMENTAL ENGINEERING. [ 432. ders should be of ample size, and, so far as possible, free from bends. Three-quarter-inch pipes are preferred, and the indi- cators should be attached one at each end of the cylinder. It should be remembered that indicator-springs which are correct under steam heat are erroneous when used for cold water. When such springs are used, the actual scale should be determined, if calculations are made of the indicated work done in the water-cylinders. The scale of steam-springs should be deter- mined by a comparison, under steam-pressure, with an accurate steam-gauge at the time of the trial, and that of water-springs by cold dead-weight test. The accuracy of all the gauges should be carefully verified by comparison with a reliable mercury-column. Similar veri- fication should be made of the thermometers, and if no stand- ard is at hand, they should be tested in boiling water and melting ice. To avoid errors in conducting the test, due to leakage of stop-valves either on the steam-pipes, feed-water pipes, or blow-off pipes, all these pipes not concerned in the operation of the plant under test should be disconnected. (3) LEAKAGE-TEST OF PUMP. As soon as practicable after the completion of the main trial (or at some time immediately preceding the trial) the en- gine is brought to rest, and the rate determined-at which leak- age takes place through the plunger and valves of the pump, when these are subjected to the full pressure of the force- main. The leakage*of the plunger is most satisfactorily determined by making the test with the cylinder-head removed. A wide board or plank may be temporarily bolted to the lower part of the end of the cylinder, so as to hold back the water in the manner of a dam, and an opening made in the temporary head thus provided for the reception of an overflow pipe. The plunger is blocked at some intermediate point in the stroke (or, if this position is not practicable, at the end of the stroke), and 43 2 -] TESTING SPECIAL ENGINES. $6l the water from the force-main is admitted at full pressure be. hind it. The leakage escapes through the overflow pipe, and it is collected in barrels and measured. Should the escape of the water into the engine-room be objectionable, a spout may be constructed to carry it out of the building. Where the leakage is too great to be readily meas- ured in barrels, or where other objections arise, resort may be had to weir or orifice measurement, the weir or orifice taking the place of the overflow-pipe in the wooden head. The ap- paratus may be constructed, if desired, in a somewhat rude manner, and yet be sufficiently accurate for practical require- ments. The test should be made, if possible, with the plunger in various positions. In the case, of a pump so planned that it is difficult to re- move the cylinder-head, it may be desirable to take the leakage from one of the openings which are provided for the inspection of the suction-valves, the head being allowed to remain in place. It is here assumed that there is a practical absence of valve- leakage, a condition of things which ought to be attained in all well-constructed pumps. Examination for such leakage should be made first of all, and if it occurs and it is found to be due to disordered valves, it should be remedied before making the plunger-test. Leakage of the discharge-valves will be shown by water passing down into the empty cylinder at either end when they are under pressure. Leakage of the suction-valves will be shown by the disappearance of water which covers them. If valve-leakage is found which cannot be remedied, the quantity of water thus lost should also be tested. The deter- mination of the quantity which leaks through the suction-valves, where there is no gate in the suction-pipe, must be made by indirect means. One method is to measure the amount of water required to maintain a certain pressure in the pump- cylinder when this is introduced through a pipe temporarily erected, no water being allowed to enter through the discharge- valves of the pump. 562 EXPERIMENTAL ENGINEERING. [432. The exact methods to be followed in any particular case, in determining leakage, must be left to the judgment and ingenu- ity of the person conducting the test. (4) TABLE OF DATA AND RESULTS. In order that uniformity may be secured, it is suggested that the data and results, worked out in accordance with the standard method, be tabulated in the manner indicated in the following scheme : DUTY-TRIAL OF ENGINE. Dimensions. 1. Number of steam-cylinders 2. Diameter of steam-cylinders ins. 3. Diameter of piston-rods of steam-cylinders ins. 4. Nominal stroke of steam-pistons ft. 5. Number of water-plungers. r * 6. Diameter of plungers ins. 7. Diameter of piston-rods of water-cylinders ins. 8. Nominal stroke of plungers ft. 9. Net area of plungers sq. ins. 10. Net area of steam-pistons. sq. ins. 11. Average length of stroke of steam-pistons during trial ft. 12. Average length of stroke of plungers during trial '. ft. (Give also complete description of plant.) Temperatures. 13. Temperature of water in pump- well degs. 14. Temperature of water supplied to boiler by main feed-pump, degs. 15. Temperature of water supplied to boiler from various other sources degs. feed-water. 160 Weight of water supplied to boiler by main feed-pump Ibs. 17. Weight of water supplied to boiler from various other sources. Ibs. 18. Total weight of feed-water supplied from all sources. Ibs. Pressures. 19. Boiler-pressure indicated by gauge Ibs. 20. Pressure indicated by gauge on force-main Ibs. 21. Vacuum indicated by gauge on suction-main ins. 22. Pressure corresponding to vacuum given in preceding line Ibs. 23. Vertical distance between the centres of the two gauges ins. 24. Pressure equivalent to distance between the two gauges Ibs* 43 2 TESTING SPECIAL ENGINES. 563 Miscellaneous Data. 25. Duration of trial hrs 26. Total number of single strokes during trial 27. Percentage of moisture in steam supplied to engine, or num- ber of degrees of superheating ordeg. 28. Total leakage of pump during trial, determined from results of leakage-test i bs 29. Mean effective pressure, measured from diagrams taken from steam-cylinders M p Principal Results. 30. Duty ft .. lbs . 31. Percentage of leakage % 32. Capacity gals> 33. Percentage of total frictions f Additional Results* 34. Number of double strokes of steam-piston per minute. ....... 35. Indicated horse-power developed by the various steam- cylinders I. H. P. 36. Feed-water consumed by the plant per hour Ibs. 37. Feed-water consumed by the plant per indicated horse-power per hour, corrected for moisture in steam Ibs. 38. Number of heat-units consumed per indicated horse-power per hour B. T.U. 39. Number of heat-units consumed per indicated horse-power per minute B. T.U. 40. Steam accounted for by indicator at cut-off and release in the various steam-cylinders Ibs. 41. Proportion which steam accounted for by indicator bears to the feed-water consumption Sample Diagrams taken from Steam-cylinders. [Also, if possible, full measurements of the diagrams, embracing pressures at the initial point, cut-off, release, and compression ; also back-pressure, and the proportions of the stroke completed at the various points noted.] 42. Number of double strokes of pump per minute 43. Mean effective pressure, measured from pump-diagrams M. E.P. 44. Indicated horse-power exerted in pump-cylinders I. H. P. * These are not necessary to the main object, but it is desirable to give them. 564 EXPERIMENTAL ENGINEERING. [432. Sample Diagrams taken from Pump-cylinders. DATA AND RESULTS OF BOILER-TEST. [iN ACCORDANCE WITH THE SCHEME RECOMMENDED BY THE BOILER-TEST COMMITTEE OF THE SOCIETY.] 1. Date of trial 2. Duration of trial hrs. Dimensions and Proportions. 3. Grate-surface wide long Area sq.ft. 4. Water-heating surface sq. ft. 5. Superheating-surface sq.ft. 6. Ratio of water-heating surface to grate-surface (Give also complete description of boilers.) Average Pressures. i 7. Steam-pressure in boiler by gauge Ibs. 8. Atmospheric pressure by barometer , Ibs. 9. Force of draught in inches of water ins. Average Temperatures. 10. Of steam degs. 1 1. Of escaping gases degs. 12. Of feed-water Fuel. 13. Total amount of coal consumed* Ibs. 14. Moisture in coal . . % 15. Dry coal consumed Ibs. 16. Total refuse (dry) Ibs. 17. Total combustible (dry weight of coal, item 15, less refuse, item 1 6) Ibs. 18. Dry coal consumed per hour Ibs. Results of Calorimetric Test. 19. Quality of steam, dry steam being taken as unity 20. Percentage of moisture in steam % 21. Number of degrees superheated degs. * Including equivalent of wood used in lighting fire. One pound of wood equals 0.4 of a pound of coal, not including unburned coal withdrawn from fire at end of test. 432-] TESTING SPECIAL ENGINES. 565 Water. 22. Total weight of water pumped into boiler and apparently evaporated *. .. 23. Water actually evaporated corrected for quality of steam." .' ! . .' Ibs* 24. Equivalent water evaporated into dry steam from and at 212 F.f Ibs 25. Equivalent total heat derived from fuel, in British thermal . _ . U " its B.T.U. 26. Equivalent water evaporated into dry steam from and at 212 F. per hour . j bs Economic Evaporation. 27. Water actually evaporated per pound of dry coal from actual pressure and temperature l bs> 28. Equivalent water evaporated per pound of dry coal from and at 212 F | bs 29. Equivalent water evaporated per pound of combustible from and at 213 F j bs 30. Number of pounds of coal required to supply one million British thermal units l bs> Rate of Combustion. 31. Dry coal actually burned per square foot of grate-surface per hour 15s. Rate of Evaporation. 32. Water evaporated from and at 212 F. per square foot of heating-surface per hour Ibs. To determine the percentage of surface moisture in the coal a sample of the coal should be dried for a period of twenty- four hours, being subjected to a temperature of not more than 212. The quantity of unconsumed coal contained in the refuse withdrawn from the furnace and ash-pit at the end of the test may be found by sifting either the whole of the refuse, or * Corrected for inequality of water-level and of steam-pressure at beginning and end of test. TT I t Factor of evaporation = , H and h being, respectively, the total heat-units in steam of the average observed pressure, and in water of the aver- age observed temperature of feed. 566 EXPERIMENTAL ENGINEERING. [432. a sample of the same, in a screen having f-inch meshes. This, deducted from the weight of dry coal fired, gives the weight of dry coal consumed, for line 15. Results of actual trial, as illustrated by the committee, would be computed by the use of the following formulae : Foot-pounds of work done I. Duty = Total number of heat-units'consumed X I ' ooo > ooc x X i, 000,000 (foot-pounds). C X 144 2. Percentage of leakage = ^ ^ ^. X 100 (per cent). 3. Capacity = number of gallons of water discharged in 24 hours - x x x 7-45 x 2 4 " D X 144 A XL X jVX 1.24675 ^- - -^ (gallons). 4. Percentage of total friction THP J ' D X 60 X 33,ooo x r = L 1 - x or, in the usual case, where the length of the stroke and num- ber of strokes of the plunger are the same as that of the steam- piston, this last formula becomes Percentage of total frictions I I . \, M gp J X ioo(p.c.). 43 2 -] TESTING SPECIAL ENGINES. 567 In these formulae the letters refer to the following quanti- ties : A Area, in square inches, of pump-plunger or piston, corrected for area of piston-rod. (When one rod is used at one end only, the correction is one half the area of the rod. If there is more than one rod, the correction is multiplied accordingly.) P= Pressure, in pounds per square inch, indicated by the gauge on the force-main. / ~ Pressure, in pounds per square inch, corresponding to indication of the vacuum-gauge on suction- main (or pressure-gauge, if the suction-pipe is under a head). The indication of the vacuum- gauge, in inches of mercury, may be converted into pounds by dividing it by 2.035. S = Pressure, in pounds per square inch, corresponding to distance between the centres of the two gauges. The computation for this pressure is made by multiplying the distance, expressed in feet, by the weight of one cubic foot of water at the tempera- ture of the pump-well, and dividing the product by 144; or by multiplying the distance in feet by the weights of one cubic foot of water at the various temperatures. L = Average length of stroke of pump-plunger, in feet. N= Total number of single strokes of pump-plunger made during the trial. A = Area of steam-cylinder, in square inches, corrected for area of piston-rod. The quantity A , X M.E.P., in an engine having more than one cylinder, is the sum of the various quantities relating to the respective cylinders. f _ Average length of stroke of steam-piston, in feet. N s = Total number of single strokes of steam-piston during trial. M.E.P. = Average mean effective pressure, in pounds per 568 EXPERIMENTAL ENGINEERING. [ 432. square inch, measured from the indicator-diagrams taken from the steam cylinder. l.H.P. = Indicated horse-power developed by the steam- cylinder. C = Total number of cubic feet of water which leaked by the pump-plunger during the trial, estimated from the results of the leakage-test. D = Duration of trial, in hours. H = Total number of heat-units [B. T. U.] consumed by engine = weight of water supplied to boiler by main feed-pump X total heat of steam of boiler- pressurQ reckoned from temperature of main feed- water -f- weight of water supplied by jacket-pump X total heat of steam of boiler-pressure reckoned from temperature of jacket-water -f- weight of any other water supplied X total heat of steam reck- oned from its temperature of supply. The total heat of the steam is corrected for the moisture or superheat which the steam may contain. For moisture, the correction is subtracted, and is found by multiplying the latent heat of the steam by the percentage of moisture, and dividing the product by 100. For superheat, the correction is added, and is found by multiplying the number of degrees of superheating (i.e., the excess of the temperature of the steam above the normal tem- perature of saturated steam) by 0.48. No allow- ance is made for heat added to the feed-water, which is derived from any source, except the engine or some accessory of the engine. Heat added to the water by the use of a flue-heater at the boiler is not to be deducted. Should heat be abstracted from the flue by means of a steam- reheater connected with the intermediate receiver of the engine, this heat must be included in th* total quantity supplied by the boiler. The following example is one of those given by the com- 43 2 -] TESTING SPECIAL ENGINES. 569 mittee to illustrate the method of computation. The figures are not obtained from tests actually made, but they correspond in round numbers with those which were so obtained: EXAMPLE. Compound Fly-wheel Engine. High-pressure cylinder jacketed with live steam from the boiler. Low-press- ure cylinder jacketed with steam from the intermediate re- ceiver, the condensed water from which is returned to the boiler by means of a pump operated by the engine. Main steam-pipe fitted with a separator. The intermediate receiver provided with a reheater supplied with boiler-steam. Water drained from high-pressure jacket, separator, and reheater col- lected in a closed tank under boiler-pressure, and from this point fed to the boiler direct by an independent steam-pump. Jet-condenser used operated by an independent air-pump. Main supply of feed-water drawn from hot-well and fed to the boiler by donkey steam-pump, which discharges through a feed-water heater. All the steam-pumps, together with the independent air-pump, exhaust through the heater to the at- mosphere. DIMENSIONS. Diameter of high pressure steam-cylinder (one) 20 in. Diameter of low-pressure steam-cylinder (one) 40 " Diameter of plunger (one) 2 Diameter of each piston-rod 4 Stroke of steam-pistons and pump-plunger 3 ** GENERAL DATA. 1. Duration of trial (D) IO hrs - 2. Boiler-pressure indicated by gauge (barometric press- ure, 14.7 Ibs.) I2 lbs - 3. Temperature of water in pump-well o degs. 4. Temperature of water supplied to boiler by main feed- pump, leaving heater 5. Temperature of water supplied by low-pressure jacket- pump 6. Temperature of water supplied by high-pressure jacket, separator, and reheater-pump, that derived from separator being 340, and that from jackets 290 3oo 570 EXPERIMENTAL ENGINEERING. [ 432- 7. Weight of water supplied to boiler by main feed-pump 18,863 Ibs. 8. Weight of water supplied by low-pressure jacket-pump 615 " 9. Weight of water supplied by pump for high-pressure jacket, separator, and reheater-tank, of which 210 Ibs. is- derived from separator 1 ,025 " 10. Total weight of feed-water supplied from all sources 20,503 " n. Percentage of moisture in steam after leaving sepa- rator 1.5$ DATA RELATING TO WORK OF PUMP. 12. Area of plunger minus % area of piston-rod (A) 307.88 sq. in. 13. Average length of stroke (L and L s ) 3 ft. 14. Total number of single strokes during trial (./Vand N s ) 24,000 15. Pressure by gauge on force-main (P) 95 Ibs. 16. Vacuum by gauge on suction-main 7.5 in. 17. Pressure corresponding to vacuum given in preceding line (/) 3. 69 Ibs. 18. Vertical distance between centres of two gauges 10 ft. 19. Pressure equivalent to distance between two gauges (s) 4.33 Ibs, 20. Total leakage of pump during trial, determined from results of leakage-test (C) 3,078 cu. ft. 21. Number of double strokes of pump per minute 20 22. Mean effective pressure measured from pump-dia- grams 105 Ibs. 23. Indicated horse-power exerted in pump cylinders. . .. U7-55 I.H.P. DATA RELATING TO WORK OF STEAM-CYLINDERS. 24. Area of high-pressure piston minus i area, of rod (A n ) 307.88 sq. in. 25. Area of low-pressure piston minus -J- area of rod (A S i) 1,250.36 " " 26. Average length of stroke, each 3 ft. 27. Mean effective pressure measured from high-pressure diagrams (M.E.P.i) 59-25 Ibs. 28. Mean effective pressure measured from low-pressure diagrams (M.E.P. 2 ) 13.60 " 29. Number of double strokes per minute (line 21) 20 30. Indicated horse-power developed by H.-P. cylinder. . 66.33 I.H.P. 31. Indicated horse-power developed by L.-P. cylinder.. 61.82 " 32. Indicated horse-power developed by both cylinders. . 128.15 " 33. Feed-water consumed by plant per indicated horse- power per hour, corrected for separator-water and for moisture in steam 15.60 Ibs. 34. Number of heat-units consumed per indicated horse- power per hour 15,652.1 B.T.TJ. 35. Number of heat-units consumed per indicated horse- power per minute 260.9 " 432.] TESTING SPECIAL ENGINES. 571 TOTAL HEAT OF STEAM RECKONED FROM THE VARIOUS TEMPERATURES OP FEED-WATER, AND COMPUTATIONS BASED THEREON. 36. Total heat of i Ib. of steam at 120 Ibs. gauge-pressure, containing 1.5$ of moisture, reckoned from o F.= I220.6-(i.5$ of 866.7) 1,207.6 B.T.U. 37. Ditto, reckoned from 215 temperature of main feed- water = 1207.6 215.9 991.7 " 38. Ditto, reckoned from 225 temperature of low-pressure jacket-water = 1207.6 226.1 981.5 " 39. Ditto, reckoned from 290 temperature of high-pres- sure jacket and reheater water = 1207.6 292.3 = . . 915-3 " 40. Heat of separator-water reckoned from 340 =353.9 343-8 10.1 41. Heat consumed by engine (//) = (18.863 X 991.7) + (6i5X98i.5) + (8i5X9i5.3) + ( 2I oX io.i)= 20,058,150 " RESULTS. Substituting these quantities in the formulae, we have: A P p s L N 307.88 X (95 -f 3-69 + 4-33) X 3 X 24,000 1. Duty = - -jf- 20,058,150 = 113,853,044 foot-pounds. c 3078 x 144 2. Percentage of leakage = j? ~ T ~ ~ r ~ X IOO=2,< 307.88 X 3 X 24,000 A L N 307.88 X 3 X 24,000 X 1.24675 3. Capacity = : ~~7T~ 10 = 2,763,716 gallons. 4. Percentage of total frictions 307-88 X (95 + 3-^9 + 4-33) J~ n j/^/T, AlT M.E.P.* ' (307.88 X 59- 2 5) + (1250.36 X 13-6) 5?2 EXPERIMENTAL ENGINEERING. [433- In the use of a system like the preceding, every precaution should be observed in the adoption of methods, as well as in taking observations. The water discharged by a pumping- engine, for example, should never be obtained by computation from the measured dimensions of the pump and the observed number of strokes, but should be measured directly. A weir is commonly arranged for this purpose. Where the delivery of the pump has been actually measured, and the pump thus standardized, its use as a meter is less liable to error, but it is best avoided whenever possible. 434. Standard Method of Testing Locomotives. The following is a reprint of a report of a committee on standard methods of testing locomotives appointed by the American Society of Mechanical Engineers, and submitted at the San Francisco meeting in 1892 : Locomotive-testing is conducted under such unfavorable circumstances and surroundings that many of the exact methods employed in testing stationary engines or boilers cannot be used. It is desirable, therefore, that locomotive-tests be always made with a special train when possible, so that the same cars shall be used for the different trips, and the weight of train be uniform. The speed of the train can also be under control, and the tests not hampered by the rules governing a regularly scheduled train. Special and peculiar apparatus is employed by nearly every different experimenter as having some extra merit of convenience or accuracy, and we have endeavored to ascertain the best practical instruments and methods for the various measurements, and to illustrate or explain them. When a dynamometer-car is not used : As a final basis of comparison of locomotives, we recom- mend as a unit the number of thermal units used per indicated horse-power per hour. The object in view in testing a loco- motive will determine the methods employed and the extent and kind of data necessary to obtain. Some tests are made to ascertain the economy of a particular kind of boiler or fire- 433-] TESTING SPECIAL ENGINES. 573 box; others, the value of employing compound cylinders; others, to ascertain the relative merits of certain coals for locomotive use. As a practical and commercial unit the amount of coal consumed per ton-mile may be used. For a coal-test we give a separate method and test blanks, Form D, for tabulating results. For a unit of comparison of boiler-test we recommend the number of thermal units F. taken up every hour by the water and steam in the boiler. For a measurement of the resistance overcome in hauling a train, a dynamometer-car is essential, and we give a method of operating a dynamometer-car and of recording results. For a uniform method of recording results of indicator- tests, we recommend the blank Form A. For tabulating general results, Form B is presented. The waste from the injector should be ascertained by catch- ing it in a vessel conveniently attached, or by starting the in- jector several times in the engine-house and catching the over- flow in a tub. The total weight of the water caught divided by the num- ber of applications of the injector gives the average waste. The observer in the cab should keep a record of the number of times the injector is applied during the trips, and thus obtain data for estimating the total waste. FUEL MEASUREMENTS. The measurement of fuel in locomotive-tests is not difficult so far as a determination of the total amount shovelled into the fire is concerned. A weighed amount may be shovelled into the tank, and the amount remaining, after a given run, be weighed to determine the amount used, provided no water is used to wet down the coal. But it is next to impossible to determine the amount of coal used at any particular portion of a run when the coal is put in the tender in bulk. If coal is put in sacks containing 125 pounds each, with a small amount of weighed coal on the foot-plate, even with heavy firing it is 574 EXPERIMENTAL ENGINEERING. [433- found quite possible for the fireman to cut open the bags, and dump the coal on the foot-plate as needed. In this way the rate of consumption on difficult portions of the run could readily be estimated. The use of water-meters and of coal in sacks obviates any need of weighing the tender, and thus re- moves one of the largest inaccuracies incident to the ordinary locomotive-tests. To determiae the amount of coal used dur- ing the trip, it is only necessary to count the number of bags which have been emptied. However, the determination of the amount of fuel used during a run is not all that is neces- sary for a test. The measurement of the fire-line before and after a test is very essential and extremely difficult. If the run is a long one, then the errors in the determination of the fire-line may not be great ; but for short runs there seems to be no way of measuring the difference between the heat-value of coal in the fire before the test and after with sufficient accuracy to give reliable data. In tests made on a heavy grade, one trip closely succeeding another, it is of course im- practicable to drop the fire and measure the amount of fuel in the ashes remaining. Such measurements are unsatisfactory and inaccurate in any case, because it is not practicable to draw the fire without wetting it, as the ashes rise into the machinery, and they are too hot to handle. When one run succeeds another within a short space of time, some other method is necessary for measuring fuel used than by dumping the coal. The test is commenced with a good fire in the furnace, and the height of coal estimated by two or more assistants engaged in the trial. At the end of the run the fire should be in the same condition as near as possible. No raw coal should be in the box and steam-pressure and pyrometer-pressure falling. APPLICATION OF THE INDICATOR. If the power of the engine is to be determined, the action of the valve-gear examined, or the coal and water used per unit of power in a unit of time, the indicator must be used. 4330 TESTING SPECIAL ENGINES. 575 This instrument should be attached to a three-way cock just at the outer edge of the steam-chest, in order that the con- necting pipes (which should be | inch in diameter) can go directly in a diagonal direction to holes tapped into the sides of the cylinder rather than into the heads (Fig. 227). By this arrangement the pipes are shorter than when they pass over FIG. 227 REDUCING-MOTION FOR LOCOMOTIVES. the steam-chest into the heads, and have but short horizontal portions, thus facilitating the rapid draining of the pipes. Moreover, if a cylinder-head is knocked out the pipes are not dragged off, and the operator and indicator escape injury. The indicator should not be placed on horizontal pipes on a level with the axis of the cylinder-heads. The indicator-pipes and three-way cock should be covered with a non-conductor, wrapped with canvas and painted. The indicator itself should be wrapped as high as the vent-holes in its steam-cylinder. EXPERIMENTAL ENGINEERING. [ 433* The indicator-gear may be a rigid, true pantograph motion, either fixed or adjustable in height (Fig. 228) ; or it may be a simple pendulum connected by link to the cross-head with a wooden quadrant 2 inches thick, and having a radius such as will make the indicator-card 3 inches long. The cord of the indicator should be 8 or 10 inches long, and connected with a rod reaching forward from the panto- graph. In order to determine the steam-chest pressure, the indica- tor should be so piped that a steam-chest diagram can be mid-position Rigid Non Adjustable FIG. 228 REDUCING-MOTION. drawn by it. A steam-gauge on the chest is inaccurate and difficult to use. Indicator-diagrams should be taken at equal distances in- stead of at equal time-intervals, in order to properly average the power. They should therefore be taken at mile-posts. The signal for taking diagrams should be given by the observer in the cab, who can pull a cord and ring a bell at the front of the engine, or blow the whistle. For the safety of the operator at the indicator, it is recom- mended that the seat be on a piece of boiler-plate above the cylinder, and so arranged that a piston or cylinder-head can pass out 1 without injuring him. 433-] TESTING SPECIAL ENGINES. S77 The person who takes the indicator-diagrams should be thoroughly sheltered by a temporary box containing a seat placed on the front end of the engine. Besides the usual indi- cator, there should be located near the observer a revolution- counter, which should be so arranged that after starting out the instrument will continue to record the revolutions for a period of exactly one minute, starting every time from zero, and when the minute has elapsed the counter will stop. Such an instrument is already in existence for taking the continuous revolutions of dynamos and high-speed engines, and little or no difficulty would be experienced in obtaining an instrument capable of taking the revolutions from some reciprocating part of the machinery. It is desirable also to have an electric connection between the indicator and the recording apparatus in the dynamometer- car, so that at the instant an indicator-diagram is taken, the fact may be registered on the dynamometer-diagram, see Article 181, page 218; and the cards should be numbered con- secutively, and the record likewise. Besides the person taking the indicator-diagrams, another person should be located in the cab of the engine, whose duty it should be to observe the point of cut-off given by the posi- tion of the reverse-lever, the position of the throttle-lever, and the boiler-pressure, all of which conditions should be recorded in a log-book for this purpose. Besides recording on the dynamometer-diagram the fact that an indicator-card is being taken, a bell should be rung at the same time, so as to call the attention of the observers in the dynamometer-car to this tact. LOCOMOTIVE-BOILER TESTS. GENERAL DIRECTIONS. First. The drawing of the boiler to accompany the report of tests should be particular in specifying the construction in de- tail with reference to coal-burning and generating steam, such as heating surface, grate area and the distribution of openings through the grate, volume of fire-box, size and thickness of 5/8 EXPERIMENTAL ENGINEERING. [433- flues, size of smoke-box, and the arrangement for draught, together with the thickness of walls between the heated gases and the water in the boiler ; the weight of the boiler itself should be given, and the number of cubic feet of water-space and of steam-space in the boiler, the division between the two to be taken at the middle of the range of the gauges. Second. Boilers for tests should be thoroughly cleaned on both sides of the heating surface, by a removal of the flues, before any test is commenced, and these surfaces should be kept clean by frequent washing during the test. Exception. When it is desired to make a comparison of boilers for the purpose of determining a difference between them as to incrustation, they should first be tested as above when clean, and then tested again without cleaning further than the ordinary washing out of the boilers after the lapse of some months' service. The results are to be reduced to evaporation per square foot of heating surface ; both boilers using the same water during the period of testing. Third. In case the measure of the capacity of the locomo- tive boiler for generating steam be desired, without reference to the engines forming the locomotive, this capacity should be measured by the number of British thermal units, taken up per hour by the water and steam in the boiler, which may be readily determined from the observed data of temperature of water fed to the boiler, pounds of water evaporated per hour, and steam-pressure under which this evaporation occurs. Use any good set of steam-tables, such as Peabody's or Por- ter's, found in Appendix, or in Richard's Steam-engine Indica- tor. In such cases it will be necessary to specify all the perti- nent conditions under which such measure of the capacity of the boiler is made, so that in comparing with the capacity of another boiler all such conditions may be made as nearly alike as possible. It is, however, believed that a measure of the capacity of a locomotive boiler, without any reference to the capacity or efficiency and method of working of the engines on the locomotive which such boiler feeds, will not be of par- ticular value in comparison of boilers, unless the conditions 433-] TESTING SPECIAL ENGINES. 579 under which the engines are worked with different boilers are identical, or nearly so. Fourth. On account of the important influence which the temperature, and especially the moisture of the atmosphere, has upon the results obtained in a boiler-test, it is necessary to compare two or more boilers at the same place and at the same time, to get results which may be strictly comparable. The temperature of the air should then be noted for record. Fifth. To properly determine the amount of water fed to a locomotive boiler in service on a locomotive during any test, it is necessary to use a good water-meter, which should have its maximum error determined by previous tests and given with the report. Sixth. The coal used should be dry when weighed, and placed in sacks, each containing 100 or 125 Ibs., care being taken to insure that all scales used are accurate. When an un- usually large amount of coal is needed, a weighed quantity of coal may be placed in the front of the tender and used first, and the test finished with coal from the sacks. An analysis of the coal used should accompany the report, which should show the volatile matter, the fixed carbons, etc., the moisture, and the ash contained in the coal. The ashes should be dried if they contain any moisture, and carefully weighed and re- corded after each test-run. Seventh. The temperature of the smoke-box gases should be measured by a good pyrometer, located near enough to the flues in the smoke-box to get the average temperature of the gases after they have passed the heating surface, and before they are mixed with the exhaust steam. It is suggested that pyrometers, such as that offered by Schaeffer & Budenberg, or Weiskopf, are suitable for this purpose. The location of pyrometers is shown at /, Fig. 229. These instruments cost about thirty-five dollars. They should register up to 1000 F. See Article 296. Eighth. The degree of exhaustion in the smoke-box should be measured and recorded by means of a simple manometer- gauge. See Article 273. EXPERIMENTAL ENGINEERING. [ Ninth. The quality of the steam furnished by the boiler to the engines should be determined by the most approved methods: See Chapter XIII. Tenth. Samples of gases passing from the flues to the smoke-box should be analyzed and results reported. The FIG. means of taking such gases so as to insure perfect samples is to be further considered, and definite means prescribed. See Article 358, page 423. COAL TESTS. Directions to be observed in Supervising and Conducting Coal- trials. The locomotive selected should be in good condition, 433-] TESTING SPECIAL ENGINES. 581 and either a new engine or one that has lately undergone repairs. The boiler should be washed before commencing the trial, the steam-gauge tested, the flues cleaned, and the exhaust nozzles cleaned and measured, which operations should be per- formed also whenever the kind of coal is changed. Instruc- tions should be given to round-house foremen that no repairs or alterations of any sort be made to the engine without the approbation of the conductor of the trial. The same engine- man and fireman should operate the engine throughout the trial, and the same methods of firing and running should be strictly adhered to. The run selected should be one in which the same distance is covered on each trip. The trains should be through trains and unbroken from end to end of the run, and the same number of cars and same lading should be pro- vided each trip. The same speed should, if possible, be pre- served on all trips. The conductor of the trial should be familiar with correct methods of firing and running locomotives, and should insist that the fireman adhere to approved methods of firing, and that the same methods be preserved throughout the duration of the trial, so that all coals shall receive the same treatment. (See Chapter XIV, on Heating Values of Fuels, and Chapter XV, on Steam-boiler Trials.) He should also see that the coal supplied at coaling points is of the proper kind, and should weigh the coal personally, and keep an accurate record of the following items : The coal consumed. The amount of ash. The amount of cinders in smoke-box. The water evaporated. The number of cars in train. The weight of cars as marked thereon. The weight of lading. The state of the weather. The direction and estimated velocity of wind. The temperature of the atmosphere. 582 EXPERIMENTAL ENGINEERING. [ 433. The temperature of the. feed-water. . The time on road. The steam-pressure. The exhaust-nozzles. The conductor should enter the above observations in a log-book, together with notes of repairs to engine, and any other items that might be of import. REPORT OF COAL-TRIALS. In order that coal-trials maybe similar and consequently comparative, the following data should be observed (see Arti- cle 343> .page 407) : First. Dates between, which trials were conducted. Class of locomotive. Service in which trials were made, mentioning locality, etc. Name of conductor of trial. * '_,""/. . . .'.;_.._ i. . . ' ... : i i - '-' . . ^ Second. COAL A. Kind of coal. : Name of mine and operator. Location of mine. Physical quality of coal (appearance). : Steaming quality of coal. Kind of fire made; ... Clinkers and ashes. Cfcnders in smoke box. Cleaning ash-pan and smoke-box. Labor involved in firing. COAL B Same as above. GENERAL REMARKS, Comparison of evaporation (pounds of water evaporated per pound of coal). 433'] TESTING SPECIAL ENGINES. 583 Comparison of coal consumed per 100 tons hauled one mile. Value coal A, 100$. Value coal B. Comparative value. Coal A is 100$ more or less valuable than coal B. A table of engine-performance and a table of general re- sults of engine-performance for each coal must accompany the report. (See Form D, page 584.) WATER-MEASUREMENTS. It has been found during the last year or two that meters are reliable and accurate within less than one per cent for measuring the water used by a locomotive. (The experience of the author does not accord with this statement see Article 214, page 256.) The meters should be specially made for the purpose and, if possible, free from any material that is injured by contact with hot water. They should be placed so as to be read from the cab. In mounting these meters, all pipes should be thoroughly cleaned before they are put into position, and a sufficiently large strainer should be placed between the meter and the tank. A most essential feature is to have a good flap check-valve be- tween the injector and the meter ; otherwise the hot water may flow backward and ruin the rubber recording-disks in the meter. As a check upon the meter, however, other means of measuring the water should be employed. The most convenient method is to use a float attached to a wooden bar which slides upon a graduated rod, the lower end of which rests upon the bottom of the tank. This rod is graduated to show 1000 Ibs., and subdivided to 250 Ibs. The method of graduating the rod is as follows: Fill the tank, place the bar and float in the proper position for read- ing, and mark the stationary rod zero at a level with the top of the float bar. Draw from the tank IOOO Ibs., place the measuring device in position again and mark the rod, calling this mark I. Again draw off 1000 Ibs., mark the rod 2, and so continue until the water is all drawn. If the tank has a uni- 534 EXPERIMENTAL ENGINEERING. [434- R-PRESSURE, 000 LBS. / Coal. Remarks. i 1 PQ 3[Ift J3dSUOJ,OOI jad paumsuoo JBO3 31! W OUQ painnq suox 1 J < suox ui UIBJX ;o jq3pM pj;ox 5 H I!W aad JE3 aad [603 v J| < O JB03 -q[ aad pajBj -odEA3 J3jEA\ "sqi ! 1 1 ^ S^ to du x J3d paiBa -odBA3 a3;n^v\ 'sqq 1 . w > a I 3^EJ3AV | > tt c ^ w*s 3 = a tf'^a ' 1 O "* CJ O %d* H^ _j '33BJ9AV 3jnss3jd-uiB3JS 1 3#EJ3AV J35BAV-P33 j jo aaniBaaduiax ! i i < * '53BJ3AV ajgqdsotu -IV ) 3->niBaadui3X 1 | $4 J3q3B3A\ Z 1 3 i 4> ^d gf 1 S 1 <5 ' d ? J X puno^j ;o jsqainM i c f . * U-> \O ' C-N 00 0, ^ ^ 434-] TESTING SPECIAL ENGINES. 585 form horizontal section, several thousand pounds can be drawn off at once and the rod subdivided accordingly. In general the float is placed in the man-hole of the tank; but as this is not in the centre of gravity of the water-space, its readings are not quite correct if the two ends of the tank change their relative heights. This can be overcome by having a spe- cial small opening made at the centre of gravity of the tank, or as near it as possible, and using a small float. Another but less convenient way is to place a glass tube, on each side of the tank opposite the centre of gravity of the water-space, and to graduate scales behind them by the same method as above described. The objections to this method are the inconvenience in reading the scales (especially at way stations where there is but little time), their liability to freezing in cold weather, and the possibility of injuring them at any time. The float is always convenient and serviceable. When locomotive boilers are being fired hard, the water rises above the normal level, and a measurement of water just after the injectors have been throwing comparatively cold water into the boiler is not an accurate one ; the water shrinks and swells according as the firing is hard or as the locomotive is being worked. Hence measurements taken under these vari- able conditions are necessarily approximations. There is also a continuous movement of the water in the water-glass, and a mean of the oscillations is not quite satisfactory. Although the amount of water fed into the boiler can be determined ex- actly by the use of meters, yet the inaccuracies of the location of the water-line render water-measurements on short runs iilmost impracticable. The six-hour test for a stationary engine is considered satisfactory when successive tests will give the same results ; but in locomotive work, unless the engine be kept quiet, as it would be when tested in a shed, a short test is of little or no value. It may be accepted that a determination of the water-line by the sound of the gauge-cocks is too uncer- tain to be admissible in locomotive-tests unless the run is a long one. In such cases the total amount of water used is so large 586 EXPERIMENTAL ENGINEERING. [ 434- that any errors in estimating the water-level at the beginning or the end of the trip practically disappear. A locomotive which is undergoing a test should have a water-glass on the boiler. Behind this should be a strip of wood graduated, and surrounding the glass and fastened to the wood should be a copper wire at the height at which the water should be left at the end of every trip. The tank-measure- ment should not be taken at the end of the trip until the water in the boiler is at the standard height. The temperature of the water should be taken as it enters the tank at every station where water is taken, and tank reading should be taken before and after each rilling. Leakage of Boiler. To test for leakage, keep up the pres- sure to be carried, as nearly as possible, without blowing off, and note the fall of water in ;the water-glass in a given time, say four hours. Of course the injector must not be applied during this interval. The water-meter can then be used to determine the amount lost by leakage by reading the dial, applying the in- jector until the water reaches the original level, and then taking a second reading. The difference will be the amount of water lost. All boilers lose more or less from this cause, and if the test is to be a comparison between two different styles, the necessity for this information is obvious. * * * # * * * Before beginning a test, the pistons and the slide and throttle valves of the engine should be made tight. The point of cut- off for each notch of the quadrant should be ascertained, and the cut-off should be painted in white on the quadrant, or on boiler-jacket, with pointer or lever. All leaks about the engine should be stopped. A graduated scale and index should be attached to the throttle-rod to indicate its opening. A special steam-gauge with a long siphon should be used for the boiler-pressure and attached to the front of the cab at the left side, so that it will not become incorrect from overheating. Readings of the gauge, reverse quadrant, throttle-scale, and boiler-height-scale should.be taken frequently, the first as often 434-] TESTING SPECIAL. ENGINES. 587 as once in two and one-half, five, or ten minutes, depending on length and character of run, and all with each indicator- diagram, if the latter are being taken. Just before beginning atrip the water in the boiler should be at the standard height and the tank reading taken in order to ascertain the amount of water used while running, or per in- dicated horse-power per hour. Extraordinary efforts should be made to prevent blowing off before train time and while running. The number of times and the length of time s'afety-valve is blowing off should be recorded. No water should be taken from the tank for any purpose ex- cept supplying the boiler, and the boiler should not be blown off during a test if it can be avoided. If it cannot be avoided, the water should be at the standard height before and after blowing. . _ W P4 W * g [Bpiui japuij^ 'd 'T Jo jqSitf OH g LT ; r> ,-s -U1B3JS JSPUH-^D *d "1 J0 l^ltf o 5 jaAisoay ui ajnsssjd i H j r^ C_) ,; ;B ^oBg pniiX D ''d^H ^IPI (J W | jpBg jsBaq japuijX^ - d 'H JO 'J 3 T Q i {Hniuj japuiiX3 'd 'H Jo ipq 5 (X jsaqD-uiBSJS '^ 'H J0 1J 3 T aSnB3-J3iiog a^ojjs jo juao jad 'd 'T 1^ 33{OJis jo ssqoui 'd 'T asjojjs jo JU3D jad 'd 'H S ^U 00 3310JJS jo saqoui 'd 'H C/) - 3} nu. C njadiaaj' P 3ads-uo, 8 ,d w Pti ajnuioi jad suonnjoAay d i ! ' 3m]L S C e 1 s a - ON c acting at the crank-pin ; Z and P b , auxiliary quantities. We have y__ tf cos 2 6 n * sin a & -f sin 4 n* sin 2 # 3 N = (P a - P p ) sec ft cos />=(/>,-/>,) sec A When the accelerating forces are not included, T = P a sec p sin (0 -f /?) ; P e = P a sec p. i In this work is discussed only the experimental method of determining the inertia of an engine as developed by Mr. E. F. Williams of Buffalo, N. Y., and published in the American Machinist in 1884 and '5. 437. The Williams Inertia-indicator. This instrument draws a curve (see Fig. 234) closely resembling the theoretical inertia-diagram, and similar in kind to an indicator-card. The horizontal length of the diagram corresponds to the stroke. The abscissa of any point of the curve identifies the position of the piston at a corresponding point in its travel, and its ordi- nate measures to a known scale the force required to give to a mass of known weight (one or two pounds) the acceleration, positive or negative, of the piston at that point of its stroke. The product of this force into the weight of the reciprocating parts, in pounds, gives for that point of stroke the positive or negative horizontal force at the crank-pin due to the inertia of the parts. The instrument is shown in Fig. 231 attached to the cross-head of an engine, and in Fig. 232 in plan. The frame P is rigidly attached to the cross-head A by two studs/ and r, the former serving also as a pivot for the arm B. The upper end of B is pivoted to one end of a horizontal bar 7 whose other end is attached by a pin to some fixed support. In this way B swings back and forth, its lower end, together 600 EXPERIMEN TA L ENGINEERING. [ 437 FIG. 232. THE WILLIAMS INERTIA-INSTRUMENT. PLAN VIEW d FIG. 233. SPRING TO INERTIA-INSTRUMENT. d \ FIG. 231. THE WILLIAMS INERTIA INDICATOR. 43 7-] DE TERM IN A TION OF INER TIA . 60 1 with the frame P and the parts carried by it, travelling with the cross-head. Within the case or cage d (shown fn section in Fig. 233) the weight h is free to slide horizontally on steel friction rollers, except as controlled by the spring. This spring, whose tension is known by calibration, is the only means by which the motion of the cross-head is communicated to the weight k, and it must therefore be extended or compressed by an amount which measures the force needed to overcome the inertia of the weight. For convenience h may be made to weigh, including the parts moving with it, exactly one pound. It is joined by a light rod e to the bent lever a which moves a pencil in a direc- tion at right angles to that of the cross-head motion. By the vibration of the arm B the paper is carried under the pencil on the curved platform b shown in Figs. 231 and 232. This can at pleasure be drawn upward by the cord m t and kept in contact with the pencil for one or more revolutions while the engine is in motion. The paper is put in place while the engine is at rest, and the neutral line x, Fig. 232, is drawn by swinging the arm B back and forth by hand. As soon as the engine is run- ning under the conditions desired, contact may be made and the diagram drawn. In using the instrument so as to make a diagram from 2 to 3 inches long, the arm B may be varied in length to suit the stroke of the engine. To maintain a given average length of ordinates for widely differing speeds, the scale maybe changed by changing the spring, or the weight, or both. For obtaining the effect per pound weight of the recipro- cating masses, determine the scale as follows: The force exerted by an 8o-lb. indicator-spring when it is compressed or extended \ inch, causing a pencil-movement of one inch, is 80 Ibs. per square inch of indicator piston-area. The latter being one-half square inch, the actual force on the spring is 40 Ibs. If, then, an 8o-lb. spring with a 2-lb. weight be used, a i-inch ordinate, will mean 40 Ibs. exerted by the spring in total, or a force of 20 Ibs. per pound of the mass it moves. 602 EXPERIMENTAL ENGINEERING. [ 438, Thus a scale 20 means a force, for each inch of ordinate measured from the neutral line, equal to twenty times the weight of the moving body under investigation. In other words, each twentieth of an inch in length of ordinate repre- sents a force equal to the weight of the reciprocating masses. An 8o-lb. spring with a i-lb. weight, scale 40 " 8o-lb. " " " 2-lb. " " 20 " 40-lb. " " " i-lb. " " 20 " 20-lb. " " " i-lb. " " 10 438. The Inertia-diagram drawn by the Instrument In interpreting the diagram several points are to be noted : 1. The evenness and general form of the diagram are largely influenced by the smoothness of running of the engine, which depends on the accuracy of bearing surfaces, and the degree in which the weight of reciprocating parts, their veloci- ties, and the varying steam-pressures are suited to each other. 2. The curvature of the lines traced depends chiefly on the ratio of crank-length to that of connecting-rod ; this ratio should be determined by measurement. 3. In combining the diagram with an indicator-card the ordinates should represent forces in pounds per square inch of piston-area, and in the same scale as that of the indicator-card. For this we determine by independent measurement (i) the force exerted by the spring for a given length of ordinate from the neutral line ; (2) the ratio of the weight of the reciprocating parts of the engine to that of the parts of the instrument moved by the spring ; and (3) the area of the engine-piston. 4. The difference in length of the corresponding ordinates in the inertia and indicator diagrams, the latter corrected for back pressure or compression, represents the net horizontal force transmitted to the crank-pin. For combination with a steam indicator-card, the force per square inch of piston-area is required. This is best obtained by getting the weight-ratio or the weight of reciprocating parts per square inch of piston-area. This multiplied by the scale of the.inertia-diagram gives the engine-wale or scale of pounds per 438.] DETERMINATION OF INERTIA. square inch at the speed at which the diagram was taken An example will make this clear. The inertia-diagram in Fig 234 taken from a very smooth-running engine, was obtained with an Scale 40 265 revs, per min. llj'cc 16" Porter- Allen FIG. 234. INERTIA-DIAGRAM. Scale 4O 265 revs, per min* 4.4.16 " sec* FIG. 235. INERTIA AND INDICATOR DIAGRAMS. 80 spring and a one-pound weight. Hence the diagram-scale is 40. But for this engine the weight-ratio was 3. Hence 40 X 3 = 1 20 is the engine-scale. Having, now, this inertia-diagram (Fig. 234) whose engine- scale is 120, suppose we are to combine it with an indicator* diagram (Fig. 235) from the same engine at same speed, and taken with a 40 spring. The scale of the inertia-diagram can 604 EXPERIMENTA L ENGINEERING. [433. be changed from 120 to 40 by drawing it with the ordinate of each point increased three times, giving the curve ab in Fig. 235. The ordinates to the compression curve on the back stroke can be deducted from the corresponding ordinates of the inertia curve ab, and the included area shaded, thus exhibiting the modification of the steam-forces by the inertia of the recip- rocating parts. By vertical measurement of the shaded por- tion, the true distribution of horizontal forces on the crank-pin during the backward stroke may be obtained. Important Features of the Experimental Diagram. Sup- pose that in Fig. 236 / and c are the positions respectively FIG. 236. RELATIVE MOTION OF CRANK-PIN AND PISTON. of the cross-head and crank-pins with crank on its centre, Then, were it not for the angle of the connecting-rod, the cross-head pin would go to p' when the crank has moved to c" , pp' being equal to cc'. But its true place is at p" ; thus in the quarter-turn of the crank from c to c' the cross-head has gone a distance p'p" past its mid-stroke, and is then moving at the same speed as the crank-pin, while its maximum speed was attained before reaching mid-stroke. Again, on the return-stroke, when the crank is lowest, the piston has not gone half-way. This shows that the acceleration is greater when the piston is at the head 438.] DETERMINATION OF INERTIA. 60 5 end of cylinder. The same thing is shown in Fig. 237, xy being much greater than x'y' , while the fact that point of crossing of yy' and xx' is at the left of the centre shows that the FIG. 237. INERTIA-DIAGRAM. zero of acceleration, which of necessity corresponds withmaxi- mum velocity, falls where it should. Scale i~ 20 Force Units. 1ft. Stroke, 1 Rev. per Sec. Connecting Rod~6 Cranks. FlG 23 8. INERTIA-DIAGRAMS. 6o6 EXPERIMENTAL ENGINEERING. [ 438. gram may be further tested by comparing the area below the neutral line with that above it by means of a planimeter. In Fig. 238 the inertia-diagrams for forward and backward strokes have been separated. The negative and positive signs show respectively where the inertia opposes and assists the steam-pressures. The curve y"y'" belongs to the forward stroke and y'y to the return. In practical use the diagram should be divided into ten or more equal spaces, and the ordinate at the centre of each space being numbered, the crank-positions corresponding, may be found as shown in Fig. 239, and the relative velocity of 01 2 3 4 5 Q 7 8 9100 FIG. 239. CRANK-POSITIONS CORRESPONDING TO GIVEN PISTON-POSITIONS. piston and crank obtained. The method of dividing the dia- gram shown in Fig. 238 is convenient in transferring the curve to a steam indicator-card similarly divided. Care being taken to draw both to the same scale and in pounds per square inch of piston, the inertia curves may be drawn on an indicator- card arranged as shown in Fig. 240. Here the back-stroke steam-card has been drawn inverted and in contact with the for- ward card in its normal position, the two back-pressure lines being made coincident and used as the neutral inertia line. 438-] DETERMINATION OF INERTIA. 60 7 The ordinate lines are then produced to cut the line X 'X ', which serves as a base-line from which to lay off ordinates of the net horizontal forces at the crank-pin. The actual forces FIG. 240. COMBINED DIAGRAMS. at the crank-pin are thus more clearly revealed for both strokes, and the areas above and below X'X' respectively, give the actual work on the crank-pin for forward and return strokes. CHAPTER XXI. THE STEAM-INJECTOR-THE PULSOMETER. 439. Description of the Injector. The steam-injector is an instrument designed for feeding water to steam-boilers, although it can be and often is used as a pump to raise water from one level to another.* It has been used as an air-com- pressor, and also for receiving the exhaust from a steam-engine, FIG. 241. THE MACK NON-LIFTING INJECTOR. taking the place in that case of both condenser and air-pump. It was designed by Henri Jacques Giffard in 1858. In its most simple form (see Fig. 241) it consists of a steam- nozzle, the end of which extends somewhat into a chamber or converging tube called the combining or suction-tube ; this * See Cassier's Magazine, January and February, 1892 ; Thermodynamics, by D. Wood, page 279 ; Thermodynamics, by C. H. Peabody, page 152. 608 439-] THE STEAM-INJECTOR THE PULSOMETER. 609 connects with, or rather terminates in, a third nozzle or tube, A (Fig. 241), termed the " forcer." At the end of the combin- ing-tube, and before entering the forcer, is an opening connect- ing the interior of the nozzle at this point with the surrounding area. This area is separated from the outside air by a check- valve, E, opening outward in the automatic injectors, and by a globe valve termed the overflow-valve in the non-automatic injector. The injector-nozzles are tubes with ends rounded to conform to the form of the " vena contracta " as nearly as pos- sible, and thus receive and deliver the fluids with the least pos- sible loss by friction and eddies. Some of the injectors are quite complicated, and adjust FIG. 242. THE SELLERS INJECTOR. themselves automatically by varying the openings through the tubes to suit changes in steam-pressure. Ficr 242 is a section of the Sellers injector of 1876; in this injector the steam-nozzle C can be inserted a greater or less distance, as required, into the combining-chamber NN. overflow P is closed by a valve K operated by a rod L con- nected to the starting-lever T. The tube NNCO moves 6io EXPERIMEN TA L ENGINEERING. [ 440. automatically to vary the opening at C with change of steam- pressure. In some of the injectors the tubes are so arranged that the discharge of one injector is made the feed for a second injector. This makes what is termed a double injector, of which familiar illustrations are to be seen in the Hancock, Park, and World injectors. STEAM QVIRFLOWL FIG. 243. THE HANCOCK INSPIRATOR. 440. Thermodynamic Theory of the Steam-injector. As a thermodynamic machine the injector is nearly perfect, since all the heat received by it is returned to the boiler, ex- 440.] THE STEAM-INJECTOR THE PULSOMETER. 6ll cepting a very small part that is lost by radiation ; conse- quently the thermal efficiency should be in every case nearly 100 per cent. Its mechanical efficiency, or work done in lifting water, compared with the heat expended, is small, because its heat-energy is principally *used in warming up the cold water as it enters the injector. Let r equal the heat of evaporation in B. T. U. of a pound of dry steam ; x, its quality ; q, heat of the liquid of the entering steam in thermal units above 32; q^, heat of dis- charge-water in thermal units above 32 ; h, the total heat in a pound of wet steam ; w, the weight of steam per hour uncorrected for calorimeter-determinations ; W, the weight of water supplied ; /, the temperature of the feed-water ; /', the temperature of the delivery. Then we have, as the heat in one pound of the steam supplied, above 32, k = xr + q ........ (I) If the mechanical work consist of W pounds of water lifted n feet by pressure and s feet by suction, the heat equivalent F of the mechanical work is F=[(n+s)W+wn]A, . . . '.. . (2) if delivered from the end of the discharge-pipe without sensible velocity. In case there is a velocity of v l feet per second at delivery from discharge-pipe, the additional energy L, in heat- units, is The heat-units taken up by the feed-water are K= W(t' -t). 'J . ...... (4) The thermal efficiency E, if the injector is used for feeding boilers, is F+L + * -, ... 612 EXPERIMENTAL ENGINEERING. [44 1- If used as a pump, the heat K received by the discharge-water is to be neglected, and the efficiency E p is 441. Mechanical Action of the Injector. In this case we consider only the impact of the jet of steam at high velocity against the mass of water. The case being similar to that of a small inelastic ball, moving at high velocity, impinging on a large ball. Denote the velocity of the steam by v t that of the water before impact by 1 7/ , and after impact by V l \ then by the principles of impact of inelastic bodies, wv ,_ ~" ~~ ~~~ When water is supplied the injector under pressure, the sign of V l is positive, otherwise it is negative. The use of this equation requires the velocity of the steam, v\ that of the supply, V.i ; and of the discharge, F, to be given. The velocity of the steam, v, will not differ essentially from 1400 feet per second for the conditions in which it is used in the injector (see Article 230, page 273). The velocity of the water discharged, F, from the injector may be found by dividing the volume that is delivered in cubic feet per second, c, by the area of the discharge in square feet, A ; that is, 144 in which C represents the discharge in cubic feet per hour, and a the area of the discharge-nozzle in square inches. 441-] THE STEAM-INJECTOR THE PULSOMETER. 613 The velocity of the water supplied, V l , in the suction-pipe maybe found by ascertaining the equivalent head, n l , that will produce the same velocity. If / be the absolute pressure per square inch in the combining-chamber ; b, the pressure per square inch, as shown by a barometer or pressure-gauge, on the water-supply ; w", the weight of a cubic foot of water at the temperature of the supply ; s, the suction-head in feet, then V = ~ The velocity of the suction is, however, expressed more con- veniently by considering a body of water with a head, s, acting to accelerate or retard the whole mass of water in the injector. Let A be the smallest section of the water-jet, w" the weight of a unit of water ; then the pressure due to s feet of water will be saw" . As this acts on a mass of water Vaw" -r- g, the velocity imparted would be The total momentum produced by the suction would be J^7 J_ ,/c-,r\ / W\ S v S in which v ' H^-r- iv. The momentum produced by the suction would be negative, unless water was delivered to the injector under pressure. As shown in equation (7) the momentum of the suction is i, which for one pound of steam would be - ' -- = ?j . <5 614 EXPERIMENTAL ENGINEERING. [ 442. Substitute this value for the momentum of the suction in equation (7), representing W -^- w by y. We have or From which The plus sign to be employed before s when the suction- water is supplied under pressure ; otherwise the negative sign is to be used. If the friction in the pipe be neglected, V = and we have v \/2gn 2gn sg (13) 442. Limits of the Injector. Maximum Amount of Water Lifted. This may be obtained from equation (12) or (13), but it can be obtained with sufficient accuracy by neglecting the WV momentum - due to the suction-water in equation (7) ; in o this case from which W v v 1400 r = -- = 77 i= . __ I = , __ i, nearly. (14) V2gn 442.] THE STEAM-INJECTOR-THE PULSOMETER. 615 The maximum ratio of water to steam is shown by the fol- lowing table : Delivery Pressure above that on Injector. Maximum Ratio of Water to Steam by Weight. Delivery Pressure above that on the Injector. Maximum Ratio of Water to Steam by Weight. 10 36.5 55 15.5 15 29.8 60 14.7 20 2 5 .6 65 14-3 25 23-8 70 13-7 30 20.9 75 13-3 35 19.5 80 12.9 40 17.87 85 12.6 45 17.0 90 12. 1 50 16.2 IOO H-5 The minimum amount of water required must be sufficient to condense the steam, in which case w t f - (is) in which h is the heat in one pound of entering steam ; ^ a , the heat of the liquid in the delivery, both reckoned from 32 ; /', the temperature of the delivery ; /, that of the feed-water, so that the ratio cannot be greater than shown in equation (14) nor less than that shown in equation (15). Temperature of Feed-water. As the temperature of the feed-water increases vapor is given off which increases the pressure, b, in equation (9) on the surface of the supply-water, and reduces the height through which the water can be lifted. If the temperature of the feed-water is greater, the amount required to condense the steam must also be greater; but as the amount lifted by a given amount of steam cannot exceed the approximate value given in equation (14), we shall have at the extreme limit at which the injector works, the values of y as given in these two equations equal to each other, from which the maximum temperature of feed-water becomes 6i6 EXPERIMENTAL ENGINEERING. [ 442- The following table gives approximately the limiting values of suction-head in feet and temperature of feed-water : LIMIT OF SUCTION-HEAD IN FEET. Steam-pressure 100 Ibs Absolute. Temperature of Feed-water. Degs. Fahr. Pressure of Vapor. Pounds per sq. inch. Limit of Suction- head in case of Vacuum. Feet. Delivery 212 Fahr. Number of Pounds Delivery 180 Fahr. Number of Pounds of Water to con- of Water to con- dense one of Steam. dense one of Steam. 70 0.36 32-96 7.04 8.81 80 0.50 32.6 7-57 9.61 90 0.69 32.2 8.19 10.76 100 0.94 31-4 8.92 12. II no 1.26 30.9 9.80 13.84 1 20 1.68 . 29.7 10.87 16.15 130 2.22 27-3 12,20 19.32 140 2.8 7 25-9 13.89 24.22 150 3-70 24.8 16.13 32.3 1 60 4.72 22.5 19.23 48.45 170 5.98 19.6 23.81 96.90 1 80 7-50 16.9 31.25 190 9-33 9-9 45-46 200 11.52 . 9-3 83-33 210 14.12 i.i 500.9 MAXIMUM TEMPERATURE FEED-WATER. Gauge Press- Maximum Temperature of Feed-water. Degrees Fahr. Gauge Press- Maximum Temperature of Feed-water. Degrees Fahr. ure. Pounds per sq. inch. Discharge 180 Fahr. Discharge 212 Fahr. ure. Pounds per sq. inch. Discharge 180 Fahr. Discharge 212 Fahr. 20 142 173 70 109 139 25 137 1 68 75 107 137 30 133 164 80 105 134 35 129 1 60 90 99 129 40 126 156 100 95 125 45 123 153 no 9i 121 50 120 150 120 87 H7 55 H7 147 130 83 U3 60 114 144 140 80 no 65 in 141 150 77 107 444-] THE STEAM-INJECTOR-THE PULSOMETER. 6l? A series of carefully conducted experiments* made at Sib- ley College, Cornell University, to determine the efficiencies of different steam injectors, confirm the results expressed in the preceding computations. 443. Directions for Handling and Setting Injectors. Injectors are of two general classes, lifting and non-lifting. In the first class water is drawn in by suction and then discharged against a pressure ; in the second class water flows in under pressure and is discharged against a greater pressure. As there is a limit to the temperature at which water will be handled by the injector, variations in steam-pressure will affect the discharge and may cause it to stop altogether. This may be regulated to a certain extent by manipulating the valves of the steam and water supply ; some injectors are self- adjusting in this respect and are termed automatic. The general directions for starting an injector are to open the overflow, turn on steam until the water appears at the overflow, and the temperature of the injector is sufficiently low to condense the steam. Then close the overflow and the in- jector should discharge against a pressure equal to or greater than the steam-pressure. In many of the injectors the over- flow valve will open whenever the pressure in the injector becomes greater than that of the atmosphere. In several kinds the overflow is closed by a valve regulated independ- ently or connected by a lever to the starting handle so as to be opened and closed at the proper time by the simple opera- tion of admitting steam. Injectors will not work with oily or dirty water, and are liable to be stopped by anything that will not pass the nozzles. In general they are to be connected by pipe-fittings made up without red lead and arranged so as to deliver water into a pipe leading to the boiler, in which is placed a check-valve to remove the boiler-pressure when starting the injector. 444. Directions for Testing. For testing the injector use two tanks, both of which are to rest on weighing-scales. * See Cassier's Magazine, Feb. 1892. 6l8 EXPERIMENTAL ENGINEERING. [ 444- Fill one of the tanks with water, and locate the injector any convenient distance above or below this tank, and arrange it so as to deliver water into the second tank. If the water that escapes at the overflow is arranged to run into the tank from which the water is taken, no correction will be required ; otherwise it must be caught and weighed. Place a valve in the delivery-pipe, some distance from the injector or beyond an air-chamber, and regulate the delivery head by partly opening or closing this valve. The delivery- pressure, which can be reduced to head in feet of water, can be measured by a pressure-gauge in the delivery-pipe ; the suction- pressure is observed in a similar manner by using a vacuum- gauge or a manometer. The water received, W, is that taken from the first tank ; the amount delivered, W -\- w, is that weighed in the second tank ; the difference is w, the steam used. Arrange thermometers to take the temperature of the water as it enters and leaves the injector. Make runs with discharge-pressures equal respectively to one-fourth, one-half, three-fourths, once, and one and one- fourth times that on the boiler. During each run take obser- vations, as required by the blank log furnished, once in two minutes. Determine the limits at which the injector stops working, for temperature of feed-water, suction-head and delivery-head. Careful trials show that the thermodynamic efficiency of any injector is 100 per cent ; by assuming this as true the sec- ond tank may be dispensed with, and the amount of steam computed from its heating effect and known quality on the water passing through tlue injector. In the report, describe the injector tested, explain method of action, and submit a graphical log, with time as abscissa, as well as an efficiency curve for varying pressures of discharge, also for varying temperatures of discharge. Fill out the log and make complete report, after the stand- ard form. 445-] THE STEAM-INJECTOR-THE PULSOMETER. 619 445- Form for Data and Results of Injector-test. o .i fe e c3 V S < . Q < - _0 5 4 I be I 620 EXPERIMENTAL ENGINEERIA T G. [445- jS "9 1 !p + , S ^ ^ , ^ ^ f^+ + i* 3 'o * ^ 1" ~ x i" i ,,,,,,,,,,,, Quantities. : : : % | : ^ : ' \ 1 " * H : I I S Si 1* a j ffl o .a o * ^ .1 c 1 ? I & . a 1 | | t S I f | 1 s | I i I 1 a s 1 6f : I 1 s I. 5 S 2 52o-S^ ^^^uaao c c c>o cu' >< ^"a O. *o ui en 4? S S 1 "g I g f 1 I 1 ft, a: 5 1 a o o i 1 8 3 i "S, S 1 . j ^ SSW^EW wHiffifefcOH K> it- II T Formula. .Q ^5 C ^ fl> rt S ~F jv N REMARKS. i S^^ + ^^SX ^-^s^uCjKi^ ^" jT 1 g . ..*..*. ::::::: S 1 S ' J "2 . 1 ' : : :-::-:S g 3 -:^ 1 ' 3 ^ :::::::2i s ^ 3 : u >- : u : f3 t/! 'o-.^a.w S5 ; tj >, ^3 s ; -r ^ S. ^ ^ B ' "S S d Quantities. rl'O O < o2 1 ^33 | l^- S 11 i 8 1 P ^ i f : Mt I : ^ u j =oSfeco - & : 3 S3 2-co-o-d c - -^ , n i ri j 11 1 1 1 1 1 j i 1 -g 5 5 & 1 8. g 1 1 i f ? 1 1 1 1 fe.Ss&a^i's "s s S S s i J. 2 "o a 5t3 aa l>.S< 0,9-^^^^^ ^ - c 5 -2 fe " S ^ "2 "2 S S . .H '" 'S 'G '5 a ^o^t3l>> 5S---B-2 | | I Qc/J^^^QQfX 0> > > S 44&] THE STEAM-INJECTOR THE PULSOMETER. 621 446. The Pulsometer. This is a pump consisting of two bottle-shaped cylinders joined together with tapering necks, into which a ball C is fitted so as to move in the direction of least pressure, with a slight rolling motion, between seats formed in the passages. These chambers connect by means of open- ings fitted with clack-valves, E E, into the induction-chamber D. The water is delivered through the passage H, which is connected to the chamber by openings fitted with valves G. Between the chambers is a vacuum-chamber J which connects with the induction-passage D. Air is supplied the chambers by small air- valves moving inward, which open when the pressure is less than atmos- pheric. The method of working is as fol- lows: Conceive the left Chamber full FIG. 244. THE PULSOMETER. of water, and a vacuum in the right chamber ; steam enters to the left of the valve C, presses directly on the surface of the water, and forces it past the check-valve G into the delivery- passage H and air-chamber J\ at the same time the right chamber is filling with water, which rushes in and by its momentum moves the valve C to the left. The steam in the left chamber condenses, forming a vacuum, and the operation described is repeated, except that the conditions in the t\vo chambers are reversed. All the steam entering is condensed and forced out with the water, increasing its temperature. The analysis is very similar to that of the injector, except that the steam acts by pressure instead of by impact. The theory is fully stated in " Thermodynamics," by Prof. De Volson Wood, page 293. Thus: if w equal the weight of steam, W the weight of water raised, / the temperature of the supply, /, that of the delivery, r the latent heat of evaporation of the ""*' ffy 0* THK WI7IESI1 622 EXPERIMENTAL ENGINEERING. [ 447* steam, T the temperature of the steam, n the delivery-head, n l the suction-head, n -\- n^ the total head, no allowance being made for variation, we have The heat equivalent of the mechanical work done, The heat expended, in thermal units, h = w( T t -f- The efficiency, JT|- Neglecting the work of lifting the condensed steam, A(n, + n} h = , nearly. The following form for data and results of test is used by the Massachusetts Institute of Technology : 447. Form for Data and Results of Test on Pulsometer. No Date 189.. o e 3 g Total Av... 8 H Flow of Steam. Water. Heads. Calorimeter. Cou bii c I J Difference. Boiler-pressure. Orifice-pressure. Pressure at Pulsom- eter. Temp, at Pulsometer. c G 1 C O t V Q r::i 1-4 O ^ j ^c '3 ^ rtfc en BS 5.& Temp, of Suction, De- grees F. Temp, of Discharge, Degrees F. Suction-gauge, Ins. of Hg. Discharge-gauge, Lbs. per Sq. In. Actual Suction, in Ft. c 1 , the driv- ing-piston. The driving-piston is connected to the mechanism as shown. The displacing-piston, A, is a vessel made, of some non-conducting substance, and its office is to move a body of air alternately from the space above to that below it. As shown in the figure, the piston A is at the upper end of its stroke, and the piston B is moving rapidly upward, being driven by the expansion of the air in the lower part of the receiver d. The air in the upper part of the receiver is cooled by water which has been raised by the pump r, and which circulates in the annular space xx. ""On the re'turn stroke of the piston B the plunger A at first descends somewhat faster, and thus by transferring air main- tains a nearly uniform pressure upon the piston. When the pistoln B reaches the position shown in Fig. 245 on its down- ward stroke, the plunger A will be at the bottom of its stroke, and all the working air will have been transferred above and its temperature maintained at its lower limit, while it is com- pressed by the completion of the downward stroke of the piston B, after which the plunger will rise to the position shown in the figure and the temperature and volume are both increased at nearly constant pressure. The mass of air in the engine remains constant. 450. The Rider Hot-air Engine. In this engine the compression-piston A and the power-piston C work in sepa- rate cylinders, which are connected together by a rectangular passage D in which arc placed a large number of thin metallic plates, forming the regenerator, whose office is to alternately abstract from and return to the air the heat in its passage backward and forward. The same air is used continuously ; it may be admitted to the cylinders by a simple check-valve 0, opening inward. The engine is used entirely as a pumping- engine, and the water so raised circulates around the compres- sion-chamber B. The operation of the engine is briefly as follows: The compression-piston A first compresses the cold air in 626 EXPERIMENTAL ENGINEERING. [ 450. M FIG. 247. THE RIDER HOT-AIR PUMPING-ENGINK. 45 2 -] HOT-AIR AND GAS ENGINES. 627 the lower part of the compression-cylinder B, when, by the advancing or upward motion of the power-piston C and the. completion of the down stroke of the compression-piston A, the air is transferred from the compression-cylinder B through the regenerator D and into the heater E without appreciable change of volume. The result is a great increase of pressure, corresponding to the increase of temperature, and this impels the power-piston up to the end of its stroke. The pressure still remaining in the power-cylinder and reacting on the com- pression-piston A forces the latter upward till it reaches nearly to the top of its stroke, when, by the cooling of the charge of air, the pressure falls to its minimum, the power-piston de- scends, and the compression again begins. In the mean time, the heated air, in passing through the regenerator, has left the greater portion of its heat in the regenerator-plates to be picked up and utilized on the return of the air towards the heater. 451. Thermodynamic Theory. The thermodynamic theory of the hot-air engine will be found fully discussed in Rankine's Steam-engine and in Wood's Thermodynamics, from which it is seen that these engines may work under the conditions of change of temperature with either constant press- ure or constant volume, or under the condition of receiving and rejecting heat at constant pressure. The thermodynamic efficiency is found by dividing the range of temperatures of the fluid by the absolute temperature of the heated fluid. 452. Method of Testing. The method of testing hot-air engines does not differ essentially from that for the steam- engine. An indicator is to be attached so as to measure the pressures. Knowing the pressures and volumes, the corre- sponding temperatures can be computed from the formula . | ;||^ ^ = * = 53 . 2I , -- ;; in which is the pressure in pounds per square foot, v the 628 EXPERIMEN TA L ENGINEERING. [ 453- corresponding volume in cubic feet, and T the absolute tem- perature. From this The quantities which should be taken in each test are shown on the following blank for data and results : 453. Forms for Data and Results of Test of Hot-air Engine. MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL UNIVERSITY. Test of Hot-air pumping-engine. Fuel , At.. Date. 189. , LOG OF TRIAL. By Symbol. A' W P / t t' t" ff G w Number. 1 H Wa , ti u C i'l ter. I Pressures. Temperatures. Revolutions. Fuel. Leakage Pressure- gauge. Suction- Gauge. a o Ou tt s I Water at Weir. Jacket. as s S c <5 Gas-engine by... ,189.. Object of test Dimensions of Engine. Diameter of piston . In. Area of piston Sq. In. Length of stroke Ft. Piston-displacement Cu. ft. Clearance " " Percent Diameter piston-rod In. " crank-pin, . .. .. . " Data. Duration trial, hours Gas, total cu. ft. Gas per hour Air, total.. " Air per hour " Ratio gas to air Jacket-water, total, Ibs per hour, Ibs tempt, inj F " discharge F^ range F Revolutions, total per hour per minute. , Explosions, total " per hour per minute Temperature, exhaust F " room F Gas, weight of cu. ft. -Ibs Air, ' " " Mixture, " " Specific heat, gas " " . air Thermal equiv., cu. ft. gas. .B.T.U, Dynamometer work, total, ft. -Ibs. . " " per hr. " .. " D. H. P Indicated M. E. P H. P Weight of gas per hour, Ibs. ...... " air " " ... Cubic foot gas per I. H. P " " " D. H. P , I. H. P.-J-D. H. P..... I. H. P. - D. H. P.. Heat per Hour. Supplied B. T. U, Absorbed by jacket-water. " Exhausted " Thermal equiv. work " Radiation and loss. . " Thermal efficiency Thermal units per I. H. P LIST OF TABLES. PAGE I. U. S. STANDARD AND METRIC MEASURES. . . 638 II. NUMERICAL CONSTANTS 640 III. LOGARITHMS OF NUMBERS 653 IV. LOGARITHMIC FUNCTIONS OF ANGLES 655 V. NATURAL FUNCTIONS OF ANGLES 661 VI. COEFFICENTS OF STRENGTH OF MATERIALS 665 VII. TEST OF ALUMINIUM BRONZES .' 665 VIII. WOODEN PILLARS AND BEAMS 667 IX. STRENGTH OF METALS AT DIFFERENT TEMPERATURES 663 X. IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES 669 XI. COEFFICIENT OF FRICTION 670 XII. MOISTURE ABSORBED BY AIR 671 XIII. RELATIVE HUMIDITY OF THE AIR 671 XIV. TABLE FOR REDUCING BEAUM'S SCALE-READING TO SPECIFIC GRAVITY 672 XV. PORTER'S STEAM-TABLES 673 XVI. BUEL'S STEAM-TABLES 678 XVII. ENTROPY OF THE LIQUID 684 XVIII. HYPERBOLIC NAPERIAN LOGARITHMS 684 XIX. DISCHARGE OF STEAM: NAPIER FORMULA 685 XX. WATER IN STEAM BY THROTTLING CALORIMERER 685 DIAGRAM FOR DETERMINING PER CENT OF MOISTURE IN STEAM. 685 XXI. FACTORS OF EVAPORATION 687 XXII. COMPOSITION OF FUELS OF U. S 688 XXIII. REDUCING BAROMETER OBSERVATIONS TO FREEZING-POINT 689 XXIV. HORSE-POWER PER POUND MEAN PRESSURE 690 XXV. WATER COMPUTATION TABLE 691 XXVI. ELECTRICAL HORSE-POWER TABLE 693 XXVII. HORSE-POWER OF SHAFTING 694 XXVIII. HORSE-POWER OF BELTING 694 SAMPLE-SHEET OF PAPER 694 637 638 EXPERIMENTAL ENGINEERING. s^ . M ID r- o i-i TO oo ti TOO M O M ID O COOO M T t^ O M TO O i-i co r^ o T t^ IH Too i i in in w tn bo l> l> 4) W OJ o P C u *"" *" *"" ~~ rt 6 S 6 E M i II I CQ OOMMMMCO ! l|sS ID o TOO co r^ M o i-i O M O ID C4 CO ID M CO o o T o o T M ^ M M r^co ON M CO M rf ID S -n^ * Is 1 ri 6 ^ O i-i M CO CO T iDO O O O en CO O CO M M CO ~ T CUBIC bic Feet Cubic 'etres. M co ID r^* co O M T *D coO OM mOM IDCO CO O T co M Oco O T II II II II Z 11 II o *5 1 i h i J2' ^ 1 u w OOOOOOOOO 4; ^ 'S. c fcfl .-3 a a o ^.| 1 w c< S'l-iS t^ T !- OO co O i^ T co r^o T co M i * Oco co t^ " ' *D o co r*- o ^r JiifU c^ >,( S ^ EASU URVEY. da^S M CO TO CO O i-i CO T 3 1- 1 o 1 ft Ji^i ! JS II II II II II II II II II M M CO T iDO r^CO O o a,- coO rf M O O r^ ID co Q 2S T O TOO coco M r->- M HH M. co rf inO l^-co O IP t * co co r-* O rf r^. M IDCO M inOO i-iO M r^Mco rf O COCO M t^ i-i O O ^ flj ^ *t3 ro W > W DC ^wS Q M d co ^~ 10 invo r** h D J SQUA Square Ft. to Square Deci- metres. O^co r** O *-o rt" co c^ M C^ moO HH rf t^ O COO O^co r^* t^O 10 vo r^ co M c^ co ^" u^ o r^oo WEIG1 Avoirdu- pois Ounces to Grammes. COO ID CO I-i OCOO ID M IDCO i-i rf I^. O M ID M M M M M M I|l| jl STAN )ENHAL jp|| N ^o ir> r^cc O *-* co u^ tn O ^> O *^ ^^ *O ^" O rj- s coco d t^ p- sO O O w OmNco XOMCO M -* a OCO CO t^O ID rf rf CO co r^o inrfcOM i-i O O M O "~> M CO ID l-l CO *"~ ' V c Q W Z n n n n n n n n n O So i-i i-i M COCOrf^DiD rt c rt 3^ 03 , Jl fi-i M co T mo r^co MOO TOO MCO T TOO MOO TOO M O Too co r^ M O O ID O v^, a; ^ *a S *? o J^ Q ^ rt ^ W iiri M CO TO CO O "i M T 11 co r^mTM i-i Oco O | |jMl 5 2 M T m r> O IH co mo OOOOO^-wi-i'-i TCO MO O Too MO O co r^ M mco MOOT M M M M M CO CO rt rt rt li i> rt *j T1 4_i . *^ hr en g t rt o* 5 4| 1-1 M T 'D r^-oo O >-< M 2 OMCOTOOMCOT CO ^ O TOO DCO M OM OIDMCO TOr^ |rt 2"rt Si ti.2 PC >,2 O i-i M co T IDO r^co a 2 c'3 $TI O ^ CQ [L! i-i M M M coTTinin 6 n M CO T IDO I-CO 3 Feet to Metres. 5||||*||| d d o M' M' ci CAPAC ift r^ ID M o r^ T M OO ID M r^ cooo T O D M O Ooo oo i^* r* r^-O O a ir>oo w T r^ O c^O M H-I i-i M M M |1| Inches to milli- metres. M mr^-O M mr-O M ill OOO Oco oo co r^co r^ co O f""^ T i 1 co ID M COt^M TOO M IDOCO M M M M M M CO o o 5 ^ *;*C H *" H M c H a C 3 3 II II II II II II II II II W M CO T IDO t^CO O II II II II II * 4 I M ^ fc 4.8 15.080 18.096 23.04 H0.592 2.1909 .6869 4-9 15-394 18.857 24.01 117.649 2.2136 .6985 5.0 15.708 I9.635 25.00 125.000 2.2361 .7100 5- 1 I6.O22 20.428 26.01 132.651 2.2583 .7213 5-2 16.336 21.237 27.04 140.608 2 . 2804 7325 5-3 16.650 22.O62 28.09 148.877 2.3022 -7435 5-4 16.965 22.902 29.16 157.464 2.3238 -7544 5-5 17.279 23.758 30.25 166.375 2.3452 .7652 5.6 17-593 24.630 3I-36 I75.6I6 2.3664 .7758 5-7 17.907 25.518 32.49 185.193 2.3875 .7863 5-8 18.221 26.421 33-64 I95-II2 2.4083 .7967 5-9 18.535 27.340 34.81 205-379 2.4290 .8070 6.0 18.850 28.274 36.00 216.000 2-4495 .8171 6.1 19.164 29.225 37-21 226.981 2.4698 .8272 6.2 19.478 30.191 38.44 238.328 2.4900 8371 6-3 19.792 3LI73 39-69 250.047 2-5100 .8469 6.4 2O.I06 32.170 40.96 262 . 144 2.5298 .8566 6.5 6.6 6.7 20.420 20.735 21.049 33.183 34.212 35-257 42.25 43.56 44.89 274.625 287.496 300.763 2-5495 2.5691 2.5884 .8663 8758 .8852 6.8 6.9 21.363 21.677 36.317 37-393 46.24 47.61 314.432 328.509 2.6077 2.6268 .8945 .9038 7.0 21.991 38.485 49.00 343-000 2.6458 .9129 7-i 7.2 22.305 22.619 39-59 2 40.715 50.41 51.84 357- 9 11 373-248 2.6646 2.6833 .9220 .9310 / 7-3 7-4 22.934 23.248 41.854 43.008 53-29 54.76 389.017 405.224 2.7019 2 . 7203 9399 .9487 7-5 7-6 7-7 7-8 7-9 23.562 23.876 24.190 24-504 24-819 44.179 45-365 46.566 47.784 49.017 56.25 57.76 59-29 60.84 62.41 421.875 438.976 456.533 474-552 493-039 2.7386 2.7568 2.7749 2.7929 2.8107 9574 .9661 9747 .9832 .9916 8.0 8.1 8.2 8.3 8-4 25.133 25.447 25.761 26.075 26.389 50.266 51-53 52.810 54.106 55.4i8 64.00 65.61 67-24 68.89 70.56 512.000 53L44I 55L468 57L787 592.704 2.8284 2.8461 2.8636 2.8810 2.8983 2.OOOO 2.0083 2.0165 2.0247 2.0328 8-5 8.6 8-7 8.8 8.9 26 . 704 27.018 27.332 - 27.646 27.960 56.745 58.088 59-447 60.821 62.211 72.25 73-96 75.69 77-44 79.21 614-125 636.056 658.503 681.473 704.969 2.9155 2.9326 2.9496 2.9665 2.9833 2.0408 2.0488 2.0567 2.0646 2.0724 642 EXPERIMENTAL ENGINEERING. CONSTANTS Continu >d. tt nit * 4 3 3 *r h 9 28.274 63.617 81.00 729 . ooo 3 . oooo 2.0801 Q.I 28.588 65.039 82.81 753.571 3.0166 2.0878 9-2 28.903 66.476 84.64 778.688 3 0332 2.0954 9-3 29.217 67.929 86.49 804.357 3 0496 2.1029 9.4 29-53I 69.398 88.36 830.584 3.0659 2. IIO5 9-5 29.845 70.882 90.25 857.375 3.0822 2.IT79 9.6 30.159 72.382 92. 16 884.736 3.0984 2.1253 9-7 30.473 73.898 94.09 912.673 3-II45 2.1327 9-8 30.788 75-430 96.04 941.192 3-I305 2 . 1400 9.9 31.102 76.977 98.01 970.299 3.1464 2.1472 IO.O 3i.4r6 78.540 IOO.OO IOOO.OOO 3-1623 2.1544 10. I 31-730 80.119 102.01 1030.301 3-1780 2.l6l6 IO.2 32.044 81.713 104 . 04 1061.208 3-1937 2.1687 10.3 32.358 83.323 106.09 1092.727 3-2094 2.1757 10.4 32.673 84.949 108.16 1124.863 3.2249 2.1828 10.5 32.987 86.590 110.25 1157.625 3 2404 2.1897 10.6 33-301 88.247 112.36 1191 .016 3.2558 2. 1967 10.7 33-615 89.920 114.49 1225.043 3.2711 2.2O36 10.8 33.929 9! .609 116.64 1259.712 3-2863 2.2IO4 10.9 34-243 93.313 118.81 1295.029 3-3015 2.2172 II. 34-558 95-033 121 .OO 1331 .000 3-3166 2.2239 li. i 34-872 96 . 769 123.21 1367.631 3.33I7 2.2307 II. 2 35-186 98.520 125-44 1404.928 3.3466 2.2374 "3 35-500 IOO.29 127.69 1442.897 3o6i5 2.2441 11.4 35-814 102.07 129.96 1481.544 3-3764 2.2506 II. 5 36.128 I03.S 7 132.25 1520:875 3-3912 2.2572 II. 6 36.442 105.68 I34.56 1560.896 3-4059 2.2637 ?' 36.757 107.51 136.89 1601 .613 3-4205 2.2/O2 II. 8 37-07I 109.36 139.24 1643.032 3.4351 2.2766 11.9 37-385 - III. 22 141.61 1685.159 3-4496 2.2831 12.0 37.699 113. 10 144.00 1728.000 3-4641 2.2894 12. 1 38.013 114.99 146.41 1771.561 3.4785 2.2957 12.2 38.327 II6.QO 148.84 1815.848 3.4928 2.3O2I 12.3 38.642 118.82 151.29 1860.867 3 5071 2.3084 12.4 38.956 120.76 153.76 1906.624 3-5214 2.3146 12.5 39.270 122.72 156.25 1953.125 3-5355 2 . 3208 12.6 39-584 124.69 158.76 2000.376 3.5496 2.3270 12.7 39-898 126.68 I6I.29 2048.383 3.5637 2.3331 12.8 40 . 2 1 2 128.68 163.84 2097.152 3-5777 2.3392 12.9 40.527 130.70 166.41 2146.689 3-59!7 2-3453 13.0 40.841 132.73 169.00 2197.000 3 6056 2.3513 13-1 41.155 134.78 171.61 2248.091 3.6194 2-3573 13.2 41.469 136-85 174.24 2299.968 3.6332 1 2.3633 NUMERICAL CONSTANTS. CONSTANTS Continued. 643 m n-a *'J * ** Tn h 13-3 4L783 138.93 176.89 2352.637 3.6469 2.3693 13-4 42.097 141.03 I79-56 2406 . 104 3.6606 2.3752 13-5 42.412 143.14 182.25 2460.375 3.6742 2.3811 13-6 42.726 145-27 184.96 2515-456 3.6878 2.3870 13-7 43.040 147.41 187.69 2571.353 3.70I3 2.3928 13-8 43-?54 149-57 190.44 2628.072 3.7'48 2.3986 13-9 43-663 I5I-75 193-21 2685.619 3-7283 2.4044 14.0 43.982 153-94 196.00 2744.000 3.7417 2.4101 14.1 44 . 296 156.15 198.81 2803.221 3-7550 2.4159 14-2 44.611 158.37 201.64 2863.288 3-7683 2.4216 14-3 44-925 160.61 204.49 2924.207 3.7^15 2.4272 14.4 45-239 162.86 207.36 2985.984 3-7947 2.4329 14.5 45-553 165.13 210.25 3048.625 3.8079 2.4385 14.6 45.867 167.42 213. 16 3 i i 2 . i 36 3.8210 2.4441 14.7 46.181 169.72 216.09 3176.523 3.8341 2-4497 14.8 46 . 496 172.03 219.04 3241.792 3-847I 2-4552 14.9 46.810 174-37 222.01 3307.949 3.8600 2.4607 15.0 47.124 176.72 225.00 3375.000 3.8730 2.4662 I5- 1 47-438 179.08 228.01 3442.951 3.8859 2.4717 15.2 47-752 181.46 231.04 3511.808 3.8987 2.4772 15-3 15-4 48.066 48.381 183-85 186.27 234.09 037.16 3581.577 3652.264 3-9^5 3.9243 2.4825 2.4879 ISJ.C 48.695 188.69 240 25 3723.875 3-9370 2-4933 *O ' 3 15.6 15-7 15-8 15-9 49.009 49-323 49-637 49-951 191.13 193-59 196.07 198.56 243-36 246.49 249.64 252.81 3796.416 3869.893 3944-312 4019.679 3-9497 3-9623 3-9749 3-9875 2.4986 2.5039 2.5092 2.5146 16.0 16.1 16.2 16.3 16,4 50.265 50.580 50.894 51.208 51.522 201.06 203.58 206.12 208.67 211.24 256.00 259.21 262.44 265.69 268.96 4096.000 4173.281 4251.528 4330.747 4410.944 4.0000 4.0125 4.0249 4-0373 4.0497 2.5198 2.5251 2.5303 2.5355 2.5406 16.5 16.6 16.7 16.8 16.9 51-836 52.150 52.465 52.779 53-093 213-83 216.42 219.04 221.67 224.32 272.25 275-56 278.89 282.24 285-61 4492.125 4574.296 4657-463 4741.632 4826.809 4.0620 4-0743 4.0866 4.0988 4.1110 2.5458 2.5509 2.5561 2.5612 2.5663 17-0 17,1 17.2 17-3 17.4 53-407 53-721 54-035 54-350 54.664 226 98 229.66 132-35 235.06 237-79 289.00 292.41 295-84 299.29 302 76 4913.000 5000.211 5088.448 5177-717 5268.024 . . " - 4.1231 4.I352 4-M73 4-1593 4.1713 1 1 2.5713 2.5763 2.5813 2.5863 2.5913 n , m 644 EX PER [MEN TA L ENGINEERING. CONSTANTS Continued. n nit ,*! 4 * v n 3 V7* 17-5 54-978 240.53 306.25 5359-375 4-1833 2.5963 I 7 .6 55.292 243.29 309.76 545L776 4.1952 2.6012 17-7 55-606 246 . 06 3^3-29 5545-233 4.2071 2.6061 17-8 55.920 248.85 316.84 5639-752 4.2190 2.6109 17-9 56.235 251.65 320.41 5735-339 4.2308 2.6158 18.0 56.549 254-47 324.00 5832.000 4.2426 2.6207 18.1 56.863 257.30 327-61 5929.741 4-2544 2.6256 18.2 57-177 260.16 33L24 6028.568 4.2661 2 . 6304 18.3 57-491 263.02 334.89 6128.487 4-2778 2.6352 18.4 57.805 265.90 338.56 6229.504 4-2895 2 . 6401 18.5 58.119 268.80 342.25 6331.625 4-3012 2 . 6448 18.6 58.434 271.72 345-96 6434.856 4-3128 2-6495 18.7 58.748 274-65 349.69 6539-203 4-3243 2-6543 18.8 59-062 277-59 353-44 6644.672 4-3359 2.6590 18.9 59-376 280.55 357.21 6751.269 4-3474 2.6637 19.0 59-690 283.53 361.00 6859.000 4.3589 2.6684 19.1 60.004 286.52 364.81 6967.871 4.3703 2.6731 19-2 60.319 2S9.53 368 . 64 7077.888 4.3818 2.6777 19-3 60,633 29 2 .55 372.49 7189.057 4-3932 2.6824 19-4 60.947 295-59 376.36 7301-384 4.4045 2.686 9 19-5 6l.26l 298.65 380.25 74I4-875 4-4T59 2.6916 19.6 61.575 301.72 384-16 7529-536 4-4272 2 . 6962 19-7 61.889 304.81 388.09 7645-373 4.4385 2 . 7008 19.8 62.204 307.91 392.04 7/62.392 4.4497 2.7053 19.9 62.518 3II-03 396.01 7880.599 4 . 4609 2 . 7098 20.0 62.832 3T4.I6 400 . oo 8000.000 4.4721 2.7I.J4 20.1 63.146 317.31 404.01 "8120.601 4.4833 2.7189 2O. 2 63.460 320.47 408.04 8242.408 4-4944 2./234 20.3 63.774 323.66 412.09 8365.427 4-5055 2.7279 20.4 64.088 326 8 5 416,16 8489.664 4-5166 2.7324 20.5 64.403 330.06 420.25 8615.125 4.5277 2.7368 20. 6 64.717 333-29 424.36 8741.816 4.5387 2.7413 20.7 65.031 336.54 428.49 8869.743 4-5497 2-7457 20.8 65.345 339-80 432.64 8989.912 4 - 5607 2.7502 20.9 05.659 343-07 436.81 9129.329 4.57I6 2-7545 21.0 65.973 346.36 441.00 9261.000 4.5826 2.7589 21. 1 66.288 349.67 445.21 9393-931 4-5935 2.7633 21.2 66.602 352.99 449-44 9528.128 4-6043 2.7676 21.3 66.916 356.33 453.69 9663-597 4-6152 2.7720 21.4 67.230 359-68 457.96 9800.344 4.6260 2.7763 21.5 67.544 363-05 462.25 9938.375 4.6368 2 . 7806 21.6 67.858 366 . 44 466.56 10077.696 4.6476 2.7849 21.7 68.173 369-84 470.89 10218.313 4-6583 2.7893 JV UME RICA L CONS TA N TS. CONSTANTS Continued. 645 n nn 4 . " *- fc 21.8 68.487 373.25 475.24 10360.232 4.6690 2.7935 21.9 68.801 376.69 479.61 10503-459 4-6797 2.7978 22.0 69.115 380.13 484.00 10648.000 4.6904 2.8021 22-1 69.429 383.60 488.41 10793.861 4.7011 ! 2.8063 22.2 69-743 387-08 492.84 10941 .048 4.7117 2.8105 22-3 70.0^8 390.57 497-29 11089.567 4.7223 2.8147 22.4 70.372 394.08 501.76 11239.424 4-7329 2.8189 22.5 70.686 397-61 506.25 11390.625 4 7434 2.8231 22 .6 7 i . ooo 401.15 510.76 11543.176 4-7539 2.8273 22. 7 71.314 404.71 515 2 9 11697.083 4-7644 2.8314 22.8 71.268 408.28 519.84 11852.352 4-7749 2.8356 22-9 71.942 411.87 524-41 12008.989 4.7854 2-8397 23.0 23-1 23-2 23-3 23-4 72-257 72.571 72.885 73-199 73-5I3 4I5-48 419.10 422.73 4-26-39 430.05 529.00 533-61 538.24 542-89 547.56 12167.000 12326.391 12487.168 12649.337 12812.904 4-7953 4.8062 4.8166 4.8270 4.8373 2.8438 2.8479 2.8521 2.8562 2.8603 23.7 23.8 23-9 73-827 74.142 74.456 74-770 75-084 433 74 437-44 441 - 1 5 444.88 448.63 552.25 556.96 561.69 566.44 571.21 12977.875 13144.256 13312.053 13481.272 13651.919 4-8477 4.8580 4.8683 4.8785 4.8888 2.8643 2.8684 2.8724 2.8765 2.8805 g 39 576.00 13824.000 4.8990 2.8845 24 o 24.1 24.2 24.3 24.4 75-712 76.027 76.341 76.655 456.17 459-96 463.77 . 467.60 580.81 585.64 590.49 595.36 13997.521 14172.488 14348.907 14526.784 4.9092 4-9I93 4.9295 4-9396 2.8885 2.8925 2.8965 2.9004 24.5 24.6 24.7 24-8 24-9 76.969 77-283 77-597 77.911 78.226 471.44 475-29 479.16 483-05 486.96 600.25 . 605 . 16 610.09 615.04 620.01 14706.125 14886.936 15069.223 15252.992 15438.249 4-9497 4-9598 4-9699 4-9799 4.9899 2.9044 2.0083 2.9123 2.9162 2 . 9201 25.0 25.1 25.2 25-3 25.4 78.540 78.854 79.168 79.482 79.796 490-87 494.81 498.76 502.73 506.71 625.00 630.01 635-04 640.09 645-16 15625.000 15813.251 16003.008 1^194.277 16387.064 S.ODOO 5.0099 5.0299 5-0398 2.9241 2.9279 2.9318 2.9356 2-9395 25-5 25.6 25-7 25-8 25-9 80.111 80.425 80.739 81.053 81.367 510.71 514-72 5i8.75 522.79 526.85 650.25 655-36 660.49 665.64 670.81 16581.375 16777.216 16974.593 17173-512 17373-979 . 5-0497 5.0596 5.0695 5-0793 5-0892 . 2-9434 2-9472 2.9510 2-9549 2.9586 ^ 646 EXPERIMEN TA L ENGINEERING. CONSTANTS Continued. ft nir * 2 4 * * h 26.0 81.681 530-93 676 . oo 17576.000 5.0990 2.9624 26.1 81.996 535-02 681.21 I7779-58I 5.1088 2.9662 26.2 82.310 539- r 3 686.44 17984-728 C-IiSS 2.9701 26.3 82.624 543.25 691 .69 18191.447 5.1283 2.9738 26.4 82.938 547-39 696.96 18399.744 5.12^0 2.9776 26.5 83.252 551-55 702.25 18609.625 5.1478 2.9814 26.6 83.566 555-72 707.56 18821.096 5-1575 2.9851 26.7 83.881 559-90 712.89 19034.163 5.1672 2.9888 26.8 84.195 564.10 718.24 19248.832 .1768 2.9926 26.9 84.509 568.32 723.61 19465 . 109 5.1865 2.9963 27.0 84.82^ 572.56 729.00 19683.000 5-1962 3.0000 27-1 85.137 576.8o 734.41 19902.511 5-2057 3.0037 27.2 85-451 581.07 739-84 20123.648 5.2153 3.0074 27-3 85.765 585.35 745.29 20346.417 5.2249 3.0111 27.4 86.080 589.65 750.76 20570.824 5-2345 3-oi47 27-5 86.394 593-96 756.25 20796.875 5 2440 3.0184 27.6 86.708 598.29 761.76 21024.576 5-2535 3.0221 27.7 87.022 602 . 63 767.29 21253-933 5.2630 3.0257 27.8 87.336 606 . 99 772.84 21484.952 5-2725 3.0293 27.9 87.650 611.36 778.41 21717.639 5.2820 3.0330 28.0 87.965 615.75 784.00 21952.000 5-2915 3-0366 28.1 88.279 620.16 789.61 22188.041 5 3009 3.0402 28.2 83.593 624.58 795-24 2242^.768 5-3103 3 0438 28.3 88.907 629.02 800.89 22 65.187 5.3197 3-0474 28.4 89.221 633.47 806.56 22906.304 5-3291 3.0510 28.5 89-535 637.94 812.25 23149.125 5.3385 3-0546 28.6 89.850 642.42 817.96 23393-656 5.3478 3-0581 28.7 90 164 646.93 823.69 23639.903 5-3572 3-0617 28.8 90.478 651-44 829.44 23887.872 5-3665 3.0652 28.9 90.792 655.97 835-21 24137.569 5-3758 3.0688 29.0 91.106' 660.52 841.00 24389.000 5-3852 3-0723 29.1 91.420 665.08 846.81 24642.171 5 3944 3-0758 29.2 91-735 669.66 852.64 24897.088 5-4037 3-0794 29-3 92.049 674.26 858.49 25153.757 5-4129 3.0829 29-4 92.363 678.87 864.36 25412.184 5-4221 3.0864 29 5 92.677 683.49 870.25 25672.375 5-4313 3.0899 29.6 92.991 688.13 876.16 25934.336 5-4405 3-0934 29.7 93.305 692.79 882.09 26198.073 5-4497 3.0968 29.8 93.619 697.47 888.04 26463.592 5.4589 3.1003 29.9 93-934 702.15 894.01 26730.899 5. .4680 3-1038 30.0 94.248 706.86 goo. oo 27OOO.OOO 5.4772 3.1072 30.1 94-562 711.58 906.01 27270.901 5.4863 3-1107 30.2 94.876 716.32 912.04 27543.608 5-4954 3.1141 N U ME RICA L CONS TA N TS. CONSTANTS Continued. 647 tin 4 ifl m* * h 30.3 95.190 721.07 918.09 27818.127 5-5045 3.1176 30-4 95 - 505 725.83 924.16 28094.464 5.5136 3.1210 30.5 95.819 730.62 930.25 28372.625 5.5226 3.1244 30.6 96.133 735-42 936.36 28652.616 5.5317 3.1278 30-7 96.447 740.23 942.49 28934.443 5.5407 3-1312 30.8 96.761 745.06 948.64 29218.112 5-5497 3.1346 30-9 97-075 749.91 954.81 29503.629 5.5587 3-1380 3i.o 97.339 754-77 961.00 29701.000 5-5678 3.I4U 3 1 -! 97.704 759.65 967.21 30080.231 5.5767 3.1448 31-2 98.018 764-54 973-44 30371.328 5-5857 3-1481 3^-3 98.332 769-45 979-69 30664 . 297 5 5946 3-1515 31-4 98.646 774-37 985-96 30959.144 5-6035 3-1548 3i-5 31.6 98 . 960 99.274 779-31 784.27 992.25 998.56 31255.875 31554.496 5-6124 5.6213 3-1582 3.1615 3 r -7 99.588 789.24 1004.89 31855.013 5-6302 3-1648 31.8 99 93 794-23 1011.24 32157.432 5.6391 3.1681 3i-9 IOO.22 799 23 1017-61 32461.759 5-6480 3.I7I5 32.0 100.53 804.25 1024.00 32768.000 5-6569 3.I748 32.1 32.2 32.3 32-4 100.85 101 . 16 101.47 101.79 809.28 8i4-33 819.40 824.48 1030.41 1036.84 1043.29 1049.76 33076.161 33386.248 33698.267 34012.224 5-6656 5.6745 5-6833 5.6921 3.1814 3-1847 3.1880 32-5 32.6 32.7 32.8 32.9 102.10 102.42 102.73 103.04 103.36 829.58 834.69 839.82 844.96 850.12 1056.25 1062.76 1069.29 1075.84 1082.41 34328.125 34645.976 34965.783 35287.552 35611.289 5 7008 5-7096 5.7i83 5-7271 5.7358 S-W 3-1945 3.1978 3.2010 3-2043 33-0 33-2 33-3 33-4 103.67 103-99 104.30 104.62 104.93 855.30 860.49 865.70 870.92 876.16 1089.00 1095.61 1102.24 1108.89 1115.56 35937.000 36264.691 36594 368 36926.037 37259.704 5-7446 5.7532 5-7619 5-7706 5.7792 3-2075 3.2:08 3-2140 3-2172 3-2204 33-5 33-6 33.7 33-8 33-9 105.24 105.56 105.87 106.19 106.50 881.41 886.68 891.97 897-27 902 . 59 1122.25 1128.96 1135.69 1142.44 1149.21 37595-375 37933.056 38272.753 38614-472 38958.219 5-7379 5.7965 5.8051 5-8i37 5-8223 3.2237 3.2269 3-2301 3-2332 3-2364 34-0 34-i 34-2 34-3 34-4 106.81 107.13 107.44 107.76 108.07 907.92 913-27 918.63 924.01 929.41 1156.00 1162.81 1169.64 1176.49 1183.36 39304.000 39651-821 40001.688 40353-607 40707-584 5.8310 5.8395 5.8480 5.8566 5.8651 3.2396 3-2428 3.2460 3.2491 3 2522 648 EXPERIMENTAL ENGINEERING. CONSTANTS Continued. n nit ^t 4 ** h 34-5 108.38 934.82 1190.25 41063.625 5-873U 3-2554 34-6 108.70 940.25 II97.I6 41421.736 5.8821 3.2586 34-7 IOg.01 945.69 1204.09 41781.923 5 . 8906 3.2617 34-8 109.33 951.15 1 2 1 1 . 04 42144.192 5.8991 3.2648 34-9 109.64 956.62 I2I8.0I 42508.549 5.9076 3.2679 35-0 109 . 96 962 . I I I225.OO 42875.000 5-9161 3.2710 35-1 110.27 967.62 1232.01 43243-551 5-9245 3.2742 35-2 110.58 973.H 1239.04 43614.208 5.9329 3-2773 35-3 no. go Q78.68 1246.09 43986.977 5 9413 3-2804 35-4 III .21 984.23 1253,16 44361.864 5-9497 3-2835 35-5 in. 53 989.80 1260.25 44738.875 5.9581 3.2866 35-6 111.84 995.38 1267.36 45118.016 5.9665 3.2897 35-7 112.15 1000.98 1274.49 45499- 293 5-9749 3.2927 35-8 112.47 1006 . 60 1281.64 45882.712 5.9833 3.2958 35-9 112.78 1012.23 I288.8I 46268.279 5.9916 3.2989 36.0 113.10 1017.88 1296.00 46656 ooo 6 . oooo 3-30r9 36.1 113.41 1023.54 1303.21 47045.881 6.0083 3-3050 36.2 113-73 IO2g.22 1310.44 47437-928 6.0166 3.3080 36.3 114.04 1034.91 1317.69 47832.147 6.0249 3-3III 36-4 H4.35 1040.62 I324-96 48228.544 6.0332 3.3I4* 39-5 114.67 1046.35 1332.25 48627.125 6.0415 3.3I7I *6.6 114.98 1052.09 I339.56 4g027.8g6 6.0497 3.3202 36 7 II5-30 1057.84 1346.89 49430.863 6.0580 3.3232 36.8 115.61 1063.62 1354.24 49836.032 6.0663 3.3262 36.9 115.92 1069.41 I36l.6l 50243.409 6.0745 3.3292 37-0 116.24 1075.21 1369.00 50653.000 6.0827 3-3322 37-1 U6-55 1081.03 1376.41 5 i 064 .811 6 . 0909 3-3352 37-2 116.87 1086.87 1383.84 51478.848 6.0991 3.3382 37-3 r: 7 - 18 1092.72 1391 -2g 51895.117 6.1073 3-3412 37-4 117.50 1098.58 1398.76 52313.624 6.H55 3-3442 37-5 117.81 1104.47 1406.25 52734-375 6.1237 3-3472 37-6 118.12 1110.36 1413.76 53I57-376 6.1318 3.3501 37-7 118.44 1116.28 1421 .29 53582.633 6.1400 3-3531 37-8 118.75 1122.21 1428.84 54010.152 6.1481 3-356r 37-9 119.07 1128.15 1436.41 54439.939 6.1563 3-3590 38.0 119-38 II34-H 1444.00 54872.000 6.1644 3-3620 38.1 119.69 1140.09 1451-61 55306.341 6.1725 3 3649 38.2 120.01 1146.08 1459-24 55742.968 6 . i 806 3.3679 38.3 I2O.32 1152.09 1466.89 56181.887 6.1887 3.3703 38-4 120.64 1158.12 1474.56 56623.104 6.1967 3-3737 38-5 120.95 1164.16 1482.25 57066.625 6.2048 3.3767 38.6 121.27 II7O.2I 1489.96 57512.456 6.2I2O 3.3T96 38-7 121.58 1176.28 1497.69 57960.603 6.22O9 3-3825 NUMERICAL CONSTANTS. CONSTANTS Continued, 649 n nit *? 4 * Vn V~n 38.8 121.89 1182.37 1505.44 58411.072 6.2289 3.3854 38.9 122.21 II88.47 1513.21 58863.869 6.2370 3.3883 . O O -! M M W \r> ir> in in \n M M M M (-1 1809.56 l8l7.II 1824.67 1832.25 1839.84 2304.00 23I3.6I 2323.24 2332.89 2342.56 110592.000 111284.641 111980.168 112678.587 "3379-94 6.9282 6-9354 6.9426 6.9498 6.9570 3.6342 3-6368 3 6393 3.6418 3.6443 48.5 48.6 152.37 152.68 1847.45 1855.08 2352.25 2361.96 114084. 125 114791.256 6.9642 6.9714 3-6468 3 - 6493 48.7 48.8 153-00 I53-3I 1862.72 1870.38 2371.69 2381.44 115501.303 116214.272 6.9785 6.9857 3-6518 3-6543 48-9 153-62 1878.05 2391.21 116930.169 6.9928 3-6568 49.0 153-94 1885.74 2401.00 117649.000 7.0000 3.6593 49.1 I54-25 I893-45 24I0.8I 118370.771 7.0071 3.6618 49-2 154.57 1901.17 2420.64 119095.488 7-0143 3.6643 49-3 154-88 1908.90 2430.49 119823.157 7.0214 3.6668 49.4 155.19 1916.65 2440.36 120553.784 7.0285 3.6692 49-5 155-51 1924.42 2450.25 121287.375 7-0356 3-6717 49.6 155-82 1932.21 2460.16 122023.936 7 0427 3-6742 49-7 156.14 1940.00 2470.09 122763.473 7.0498 3-6767 49.8 156.45 1947.82 2480.04 123505.992 7.0569 3-6791 49-9 156.77 I955-65 249O.OI 124251.499 7.0640 3.6816 50.0 157-08 I963-50 25OO.OO 125000.000 7.0711 3.6840 51.0 I6O.22 2042 . 82 26OI.OO 132651.000 7.1414 3.7084 52.0 163.36 2123.72 27O4.OO 140608.000 7.2111 3.7325 53-0 166.50 2206.19 28O9.OO 148877.000 7.2801 3-: : "3 54-0 169.64 229O.22 2916.00 157464.000 7.3485 3.7798 55-0 172.78 2375.83 3025.00 166375.000 7.4162 3.8030 56.0 175 93 2463.01 3136.00 175616.000 7.4833 3.8259 57-0 I7Q-07 2551 76 3249.00 185193.000 7.5498 3.8485 58.0 182.21 2642.08 3364.00 19511.2.000 7-6158 3.8709 59-o 185-35 2733-^7 348I.OO 205379.000 7.6811 3.8930 60.0 188.49 2827.44 3600.00 216000.000 7.7460 3-9M9 61.0 191.63 2922.47 3721.00 226981.000 7.8102 ; 62.0 194-77 3019.07 3844.00 238328.000 7.8740 3.9579 63.0 197.92 3117.25 3969.00 2500.47.000 7-93! 3 -97'' i 64.0 201 .06 3216.99 4096 . oo 262144.000 8.0000 4.0000 65.0 204 . 2O 3318.31 4225.00 274625.000 8.0623 4.0207 66.0 207.34 3421 .20 4356.00 287496.000 8.124) 4.0412 6 5 2 EXPERIMEN TA L ENGINEERIN G. CONSTANTS Continued. n nir .? 3 v- 3_ 4 67.0 210.48 3525.66 4489 oo 300763.000 8.1854 4.0615 68.0 213.63 3031.69 4624.00 314432.000 8.2462 4.0817 69.0 216.77 3739.29 4761 .00 328509.000 8.3066 4.IOI6 70.0 219.9! 3848.46 4900 . oo 343000.000 8.3666 4.I2I3 71.0 223.05 3959.20 5041.00 357911.000 8.4261 4 . 1408 72.0 226. 19 4071.51 5184.00 373248.000 8.4853 4.1602 73-o 229.33 4185.39 5329.00 389017.000 8.5440 4-1793 74.0 232.47 4300.85 5476.00 405224.000 8 . 6023 4.1983 235-62 4417.87 5625.00 421875.000 8.6603 4.2172 76.0 238.76 4536.47 5776.00 438976.000 8.7178 77.0 241.90 4656.63 5929 oo 456533.000 8.7750 4-2543 78.0 245-04 4778.37 6084 . oo 474552.000 8. 318 4.2727 79-0 248.18 4901.68 6241 .00 493039.000 8.SS82 4-2908 80.0 25L32 5026.56 6 po . oo 512000.000 8-9443 4-3089 81.0 254-47 5I53-OI 6561.00 531441.000 9.0000 4.3267 82.0 257-6I 5281.03 6724.00 551368.000 9-0554 4-3445 83.0 260.75 54IO.62 6889.00 571787.000 9.1104 4.3621 84.0 263.89 554I-78 7056.00 592704.000 9.1652 4-3795 85.0 267.03 5674.50 7225.00 614125.000 9-" I 95 4-3968 86.0 270.17 5808.81 7396.00 636056.000 9.2736 4.4140 87.0 273-32 5944.69 7569.00 658503.000 4.4310 8S.o 276.46 6082.13 7744-00 681472.000 9.3808 4.4480 89.0 279.60 6221 .13 7921.00 704969.000 9-4340 4.4647 90.0 282.74 6361.74 8100.00 729000.000 9.4868 4.4814 91.0 285.88 6503.89 8281.00 753571.000 9-5394 4.4979 92.0 289.02 6647.62 8464 . oo 778688.000 9-59'7 4.5144 93-O 292.17 6792.92 8649 . oo 804357.000 9-6437 4.5307 94-o 295.31 6939.78' 8836.00 830584.000 9.6954 4-5468 95.o 298.45 7088.23 9025.00 857375.000 9-7468 4.5629 96.0 301.59 7233.24 9216.00 884736.000 9.7980 4-5789 97-o 304 - 73 7389.83 9409 . oo 912673.000 9.8489 4-5947 98.0 307-87 7542.98 9604 . oo 941192.000 9.8995 4.6104 99.0 311.02 7697-68 9801.00 970299.000 9-9499 4.6261 100. 314-16 7854.00 IOOOO.OO IOOOOOO.OOO 10.0000 4.6416 LOGARITHMS OF NUMBERS. 653 III. LOGARITHMS OF NUMBERS. 654 EXPERIMEN TA L ENGINEERING. LOGARITHMS OF NUMBERS Continued. No, o 1 2 3 4 5 6 7 8 9 55 7404 7412 7419 7427 7435 7443 745i 7459 7466 7474 56 7482 7490 7497 7505 75*3 7520 7528 7536 7543 755 1 57 7559 7566 7574 7582 7589 7597 7604 7612 -7619 7627 58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 59 7709 7716 7723 773i 7738 7745 7752 7760 7767 7774 60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 62 63 7924 7993 793i 8000 7938 8007 7945 8014 795 2 8021. 7959 8028 7966 8035 7973 8041 7980 8048 7987 8055 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 66 3i95 8202 8209 8215 8222 8228 8235 8241 8248 8254 67 8261 8267 8274 8280 8287 8293. .8299 8306 8312 8319 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 838-2 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 70 8451 8457 8463 8470. 8476 8482 8488 8494 8500 8506 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 73 8633 8639* 8645 8651 8657 8663 8669 8675 8681 8686 74 8692 8698 8704 8710 8716 8722 8727 8733 ^8739 8745 75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 79 8976 8982 8987 8993 8998 9004 9009 9015' 9020 9025 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 81 9085 9090 9096 9101 9106 9112 9117. 9122 9128 9133 82 9138 9H3 9149 9154 9159 9165 9170 9175 9180 9186 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 85 9294 9299 9304 9309 93*5 9320 9325 ^9330 9335 9340 86 9345 935 9355 9360 9365 937 9375 9380 9385 9390 87 9395 9400 9405 9410 94i5 9420 9425 9430 9435 9440 88 9445 945 9455 9460 9465 9469 9474 9479 9484 9489 89 9494 9499 95/>4 959/ 95*3 95'8 9523 9528 9533 9538 go 9542 '9547 9552 9557 9562 9566 9571 9576 958i 9586 gi 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 93 9685 9689 9694 9699 973 9708 97*3 9717 9722 9727 94 9731 9736 974i 9745 975 9754 9759 9763 9768 9773 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 97 9868 9872 9877 9881 9886 9890 9894 .9899 9903' 9908 98 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 999 6 No, O 1 2 3 4 5 6 7 8 9 LOGARITHMIC FUNCTIONS OF ANGLES. 655 IV. LOGARITHMIC FUNCTIONS OF ANGLES. Angle. Sin. D.I'. Cos. D. 1'. Tan. D. 1'. Cot. 0' ^-rOO / 0.0000 00 00 90 0' o icy 20' o 30' D 40' o 5 c/ 74637 .7648 .9408 8.0658 .1627 30I.I 1 76.0 125.0 96.9 70.2 .0000 .0000 .0000 .0000 .0000 O .0 .0 .0 .1 74637 .7648 .9409 8.0658 .1627 30I.I 176.1 124.9 96.9 7Q.2 2.5363 .2352 .0591 1.9342 8373 89 50* 89 40' 89 30' 89 20' 89 lo' 1 0' 8.2419 66".Q 9-9999 .0 8.2419 67.O 1.7581 89 0' 1 10' 1 20' 1 3 0' 1 4 0' 1 50' .3088 .3668 4179 .4637 .5050 58.0 5 I.I 45-8 4r-3. -27.8 '9999 9999 . -9999 ' 19998 .9998 .0 .0 .1 .0 .1 .3089 .3669 .4181 4638 5053 58.0 '51-2 45-7 '41-5 37.8 .6911 .6331 .5819 .5362 .4947 88 50* 88 40' 88 3C/ 88 20' 88 10' 2 0' 8.5428 -74. 8 9.9997 o 8.5431 34.8 1.4569 88 0' 2 JO' 2 20' 2 30' 2 40' 2 50' 577 6 .6097 .6397 .6677 .6940 32-1 30.0. 28.0 . 26.3 24 8 9997 .9996 .9996 9995 9995 .1 .0 .1 . .0 .1 5779 .6101 .6401 .6682 .6945 ,32-2 30.0 . 28.1 26.3 24.9 .4221 .3899 3599 33'8 3055 87 50' 87 40' 87 30' 87 2' 75 o 20 r 75 10' 15 0' 9-4I30 9.9849 9.4281 .)* o-57 J 9 75 0' Cos. D.I'. Sin. D.I'. Cot, D. 1'. Tail. Angle. LOGARITHMIC FUNCTIONS OF ANGLES. LOGARITHMIC FUNCTIONS OF ANGLES Continued. 6 5 7 Angle. Sin. D. 1'. Cos. D. 1'. Tan. D. 1', Cot. 15 O' 9.4130 A 7 9-9849" .? 9.4281 r.o ' 0-5719 75 (X 15 10' 15 20' 15 30' 15 40' 15 50' 41.77 4223 .4269 43 * 4 4359. 4-6 4.6 4-5- 4-5 ..9846 9843 .9839 ,,9836 .9832. 3 4 3 4 4331 '438! 443 4479 4527 5- 4-9 4-9. 4.8 48 5669 '5 6l 9 5570 5521. 5473 74 so' 74 40' 7430' 74 .20' 74 10' 16 Q' 9.4403 4.4. A. A. 9.9828 ** 94575 4.7 0-5425 74 0' 16 10' I 6 20' i 6 30' i 6 40' i 6 50' 4447 449 * 4533 457 6 .4618 4-4. 4.2 4-3. 4.2 4i .9825 .9821 9817 .9814 .9810 4 4 '3- 4 .4622 .4669 -.4716 .4762 -.48^8 4-7 4-7. 4-6 4.6 4 C .5378 5331 .5284 5238 5 ! 92 73 50' 73 40' 73 30 7 73 20' 73 10' 17 0' 9-4659 9,9806 4'~ 94853! A-e 0.5147 73 0' 17 10' 1 7 '20' 17 30' 17 40' 17 50' .4700' .4741 .4781 .4821 .4861 .1 4-1. 4,0 4.4. 4.0 '.9802 .9798 9794 .9790 .9786 .,4 4 4 4 ' ' .4898 4943 4987 -5031 575 4-5 44 44 4.4 4-"? .5102 557 5013 .4969 4925 72 50' 72 40' 72 30' 72 2C/ 72 lo 7 18 O' 9.4900 o-y 9.9782 A 9.5118 4..1 0.4882 72 -97 02 .9697 .9692 '.9687 .9682 .9677 4 5 5 5 5 5 .c 9-5842 .5879 59^7 5954 W .6028 3-7 3-8 3-7 3-7 3-7 3-6 0.4158 .4121 .4083 .4046 .4009 3972 69 0' 68 50' 68 4 c/ 68 30' 68 2 .6720 J 3280 64 50' 25 20' ^313 7 .9561 6 .6752 3-2 3248 64 40' 25 30' .6340 1:1 9555 5 .6785 3 3215 64 30' 25 40' .6366 --> f\ 9549 .6817 3183 64 20' 250 50' .6392 2 6 9543 .6 .6850 3-3 1.2 315 64 10' 26 0' 9.6418 26 9-9537 .7 9.6882 i.2 0.3118 64 O' 26 10' .6444 ? ft 953 .6914 .3086 63 50' 26 20' .6470 9524 ' .6946 .2 3054 63 40' 26 30' 6495 2 'r .9518 C. .6977 3- 1 3023 63 30' 26 40' .6521 2.6 .9512 .7009 .3-2 .2991 63 20' 26 50' .6546 2 -5 2 4 955 7 .6 .7040 - 1 1 2 .2960 63 10' 27 o' 9.6570 o c 9-9499 7 9.7072 ?.I 0.2928 63 0' 27 lo' 6 595 9492 (\ 7 I0 3 2897 62 50' 270 20' .6620 - 2 -5 .9486 7*34 .2866 62 40' 27 30' .6644 2 -4 9479 Y - 1 2835 62 30' .6668 2.4 9473 1 .7196 J< 2804 62 20' 27 50' .6692 2 -4 2 4. .9466 7 .7 .7226 3- 7.1 2774 62 16' 28 0' 9.6716 24. 9-9459 .6 9-7257 0.2743 62 0' 28 16' .6740 9453 .7287 2713 61 50' 28 .20' .6763 2-3 .9446 73^7 3' .2683 61 40' 28 30' .6787 2-4 9439 7 7348 3- 1 .2652 61 30' 28 40' .6810 2-3 9432 7 7378 .2622 6i c 20' 28 50' .6833 2 -3 2-3 .9425 7 .7 .7408 3- 1.O .2592 61 10' 29 O' 9.6856 2.2 9.9418 .7 9-7438 2.Q 0.2562 Gl 0' 290 10' .6878, .9411 .7467 2533 60 50' 2 9 20' .6901 2-3 .9404 7 7497 3- 2503 60 40' 29 30' .6923 2.~ 9397 7 .7526 2.9 2474 60 30' 29^ 4 0' .6946 2-3 9390 7556 2444 60 20' 2 9 50' .6968 2 2 .9383 8 .7585 2-9 2 Q 2415 60 to' 30 0' 9.6990 9-9375 9.7614 0.2386 60 0' Cos. D.I'. .Sin. D. 1'. Cot. D. 1 . Tan. Angle. LOGARITHMIC FUNCTIONS OF ANGLES. LOGARITHMIC FUNCTIONS OF ANGLES Continued. 659 Angle. Sin. D.I'. Cos. D.I'. Tan. D. 1'. Cot. 30 0' 9.6990 2 2 9-9375 7 9.7614 j n 0.2386 60 Of 30 10' 3 20' 30 30' 3 4 0' 30 50 A .7012 7033 .7055 7076 .7097 2.1 2.2 2.1 2.1 2 I .9368 .9361 9353 .9346 .9338 :1 I .7 .7644 7673 . .7701 7730 7759 O'^ 2.9 2.8 2.9 2.9 2 Q 2356 .2327 .2299 .2270 .2241 9 5 () .071-1 49 40' 4 30' .8125 1.4 .8810 93 I 5 ? 6 .0685 49 30' 40 40' .8140 .8800 9341 .0659 49 20' 40 50' 8i55 5 I 4. .8789 I.I .9366 26 .0634 49 io' 41 0' 9.8169 " 9.8778 I I 9.9392 2.C 0.0608 49 0' 41 io' .8184 .8767 .9417 .0583 48 S ' 41 20' .8198 1.4 .8756 9443 ~: 0557 48 40' 41 30' .8213 5 8745 .9468 | .0532 48 30' 41 40' .8227 1.4 8733 9494 . . .0506 48 20' .8241 1.4 .8722 I.I ~9S*9 2-5 .0481 48 io' 42 0' 9-8255 1.4 9.8711 1.2 9-9544 2.6 0.0456 48 0' 42 lo 7 .8269 .8699 '957 .0430 47 50' 42 20' .8283 1.4 .8688 9595 2-5 .0405 47 40' 42 30' .8297 1.4 .8676 .9621 2.0 .0379 47 & 42 40' .8311 I; 4 .8665 .9646 2-5 0354 47 20' 42 50' .8324 1.4 .8653 1.2 .9671 5 2.6 .0329 47 io' 43 0' 9-8338 I.I 9.8641 9.9697 0.0303 47 0' 43 io' 8351 .8629 .9722 .0278 46 50' 43 20' .8365 1.4 .8618 9747 jl .0253 46 40' 43 30' .8378 .8606 T *> .9772 2 -5 ? Ct 46 30' 43 40' 43 5' .8391 .8405 1.4 .8594 .8582 r.2 .9798 9823 2-5 .0202 .0177 4 6 C 20' 46 io' 44 O' 9.8418 J I. -I 9.8569 3 I 2 9.9848 2.5 26 0.0152 46 0' 44 io' 44 20' .8431 .8444 p .'3 8557 8545 1.2 .9874 .9899 2-5 .0126 .OIOI 45 5' 45 40' 44 30' 8457 .'3 8S32 '3 .9924 2-5 .0076 45 30' 44 40' .8469 .8520 .9949 2-5 ? 6 .0051 45 20' 44 50 7 .8482 3 .8507 p 1.2 9975 .0025 45 'P' 45 0' 9.8495 9.8495 o.oooo 0.0000 45 0' Cos. D.I'. Sin. D. 1' Cot, D. 1' Tan. Angle. NATURAL FUNCTIONS OF ANGLES. 661 V. NATURAL FUNCTIONS OF ANGLES. A. Sin. Cos. A. sin. Cos. j A. Sin. Co 3H5 3173 .9502 .9492 9483 SoJ 40- 30 40; 50' .06395 .06685 .9980 .9978 20' 10' 10' 20' 1937 19^5 .9811' .9805 50; 40 40' 50' 3201 _3i 8 . 9474 _l 9 _i^i 10' 4 .06976 .9976 86 L 30' 1994 9799 19 C J^! 9455 71 rrJ 10' 20' .07266 O7C C6 9974 QQ7I So; 4 4 U 50' 2051 9793 9787 10' 10' 20' 3283 331' .9446 943 6 i>, 4 30' W.).> w .07846 yy/ m .9969 SO' 12 2079 .9781 78<- 30j 3338 .9426 3 S 40' So' '.08136 .08426 19967- .9964 20' 10' 10' 20' 2108 2136 9775 .9769 50; 40' 40' 5 0' JJi _3_3_9_.> 94 '7 _j947_ 10' TftC 5 10' 20' 30' 4 0' 5 0' .08716 7xjoo5~ '09295 .09585 .09874 .10164 .9962, 9959 9957 9954 995 ' .9948 85^ 50' 40' 30; 20' 10' c ic t 50' 13 10' 20' ., r 2164 2193 2221 "2250 22 7 8 .2306 2'"M 973 9757 .97_5p_ 9744 .9737 973 .9724 30' 20'- 10' 77 C 50; 40 30' 20" 10' 20' 30; 40' 50' 21 3420 3448 3475 35 2 3529 3557 3584 9397 9387 9377 93 6 7 935^ 9346 933 4 V $ $ 10' G9 6 10' 20' 3 0' 10453 .10742 .11031 .11320 9945 .9942 9939 993 6 5 oJ 40' 30' ? 50' 14: **j* 23^3 2 1 9 -I .2419 .9717 .9710 ^9703 20' 10' 76 C 10' 20' io' .3611 .3^38 3^5 93 2 5 .93 '5 934 5 /' 40 30 -> o r .11609 i r8r>^ .993 2 20' 10' 10' -><-/ .2447 JAIjf . .9696 0680 50' 40' Sf 39 a 37 '9 9283 10' 5 ~4/ u c/ 000 77^6 0272 8 C 7 .12187 .9925 83 X 2^4 f ^n' 51^ co' 10' 20' 30' .12476 .12764 .13053 .9922 .9918 .9914 5' 40' 30' 40' 50' 15 .*>.? 2 .2560 .2 5 8S .9674 .966^ 9^59 10' 75 IC/ 20' ^ .3773 %z & 2 7 925 .9239 5, 40 ^ Cos. -- Sin. . A. i Cos. Sin. i ' A. ^ Cos. i Sin. i 662 EXPERIMENTAL ENGINEERING. NATURAL FUNCTIONS OF ANGLES Continued. A. Sin. Cos. A. Sin. Cos. A. Sin. Cos. 30' .3827 .9239 30' 30 .5000 .8660 60 y* .6088 7934 30; 40 50' Sit .9228 .9216 20' 10' 10' 20' 5025 55 .8646 .8631 s ; 40' 4 o' 5 o' .6lII .6134 .7916 .7898 20' 10' 23 .3907 .9205 67 30' 5075 .8616 30' 38 6157 .7880 52 10' 20' 3934 .3961 .9194 .9182 50' 40' 40 50' .5100 5125 .8601 8587 20' 10' 10' 2C y .6io .6202 .7862 .7844 50;- 40' 36; .3987 .9171 30' 31 SIS .8572 59 30' .6225 .7826 3 o; 40' 50' .4014 .4041 9'59 .9147 20' 10' 10' 20' 5'75 .5200 8557 .8542 5 oJ 40' 40' 50' .6248 .6271 .7808 ^7790 20' ID' 24 .4067 .9135 66 30; 5225 .8526 30' 39 .6293 .7771 51 to' 20' .4094 .4120 .9124 .9112 5 ; 40' 40 50' 5250 5275 .8511 .8496 20' 10' 10' 20' .6316 .6^8 7753 7735 50; 40' 30; .4147 .9100 3 o; 32 5 2 99 .8480 58 C 3 0' .6361 .7716 30' 4 0' 5' .4173 .4200 .9088 9075 20' 10' 10' 20' .5324 .^48 .8465 .8450 50' 40' 40' 50' t>3*3 .6406 .7698 .7679 20' 10' 25 .4226 .9063 65 30; 5373 * 43 i 30' 40 .6428 .7660 50 10' 20' 4253 .4279 .9051 .9038 50; 40' 40' 5 U 10' 20' "3476 .3508 2.9042 2.8770 2.8502 71 C 50; 40 40' 50' .07870 .08163 .08456 12.7062 12.2505 11.8262 g io' 12 10' 20' .2126 ^156 .2186 4.7046 4.6382 4-5736 78^ 50' 40' 5 0' 3541 3574 2.8239 ^.798o 2.7725 30 20' 10' 7/jC 5 .08749 11.4301 85 U .2217 4.5 10 7 30 1Q> 20 3_64p fiZlZ. 5 T MOOV IG' 20' 30' .09042 '09335 .09629 11.0594 10.7119 10.38^4 50' 40' ^o' 4 / 50' 13 .2247 .2278 .2309 4-4494 3897 10' 77 IO' 20' 30; 373 3700 3739 2-7 2 - J> 2.6985 2,6746 40 7 g 40' .09923 .10216 10.0780 9.7882 20' io' io' 20' .2339 237 4-2747 4-2193 50; 40 4 50' >|O 377 2 3_8.5 " >"tf ->"n 2.6279 10' 69 C 6 .10510 9.5I44 8-1 " 2 5826 Cf/ io' on' .10805 o ooo 5' 4-O 4 5' .24j2 .2462 4.0611 10' 20 7 W- .3906 2.5605 40' 30' 4 0' 50' 7O u . 1 1 099 ."394 .11688 ."983, T ~a.-Q 8*5555 30 20' 10 83 14 C io' 2d 7(7 i?J 2555 .2586 4.0108 3-8667 7(i 50; 40' 30' 40' 5 0' 22 3939 3973 .4006 74040 2.5380 2-5172 2.4960 2-475 \o' 68 .12270 AOf 3 8208 ? o' i 2 jlCA CQ* io' 2O f 3 0' .12574 .12869 -1 3.^5 7-953 c 7.770, 7-595' 5 40 3 4 1 50' 15 C . _U 1 / .264* ' 7^67^ 3.7760 T732i IO 7 75 20' *L .410 2-434 2.414 $. Cot. . Tan. . A. - - - Cot. Tan. __ A. Cot. Tan. " 664 EXPERIMENTAL ENGINEERING. NATURAL FUNCTIONS OF ANGLES Continued. A. Tan. Cot. A. Tan. Cot. A. Tan. Cot. 30' .4142 2.4142 30' 30 5774 I.732I 60 3; .7673 I.332 30' 4 0' 5 0' .4176 .4210 2-3945 2-375 20' 10' 10' 20' .5812 S8Si 1.7205 1.7090 50; 40' 4 o' 5 o' .7720 7766 1.2954 1.2876 20' iof 23 4245 2-3559 67 3 OJ .5890 1.6977 3oJ 38 .7813 1.2799 52 10' 20' .4279 43 i 4 2.3369 2.3183 50' 40' 4 50' 5930 5969 1.6864 I-6753 20' 10' 10' 20 7 .7860 .7907 1.2721 1.2647 5 : 40' 30' 4348 2.2998 30' 31 .6009 1.6643 59 3; 7954 1.2572 3 o' 40 50' 4383 .4417 2.2817 2.2637 20' 10' 10' 20' .6048 .6088 1.6534 1 .6426 5; 4 o' 40 5' ^8050 1.2497 1.2423 20' 10' 24 445 2 2.2460 66 30; .6128 1.6319 30' 39 .8098 1,2349 51 10' 20' .4487 .4522 2.2286 2.2113 50' 40' 4 0' 5 0' .6168 .6208 I.62I2 1.6107 20' 10' 10' 20' .8146 Sips 1.2276 1.2203 50' 40' 30' 4557 2.1943 3o; 32 .6249 1.6003 58 3; .8243 1.2131 3o' 4 cy 50' 4592 .4628 2.1775 2.1609 20' 10' 10' 20' .6289 .6^0 1.5900 I-5798 50; 40' 4 o' 5 o' .8292 8342 1.2059 1.1988 20' 10' 25 .4663 2.1445 65 30' 6371 I-5697 3' 40 .8391 1.1918 SOP 10' 20' .4699 4734 2.1283 2.1123 50' 40' 40 5^ .6412 .6453 I -5597 1-5497 20' 10' 10' 20' .8441 .8 4 QI 1.1847 1.1778 5 c/ 40' 30; .4770 2.0965 30' 33 .6494 1-5399 57 3' 8541 1.1708 30; 4 0' 50' .4806 .4841 2.0809 2-0655 20' 10' 10' 20' .6536 6 S77 i-530i 1.5204 5 ! 4 o' 40 7 5' .8591 .8642 1.1640 i- I 57i 20' 10' 26 C .4877 2.0503 64 30; .6619 i.$io8 3 ; 41 8693 1.1504 49 id' 20' 4913 495 2-0353 2.0204 5 oJ 40' 4 0' 5 0' .6661 .6703 1.5013 1.4919 20' 10' 10' 20' .8744 .8 7 Q6 1.1436 1.1369 50' 40' 30' .4986 2.0057 30' 34 .6745 1.4826 56 3; 8847 1.1303 3' 4 0' 5 0' .5022 5059 1.9912 1.9768 20' 10' 10' 20' .6787 .6830 M733 1.4641 5 ! 4 o' 40' 50' .8899 .8952 1.1237 1.1171 20' 10' 27 5095 1.9626 63 30' 6873 1-455 3 o' 42 .9004 1.1106 48 10' 20' 5132 .5169 1.9486 1-9347 5; 40' 40' & .6916 6959 1.4460 1437 20' 10' 10' 20' 957 .9110 1.1041 1.0977 50; 40' 30; .5206 1.9210 3 o; 35 .7002 1.4281 55 3' .9163 1.0913 3; 4 0' 5 0' .5243 .5280 1.9074 1.8940 20' 10' 10' 20' .7046 .7089 I4I93 1.4106 50' 40' 4' 5' .9217 .9271 1.0850 1.0786 20' 10' 28 5317 1.8807 62 30' 7133 1.4019 3; 43 .9325 1.0724 47 \d 20' 5354 5392 1.8676 1.8546 5 oJ 40' 40 7 50' .7177 .7221 1-3934 1,3848 20' 10' 10' 20' 93 80 9435 i. 066 f 1.0599 50; 4' 30' 5430 1.8418 30' 36 .7265 1-3764 54 3; 949 1.0538 3; 40' 5 0' 5467 5505 1.8291 . 1.8165 20' 10' 10' 20 7 7310 7355 i .3680 I -3597 s ; 40' 40' 5' 9545 9601 1.0477 1.0416 20' 10' 29 5543 1.8040 61 30; .7400 I -35 I 4 3' 44 9657 '0355 46 10' 20' 5581 .5619 1.7917 1.7796 50' 40' 4 0' 50' 7445 .7490 1.3432 i.335i 26' 10' 10' 20' 97*3 977 1.0295 i .0235 5; 4' 3 ; .5658 r-7675 30' 37 7536 1.3270 53 & .9827 1.0176 30' 4 o' 5 o' .5696 5735 I-7556 1-7437 20' 10' 10' 20' .7581 .7627 1.3190 1.31 ii 50; 40' 40' 5 0' .9884 9942 i.oi 17 1.0058 20' 10' 30 5774 1.7321 60 3 0' 7673 1.3032 3' 45 I.OOOO I.OOOO 45 Cot. Tan. A. Cot. Tan. A. Cot. Tan. A. COEFFICIENTS, STRENGTH OF MATERIALS. 66 5 VI. TABLE OF COEFFICIENTS, STRENGTH OF MATERIALS. Ultimate Strength. Tons per Square Inch. Moduli. Tons per Sq. Inch. Tension. Com- pression. Shearing. Elasticity. Rig. T C .9 E I 5*-ioi 7 14 15-20 27-29 24 22 19 2/-29 25 19-24 25-50 26-32 30-45 40-65 So 72 70 150 10-14 15-16 28 8-13 22 11-23 15-26 2-3 7-10 2 0-9 ii-3i 4 4-7 4-6 4-7 25-65 42 36-58 60-75 2O ' 35 5 3 4 2i 2-4 4 3* afr* I*-2i ii-3 i-6 9-13 II ] 18-22 1 ~ 1 S. J ? 10-14 i \ 5000 to 6000 12,000 to 13,000 12,000 L to 13,000 J 13,000 7000 8000 5500 6400 4500-6000 6000 5500 1000 800 600 950 750 650 ..... 1300 to 2500 5000 5000 to 5200 2800 1500 22OO 1700 2400 Wrought-iron Finest Low- ( with grain., moor plates:"} across ' Bridge-iron: ) ^ ss "' " Wire Steel Copper Wire Timber Stone From Vol. XXII.,' Encyc. Britannica. 666 EXPERIMENTAL ENGINEERING. VII. TEST OF CAST ALUMINIUM BRONZES. [Made by J. E. KRESS in 1891 at Sibley College Laboratories.] Composition. Strength per Sq. Inch. CO 6 ,c o q 1 Moduli. oo No. Material. J i 1 E 'a5 _C la' "o S c -a c . 3 S. . ,c O G 3-3 re o 1) |3 o ^ 1) 4J 11= ^J 3 11 II J 11 'S 3 s o cr u w P w S I Al. brass. . . . p ? 45,186 62,722 7.5 5-0 20.8 11,859,900 2 Al. bronze. . IO 90 26,281 46,570 5-7 7-83 12.5 5,696,800 3 5 95 8,473 33,730 39-i 46.3 .66 12,838,000 4 80 20 12,018 18,400 26 9.4 13 17,180,000 5 90 IO 6,856 17,066 54 7-7 56 9,203,600 6 92 8 5,242 14,154 50 1.36 -36 8,593,000 7 94 6 3,094 H.9I3 58 2.02 .12 9,253,000 8 96 4 2,977 16,567 25 3.48 . 13 7,539,300 9 98 2 3.048 13,323 25 3-54 17 5,990,900 10 Aluminum. . 99 2,234 9.776 2-5 3-54 .14 5,990,900 ii " 99-3 i, 612 6.4 4.17 .06 5,385,500 12 Al. bronze. . 10.5 89.5 28,102 72^064 7-1 8.9 10.6 6,900,700 13 5 95 6,795 29,132 21.5 34-i 45 10,214,000 14 2 98 3,448 24,986 14.6 .07 17,828,400 15 I 99 2,565 16,123 10.5 22.2 .08 9,461,900 16 7 93 13,650 40,794 18.1 28.6 9 9-537,900 17 Pure copper. IOO 2,297 16,508 17.0 I8. 5 1. 10 5,945,000 Nos. 10 and n were commercially pure Al, with composition about as follows: Al, 97 to 99; silicon, graphitic, o.i to i.o; silicon combined, 0.9 to 2. 8; iron, 0.04 to 0.2 per cent. WOODEN PILLARS AND BEAMS. 66 7 VIII. WOODEN PILLARS. Experiment of Prof. Lanza on pillars 2 to 14 feet long, 6| to 10$ inches in diameter, in some cases slightly tapered at the top. In all cases they failed by crushing. ULTIMATE RESISTANCE TO COMPRESSION. Pounds per Square Inch. Kind of Timber. Maximum. Minimum. Mean. White Oak. . . . d l8 3 30-7 .140 46,168 37-0 230 42,100 33-2 320 30,380 15-6 IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES. 669 X. IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES. Specific Gravity. Water, i. Specific Heat. Water, i. Absorbing and Radiat- ng Power of Bodies in Jnits of Heat per Square r oot for Dif- ference of i. Conducting Power in Jnits of Heat per bquare Foot of Sur- face with Difference of 1. Weight in founds Melting Points, tegrwi Fahr. Meta\s from 32 to 212 ,6l tO 2. 65 6.712 9.823 8: 7 88 7.5 7.744 19.258 n. 3 52 13.598 8.800 16.000 10.474 7-834 7.291 7.191 3.784 3-156 2.240 2.686 2.650 .86 55 44 1-43 I.OO 2.89 2.03 9 ,88 .0006 .87 1. 000 .922 .00122 .00127 .000089 .00198 .0508 .0308 0939 .092 .1298 .1138 .0324 .0314 0333 .1086 .0324 .056 .1165 .0502 0953 .2149 .2174 .2 .2694 .2158 3 .2415 .2411 .203 .1977 .2O26 .6588 .416 i .000 504 .238 .2412 3.2936 .9210 Per cu. in 0.0956 0.2428 0-3533 0.2930 0.3179 0.2707 0.2801 0.6965 0.4106 0.4918 0.3183 0.5787 0.3788 0.2916 0.2637 0.26 Per cu. ft. 174.0 197.0 140.0 168.0 165.0 & 33 5 127.0 57-S 55.0 .050 54-37 62.35 57-5 .0807 .0892 00559 1234 810 2: g *t/> I Q h i "o > if .y s Ji !b I VOLUME. Ajisusp umuitxBtn jo saniBasdaiai IB J3}EA\ psiipstp jo iqSi3M i^nba jo aumioA O} THESIS JO SOiniOA JO OUB^ - jfcssssa&j* ?I^E , o 45? (N M 133J Diqno u; uiB3is jo pnnod B JQ z>or C i^lllliil IS! 'C m moo m -^- c*j i spunod ui C OJB3}S jo looj oiqno B jo iqSis^ co O >- QUANTITIES OF HEAT. UOUBJOdBA3 JO S7IUn UI ' O z SAOqB UOireJodBA3 JO }E3tJ IBJOX ^ W O^ tx ^ w PvOO Ex -^ W c> ^-oo - ro ir> t^ ON - oo o?oo"oo f *ii 'a a c ll^ \ irivD -^t* -^-vO "t 1 O *^OO ON O ^* t- VO ^-GO O\ t^v moO m moo O 1 1 NO NC NO ^r N N ? NO tvoo m O looo- M ro m t^ ON O 11 It ? . O O O-O-O^^ONOO* O oo NO t> vo ON O O O M 1-1 HI 111 u 'C a HJT ON S^ Sw OO" R. tx in N o NO oo mvo m 1 1 ; ?f? Pit Ooo *>< row rom ON O o" ro t^ N m * 5 C^NO NO m t-. N N Si J 00 00 OO & 5 M &% !? ^^VO sssjSap it3qu3jqB j 'a-imeaadmaj. - rOvO '-^ r^j O> ON ro N SO " re N Ovo (MOO ro S ^ino r^ t^ooco o 00 O ONNO r^ W tn ON ON O O O n N ^ (?) i? qoui ajnnbs jad spunod ui 'UUUIOKA e SAoqe djnssaj^ H w ro -^ mxo l^OO j^ .... ^ 1 PROPERTIES OF SATURATED STEAM. 6?g oo oo N Ooo oo Ix n o 10 M o>oo S8? ON 00 00 t-*vo vo 10 -^- *$ i I (^ 5^ O c?^* ft o^^ $t- IiO to lOvo VO VO vo vo tx. t^ O O O O O O CM o (N M \o N CO U1VO VO 1000 M vO CO HI MOON! txiomOI^^MCO O M IH i w ro -^- 10 tovo t^ r^c ?t-| ?t-i :.? ! s? W M M M , O M w O O-O v & 8. 5V 8> VO 10 - M > > > < * O CO IO ' Cx N vo CO cooo r^ >-< ( O W IO t t^ O t- 1 CO lOVO CO O vo oo moo r^ ro o 10 fio vOQ -*f^Q f1>n<^ <^ ^J-v5 t.3O O "i C1 ro f* IO >O 10 IOVO vo vO VO \O v ' t-CO 00 M cssi .l-.^^cS-dlS^; 0000000000000000 o-co \o' 10 4 PO N M 6 e> OOOOOOOOOOOO CO 00 03 CO ji ;o 00 09 00 OO 00 00 i 00 OO 10 I 13 M fO -4-^0 00 6 H n ct w w N ror ^ WC4WWWNW , w M 68o EXPERIMENTAL ENGINEERING. spanod ui 'uinnoBA B aAoqB amssajj - 10 mvO ***w*a M w ro ^ mO t^ t^* fx lx tx t* VOLUME. Aiisuap uiniuiXBiu jo ajruBjadmai IB JSJBM pauusip jo ;qi3M iBnbs jo amhioA oj uiBajs jo oun[OA jo OIIB^ - ^^ txc.ocvovooo woo torn slll^ * *-^-* m roro core oiqna ui oreads jo punod B JQ 5 !N O ^^RSS-RJcfffS- ga.oTRvgVS spunod ui l mB3js jo }ooj oiqnD B jo jqSp^V is HI O- tx tx QUANTITIES OF HEAT. uot^BJodBAS jo situn ui ' O z S-8S? 5^ ^ ^^ 5. 5^ ? S> lo IO\O \O VO Cx JN, $ "rt H 1 a e *o c "rt O-O^ A or// 8.8.K. IO s OvvO O l^ CO ^ w VO O N -^-VO t^OO O^ O> OOO 1000 - * 1^ rovo N gl{|| *o e^ Ifj? o w o ONOO t^vo fOQ l^rot^O W O^* fill Igs P APuorE !!! M-VD oo ov o tx rroo N o O^O roO r^-i-^i r^-^-O < R C S. < ^ < S. C R < ?. S. ( ^. S S 1^00 OO s O "n ^, ||1 S % Q. aoaam VO (T) O O'OO O> ^ ^OO N vo oo ro 1000 O >o oooooooooooooooooooo CO 00 CO CC CO OO o^2^o Ji-S^o" = w v N l' s !|i v>< ft N W S- ^ v8 2 ^vo Svo^ 5o ro <*- 10 loves vo vo vo vo vo vo 1 ?; to ?5-cH ro 4- lovd fvco saaaSap jiaquajqBjj 'aaniBjaduiaj, - IB ir ^"vo O 1 ro 5- 5 f^ O^ * vo t-> t^.oo oo oo oo oo oo t^ 00 O rnvo O * C^vo b C^ libilt ipui sjBnbs aod spunod UJ 'uitmaBA 9AoqB aansssjjj - ^ -"***8 R M PROPERTIES OF SATURATED STEAM. 68 1 S 2 T ? ST'S 682 EXPERIMENTAL ENGINEERING. qoni 3JBtibs jsd spunod ui 'ranrioBA B 3Aoqn ajnssgjj ^ 'oOOvO r-W^wo.veooO ftftRS^MS, ! MHMMHHHMMM VOLUMB. Ajisuap uinai!XBaj jo ajnjB4adm3j IB 431BM pannsip jo jqSiaM jBnba jo auihtoA o; uiBajs jo aranioA jo OUB'JJ ^ &M |>ff{J2<3o jjog S1HHS8 NNNNNNNOWN otqnD ui tnrais jo punod B JQ s !} 00 g N_ >JOO C^VO 0_ to c g R?h r, 3 . -------- spunod ui 'ureais jo ^ooj oiqno B jo ?n.3i9M. =4 IK vo oo 5 8* cf t ro tovo"oo V c- NNMNN'Sp)N N S x S^ O ^-oo w in o ro t - CJ roi/i\O f^C^C QUANTITIES OF HEAT. aouBJodBAs jo siiun ut ' O z SAoqB uoiiBJodeAa jo jBaq IBJOX Iff ^^ &&88 '0^*0^ 8 o c"^ *o c "a M ||V4 A or// Ssi O ON t~- ^ O, mvo OO O< C?> 10 m ct M ooo vo * N * ro 10 t-xoo N "*-vo oo ^a^S $> JOVC'M o" S 10 10 10 oooooooooooooooooooo' |l ! 4- -4- -4- vo ^K < Soo" : 5-^^S comNNMwOOOO VCM^VCVCVO^D^C'^C OOCOOOOOOOOOOOOO OO 00 00 oooooocoooooooooooco w~ A Pu or E Iff T- io io IOVO vo vo t^. tt t-- C T'O (^5*0 O N 00 00 OO oooooooooooooocooooo oooooooooooococo ||l S o a n . fc M , B1W%SS imS V* lis ^km t^ r^-vo vo 10 10 v- 4* ODOOOOOOOOOOOCOO t^ tx tx t> tx c^ 1^ t-- Pit \ S?fg8 8Si?j?f SSS s.fj,s.s.s^{rj? 2 2 S rocowcorocororococr, saaaSap ipqaajqBjj 'aanj^jaduiax K. HIS ar^Hiss t5?*sa sis K W N CO TJ- ^- ir> ir>vo t 1 ^ t^.oo oo s O M H qoui ajBnbs jad spunod ui 'cannoBA B aAoqe sjnssaaj "i M a>o M d PO -^f lOO t^OO ON O M Nf ^,Ovo.xOO PROPERTIES OF SATURATED STEAM. 683 g o o o so t^oo Os 8 P-,88,8 :1 ro if- T CO Os roso oo oo lotxrnioqooosrr-. ooo t-oo oo O OS O>00 00 00 Os O M N so M rooo so ^*-wsoooo^rN.oioio 00 ro o-so 10 I ioso t^ 0> (Si 10 O- fTOO m tvso rt- ro CSI I 1-0 O*OO 00 txsO SO IO IO tx N 00 t^ <3 SO o a-. 10 v>.- S 5 ^ ^ 2*% {oscf wr^roforn i^S 1 ^ * IOSO t t.00 Os " SO 00 N ?SO 00 Si 10 *- 10 10 10 10 ioso so so ^llhff rjlflifl > m * h O w -* >oso r-x t^ t^ N. M ro T \ftO^Ot^OO^t^(> M M M (SI so 10 r^* ro t-ctso O< Qs Os O> Os ^ k 'O'O 2 ioscTo'c^ *S> 5-* b Os (O Os t~ 10 I lOScf 00 >i aoaSaoooao o?o?o?oo'oo oo oo oo oo co 00 00 0?OtTo? OOOOOOOOOOOOOOOOOOOO 5*2 8 ?y? 3 M rOOO >O vO tx O * rOOO >O vO tx M oo o ^- cs H v, u I ^ *=? o?oo oooooooooooo t^ t^ \O to M O t- O> O Os fO i-i N IOOO * o-oooo o> 1000 moo ^.*-'odsd rodoo IOP f^ P.NOO mOsM-0 l r os Os m CO m ^- ^ 10 ro co ro co ro o O * n w so H O O 00 **O W W tnoo" - oiob 684 EXPERIMENTAL ENGINEERING. XVII. ENTROPY OF THE LIQUID. (Page 315.) Absolute Steam Pressure. Entropy of the Liquid. Absolute Steam Pressure. Entropy of the Liquid. P e / e I 0.1329 65 0.4337 IO 0.2842 70 0.4402 15 0.3143 75 0.4464 20 0.3363 80 0.4522 25 0-3539 85 0-4579 30 0.3685 90 0.4633 35 0.3811 95 0.4686 40 0.3921 100 0-4733 45 0.4020 105 0.4780 5 0.4109 no 0.4826 55 0.4191 115 0.4869 60 0.4267 120 0.4911 XVIII. HYPERBOLIC NAPERIAN LOGARITHMS. N. Log. N. Log. N. Log. N. Log. N. Logr. .00 0.0000 30 .8329 3-60 .2809 4.90 .5892 6.40 .8563 .05 0.0488 35 .8544 3-65 .2947 4-95 5994 6.50 .8718 .10 0.0953 .40 8755 3-7 3083 5.00 .6094 6.60 .8871 15 0.1398 45 .8961 3-75 .3218 5-05 .6194 6.70 .9021 .20 0.1823 50 .9163 3-8o 3350 5.10 .6292 6.80 .9169 25 0.2231 55 9361 3.85 .3481 5-15 .6390 6.90 93*5 3 0.2624 .60 9555 3-9 .3610 5-20 .6487 7.00 9459 35 0.3001 65 .9746 3-95 3737 5-25 .6582 7.20 9741 .40 0.3365 9933 4.00 3863 5-30 .6677 7.40 .0015 45 0.3716 75 .0116 4-05 3987 5-35 .6771 7.60 .0281 So 0.4055 .80 .0296 4.10 .4110 5-40 .6864 7.80 0541 55 0.4383 85 0473 4- *5 .4231 5-45 6956 8 oo .0794 .60 0.4700 .90 .0647 4.20 435* 5-50 .7047 8.25 . IIO2 65 0.5008 95 .0818 4-25 .4469 5-55 7138 8.50 .1401 .70 0.5306 3-00 .0986 4-3 .4586 5-6o .7228 8-75 .1691 ; 8 7 o 0.5596 0.5878 3-05 3.10 '154 4-35 4.40 .4701 .4816 5.65 5-70 73^7 745 9.00 9-25 .1972 .2246 .85 0.6152 3-5 M74 4-45 .4929 5-75 9-50 25'3 .90 0.6419 3-20 .1632 4-50 .5041 5-80 7579 9-75 2773 95 0.6678 3-25 .1787 4-55 5I5 1 5.85 .7664 IO.OO .3026 .00 0.6931 3-30 1939 4.60 5261 5-9 7750 II .00 3979 05 0.7178 3-35 .2090 4-65 5369 5-95 .7834 12.00 4849 .10 0.7419 3-40 2238 4.70 5476 6.00 .7918 13.00 5649 15 0.7655 3-45 2384 4-75 5581 6.10 .8083 14.00 .6391 .20 0.7885 35 .2528 4.80 . 5686 6.20 .8245 15.00 .7081 25 0.8109 3-55 .2669 4-85 -S7QO 6.30 .8405 16.00 .7726 DISCHARGE OF STEAM. 685 XIX. DISCHARGE OF STEAM IN POUNDS PER HOUR CALCULATED BY NAPIER'S FORMULA Absolute Pounds of Steam. Pressure. Pounds. Diameter of Orifice 3*2 inch. Diameter of Orifice ^ inch. Diameter of Orjficc * inch. I 0.039 0.158 0.631 2 0.079 0.316 1.262 3 O.II8 0-473 1.893 4 0.158 0.631 2-524 5 0.197 0.789 3 155 6 0.237 0.947 3.786 7 0.276 1.104 4-417 8 0.3*5 1.262 5.048 9 0-354 1.420 56SO 10 0-395 1.578 6.31 r 20 0.789 3-155 12.622 30 I.I83 4-733 iS-937 40 1.578 6.311 25-244 50 1.972 7.880 31.556 60 2.367 9.467 37-867 70 2.761 11.045 44.178 So 3.156 12.623 50.488 go 3-550 14.200 56.800 100 3-947 15.778 63."5 XX< PER CENT OF WATER AND STEAM EXHAUSTING INTO ATMOSPHERE. BY THROTTLING CALORIMETER. (Per cent of moisture.) Tempt, in Calorimeter. Gauge-pressure on M.iin Steam-pipe. Degrees Fahr. 40 45 5 55 60 65 7 75 80 0233 .0253 .0271 .0290 .0307 .0322 .0338 354 .0368 220 225 230 0207 0181 0154 0128 .0227 .0201 .0173 .OI47 .0245 .0218 .0192 .0165 .0263 .0237 .0210 .0184 .0280 0253 .0227 .0200 .0296 .0269 .O242 .0215 .0311 .0284 .0-57 .0230 .0327 .0300 0--73 .0246 .0346 .0313 :%, 240 245 OIO2 .0076 .0049 .OI22 .OOQS .0069 .0139 .0112 .0086 .0157 .0130 .0104 .0173 .0147 .OI2O .0189 .0162 0'35 .0204 .0177 0150 .0219 .0192 .0165 :Z .0179 .0023 .0042 .0059 .0077 .0093 .0108 .0123 .0,38 .0152 '53 260 .OOO5 .OOl6 .0033 .0051 .0066 .008l .0090 .0111 .0125 265 .0030 .0010 .0006 .0024 .0040 0055 .0069 .0084 .oogS .0057 .0037 .0020 .OOO2 .0013 0028 .0042 .00=17 - .0083 .0063- .0047 .oo?9 .0013 .OOOI .0015 .C0 3 o .0043 280 285 .OIO9 .0136 .0089 .0116 ! .0073- .OIOO .0056 0082 .0067 0026 .0053- .OOIt .0038- .0003 .0024- .00:5 .ouia Diff. i Fahr ... .00052 .00052 1 .00053 .00053 .00053 .00054 .00054 .00054 .00054 ^ ^nd'lltiplied by the value of the latent heat w ,li give the decree - \o o 10 o uvo 10 o i- ON *- o 'too rn f> MOO N tx t. M vo (*) N N - - OOO OSOO tx tvvo VOIO Ul^^mro NM-MO SIS!? ' s t> * SO' in **100 f^OO ^ 00 X w 8. ^ ". O^O w in * *r < OOO *O>*Of1 ffm 688 EXPERIMENTAL ENGINEERING. XXII. (Page 414.) COMPOSITION OF VARIOUS FUELS OF THE UNITED STATES. C. H. O. tr. s. Mois- ture. Ash. Spec. Grav. 78 6 o 8 14 8 Rhode Island " . 8s- 8 IO.5 3 7 1 85 Massachusetts " 92 o 83 i 6.0 7 8 2.O 9 I 1.78 Welsh " g, 2 6 7 80 S 8 "5 75-8 2O. 2 ^9 4 ^8. 8 i 8 j ,. 41 28 o .1 t< 52.0 39 -o 62 6 58.2 Illinois and Indiana (Cannel) Bituminous 36.6 3 9 48 4 48 8 2 8 12. O 1.45 56.5 42 6 Virginia ^ 18.6 California and Oregon Lignite 3.9 13.7 0.9 i .5 16.7 13.2 i. 32 STATE. COAL. KIND OF COAL. Per Cent, of Ash. THEORETICAL VALUE. In Heat Units. In Pounds of Water Evaporated. Anthracite ... 3-49 6.13 2.90 15.02 6.50 10.77 5.00 5-60 9-50 2.75 2.00 14.80 7 .00 5 .20 5-6o 5-50 2.50 5-66 6.00 13.98 5.00 9-25 4-5 4-5 3-40 14,199 13-535 14,221 i3,M3 13,368 i3,i55 14,021 14.265 I2i3 2 4 i4,39t 15,198 13.360 9,326 13.021; I3,i 2 3 12,6^9 13,588 14,146 13,097 12,226 9,215 13,562 13,866 12,962 ",55* 20,746 14.70 14.01 14.72 13.60 13-84 13.62 14.51 14.76 12.75 14.89 16.76 'I:S 13.48 13-58 13.10 14.38 14.64 13-56 12.65 9-54 14.04 14-35 13-41 11.96 21.47 It U H M (i .. .. Semi-bitutnaious t ( Stone's Gas N Youghiogheny M Brown Kentucky Caking it u Illinois Bureau County ti T /I* Block ncnana Caking , Cannel Maryland Arkansas Lignite t< Texas t it asnington. . . . nsy ni COMPOSITION OF VARIOUS FUELS. 689 ANALYSES OF ASH. Specific Grav. Color of Ash. Silica. Alum- ina. Oxide Iron. Lime. nesia. Loss. Acids S.&P. Pennsylvania Anthracite Bituminous \V>'sh Anthracite 559 372 Reddish Buff. Gray. 45-6 76.0 42.75 31.00 A.A. 8 9-43 2.60 1.41 o-33 0.48 0.40 .... Scotch Bituminous .26 37-6 52.0 r g 3-7 i.i 2 6 vST XXIII. FOR REDUCING BAROMETRIC OBSERVATIONS TO THE FREEZING-POINT. Reading of Ba- rometer. Correction at 10 Fahr. Correction at 40 Fahr. Correction at 70 Fahr. Correction at 90 Fahr. Inches. Inches. Inches. Inches. Inches. -f 27 0.045 0.028 0.100 0.148 27.5 0.046 0.028 0.102 O.I5I 28.0 0.047 0.029 o. 104 0.153 28.5 0.048 0.029 o. 1 06 0.156 29 0.049 0.030 0.108 0.159 29.5 0.050 0.030 o. 109 0.162 30.0 0.051 0.031 O.III 0.164 30-5 0.052 0.032 O.II3 0.167 31-0 0.053 0.032 O.II5 0.170 690 EXPERIMENTAL ENGINEERING. XXIV. HORSE-POWER PER POUND MEAN PRESSURE. Diameterof Cylinder. Inches. SPEED OF PISTON IN FEET PER MINUTE. 100 240 800 350 400 450 500 550 COO 650 .750 4 .038 .091 .114 133 152 .171 .19 .209 .228 247 .285 .048 "5 .144 .168 .192 .216 .24 .264 .288 312 .360 5 .06 .144 .18 .21 .24 27 30 33 .36 '39 450 5* .072 -173 .216 .252 .288 324 36 396 432 .468 540 6 .086 .205 .256 299 342 385 .428 .471 555 .641 6* 7 7* .102 .116 134 245 .279 .321 307 .348 .401 391 .408 .468 534 .464 .512 ; 563 .6 4/ 735 :S .699 .802 .698 .756 .869 .800 874 .002 8 365 -456 532 .608 .685 .761 837 .912 .989 .121 8i .172 4 J 3 .516 .602 .688 774 .86 .946 .032 .118 .290 9 .192 .462 577 .674 .770 .866 963 059 154 251 -444 9* .215 SIS .644 751 859 .966 1.074 .181 .288 395 .610 IO 238 57 1 .714 .833 952 1.071 1.190 309 .428 547 .78.5 10} .262 63 .787 .919 1.050 1.181 1 -3 X 3 444 575 .706 .969" II .288 .691 .864 1. 008 1.152 1.296 1.44 584 .872 .160 11} 314 754 943 I.I 1.257 1.414 1-572 .729 .886 43 -357 12 342 .820 1.025 I -195 1.366 1.540 1.708 .880 .050 .222 i .564 13 .402 964 1.206 1.407 i. 608 1.809 2.OI .211 .412 .613 ! 3.015 14 IS .466 535 1.119 1.285 '398 i. 606 1.631 1.873 1.864 2.131 2.097 2.409 2.331 2.677 .564 945 797 .212 3.029 i 3.495 3-479 ! 4.004 16 .609 1.461 1.827 2.131 2.436 2-741 3-45 3-349 -654 3.958 4.567 J7 .685 1.643 2.054 2.396 2-739 3.081 3-424 3.766 .108 4.450 5.135 18 1.849 2.312 2.697 3-083 3-468 3-854 4-239 .624 5.009 j 5.780 19 ^859 2.061 2-577 3 006 3.436 3-865 4-295 4-724 -154 5.583 6.442 20 21 952 .049 2.292 2.518 2-855 3.148 3-331 3.672 3.807 4.285 4.722 4-759 5-247 5-234 5-771 5-731 6.296 6.186 7.138 6.820 7.869 22 2 3 152 259 2.764 3.021 3-776 4.031 4-405 4.607 5-035 5-183 5.664 5-759 6.294 6-334 6.923 6.911 7-552 7.486 8.638 8.181 9.44 24 370 3.289 4.111 4-797 5.482 6. 167 6-853 7.538 8.223 8.908 10.279 25 .487 3-569 4.461 5-105 5.948 6.692 7-436 8.179 8-923 9.566 in. 053 26 .609 3.861 4.826 5-630 6 -435 7-239 8.044 8.848 9.652 10.456 12.065 27 -733 4-159 5- I 99 6.066 6.932 7-799 8.666 9-532 10 399 11.265 12.998 28 .865 4-477 5-596 6.529 7.462 8-395 9-328 10.261 11.193 12.125 13.991 29 .002 4.805 6.006 7.007 8.008 9.009 10.01 II. Oil 12.012 13.013 15.015 3 .142 5-I4 1 6.426 7-497 8.568 9.639 10.71 11.781 12.852 13.923 16.065 31 .288 5.486 6.865 8.001 9.144 10.287 "43 12-573 13.716 14.866 17.145 .436 5.846 7-308 8.526 9-744 10.962 12. 18 I3-398 14.616 15.834 18.270 33 590 6.216 7.770 9.065 10.360 11.655 12.959 I4-245 15-54 16.835 19.425 34 .746 6-59 8.238 9.611 10.984 I2 -357 13-73 15-103 16.476 17.849 20.595 35 .914 6-993 8-742 10.199 11.656 13-113 14-57 16.027 17.484 18.941 21.855 36 3.084 7.401 9.252 10.794 12.336 13-878 I5-42 16.962 18.504 20.046 23.130 3-253 7.819 9-774 11.403 13.032 14.861 16.29 17.919 I9-548 21.177 124.433 38 8.246 10.308 12.026 13-744 15-462 I7 .i8 18.898 20.6l6 22.334 25.770 39 3.620 8.648 10.86 12.67 14.48 16.29 18.1 19.91 21 .62 23.53 27.150 4 3.808 9.139 11.424 13 328 15.232 17.136 19.04 20.944 22.848 24.752 128.560 4i 4.002 9.604 12.006 14.007 16.008 18.009 20.00 22. Oil 24.012 26.013 30.015 4 2 4.198 10.065 12.594 14-693 16.792 18.901 20.99 23.089 25.188 27.287 31.485 43 4.40 10.56 13.20 15-4 17.6 19.8 22.OO 24 2 26-4 28.6 33.00 44 4.606 11.046 13.818 16.121 18.424 20.727 23.03 25-333 27.636 29.939 34-545 45 4.8l8 "563 14-454 16.863 19.272 21.681 24.09 26.399 28.908 31.317 36.135 46 5.043 12.086 15.128 17.626 20. 144 22.662 25.18 27.6 9 8 3O.2l6 32.754 37.770 47 12.614 15-768 18.396 2I.O24 23.652 26.28 28.908 .',t.536 34.164 39.420 48 5^82 12.846 16.446 19.187 21.928 24.669 27.41 30.151 35-633 41.115 49 50 5.7I4 5-95 12.913 14.28 17.142 17-85 19.999 20.825 22.856 2 3 .8 25-713 26.775 28.57 29-75 3L427 32.725 34.284 35-7 37-14* 38.675 42.855 44-625 51 6.180 14.832 18.54 21.665 24.76 27-855 30.95 34.045 37.08 40.205 46.425 S 2 6.432 !5-437 19.296 22.512 25.728 28.944 32.16 35-376 38.592 41.808 48 240 53 54 6.684 6.940 16.041 16.656 20.052 20.82 23-394 24.29 26.736 27.76 30.078 31.23 33-42 34-7 36.762 38.17 40.104 41.64 43 446 45- 11 50.130 5* '5 fl 57 7.198 7.462 7-732 I7-275 17.909 iS-557 21.594 22 . 386 23.196 25-193 26.117 27.062 28.792 29 848 30.928 32- 39 1 33-579 34 794 35-99 37-31 38.66 39-589 41.041 42.526 43-188 44-772 46.392 46.787 48.503 50.258 S3 -985 57-99 58 8.006 19 214 24.018 28.021 32.024 36.027 40.03 44-033 48-036 52-039 60.045 59 60 8.284 8.566 19.902 20.558 24.853 25.698 28.964 29.981. 33-I36 34.264 37-278 38.547 41.42 42-83 47-"3 48.704 5L396 53-846 62.13 64.245 WA TEK-COMP U TA TfON TABLE. 691 * s s o o oo o "> N mGO O tO tOCO O N *^O OO i N tnoo N moo M UI-/D >!>. i l^rxt^cooooo O O OO OO toco to O oo O , . . O to to o .o 10 toco co co oo co r^ o *"t* r^ *^ "^co - ^oo ^^ tr>oo ** /^co ^ *too ^ HH M M N N tototo^T^Tj-mioir>ooorf^r>>coo6"co N co Tt O rf- O toco NO O tot^O ^t*r^O N moo too co O to O O to r^ N O^N M oco O IH o I s -* coco oo to M O N rfo to O r^ 09 oorfOir>wvr)O*1'CONOOtor^OtoOONtr)i^Otoiot^ON-tO I^I^^-MO O i- O toi^ooo tototor>oo rj-!too e toto-n ototnr>o M COM mo O TCOQO M NO r^o too OO'TtON r jftr* w ( r^ M o to to ^-ON ^ tf tn O> p Tj-u-^TfON OO M r^ Tt noo OeO in N CH H 692 EXPERIMENTAL ENGINEERING, XJ en en en en en en enco O tcq Ocoo tN Ocoo tx en o vr> M rx \r> rx rx in inoo M t rx o en in t mco en oco ON rx en N en too rx o O M Oco intN OO M o O in w O O tO co O O Ooo O oo O "-" N en N rx o\ o N toco On N en m rx co o" w N cntOO rxoo Oi-i N ent^n M 3-co M rf Jx o en rx o eno ONO ON moo M t rx o en rx o eno o 1-1 M M N cs N cncnenttttmin mo O O rx rx rxco co oo OOOO too NO ttttttttoo NCO too NCO to en m ix o M en mco O OO O too NO O OOO t O tx i^co N rx m in M N r^-o O rx en m rx o^ w cntoco OO CM cnmoco OO M N en t "">' M t rx O t rx O eno OenO ON mco 1-1 moo CH t rx O tOO N ininmmmminO -rONO O too NO O tooo tN Ooo rx rx m N O OO enco eno NCO cnco M to rxoo ro tmoo oo ** O M t fx O en O O e*~ O O N m O N in co ~* t rx O t rx O en O O N m co f.4 Oooo tttttt to oo O N to co O N to co en rx w m o en in to co tOO N oo to rx M o enN cnr-N Oco OO oo in m o^co inmcnOco rx in M rx M in o O NO O enmo rxo incntOco OOO rx c> - ento'co O "- entO rx e> O N cnt mo r^oo OO M N entm O cnr^O mo Oenr^ON moo >-< moo M tr->.Q eno Oeno ON moo M M M N c^i N N en en en t t t in in m o O O r^- i^ t^* 1^ co oo oo O O O S .54 OOOQenenencnenenenOOOOOOOOOOOOcocooOcococo m N r^ O OO cnOr^tMONONOONONQON eno en t Oco en t w OO m en O m C t O m o m o N t m o O m en en in t^ oo oo oo O eno O eno ON mON mod * tr-- tt^O eno ON moo N mob y Mi-iMMNNNcncncnt'J-tinmmoooi^.t^r^r-.coooooooo OooONOOOOOOOtNOcootNOoootNi-ir^cnomi-i tN OenOcoo tN Oco eno "-" r^o r>>o mw o <-> t" N enoo fr MMO^t^inen>-tootONr->.cnocnr^Oent'-nmtNNtor-r^r^ ^H ^ en t O co O N en mo co O * N t m f*^ oo O O *"* N en t mo 1^ co O H O eno ONO ON inoo too M t r^ O eno O eno ON mco >-< t r> ^ ^w>-itHNNNencnentttinmmooor^r^r^r^oococooOO > f.^ 3 NOOtr^.i-^i^r^r^r^ i~^o NOO too NCO to r^N to co o N t J>C ^ t en -H o O Oco r^O m to O >n m en too en >* NOoo N O enoo rj O O Oco in en M OO N t^t-i mN r^cio OM en t t en M o enmOOO *^ r^Oi-'enmr>.coONeninOooO'-'Nenmor^aoOO | -' oi ONOONmoONmcotr^Otr-^OenoONinONmooi-iti [z] O'-'i-'MNNNcncnentttininjnooooi^r^r^.cococoOOO H cntNOMMi-iMiH MM OtO OOi-'ONi-iM enco in O O N co O !> r^O cn-i Ooo innno O enoo O too O N cncnN O ON enmmm t o co O N t m fx QN Q s ! en in o co o O N en t m o fx rx ON o ** N en ON m o N moo M too M t r^ o eno O eno ON moo >-> too ** -f t~- O M HH ^^ N N N en en en t t t m in mo O O O tx t^* ixco co co O O O co O t N fx f^ t*x t^ r^ ix f^ o CM -^"O on o N tO co O N O en r* >H in O N t t N M N en t in o fx cnco m -t m c^ t M o ** *n O N co t^* M oo O mmtN Ocoo cnotoo NOO tocno o M N M Ooo O N ttt M en in fxco O N t m rxco O M en to rxco O >-< N en t to ixco O O ON mco M mco M trxQ tixQ eno ONO ON moo * tr^o cnr- O M M M N N N enenentttminininooO rxtxtxcooooo OO-O OOOOOOOOOOOOOOOOOOQOOOOQOOOOQ N mo m N tO co O N to NOONONOONONOOOOcoO en en N O r^o t M co en rx o tx cnco N moo Oi-HMOOrxO^cnent co N inoo > t rx i t r^ O eno O eio O N mco >-> mco M t i^ O mo O M M M c^i N N en en en t t t m m in ino O O r^ fx txco co co O O O N m t mo ?xco o O M N en t mo rxco O O M N en t mo rxco O O cncncncncncncncnttttttt tt ttJiuiuimininmminino ELECTRICAL HO-RSE-POWER TABLE. VOLTS OR AMPERES. 693 frj p< J W ^ S ^^ -** ^ txoo O\ O M W l O* - o |0 t^. O j. 5)00 O r^ inr - yl OOOMH.fS - I OOOOO' HHMMWC '* NWC< 'W cr > frir ^ f ^ N -^-vO 00 O 0* ' TJ-OO ^o co 1-1 oo vo m o oo ro OlNroiotiONOMT'^^ONwrO'* M " 1 - M ' H w* : ' c)Ci M M(r "^ " 2 " ^-00 (N VO O * C^> WWM M rlHI-lN P O , 8888 5 S S S 5 S S 858388 o M j:- 1 d ^a Ss 5.^5 II II II II l la < s'g. , gs j w jf *1| h| SXIOA 694 r A/S^TAL ENGINEERING. xxvii. \ r HORSE-POWER LINE-SHAFTING WILL TRANSMIT WITH SAFETY. BEARINGS, 8 TO 10 FT. CENTRES.\^) Diameter of Shaft Horse-power in one Diameter of Shaft Horse-power in one Diameter of Shaft Horse-power in one in Inches. Revolution. in Inches. Revolution. in Inches. Revolution. 4t .008 .0156 3? .216 .272 IS .728 2.195 I A .027 3yV 343 6}| 2.744 iff 043 3~fi" .424 3.368 J Tf .064 3il .512 7il 4.096 I .091 .125 .166 1 .728 I.OO 1.328 1 9iV 4.912 5.824 6.848 For jack-shafts, or main section of line-shafts, allow only three-fourths of the horse-power given above, and also provide extra bearings wherever heavy strains occur, as in main belts or gears. XXVIII. HORSE-POWER BELTING WILL TRANSMIT WITH SAFETY. Width of Horse-power per 100 Feet. Velocity of Belt. Width of Horse power per too Feet. Velocity of Belt. Belt Belt in Inches. in Inches. Single Belt. Double Belt. Single Belt. Double Belc. I .09 .18 12 .09 2.18 2 .18 -36 14 27 2-55 3 .27 55 16 45 2.91 4 .36 73 18 .64 3-27 5 45 .91 20 .82 3.64 6 55 1.09 22 2.00 4.00 7 .64 1.27 24 2.18 4-36 8 .73 1.46 28 2-55 5-09 9 .82 1.64 32 2.91 5-S2 10 .91 1.82 36 3-27 6-55 ii I.OO 2.OO 40 3.64 7.27 In the calculations for horse-power in the .above table, the belt is assumed to run about horizontally; the semi-circumference of smaller pulley has been considered as the ordinary arc-contact of belt. Any reduction of this contact will make approximate proportional reduction of horse-power. B. C. CAKPCNTtH, ITHACA N. Y. ttt INDEX. PAGB Abrasion Test of Materials of Construction 146 Adiabatic Curve, The , 497 Admiralty Test of Materials 152 Air, Absorption of Moisture (Table) 671 , Flow of , 268 , Humidity of (Table) 671 Orifices, Flow through 269 Pipes, Flow in 271 Thermometer 343 Alden Brake 213 Aluminum Bronzes, Test of (Table) 666 Anemometers, Calibration of 279 , Description of 278 B Barometer Observations reduced to Freezing Point (Table) 689 Beaume's Scale reduced to Specific Gravity (Table) 672 Belts, Friction of 173 , Horse-power of (Table) 694 Belt-testing, Directions 238 , Machines for 236 , Method of 3.35 , Report , Form of 2 -l Bending Test of Materials of Construction. . , 146 Boilers, Efficiency of 443 , Efficiency of Furnace 444 , Horse- power of 445 695 696 INDEX. PAGE Boiler Tests, Combustible 443 , Evaporation, Actual, Definition of 443 Equivalent, Definition of 443 Factor, Definition of , 443 , Graphical Log 445 , Method of Standard Testing 445 , Abbreviated Directions 458 , Objects for 442 , Report, Form of A. S. M. E 442 , Sibley College Form 457 Brake, see Dynamometer. Brick, Method of Testing 158 Bridge Materials, Method of Testing 148 C Calculations, Accuracy of Numerical 15 Calorimeter, Fuel, Combustion, when Perfect , 416 , Berthelot Calorimeter 420 , Berthier " 420 , Favre and Silbermann Calorimeter 416 , Heat Equivalent of Calorimeter 416 , Principles 415 , Samples of Fuel, How obtained 416 , Thompson Calorimeter 419 Calorimeters, Steam, Barrel 372 , Barrus Continuous 380 , Barrus Superheating 386 , Chemical c 404 , Comparative Value of 405 , Condensing 365 , Continuous Jet 375 , Equivalent of Calorimeter 371 , Errors in Calorimetric Processes 361 , Heisler Calorimeter 391 , Hoadley Calorimeter.. '. 377 , Kent Calorimeter 379 , Peabody Calorimeter 388 , Quality, Definition of ... 361 , Quality determined graphically 394 , Sample of Steam 369 , Steam Tables, Use of 362 , Separating Calorimeter 398 , Superheating Calorimeter 34 , Throttling Calorimeter 35 INDEX. 697 PAGE Car- wheels, Test of t Aj Cast-iron, Testing Bridge Materials 151 , Test Pieces, Form of ng Cathetometer, The 54 Cements, Description 161 , Method of Testing X 62 , Report, Form of 167 Cement Testers, Fairbanks' 102 , Fuertes* 103 , Olsen's 104 Chains, Test Specimens, Form of 119 Chronograph, The. 515 , The Tuning-fork 516 Clearance of Engines from the Indicator-diagram 502 Compression, Formulae of 63 Compression Tests, Method 134 , Specimens 122 Condensation and Re-evaporation from the Indicator-card ... 503 Condenser Test 520 Constants, Numerical (Table) 640 D Deflectometer for Transverse Testing "5 Draught-gauges 3 Drop Tests of Materials of Construction I Ductility, Definition of , Method of Measuring Dynamometer, Absorption , Alden Brake 2 , Constants of - , Designing , Fan Brake , Horse-power , Hydraulic Friction , Operation 2 , Prony Brake 2 7 ,Pump 2I ? , Self-regulatiug 2 .Strap-brake 2 Dynamometer, Traction, The Giddings Recording Dynamometers, Transmission ......... ^ 3S ' Differential, The 22 7 698 INDEX. PAGE Dynamometers, Transmission, Emerson's Power-scale 231 , Lewis, The 224 , Morin's Rotation 219 , Pillow-block, The 224 , Steelyard, The 222 , Van Winkle Power-meter, The 233 E Efficiency Tests , xx Elastic Curve 139 Elastic Limit 58 Elasticity, Modulus of 59 , Modulus of, from Sound 63 , Modulus of, in Tensile and Shearing Strains 73 Electrical Horse-power (Table) 693 Engines, Pumping, Method of Testing 552 Engine Testing, Calibration of Apparatus 520 , Clearance, Determination of 525 , Efficiency-tests 531 , Friction-tests , 531 , Hirn's Analysis. . , 532 , Indicator Practice 526 , Objects of * 512 , Piston Displacement 525 , Preparation for 523 , Speed Measurements 513 , Quantities to be observed , 525 , Valve-setting , 528 , Water Consumption, Measurements of 518 Entropy of the Liquid (Table) 684 Errors, When to neglect 14 Evaporation, Factors of (Table) 687 Experiments, Classification of xix , Graphical Method of representing :.. . 16 , Objects of xvii , Relation to Theory xviii Extensometers, Attachment of. ... ...... 128 , Boston Micrometer, The 112 , Buzby Hair line, The 107 , General Requirements 106 , Henning, The no , Marshall, The in , Paine, The 107 INDEX. 699 I ACE Extensometers, Sibley, The II3 , Thurston, The JO Q , Wedge Scale .*.'!.* 107 F Factor of Safety , 59 Fatigue of Metals 146 Favre and Silbermann's Calorimeter. ... 416 Flexure, Table of External Moments of 69 Fluids, Compressible, Flow of 267 Flue-gas Analysis, see Gas Analysis. Forging-test of Materials 146 Formulae, Empirical, Deduction of 6 for Approximate Calculation n Fracture, Character of, in Materials 123 Friction, Angle of Repose. Definition of , 170 , Belts, Friction of 173 , Coefficient of, Definition of 170 " (Table) 670 , Collars, Friction on , 173 , Cords, " of 173 , Formulae '7 1 , Journals, Friction on 1 7 2 , Laws of 1 75 , Lubricants, Friction of 174 , Motion, " " I 7 l , Normal Force, Definition of 170 , Pivots, Friction of 172 , Rest, " " *7 , Rolling Friction > , Teeth of Gears, Friction of - 173 , Total Pressure, Definition of 17 Fuels, Calorimeters for 4 , Combustion of 47 , Composition of 4 "(Table) 6 , Heating Value Determinations 4'o , Heat of Combustion 4o , Temperature produced by Combustion 412 , Total Heat of Combustion with Oxygen (Table) 4'o Furnace, Efficiency of G Gas Analysis, Computations , Form of Report 439 700 INDEX. PAGE Gas Analysis, Method 424 , Object of , 423 , Reagents, how prepared 425 , Samples of Gas, how obtained 427 , Elliot's Apparatus 429 , Fisher Orsat Apparatus 431 , Hempel's Apparatus 433 , Wilson's Apparatus 431 Gas-engines 630 , Testing 632 , Form for Report of Test 635 Gas, Measurement of Flow , 274 Gas-meters 275 Gauges, Pressure, Calibration and Correction 338 , Forms for Calibration. .... 340 , Crosby Apparatus for Testing 335 , Bourdon 329 , Diaphragm 33 1 , Draught 323 , Manometer > 317 , Manometers with Piston 327 , Mercury Columns 321 , Recording 333 , Square Inch 337 , Vacuum 332 H Hammer-test of Materials 146 Hardening Test of Materials t 146 Heat of Combustion, see Fuels. Heat, Absorption of (Table) 669 , Conduction of (Table) 669 , Mechanical Equivalent of 311 , Melting Points (Table) 354 , Radiation of (Table) 669 , Specific ; 310 , Determinations of 354 , Specific (Table) 669 Hirn's Analysis of the Steam-engine : Compound Engine, Application to 545 Example 547 Non-condensing Engine, Application to 545 Report, Forms for 540 Theory of 532 Triple-expansion Engine, Application to 545 INDEX. 701 PAGE Horse-power of Belting (Table).- , Electrical (Table) _ 693 , Indicated, Dynamometric 4^0 of Shafting (Table) 694 per Pound M. E. P. (Table). . . 690 Hot-air Engines 624 , Ericsson 524 , Rider 625 , Thermodynamic Theory 627 , Testing , . 627 , Form for Data and Results 628 , Indicator-diagram 629 Humidity of the Air (Table) 671 Hydraulic Machinery, Classification 279 Hydraulic Motors, Classification 279 , Forms for Report of Tests 298 , Formulae 280 , Hydraulic Power System 281 , Hydraulic Ram 293 , Directions for Testing 297 I Impact Machine, Heisler's Directions for Testing by 143 Test, Method of A. S. M. E 101 Inertia Diagram 6 l Indicator, The Williams 599 , Moment of, Experimental Determination 70 " " (Table) 68 Indicator, Dimensions of Parts of (Table) 47O , Operation and Attachments of 485 Pencil-movement, Test for Parallelism 481 Reducing-motion 47^ Spring, Calibration of 479 , Standardization of 478 Drum-motion, Accuracy of 48 1 Drum-spring Tension (Table) . 4 Drum-spring, Adjustment and Calibration 484 , Steam-engine, Arc 4& , Bachelder 4&9 , Calkins 4^7 , Crosby 465 , McNaught 46i , Perfection 4^8 702 INDEX. PAGE Indicator, Steam-engine, Richards 462 , Straight Line 469 , Straight Lyne 468 , Tabor 464 , Thompson 463 , Watt 461 Indicator-diagrams, Adiabatic and Saturation Curves 497 , Compound and Triple-expansion Engine 507 , Clearance from the 502 , Condensation and Re-evaporation 503 , Discussion of the 505 , Form of the 495 , Measurements of the 493 , Parts of the 489 , Steam-chest and Crank-diagrams 509 , Steam Consumption from the Diagram 499 Injector, Description 608 , Forms for Results of Test 619 , Handling 617 , Limits 614 , Mechanical Action 612 , Tables of the Limits of the 616 .Testing 617 , Thermodynamical Theory 610 Investigation, Methods of xviii Iron, Admiralty Tests of 152 Iron in Bridge Materials, Tests of .... 148 L Least Squares, Method of I Locomotive Testing, Boiler Leakage 586 , Boiler Tests 377 , Calorimeter, Application of 593 , Coal Tests 580 , Form of Report 584 , Dynamometer Records 587 , Fuel Measurements 573 , Indicator, Application of the 574 , Performance, Form of Report of 591 , Speed Measurements 588 , Standard Method 572 , Water Measurements 583 , Wind Resistance, Measurements of 589 INDEX. 703 PAGE Logarithms (Table) Logarithms (Hyperbolic Table) 684 Logarithmic Functions of Angles (Table) 6ce Lubricant Testing x -e M Materials of Construction, Tests of, Admiralty Tests 152 , Brick Tests 158 , Bridge Materials Tests 148 , Cement " j6i , Coefficients (Table) " 665 , Compression " I3 ^ , Drop " I44 , Impact " 143 , Mortar " !6i , Paving Material " 159 ,Pipe " 154 , Stone " 155 , Special " 145 , Tension " 125 Tests for Different Materials (Table) 148 , Torsion 140 , Transverse 135 Measures, U. S. Standard and Metric (Table) 638 Meters, Gas 275 , Water 255 Measuring Machine, The Sweet 52 Melting Points (Table) 671 Micrometer Calipers 51 Micrometer Screws, Accuracy 50 , Cornell University, Errors of 51 , Description 50 Moisture absorbed by Air (Table) 671 O Observations, Rejection of Doubtful 13 Oils, Acid Test .' 186 , Adulteration of 1 76 , Burning Point 182 , Chill Point : 1 86 , Coefficiency of Friction 194 , Cold Test 185 704 INDEX. 1 PA.GE Oils, Density 176 , Durability 198 , Electrical Conductivity 186 , Evaporation 184 , Feed, Limited Test with 203 , Flash-point 182 , Form for Report of Test 205 , Gumming Test 182 , Heat, Effect of 182 , Viscosity 177 , Viscosity, Method of Measuring , 181 , Table of Determinations 181 Oil-testing 175 Oil-testing Machines, Ashcroft's : 199 , Boult's 199 , Rankine's 187 , Richie's ,. 196 , Thurston's 189 Oil, Viscosimeters for Testing, Gibbs' , 179 , Perkins' 179 , Pipette, The 178 , Standard Orifice, The 180 , Stillman's 180 , Tagliabue's 1 79 P Paving Materials, Method of Testing 159 Pipes and Pipe-fittings, Method of Testing. 147 , Cast-iron, Specifications for 1 54 Pilot's Tube 264 Planimeters, Adjustment. 42 , Calibration > 44 , Coffin, The 33 , Mean Ordinate by the Polar 31 , New, The 36 , Polar, The 24 , Roller, The 37 , Special 49 , Suspended, The 33 Pressure-gauges 323 Prony Brake , 207 Pulsometer, The 621 Tests, Form for Data and Results. 622 INDEX. 70S PAGE Pumping-engines, Testing ,. 552 Pumps, Classification 300 , Duty and Capacity 300 , Efficiency Test 302 , Form of Report of Tests 304 , Piston Displacement, Measurement of Delivery .'. . . 302 , Slip 302 , Testing, Directions for 303 , Work, Measurements of Useful 301 Punching Test of Materials 146 Pyrometers, Air 353 , Calorimetric 353 , Clay Wedgewood's 352 , Electric 357 , Hoadley's Calorimetric 354 , Metallic 352 , Siemens' 357 Q Quality of Steam, see Calorimeters. Radiation of Heat (Table) 669 Resilience of Metals 58 " Rest" of Metals 147 Rigidity of Materials 58 , Modulus of 59 , by Swinging under Torsion Rivet-iron, Tests for 150 Rope, Form of Test-pieces 120 Saturation Curves 497 Shafting, Horse-power of (Table) 694 Slide-rule, The 20 Specific Gravity (Table). 669 Specific Heat (Table) : 669 706 INDEX. PAGd Speed-recorder, Autographic 518 Steam, Consumption of, from the Indicator-diagram 499 , Discharge of (Napier's Formula, with Table) 274 , Entropy of the Liquid (Table)' 273 , Flow through an Orifice.. 272 Pressure, Relation of, to Temperature 311 , Units of 308 Properties and Thermodynamic Conditions, Definitions ,.. 312 Tables, Buel's > 678 Porter's , . . . 673 Relative Accuracy of 316 Steam-engines, Effects of Inertia on 598 , Efficiencies of 511 , Experimental , 594 at Sibley College, Dimensions of 595 , , Testing of, see Engine-testing. Steel, Admiralty Tests of 152 Bridge Materials, Tests of 150 Lloyd's Tests 153 Stone, Testing of 155 Strain, Definition of. ... . . 59 Strain-diagram, The 59 , Autographic 125 , in Tension 1 24 Strength of Materials, Coefficients of 58 " (Table) 665 , Definitions 57 , Temperature, Variations of (Table) 668 Stress, Definition of 58 in Materials, Thermodydamic Relations of 76 Stresses, Combined 74 Tachometer, The 262 Temperature, Effect on Strength of Materials., 147 Tensile Strength, Notation and Formulae 62 Tension Tests, Method 125 , Object 125 , Report, Form of , 129 , Specimens, Form of 116 INDEX. 707 PAGE Testing Machines, Calibration , Description ~g , Emery, The g, , Government Specifications g 2 , Olsen, The 92 , Riehle, The g 9 Test-pieces, Form of ! X 5 Thermometers, Calibration ^- 2 , Method of inserting, in Steam-pipe 370 , Table of Boiling-points 393 Thermometers, Air 343 , Construction 348 , Correction of Determinations 349 , Form of Report 351 , Formulae , 346 , Practical Uses 349 Thermometers, Alcohol 343 Thermometers, Mercurial 341 Torsional Stress, Formulae 71 Torsion Test, Method with Thurston's Machine 140 , Object 140 , Record, Form of 142 , Specimens, Form of 122 ,. Strain-diagram, The 98 Torsion Testing-machines, Olsen 101 , Riehle 99 , Thurstonr 99 Traction-dynamometer , 218 Transverse Stress, Formulae 66 Transverse Tests, Deflectometer for 115 , Object 135 , Report, Form of 137 , Specimens, Form of i 122 Turbines, Classi fication 287 , Fourneyron's 290 , Reaction Wheel.... : 291 , Testing, Directions for 297 , Theory 288 V Valve-setting 528 Venturi Tubes 2 49 708 INDEX. PACK Vernier, The '. . 23 Vernier Caliper, The , , . . . 49 Viscosity of Metals 60 Viscosimeter, see Oil Viscosimeter. W Water Computation Table 691 Water, Diaphragm, Flow through Perforated 252 , Discharge Formulae 242 , Measurement of Flow, General Methods 253 , Nozzles, Calibration of 259 , Efflux through^ 247 , Orifices^ Flow through . 259 , Pendulum, The Hydrometric 267 , Pipes, Flow in , 250 , , Measurement of Flow in 260 , Pitot's Tube 264 , Pressure, Flow under 248 , Streams, Measurement of Flow in 262 , Tachameter, The 262 , Venturi Tubes, Calibration of 259 , Efflux through 24 7 Water-meters, Calibration 258 , Classes 255 , Errors 256 Water-motors, Method of Testing 294 , Backus, Special Directions for Testing 296 , Pelton, The 296 Water-pressure Engines, Description 281 , Direction for Testing 297 Water-weirs 254 Water-wheels, Breast 285 , Impulse 286 , Overshot 283 , Poncelet's 285 , Undershot 285 , Vertical 282 Weights of Materials (Table) 669 Weirs, Accuracy 254 , Calibration 258 , Errors, Effect of. . 255 1\T~:~~ l?.^.. mill on INDEX. 709 Weirs, Formulae 244 , Head, Measurement of 253 , Hook-gauge, The 254 Welding Test of Materials 145 Wooden Pillars, Strength of (Table) 667 Wood Test-pieces, Form of 118 OVERDUE. SEP 5 1932 SEP 11 1! OCr 260ct'6lPA OCt UNIVERSITY OF CALIFORNIA L.URAR'S