> x>*^>:> 'S "!*K "S i?r C ?Z I 03 >jooe i V ^ ; >V> : THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES GIFT OF John S.Prell >> > > > > ^ J A NEW TREATISE STEAM ENGINEERING PHYSICAL PROPERTIES OF PERMANENT GASES DIFFERENT KINDS OF VAPOR BY JOHN W. NYSTROM, C. E. NEW YORK G. P. PUTNAM'S SONS 182 FIFTH AVENUE Entered according to Act of Congress, in the year 1876 by JOHN W. NYSTROM, In the office of the Librarian of Congress, at Washington. Eagineerng Library TJ PREFACE. THE object of this treatise is to furnish a variety of matters pertain- ing to STEAM ENGINEERING which appear to be wanting in that pro- fession, and which have heretofore not been published. The authors consulted for this work are eminent experimenters, such as Regnault and Rudberg on steam and gases, Faraday, Pelouze a*nd Andrews on carbonic acid, Favre and Silberman on heat of com- bustion, Kopp on volume of water, Fairbairn and Tate on volume of steam. None of these savans, however, are responsible for the formu- las and tables herein deduced from their experiments. Where physical sciences are not sufficiently developed to establish a law of action mathematically, experiments are made for the purpose of guiding us to the law ; but it can rarely ever be expected that ex- periments alone can give perfect results, but they give an approxima- tion to the law of variation, which must finally be adjusted and estab- ^ lished by the aid of mathematics. This is what has been attempted s in the present work. It was at first not intended to include in this work the steam-tables .^ which are published in the author's Pocket-Book, but after having ^ carefully investigated the Fairbairn experiments and formula for vol- ume of steam and concluding that they could not be relied upon, it \ was therefore decided to calculate new steam-tables and extend them to a pressure of 1000 pounds to the square inch. The relation between temperature and pressure of steam is also slightly altered in the new steam-tables so as to conform to a uniform curve or law, because the average curve adopted by Regnault does not follow a regular law, and therefore indicates that there must have been some inexactness in his experiments. When the author worked out the first steam-table in the Navy De- partment under the direction of Chief-engineer Isherwood, the irreg- ularity of the Regnault curve was then demonstrated with attempts 3 733250 PREFACE. to correct it, but the Chief would not allow any deviation from that curve. The difference is, however, within probable experimental errors, and so small that it is not of much importance in practice. The author believes that the relation between temperature, pres- sure and volume of steam, as given in these new tables, is nearest right. The old steam-tables are, however, referred to and used in the body of this work for the reason that many readers may have more faith in them than in the new tables, which are equally applicable to the examples. Many mathematical proofs have been omitted in this work in order to avoid extensive algebraical demonstrations, which are objection- able to the general reader who only needs the resulting formulas for the insertion of his given numerical values. The .principal formulas are accompanied with examples and also tables ranging between practical limits, showing at a glance the rela- tion between and proportion of the operating elements. The calculus has been resorted to in only a few cases of necessity where the result could not otherwise be reached. The numbers of the examples are arranged to correspond with the numbers of the formulas, and therefore do not run in order. Profound and high-sounding terms, like "potential and kinetic energy," etc., are not used in this work, which limits itself to simple terms such "as are used in the shop, and which express the true mean- ing of the respective cases. The appendix on " Mechanical Terms " is added to this work to furnish an idea of the unsettled condition of that subject. Similar discussions have been published in pamphlet form and dis- tributed gratis to institutions of learning. ALPHABETICAL INDEX. A. PAGE Air, compression and expan- sion of ... 128 " for combustion . 51, 53 " quantity of, for draft 62 " work of compression and ' expansion . . .132 Alcohol vapor, properties of 164 Ammonia vapor . . .166 Appendix .... 171 Aqueous vapor, properties of 139 Atmospheric pressure, horse- power of . . . .27 Available heat of combus- tion . . . .51,53 B, Benzine, vapor of . .165 Boilers, explosions . .82 " generating steam . 18 " horse-power by B and a . . 37,40 " inspector's rule for . 89 " lap-joint, riveted 92 to 105 " legal horse-power of 35 " plates must be stamped 89 " standard efficiency of 52 " stays on flat surfaces 108 " strength and safety of. . . 89-109 Boiling point of different liquids . . . .168 Burning of smoke . . 57 0. PAGE Carbonic acid, properties of . 136 Cause of boiler explosions . 86 Chimneys, general properties of ... 42,122 " correction for height of . . 41 " horse-power of .123 Collapse, strength of gue for 106 Combustion of coal per height of chimney . . .41 Combustion, incomplete . 47 heat of . . 46 power of . .43 " products of . 56 properties of air for . . 45 Colors for tempering steel 63 Condenser, fresh water . . 67 Correction for temperature of feed-water ... 21 Correction for height of chim- ney 41 Covering steam-pipes . .81 D. Distillation of petroleum . 168 Destructive work of boiler explosions . . .85 Draft, velocity of, in chimneys 60-122 Draft, natural, in furnaces 59 " temperature of . .45 " quantity of air for . 62 5 ALPHABETICAL INDEX. Dryness or humidity of steam 143 Dynamical terms . . .171 Dynamics, principles of . 14 E. Economy of heating feed- water . . . .54 Elasticity of permanent gases 112 Ether, vapor of ... 165 Equivalent work of heat in steam . . . .142 Equivalent of heat, dynamic 30 Evaporation from and at 212 53 legal horse-pow- er of . . 40 " natural effect of 23 per square foot of Q .... 66 Expansion and compression of air . . . 129-133 Explosion of steam-boilers . 142 F, Fairbairn and Tate, steam- volume . . . 19-144 Feed-water, heating of . .54 " quantity of . 76 reduction for tem- perature . 22 Feed-pump, capacity of .77 Felt covering for steam-pipes 82 Fire, management of . .55 Fire-grate, spaces between . 57 Flues, strength of, for collapse 106 Fresh water condenser . .57 Fuel, heat generated by . 48 Fuel, properties of .50 Furnace draft, natural . . 59 G. Gases in chimney, tempera- ture of . 64 Gases in chimney, velocity of 122 " permanent . . . 112 " specific heat of . .119 Gauge, water, for draft . . 61 Grate-bars, spaces between . 57 H. Heat, available by combustion 53 " of combustion . . 46 " in water and steam, units of . . .141 " permanent gases . . 1 20 " lost by radiation . 78-82 " lost through chimneys 63 " physical constitution of 18 Height of chimneys . 42, 123 Horse-power of steam, natural of .... 20,23 Horse-power of steam-boil- ers . . . . 32,36 Horse-power of boilers by E3 and Q . . 37, 40 Horse-power of chimneys 42, 1 23 " by volume of steam . . 74 Humidity of steam . .143 Hyperbolic logarithms . . 29 I and J. Inflammation of petroleum . 168 Inspectors for steam-boilers . 89 Joints, lap-, for riveted boilers 92-105 K. Kabyl, French ether ship . 1 64 Kerosene . 169 Lap-joints, single and dou- ble riveted 92-105 ALPHABETICAL JXDEX. Lateut heat in water and steam . . . 139-141 Laughing-gas . . .166 Law of the United States, steam-boilers . . .89 Legal horse-power of steam- boilers . . . 35-40 Letters, standard notation of 10 Locomotive without fire . 110 Logarithms, hyperbolic . 29 Loss of heat through chim- neys . . . .63 Loss of heat by radiation 78-82 M. Mean pressure of steam 28, 160 Mechanical terms . . .12 Moisture in fuel . . .49 N. Natural effect of full steam 19, 20 " " of expanded steam . . . .26 Natural effect of furnace draft . . . .59 Notation of letters, stand- ard 10 o. Oils of petroleum . .169 Oxygen and hydrogen in fuel 49 P. Petroleum as fuel . . .53 " oils, properties of . 1681 Permanent gases . . . 112 \ Plates for boilers to be stamp- ed 89 Power of combustion . . 43 " " steam without fire . 110 " lost by radiation . 79 PAGE Primary source of power . 1 7 Products of combustion . 56 Protoxide of nitrogen . .168 Prevention of boiler explo- sion 86 Q. Quantity of steam escaping . 72 of feed-water . . 76 R. Radiation of heat from pipes 78-82 Reduction for temperature of feed-water ... 22 Reduction for height of chim- ney 41 Revolutions and steam-pres- sure 74 Riveted lap-joints . 92-105 S. Safety-valves . . 71,67 Sit for safety-valves . . 69 Smoke, burning of . . 57 Specific heat of gases . .119 Staying of boilers . .108 Steam engineering . .17 " engine versus water- wheel .... 17 Steam, natural effect of .19 " volume, Fairbairn's 19,144 " boiler explosions . 82 " boiler experiments . 1 8 " expansion of . 19, 24 " equivalent work of 19, 20 " velocity through open- ings . . .70 " quantity escaping . 72 " power without fire . 110 " or aqueous vapor . 139 " dryness or humidity of 143 ALPHABETICAL INDEX. PAGE Steam, superheating of . . 147 Steam-pressure and revolu- tions 74 Stamped boiler-plates . . 89 Strength of boilers . 88-109 " flues for collapse 106 Superheating steam . . 147 Spherical ends of boilers . 162 T. Technical terms . . 15-170 Tempering steel, colors of . 65 Thermo-dynamics . . 30 Temperature of feed-water . 22 Temperature of gases in chimneys . . . .64 Turpentine vapor . . .164 U. Uncombined oxygen and hy- drogen . . . .49 United States law for steam- boilers . . . .89 Units of heat in steam and water . . . .141 Units of heat in permanent . 120 Units of heat, definition of . 46 " of heat of combustion 46 V, Vapors, different kinds of .164 Velocity of draft in furnaces . 60 Velocity of steam through openings . . . .70 Volume of steam, horse-power by 74 Volume, ultimate, of gas . 115 Volume of water, temper- ature . . . .140 Volume of steam . . 19,144 W. Water, feed, temperature of 20, 22 Water and steam-power com- pared . . . .17 Water-gauge for furnace draft 61 Water volume . . .140 Work of steam, natural 19, 20 Work of steam-boiler explo- sions . . . .85 Z. Zero of temperature, absolute 113 ISDEX TO TABLES. TABLE No. PAGE 1. Reduction for temperature of feed- water . . . .22 2. Natural effect of evaporation of water in horse-power . . 23 3. Hyperbolic logarithms 29 4. Legal horse-power of steam-boilers by evaporation . . 36 5. Economy and gain of power by heating the feed-water . 39 6. Horse-power by fire-grate and heating-surface . . .40 ' 7. Correction of horse-j>ower for height of chimney . . .41 8. Consumption of coal per square foot of grate for different heights of chimney ....... 41 9. Properties of air for combustion 45 10. Incomplete combustion with different quantity of air supplied 47 11. Properties and ingredients of different kinds of fuel . . 50 12. Percentage of power or fuel gained by heating feed- water . 54 13. Products of combustion, specific gravity and volume . . 56 14. Water-gauge for chimney draft 62 15. Area of safety-valves and velocity of steam passing into air 71 16. Percentage of heat or power gained by covering steam-pipes 82 17 to 22. Strength of steam-boilers, U. S. rule . . . 92-97 23. Proportions of single- riveted lap-joints for steam-boilers . 102 24 and 25. Double-riveted lap-joints, proportions of . . .104 26. Coefficient for strength of lap-joints in steam-boilers . .105 27. Distance in inches between boiler-stay for steam-boilers . 109 28. Specific heat of permanent gases . . . . . .119 29. Horse- power of chimneys 123 30. Properties of permanent gases 124-127 31. Compression of air by external force 134 32. Expansion of air by external force . . . . . 135 33. Volume of carbonic acid gas 137 34. Pressure and temperature of carbonic acid vapor . . 138 35. Comparison of volume and temperature of steam . .144 36 to 45. Properties of water and steam .... 150-159 46 and 47. Mean pressure of steam 160 48. Properties of different kinds of vapors .... 167 49. Distillation and inflammation of petroleum oils . . . 169 STANDARD NOTATION OF LETTERS. IT has been attempted throughout this work to adopt a standard notation of letters, for which some new characters have been added to distinguish different quantities which have heretofore been denoted by identical letters. It is of great importance in technical works that the formula should be clear at a glance without special reference to the meaning of its characters. The characters B, a, T, t, rf, V, IP, %?, and c have been made especially for this work. The letters T and t denote time, T and t temperature. F and v denote velocity, ^ and 3f volume. P and p denote pressure, and ^ power. Mr. W. Barnet Le Van proposed the letter "^ to denote volume of steam, as a distinction from F, which is used to denote velocity. Differential is denoted by 8, and is placed close to its variable quantity, like fix (not c x), because the two letters denote only a single quantity. The common letter d is needed for denoting diameter, distance, depth and other quantities. The character 8 is more distinct in denoting the differential, which is not a common notation, and should be conspicuous like the integral The character 8 ought not to be used for any other notation but differential. The special characters B and a, denoting grate surface and heat- ing surface, are new and explicit for steam-boiler notations. The characters "$, denoting weight in pounds per cubic foot, and 6 cubic feet per pound, are also explicit notations which ought to be permanently maintained. 10 NOTATION OF LETTERS. 11 P p *ft .0" H' L U W w Ibs. STEAM NOTATION. absolute steam-pressure, Ibs. per sq. in. steam pressure above that of atmosphere. steam volume compared with that of its water. units of heat per pound in steam. units of heat per cubic foot in steam. latent heat per pound in steam. latent heat per cubic foot in steam. pounds per cubic foot. cubic feet per pound. temperature Fahr. of steam. thermodynamic equivalent. grade of expansion of steam. WATER NOTATION. volume of water, that at 39 or 40 = 1. temperature Fahr. of water. latent heat per pound in water from 32. latent heat per cubic foot of water. units of heat per pound of water. units of heat per cubic foot of water. weight in pounds per cubic foot of water. fraction of a cubic foot per pound of water. cubic feet of water. cubic inches of water. pounds of water. DYNAMICAL NOTATIONS. F= force in pounds avoirdupois. F= velocity in feet per second. T= time of action in seconds. *S= V T, space in feet or cubic feet. ^ = F V, power in effects or second foot-pounds. IP = 550 , horse-power, Watt's unit. K=F V T, work in foot- pounds. STEAM-BOILER NOTATION. H = area of firegrate in square feet. Q = area of heating surface in square feet. D = diameter of boiler in inches. d = diameter of staybolts in in- ches. t = thickness of boiler-plates in inches. S = breaking-strain per square inch of iron. H = height of chimney in feet. A = cross-area of chimney in square feet. PERMANENT GASES NOTATION. "ft and %f = volumes. T and t = actual temperatures. C and t = ideal temperatures. P and p = absolute pressures. ^ = pound per cubic foot. h = units of heat. S=* specific heat, constant volume. s = specific heat, any vol- ume and pressure. W= weight of gas in pounds. MECHANICS. DEFINITIONS OF THE PRINCIPAL. TERMS IN MECHANICS. MECHANICS is that branch of natural philosophy which treats of the three simple physical elements force, velocity and time, with their combinations, constituting the functions power, space and -work. Mechanics is divided into two distinct parts namely, Statics and Dynamics. STATICS is the science of forces in equilibrium or at rest. DYNAMICS is the science of forces in motion, producing power and work. QUANTITY is any principle or magnitude which can be in- creased or diminished by augmentation or abatement of homogeneous parts, and which can be expressed by a number. ELEMENT is an essential principle which cannot be resolved into two or more different principles. FUNCTION is any compound result or product of two or more different elements. A function is resolved by dividing it with one or more of its elements. Force, velocity and time are simple physical elements. Power, space and work are functions of those elements. These six terms represent the principal elements and functions in Mechanics. All creation, work or action, of whatever kind, whether mechanical, chemical or derived from light, heat, electricity or mag- netism all that has been and is to be done or undone is compre- hended by the product of force, velocity and time. DEFINITIONS OF TEEMS. 13 FORCE is any action which can be expressed simply by weight, without regard to motion, time, power or work. It is an essential principle which cannot be resolved into two or more different prin- ciples, and is therefore a simple element. VELOCITY is speed or rate of motion. It is an essential prin- ciple which cannot be resolved into two or more principles, and is therefore a simple element. TIME is duration or that measured by a clock. It is an essential principle which cannot be resolved into two or more different prin- ciples, and is therefore a simple element. POWER is the product of the first and second elements, force and velocity, and is therefore a function. SPACE is the product of the second and third elements, velocity and time, and is therefore a function. WORK is the product of the three simple elements force, velo- city and time, and is therefore a function. Work is also the product of the element force and function space, because the function space contains the elements velocity and time. W^ork is also the product of the function power and element time, because the function power contains the elements force and velocity. MOMENTUMS are of two kinds namely, Static and Dy- STATIC-MOMENTUM is the product of force and the lever upon which it acts, and is therefore a function. DYNAMIC-MOMENTUM is the product of mass and its velocity, which is equal to the product of the force and time that has produced the velocity of the mass, and is therefore a function. MASS is the real quantity of matter in a body, and is propor- tionate to weight when compared in one and the same locality. Mass is an essential principle which cannot be resolved into two or more principles, and is therefore a simple element. The new treatise on "Elements of Mechanics," published by Porter & Coates, Philadelphia, gives complete explanations, with practical examples of the mechanical elements and functions. 14 MECHANICS. STATICS. ALGEBRAICAL AND GEOMETRICAL EXPRESSIONS OF THE FUNDAMENTAL PRINCIPLES OF STATICS. Levers of Different Kinds. First. ~ | Third. fz T ^ !< a i* fg ' /yv\ F: W = l:L. .P: TF=/:i. F: FF=/:i. Static Momentum. ^=1*7. Static Momentum. Fi=TF;. Static Momentum. FL= Wl. -f- F "T' *-f " I ' r "T' "~T~' .Pa Fa i Fa ~TF+X FF-F* ' F-W' TFa TFa L Wa W+F' JF-1?' F-W' DYNAMICS. ALGEBRAICAL AND GEOMETRICAL EXPRESSIONS OF THE FUNDAMENTAL PRINCIPLES OF DYNAMICS. Elements. Force = F. Velocity -F. Time = T. Functions. Power = F V. Space 8- V T. WorkK-FVT. = M y\ These are the fundamental principles in Mechanics. REJECTED TERMS. 15 REJECTED TERMS IN MECHANICS. The author has rejected a great number of terms in Mechanics which are considered useless, confusing and without definite mean- ings, a list of which is given below and on the next page. High-sounding terms without definite meaning render the subject of Mechanics difficult to learn, for which reason the author has de- cided to employ only such terms as are used in the shop. The language of Mechanics used in schools and text-books differs so much from that used in practice that when a graduate student con- verses with a practical man on that subject, they do not understand each other, and the latter derides the former as theoretical. This is the principal reason why theoretical sciences are so little available in practice. In the Appendix to this book is given an example of the language of Mechanics as used in institutions of learning, from which it will be perceived that the author has good reasons for having undertaken a revision of the subject. The list of rejected terms on the next page is taken from the new treatise of "Elements of Mechanics," to which the following list of expressions and terms is added : Mechanics of a material point . . . W. p. 165. Forces in space W. p. 182. Principles of virtual velocity . . . W. p. 185. Couples W. p. 200. Dynamical stability . . . . . W. p. 269. Modulus of a machine M. Intensity of force W. p. 164. Strength of impact . . . . W. p. 102. Intensity of the effort B. p. 49. Effort of mechanical work . . . . B. p. 57. Living force impressed . . . . B. p. 82. Equilibrium in a knot . . . . W. p. 281. These kinds of terms and expressions convey no definite meaning, and are not used in practice. REJECTED TERMS. DYNAMICAL TERMS. Rejected Terms. Effort of force. Efficiency of force. Acting force. Force of motion. Working force. Quantity of moving force. Quantity of motion. Mode of motion. Mode of force. Moment of activity. Mechanical power. Mechanical effect. Quantity of action. Efficiency. Rate of work. Dynamic effect. Quantity of work. Actual total quantity of work. Total amount of work. Actuated work. Vis- viva. Living force. Energy. Actual energy. Potential energy. Kinetic energy. Energy of motion. Energy of force. Heat a form of energy. Heat a mode of motion. Mechanical potential energy. Quantity of energy. Stored energy. Intrinsic energy. Total actual energy. Work of energy. Equation of energy. Equality of energy. Reason for Rejection. Means simply force. All forces act. Means motive force. Has no definite meaning. Means simply power. Used for power or work. Means simply work. Formula for work. Primitive and realized work. 141 STEAM ENGINEERING. 1 . A STEAM-ENGINE is only a tool by which the power generated in the steam-boiler is transmitted to where the work is executed, like a water-wheel which transmits the power of a waterfall to its des- tination. ,In hydraulics we define correctly the power of a waterfall, which is called "the natural effect of the fall," in distinction from the power transmitted by the water-wheel ; but in steam engineering we have heretofore not defined correctly the natural effect generated in the steam-boiler as distinct from that transmitted by the engine. A badly-constructed water-wheel may transmit only twenty per cent, of the natural effect of the waterfall, whilst a properly-con- structed wheel may transmit as high as eighty per cent, or more of the power of the fall. Such is the case also with steam-engines. A badly-constructed steam-engine transmits a much smaller percent- age of the natural effect from the boiler than does a better constructed engine. Therefore the power obtained by indicator diagrams from the engine is not a correct measure of the power or steaming capacity of the boiler. 2. From experimental data we have given the volume of steam generated by the evaporation of a given volume of water, which steam volume multiplied by the steam pressure, gives the work done by the steam. This work divided by the time in which it is exe- cuted, gives the natural effect or power of the evaporation, independ- ent of the power transmitted by the steam-engine, supposing that the steam is fully admitted throughout the stroke of the piston. When the steam is expanded in the steam-cylinder, the above de- fined power multiplied by 1 + the hyperbolic logarithm for the expan- sion, gives the natural effect of the steam. 3. The primary source of power is derived from the combustion of fuel in the furnace generating heat which penetrates the heating surface into the water which is thus evaporated. The act of combustion is power, which, multiplied by time, is work. The act of evaporation is power, which, multiplied by time, is work. 18 STEAM ENGINEERING. Fig. 1. The natural effect or power of combustion is not wholly transmitted to evaporation, but part of it escapes through the chimney. The physical constitution of heat is not yet well understood, for which reason we cannot give an intelligent explanation of the dy- namic elements of combustion and evaporation ; but one thing ap- pears to be certain namely, that the temperature of the heat repre- sents force, which is the origin of all power and work. It is also known and demonstrated that heat is convertible into work ; and con- sequently, heat must be the product of the three simple physical ele- ments, force, velocity and time. If the temperature of the heat represents force, then the space occu- pied by the heat must evidently represent the product of velocity and time. Here it is necessary to refer the reader to the author's New Treatise on Elements of Mechanics, published by Porter & Coates, Philadelphia. a 4. The expression "horse-power of a steam-boiler" is understood to mean the horse-power of evaporation in the boiler, which power is derived from the heat in the furnace. For simplicity of illustration, let the steam-boiler be represented by the tube A B, of one square foot sec- tion, with a bottom at A and open at the top B. One cubic foot of water W is placed on the bottom in the tube and covered with a tight piston loaded with a weight Q. A burning lamp L is placed under the bottom to heat the water for making steam. The steam-pressure thus generated will raise the pis- ton with the weight Q to a height S, and the work accomplished by the steam will be the weight Q (which must include the pressure of the atmosphere on one square foot, and also the weight of the piston, which is supposed to move without friction) multiplied by the height S which the piston is raised. This work divided by the time in which it is accomplished, gives the power of evaporation, which is generally termed the power of the boiler. Assume the steam-pressure to be 100 pounds to the square inch above vacuum, then 100 x 144 = 14400 pounds, the required weight of Q. When all the water that is, one cubic foot is evaporated, the steam Q. NATURAL EFFECT OF STEAM. 19 volume will be 267.8 cubic feet ; and as the section of the tube is one square foot, the piston must have been lifted 267.8 feet, minus the one foot occupied by the water, or S= 266.8 feet. The work accomplished by the steam will then be 266.8x14400 = 3,831,920 foot-pounds. Suppose this work to be accomplished in the time of one minute, and the power of the evaporation will be, 3831920 . = 116.12 horse-power. 33000 This should be the natural effect of the steam without expansion. 5. Now, diminish the weight Q gradually, so as to allow the steam to expand say to double its volume. Then, the hyperbolic logarithm for 2 = 0.69315, multiplied by the primitive horse-power 116.12, gives 80.488 horse-power gained- by the expansion alone, and the gross effect of the steam will be 116.12 + 80.488 = 196.608 horse-power. It will be noticed that the one cubic foot of steam which displaced the water was lost in the natural effect of the evaporation ; and that is the steam-volume required for pumping the feed-water into the boiler in order to maintain a constant height of water-level. By the aid of algebra the above argument can be made general for any steam-pressure and dimension of boiler, for which we will adopt the following notation of letters : W= cubic feet of water of temperature 32 Fahr. evaporated in the time T seconds. P= steam-pressure in pounds per square inch above vacuum. ^r = volume of steam compared with that of its water at 32 Fahr. This volume can be found in Nystrom's Pocket-Book, pages 398, 399, calculated from the formula of Fairbairn and Tate, which is yet the highest authority on that subject. = power in effects, or second-foot-pounds. EP = horse-power of evaporation. S = space generated by the steam in cubic feet. jP= force in pounds. V= velocity in feet per second. T= time of operation in seconds. K-= work in foot-pounds done in the time T by the steam. X= grade of expansion of the steam. The Fairbairn's formula for the volume of steam compared with water at 32 Fahr. is 20 STEAM ENGINEERING. See arguments on dryness and humidity of steam, in regard to Fair- bairn's steam-volume. The space S, generated by the steam in cubic feet, will be S=W(tf-l') .... 1 6. This space multiplied by the steam-pressure will be the work done by the steam; and as the space or steam-volume is expressed in cubic feet, the steam-pressure must be expressed per square foot, or 144 P. The unit 1 in the factor (^-1) represents the primitive volume occupied by the water evaporated, and which unit of volume is con- sumed in feeding the boiler with water, as before explained. The work accomplished by the steam will then be in foot-pounds. K= TF(^-l) 144 P ... 2 Work is the product of the three simple physical elements, force F, velocity V and time T, or K=FVT .... 3 Power is the product of the two elements force F and velocity F, or %=FV .... 4 This power is expressed in effects, each of a force of one pound, moving with a velocity of one foot per second, of which there are 550 effects per horse-power, or FV H> = ..... 5 550 The formulas 2 and 3 give the work = T . . 6 Work is the product of power and time, and consequently, if we eliminate the time from the work, we obtain the power, or of which the horse-power will be This formula reduces itself to H>^P(t-l) 9 3.819 T This is the natural effect or gross horse-power of evaporation of water into steam without expansion. NATURAL EFFECT OF STEAM. 21 7. The quantity of water which must' be evaporated under a pressure P in the time T in order to generate a given horse-power will be Assuming the quantity of water evaporated per hour as a measure of gross horse-power of evaporation, we have the time 2 7 =3600 sec- onds. Then 3.819 x 3600 = 13748.4. Insert this value for 3.819 T in formula 9, and the gross horse-power of evaporation per hour will be WP(# 1) 13748.4 ' The quantity of water evaporated per hour per gross horse-power will be ; 13748.4IP 19 Logarithm for 13748.4 = 4.1382522. 8. The steam volume tf is compared with that of water at 32 Fahr. ; therefore, in determining the gross horse-power of evaporation of water of a higher temperature, the action must be reduced to that from water at 32. This reduction is accomplished by the following formula, in which letters denote : t = actual temperature of the feed-water supposed to be higher than 32. T = temperature of the steam of pressure P. W= cubic feet of water that would have been evaporated from the temperature 32. W = cubic feet of feed-water evaporated from temperature t. $"= volume of water at temperature t, compared with that at 39. w= W'f 1082 + 0.305 1 13 This formula is derived from the units of heat required to evap- orate water of temperature 32 to steam of temperature T. This reduction is required for comparing the relative steaming capacity of different boilers fed with water of different temperatures. The reduction varies very little for different pressures namely, from 20 to 150 pounds the difference will show only on the third decimal ; for which reason we may practically omit the steam-pressure and calculate the reduction only for different temperatures of the feed- water, as is done in the following Table I. 22 STEAM ENGINEERING. When the exact relation between pressure, temperature and volume of steam is known, the reduction will likely be independent of the pressure or temperature of the steam. See Humidity of Steam. TABLE I. Reduction for Temperature of Feed- water. Temp. /. Reduction Jl. Logarithm. Temp. t. Reduction R. Logarithm. 40 0.9932 9.9970367 130 0.9105 9.9592620 50 0.9851 9.9934803 140 0.9000 9.9546693 60 0.9761 9.9895039 150 0.8912 9.9499637 70 0.9671 9.9854546 160 0.8815 9.9451979 80 0.9577 9.9812455 170 0.8719 9.9404765 90 0.9486 9.9770612 180 0.8625 9.9357359 100 0.9392 9.9727643 190 0.8529 9.9308916 110 0.9296 9.9683116 200 0.8432 9.9259440 120 0.9199 9.9637468 212 0.8317 9.9199515 9. The actual quantity of feed-water of temperature t, multiplied by the reduction in the table, gives the quantity of water that would have been evaporated when heated from temperature 32 Fahr. Example 11. A steam-boiler evaporating W= 125 cubic feet of water per hour under a pressure of P= 75 pounds to the square inch above vacuum, or 60 pounds above the atmosphere, the temperature of the feed- water being t = 110. Required the natural effect or horse-power of the evaporation ? Formula 11. ff = 125 * 75 < 348 - 15 ' ^236.73 horses. 13748.4 That is, 0.528 cubic feet of water evaporated per hour per horse- power, or 1.893 horse-power per cubic foot of water evaporated per hour. Making correction for the temperature of the feed-water 110 (see Table), the horse-power will be 168.53x0.9392 = 220.06 horse-power, the natural effect of the evaporation. Example 12. What quantity of water of temperature t = 90 must be evaporated under a pressure of P=90 pounds to the square inch in order to generate a natural effect of IP = 150 horse-power ? 13748.4x150 Formula 12. = 78.043 cubic feet. 90(294.61-1) This volume corrected for temperature gives 78.043 : 0.9486 = 82.275 cubic feet, the quantity of water required. NATURAL EFFECT OF STEAM. 23 TABLE II. Natural effect of evaporation of water by heat converted into horsepower. Steam pressure ab. vacm. Water eva 1 Cubic feet. 3orated per orsepower. Cubic in. hour per Pounds. Horse- power per cub. ft. Equiva- lent work per unit of heat. P w W Ibs. H> J 5 0.6024 1041.0 29.852 1.6600 46.584 10 0.5796 1002.0 28.723 1.7253 48.032 14.7 0.5701 985.2 28.252 1.7540 48.583 20 0.5641 974.7 27.954 1.7727 48.902 25 0.5593 966.5 27.717 1.7879 49.040 30 0.5553 959.6 27.518 1.8008 49.403 35 0.5516 ' 953.2 27.337 1.8130 49.665 40 0.5483 947.4 27.170 1.8238 49.832 45 0.5451 941.9 27.012 1.8345 50.150 50 0.5420 936.6 26.861 1.8450 50.244 55 0.5391 931.5 26.715 1.8549 50.440 60 0.5362 926.6 26.573 1.8649 50.651 65 0.5334 921.6 26.429 1.8747 50.861 70 0.5305 917.1 26.300 1.8850 51.060 75 0.5280 912.5 26.168 1.8936 51.265 80 0.5254 907.9 26.038 1.9033 51.470 85 0.5228 903.5 25.910 1.9127 51.670 90 0.5203 899.1 25.783 1.9219 51.865 95 0.5178 894.7 25.660 1.9312 52.077 100 0.5153 890.5 25.537 1.9406 52.264 105 0.5129 886.2 25.415 1.9497 52.513 110 0.5104 882.0 25.295 1.9592 52.722 115 0.5081 877.9 25.177 1.9681 53.053 120 0.5057 873.8 25.060 1.9774 53.137 125 0.5034 869.8 24.945 1.9865 53.351 130 135 0.5008 0.4988 865.3 861.9 i 24.815 24.718 1.9968 2.0048 53.572 53.788 140 0.4965 858.0 24.606 2.0140 54.000 145 0.4943 854.1 24.494 2.0230 54.206 150 0.4921 850:4 24.387 2.0321 54.427 24 STEAM ENGINEERING. The preceding Table II. gives the horse-power per evaporation per hour of water, expressed either in cubic feet, cubic inches or pounds ; also the thermo-dynamic equivalent of heat as realized by the steam without expansion. When the water evaporated is expressed in pounds, the formulas 11 and 12 will appear as follows : Ibs = pounds of water evaporated in the boiler per hour. 15 The correction for temperature of feed-water will be the same by Table I. as when the water is expressed in cubic feet. One cubic foot of water at 32 weighs 62.387 pounds. Fig. 2. 857721 Logarithm for 857721 = 5.9333463. 857721 IP EXPANSION OF STEAM. 10. When steam is working expansively, more power is realized per water evaporated than that given by the Formula 11. Let A B C D, fig. 2, represent a section of a steam cylinder of in- definite length, in which is fitted a piston a b, upon which the full steam-pressure P is acting in the distance /, enclosing the steam-vol- ume A B a b, to be expanded. The work accomplished by the full steam- pressure P can be represented by the area A B a b, or P I. When the admittance of steam is cut off, the piston is moved by the expansion of the steam, and the pressure decreases as the steam-vol- ume increases ; so that when the volume is doubled the pressure will be one-half or 0.5 P, and when the piston has moved two volumes by the expansion that is, three volumes in all the pressure will be JPata'6'. Let the line A B represent the axis of ordinates and B C the axis of abscissa. EXPANSION OF STEAM. 25 x = distance generated by expansion. y = ordinate pressure of the expanded steam. Then P:y =*+*:* ... 1 11. Calculate the ordinate pressure y for several positions of the piston, and set them off as shown in the figure. Join these ordinates by the curve acde, and the work done by the expansion is represented by the area bounded within that curve and P x y. k = area, or work of expansion alone, expressed in units of P I, the work done by the full steam-pressure. Then - dk = l+x We have assumed P I as unit for the measurement, in which case P= 1 and 1 = 1, and the differential work will be 1+x k = I = hyp.log. ( 1 + x) The factor (l+x) represents the whole motion of the piston, of which x is the portion worked with expansion. 8 = whole stroke of the piston. I = part of the stroke worked with full steam. X= grade of expansion that is, when the steam is expanded to double its volume, then X= 2 ; when three times the volume, X= 3, and so on. jr=p(i+*) .... 6 The work done by the expansion will then be k = hyp. log. X= hyp. log.- ... 7 That is to say, the effect gained by the expansion is equal to the hy- perbolic logarithm for the expansion. When the steam is expanded say four times, then hyp. log. 4 = 1.38629, or the gain will be 138 per cent, over the effect of that worked with full steam, and the gross effect K will be 238 per cent. jfiT= 1 -+ hyp.log.X= 1 + hyp.log.- . . 8 STEAM ENGINEERING. The natural effect or horse-power of evaporation without expan- o 13748.4 which multiplied by ( 1 + hyp. log. X^), will be the natural effect or horse-power of evaporation with expansion, or .. 1348.4 12. This formula gives the natural effect of evaporation of water into steam, and which, divided into the power given out or transmit- ted by a steam-engine, gives the efficiency of that steam-engine, as the natural effect of a waterfall divided into the power transmitted by the wheel gives the efficiency of that water-wheel. A compound en- gine working with a high degree of expansion and condensation of the steam may utilize or transmit as high as 80 per cent, of the nat- ural effect of the steam, whilst a high-pressure or non-condensing en- gine working against atmospheric pressure may transmit only 40 per cent, of the natural effect. The expansion X in compound engines is equal to the volume of full steam in the small cylinder, divided into the cubic content of both cylinders. The cubic content of one steam-port in the small cylinder should be included in the volume of full steam, and the cubic content of one steam-port of each cylinder should be included in the volume of the two cylinders. Example 10. A set of steam-boilers, evaporating W= 640 cubic feet of water per hour, under a pressure of P=65 pounds to the square inch, supply steam to a compound engine in which the steam is ex- panded X= 8 times. Required the natural effect of the steam ? Hyp.log.8 = 2.07944. ^ = 397.51. . 640x65x396.51x3.07944 , IP = - - -- - = 3694.6 horse-power, the natural effect required. It is supposed in this example that the temperature of the feed- water was 32, for which there is no reduction. The water evaporated per hour per horse-power, in this example, is 0.1723 cubic feet, or 5.773 horse-power per cubic feet evaporated per hour. POWER OF ATMOSPHERIC PRESSURE. 27 EFFECT OF ATMOSPHERIC PRESSURE OPPOSING THE NATURAL EFFECT OF THE STEAM. 13. The volume of air displaced by the steam will be This volume, multiplied by the atmospheric pressure per square foot, will be the work of resistance of the atmosphere, or F(^-l)Xx 14.7x144 ... 2 That is, 2116.8 TFX(^-l) per hour. This work, divided by 550 x 3600 seconds, gives the horse-power of its execution, or . 2116.6 WXty-l)_ WXtf-V 3 550x3600 935.37 This horse-power, subtracted from Formula 10, will give the natural effect of. the steam above that of the atmosphere, or g WPtf-1) (1 + hyp.log.X) WXtf-V) 13748.4 935.37 _ 935.37 \ 14.698 This should be the natural effect of steam working through a non- condensing engine, which, divided into the indicated horse-power, gives the efficiency of the motor. Example 5. A steam-boiler evaporating W= 85 cubic feet of water per hour, under a pressure of P=100 pounds to the square inch, sup- plies steam to a non-condensing engine, cutting off at one-third the stroke, making X=3 the expansion, the temperature of the feed-water being t = 120 Fahr. Required the natural effect of the steam above that of the atmosphere ? Hyp.log.Z = 1.0986. tf = 267.8. 85x266.8/100x2.0986 \ = " 14.698 ~ Correction for temperature of feed-water t = 120. 273.37 x 0.91 99 = 251.48 horse-power that is, 0.338 cubic feet of water evaporated per hour per horse-power, or 2.958 horse-power per cubic foot of water evaporated per hour. 28 STEAM ENGINEERING. MEAN PRESSURE. 14. When the steam is expanded in the cylinder, the mean pressure throughout the stroke of piston will be less than the initial pressure. .F=mean pressure in pounds per square inch. P= initial pressure. X= grade of expansion. s = length of stroke in inches. I = part of stroke with full steam, in inches. PI The mean pressure during the expansion will be hyp.log.X, PI which, added to , gives the mean pressure throughout the stroke, or , PI PI, F= + hyp.log.X ... 1 8 S X=*-, which, inserted for JTin formula 1, gives , PI PI , s PlL , s\ jP= + hyp.log. - = ( 1 + hyp.log.-] . 2 The mean pressure for different pressures and expansion of steam is calculated by this formula, and given in a table farther on. HYPERBOLIC LOGARITHMS. 15. The common logarithm multiplied by 2.30258509 gives the hyperbolic logarithm, and the hyperbolic logarithm multiplied by 0.43429448 gives the common logarithm. The following table contains the hyperbolic logarithms for numbers up to 39, which is considered sufficient for application to expansion of steam. HYPERBOLIC LOGARITHMS. 29 TABLE III. Hyperbolic Logarithms. No. Logarithms. No. Logarithms. No. Logarithms. No. Logarithms. 1. 0.00000 4. 1.38629 7. 1.94591 10 2.30258 1.1 0.09530 4.1 1.41096 7.1 1.96006 11 2.39589 1.2 0.18213 4.2 1.43505 7.2 1.97406 12 2.48491 1.3 0.26234 4.3 1.45859 7.3 1.98787 13 2.56494 1.4 0.33646 4.4 1.48161 7.4 2.00149 14 2.63906 1.5 0.40505 4.5 1.50408 7.5 2.01490 15 2.70805 , 1.6 0.46998 4.6 1.52603 7.6 2.02816 16 2.77259 1.7 0.53063 4.7 1.54753 7.7 2.04115 17 2.83321 1.8 0.58776 4.8 1.56859 7.8 2.05415 18 2.89037 1.9 0.64181 4.9 1.58922 7.9 2.06690 19 2.94444 2. 0.69315 5. 1.60944 8. 2.07944 20 2.99573 2.1 0.74190 5.1 1.62922 8.1 2.09190 21 3.04452 2.2 0.78843 5.2 1.64865 8.2 2.10418 22 3.09104 2.3 0.83287 5.3 1.66770 8.3 2.11632 23 3.13549 2.4 0.87544 5.4 1.68633 8.4 2.12830 24 3.17805 2.5 0.91629 5.5 1.70475 8.5 2.14007 25 3.21888 2.6 0.95548 5.6 1.72276 8.6 2.15082 26 3.25810 2.7 0.99323 5.7 1.74046 8.7 2.16338 27 3.29584 2.8 1.02962 5.8 1.75785 8.8 2.17482 28 3.33220 2.9 1.06473 5.9 1.77495 8.9 2.18615 29 3.36730 3. 1.09861 6. 1.79175 9. 2.19722 30 3.40120 3.1 1.13140 6.1 1.80827 9.1 2.20837 31 3.43399 3.2 1.16314 6.2 1.82545 9.2 2.21932 32 3.46574 3.3 1.19594 6.3 1.84055 9.3 2.23014 33 3.49651 3.4 1.22373 6.4 1.85629 9.4 2.24085 34 3.52636 3.5 1.25276 6.5 1.87180 9.5 2.25129 35 3.55535 3.6 1.28090 6.6 1-.88658 9.6 2.26191 36 3.58352 3.7 1.30834 6.7 1.90218 9.7 2.27228 37 3.61092 3.8 1.33046 6.8 1.91689 9.8 2.28255 38 3.63759 3.9 1.36099 6.9 1.93149 9.9 2.29171 39 3.66356 30 STEAM ENGINEERING. THERMO-DYNAMICS. 16. The thermo-dynamic equivalent of heat as adopted by Joule is 772 foot-pounds of work per unit of heat. Different authors have given different values of this equivalent namely, Foot-pounds. Joule 772 Favre- 750 Him 723 Quintus 712 Foot-pounds. Joule in 1843 ... 835 Le Roux " 1857... Regnault " 1871... Violle " 1874... 832 792 790 It is not necessary for the purpose of this elementary treatise to enter into an investigation of what is the true equivalent of heat, be- cause a constant equivalent cannot be realized in the working of a steam-engine ; for which reason Ave will here limit ourselves only to the operation of evaporating water into steam, and its transmission through a steam-engine w T ith or without expansion. The thermo-dynamic equivalent of heat is the ratio obtained by dividing the work in foot-pounds by the number of units of heat which performs that work. Formula 2, 6, gives the work of evaporation of a volume of water W, under a steam-pressure P, without expansion, or H' = units of heat per cubic foot of steam. (See Nystrom's Pocket- Boole, pages 400, 401.) J= thermo-dynamic equivalent of heat, which is the work accom- plished per unit of heat expended. X= grade of expansion of steam. The heat utilized by the evaporation* of water will then be H' JF( $-!), which, divided into the work, Formula 2, gives the equivalent, H' U4P H' THERMO-DYNAMICS. 31 17. The column J, Table II., is calculated by this formula, and it will be seen that the equivalent varies with the steam-pressure. When the steam is expanded, the equivalent will be increased by the hyperbolic logarithm of the expansion. When the steam is ex- panded say twice its volume, then X= 2, for which the hyperbolic logarithm is 0.693, or 69 per cent, is gained by that expansion ; there- fore the gross equivalent realized by steam working expansively will be From this formula we obtain the grade of expansion required for any value of the equivalent J namely, Example 5. How much must steam of pressure P=100 pounds to the square inch be expanded in order to realize Joule's equivalent ,7=772? - 1 = 13.771. The number corresponding to this logarithm is 777830 that is to say, the steam must be expanded 777830 times its primitive volume in order to realize 772 foot-pounds per unit of heat ; but the steam will condense to water and freeze to ice long before that expansion is reached, showing the inapplicability of Joule's equivalent to dynamics of steam. By the new steam formulas given farther on, the thermo-dynamic equivalent is constant, 51.5 foot-pounds of work per unit of heat that is, for full steam ; and when expanded, the equivalent will be This is probably the correct thermo-dynamic equivalent of heat as realized by steam. 32 STEAM ENGINEERING. HORSE-POWER OF STEAM-BOILERS BY EVAPORATION. 18. Heretofore it has been the custom to rate the power or steam- ing capacity of a boiler by the indicated horse-power transmitted by the steam-engine, and it has been found that one and the same boiler, fired under equal circumstances, but supplying steam to different engines, has produced widely different indicated horse-power, thus demonstrating that the power transmitted by the engine is not a cor- rect measure of the real power or steaming capacity of the boiler. The question then arose, How can the power of the boiler be correctly determined independent of the working of the engine ? When a steam-user orders a boiler from a boiler-maker, it is gen- erally specified in the contract what power the boiler must generate ; but when finished and tried, the parties concerned do not agree as to what is the correct horse-power of the boiler, and law-suits have thus been instituted and unjust verdicts rendered for want of a definite rule by which to settle the question indisputably and satisfactorily to both parties. In one case a boiler-maker contracted to furnish three boilers of 75 IP each, or in all 225 IP, for a price of $40 per horse-power, or in all $9000; but on trial, only from 100 to 130 IP was generated, ac- cording to indicator diagrams from the steam-engine. 19. The steam-user, finding that power insufficient for his work, declined to pay the full price, $9000, had the boilers taken out and replaced by new ones of the requisite power, furnished by another boiler-maker. The first boiler-maker maintained that his boilers were of the requisite power, and sued the steam-user in order to recover the full price, $9000. Several experts on steam-boiler performance were called as witnesses, and the trial of the case lasted four days, most of which time was consumed in arguing what quantity of water evap- orated per hour is equivalent to one horse-power; but none of the experts appeared to understand the subject. The judge remarked that scientific evidence could not be admitted in the case, and asked if there was any reliable authority on the subject, and was answered no. One expert witn ess stated that the boilers evaporated 100 cubic feet of water per hour under a steam-pressure of 75 pounds to the square inch, but could not state how much horse-power that evaporation would be equivalent to. No evidence was given to the fact that the boilers did not come up to 225 horse-power, and the jury rendered a verdict for the boiler-maker to receive the full pay, $9000. HORSE-POWER OF STEAM-BOILERS, 33 The evaporation of 100 cubic feet of water per hour under a pres- sure of 75 pounds to the square inch is equivalent to 160 IP, and the boilers consequently did not come up to the 225 IP contracted for. Cases of this kind have frequently occurred and caused much incon- venience to the parties concerned. The horse-power of a steam-boiler can be determined correctly by the quantity of water evaporated per unit of time independent of the working of the steam-engine, supposing that all the water is evapo- rated and nothing carried over in the form of foam, known as priming. A distinct line can thus be traced between the efficiencies of the power- generator and the motor. 20. The horse-power given by the indicator diagrams depends much upon the construction of the engine, the regulation of the steam- valves, the grade of expansion used and the correctness of the indicator, with which the boiler-maker has, nothing to do, and for which the perform- ance of the boiler should not be held responsible. The steam-engine may be connected with the boiler by a long, nar- row and uncovered steam-pipe, in which steam may condense by ra- diation of heat, and the steam cylinder may be uncovered, which reduces the indicated horse-power. 21. A condensing or compound engine working with a high de- gree of expansion indicates much more power per water evaporated than does a non-condensing engine working with full steam, which difference of power depends upon the engine-builder, and not upon the boiler-maker. The question may arise whether the steam-pressure of the horse- power should be taken above vacuum or above the atmospheric pres- sure. The boiler-maker may argue that the steam generated in his boiler drives out the atmospheric pressure, and thus claim the right to be credited with the gross power of the steam supplied from his boiler. The steam-user, on the other hand, cannot realize allthat power for his work, and is therefore not willing to pay for more than value received. The boiler-maker does not undertake to remove the atmo- spheric pressure from the back side of the cylinder-piston, which is partly done by the engine-builder making a condensing engine, for which the power of the boiler should include only the pressure indi- cated by a proper steam-gauge or safety-valve, which is the pressure for estimating the power of a non-condensing engine. 22. The legal horse-power of a steam-boiler fired with a given kind or quality of fuel should therefore be that passing from the boiler into the steam-pipe, with the pressure above that of the at- 34 STEAM ENGINEERING. mosphere, independent of the indicated power transmitted by the steam-engine. When a water-owner rents out a waterfall, he only furnishes the natural effect, and does not hold himself responsible for the efficiency of the water-wheel which the miller may employ for realizing the power of that fall. It is to the interest of the miller to use the best wheel that will utilize the highest percentage of the definite natural effect of the waterfall. So it should be also with boilers and engines. The boiler-maker furnishes a steam-boiler generating a definite natural effect of unex- panded steam, and it is to the interest of the steam-user to employ the best construction of engine in order to utilize the highest percentage of the natural effect of that steam. The price of a steam-boiler should be rated according to the natural effect it generates with a given quality and quantity of fuel consumed per unit of time, and the boiler-maker should not be entitled to remu- neration for the effect realized by the superior construction of the steam-engine, which credit is due to the engine-builder, who is paid therefor by the steam-user. 23. The legal horse-power of a steam-boiler should therefore be that determined by Formula 11, 7, with the exception that the steam- pressure p should be taken above that of the atmosphere namely, 13748.4 The water required to be evaporated per hour for a given horse- power is w 13748.4 H> log. 13748.4 = 4.1382522. W= cubic feet of water of temperature 32 Fahr. evaporated per hour. ^ = steam-volume compared with that of its water at 32 Fahr. See pages 400, 401, Nystrom's Pocket-Book. When the water evaporated per hour is expressed in pounds, the Formulas 1 and 2 will be 857721 857721 IP - Xt-D HORSE-POWER OF STEAM-BOILERS. 35 The term "legal" is used on the ground that the formulas are based upon Watt's unit of horse-power, which unit is legalized all over the civilized world, differing only slightly in different countries, to accommodate the different units of weight and measure ; therefore the legalization of Watt's rule for horse-power makes the formulas in this paragraph legal. Watt's unit for horse-power is 33000 minute-foot-pounds, which is the same as 550 second-foot-pounds, the standard upon which the formulas are based. Example 3. What is the horse-power of a boiler evaporating fts. = 640 pounds of water per hour of temperature t = 80, to steam of p = 80 pounds to the square inch ? 640x80(280.5-1) 857721 Correction for temperature of feed-water 80 will be 0.9577 x 166.84 = 159.78, the horse-power required. Example 1. A steam-boiler evaporating TF= 64 cubic feet of water per hour, under a pressure of p = 85 pounds to the square inch above that of the atmosphere, the temperature of the feed-water being t = 120 Fahr. Required the legal horse-power of the boiler? Correction for temperature 120 of the feed-water will be, see Table I., page 22. IP = 0.9199 x 105.57 = 97.113, the legal horse-power required. Example 2. How much feed-water of t = 90 must be evaporated per hour under a pressure of p = 65 pounds to the square inch above that of the atmosphere in order to generate a legal horse-power IP = 360 horses of the boiler? Correction for temperature t - 90 W= 232.8 : 0.9486 = 245.43 cubic feet, the quantity of water required. The following Table IV. is calculated from the above formulas, giving the quantity of water expressed in cubic feet, cubic inches or pounds required to be evaporated per hour per horse-power, and also the horse-power per cubic foot of water evaporated per hour under different pressures. 36 STEAM ENGINEERING. TABLE IV. Legal Horse-power of Steam-boilers per Rate of Evaporation of "Water to Steam. Steam pressure ab. atm. Water e Cubic feet. /aporated per horse-power Cubic in. hour per Pounds. Horse- power per cub. ft. Work, ft.-lbs. per unit of heat. P w W Ibs. B? J 5 2.2562 3898.8 140.76 0.4433 12.225 10 1.3983 2416.2 87.235 0.7150 19.616 15 1.1106 1919.0 69.284 0.9005 24.701 20 0.9654 1668.1 60.226 1.0358 28.380 25 0.9770 1515.4 54.711 1.1403 31.145 30 0.8176 1411.9 51.010 1.2231 33.433 35 0.7743 1338.1 48.308 1.2914 35.171 40 0.7412 1280.9 46.244 1.3490 36.683 45 0.7150 1235.5 44.605 1.3986 37.988 50 0.6935 1198.3 43.264 1.4420 39.124 55 0.6755 1167.2 42.140 1.4804 40.118 60 0.6600 1140.6 41.180 1.5150 41.012 65 0.6467 1117.5 40.345 1.5463 41.819 70 0.6349 1097.1 39.607 1.5750 42.551 75 0.6243 1078.9 38.951 1.6016 43.221 80 0.6149 1062.5 38.360 1.6263 43.854 85 0.6062 1046.6 37.822 1.6495 44.425 90 0.5983 1033.9 37.328 1.6713 45.011 95 0.5910 1021.3 36.873 1.6919 45.533 100 0.5847 1009.6 36.451 1.7115 46.027 105 0.5779 998.67 36.056 1.7303 46.495 110 0.5720 988.44 35.686 1.7482 46.949 115 0.5664 978.75 35.337 1.7655 47.390 120 " 0.5611 969.62 35.007 1.7822 47.812 125 0.5561 960.96 34.694 1.7982 48.213 130 0.5513 952.65 34.394 1.8073 48.604 135 0.5468 945.00 34.111 1.8288 49.737 HOESE-POWER OF STEAM-BOILERS. 37 HORSE-POWER OF STEAM-BOILERS BY FIRE-GRATE AND HEATING SURFACE. 24. The evaporating capacity of a steam-boiler fired with a given kind or quality of fuel depends upon the extent of area of fire-grate and heating surface. B = area of fire-grate in square feet. Q = heating surface in square feet. W= cubic feet of water of temperature 32 Fahr. evaporated per hour. In ordinary steam-boilers the average evaporation with natural draft is TF=0.4 1 /B~a, .... 1 under the condition that the heating surface should be between 18 and 36 times the area of the fire-grate. This water, multiplied by the steam-volume, gives the space gen- erated per hour by the steam, or >S r =0.4(^-l) 1 /B a, ... 2 S = cubic feet of steam generated per hour. This space, multiplied by the steam-pressure per square foot 144 P, gives the work accomplished by the steam per hour. .. 3 K= 57.6 P(ir- l)i/Bfa ... 4 This work, divided by 33,000 pounds times 60 minutes = 1,980,000, gives the horse-power of the boiler expressed by area of fire-grate and heating surface. 1980000 34400 This formula gives the gross effect or horse-power of the steam above vacuum ; but for the practical rating of the power of a steam- boiler, the pressure should be taken above that of the atmosphere, or 34400 38 STEAM ENGINEERING. 25. Although thi.s formula gives the average horse-power of a steam-boiler, it cannot be termed legal because the evaporation is the real power of the boiler, which depends upon the firing, circula- tion of water and other variable circumstances not included in the formula. The volume ("^ 1) varies inversely with the pressure, and the product^ (ft - 1) varies nearly as the cube root of the pressure p, for which we may practically place p (^ - 1) = 5000 y'p, and the horse- power of the boiler will be for a chimney 50 feet high, xlr . , o See Table of Corrections for Height of Chimney. This formula should not be used for less pressure than p = 15 pounds to the square inch. Example 8. Required the horse-power of a steam-boiler with fire- grate B = 130 square feet, and heating-surface L3 = 3372 square feet, carrying a steam-pressure of p = 50 pounds to the square inch above that of the atmosphere ? , 1^50/130x3372 Formula 42. IP = *- x = 354.53 horse-power. 6.88 This is the horse-power the boiler would generate without expand- ing the steam. Example 1. Required the quantity of water evaporated per hour by the fire-grate B = 130, and heating-surface O = 3372 square feet? Formula 1. W= 0.4/130x3372 = 264.8 cubic feet. The efficiencies of steam-boilers can readily be compared with these formulas. When the steam is expanded in the engine, the power derived from the boiler may practically be estimated as follows : This formula should not be taken for the horse-power of the steam- boiler, but for that transmitted by the engine. In the preceding example we have the horse-power IP = 354.53 when working with full steam ; but if the steam is expanded say X=B times, we have hyp.log.B = 1.0986 and 2.0986x354.53 = 744 HORSE-POWER OF STEAM-BOILERS. 39 horse-power, of which 70 per cent, may be transmitted through the engine, or IP = 744 x 0.7 - 520.8 horse-power, which would probably be indicated by diagrams. It is supposed in the preceding examples that the temperature of the feed-water is 32. For any other temperature up to 212, use the correction in the following Table V., corresponding to the actual temperature of the feed-water, as follows : R = correction in the Table V. H> 6.88 TABLE V. Gain of Power or Water evaporated by heating the Feed-water from 32 to t. Temp. t. Gain R. Logarithm. Temp. t. Gain R. Logarithm. 40 1.0068 0.0029432 130 1.0983 0.0407210 sa 1.0151 0.0065088 140 1.1111 0.0457531 60 1.0245 0.0105120 150 1.1221 0.0500316 70 1.0340 0.0145205 160 1.1344 0.0547662 80 1.0441 0.0187421 170 1.1469 0.0595256 90 1.0542 0.0229230 180 1.1594 0.0642333 100 1.0647 0.0272273 190 1.1725 0.0691129 110 1.0757 0.0316912 200 1.1859 0.0740481 120 1.0870 0.0362295 212 1.2023 0.0800128 The horse-power given by Formulas 8, multiplied by the correction for height of chimney, Table VII. , gives the horse-power which may be expected from the boiler. The following Table VI. gives the horse-power of boilers per square foot of grate-surface for different proportions of heating-surface, when the steam is worked without expansion through a non-condensing engine, and the temperature of the feed-water is 32. 40 STEAM ENGINEERING. TABLE VI. Horse-power per Square Foot of Fire-grate for Chimney 50 Feet High. Steam pressure. a = i6B Proportion of flre-gr a = 20 B a = 25 B ate and heal a = 30B ing surface. a = 35B a=4oB P IP IP IP IP IP IP 25 1.7 1.91 2.14 2.33 2.52 2.63 30 1.81 2.02 2.27 2.48 2.67 2.8 35 1.91 2.13 2.38 2.61 2.81 2.95 40 2. 2.23 2.49 2.73 2.94 3.08 45 2.08 2.32 2.59 2.84 3.06 3.2 50 2.15 2.4 2.68 2.94 3.17 3.32 55 2.22 2.48 2.77 3.03 3.28 3.42 60 2.29 2.55 2.85 ' 3.12 3.37 3.52 65 2.35 3.62 2.93 3.2 3.46 3.62 70 2.4 3.67' 2.99 3.27 3.53 3.7 75 2.46 2.74 3.07 3.36 3.63 3.8 80 2.51 2.81 3.13 3.43 3.71 3.88 85 2.57 2.87 3.2 3.51 3.79 3.96 90 2.62 2.92 3.26 3.57 3.85 4.04 95 2.66 2.97 3.32 3.63 3.93 4.11 100 2.71 3.02 3.38 3.7 4. 4.19 110 2.8 3.12 3.49 3.82 4.13 4.32 120 2.88 3.21 3.59 3.93 4.24 4.44 130 2.96 3.3 3.68 4.04 4.36 4.57 140 3.03 3.38 3.78 4.14 4.47 4.68 150 3.11 3.46 3.87 4.23 4.57 4.79 160 3.17 3.54 3.95 4.33 4.67 4.89 170 3.23 3.62 4.03 4.42 4.77 4.99 180 3.3 3.68 4.11 4.5 4.86 5.09 190 3.36 3.74 4.21 4.58 4.94 5.18 200 3.41 3.81 4.26 4.64 5.03 5.27 210 3.47 3.88 4.32 4.74 5.11 5.36 220 3.52 3.93 4.39 4.81 5.2 5.44 230 3.58 3.99 4.46 4.88 5.28 5.52 240 3.63 4.05 4.52 4.95 5.35 5.6 250 3.68 4.11 4.59 5.03 5.42 5.68 260 3.72 4.16 4.65 5.09 5.49 5.75 270 3.77 4.21 4.70 5.16 5.57 5.82 280 3.82 4.26 4.76 5.22 5.63 5.9 290 3.87 4.31 4.82 5.28 5.69 5.96 300 3.9 4.36 4.87 5.34 5.75' 6.03 i HEIGHT OF CHIMNEYS. 41 TABLE VII. Correction of Horse-power per Square Foot of Grate for Different Heights of Chimneys in Feet. Height Chim- ney. Correc- tion. Height Chimney. Correc- tion. Height Chimney. Correc- tion. Height Chimney. Correc- tion. feet. r. feet. r. feet. r. feet. r. 10 0.5 75 1.20 180 1.78 310 2.27 15 0.59 80 1.23 190 1.82 320 2.30 20 0.67 85 1.27 200 1.86 330 2.33 25 0.74 90 1.30 210 1.90 340 2.36 30 0.8 95 1.33 220 1.94 350 2.40 35 0.85 100 1.36 230 1.98 360 2.43 40 0.91 110 1.42 240 2.02 370 2.46 45 0.96 120 1.48 250 2.06 380 2.49 50 1.00 130 1.53 260 2.10 390 2.52 55 1.04 140 . 1.58 270 2.13 400 2.55 60 1.08 150 1.63 280 2.16 410 2.57 65 1.12 160 1.68 290 2.20 420 2.60 70 1.16 170 1.73 300 2.23 430 2.63 Allowance is made in the above table for radiation or conduction of heat from the gases through the walls of the chimney. TABLE VIII. Consumption of Coal in Pounds per Hour per Square Foot of Grate, for Different Heights of Chimney. Height Chim- ney. Consunipt. coal. Height Chimney. Consumpt. coal. Height Chimney. Consumpt. coal. Height Chimney. Consumpt. coal. 10 7.00 75 16.8 180 25. 310 31.8 15 8.25 80 17.2 190 25.5 320 32.2 20 9.4 85 17.8 200 26. 330 32.7 25 10.4 90 18.2 210 26.5 340 33.1 30 11.2 95 18.6 220 27.2 350 33.6 35 12. 100 19. 230 27.7 360 34. 40 12.8 110 19.9 240 28.3 370 34.4 45 13.4 120 20.7 250 28.9 380 34.9 50 14. 130 21.4 260 29.4 390 35.3 55 14.6 140 22.1 270 29.8 400 35.7 60 15.1 150 22.9 280 30.3 410 36. 65 15.7 160 23.5 290 30.8 420 36.4 70 16.2 170 24.2 300 31.2 430 36.8 It is not expected that this gives the correct consumption of coal, which depends much upon the kind of coal and manner of firing, but it gives the proportionate consumption to the height of the chimney. See horse-power of chimney, Table XXIX., page 123. 42 STEAM ENGINEERING. CHIMNEYS. 26. The proportion of a chimney to the horse-power of the steam generated and consumption of fuel on the fire-grate is a very difficult problem to solve theoretically. It is certain, however, that the horse- power of a chimney, as well as the consumption of fuel on the fire- grate, is directly as the section area and square root of the height of the chimney. The term "horse-power" in this connection means the power of draft in a chimney required for the combustion generating heat for evaporation of water to steam of a given horse-power. The following formulas are derived from both theory and prac- tice, and the horse-power is that generated by full steam without ex- pansion : IP = horse-power of chimney. B = area of fire-grate in square feet. A = section area of chimney in square feet. jET= height of chimney in feet when A = 0.16 B. C = pounds of coal consumed per hour on the fire-grate. r = coefficient for correction in the preceding Table VII. Horse-power, IP = 10Ar 1 Consumption of fuel, C=14Br 2 Area of chimney, Area of grate, B = 4 14 r -rr> Correction, r = 5 1U A. C 1 Correction, r = . . 6 n .- Correction, 10.755 Example 1. Required the horse-pOAver of a chimney -H"=80 feet high above grate and A = 4 square feet cross-section ? Correction for 80 feet = 1.23. IP = 10x4xl.23 = 49.2 horse-power. POWER OF COMBUSTION. 43 Example 2. How much coal will be consumed per hour on a fire- grate B = 150 square feet connected with a chimney H = 60 feet high? Correction for 60 feet is 1.09. (7= 14 x 150 x 1.09 = 2289 pounds. Example 6. What height of chimney is required for a draft con- suming (7=1216 pounds of coal per hour on a grate E3 = 64 square feet? Correction, r = 1.357. 14x64 The height of chimney in the table corresponding to this correction is H= 100 feet. Example 5. A chimney is to be constructed for a boiler having a grate surface of B = 48 square feet. The section area of the chimney is. made A = 0.16 B = 0.16 x 48 = 7.68 square feet. How high must the chimney be that the draft'will generate IP = 192 horse-power? 192 Correction, r = = 2.5. Height H= 390 feet. J.U x / .00 The smoke-stacks for steamboats are generally made cylindrical or parallel that is, of equal section from boiler to top ; but brick chim- neys for factories are generally made taper, with about 45 per cent, more section area at the bottom than at the top. The area A in the preceding formulas and examples should be that at the top of the chimney. POWER OF COMBUSTION. 27. On account of the physical constitution of heat not being well understood, an intelligent explanation of dynamics of combustion cannot be given. Combustion is the operation of combining oxygen with fuel, which generates heat ; and the more rapidly that combination is performed, the higher will be the temperature of the heat. The chemical combination of oxygen with a definite weight of fuel generates a definite quantity of heat, which is convertible into work, or the product of the three simple physical elements force, velocity and time, represented by F V T. Of this work, the thermo-dynamic equivalents may be represented as follows : F= force, which is convertible into temperature of the heat, V= velocity, or rate of combustion, which is proportioned to the area of the fire-grate. FV*= power, the act of combustion, or combination of oxygen and fuel. 44 STEAM ENGINEERING. V T= space, or the volume occupied by the heat. FVT= work, which represents the quantity of heat generated by the combustion in the time T. For a definite quantity of heat generated in a long time T the power F V must be small, and for a short time T the power F V must be larger ; but for a constant power F V either one of the ele- ments F and V may vary at the expense of the other. 29. For a definite quantity of fuel consumed per unit of time on different extent of grate-surface, the temperature of combustion should be inversely as the grate-surface that is to say, a forced draft should generate a higher temperature of the fire than would be attained by natural draft. The combustion per unit of time is as the square root of the pressure of the air. The fuels generally used for generating heat are carbon, hydrogen and sulphur, of which only carbon, which is the predominant fuel used in steam-boilers, will herein be considered. Carbon forms two compounds with oxygen namely, carbonic oxide G 0, and carbonic acid C 2 , the equivalent of carbon being 6, and that of oxygen 8 that is to say, 6 pounds of carbon united with 8 pounds of oxygen forms carbonic oxide, which is a transparent, colorless gas which when ignited will burn with a faint flame, taking up another atom of oxygen, and forms carbonic acid, composed of 6 pounds of carbon and 8x2 = 16 pounds of oxygen. One pound of carbon combined with 16 : 6 = 2f pounds of oxygen forms 31 pounds of carbonic acid, which is complete combustion of the carbon. AIR FOR COMBUSTION. 30. The oxygen required for combustion is supplied from at- mospheric air, which is a mechanical mixture of 23 weights of oxygen to 77 of nitrogen in 100 weights of air. 21 volumes of oxygen to 79 of nitrogen in 100 volumes of air. One cubic foot of dry atmospheric air, of temperature 60 Fahr. and under a pressure of 30 inches of mercury, weighs 532 grains, or 0.076 of a pound, and 13.158 cubic feet weighs one pound. One pound of air contains 0.23 pounds of oxygen, and 13.158 : 0.23 = 57.21 cubic feet of air to make one pound of oxygen. The combustion of one pound of carbon requires 2$ pounds of oxy- gen ; therefore 57.21 x 21 = 152.56 cubic feet of dry air, of temperature 60, is required for the complete combustion of one pound of carbon. TEMPERATURE OF DRAFT. 45 Carbonic oxide requires 57.21 xlj = 76.28 cubic feet of air per pound of carbon consumed. Different temperatures of the air require different volumes for the combustion of one pound of carbon, as shown in the accompanying Table IX. TABLE IX. Properties of Air for Combustion. Temp, of air. Fahr. Volume of air. 1 at 32. Weight per cub. foot. v C 1 Ib. of air. ubic feet of 1 Ib. of oxygen. air required Comb. 1 11 carb. acid. for ). carbon, carb. oxide. 10 0.9554 0.08414 11.885 51.674 137.804 68.902 20 0.9756 - 0.08236 12.142 52.792 140.778 70.389 ' 32 1.0000 0.08023 12.464 54.191 144.510 72.255 40 1.0162 0.07886 12.681 55.135 147.026 73.513 50 1.0365 0.07718 12957 56.335 150.226 75.113 60 1.0567 0.07600 13.158 57.209 152.556 76.278 70 1.0760 0.07453 13.417 58.335 155.560 77.780 80 1.0973 0.07311 13.678 59.470 158.586 79.293 90 1.1176 0.07146 13.994 60.843 162.248 81.124 100 1.1378 0.07051 14.182 61.661 164.430 82.215 110 1.1581 0.06928 14.434 62.756 167.348 83.674 120 1.1784 0.06808 14.688 63.861 170.296 85.148 TEMPERATURE OF DRAFT. 31. In comparative experiments on evaporation or steaming capacities of boilers supplied with air of widely different tempera- tures, various opinions have been advanced as to what would be the proper allowance for temperature of the air. When the air of different temperatures enters the furnace under constant pressure or natural draft, what is gained by the warmer air is lost by less oxygen per volume. In a cold atmosphere there is better draft in the chimney than in warmer air ; but when the air is supplied and heated under pressure, as in a blast-furnace, then there is an advantage in the combustion by the hot air. In a cold atmosphere more heat will no doubt be radiated from the boiler and steam-pipe, but the generation of heat in the furnace and steam in the boiler will not be materially diminished, although the cold air enters the fire with less velocity than does warmer air. 46 STEAM ENGINEERING. HEAT OF COMBUSTION. 81. The heat of combustion means the quantity of heat generated by the burning of a given weight of fuel, and which is a distinct quan- tity from that of the temperature of the fire. The English unit of heat is that required to elevate the temperature of one pound of water from 39 to 40 Fahr. The experiments of Regnault show that the elevation of the temperature of one pound of water from 32 to 212 or 180 requires 180.9 units of heat that is to say, for higher temperatures than 39 to 40 it requires a little more than one unit of heat to elevate the temperature of one pound of water one degree ; but the difference is so small that in practice we may consider one unit of heat as standard for elevating the tempera- ture of one pound of water one degree at all temperatures below that of the boiling point. The experiments of Favre and Silberman show that the combus- tion of one pound of carbon to 2& pounds of carbonic oxide generates 4400 units of heat, and to 2f pounds of carbonic acid 14,500 units of heat. That is to say, the acid generates 14,500 : 4400 = 3.27 times more heat than does the oxide, showing the importance of burning the fuel completely to acid. If it requires, say, 150 cubic feet of air for burning one pound of carbon to acid, it requires only 75 cubic feet for the burning to oxide. Now, if the supply of air is between 150 and 75 cubic feet, both the gases will be formed and mechanically mixed, but not chemically combined, in the combustion chamber. Suppose 120 cubic feet of air is supplied per pound of carbon consumed, what will be the proportion of oxide and acid formed? and how many units of keat will be generated per pound of carbon consumed ? Assuming the temperature of the air to be 60, it requires 57.21 cubic feet to make one pound of oxygen, and 120 : 57.21 = 2.0975, say two pounds of oxygen. 56 21 x 2 Carbonic oxide = ' = 1.1666 pounds. oo x o 44 Carbonic acid = = 1.8333 pounds. One pound of carbonic oxide generates 1650 units of heat. One pound of carbonic acid generates 3960 units of heat. Then 1650 x 1.1666 + 3960 x 1.8333 = 9184.75 units of heat generated by the com- bustion of one pound of carbon with the oxygen of 120 cubic feet of air. With 30 cubic feet, or 25 per cent., more air the carbon would FORMULAS FOR HEAT AND COMBUSTION. 47 have been consumed to acid, and generated 14,500, or nearly 58 per cent, more heat. This shows the importance of supplying a sufficient quantity of air to the furnace for the complete combustion of the carbon to carbonic acid. 2 32. FORMULAS FOR HEAT AND COMBUSTION. CO = pounds of carbonic oxide, "I CO, = pounds of carbonic acid, / formed b ^ combustlOD - (7= pounds of carbon consumed by = pound of oxygen. h = units of heat generated by the combustion. 56 (7-21 C0 = C0,- 12 33 0-44 C 12 7i = 3960 (CO,) + 1650 (CO) ... 3 The following Table X. is calculated by the above formulas, making C= 1 pound of carbon. The first column contains the oxygen sup- plied for the combustion of one pound of carbon, and the second col- umn the cubic feet of air containing the oxygen in the first column : TABLE X. Operation of Incomplete Combustion of Carbon. Per Ib. of Oxygen Ibs. Carbon. Air 60 cub. feet. Carbon! CO Ibs. : Oxide. Units of heat. Carbon C0 2 Ibs. c Acid. Units of heat. Total units of heat. Percent- age of heat lost. U 76.278 2i 4400 4400 69.65 1.4 80.092 2.2222 3666.6 0.1833 726.0 4713.6 67.02 1.5 85.813 2.0416 3368.6 0.4583 1813.4 5182.0 64.26 1.6 '91.534 1.8666 3080.0 0.7333 2904.0 5984.0 58.73 1.7 97.265 1.6916 2791.3 0.9258 3666.1 6457.4 55.47 1.8 102.99 1.5166 2502.5 1.2833 5082.0 7584.5 47.69 1.9 108.71 1.3416 2213.8 1.5583 6169.7 8382.5 42.19 2.0 114.42 1.1666 1925.0 1.8333 7260.0 9185.0 36.66 2.1 120.14 0.9916 1636.3 2.1083 8349.0 9985.3 31.14 2.2 125.86 0.8166 1347.5 2.3833 9438.0 10785 25.62 2.3 131.58 0.6416 1058.8 2.6583 10527 11586 20.10 2.4 137.30 0.4666 770.0 2.9333 11616 12386 14.58 2.5 143.02 0.2916 481.3 3.2083 12705 13186 9.06 M 152.55 0.0000 0000 3.6666 14500 14500 0.00 48 STEAM ENGINEERING. Suppose 120.14 cubic feet of air is supplied per pound of carbon con- sumed, the results will be as in the table namely. Carbonic oxide CO = 0.9916 Ibs. of 1636.3 units of heat. Carbonic acid CO., = 2.1083 Ibs. of 8349. units of heat. Products of combustion = 3.0999 fts. of 9985.3 units of heat. The loss by incomplete combustion is 31.14 per cent., as shown in the last column of the table. This table shows the operation of incomplete combustion with a dif- ferent supply of air per pound of carbon consumed. For instance, if 114.42 cubic feet of air is supplied per pound of carbon consumed, it will generate 1.16 pounds of CO of 1925 units of heat and 1.83 pounds of CO, of 7260 units of heat ; in all 9185 units of heat, with 36.6 per cent, loss of that if 152.55 cubic feet of air had been supplied. When less air is supplied than is required for forming carbonic a'cid, the produce of combustion will form smoke with unconsumed particles of carbon ; and when more air is supplied than is required for forming carbonic acid, the excess will be heated by the products of combus- tion, which heat is thus lost and carried up through the chimney. FUEL. 33. The fuels generally used in steam-boilers for combustion to generate heat are wood, charcoal, peat, mineral coal and coke, none of which is pure carbon, as heretofore assumed in the operation of com- bustion, but contains various proportions of carbon, hydrogen, oxygen and involatilizable matter forming ash. The hydrogen in the fuel, combined with oxygen by combustion, generates about four times as much heat per weight of hydrogen consumed as does an equal weight of carbon. The combustion of one pound of hydrogen by 8 pounds of oxygen forms steam and generates 62032 units of heat; there- fore, if one pound of fuel contains, say 0.9 of a pound of carbon and 0.1 of a pound of hydrogen, the heat generated by the combustion will be Hydrogen, 62032 x 0.1 = 6203.2 units of heat. Carbon, 14500 x Q.9 - 13050 " Total, = 19253.2 units of heat. When the fuel contains only carbon and hydrogen, the following forms for combustion give the units of heat generated : a = fraction of carbon j ^ Qne d of ^ H' - " hydrogen ) MOISTURE IN FUEL. 49 = pounds of oxygen required for the complete combustion per pound of fuel. A = cubic feet of air at 60 required for the combustion of one pound of fuel. The units of heat generated per pound of fuel consumed will be A = 62032IP + 145000' ... 3 MOISTURE IN FUEL. 34. When a fuel contains both oxygen and hydrogen partly com- bined in the form of water or moisture, that part of the fuel will be inert in the generation of heat. One-eighth of the oxygen will be eqtfal to the inert part of the hydrogen, so that the heat generated by the hydrogen in the fuel will be h = 62030 (if' - ) . 4 \ 8 / Heat by the carbon, h = 145000' ... 5 The sum of these two formulas will be the heat generated by the fuel when sufficient oxygen is supplied for its combustion namely, h = 1 4500 1 C' + 4.28(5"' - | 6 fc" +4.28(5"'- C' , H' and O are fractions in one pound of the fuel. The weight of oxygen required for this combustion will be The cubic feet of air of 60 required for this oxygen is A=l UNCOMBINED OXYGEN AND HYDROGEN IN FUEL. 35. When the oxygen and hydrogen in a fuel are not chemically combined, their combination by combustion will generate heat, and the oxygen required for the combustion of the C' and H' will be diminished by (7. When a fuel contains the three combustibles carbon, hydrogen and sulphur, the heat generated by its complete combustion will be h = 14500 C' + 620305"' + 4032S' . . 9 4 50 STEAM ENGINEERING. The proportion of ingredients in fuel varies very much, even in the same kind of fuel like mineral coal, for which analyses and experiments must be made with each fuel to determine its correct heating power. The following Table XI. gives the average proportion and property of different fuels, compiled from analyses and experiments by the most reliable authors. TABLE XI. Proportions of Ingredients in, and Heat G-enerated by, the Combustion of One Pound of Fuel. Ingredients in One Pound of Fuel. 111 Combustibles. Non-combustibles. Per pound of fuel. Fuels. Car- Hydro- Sul. Nitro- Oxy- Ash. Air. Heat. Water rs? bon. gen. phur. gen. gen. evap. C' ir S' Jf a Cu. ft. h. Ibs. 1 153 14500 124 5 03 1 459 62032 53 1 18 Sulphur 1 114.4 4032 3.44 182 Peat dry 056 006 23 15 100 99S4 8.42 74 Woods Oak 048 006 041 005 784 7580 6 47 967 ' White Pine 0.49 0.08 0.39 0.04 88.7 8966 7.65 8.17 Birch 048 0.07 040 05 82.6 8300 707 884 Charcoal, Oak 0.88 0.03 0.06 0.03 144 13760 11.7 5.34 Pine 0.72 0.06 0.04 0.15 0.03 138.5 12921 11. 5.67 Maple 0.70 0.05 0.05 0.17 0.03 121 13411 11.45 5.67 Bituminous Coal 0.84 0.05 0.015 0.012 0.03 0.05 147 14780 12.62 4.94 Anthracite Coal 0.88 0.01 0.06 135 12760 10.9 5.73 Coke 0.8V 0.02 0.02 0.008 0.002 0.06 142 13865 11.85 5.27 1 765 4400 3 76 166 CO burning to CO 2 0.4286 0.5714 76.5 10100 8.63 7.25 Alcohol 0.520 0.137 0343 122 75 12339 10 55 593 Tallow 079 117 0093 169 15550 1327 4.7 Bees' Wax, White 0.815 0.139 0.045 186 18900 16.12 3.88 The pounds of water evaporated per pound of coal, as given in the table, is equal to the units of heat per pound of steam, of pressure p = 50 Ibs. to the square inch above that of the atmosphere = 1172.8 units, divided into the units of heat generated by the combustion of one pound of coal. The units of heat per pound of steam of any pressure is h = 1082 + 0.305 T ... 10 This is the heat required to elevate the temperature of one pound of water from 32 Fahr. to boiling-point and evaporate it to steam of temperature T. See table, pages 400, 401, Nystrom's Pocket-Book. PROPERTIES OF FUEL. 51 When the feed-water is of higher temperature, a reduction is re- quired as follows : w = pounds of water heated from temperature t and evaporated to steam of temperature T per pound of fuel consumed. h' = units of heat of combustion of one pound of coal available in evaporation. This is the proper formula for comparing the evaporative quality of different fuels consumed in similar boilers ; and when similar fuels are used in different kinds of boilers, this formula gives the relative efficiency of the boilers. Example. Two different kinds of fuel A and J5 are experimented with in one or similar boilers. One pound of the fuel A evaporates w = 7.5 Ibs. of water from t = 96 to steam of T= 297.84. One pound of the fuel B evaporates w = 9 Ibs. of water from =115 to steam of !F= 31 1.86. Required the available units of heat per pound of each fuel, and their relative steaming quality ? A. h' = 7.5(1114 + 0.305 x 297.84 - 96) =8203.3 units of heat. B. h' = 9(1114 + 0.305 x 311.86 - 115) = 11917 units of heat. The fuel B is 45 J per cent, better than the fuel A. It is supposed that the firing and draft to the grate and other cir- cumstances are alike in both experiments. Example 11. Two different kinds of boilers C and D are fired with the same kind of fuel. The boiler C evaporates, per pound of coaJ consumed, w = 6 Ibs. of water from t = 60 to steam of T= 393.94. The boiler D evaporates, per pound of fuel consumed, w = 8 Ibs. of water from t = 85 to steam of T= 320.1. Required the relative qualities of the two boilers ? C. h' = 6(1114 + 0.305 x 393.94 - 60) = 7044.9 units of heat. D. h' = 8(1114 + 0.305x320.1 -85) =9013.04 units of heat. D Q01 3 04. Relative quality of boilers, ^ = = 1.2794. C /044.9 The boiler D is nearly 28 per cent, better than the boiler C. 52 STEAM ENGINEERING. QUALITY OF BOILERS AND FUEL COMPARED WITH A STANDARD MEASURE. 36. The most simple and correct way of comparing the quality or economy of different boilers fired with the same kind of fuel, or of different kinds of fuel consumed per hour in the same kind of boilers, is to compare the units of heat realized by evaporation with the total units of heat 14500 due to the combustion of one pound of carbon to carbonic acid. In the preceding four examples A, B, C and D we have the rela- tive economy as follows : A = - = 0.56575, or 56 J per cent. _ 14500 _ 0.4858, or 48 1 per cent. = 0.6216, or 62 per cent. 14500 Logarithm, 14500 = 4.1613680. The fuel B gave the best result, and the boiler C the poorest ; but the question now arises whether or how much of the economy is due to the fuel or to the boiler. The percentage of carbon in a fuel ought to determine its quality, but it is well known that different kinds of fuel of equal proportions of carbon give widely different results in the evaporation of water or generation of steam. Theoretically, the percentages given in the last four examples, divided by the percentage of carbon in the respective fuels, should give the relative quality of the respective steam-boilers. Suppose the fuel used in the boilers C and D to contain 0.75 of carbon ; the quality of these boilers, compared with the natural effect as a standard, will then be C= =64.6 per cent. 0.75 62 D - - = 82.6 per cent. 0.75 This mode of comparing the quality of boilers with the natural effect as a standard impresses the mind at once with merits or economy of the boilers. PETROLEUM AS FUEL. 53 EVAPORATION FROM 212. 37. The comparison of steam-boiler performance with the evapora- tion of water from and at 212 Fahr. to steam under atmospheric pressure is a clumsy standard which repeatedly requires explanation, and even then is not always well understood. There have been many cases in which boilermakers maintained that the horse-power of their boilers should be calculated by the evaporation of water from and at 212, while water cannot be pumped into the boiler at tha tempera- ture. When the water is heated between the feed-pump and the boiler, it is done so at the expense of the heat generated in the fur- nace or by the exhaust steam, and the power thus gained should not be credited to the boilermaker. 38. PETROLEUM AS FUEL. Substances. Pounds. Cu. ft. air. Units of heat. Carbon 0.84 126 121SO Hydrogen 0.16 55 9925 1 00 181 22105 One volume of petroleum requires 8400 volumes of air for complete combustion. One gallon of petroleum weighs 6.7 pounds. One pound of petroleum occupies 34.55 cubic inches. One cubic foot of petroleum weighs 50 pounds. Specific gravity of petroleum, 0.8. One barrel of petroleum contains about 42 gallons, and costs in Philadelphia about six dollars, making about fifteen cents per gallon. One barrel of petroleum weighs about 282 pounds. Eight barrels of petroleum weigh about one ton. One ton of petroleum costs about 45 dollars. PERCENTAGE OF AVAILABLE HEAT OF COMBUSTION. 39. When the percentage of carbon in a fuel is known (omitting hydrogen and sulphur), we can determine correctly the heat generated per pound of fuel completely consumed. C' = fraction of carbon per pound of fuel. The heat h generated per pound of fuel consumed will be h = 14500 C", the gross units of heat. h' = available heat generating steam. Percentage of available heat = .... 1 54 STEAM ENGINEERING. Percentage of lost heat = 1 Tihe lost heat escapes with the gases of combustion through the chimney. The available heat h' is found by Formula 11, page 51. ECONOMY OF HEATING THE FEED-WATER. 40. The following Table XII. gives the percentage of gain or loss of power or fuel by different temperatures of feed-water heated or cooled. The first column contains the temperature of the feed-water at which it enters the boiler, and the top line contains the temperature from which the water is heated or cooled. Suppose water to enter the feed-pump at 32 and to be heated to 160, there will be 13 per cent, gained in power and fuel. When water enters the feed-pump at 60 and is heated to 150, there will be 10 per cent, gained. Suppose the water in the heater is 180, which, when passing in a long pipe to the steam-boiler, is reduced to 150, the loss will then be 3 per cent. The signs mean + for gain and - for loss : TABLE XII. Percentage of Power or Fuel Gained by Heating the Feed-water. Hi w^ H 32 Temp 40 erature 50 from v GO rhich tl 70 ie Feed -water 80 100 s Heated 01 120 140 Cool 160 d. 180 200 32 0.0 -1 -1.5 -2 -3.4 -4.4 -6.5 -9 -11 -13 -iei-19 40 + 1 0.0 -0.5 -1 -2.4 -3.4 -5.5 -8 -10 -12 -15 -18 50 + 1.5 + 0.5 0.0 -0.5 -2 -3 -4 -7 -9 -11 -14 -17 60 + 2 + 1 +0.5 0.0 -1.4 -2.4 -3.5 -6 -8 -10 -14 -16 70 +3.4 + 2.4 + 2 + 1.4 0.0 -1 -3 -5 fj -9 -13 -15 80 +4.4 + 3.4 + 3 + 2.4 + 1 0.0 -2 -4 -6 -8 -12 -14 90 + 5.4 + 4.4 + 4 + 3.4 + 2 + 1 -1 -3 -5 -7 -11 -13 100 + 6.5 + 5.5 + 5 + 4.4 + 3 + 2 0.0 -2 A -6 -9.5 -12 110 + 7.6 + 6.6 + 6 + 5.6 + 4.2 + 3.2 + 1 -1 -3 -5 -8 -11 120 + 8.7 + 7.7 + 7 + 6.7 + 5.3 + 4.3 + 2.2 0.0 -2 -4 -7 -10 130 + 9.8 + 8.8 + 8.3 + 7.8 + 6.4 + 5.4 + 3.3 + 1 -1 -3 -6 -9 140 + 11 + 10 + 9 + 9 + 8 + 7 +4.5 + 2 0.0 _2 -5 -8 150 + 12 + 11 + 10 + 10 + 9 + 8 + 5.5 + 3 + 1 -1 -3 -7 160 + 13 + 12 + 11 + 11 + 10 -t-9 + 6.5 + 4 + 2 0.0 -2 -6 170 + 15 + 14 + 12 + 12 + 12 + 11 + 8 + 6 +4 + 2 -1 -4 180 + 16 + 15 + 14 + 14 + 13 + 12 + 9 + 7 + 5 + 3 0.0 -3 190 + 17 + 16 + 15 + 15 + 14 + 13 + 10 + 8 + 6 + 4 -1 -2 200 + 19 + 1X + 17 + 17 + 16 + 15 + 12 + 10 + 8 + 6 -3 0.0 212 + 20 + 19 + 18 + 18 + 17 + 16 + 14 + 11 + 9 + 7 -4 + 1 MANAGEMENT OF FIRE. 55 MANAGEMENT OF FIRE IN STEAM-BOILERS. 41. When the air enters under the fire-grate into the incandescent coal, its oxygen unites with the carbon and forms carbonic acid gas C0 2 , which rises through the thick layer of coal and absorbs another atom of carbon, forming carbonic acid CO. This carbonic oxide carries with it small particles of unconsumed carbon, forming smoke, which passes through the flues and tubes, and finally through the chimney into the air ; the result of which is an extravagant waste of fuel. The heat generated by forming carbonic oxide is only 30 per cent, of that generated by forming carbonic acid, together with the carry- ing off of unconsumed carbon in form of smoke, reduces the realized heat to a very small percentage of that due to the complete com- bustion of the fuel. " Therefore, in order to realize the greatest economy and effect of fuel, it must be consumed to carbonic acid, which is accomplished by keeping a very thin and even layer of fire on the grate, and by having a strong draft. For anthracite coal the thickness of the fire should be between 4 and 6 inches, and for bituminous coal from 6 to 8 inches. The carbonic acid formed will then rise to the upper surface of the fire before it can take up another atom of carbon, and the oxygen in the excess of air not utilized in the fire will unite with the uncon- sumed carbon rising above the coal, and form the flame. Anthracite coal forms very little or no flame, for the reason that its hardness does not admit of faster distillation of carbon than what is immediately consumed by the oxygen of the air in contact there- with. Bituminous coal is more easily volatilized, and the bituminous matter distills faster than it is consumed in the coal fire. The oxygen of the air, passing through the incandescent coal, consumes the gaseous carbon above the coal, forming a flame which may extend some ten feet from the furnace through the flues. The area of entrance for air through the coal should not be less than one-fortieth (^ of the area of the fire-grate, and the coal layer should be of even thickness and cover completely the whole grate- surface, so that no air can enter without passing through or between incandescent coal. Should a part of the grate be uncovered with coal, a body of air will enter and reduce the temperature below that of ignition in that part of the furnace bv which smoke is formed. Ashes and clinkers in the grate prevent the free access of air, and carbonic oxide and smoke are formed. An experienced fireman can 56 STEAM ENGINEERING. see by the light in the ash-pit the condition of the fire in the grate, and he slices the fire accordingly. When the furnace is charged, the coal should be spread evenly all over the fire, and the furnace doors should not be kept open longer than is necessary for the charge. PRODUCTS OF COMBUSTION. 42. The term "products of combustion" should mean only the binary compound of oxygen and combustibles formed in the operation of combustion, such as carbonic oxide, carbonic acid, steam and sul- phurous acid ; but, practically, all the gases in the furnace, including nitrogen and smoke, are termed products of combustion. When hydrogen is consumed in the furnace and forms steam, that steam is then a product of combustion ; but when evaporated from moisture in the fuel, it is not a product of combustion in the furnace. TABLE XIII. Properties of Products of Combustion. Gases of Combustion. Ato Symbol. mic Weight. Spe Gravity. Jiflc Volume. Weight ar at Ibs. per cu. ft. d volume >0. cu. ft. per Ib. N 2 N H C S CO co t HO H 2 O H& NO S0 2 36 8 14 1 6 16 14 22 9 8 14 22 32 1. 1.104 0.972 0.0693 0.8380 1.123 0.972 1.527 0.625 0.555 0.98 1.525 2.247 1. 0.9058 1.0288 14.430 1.1933 0.8904 1.0288 0.6549 1.6 1.8018 1.0204 0.6557 0.4450 0.0760 0.0839 0.0740 0.000267 0.06369 0.0853 0.0740 0.11505 0.0475 0.04218 0.07448 0.1159 0.19077 13.158 11.9189 13.5135 189.86 15.701 11.723 13.5135 8.6900 21.0526 23.7079 13.4264 8.6281 5.2415 Oxygen Nitrogen Carbon Carbonic acid Steam Carburetted hydrogen... Bicarbu retted hydrogen Nitrous oxide GRATE-BARS. 43. The proportion of thickness of grate-bars to the air-space be- tween them varies between 1 and 3 to 1, depending on the kind of fuel used on the grate that is to say, the area of air-passage between the bars varies between 25 and 50 per cent, of the grate-surface. SMOKE-BURNING. 57 The following table gives the spaces between the grate-bars in frac- tions of an inch, as generally used for different kinds of fuel. SPACE BETWEEN GRATE-BARS. Lehigh anthracite pea coal ^ of an inch. Schuylkill " " " f " Lehigh " chestnut coal f " " Lehigh " stove " " " Lehigh " broken " f " Cumberland bituminous coal ^ " " Ordinary wood ^ to 1 " Sawdust j\ to $ " SMOKE-BURNING. 44. The burning of smoke has, since the time of Watt, received a great deal of attention, but not with much success, owing, first, to in- sufficient knowledge of the chemistry of smoke, which in Watt's time was not sufficiently developed for that purpose ; and secondly, the physical properties of smoke have not been properly considered in the attempt to burn smoke. When the science of chemistry was sufficiently advanced to enable us to determine correctly the elements of combustion and of smoke, we have still not fully considered the physical properties bearing upon the success in smoke-burning. . It is well known that smoke consists of small particles of carbon mixed with carbonic oxide, both of which are combustibles, with a sufficient supply of oxygen at a temperature above that of ignition between 700 and 800 Fahr. It appears, therefore, that a sufficient supply of air among the smoke in the furnace would accomplish the object, but unfortunately such has not been the result. Suppose a case of one pound of carbon being consumed by the oxy- gen of 103 cubic feet of air, which, according to Table X., will form Carbonic oxide CO = 1.5166 Ibs. = 20.494 cubic feet. Carbonic acid C0 2 = 1.2833 Ibs. = 11.126 " Nitrogen N =6.2075 Ibs. = 81.370 " " Products of combustion = 9.0074 Ibs. = 112.990 cubic feet. The volume is here taken at 60 Fahr. ; but at a temperature above that of ignition, say 800, the volume of the products of combustion will be 2.5 x 1 13 = 282.5 cubic feet. (See Law of Gases.) Of this volume only 2.5x20.5 = 51.25 cubic feet is combustible or 58 STEAM ENGINEERING. carbonic oxide, which requires the oxygeu of 76.5x1.5166 = 115.9 cubic feet of air at 60 for combustion to carbonic acid. The gases of combustion are not chemically combined, but me- chanically mixed in the furnace, and arrange themselves into layers according to their specific gravity, the lightest occupying the top and the heaviest the bottom of the furnace or flues. The specific gravity of nitrogen and carbonic oxide being alike, these two gases will mix ; but the nitrogen, which is a non-supporter of combustion, occupies four times the volume of that of the combustible carbonic oxide. We see here the difficulty of uniting the oxygen of 116 cubic feet of air at 60 with 2.5x11.126 = 37.8 cubic feet of carbonic oxide, which is already mixed with 2.5x81.37 = 203.42 cubic feet of nitro- gen ; therefore the burning of carbonic oxide to carbonic acid by additional supply of air to the furnace may be considered very difficult, if not impossible. When the carbonic oxide is mixed with free carbon at a tempera- ture above that of ignition, the oxygen of a supply of air is easier united with these combustibles, but even then the large quantity of nitrogen will interfere with that combustion. The smoke is formed first when the temperature of the products of combustion is reduced below that of ignition, before which time the free carbon is incandescent. In most of the attempts made to burn smoke by additional supply of air, the air has been admitted under the gases of combustion that is, from behind or from the top of the bridge, where it first comes in contact with the carbonic acid, and perhaps sulphuric acid, which prevents the air from being mixed with the combustibles before the temperature is reduced below that of ignition. The admission of a small quantity of air through the fire-door or to the upper part of the furnace has proven partly successful in burn- ing some smoke, but the most economical combustion of the fuel is when the furnace and fire are so arranged that the fuel is completely consumed by the air entering through the grate into the fire. NATURAL FURNACE-DRAFT. 45. The natural draft to a furnace is caused by the column of heated gases in the chimney being lighter than an equal column of the surrounding air. The weight of a cubic foot of dry air at 60 is 532 grains ; and suppose the hot gases in the chimney to weigh 286 grains per cubic foot, then a chimney of one square foot section, and say 50 feet high, would contain 50 cubic feet, and the weight of the hot gases DRAFT IN FURNACES. 59 50x286 = 14300 grains. The weight of an equal column of air at 60 would weigh 50 x 532 = 26600 grains, and 26600 - 14300 = 12300 grains, which will be the pressure per square foot of the draft. The height of a column of air answering to this pressure is 12300 : 532 = 23.12 feet. The velocity of the draft through the fire (which is the smallest aperture of entrance) will be equal to that a body would attain by falling vertically a height of 23.12 feet namely, 36.44 feet per second. The combustion of one pound of carbon produces by 153 cubic feet of air, Carbonic acid CO., = 3.6666 Ibs. = 31.86 cubic feet. Nitrogen ^=8.9455 Ibs. = 120.87 " " Total . . . . =12.6121 Ibs. = 152.73 " " We see here that the volume of the gases of combustion is nearly equal to that of the air supplied, but their specific gravity is slightly more namely, as 12.612 : 11.552 = 1.0918. Some carbonic oxide, which is lighter than air, always accompanies the gases, for which we may with safety assume the sp. gr. of the gases of combustion to be equal to that of air of the same temperature. Therefore the sp. gr. of the hot gases in the chimney will be equal to the reciprocal of the volume expansion by heat, which is denoted by x in the Table XXX. for law of gases. For a temperature of 500 of the gases in the chimney the volume is # = 1.9491, which reciprocal is 0.51308, the required specific grav- ity of the gases. The height of the chimney is to the height of a column of cool air of equal weight to that of the hot air as 1 : ( 1 I. V *J A = section area of the chimney, and B = area of the fire-grate in square feet. V= velocity of the air through the fire. v = ascending velocity of the gases in the chimney. H= height of the chimney in feet above the fire-grate. The area for passing the air through the fire should be about one- fortieth (^) of the area of the fire-grate. The area of the chimney is generally made about 0.16 of the area of the fire-grate. 7=5 60 STEAM ENGINEERING. The theoretical coefficient should be 8 instead of 5. BF Example 1. The height of a chimney is H= 75 feet, and the tem- perature of the ascending gases 450. Required the velocity of the air through the fire ? Formula 1. V- 5-J 75 (1 - J- 29.38 feet per second. Example 2. Required the velocity of the ascending gases in the chimney when B = 3'6 square feet and A = 5.76 square feet? Formula 2. v = 1/75 + 0.4588 = 4.58 feet per second. 8x5.76 It is assumed in these examples that the temperature of the air is 32, but for other temperatures of the air a corresponding reduc- tion should be made of the temperature of the hot gases ; for exam- ple, when the air is 75 and the gases 450, then 75 - 32 = 43, and 450-43 = 407, the temperature for the velocity of the ascending The factor /I J in the Formulas 1 and 2 denoted by z in Table XXX. is =(l--|- \ */ , in which, 493+ T-t f= temperature of the ascending gases in the chimney, and t = temperature of the surrounding air. As in Formula 1, the coefficient 5 in Formula 4 should be 8 by the acceleration of gravity V= 8\/gS; but the friction and turning of the gases amongst the incandescent fuel and returning tubes reduce the velocity over 30 per cent., for which reason the coefficient is re- duced from 8 to 5. WATER-GAUGE FOR CHIMNEY DRAFT, 61 WATER-GAUGE FOR CHIMNEY DRAFT. 46. The difference of pressure between the hot gases in the chim- ney and the surrounding atmosphere is very small, and is therefore measured by a column of water. A cubic foot of water at 32 Fahr. weighs 62.387 pounds, whilst a cubic foot of air of the same temperature weighs only 0.0804186 of a pound; therefore a column of air must be 62.387 : 0.0804186 = 766.25 times higher than a column of water for the same pressure. The height of a column of air corresponding to the difference of pressure in and outside the chimney is x = volume expansion of gases by heat corresponding to the tem- perature of the gases in the chimney from the Table XXX. of law of gases. 77= height of the chimney in feet above grate. This height H', divided by 766.25, gives the height of a column of water of equal pressure, and multiplied by 12 gives the height in inches, denoted by 7. 1 766.25V x] 63.854V */ ' ' 2 H(T-t) 63.854(493+ T-t) The following Table XIV. is calculated from this formula for dif- ferent temperatures T of the gases in the chimney, and that of the air t = 32, and for different heights 77 of chimney. The water-gauge should be placed as near the level of the fire-grate as practicable. 62 STEAM ENGINEERING. TABLE XIV. "Water-gauge in Inches for Chimney-draft. Height of Chimney. 400 Tern 450 leratnres j 500 9 of Oases I 550 n the I 'iiin 600 ney. 700 800 H. L /. /. 1. /. L /. 10 0.0669 0.0718 0.0762 0.0802 0.0838 0.0901 0.0974 15 0.1000 0.1077 0.1143 0.1203 0.1257 0.1356 0.1430 20 0.1338 0.1437 0.1525 0.1604 0.1677 0.1802 0.1907 30 0.2008 0.2155 0.2287 0.2407 0.2515 0.2703 0.2861 40 0.2678 0.2874 0.3050 0.3209 0.3354 0.3604 0.3815 50 0.3346 0.3592 0.3812 0.4011 0.4192 0.4505 0.4768 60 0.4016 0.4311 0.4575 0.4814 0.5031 0.5406 0.5722 70 0.4685 0.5029 0.5337 0.5616 0.5870 0.6307 0.6676 80 0.5354 0.5748 0.6100 0.6418 0.6709 0.7208 0.7630 90 0.6024 0.6466 0.6862 0.7221 0.7547 0.8109 0.8584 100 0.6693 0.7185 0.7625 0.8023 0.8385 0.9010 0.9537 125 0.8366 0.8981 0.9531 1.0028 1.0481 1.1262 1.1921 150 1.0039 1.0777 1.1437 1.2034 1.2577 1.3515 1.4305 175 1.1712 1.2573 1.3343 1.4039 1.4673 1.5767 1.6689 200 1.3386 1.4370 1.5250 1.6046 1.6770 1.8020 1.9074 250 1.6732 1.7962 1.9062 2.0057 2.0962 2.2525 2.3842 300 2.0079 2.1555 2.2875 2.4069 2.5155 2.7030 2.8611 400 2.6772 2.8740 3.0500 3.2092 3.3540 3.6040 3.8148 47. QUANTITY OF AIR BY NATURAL DRAFT. Q == cubic feet of air passing through the fire per hour by natural draft. = 90SF=450B The average quality of coal may be assumed to contain 0.75 of pure carbon, and 153x0.75 = 115 cubic feet of air required per pound of coal consumed. For safety say 140 cubic feet. L = pounds of coal consumed per hour per square foot of grate. . . . . . . 2 L = : Example 8. How much coal will be consumed per hour per square foot of grate by a chimney of H = 60 feet high, the temperature of the ascending gases being 500 ? LOSS OF HEAT. Formula 3. L = 3.2^/60 (1 - ) = 1 7.28 pounds. \ \ 1.J49 I The height of the chimney required for the combustion of L pounds of coal per hour per square foot of grate will be U 10.29(14). LOSS OF HEAT BY THE ESCAPING GASES OF COMBUSTION. 48. The heat carried off by the gases of combustion is lost for the generation of steam, but utilized for creating draft to the furnace. The higher the chimney is, the more will that heat be utilized for creating draft. The economy consists in making the chimney high and redu- cing the temperature of the ascending gases by absorbing more of the heat for evaporation. The specified heat of the gases of combustion averages 0.25. See Specific Heat. The weight of the gases per pound of carbon consumed to carbonic acid is 12.612 pounds, and the heat carried off will be A = 12.612x0.25 (T-t) ... 1 A = 3.153(T-t) . . . . . 2 e = fraction of carbon per pound of coal. L = pounds of coal consumed per hour per square foot of grate. A = units of heat passing through the chimney per hour. The percentage of heat lost by the escaping gases will then be 0.02175 (T-t) .... 4 Example 4- The temperature of the ascending gases being !F= 480, and that of the surrounding air t = 72, required the percentage of heat lost through the chimney ? 0.02175(480 - 72) =8.87 per cent. It is supposed in this example that all the carbon is perfectly con- sumed to carbonic acid. 64 STEAM ENGINEERING. TEMPERATURE OF THE GASES IN THE CHIMNEY. 49. This is a very difficult problem to solve theoretically, on ac- count of the various circumstances involved therein making a very complicated mathematical demonstration, the result of which would probably not' give a closer result than does the following formula, which is set up from practice ; namely, '=300^- B + a T = temperature of the gases when entering the chimney. Example 1. A steam-boiler of B = 96 square feet fire-grate and _1 = 2880 square feet of heating surface is connected with a chimney H= 47 feet high. Steam pressure p = 62 pounds to the square inch. Required the temperature of the gases in the chimney ? '-300^ -403., P., By this formula we can find the temperature in any part of the flues or tubes by subtracting that part of the heating surface which the fire has not reached, or by taking the heating surface exposed to the fire up to the point where the temperature is required. Example. Required the temperature at the bridge in the boiler of the preceding example, in which the heating surface in the furnaces alone is Q = 245 square feet ? It is assumed in this formula and examples that the cross-section of the chimney is A = 0.16 B. The temperature in the chimney ought not to be more than 100 above that of the steam in the boiler, and the heating surface not more than a = 36 B. The proper proportion between the fire-grate and heating surface depends upon the steam-pressure, or rather the temperature of the steam and that of the gases in the chimney. When the temperature of the latter is reduced below that of the former, heat is conducted from the water back into the flue, which operation is a waste of fuel, material and labor in the first construction of such boilers. In locomotive boilers with very long and narrow tubes and exhaust draft in the chimney, the temperature of the gases has often been TEMPERATURE IN CHIMNEYS. 65 reduced below that of the water and steam in the boiler, the result of which is a Avaste of fuel. In marine boilers the heating surface rarely exceeds 36 B, and the temperature of the gases in the chimney is then about 100 over that of the steam in the boiler. Stationary boilers are sometimes made with heating surface = 50 H, and the temperature of the gases in the chimney has been reduced below that of the steam ; but the water evaporated per pound of com- bustibles has been less than with smaller proportions of heating surface. For very low steam-pressure the heating surface may advantage- ously be made = 50 B. When there is no heating surface, but the chimney is connected directly to the fire-grate, so that all the heat ascends in the chimney, the temperature will then be T=300l/7,/2T2. ... 2 Example 2. Required the temperature in a chimney H = 62 feet high, connected directly with the fire-grate without water-heating sur- face, but that all the heat passes up the chimney ? T= 3001/7 ,/62 + 2 = 2244.5 Fahr. 50. TEMPERING OF STEEL. The temperature of the gases in the chimney depends much upon the construction of the boiler and the proportion of fire-grate and heating surface. A simple way of measuring this temperature ap- proximately is by inserting a polished iron wire about \ of an inch in diameter ; the color of tempering will show the temperature, corre- sponding with the following table. The property of heat to color steel or iron can be applied for ascer- taining the temperature in flues and chimneys of steam-boilers, and for other temperatures limited between 430 and 600 Fahr. Yellow, very faint, for lancets 430 " pale straw, for razors, scalpels 450 " full, for penknives and chisels for cast iron.... 470 Brown, for scissors and chisels for wrought iron 490 Red, for carpenters' tools in general 510 Purple, for fine watch-springs and table-knives 530 Blue, bright, for swords, lock-springs 550 " full, for daggers, fine saws, needles 560 " dark, for common saws 600 5 66 STEAM ENGINEERING. EVAPORATION OF POUNDS OF WATER PER HOUR PER SQUARE FOOT OF HEATING SURFACE. 51. The evaporation per heating surface varies directly as the l.V power of the difference between the temperature of the gases of com- bustion and that of the water in the boiler. The temperature of the gases is determined by Formula 1, paragraph 49, and the tem- perature of the water is the same as that corresponding to the steam- pressure. The evaporation per heating surface will therefore be dif- ferent in different parts of the boiler. h = units of heat passed through each square foot of heating sur- face per hour. H= units of heat per pound of steam generated. (See Steam Table, Nystrom's Pocket-Book.) T= temperature of the gases of combustion at the place in the boiler where the rate of evaporation is calculated. t = temperature of the water or steam. Ibs = pounds of water evaporated per hour per square foot of heating surface at the place where the temperature of the gases is T. Units of heat, 7i = 0.505 /(T- t) 3 . . . 1 0.505]/(T-t) 3 Evaporation, Ibs. = - -^. . . 2 H Example 1. The temperature in a boiler furnace is T=1200\ and steam pressure 80 pounds to the square inch, which corresponds to t = 324 temperature of the steam. Required the units of heat passing through each square foot of heating surface per hour ? and how much water will be evaporated per square foot of heating surface per hour ? Units of heat, h = 0.505J/U200 324J 3 = 1 3093. Evaporation, Ibs. = -- = 11 .09 pounds. 1180.7 Example 2. In the same steam-boiler as in the preceding example, the temperature of the gases entering the chimney is r=460. Re- quired the evaporation per square foot of heating surface at the end of the boiler where the gases of combustion enter the .chimney ? Evaporation, Ibs = - 50 V ( 46Q " 324 ) 3 = .678 of a pound. 1180.7 The rate of evaporation can thus be calculated in any part of the boiler by first calculating the temperature T from Formula 1, in paragraph 49. SAFETY-VALVES. 67 FRESH WATER CONDENSERS. 52. Fresh water condensers are generally made of brass tubes about | of an inch diameter and tinned outside. h = units of heat conducted per hour through each square foot of tubes. !F = tempera cure of the steam entering the condenser. t = temperature of the water entering the condenser. B = area of fire-grate in square feet. Q = heating surface in square feet. A = tubular area in square feet in the condenser, required to con- dense the steam generated by the boiler B Q. B a. .... 2 Example 2, How much tubular condensing surface is required for a boiler of B = 128 square feet fire-grate, and heating surface LJ = 3850 square feet ? Condensing surface, A = 3.5 j/ 128x3850 = 2457 square feet. SAFETY-VALVES. 53. The area of a safety-valve should be sufficiently large to let out all the steam the boiler can generate without increasing the nor- mal working pressure of the boiler, and without the valve lifting more than one-forty-eighth (^) of its diameter. A = area in square inches of the inner circle of the valvesit. a = area through which the steam escapes, which is equal to the circumference of the inner circle of the valvesit multiplied by the height the valve is lifted. p = steam-pressure in pounds per square inch above that of the atmosphere. ^j9 = weight in a fraction of a pound per cubic foot of the steam of pressure p. (See Steam Table, Nystrom's Pocket-Book.} ^ = steam-volume compared with that of its water at 32 Fahr. H = height in feet of a column of steam of one square foot section, which weight would be equal to the steam-pressure per square foot, or 1 44 p. F= velocity in feet per second of the steam through the safety- valve. STEAM ENGINEERING. The weight of a column of steam of height H and weight per cubic foot f will then be Tf. That is to say, 144^ = 5"^. ... 1 Height of column, H= lil?. ... 2 Velocity of steam, F= 8 1 /"B'= 96 J-2- v 3 = cubic feet of steam discharged through the safety-valve per second. aV 8a -_ 96 a J 2 That is to say, the steaming capacity of the boiler in cubic feet of steam per second should not exceed Q- The steaming capacity of a boiler fired with a given kind or qual- ity of fuel depends upon the area of the fire-grate and heating surface. With natural draft the average evaporation of water of 32 to Q cubic feet of steam per second in ordinary boilers is 9000 This should be equal to the escape of steam through the safety- valve, Formula 5, or " 3Vy " 9000 From this formula we obtain the requisite area a of the safety-valve for letting out all the steam the boiler can generate namely, Allowing for the contraction of the steam through the valve, 35 per cent. For guiding wings of the valve 20 " " For steam generation, Formula 6 20 " " Reduction for safety 75 " " SfT OF SAFETY-VALVES. 69 Limiting the valve to lift only one-forty-eighth of its diameter, the coefficient 6000 in Formula 8 will be reduced to 288, when A is the area of the inner circle of the valvesit. . ... 9 288 \f This should be the reliable formula for the requisite area of the safety-valve of a steam-boiler. Example 9. A steam boiler of B = 130 square feet of fire-grate and a = 3372 square feet of heating surface, carrying p = 49 pounds of steam-pressure per square inch above that of the atmosphere. Re- quired the area A of the safety-valve ? The steam volume at p = 49 is ^ = 403.29, and weight per cubic foot of steam ^ = 0.15469 of a pound. The area of the safety-valve will then be _ 52.092 square inches. The Formula 9 can be reduced to a very simple form by the aid of a table, for which make 10 SIT OF SAFETY-VALVES. 54. The sit of a safety-valve should be flat, and not conical. A flat joint is easier ground and kept tight than a conical one. The width of a valvesit should not be more than one-tenth (-fa) of the cube root of the diameter of the valve, and even one-sixteenth will answer the purpose. For conical valves the area should be A = M C08.V. v = angle of the valvesit to the plane of the valve. For an angle of 45 cos.45 = 0.707, and, A _ 0.707 M 70 STEAM ENGINEERING. The columns M and N, in the following Table XV., are calculated from the Formulas 10 and 11 for different steam-pressures in the first column p. The formula for area of safety-valves will then be simply A Example 3. Required the area of a safety-valve for a boiler of B = 36 square feet fire-grate, and a = 1024 square feet heating sur- face, to carry p = 85 pounds steam-pressure ? (See Table XV.) A = 5 = 9.375 square inches. 20.52 If the same boiler should be limited to p = 20 pounds steam- pressure, the area of the safety-valve should be, 1/36 x 1024 , A = = 31.44 square inches. 6.107 The steam-volume in the following table is calculated from Fair- bairn's formula. VELOCITY OF STEAM FORCED BY ITS PRESSURE INTO AIR OR VACUUM. 55. The velocity of steam forced by its pressure into the atmo- sphere is When the steam passes into a vacuum, the velocity will be ^P = weight in pounds per cubic foot of steam. P = pressure per square inch above vacuum. When the steam passes into a partial vacuum of pressure^/ that is, the difference between the atmospheric pressure and that into which the steam passes the velocity will be F-i SAFETY- VAL VES. 71 TABLE XV. Area of Safety-valves and Velocity of Steam Passing into the Air. Steam pres- sure. 288 \p yVf- Vf= Velocity. 96 N~ ''airbairn's Steam volume. Weight per cubic foot of steam. P- M. Logarithms. N. V. t- f 5 2.333 0.3680283 9.883 948.77 1219.7 0.05119 10 3.675 0.5652855 12.56 1205.7 984.23 0.06338 15 4.911 0.6911552 14.09 1352.6 826.32 0.07550 20 6.107 0.7858060 15.12 1451.5 713.08 0.08749 25 7.274 O.S617983 15.86 1522.5 627.91 0.09936 ' 30 8.427 0.9256803 16.43 1577.3 561.50 0.11111 35 9.570 0.9089105 16.89 1621.4 508.29 0.12273 40 10.70 1.0292700 17.26 1656.9 464.69 0.13128 45 11.82 1.0726430 17.58 1707.6 428.42 0.14566 50 13.21 1.1208622 17.85 1713.6 397.51 0.15694 55 14.04 1.1473753 18.09 1734.8 371.07 0.16812 60 15.14 1.1800772 18.30 1756.8 348.15 0.17919 65 16.23 1.2103496 18.49 1774.0 328.06 0.19015 70 17.32 1.2385479 18.66 1791.3 310.36 0.20101 75 18.39 1.2647646 18.82 1806.7 294.61 0.21185 80 19.46 1.2891428 18.97 1821.1 280.50 0.22241 85 20.52 1.3121774 19.10 1833.6. 267.80 0.23296 90 21.59 1.3342526 19.23 1846.1 256.31 0.24340 95 22.66 1.3552599 19.35 1857.6 245.86 0.25375 100 23.73 1.3752764 19.47 1869.1 236.31 0.26400 105 24.78 1.3941013 19.57 1878.7 227.56 0.27421 110 25.81 1.4117624 19.67 1888.3 219.50 0.28422 115 26.85 1.4289443 19.76 1897.0 212.07 0.29419 120 27.88 1.4452367 19.86 1906.6 205.18 0.30406 125 28.91 1.4610481 19.95 1915.2 198.78 0.31385 130 29.95 1.4763323 20.05 1924.8 192.83 0.32354 135 30.99 1.4912226 20.14 1933.4 187.26 0.33315 140 32.11 1.5066060 20.24 1943.0 181.69 0.34276 72 STEAM ENGINEERING. a = area in square inches through which the steam escapes. Q = cubic feet of steam passing through the opening a per second. m = coefficient of contraction of the steam-jet, which varies from 0.64 to 1. For steam escaping through valves or cocks the coefficient can he taken to m 0.75. 144 Placing m = 0.75, we have 56. When steam passes into air of atmospheric pressure, the velocity and cubic feet of steam discharged per second are easily cal- culated by the aid of Table XV. namely, Velocity, V=WN ..... 8 Cubic volume, Q = Q.5aN . . . . ' . 9 Example 8. Required the velocity of steam passing from a boiler and under p = 65 pounds pressure ? V= 96 x 18.49 = 1775.04 feet per second. Example 9. Required the volume of that steam passing through an orifice of a = 1 .5 square inches ? Q = 0.5 x 1.5 x 18.49 = 13.867 cubic feet per second. Example 1. Required the velocity V of steam of pressure p = 65 pounds to the square inch above that of the atmosphere, issuing from the boiler into the air? and how many cubic feet will be discharged per second through an opening a = 0.75 of a square inch ? When the opening is through a thin plate in which the steam-jet is contracted on all sides, the coefficient is m = 0.64. Velocity, V= 96 r-rr-- = 1775 feet per second. 0. 1901o Steam discharged, Q = = 5.91 cubic feet per second. DISCHARGE OF STEAM. 73 Example 6. What quantity of steam of pressure P=85 pounds to the square inch above vacuum will pass through a cock of a = 0.45 of a square inch into a vacuum ? Q = 0.5 x QA5 f = 4.627 cubic feet. Example S. Steam of pressure p = 45 pounds to the square inch above the atmosphere is passing into a partial vacuum of 18.33 inches mercury, or p' = 9 pounds to the square inch. Required the velocity of the steam? and how much will pass through the opening of a = 1.25 square inches, the coefficient of contraction being m = 0.8 ? 7 feet per second. = 11.68 cubic feet. , 144 The horse-power per volume of steam consumed per hour is given by Formula 1, 23, in which Q-Wty-1) .... 10 g 3600j> P Q 13748.4 3.819 P 96mo HT 2 fitT 3.819HP 5.7285 13 This formula gives the horse-power of steam of pressure p escaping from a boiler through an opening a. Example 13. What horse-power is required to blow a steam-whistle 4 inches in diameter, when the opening is 0.005 of an inch, the steam-pressure being p = 60 pounds to the square inch above atmo- spheric pressure? The area of the steam-whistle is a = 4 x 3.14 x 0.005 = 0.0628 of a square inch. 74 STEAM ENGINEERING. In this case the steam passes through a taper opening, for which the coefficient m = l. 0.0628x60 IP- 5.7285 This seems to be a very high horse-power for a steam-whistle, but it is nevertheless true under the conditions assumed. g 57. HORSE-POWER OF STEAM-ENGINES BY VOLUME OF STEAM. (7= cubic feet of full steam used in each single stroke in the steam- cylinder. n = double strokes of piston per minute. p = steam-pressure in pounds per square inch. 3.819x60 Example 1. The cubic capacity of a steam cylinder is (7=6.5 cubic feet, and the piston makes n = 45 double strokes per minute with a steam-pressure of p =- 70 pounds to the square inch. Required the horse-power of the engine ? . 45 x 6.5 x 70 . IP = -- - 178.7 horse-power. 114.O/ This is the horse-power of the high-pressure engine working with full steam. If the horse-power of the same engine is calculated in the ordinary way, it will be 180.7, or one horse-power more than in the example, which is the power consumed by the force-pump feeding the boiler with water. When the steam is expanded in the cylinder, C means the volume of the full steam, and the horse-power of the full steam multiplied by 1+ hyp. log. of the expansion is the horse-power of the expanded steam. STEAM-PRESSURE AND REVOLUTIONS. 58. When the dimensions of the boiler and engines are given, to- find the relation between steam-pressure and revolutions of the engine. $ = steam-volume compared with that of its water at 32 for the given steam-pressure. STEAM-PRESSURE AND REVOLUTIONS. 75 # = cubic feet of unexpanded steam used in each revolution of the engine or engines. n = number of revolutions per minute of the engine. = correction for temperature of feed-water, Table V. r = correction for height of chimney, Table VII. . _ 150 #n Rr TM 150 n Example 1. A steam-engine of 3 feet diameter of cylinder and 5 feet stroke of piston is to make n = 70 revolutions per minute, with a boiler of B = 164 square feet of fire-grate and heating surface Q = 4850 square feet. The steam to be cut oif at half stroke; feed-water 120, for which 5 = 1.087 ; height of chimney 85 feet, for which r = 1.27. Required what steam-pressure the boiler can carry under the above conditions ? #=7.061 x5 = 35.305 cubic feet of steam for each revolution, to which add for clearance and steamport 1.7 cubic feet, making #=37 cubic feet. 150x37x70 Steam volume, y = 274.94. 1. 087 xl.27^/ 164x4850 , Find the steam-pressure corresponding to this volume (see Steam Table, Nystrom's Pocket-Book), which is 82 pounds to the square inch, the pressure required. Example 2. How many revolutions per minute may be expected from an engine using #=15 cubic feet of full steam of 50 pounds to the square inch for each revolution, when the steam-boiler is B = 84 and Q = 2480 square feet, the temperature of the feed-water being 90, for which 5 = 1.054, height of chimney 40 feet, for which r = 0.91? 76 STEAM ENGINEERING. The steam-volume for 50 Ibs. is ^ = 397.51. 397.51 x 1.054 x 0.91i/84 x 2480 , Revolutions, w = = 24.46. 150x15 Formula 4 gives the size of steam-boiler required for a given-sized engine and revolution of the same. Example 4- What size steam-boiler is required for an engine using %F= 20 cubic feet of full steam of pressure 60 pounds to the square inch, to make n = 48 revolutions per minute ; height of chimney 75 feet and temperature of feed-water 100 ? -'Sidjh^Li.l- Suppose the heating surface in the boiler to be Q = 25B, then 25 B 2 = 86086.5. The required fire-grate, B -= A/ ' -= 58.68 square feet. Heating surface, a - 58.68 x 25 - 1 467 square feet. 59. QUANTITY OF FEED-WATER BY AREAS OF FIRE-GRATE AND HEATING SURFACE. W= cubic feet of water to be fed into" the boiler per minute. d = diameter in inches of the pump-piston or feed-plunger. s = stroke in inches of piston or plunger. n = pumping strokes per minute. 150 0.7854

(T- )". . 2 For cylinders or pipes under 12 inches in diameter, the radiation per hour will be Units of heat, h= DL [450 + (12-D) 2 ](T- t) n . 3 3404.8 The volume in cubic feet of steam condensed per hour will be *! < Horse-power lost by radiation of h units of heat per hour will be 5 Example 1. How many units of heat are radiated per hour from an uncovered steam-boiler exposing A = 198 square feet of radiating sur- face in a gentle breeze of t = 45, when the steam-pressure in the boiler is p = 65 pounds to the square inch ? Units of heat, h = 0.505 x 198(311.86 - 45)' = 91206. 80 STEAM ENGINEERING. 311.86-45 = 266.86. Logarithm, 266.86 = 2.4262835 Multiply by exponent, 1.22 48525670 48525670 24262835 912.15 = 2.960065870 Add log. 198 = 2.2966652 Add log. 0.505 = 0.7032914 - 1 Units of heat, 91206 = 49600225 Example 4- How many cubic feet of steam are condensed by the radiation of h = 91206 units of heat per hour ? Latent heat, I = 170. 91206 = 170 4.9600225 Subtract log. 170 = 2.2304489 Cubic feet of steam, 536.5 = 2.7295736 Example 5. How much horse-power is lost by the radiation in the preceding examples ? C = 407.48 cubic feet, and p = 65 pounds Power lost, H> = 53 ' 5 * 65 = 2.5375 horse-power. log. 536.5 = 2.7295736 } . log. 65 -1.8129134 ) ac 4.5424870 Subtract log. 13748.4 = 4.1382521 Horse-power lost, 2.5375 = 0.4042349 Example 2. An uncovered steam-pipe is D = 8 inches diameter and L = 28 feet long, conducting steam of p = 80 pounds pressure, and temperature T=324. The temperature of the surrounding air is = 40 of brisk wind. Required the units of heat lost, the cubic feet of steam condensed per hour and the horse-power lost by radiation from the pipe ? O 00 Units of heat, h = - [450 + (1 2 -8) 2 ] (324 -4ff) lM = 33780. COVERED STEAM-PIPES. 81 The whole calculation is practically set up as follows by log- arithms : Logarithm!. 324-40 = 284 = 2.4533183 Multiply by exponent, 1.24 98132732 ' 49066366 24533183 (324 - 40) 1 - 24 = + 3.042114692 (12 - 8)* = 16 + 450 = 466 = + 2.6683859 8 x 28 = 224 = + 2.3502480 8 x 28[450 + (12 - 8) 2 ](324 - 40) 1 - 24 = + 8.0607486 Coefficient, 3404.8 = - 3.5320916 The required units of heat, . . h = 33780 = + 4.0286570 Latent heat per cubic foot, . . I = 196.84 - - 2.2943339 Cubic feet of steam condensed, . C= 171.52 = + 2.2343231 Steam-pressure, .... p = 80 = + 1.9030900 Cp= + 4. 1374131 Coefficient, .... 13748.4- -4.1382521 Horse-power lost, . . IP - 0.99807 = + 0.9991610 - 1 Say one horse-power lost by radiation. It is supposed in this example that the steam is working "a high- pressure engine without expansion. For a condensing engine take the steam-pressure above vacuum and multiply the lost power by 1+hyp.Iog. of the expansion, and the product will be the correct horse-power lost. COVERED STEAM-PIPES. 63. When the steam-pipe is covered with felt and canvas outside, there is very little heat radiated, as will be seen in the accompanying table, which gives the heat and power saved by covering of different thickness. Suppose the loss by radiation of hoat from an uncovered steam-pipe 6 inches in diameter is IP = 2 horse-power ; then, by covering the pipe with felt one inch thick will save 86 per cent, of the 2 horse- power, or 2x0.86 = 1.72 horse-power, and the loss by radiation from the covered pipe will be only 2 - 1.72 = 0.28 of a horse-power. 82 STEAM ENGINEERING. TABLE XVI. Percentage w of Heat or Power Gained by Covering Steam- pipes with Felt and Canvas Outside. Warn. j.U,e. T 1 i hlekne i s in In 1 chex o 1 r Felt < H Torerln 2 ? 3 4 D m | m m TO TO m m TO TO TO 1 65 76 81 86 92 94 96 98 99 100 2 63 74 80 85 90 93 95 97 98 99 o 61 72 79 84 89 92 95 96 98 99 4 59 71 77 83 88 92 94 96 97 99 5 57 69 76 82 87 91 94 96 97 99 6 54 67 74 81 86 91 94 95 97 99 7 r,-2 66 73 81 85 90 93 95 97 99 8 50 64 71 80 85 90 93 9-3 97 99 9 47 62 70 79 84 89 93 95 97 99 10 45 61 69 78 84 89 92 95 98 98 11 42 59 67 78 83 88 92 94 96 98 12 40 58 66 77 83 88 92 94 96 98 STEAM-BOILER EXPLOSIONS. 64. Steam-boiler explosions are caused by suddenly liberating all the work stored in the boiler. The work K is the product of the three simple physical elements force F, velocity V and time T. W 57.69-*. Then, 180.9 (57.69 -)+ 1146.6 - 15485. Complete the calculation, which will give a =5.228 pounds of steam of ... 5994.8 units of heat. w = 52.46 pounds of water of ... 9490.0 " For one cubic foot of steam add . . 184 " Total 15658.8 " The original heat was 15669. " 52.46 pounds of water at 212 = . 0.8767 cubic feet. 5.228 pounds of steam at 212 = . 135.58 " Add one cubic foot expanded four times 4 Total volume of steam . 139.58 84 STEAM ENGINEERING. That is to say, the piston has moved 139.58-1.12 = 138.46 fee.t from the position occupied when the weight (J \v;is tir.-t diminished. The work accomplished by this operation is determined as follows : 5.228 pounds of steam of pressure P= 65 = 35.7 cubic feet. 65 : 14.7 = 4.47 the expansion of the steam. Hyperbolic log. 4.47 - 1.49734. Work K= 144 x 65 x 35.7 x 1.4973 = 500330 foot-pounds. From this subtract the work of the atmosphere, which is k = 144 x 14.7 x 138.46 = 293100 foot-pounds. Then 500330 - 293100 = 207230 foot-pounds of work done against the atmosphere. Divide this work by 550 times the number of seconds occupied in its execution, and the quotient will be the horse-power of the opera- tion. 67. Now suppose the piston to be firmly fixed in the position shown by the illustration Fig. 3, and instead of gradually diminish- ing the weight Q, let it be suddenly removed, leaving the hole o open for the steam to escape. The moment the steam-pressure on the sur- face of the water is removed or reduced, the heat will generate steam of a pressure of 65 pounds to the square inch in all parts of the water ; and as there is not a corresponding pressure on its surface, the steam will lift the water bodily in the form of foam, striking the immovable piston, and thus explode the boiler. Under the conditions assumed, the work of this explosion will be 911160 foot-pounds, accomplished, no doubt, within the time of one second, in which case 207230 : 550 = 1337 horse-power of the explo- sion of only oue cubic foot of water, of which only 1 0.8767 = 0.1233 of that cubic foot was converted into steam. The mystery of steam-boiler explosions is thus explained. 68. The investigation becomes more simple by way of algebraical formulas, for which letters will denote W=^ pounds of water under steam-pressure in the boiler before explosion. w = pounds of water reduced to temperature 212, and not evap- orated in the explosion. Ibs. = pounds of water evaporated to steam in the explosion and ex- panded to the pressure of the atmosphere. h = units of heat per pound of water in the boiler before explo- sion. P = steam-pressure in pounds per square inch above vacuum in the boiler before explosion. STEAM-BOILER EXPLOSIONS. 85 (7= cubic feet of steam of atmospheric pressure generated by the heat iu the water before explosion. K= destructive work of the explosion in foot-pounds. Units of heat IF A = 181 w + 1147 Ibs. . . 3 dt<;= JF-lbs. . . ' . . 4 (JF-lbs.) + H471bs. ... 5 6 The weight per cubic foot of steam of atmospheric pressure is 0.038, and the volume of steam evaporated and expanded in the explosion to atmospheric pressure will be 996 x 0.038 = 36.7. The volume of this steam under the pressure P was 14.7 C P-14.7 The gross work done by the explosion will then be 144xl4.7PC, P - From this work should be subtracted the reaction of the atmo- sphere, which is 144x14.7 C. The remainder will be the destructive work of the explosion, namely, Example 7. A steam-boiler containing 125 cubic feet of water explodes under a steam-pressure of P=S5 pounds to the square inch. Required the destructive work of the explosion ? .Under this pressure the temperature of the water is 316.08, and weighs 57.21 pounds per cubic foot. W= 125 x 57.21 - 7151.25 pounds. 86 STEAM ENGINEERING. The steam-volume generated by the explosion is 71 T! 9^5 (7= ^(287 - 181) = 20655 cubic feet. 36.7 K= 2116.8 x 2Q6o5/ _ 85 hyp.log.-^- - 1\ = 49200550 foot-pounds, the required work of destruction. This work is equivalent to that of the explosion of 246 pounds of gunpowder, which is more than double the work of a charge from a 20-inch gun. A great part of the work of steam-boiler explosions is consumed in setting the air into vibration, which makes the report. 69. A laborer working 8 hours per day with a power of 50 effect accomplishes a work of 1,440,000 foot-pounds of work, called " work- manday." The work of the above steam-boiler explosion 49200550 : 1440000 = 34 workmandays. It would require 34 men to work one day, or one man 34 days, to do the same amount of work. The work of the steam in the boiler prior to the explosion is not included in the preceding formulas and examples, because it is an insignificant quantity compared with that of the heat in the water. The bursting of a vessel full of steam without water will cause very little damage compared with that of a vessel full of water under steam-pressure. c = cubic feet of steam in a boiler of P= pressure per square inch above vacuum. k = work of explosion of the steam only. CAUSE AND PREVENTION OF STEAM-BOILER EXPLOSIONS. 70. The bursting of a steam-boiler is a preliminary process to the explosion. In a vessel composed of any non-elastic material and filled with water hermetically sealed in it, if that water is frozen solid, the ex- pansion of the ice will most likely burst the vessel, but there will be no explosion, because there is no explosive agency in it. A steam-boiler full of cold water and tested with hydrostatic pres- sure until it bursts, will not explode ; but if that cold water is heated to a temperature corresponding to the bursting pressure, there will be an explosion. CAUSE OF BOILER EXPLOSIONS. 87 The iron in steam-boilers, like any other material subjected to bursting strain, breaks at the weakest point ; but it is difficult to find the location of that point, and very often boilers are not constructed, inspected or managed with sufficient care to guard against bursting. Thus steam-boiler explosions are caused by various neglects in guard- ing against such accidents namely, First. By long use boilers become weakened by corrosion, which acts unevenly on different kinds of iron and in different parts of the boiler, and if not properly inspected and the weakened places repaired, the boiler may burst and explode. Second. The general construction, with staying and bracing of steam-boilers, is often very carelessly executed, and results in explo- sion. This kind of explosions are often indicated long before the acci- dent occurs, by leakage of the boiler; when the engineer, not suspect- ing the approaching danger, limits the remedies generally to efforts toward stopping the leak. Leakage from bad caulking or packing Is easily distinguished from that of bad or insufficient bracing, in which latter case the fire- ought to be hauled out, the steam blown off grad- ually, and the boiler secured with proper bracing. Third. The strength and quality of iron in the original construction are not always properly selected to correspond with the duty expected of the boiler, which neglect causes explosion. Fourth. Single-riveted joints weaken the strength of a boiler abou* 50 per cent, of that of the solid plate, and boilers therefore often burst by tearing the plate between the rivets. This defect can be remedied by making double-riveted joints, which, if properly proportioned, are (by experiments) as strong as the solid plate. Fifth. Explosion is sometimes caused from low water in the boiler, but more rarely than is generally supposed. When the fire crown and flues are subjected to a strong heat and not covered with water, the steam does not absorb the heat fast enough to prevent the iron from becoming so hot that it cannot withstand the pressure, but collapses from weakness, and the boiler explodes. There are several good inven- tions for preventing too low water in boilers, which should invariably be used. Sixth. Steam-boilers often burst from strain in uneven expansion or shrinkage of the iron by sudden change of temperature. When the fire is too quickly lighted or extinguished, there is not time enough for the heat to communicate alike to and from all parts of the boiler, the effect of which has often been the cause of bursting the boiler. When cold feed-water is injected near to the fire-place, it absorbs the heat quickly and cools that part of the heating surface, and when the feed 88 STEAM ENGINEERING. is not evenly supplied, but alternately stopped and forced in with the full capacity of the pump, there will be a corresponding contraction and expansion of that part of the iron, the work of which is injurious to and may finally cause the bursting of the boiler. The feed-water should be heated to at least 100 for condensing engines and 180 for high-pressure engines, and injected at some distance from the fur- nace. Seventh. It is a very bad practice to make boiler-ends of cast-iron, composed of a flat disc of from two to three inches thick, with a flange of from one to two inches thick, with cast rivet holes. The first shrinkage in the cooling of such a plate causes a great strain, which is increased by riveting the boiler to it. Any sudden change of tem- perature in such plate, either by starting or putting out the fire, might crack the plate and cause explosion of the boiler. Such accidents can be avoided by making the boiler-ends of wrought-iron plates properly stayed or made concave on the steam side. Eight. In cold weather, when the boilers have been at rest for some time, the water in them may be frozen to ice ; then, when fire is quickly made in them, some parts are suddenly heated and expand, whilst other parts still remain cold, thus causing an undue strain which may so injure the boiler that it will not be able to bear the required steam-pressure, and explosion follows. Such accident can be avoided by a slow and cautious firing, so that all the ice may be thoroughly melted before steam is generated in any part of the boiler. Ninth. When a number of boilers are placed close together and connected to a common steam-pipe, the weakest part in either one of them is the measure of safety for all the rest ; for however strong the other boilers may be, when the weakest one bursts all the rest will most likely explode simultaneously, as has often been the case. Tenth. Steam-boiler explosions are thus not always caused by the pressure of steam alone, but most frequently by the expansion and contraction of the iron composing the boilers. A steam-boiler which is perfectly safe with a working pressure of 200 pounds may explode with a pressure- of 20 pounds to the square inch. Eleventh. See " Superheating Steam " for another possible cause of expk STRENGTH OF BOILERS. 89 STRENGTH AND SAFETY OF STEAM- BOILERS. 71. The law in the United States regulating the strength and safety of steam-boilers, passed by Congress February 28, 1871, and enforced February 28, 1872, is that all the plates used in steam-boilers shall be stamped with the number of pounds equal to the break- ing-strength per square inch section of the iron. One-sixth of the stamped number is taken as the safety or working strength of the iron in the boiler. The law requires that steam-boilers must be tested with hydrostatic pressure of 50 per cent, above the working pressure allowed. The following quotations are copied from the rules prescribed for the Boiler Inspectors : " Where flat surfaces exist, the inspector must satisfy himself that the bracing, and all other parts of the boiler, are of equal strength with the shell, and he must also, after applying the hydrostatic test, thoroughly examine every- part of the boiler to see that no weakness or fracture has been caused thereby. Inspectors must see that the flues are of proper thickness to avoid the danger of collapse. Flues of sixteen inches in diameter must not be less than one-quarter of an inch in thickness, and in proportion for flues of a greater or less diameter." " Every iron or steel plate intended for the construction of boilers to be used on steam-vessels shall be stamped by the manufacturer in the following manner, viz. : At the diagonal corners, at a distance of about four inches from the edges, and also at or near the centre of the plate, with the name of the manufacturer, the place where manufac- tured, and the number of pounds tensile strain it will bear to the sec- tional square inch." " The manner of inspecting, testing and stamping boiler-plates, by the United States inspectors, shall be as follows, viz. : " The sheets to be inspected and tested shall be selected by the in- spectors, indiscriminately, from the lot presented, and shall not be less than one-tenth of the entire lot so presented, and from every such selected sheet the inspector shall cause a piece to be taken, for the purpose of ascertaining its strength, the area of which shall equal oiie- quarter of one square inch, and the force at which this piece can be parted in the direction of its fibre or grain, represented by pounds avoirdupois multiplied by four, shall be the tensile strength, and the lot from which the test-sheets were taken shall not be marked above 90 STEAM ENGINEERING. the lowest number represented by these tests. The inspector shall also subject a piece taken from each selected sheet to repeated heating and cooling, and shall bend it short, both in a hot and a cold state, and shall draw it out under the hammer, as it is called, in order to ascertain the other qualities mentioned in Section 36 of the act afore- said ; and should these test-pieces be found deficient in these qualities, the inspectors shall refuse to place the government stamp on the lot from which these test-sheets were taken ; but if the test-pieces should prove to possess these qualities, then the inspector shall proceed to stamp the entire lot from which they were taken with the letters 'U.S.' and the figure denoting the inspection-district in which the inspection was made." " All boiler-plates tested and stamped as above shall be considered as having been inspected according to law ; but should any local or other inspector have valid reasons for believing that fraud has been practiced, and that the stamps upon any such boiler-plates are false, in whole or in part, he is empowered to re-inspect and test the same." " The provisions of this rule shall take effect as soon as the inspec- tors are appointed, and the manufacturers of boiler-plates notified of the same." The rule for proportioning the strength of boilers to the steam-pres- sure is as follows : Rule. " Multiply one-sixth ( ) of the lowest tensile strength found stamped on any plate in the cylindrical shell by the thickness ex- pressed in parts of an inch of the thinnest plate in the same cylindrical shell, and divide the product by the radius or half the diameter of the shell expressed in inches, and the quotient will be the steam-pressure in pounds per square inch allowable in single-riveted boilers, to which add twenty per centum for double riveting." No allowance is made by this rule for the metal punched away by the holes in the plate. Allowing 66 per cent, of metal between the holes, the safety strength will be one-quarter of the ultimate strength. The rule is more simply expressed by algeb'raical formulas, as follows : S = breaking-strain in pounds per square inch, stamped on the boiler-plate. t = thickness of the plate in fractions of an inch. D = inside diameter of the boiler in inches. p = steam-pressure in pounds per square inch allowable in the boiler, single riveted. STRENGTH OF RIVETED JOINTS. 91 \ 72. Safety Strength of Single-Riveted Joints. Si feteam-pressure, p = . . . . . .1 Diameter of boiler, D <= . 3p q T\ Thickness of plate, t = S Breaking-strain, >S i Example 1. A steam-boiler of D = 48 inches diameter and thick- ness of plates i = 0.375 of an inch is stamped with a breaking-strain S = 55,000 pounds. Required the steam-pressure the boiler is allowed to carry ? 55000 x 0.375 p = = 143.2 pounds to the square inch for single-riveted joints. For double-riveted joints 143.2x1.2 = 171.8 pounds to the square inbh. i 73. Safety Strength of Double-riveted Joints. C\A S f . 5 Steam-pressure, P D Diameter of boiler, D QASt P Thickness of plate, i-.2t 0.4 S Breaking-strain, S= D ?, 0.4* Example 8. A double-riveted boiler is to be constructed to carry p = 80 pounds of steam in a diameter D = 96 inches, with t = 0.3 of an inch thickness of plate. Required the stamp on the plates ? = _96^80 _ 64000st 0.4 x 0.3 The following tables are calculated from the above formulas for .sin- gle and double-riveted boilers. 92 STRENGTH OF STEAM-BOILERS. TABLE XVII. Boiler Plates Stamped 45.OOO Ibs. Safety-strain = 75OO. s| Thickness of boiler-plate in fractions of an inrh. SJ &= 0.1875 } = 0.25 & = 0.28125 & = 0.3125 ft = 0.34375 I* Riveting. Riveting. Riveting. Riveting. Riveting. y Single. J Double. Single. Double. Single. Double. Single. Double. Single. Double. D Pressures. Pressures. Pressures. Pressures. Pressures. 36 78.12 93.74 104.2 125. 117.2 140.6 130.2 156.2 143.2 171.8 38 74. 88.8 98.6 118.3 110.9 .133.1 123.3 148. 135.6 162.8 40 70.31 84.37 93.7 112.4 105.4 126.5 117.2 140.6 128.1 154.7 42 66.96 80.35 89.2 107. 100.4 120.5 111.6 133.9 122.7 147.3 44 63.92 86.7 85.2 102.2 95.85 115. 106.5 127.8 117.1 140.5 48 58.59 70.3 78.1 93.72 82.87 99.45 97.65 117.2 107.4 128.9 54 52. 62.4 69.44 83.32 78.12 93.74 86.S 104.2 95.5 114.6 60 46.87 56.24 62.5 75. 70.31 84.37 78.12 93.74 85.93 103.1 66 42.79 51.34 56.86 68.17 63.93 76.71 71. 85.2 78.1 93.72 72 39. 46.8 52. 62.4 58.55 70.26 65.1 78.12 71.61 85.93 78 36. 43. 49.34 58.86 54.67 65.6 60. 72.1 66.05 79.26 84 33.48 40.17 44.64 53.56 50.22 60.26 55.8 66.96 61.38 73.65 90 31.25 37.5 41.66 50. 46.83 56.19 52. 62.5 57.25 68.7, 96 29.28 35.53 39. 46.8 43.91 52.69 48.82 58.58 53.7 64.44 102 27.56 33.07 36.76 44.11 41.35 49.62 45.95 55.14 50.53 60.64 108 26. 31.2 34.72 41.86 39.06 46.87 43.4 52.1 47.75 57.3 120 23.43 28.12 31.25 37.5 35.15 42.18 39.06 46.87 42.96 51.56 I) | = 0.375 & = 0.4375 J-0.5 & = 0.5625 f = 0.625 36 156.2 187.5 182.3 218.8 208.3 250. 234.3 281.2 260.4 312.5 38 148. 177.6 172.6 207.1 197.2 236.6 221.8 266.2 246.6 296. 40 140.6 168.7 164. 196.8 187.4 224.9 210.8 253. 234.4 281.2 42 133.9 160.7 156.1 187.4 178.4 214. 200.8 241. 223.2 267.8 44 127.8 153.4 148.9 178.7 170. 204.5 191.7 230. 213. 255.6 48 117.2 140.6 136.7 164. 156.2 187.4 165.7 198.9 195.3 234.4 54 104.2 125. 121.5 145.8 138.9 166.6 156.2 187.5 173.6 208.4 60 93.75 112.5 109.4 131.1 125. 150. 140.6 168.7 156.2 187.5 66 85.2 102.2 99.45 119.3 113.7 136.3 127.9 153.4 142. 170.4 72 78.12 93.74 91.06 109.3 104. 124.8 117.1 140.5 130.2 156.2 78 72.1 86.53 85.39 102.4 98.68 117.7 109.3 131.2 120. 144.2 84 66.96 80.35 78.12 93.74 89.28 107.1 100.4 120.5 111.6 133.9 90 62.5 75. 72.91 87.5 83.33 100. 93.7 112.4 104. 125. 96 58.58 70.29 68.29 81.95 78. 93.6 87.8 105.4 97.6 117.2 102 55.12 66.14 64.32 77.19 73.53 88.22 82.7 99.2 91.9 110.31 108 52.1 62.5 60.77 72.93 69.45 83.3 78.1 93.7 86.8 104.2 120 46.87 56.25 54.68 65.62 62.5 75. 70.3 84.3 78.1 93.7 STRENGTH OF STEAM-BOILERS. 93 1 TABLE XVIII. Boiler Plates Stamped 5O.OOO Ibs. Safety-strain J = 8333.3. -3J Thickness of boiler-plate in fractions of an inch. S| o> ""' &= 0.1875 = 0.25 & =0.28125 ^ = 0.3125 ft = 0.34375 II Riveting. Hiveting. Riveting. Riveting. Riveting. ll Single. Double. -Miml.'. Double. Single. Double. Single. Double. Single. Double. D Pressures. 1'ressiires. Pressures. Pressures. Pressures. 36 86.8 104.2 115.7 138.9 130.2 156.2 144.7 173.6 159.1 191. 38 82.23 98.68 109.6 131.5 123.3 148. 137. 164.5 150.7 180.8 40 78.12 93.74 104.1 125. 117.1 140.6 130.2 156.2 143.2 171.8 42 74.49 89.38 99.2 119. 111.6 133.9 124. 148.8 136.4 163.7 44 71. ' 85.2 94.69 113.6 106.5 127.7 118.4 142. 130.2 156.2 48 65.1 78.12 86.8 104.1 97.4 116.9 108. 130.2 119.1 142.9 54 57.62 69.44 77.16 92.59 86.8 104.1 96.45 115.7 101. 121.3 60 52. 62.4 69.44 83.33 78.12 93.74 86.8 104.1 95.45 114.5 66 47.34 56.8 63.13 75.75 71.02 85.22 78.91 94.69 86.8 104.1 72 43.4 52. 57.87 69.44 65.11 78.13 72.35 86.8 79.57 95.48 *-0 /8 40. 48. 53.67 64.4 60.22 72.26 66.77 80.12 73.44 88.13 84 37.2 44.64 49.6 59.5 55.8 66.96 62. 74.4 68.2 81.84 90 34.72 41.66 46.29 55.55 52.08 62.5 57.87 69.44 63.65 76.38 96 32.55 39. 43.4 52. 48.82 58.59 54.25 65.1 59.67 71.61 102 30.63 36.77 40.66 48.79 45.87 55.04 51.08 61.29 56.17 67.41 108 28.81 34.72 38.58 46.29 43.4 52.08 48.22 57.85 53.03 63.63 120 26. 31.2 34.72 41.66 39.06 46.87 43.4 52.08 47.74 57.29 D | = 0.375 ^=0.4375 | = 0.5 ffe = 0.5625 | = 0.625 36 173.6 208.3 202.5 243. 231.5 277.8 260.4 312.4 289.4 347.2 38 164.4 197.3 191.8 230.2 219.3 263.1 246.6 296. 274. 329. 40 156.2 187.5 182.2 218.7 208.3 250. 234.2 281.2 260.4 312.4 42 148.8 178.6 173.6 208.3 198.4 238. 223.2 267.8 248. 297.6 44 142. 170.4 165.7 198.8 189.4 227.3 213. 255.4 236.8 284. 48 130.2 156.2 151.9 182.3 173.6 208.3 194.8 233.8 216. 260.4 54 115.7 138.9 135. 162. 154.3 185.2 173.6 208.2 192.9 231.4 60 104.1 125. 121.5 145.8 138.9 166.6 156.2 187.5 173.6 208.2 66 94.69 113.6 110.4 132.5 126.2 151.5 142. 170.4 157.8 189.4 72 86.8 104.1 101.2 121.5 115.7 138.9 130.2 156.2 144.7 173.6 78 80.12 96.15 93.71 112.4 107.3 128.8 120.4 144.5 133.5 160.2 84 74.4 89.28 86.8 104.1 99.2 119. 111.6 133.9 124. 148.8 90 69.44 83. 81.01 97.21 92.58 111.1 104.1 125. 115.7 138.9 96 65.1 78.2 75.95 91.14 86.8 104. 97.64 117.2 108.5 130.2 102 61.27 73.54 71.29 85.55 81.32 97.58 91.74 110.1 102.1 122.6 108 57.85 69.45 67.5 81. 77.15 92.6 86.8 104.1 96.44 115.7 120 52.08 62.49 60.76 72.92 69.44 83.33 78.12 93.74 86.8 104.1 11} STEAM ENGINEERING. TABLE XIX. Boiler Plates Stamped 55.OOO Ibs. Safety-strain \ - 9166.6. J Thickness of boiler-plate in fraction* of ai i inch. ll A- 0.1875 $ = 0.25 & = 0.28125 ^ = 0.3125 \\ = 0.34375 s - Riveting. Riveting. Riveting. Riveting. Riveting. n Single. | Double. Single. Double. Single. Double. Single. Double. Single. Double. D Pressures. Pressures. Pressures. Pressures. Pressures. 36 95.48 114.6 127.3 152.8 143.2 171.8 159.1 190.9 175. 210. 38 90.46 108.5 120.6 144.7 135.6 162.7 150.7 180.9 165.8 198.9 40 85.93 103.1 114.6 137.5 128.9 154.7 143.2 171.9 157.5 189. 42 81.84 98.2 109.1 130.9 122.7 147.3 136.4 163.7 150. 180.1 44 78.12 93.74 104.1 125. 117.1 140.6 130.2 156.2 143.2 171.8 48 71.61 85.93 95.43 114.6 107.4 128.8 119.3 143.2 131.2 157.5 54 63.65 76.38 84.87 101.8 95.4 114.5 106. 127.3 116.6 140. 60 57.29 68.74 76.38 91.65 85.93 103.1 95.48 114.6 105. 126. 66 52. 62.4 69.44 83.32 78.12 93.74 86.8 104.1 95.45 114.5 72 47.74 57.28 63.65 7%.38 71.6 85.92 79.56 95.48 87.52 105. 78 44. 52.8 58.76 70.51 66.1 79.32 73.45 88.13 80.79 96.95 84 40.92 49.1 54.56 65.47 61.38 73.65 68.2 81.84 75.02 90.02 90 38.19 45.82 50.92 61.1 57.28 68.73 63.65 76.38 70.01 84.02 96 35.8 42.96 47.74 57.28 53.7 64.44 59.67 71.61 65.64 78.77 ! 102 33.7 40.44 44.93 53.9 50.54 60.65 56.16 67.39 61.78 74.13 108 31.82 38.19 42.43 50.9 47.71 57.26 53. 63.65 58.32 69.99 ! 120 28.64 34.37 38.19 45.82 42.96 50.56 47.74 57.29 52.51 i 63.02 '' D 1=0.375 A- 0-4375 I- 0.5 ^ = 0.5625 | = 0.625 i 36 190.9 229.1 2-2-2.7 267.3 254.6 305.5 286.4 343.6 318.2 381.8 38 180.9 217. 217. 253.2 241.2 289.4 271.2 325.4 301.4 361.8 40 171.9 206.2 200. 240. 229.1 275. 257.8 309.4 286.4 343.8 42 163.7 196.4 190.9 229.1 218.2 261.9 245.4 294.6 27-2.S 327.4 44 156.2 187.5 182.2 218.6 208.3 250. 234.2 281.2 260.4 312.4 48 143.2 171.8 167.1 199.5 190.9 229.1 214.8 257.6 238.6 286.4 54 127.3 152.7 148.5 178.2 169.7 203.7 190.8 229 212. 254.6 60 114.6 137.5 133.7 160.4 152.7 183.3 171.8 206.2 190.9 229.2 66 104.1 125. 121.4 145.7 138.9 166.6 156.2 187.5 173.6 208.2 72 95.48 114.5 111.4 133.6 127.3 152.7 143.2 171.8 159.1 190.9 78 88.13 105.7 102.7 123.3 117.5 141. 132.2 158.6 146.9 176.2 84 81.84 982 95.48 114.6 109.1 130.9 122.7 147.3 136.4 163.7 90 76.38 91.65 89.11 106.9 101.8 122.2 114.5 137.4 127.3 152.7 96 71.61 85.93 83.54 100.2 95.48 1 114.5 107.4 128.9 119.3 143.2 102 67.4 80.88 78.33 94. 89.87 107.8 101.1 121.3 112.3 134.7 108 63.65 76.35 74.25 89.1 84.85 101.8 95.42 114.5 106. 127.3 120 57.29 68.74 66.83 80.2 76.38 91.64 89.92 101.1 95.5 114.6 STRENGTH OF STEAM-HOI l.KRS. 95 TABLE XX. Boiler Plates Stamped 6O.OOO Ibs. Safety-strain \ = 1O.OOO. c| Thickness of boiler-plate in fractions of tin inch. ^ = c " &= 0.1 875 J = 0.25 & = 0.28125 & = 0.3125 J = 0.34375 r Riveting. Riveting. Riveting. Riveting. Riveting. ^ Single. Double. Single. Double. Single. Double. Single. | Double. Single. | Double. D Pressures. Pressures. Pressures. Pressures. Pressures. 36 104.1 125. 138.9 166.6 156.2 187.5 173.6 208.3 190.9 229.1 38 98.68 118.4 131.6 157.9 148. 177.6 164.5 197.3 180.9 217.1 40 93.74 112.5 125. 150. 140.7 168.9 156.2 187.4 166.8 200.1 42 89.28 107.1 119. 142.8 133.8 160.6 148.7 178.6 163.6 196.4 44 85.22 102.2 113.6 136.3 127.8 153.3 142.' 170.4 156.2 187.4 48 78.12 93.74 104.1 125. 117.1 140.6 130.2 156.2 143.2 171.8 54 69.44 82.44 92.59 110.1 104.1 125.. 115.7 138.9 127.3 152.7 GO 62.4 75. 83.33 100. 93.71 113.4 104.1 125. 114.5 137.4 66 56.8 68.1 75.75 90.9 85.22 102.2 94.69 113.6 104.1 125. 72 52. 62.4 69.44 83.32 78.12 93.74 86.8 104.1 95.45 114.5 T8 48. 57.6 64.4 76.92 72.26 86.71 80.12 96.15 88.13 105.7 84 44.64 53.52 59.5 71.4 66.95 80.34 74.4 89.28 81.84 98.21 90 41.66 50. 55.55 66.66 62.49 75. 69.44 83.33 76.38 91.66 90 39. 46.8 52. 62.4 58.55 70.26 65.1 78.12 71.61 85.93 102 36.76 44.12 49.02 58.8 55.14 66.17 61.27 73.51 67.4 80.88 108 34.72 41.22 46.29 55.05 52.07 62.48 57.85 69.45 63.65 76.38 120 32.2 37.5 41.661 50. 46.87 56.24 52.08 62.5 57.29 68.75 D | = 0.375 ^ =0.4375 J = 0.5 & = 0.5625 f = 0.625 36 208.3 250. 242. 290.4 277.8 333.3 312.4 375. 347.2 416.6 38 197.3 237. 230.3 276.3 263.1 315.8 296. 355.2 329. 394.6 40 187.4 225. 218.7 242.5 250. 300. 281.4 337.8 312.4 374.8 42 178.6 214.3 208.3 249.9 238. 285.6 267.6 321.2 297.4 357.2 44 170.4 204.5 198.8 238.6 227.2 272.7 255.6 306.6 284. 340.8 48 156.2 187.5 182.2 218.6 208.3 250. 234.2 281.2 260.4 312.4 54 138.9 165.7 162. 194.4 185.2 220.2 208.2 250. 231.4 277.8 60 125. 150. 145.7 174.9 166.6 200. 187.4 226.8 208.2 250. 66 1136 136.3 132.5 159. 151.5 181.8 170.4 204.4 189.4 227.2 72 104.1 125. 121.4 145.7 138.9 166.6 156.2 187.5 173.6 208.2 78 96.15 115.8 112.4 134.9 128.8 153.8 144.5 173.4 160.2 192.3 84 89.28 107.1 104.1 124.9 119. 142.8 133.9 160.7 148.8 178.5 90 83.33 100. 97.21 116.6 111.1 133.3 125. 150. 138.9 166.6 96 78.12 93.74 91. 109.2 104. 124.8 117.1 140.5 130.2 156.2 102 73.53 88.23 85.78 102.9 98.04 117.6 110.3 132.3 122.5 147. 108 69.45 82.85 81.01 97.21 92.6 110.1 104.1 124.9 115.7 138.9 120 62.5 75. 73.86 8863 83.33 100. 93.74 112.5 104.1 125. 96 STEAM ENGINEERING. TABLE XXI. Boiler Plates Stamped 65.OOO Ibs. Safety-strain =10833. 3. *J Thickness of boiler-plate in fractions of an inch. r-S T^ = 0.1875 = 0.25 & = 0.28125 & = 0.3125 \% = 0.34375 1| Riveting. Riveting. Riveting. Riveting. Riveting. J Single. Double. Single. Double. Single. Double. Single. 1 Double. Single. Double. D Pressures. Pressures. Pressures. Pressures. Pressures. 36 112.8 135.4 150.4 180.5 169.2 203. 188. 225.6 206.8 248.1 38 106.9 128.3 142.5 171. 160.3 192.4 178.2 213.8 196. 235.2 40 101.5 121.8 135.4 162.5 152.3 182.8 169.3 203.1 186.2 223.4 42 96.72 116. 128.9 154.7 145. 174. 161.2 193.5 177.3 212.8 44 92.32 110.8 123'.! 147.7 138.5 166.2 153.9 184.7 169.3 203.1 48 84.63 101.5 112.8 135.4 126.9 152.3 141. 169.3 155.1 186.3 54 75.21 90.25 100.3 120.3 112.8 135.4 125.4 150.4 137.9 165.5 60 67.7 81.24 90.27 108'.3 101.5 121.8 112.8 135.4 124.1 148.9 66 61.55 73.86 82. 98.4 92.3 110.7 102.6 123.1 112.8 135.4 72 56.42 67.7 75.22 90.26 84.61 101.5 94. 112.8 103.4 124.1 78 52. 62.4 69.44 83.33 78.12 93.74 86.8 104.1 95.45 114.5 84 48.36 58. 64.48 77.37 72.54 87.05 80.6 96.72 88.66 106.4 90 45.13 54.15 60.18 72.21 67.69 81.23 75.2 90.24 82.72 99.26 96 42.31 50.77 56.37 67.64 63.44 76.13 70.52 84.63 77.57 93.09 102 39.82 47.75 53.1 63.72 59.73 71.68 66.37 79.65 73.01 87.61 108 37.61 45.12 50.15 60.15 56.42 67.71 64.7 75.2 68.95 82.74 120 38.85 40.62 45.13 54.16 50.77 60.93 56.42 67.71 62.06 74.48 D |=0.375 ^=0.4375 J = 0.5 &= 0.5625 f = 0.625 36 225.6 271. 263.2 315.8 300.8 360.9 338.4 406. 376. 451.2 38 213.8 256.6 249.4 299.3 285.1 342. 320.6 384.8 356.4 427.6 40 203.1 243.8 236.9 284.3 270.1 325. 304.6 365.6 338.6 406.2 42 193.5 232.2 225.6 270.7 257.9 309.5 290. 348. 322.4 387. 44 184.7 221.6 215.4 258.5 246.2 295.4 277. 332.4 307.8 369.4 48 169.3 203.1 197.4 236.9 225.7 270.8 253.8 304.6 282. 338.6 54 150.4 180.6 175.5 210.6 200.6 240.7 225.6 270.8 250.8 300.8 60 135.4 162.5 158. 189.5 180.5 216.6 203. 243.6 225.6 270.8 66 123.1 147.7 143.5 172.2 164. 196.8 184.6 221.4 205.2 246.2 72 112.8 135.4 131.6 157.9 150.4 180.5 169.2 203. 188. 225.6 78 104.1 125. 121.4 145.7 138.9 166.6 156.2 187.5 173.6 208.2 84 96.72 116. 112.8 135.4 128.9 154.7 145.1 174.1 161.2 193.4 90 90.24 108.3 105.3 126.4 120.3 144.4 135.4 162.4 150.4 180.5 96 84.63 101.5 98.68 118.4 112.7 135.3 126.9 152.2 141.0 169.2 102 79.65 95.5 92.92 111.6 106.2 127.4 119.4 143.3 132.7 159.3 108 75.2 90.3 87.76 105.3 100.3 120.3 112.8 135.4 125.4 150.4 120 67.71 81.25 83.98 100.8 90.26 108.3 101.5 121.8 112.8 1-35.4 STRENGTH OF STEAM-BOILERS. 97 TABLE XXII. Boiler Plates Stamped 7O.OOO Ibs. Safety-strain J = 11666.6. oj (-.Tt Thickness of boiler-plate in fractions of an inch. SJ &= 0.1875 = 0.25 & = 0.28125 ^ = 0.3125 & = 0.34375 Ijj Riveting. Eiveting. Riveting. Riveting. Riveting. "1 Single. Double. Single. | Double. Single. Double. Single. Double. Single. Double. D Pressures. Pressures. Pressures. Pressures. Pressures. 36 121.5 145.8 164.2 j 197.1 183.3 220. 202.5 243. 222.7 267.5 38 116. 139.2 153.5 184.2 172.7 217.2 191.9 230.2 211. 253.2 40 109.3 131.2 145.8 174.9 164. 196.8 182.3 218.7 200.5 240.6 42 104.1 125. 138.9 166.6 156.2 187.5 173.6 208.3 190.9 229.1 44 99.42 119.3 132.5 159. 149.1 178.9 165.7 198.8 182.2 218.7 48 91.13 109.3 121.5 145.3 136.7 164. 151.9 182.3 167.1 200.5 54 81. 97.2 108. 129.6 121.5 145.8 135. 162. 148.5 178.2 60 72.9 87.48 97.2 116.6 109.3 131.2 121.5 145.8 133.6 160.4 66 66.3 79.56 88.37 106. 99.43 119.3 110.5 132.5 121.5 145.8 72 60.75 72.9 81. 97.2 91.1 109.3 101.2 121.5 111.3 133.6 78 56.1 67.32 74.7 89.64 80.39 96.47 93.47 112.2 102.8 123.4 84 52. 62.4 69.4 83.28 78.1 93.72 86.8 104.1 95.45 114.5 90 48.6 58.32 64.8 77.77 72.9 87.48 81. 97.2 89.1 106.9 96 45.5 54.6 60.8 72.96 68.37 82.05 75.95 91.14 83.54 101.2 102 42.9 51.3 57.2 68.6 64.35 77.22 71.5 85.8 78.65 94.38 108 40.5 48.6 54. 64.8 60.75 72.9 67.5 81. 74.25 89.1 120 36.45 43.74 48.6 58.32 54.68 65.61 60.76 72.9 66.83 80.2 D | = 0.375 ^ = 0.4375 | = 0.5 & = 0.5625 |=0.625 36 243 291.6 285.7 342.9 328.5 394.2 366.6 440. 405. 486. 38 230.2 276.3 269.5 323.4 307. 368.4 345.4 434.4 383.8 460.4 40 218.7 262.4 255.1 306.1 291.6 349.9 328. 393.6 364.6 437.4 42 208.3 250. 243. 291.6 277.7 333.3 312.4 375. 347.2 416.6 44 198.8 238. 231.9 278.3 265. 318. 298.2 357.8 331.4 397.6 48 182.3 218.7 212.6 255.1 243. 290.6 273.4 328. 303.8 364.6 54 162. 194.4 189. 226.8 216. 259.2 243. 291.6 270. 324. 60 145.8 175. 170.1 204.1 194.4 233.3 218.6 262.4 243. 291.6 66 132.5 159. 154.7 185.6 176.7 212. 198.8 238.6 221. 265. 72 121.5 145.8 141.7 170.1 162. 194.4 182.2 218.6 202.4 243. 78 112.2 134.6 130.8 156.9 149.4 179.3 160.8 192.9 186.9 224.4 84 104.1 125. 121.4 145.7 138.8 166.6 156.2 187.4 173.6 208.2 90 97.2 116.6 113.4 136.1 129.6 155.5 145.8 174.9 162. 194.4 96 91.14 .109.3 106.3 127.5 121.6 145.9 136.7 164.1 151.9 182.3 102 85.8 102.6 100.1 120.1 114.4 137.2 128.7 154.4 143. 171.6 108 81. 97.2 94.5 113.4 108. 129.6 121.5 145.8 135. 162. 120 72.9 87.5 85.05 102. 97.2 116.6 109.3 131.2 121.5 145.8 98 STEAM ENGINEERING. STRENGTH OF BOILER-SHELLS. 74. The steam-pressure per square inch in the boiler, multiplied by the inside diameter of the shell in inches, is the strain on the plates per inch of length of the shell ; and as this strain is borne by two sides of the shell, only one-half of it is borne by each side. = ultimate strength in pounds per square inch of section of the plate. t = thickness of the plate in fractions of an inch. D = inside diameter of the boiler in inches. p = steam-pressure in pounds per square inch above that of the atmosphere. g 75. Ultimate Strength of Solid Shell without Riveted Joints. 2 t S Steam-pressure, p = 9 9 / Sf Diameter of boiler, D = .10 Thickness of plate, t -= ^ ...... 11 Breaking-strain, S= ...... 12 | 76. Safety Strength of Solid Shell without Riveted Joints (J of the Ultimate Strength). c Steam-pressure, p = , 13 * O Diameter of boiler, D = . . . . . .14 2p 2 /) Thickness of plate, t = -. . . . .15 Breaking-strain, . S= ^ 16 STRENGTH OF RIVETED JOINTS. 99 STRENGTH OF SINGLE-RIVETED JOINTS. 77. The post-office engineers pierce the sheets of post-stamps with small holes around each stamp in order to make the sheet tear easily for separating the stamps. This is a practical illustration of the effect of punching holes in the boiler-plates for the riveted joints. The plate is weakened in proportion as the diameter of the rivet is to the dis- tance between the centres of rivets. Suppose the diameter of the rivet to be d = 1 and distance between centres D = 3, then the strength of the solid plate is to that of the punched plate as D 3 That is, the strength of the punched plate is only 66 per cent., or of that of the solid plate. The static condition of riveted joints is that the sheering strain on the rivet is equal and opposite to the tearing strain on the plate, and the strength to resist these two strains must therefore be alike for the greatest strength of the joint. *It has been found by experiments that the sheering and tearing strength of wrought iron are nearly alike per section strained, and the slight difference varies either way according to the particular iron experimented upon, but on an average the sheering strength appears to have some advantage over that of tearing. Assuming these two strengths to be alike, the section of the rivet should be equal to the section of the plate between the rivets. d = diameter of the rivet. d = distance between centres of rivets. t = thickness of plate. Areas of sections, 0.7854 d 2 = t (3 - d). 8 = - (0.7854 d + f). The proportion between d and t averages in practice 2 t = d that is, the diameter of the rivet is made twice the thickness of the plate. For thin plates the diameter of the rivet is made larger, and for thick plates smaller, than d = 2 t, as will be seen in the accompanying table, which is set up from practice. Assuming that d = 2 t or t = 0.5 d, which, inserted for t in the above formula, will give the proportion between d and 3 namely, 0.7854 d 1 = 0.5 d(8-d) and 0.5824 d = 0.5 (8 - d). Distance d = 2.57 d between centres of rivets. This is the proportion of 3 and d, as used in practice for 1-inch plate, but the diameter of the rivet is then made much less than 2 t. 100 STEAM ENGINEERING. The punching of holes in the boiler-plate disturbs the fibres for some distance around the hole, and thus diminishes the strength, so that the section between the rivets is weaker than an equal section of the same plate not punched. This weakening amounts to from 10 to 20 per cent., according to experiment, with different kinds of iron. Allowing 37 per cent, of section punched away by the hole and 13 per cent, for disturbing the fibres by punching, there remains only 50 per cent, of strength of the solid plate in the single-riveted joint to Be relied upon for safety in practice. Experiments with strength of single-riveted joints have given as high as 70 per cent, of that of the solid plate ; but the writer is not disposed to rely upon those experiments in practice of boiler-making, for which reason only 50 per cent, is allowed in the following formulas. 78. Bursting Strength of Single-riveted Joints in Boiler-shells. Notation of letters is the same as before repeated. Steam-pressure, p = 17 Diameter of boiler, D = 18 P Thickness of plate, t = 19 Breaking-strain, S= - 20 The safety strength of materials should not be taken more than 25 per cent, of the ultimate strength. I 79. Safety Strength of Single-Riveted Joints with Punched Holes in Boiler Shells. O Steam-pressure, = 21 4Z> i W Diameter of boiler, D = . . 22 4p Thickness of plate, Breaking-strain, 8=^ ^ F .... 24 STRENGTH OF RIVETED JOINTS. 101 Example. A steam-boiler of D = 147 inches diameter is to carry jo = 60 pounds steam-pressure, and the thickness of plates = f of an inch. Required what stamp the plates must have ? The breaking-strain of the iron plates should be 54096 pounds to the square inch. By the government rule, Formula 4, the stamp need only be 40572. " 80. The government rule allows the boilers to be 25 per cent, weaker than by Formulas 21 to 24 inclusive. It is difficult to guard against all carelessness in boiler-making. When the holes in the plates are not punched to properly match one another, they form an eccentric opening, through, which a drift is driven to make the holes concentric. This drift does not only overstrain the iron, but inclines the hole so that the rivet will not be at right angles to the plate. The strength of such a rivet may be only 20 per cent, of that of a properly riveted hole. It is almost impracticable to punch the holes in boiler- plates sufficiently correct to match one another, as required for proper work. The strength of single-riveted joints with punched holes should therefore not be taken over 50 per cent, of that of the solid plate. For drilled holes known to be well fitted, 60 per cent, may be trusted upon for single-riveted joints. g 81. Safety Strength of Single-riveted Joints with Drilled Holes in Boiler Shells. 25 26 27 28 82. It is impracticable to proportion the riveted joints so perfectly that the shearing strength of the rivet be equal to the tearing strength of the plate, for the actual strength of the iron varies more than does the proportion of dimensions of the joint. 0.3 tS P D ' D _Mt8 P Thickness of plate, Break in er-strain. 5 = O3S 102 STEAM ENGINEERING. The following table gives the proportions of single-riveted joints to the nearest 16th of an inch as used in practice. It will be seen in the table that the section of the plate between the rivets is greater than the section of the rivet, except for one-eighth of an inch plate. For drilled holes make the distance between the centres of the rivets one-eighth () of an inch less than that for punched holes. TABLE XXIII. Proportion of Single-riveted Lap-joints with Punched Holes. Thickness of plate. Riv Diameter. ets. Length. Distance betw. cent. Lap of joint. Area of rivet. Area of plate. Per cent, of solid t d / 6 inches. sq. inch. sq. inch. plate. 1/8 5/16 1/2 7/8 1.1/4 0.0767 0.07031 64 3/16 7/16 3/4 1.5/16 1.1/2 0.1503 0.16406 66 1/4 1/2 1.1/8 1.1/2 1.3/4 0.1963 0.25000 66 5/16 5/8 1.3/8 1.7/8 2 in. 0.3067 0.39062 66 3/8 3/4 1.11/16 2.1/4 2.1/4 0.4417 0.56250 66 7/16 13/16 1.15/16 2.3/8 2.3/8 0.5184 0.68359 65 1/2 7/8 2.1/4 2.1/2 2.1/2 0.6013 0.75250 64 9/16 lin. 2.1/2 2.5/8 2.5/8 0.7854 0.91406 63 5/8 1.1/16 2.13/16 2.3/4 2.7/8 0.8904 1.05468 62 11/16 1.1/8 3.1/8 2.7/8 3.1/8 0.9940 1.03125 61 3/4 1.3/16 3.5/8 3 in. 3.3/8 1.3603 1.35937 60 13/16 1.5/16 3.11/16 3.1/4 3.5/8 1.3605 1.57422 60 7/8 1.3/8 3.15/16 3.1/2 4 in. 1.4840 1.85937 60 15/16 1.1/2 4.1/4 3.3/4 4.1/4 1.767 2.10937 60 lin. 1.5/8 4.1/2 4 in. 4.5/8 2.073 2.375 60 DOUBLE-RIVETED LAP-JOINTS. 83. Double-riveted joints, if properly proportioned, increase the strength of the boiler about 40 per cent, on account of the rivets being spaced farther apart, leaving more section of plate between them to resist the strain. The rivets are arranged in two rows, zig-zag, over one another, as shown in the accompanying illustration. For the greatest strength the distance between the rivets in the direction of the joint should be double the distance between the centre lines of the two rows, and the rivets will then form a right angle, or 90, with one another. DOUBLE-RIVETED JOINTS. 103 The distance between the rivets in the direction of the joint can be made 42 to 50 per cent, greater than between rivets in single-riveted joints. The diagonal distance between centres of rivet should be made equal to the distance in the direction of the joints in single riveting. Fig. 4. Double-riveted joints with punched holes, proportioned according to this rule, should be 40 per cent, stronger than single-riveted joints, and with drilled holes about 60 per cent, stronger. g 84. Safety Strength of Double-riveted Lap-joints with Punched Holes in Boiler-shells. Steam-pressure, Diameter of boiler, Thickness of plate, Breaking-strain, p = 0.35 1 S D 0.35 tS P Dp 8- 0.35 8' Dp 0.35 t 29 31 32 In the following tables for double-riveted lap-joints, one is headed A for drilled holes and the other B for punched holes, their difference being only in the distance of rivets. When the boiler-plates are stamped a low figure, say 45000, and the rivets are known to be of extra good quality, then table B should be used for drilled holes. For boiler-iron of high stamp, say 65000, and the rivets of ordinary quality, then table A should be used for punched holes. The dimen- sions in the tables are given to the nearest 16ths of an inch. 104 STEAM ENGINEERING. TABLE XXIV. A. Proportions of Double-riveted Lap-joints with Drilled Holes. Thickness Rivets. Distance between Rivets. Dist. between Lap of of plate. Diameter. Length. Central. Diagonal. Cent, lines. joint. t d I d 1/8 5/16 1/2 1.1/4 7/8 5/8 1.5/8 3/16 7/16 3/4 1.7/8 1.5/16 15/16 2.3/16 1/4 1/2 1.1/8 2.1/8 1.1/2 1.1/16 2.9/16 5/16 5/8 1.3/8 2.5/8 1.7/8 1.5/16 3.1/4 3/8 3/4 1.11/16 3.3/16 2.1/4 1.3/8 3.7/16 7/16 13/16 1.15/16 3.3/8 2.3/8 1.11/16 4 inches. 1/2 7/8 2.1/4 3.9/16 2.1/2 1.13/16 4.1/4 9/16 1 inch. 2.1/2 3.3/4 2.5/8 1.7/8 4.1/2 5/8 1.1/16 2.13/16 3.7/8 2.3/4 1.15/16 4.7/16 11/16 1.1/8 3.1/8 4.1/16 2.7/8 2.1/16 5.1/8 3/4 1.3/16 3.5/8 4.1/4 3 inches. 2.1/8 5.7/16 13/16 1.5/16 3.11/16 4.9/16 3.1/4 2.5/16 5.7/8 7/8 1.3/8 3.15/16 4.15/16 3.1/2 2.1/2 6.7/16 15/16 1.1/2 4.1/4 5.5/16 3.3/4 2.11/16 6.15/16 1 inch. 1.5/8 4.1/2 5.5/8 4 inches. 2.7/8 7.1/2 TABLE XXV. B. Proportion of Double-riveted Lap-joints with Punched Holes. Thickness Rivets. Distance between Rivets. Dist. between Lap of of plate. Diameter. Length. Central. Diagonal. Cent, lines. joint. t d I d 1/8 5/16 1/2 1.3/8 1 inch. 11/16 1.7/8 3/16 7/16 3/4 2 inches. 1.7/16 1 inch. 2.1/8 1/4 1/2 1.1/8 2.1/4 1.9/16 1.1/8 2.3/8 5/16 5/8 1.3/8 2.13/16 2 inches. 1.7/16 2.3/4 3/8 3/4 1.11/16 3.3/8 2.3/8 1.11/16 3.3/8 7/16 13/16 1.15/16 3.9/16 2.1/2 1.13/16 3.1/4 1/2 7/8 2.1/4 3.13/16 2.11/16 1.15/16 3.3/4 9/16 1 inch. 2.1/2 4 inches. 2.13/16 2 inches. 4.1/4 5/8 1.1/16 2.13/16 4.1/8 2.15/16 2.1/16 4.3/4 11/16 1.1/8 3.1/8 4.5/16 3.1/16 2.3/16 5.1/8 3/4 1.3/16 3.5/8 4.1/2 3.3/16 2.1/4 5.3/8 13/16 1.5/16 3.11/16 4.7/8 3.7/16 2.7/16 5.5/8 7/8 1.3/8 3.15/16 5.1/4 3.11/16 2.5/8 6.1/8 15/16 1.1/2 4.1/4 5.5/8 3.15/16 2.9/16 6.5/8 1 inch. 1.5/8 4.1/2 6 inches. 4.3/16 3 inches. 7 inches. STRENGTH OF LAP-JOINTS. 105 85. Safety Strength of Double-riveted Lap-joints with in Boiler-shells. Drilled Holes Steam-pressure 0.4 tS 33 Diameter of boiler P D D _OAtS ^ 34 P OK ' QAS ' oo s Dp oo 8 0.4 < ' ' ' Example 33. What pressure can be carried with safety in a boiler of D = 72 inches diameter, made of steel plates stamped S= 75000 pounds tensile strength and t = % inch thick, when the boiler is double-riveted with drilled holes? 0.4x0.5x75000 ( p = = 208 pounds to the square inch. TABLE XXVI. \ 86. Coefficients X for Safety Strength of Lap-joints. Construction of Shell. X Per cent, of strength. 05 100 04 80 035 70 Single-riveted drilled holes 0.3 60 25 50 Steam-pressure, P = XtS D Diameter of boiler, D = Thickness of plate, 37 38 39 Breaking-strain, 40 106 STEAM ENGINEERING. 87. The greatest strain in a cylindrical boiler-shell is in the direc- tion of the circumference, for which the double-riveted joints are first required in the direction of the length of the boiler. Longitudinal strain, =TcDtS=p-D t ... 41 Required thickness of metal, t = - ... 42 Transverse strain, = t S = p D . . 43 Required thickness of metal, t = *- ... 44 That is to say, the longitudinal strain is only one-half of the trans- verse strain, or that single-riveted joints with punched holes around the boiler are stronger than double-riveted joints with drilled holes longitudinally. Double-riveted joints are therefore required only longitudinally. STRENGTH OF FLUES AND TUBES FOR EXTERNAL PRESSURE TO COLLAPSE. 88. The most reliable experiments on this subject yet made are those of the late Mr. Fairbairn, who stated that the strength of the flue is inversely as its length, but he proposed different coefficients for different lengths. By analyzing closely the results of Mr. Fairbairn's experiments and by using constant coefficients, we find that the strength is inversely as the square root of the length of the flue or tube. The following formulas are deduced from the results of those ex- periments without regard to the formulas proposed by Mr. Fairbairn. D = diameter of the flue or tube in inches. L = length of the same in feet. t = thickness in fractions of an inch of the iron in the flue. p = steam pressure in pounds per square inch. S= tensile strength per square inch of iron in the flues. COLLAPSING FLUES. 107 89. Collapsing Strength of Flues subjected to External Pressure. 4 Si 2 Steam-pressure, p = . . . . . .41 DyL 4 a ft Diameter of flue, D = - 42 Pl /L Thickness of metal, t = \. . . .43 (4. K / 2 \ 2 -) 44 P D I Assuming one-fourth of the collapsing strength as safety for the flue, the formulas will simply dispense with the coefficient 4. 90. Safety Strength of Flues and Tubes from Collapsing by External Pressure. S t? Steam-pressure, p = - . . . . .45 Diameter of flue, D = l ..... 46 Pl /L Thickness of iron, < = ^^^-^. ... 47 Length of flue, L== (~^l ' ' ' ' 48 Example 4.5. A flue made of iron $=50000 pounds strength is D = 18 inches in diameter and L = 16 feet long, by i = f of an inch metal. Required what steam-pressure the flue can stand with safety ? 50000 x 3 2 p = = 97.66 pounds to the square inch. isxj/iexs 2 108 STEAM ENGINEERING. STAYING OF FLAT BOILER SURFACES. 91. Flat surfaces subject to steam-pressure in boilers must be stayed in order to keep their proper flat position as intended, and thus the whole steam-pressure on such surface must be borne by stays. A = area in square inches to be stayed, a = section area of each stay in square inches, n = number of stays required, p = steam- pressure in pounds per square inch. S = tensile strength of the iron in the stays. D = distance between the stays in inches. Ap .. IPressureon) Ap-an8 and a--^. 44 [ nS Number of stays, n = -. 45 aS each stay, _ 48 Distance, D = . 47 \ p Suppose the stays to be round of diameter d ; then a -= - 48 Allowing 28 per cent, for safety of the ultimate strength of stays, we have Safety Formulas for Stay-bolts. Diameter of stay, d = 4 Z)-* /-. 49 * S Distance apart, D - --J-. . 50 4\ a* d * Steam-pressure, p = -. . Iron required, S=* _, 51 52 Example 50. The iron for stay-bolts in a steam-boiler is d = 1 inch diameter and S = 62500 pounds strength, to be used in a pressure of p = 64 pounds to the square inch. Required the distance apart of the stays? 1 162500 The strength of all the connections of the stays must be equal to that of the solid stay. When the sections of the stays are square or rectangular, the area must be equal to that corresponding to the diameter d of the round iron. The following table is calculated for stays of one inch diameter ; but when the stays are more or less, the spaces between them should be that much more or less; for instance, if the stays are f inch diameter, the spaces in the table should be multiplied by f , and so on. STRENGTH OF RIVETED JOINTS. 109 TABLE XXVII. Distance in Inches between Boiler-stays One Inch in Diameter. Steam pressure. 45,000. Breaking str 50,000. iin in pound 55,000. s per square 60,000. nch of stay. 65,000. 70,000. P- Inches. Inches. Inches. Inches. Inches. Inches. 25 10.6 11.2 11.7 12.5 12.7 13.2 30 9.68 10.2 10.7 11.4 11.6 12. 35 8.96 9.45 9.9 10.5 10.8 11.1 40 8.38 8.84 9.26 9.84 10.1 10.4 45 7.9 8.34 8.74 9.28 9.51 9.84 50 7.5 . 7.9 8.28 8.8 9.02 9.34 ' 55 7.15 7.54 7.9 8.4 8.6 8.9 60 6.85 7.22 7.56 8.04 8.24 8.52 65 6.58 6.94 7.26 7.72 7.91 8.18 70 6.34 6.68 6.99 7.43 7.62 7.88 75 6.12 6.45 6.75 7.18 7.36 7.61 80 5.93 6.25 6.54 6.96 7.12 7.38 85 5.75 6.07 6.35 6.75 6.91 7.15 90 5.59 5.89 6.17 6.56 6.72 6.96 95 5.43 5.73 6. 6.39 6.54 6.77 100 5.3 5.6 5.86 6.23 6.37 6.6 110 5.05 5.32 5.58 5.93 6.08 6.29 120 4.84 5.1 5.35 5.68 5.82 6.02 130 4.56 4.9 5.13 5.46 5.58 5.79 140 4.48 4.73 4.95 5.26 5.38 5.58 150 4.33 4.56 4.78 5.08 5.2 5.39 160 4.19 4.42 4.62 4.92 5.03 5.21 170 4.06 4.29 4.49 4.78 4.88 5.06 180 3.95 4.17 4.36 4.64 4.75 4.91 190 3.85 4.06 4.25 4.52 4.63 4.79 200 3.74 3.95 4.14 4.4 4.51 4.66 210 3.66 3.86 4.04 4.3 4.4 4.56 220 3.57 3.77 3.94 4.2 4.3 4.44 230 3.5 3.68 3.86 4.1 4.2 4.35 240 3.42 3.61 3.78 4.02 4.11 4.26 250 3.35 3.53 3.7 3.93 4.03 4.17 260 3.29 3.47 3.63 3.86 3.95 4.1 270 3.23 3.4 3.56 3.79 3.88 4.02 280 3.16 3.34 3.5 3.71 3.8 3.94 290 3.11 3.28 3.43 3.65 3.74 3.87 300 3.06 3.23 3.38 3.6 3.68 3.81 110 STEAM ENGINEERING. STEAM-POWER WITHOUT FIRE. 92. When water is heated under high-pres- Fig - 6> sure in a closed vessel, the work so stored can be utilized for motive-power after the fire is with- drawn. Fig. 5 represents a section of a cylindrical ves- sel nearly full of hot water, above which surface steam is to be conducted to a motor through the valve and pipe a. Suppose no heat to radiate from the vessel and no discharge of steam, there will then only be a static pressure corresponding to the temperature of the water, and no work is performed. The combination of heat, water and steam enclosed in a vessel con- stantly tends to keep the presence and temperature in equilibrium that is, a given pressure corresponds with a certain temperature. Therefore, if steam is allowed to escape through the pipe a, the tem- perature and pressure in the steam-room will be lowered below that in the water, the result of which is that the excess of temperature in the water will generate more steam to establish equilibrium. W= pounds of water in the vessel. T = temperature Fahr. of the steam and water. P= steam-pressure in pounds per square inch above vacuum in the C= cubic feet of steam used per double stroke in a steam-engine. n = double strokes per minute of the steam piston. p = steam-pressure in pounds per square inch above that of the at- mosphere in the cylinder. H= units of heat per pound in the water before the engine is started. H' = units of heat per pound of the water in the vessel after the en- gine has made n revolutions. h = units of heat per cubic foot of the steam driving the engine. w = pounds of water passed through the engine in form of steam. ^ = weight per cubic foot of steam. 93. The primitive number of units of heat in the vessel is W H, and after the engine has made n revolutions, that heat will be reduced to H'(W-in)= WH-Cnh. . . . 1 The heat consumed by the engine will then be C n h. STEAM WITHOUT FIRE. Ill The weight w of steam passed through the engine is w = (7^ n, which, inserted for w in Formula 1, gives H'(W-C^ n)=WH-Cnh. . . 2 Revolutions, --E2.. . 3 Example 3. A vessel containing 200 cubic feet of water of temper- ature T=358, corresponding to a pressure of P= 150 pounds to the square inch, supplies steam which is wire-drawn to a pressure of p = 30 pounds to an engine using (7=1.5 cubic feet of steam for each revolu- tion. Required how many revolutions the engine will make before the steam-pressure in the vessel is reduced to p = 30 or P== 45 pounds ? The weight of water itf the boiler is W= 200 x 56.073 = 11214.6 pounds. H= 330.75. H'= 241.32. f = 0.11111. A = 129.51. See tables Nystrom's Pocket-Book for these data. 11214.6(330.75-241.32) Revolutions, n = = 6570.6. 1.5(129.51-0.1111x241.32) The water, evaporated to steam, will be w - 1.5 x 0.11111 x 6570.6 = 1095.1 pounds, or nearly 10 per cent, of the primitive water in the vessel. Assuming the engine to make 80 revolutions per minute, it will run -j- = 1.369 hours, with the steam generated in the vessel. 80 x 60 Practically, the radiation of heat from the vessel and steam-pipe will reduce this time perhaps 15 cents. Dr. Emile Lamm of New Orleans constructed a locomotive upon the above principle with heated water without fire, and which was used on General Beauregard's road in the year 1872. 112 STEAM ENGINEERING. PERMANENT GASES. 94. Permanent gases, in distinction from vapors, are those that cannot be condensed to liquid under ordinary temperatures and pressures. Oxygen, nitrogen and hydrogen are the principal permanent gases, and any mechanical mixture of either two or all the three will remain a permanent gas like atmospheric air, which is a mixture of oxygen and nitrogen ; but any chemical combination of either two or all the three becomes a vapor which is condensable to liquid like that of oxygen and hydrogen, forming steam, which condenses to water under temperature 212 Fahf. and freezes solid at 32. ELASTICITY OF PERMANENT GASES. 95. Permanent gases are perfectly elastic that is, the product of volume and pressure of a definite weight of gas will remain con- stant under constant temperature. For instance, if the volume is compressed to one-half, the pressure will be double; and if again ex- panded to its primitive volume, the original pressure will be restored if the temperature remains constant. When the temperature varies, the product of volume and pressure will also vary in a direct ratio to the difference of temperature. Call ^ and P volume and pressure of a definite weight of gas of temperature T. V and p = volume and pressure of the same gas, but of temperature t. P and p mean the actual pressures of the gas above vacuum. Then i*- 1+ -*--. ! That is to say, the ratio of the products of volume and pressure in- creases arithmetically as the difference of temperature. The experiments on elasticity of permanent gases made by Regnault and Rudberg show that c is constant for any difference of temper- ature within the limit of those experiments. Call Vp = 1 when t = 32, and find the value of ^ Pwhen T - 212 or a difference in temperature of 180. Under this condition the ex- periments of Regnault and Rudberg show that PERMANENT OASES. 113 , that is, 1+0.365. . . 2 Vp Consequently, 0.365 = -^-=-^ = , 3 c c of which c = = 493.15. 0.365 \^ _P T t Then = 1 + for all permanent gases. 4 vp 493.15 Drop the fraction 0.15, and say 493. Assume the pressure to be constant ' That is, = 1 5 * Then -? - 1 + ... . 6 Call V = 1 at the temperature t = 32. Then the volume if can be determined by Formula 7 for any other temperature T, and under constant pressure. For instance, suppose the temperature of the vol- ume #to be reduced to T = -461, then the volume = 461 ~ 8 2 \= This implies not only that the volume of a permanent gas can be reduced to nothing, and even negative, but that matter which exists in the universe may be rendered extinct or less than nothing, which is simply preposterous. Therefore c cannot be a constant quantity. It is generally supposed by scientific men of our days that the tem- perature 461 below Fahrenheit's zero is an absolute zero or lowest limit of temperature, which hypothesis is based upon the assumption that for all permanent gases p V 493 This formula implies that the intervals between the temperatures 8 114 STEAM ENGINEERING. progress in the same ratio as do the intervals between P -fi : p V, which the author inclines to doubt. 96. We have yet no experimental data and not sufficient knowledge on the subject by which to contradict the existence of this absolute zero at that place. It is evident, however, that matter cannot be rendered extinct, but that there must exist some low temperature at which the force of expansion of the heat is equal to or less than the force of attraction between the atoms composing the gas, which must then be a liquid, solid or powder of a definite volume ; and it is reasonable to suppose that the temperature of that volume can be further reduced. Considering that water is practically incompressible, we may assume that the atoms of oxygen and hydrogen are there in close contact, and represent the volume of these gases in a liquid or solid state. One cubic foot of water at 32 weighs 62.4 pounds, of which there are 54.6 pounds of liquid oxygen in ^ cubic foot. 7.8 pounds of liquid hydrogen in f " " 1 pound liquid oxygen =0.006105 cubic foot. 1 pound liquid hydrogen = 0.08547 " " 1 pound oxygen gas at 32 = 11.28 " " 1 pound hydrogen gas at 32 = 180 " " 11.28 1 volume liquid oxygen = : = 1847.7 volumes of oxygen 0.006105 gas at 32. 1 volume liquid hydrogen = = 2106 volumes of hydro- gen gas at 32. 1 volume oxygen gas = 0.0005412 volumes of liquid oxygen. 1 volume of hydrogen gas = 0.0004748 volumes of liquid hy- drogen. Allowing for contraction of the liquid volume by cooling from 32 to -461 or !F-t = 493, at the same rate as ice contracts, about 0.8547 of that at 32. Volume of liquid oxygen at -461 is then 0.000541 2 x 0.8547 #= 0.00046256 V. Volume of liquid hydrogen at -461 is 0.0004748 x 0.8547 # = 0.00040581 V. PERMANENT OASES. 115 This should be the ultimate volumes to which gases of oxygen and hydrogen can be reduced by cooling from +32 to -461. The oxygen and hydrogen of one cubic foot of water, dissolved into their respective gases, would occupy 1919.9 cubic feet at 32 Fahr., or 2610.66 cubic feet at 212, and under atmospheric pressure. 97. It is supposed in the preceding calculation that if one cubic foot of water is resolved into its elements and still remain in liquid form, the hydrogen would occupy % and the oxygen ^ of the cubic foot ; but such would, however, not be the case. The hydrogen would occupy the whole cubic foot, whether the oxygen is in it or not. The atoms of hydrogen may be represented by large potatoes filling a bushel, but the real capacity of the potatoes is only ^ of that bushel ; the other ^ can be filled up with buckshot, representing the atoms of oxygen. The potatoes would occupy the same space whether the shot are there or not. Such is the case with hydrogen and oxygen in water ; but when these elements are resolved into their respective gases, they will occupy 50 per cent, more volume than when chem- ically combined in the form of vapor. The result of the preceding calculation is, however, correct. It is reasonable to suppose that the so-called permanent gases be- come vapors and finally condense to liquids and freeze to solids at a low temperature, which we have not yet been able to produce, and that there is therefore a limit beyond which the volume of those gases cannot be reduced. The pressure, on the other hand, is reduced to nothing at a low temperature when the vapors condense to liquid and freeze to ice ; but that is no proof of an absolute zero having been reached beyond which there exists no temperature. Steam highly superheated behaves very much like permanent gases; and if experimented upon without knowing the lower temperatures at which it condenses to water and freezes to ice, the inference might be that there exists an absolute zero at which the pressure and volume of steam become nothing, and beyond which there exists no temper- ature. Carbonic acid gas under ordinary pressures and temperatures be- haves like permanent gases ; but at low temperatures and high pres- sures it becomes a vapor which can be condensed to liquid and even frozen solid. Water and ice evaporate under low temperatures, as shown by the experiments of Regnault and Dalton. A wet cloth exposed to very cold weather freezes stiff, but finally the ice in it evaporates and leaves the cloth dry. The formulas which the writer has deduced from the experiments 116 STEAM ENGINEERING. of Regnault and Dalton, indicate that the pressure of aqueous vapor is reduced to nothing at the temperature - 101 below Fahr. zero. Such is most likely the case with all permanent gases namely, that at some low temperature different for each kind of gas the pressure is reduced to nothing, whilst the volume remains definite, whether in the form of gas, vapor, liquid or solid. Therefore, when the matter is in the form of a gas or vapor at the low temperature where the pressure is reduced to nothing, the force of attraction between its atoms is equal to the force of expansion by heat, and the gas occupies a definite volume like a cloud in the air. Thus, the top of our atmosphere would maintain a smooth surface like the ocean, omitting the disturb- ance caused by change of temperature and currents of wind below. 98. Within the limit of our practice we can safely use the for- mula Pf T-t pV 493 ' Under constant pressure the increase of volume of any permanent gas, per degree of increased temperature that is, when T-t = l will be ,|y- 0.0020284. For simplicity in elucidating the subject and for the formation of tables, it is best to assume a standard temperature, t = 32 Fahr., at which all other quantities are compared. 493 pV The value of x is calculated for every degree of temperature from to 500, for every 10 from 500 to 1200, and for every 100 from 1200 to 2300, in Table XXX. \ 99. Variable Volume under Constant Pressure. Temperature, z = 1 Heated volume, ^ = Vx 2 Cold volume, %T= 3 Example 1. A volume %f=36 cubic feet of air is to be heated from 32 until the volume is expanded to "^ = 48 cubic feet. Required the temperature of the expanded volume ? PERMANENT OASES. 117 48 Find 1.5 in column x in the table, which corresponds to the re- quired temperature, T = 279 Fahr. If the volume V had been heated from a higher temperature, say t = 60, then 60-32 = 28 and 279 + 28 = 307, the required temper- ature. Example 2. A volume of air %P=24 cubic feet is heated from t = 48 to T= 450. Required the volume ^ ? In this case 48-32 = 16 and 450 + 16=466. Find x for 466, which in the table corresponds to x = 1.88. Volume ^ = 24 x 1.88 - 45.12 cubic feet. 'Example 3. A volume of air V = 148 cubic feet, and of tempera- ture T=250, is to be cooled down to = 32. What will be the volume of the cooled air? 140 Cold volume, #= - = 102.63 cubic feet. \ 100. Variable Pressure under Constant Volume. p Temperature, x = 4 P High pressure, P=px 5 p Low pressure, p = 6 Example 4- A volume of permanent gas enclosed in a vessel exerts a pressure of jt> = 15 pounds to the square inch, and is = 32 in temperature. To what temperature must that gas be elevated in order to increase the pressure to P=25 pounds to the square inch? or x = = 1.6666. 15 The required temperature is T=361. Had the primitive temperature in the vessel been more or less than 32, the required temperature would have been that much more or less. Example 5. A gas of temperature = 21, enclosed in a vessel 118 STEAM ENGINEERING. under a pressure of p = 12 pounds to the square inch, is to be heated to a temperature T= 180. Required the pressure of the heated gas? In this case T- 180 + 11 =191. Pressure P= 12 x 1.3224 = 15.8888 pounds per square inch. Example 6. The temperature of a permanent gas enclosed in a vessel is !F=120, and pressure P=20 pounds to the square inch, is to be reduced to t = 5. Required the pressure p of the cold gas ? In this case T= 120 + 5 + 32 = 157, and x - 1.2535. 20 Pressure, p = = 15.95 pounds per square inch. 1.2535 2 101. VOLUME AND PRESSURE BOTH VARIABLE. Temperature, x = 7 T) *fy High pressure, P = _^ 8 Low pressure, p = 9 Warm volume, ^ = *- . . . . .10 Cold volume, W= . . . . 11 px Example 7. A volume of air %f=16 cubic feet, pressure p = 15 pounds to the square inch and temperature 32 3 , is to be heated until the volume becomes ^ = 24 cubic feet and pressure P= 20 pounds to the square inch. Required the temperature of the heated air. 16x15 The required temperature is T= 530. Example 8. A volume of air ^ = 42 cubic feet and temperature T=480 has been expanded from 3^=28 cubic feet of temperature t = 62 and pressure p = 15 pounds. Required the pressure of the expanded volume? 62 - 32 = 30, and 480 - 30 = 450. x = 1 .8477. , 15x28x1.8477 Pressure, P= = 18.4Y 7 pounds. IE IR, JR, PAGE LINE FROM FOR READ TOP BOTTOM 3 6 6. 4 6.88 40 i5 3.62 2.62 40 16 3^7 2.67 55 5 acid. oxide. 69 4 ^f~ VW i P 131 H *\r v~ 137 1 68 . 2 8 1421700 491.6 14217000 391.6 PERMANENT OASES. 119 Example 9. The temperature of a permanent gas is T=248, pres- sure P=48 pounds and volume ^r = 96 cubic feet. The volume is to be reduced to V=72 cubic feet of temperature t = 72. Required the pressure p ? 72-32 = 40. 248 -40 = 208. x = 1.3569. Pressure, 48 72x1.3569 - = 47 pounds. SPECIFIC HEAT OF PERMANENT GASES. 102. The specific heat of a gas is that fraction of a unit of heat required to elevate the temperature of one pound of that gas one de- gree Fahrenheit. It is constant under constant pressure, but under variable pressure the specific heat is inversely as the square root of the pressure. TABLE XXVIII. Specific Heat under Constant Pressure and Temperature 32. Kinds of gases. Pounds per cubic foot. Cubic foot per pound. Specific Water = 1. gravity. Air = 1. Specific heat. Atmospheric air f 0.08042 0.08888 0.07837 0.00559 0.07837 0.12333 0.05021 G 12.433 11.251 12.760 178.84 12.760 8.108 19.915 0.00130 0.00143 0.00126 0.00009 0.00126 0.00197 0.00634 1.000 1.104 0.972 0.069 0.972 1.527 0.488 8 0.25 0.23 0.275 3.3 0.288 0.221 0.475 Oxygen gas Nitrogen gas Hydrogen gas Carbonic oxide. Steam S = specific heat under constant pressure, as in the table above. s = mean specific heat under any pressure and volume from 32 to T. ^> = 14.7 pounds to the square inch pressure of the gas at = 32 Fahr. P = pressure of the same gas at the temperature T. %T= volume in cubic feet of the gas at 32. ifr = volume of the same gas, but of pressure P and temperature T. W= weight in pounds of the gas experimented upon. *$ = weight in a fraction of a pound per cubic foot of the gas. h = units of heat in W pounds of gas elevated from 32 to T, or from a pressure of 14.7 to P pound. 120 STEAM ENGINEERING. \ 103. Formulas for Heat in Gases in regard to Pressure. Mean specific heat, s = S \l 1 Units of heat, h = S Jf\/^- r (2 3 -32). . . . 2 Temperature, T= Pressure of gas, P=p | Example 1. What is the mean specific heat of air, heated under constant volume from a pressure ^ = 14.7 to P=26 pounds to the square inch ? Mean specific heat, s = 0.25^^ = 0.188. Example 2. How many units of heat are there in W= 8 pounds of carbonic acid, heated from 32 to T=450, and from a pressure 14.7 to P=20 pounds per square inch? Units of heat, h = 0.221 x 8-^^(450 - 32) = 629.25. Example 3. What will be the temperature of W= 12 pounds of air supplied with h = 864 units of heat, which increases the pressure from p = 14.7 to P= 24 pounds to the square inch ? Temperature, r-^ 32 = 323.33. Example 4- What pressure will be attained by heating W= 24 pounds of carbonic oxide from 32 to T=280, with A = 2400 units of heat supplied to the gas in a closed vessel ? Pressureof gas, P-14.7 = 8 . 8513 . In this case the pressure became less than the primitive pressure, the reason of which is that the volume was expanded in order to ad- mit 2400 units of heat without increasing the temperatures over 280. HEAT IN PERMANENT OASES. 121 | 104. Formulas for Heat in Gases in regard to Volume. Mean specific heat, s = &\-jj- 5 Units of heat, h = S fJ2-?C T- 32). ... 6 Temperature, T= p\/~] + 32. . . .7 Volume, ^^aTl" r * ' * ^ Example 5. Required the mean specific heat of hydrogen gas, heated from 32 to-T=450, and the volume increased 50 per cent.? a; = 1.8477. Specific heat, s = 3.3 -J - = 2.9733. .L x 1,04 / / Example 6. How many units of heat are required to heat ^=36 cubic feet of nitrogen gas from 32 to T=400, and expand the volume to ^ = 40 cubic feet ? Units of heat, h = 0.275 x 0.07837 J^ 6 * , 4 (400 - 32) = 227.75. 1 . i 4uo By the aid of the following table the preceding formulas and calcu- lations can be much simplified by calling The value of y is calculated for different temperatures in the table, by the aid of which the units of heat in any gas can be found by the following formulas. y = . 10 . 11 13 122 STEAM ENGINEERING. Having giveii the weight W, volumes ^ and #, and the units of heat h, in any permanent gas, calculate the value ofy by Formula 12- or 13, which gives the corresponding temperature of the gas in the table. Example 11. How many units of heat are required to elevate the temperature of #=160 cubic feet of air from 32 to T=480, and expand the volume to ^ = 240 cubic feet ? In the table find y = 324.29 for 480. Units of heat, h = 324.29 x 0.25 x 0.08042/160x240 = 1277.6. Example 13. What will be the temperature of ^ = 36 cubic feet of carbonic acid heated from 32 and volume #=24 cubic feet, when h = 140 units of heat has been expended on it? 0.221x0.1233/36x24 This corresponds to a temperature T= 185 in the table. DRAFT IN CHIMNEYS. 105. The draft in a definite chimney depends upon the temper- ature of the ascending gases. The higher the temperature is, the lighter will the gases be, and consequently create a stronger draft under the fire-grate, as before explained, 45. The velocity of the air through the fire-grate is Call Z= ( 1= ^) 2 Then the velocity F' = 8/2T2T . . . . . 3 The value of z is calculated for different temperatures of the gases in the chimney, and is contained in column z in Table XXX. Example 3. The height of a chimney is H = 144 feet, and temper- ature of the gases T=520. Required the velocity of the draft through the fire-grate ? See Table XXX. for temperature 520, which corresponds to z = 0.4977. V = 8/144x4977 = 67.8 feet per second. HORSE-POWER OF CHIMNEYS. 123 TABLE XXIX. Horse-power of Chimneys. Formula 1, \ 26, page 42. For safety this table gives the horse-power about 25 per cent, less than may be attained in practice. || Area of chimney in square feet at the top. i 0.5 1 2 4 10 15 20 30 40 Feet. EP IP IP IP H> IP IP IP IP I?" 20 3.35 6.7 13.4 26.8 40.2 67 100.5 134 201 268 25 3.7 7.4 14.8 29.6 44.4 74 111.0 148 222 296 30 4.0 8.0 16.0 32.0 48.0 80 120.0 160 240 320 35 4.25 8.5 17.0 34.0 51.0 85 127.5 170 255 340 40 4.5 9.0 18.0 36.0 54.0 90 135.0 180 270 360 45 4.75 9.5 19.0 38.0 57.0 95 142.5 190 285 380 50 5.0 10.0 20.0 40.0 60.0 100 150.0 200 300 400 55 5.2 10.4 20.8 41.6 62.4 104 156.0 208 312 416 60 5.4 10.8 21.6 43.2 64.8 108 162.0 216 324 432 '65 5.6 11.2 22.4 44.8 67.2 112 168.0 224 336 448 70 5.8 11.6 23.2 '46.4 69.6 116 174.0 232 348 464 75 6.0 12.0 24.0 48.0 72.0 120 180.0 240 360 480 80 6.15 12.3 24.6 49.2 73.8 123 184.5 246 369 492 85 6.35 12.7 25.4 50.8 76.2 127 190.5 254 381 508 90 6.5 13.0 26.0 52.0 78.0 130 195.0 260 390 520 95 6.65 13.3 26.6 53.2 79.8 133 199.5 266 399 532 100 6.8 13.6 27.2 54.4 82.8 136 204.0 272 414 544 110 7.1 14.2 28.4 56.8 85.2 142 213.0 284 426 568 120 7.4 14.8 29.6 59.2 88.8 148 222.0 296 444 592 130 7.65 15.3 30.6 61.2 91.8 153 229.5 306 459 612 140 7.9 15.8 31.6 63.2 94.8 158 237.0 316 474 632 150 8.15 16.3 32.6 65.2 97.8 163 244.5 326 489 652 160 8.4 16.8 33.6 67.2 100.8 168 252.0 336 504 672 170 8.65 17.3 34.6 69.2 103.8 173 259.5 346 519 692 180 8.9 17.8 35.6 71.2 106.8 178 267.0 356 534 712 190 9.2 18.2 36.4 72.8 109.2 182 273.0 364 546 728 200 9.3 18.6 37.2 74.4 111.6 186 279.0 372 558 744 210 9.5 19.0 38.0 76.0 114.0 190 2850 380 570 760 220 9.7 19.4 38.8 77.6 116.4 194 291.0 388 582 776 230 9.9 19.8 39.6 79.2 118.8 198 297.0 396 594 792 240 10.1 20.2 40.4 80.8 121.2 202 303.0 404 606 808 250 10.3 20.6 41.2 82.4 123.6 206 309.0 412 618 824 260 10.5 21.0 42.0 84.0 126.0 210 315.0 420 630 840 270 10.65 21.3 42.6 85.2 127.8 213 319.5 426 639 852 280 10.8 21.6 43.2 86.4 129.6 216 324.0 432 648 864 290 11.0 22.0 44.0 88.0 132.0 220 330.0 440 660 880 300 11.15 223 44.6 89.2 133.8 223 334.5 446 669 892 310 11.35 22.7 45.4 90.8 136.2 227 340.5 454 681 908 320 11.5 23.0 46.0 92.0 138.0 230 345.0 460 690 920 330 11.65 23.3 46.6 93.2 139.8 233 349.5 466 699 932 340 11.8 23.6 47.2 94.4 1-41.6 236 354.0 472 708 944 350 12.0 24.0 48.0 96.0 144.0 240 360.0 480 720 960 360 12.15 24.3 48.6 97.2 145.8 243 364.5 486 729 972 370 12.3 24.6 49.2 98.4 147.6 246 369.0 492 738 984 380 12.45 24.9 49.8 99.6 149.4 249 373.5 498 747 996 390 12.6 25.2 50.4 100.8 151.2 252 378.0 504 756 1008 400 12.75 25.5 51.0 102.0 153.0 255 382.5 510 765 1020 124 PERMANENT GASES. TABLE XXX. Physical Properties of Permanent Gases. Temp. hte rv pv T-t V* 1-L X T ffi: PV pv T-t V* 4 T F3?: PV pv T-t Vx l-L x T X y Z T X y z T\ x y Z -180 0.5700 - 280.9 - 0.261 82 1.0000 0.0000 O.OOdO 82 1.1014 47.1)4.", 0.0920 -170 0.5903 - 262.9 -0.306 33 1.0020 0.9990 0.0019 83 l.KKM 48.552 0.0935 -160 0.6106 -245.8 - 0.362 34 1.0040 1.9960 ).oo:;.i 84 1.105449.459 0.0954 -150 0.6308 -229.3 -0.415 35 1.0061 2.9909 0.0059 sr> 1.1075 50.362 0.0969 -140 0.6511 -213.2 -0.464 36 1.0081 3.9839 0.0079 86 .1095 51.266 0.0986 -130 0.6714 -197.7 -0.511 37 1.0101 4.9750 0.0099 87 1.111552.168 0.0999 -120 0.6917 - 187.8 - 0.554 38 1.0121 5.9640 0.0118 88 1.1135 r,;;.oi;<) 0.1019 -110 0.7120 -168.3 - 0.595 39 1.0142 6.9508 0.0187 89 1.1156 53.91)6 0.1035 -100 0.7322 -154.3 - 0.634 40 1.0162 7.9360 0.0157 90 1.117654.851 0.1051 -90 0.7524 - 140.7 -0.671 41 1.0182 8.9192 0.0176 91 1.1196 55.760 0.1069 -80 0.7727 - 127.4 - 0.706 42 1.0203 9.9000 0.0195 92 1.1217 156.652 0.1083 -70 0.7930 -114.5 - 0.739 43 1.0223 10.880 0.0215 n:; 1.1237 57.555 0.1099 -60 0.8133 -102.0 -0.770 44 1.0243 11.857 0.0234 94 1.1257 58.436 0.1118 -50 0.8336 - 89.82 -0.800 45 1.0264 12.834 0.0253 95 1.1277 59.326 0.1130 -40 0.8540 -77.91 - 0.829 46 1.0284 13.805 0.0272 96 1.1297 60.214 0.1149 -30 0.8742 -66.31 -0.856 47 1.0304 14.777 0.0291 1)7 1.1318 61.098 0.1165 -20 0.8945 -54.98 -0.882 48 1.0325 15.746 0.0315 98 1.1338 61.983 0.1179 -10 0.9148 -.43.91 -0.907 49 1.0345 16.714 0.0329 99 1.1358 62.867 0.1191 0.9352 -33.01 - 0.930 50 1.0365 17.680 0.0349 100 1.1378 63.749 0.1210 1 0.9371 - 32.06 -0.933 51 1.0385 18.666 0.0365 101 1.1399 64.627 0.1227 2 0.9391 - 30.96 - 0.935 52 1.0406 19.606 0.0389 102 1.1419 65.506 0.1243 3 0.9411 -29.89 -0.937 53 1.0426 20.567 0.0402 103 1.1439 66.384 0.1257 4 0.9432 -28.83 - 0.939 54 1.0446 21.575 0.0429 10411.1459 67.260 0.1273 5 0.9452 -27.77 - 0.942 55 1.0466 22.482 0.0444 105 1.1480 68.132 0.1288 6 0.9472 -26.72 - 0.944 56 1.0487 23.463 0.0464 106 1.1500 69.005 0.1304 7 0.9492 - 25.67 - 0.946 57 1.0507 24.390 0.0485 107 1.1520 69.877 0.1319 8 0.9513 - 24.62 - 0.949 58 1.0527 25.341 0.0503 108 1.1541 70.745 0.1334 9 0.9533 - 23.56 -0.951 59 1.0547 20.21)0 0.0521 109 1.1561 71.613 0.1349 10 0.9554 - 22.51 - 0.953 60 1.0567 27.260 0.0539 110 1.1581 72.481 0.1364 11 0.9577 -21.46 -0.956 61 1.0588 28.184 0.0557 111 1.1602 73.344 0.1379 12 0.9594 -20.42 - 0.958 62 1.0608 29.128 0.0574 112 1.1622 74.208 0.1393 13 0.9614 - 19.38 - 0.960 63 1.0628 30.070 0.0592 113 1.1642 75.072 0.1408 14 0.9635 -18.34 - 0.962 64 .0649 31.010 0.0610 114 1.1663 75.929 0.1423 15 o.'.t* 555 - 17.30 - 0.964 65 .0669 31.949 0.0627 115 1.1683 76.790 0.1438 16 0.9675 -16.26 -0.966 66 1.0689 32.896 0.0645 116 1.1703^77.648 0.1452 17 0.9676 -15.23 -0.966 67 1.0709 33.822 0.0662 117 1.172478.502 0.1469 18 0.9716 -14.22 -0.971 68 .0720 34.770 0.0671 118 1.174479.358 0.1486 19 0.9734 -13.18 - 0.972 69 1.0740 35.703! 0.0688 119 1.1764 80.212 0.1499 20 0.9756 -12.15 -0.975 70 1.0760 36.633 10.0706 120 1.178481.066 0.1515 21 0.9777 -11.13 -0.977 71 1.0780 37.563 0.0723 121 1.180581.914 0.1528 22 0.9797 -10.11 -0.979 72 1.0811 38.470 0.0749 122 1.1825182.764 0.1541 23 0.9817 - 9.089 -0.981 73 1.0831 39.396 0.0766 123 1.184583.621 0.1559 24 0.9837 - 8.069 -0.983 74 1.0851 40.320 0.0783 124 1.1866 84.457 0.1571 25 0.9856 -7.051 -0.985 75 1.0871 41.2M) 0.0800 125 1.1886 85.303 0.1586 26 0.9878 -6.031 1-0.988 76 1.0892 42.160 0.0817 126 1.1906 86.148 0.1601 27 0.9898 -5.029; -0.990 77 1.09i2 43.079 0.0833 127 1.192786.9880.1615 28 0.9917 -4.017 -0.991 78 1.0932 43.995 '0.0870 128 1.1947 87.830 0.1629 29 <).5 i252| 1.4462 182.94 0.3086 153 1.2454 108.430.1967 203 1.3468 147.44 0.2575 1 253 1.4582 183.64 0.3096 154 1.2475 109.230.1984 204 1.3488 148.18 0.2586 254 1.4402 184.34 0.3104 155 1.241)5 110.04 0.1996 205 1.3508 ! 148.92 0.2597 255 1.4522 185.04 0.3112 156 1.2515 110.84 0.2003 206 1.3529 149.660.2608 256 1.4543 185.74 0.3122 157 1.2535 111.650.2022 :207 1.3549 150.39 0.2619 257 1.4563 186.44 0.3131 158 1 .2556 112.450.2035 208 1.3569 151.12 0.2630 '258 1.4583 187.14 0.3141 159 1.2576 113.25 0.2047 '209 1.3589 151.85 0.2641 259 1.4604 187.84 ! 0.31 51 160 1.2596 114.05 0.2060 i210|l.3610| 152.58 0.2652 260 1.4624 ! 188.54 0.3159 161 1.2616:114.850.2072 211 1.3630 153.32 0.2663 261 1.41)44 189.24 0.3169 162 1.2637 115.640.2086 ! 212 i 1.3650; 154.06 0.2674 262 1.4664 189.93 0.3178 163 1.2657 116.44,0.2098 ;213 1.3670 154.80 0.2685 263 1.4685 il90.62iO.3187 164 1.2677 117.24 0.2111 214 1.3691 155.54 0.2695 264 1.4705 1191.32 0.3199 165 1.2697:118.040.2123 215 1.37111156.28 0.2705 265 1.4725 192.01 0.3209 166 1.27171118.83 0.2136 216 1.3731 157.02 0.2716 266 1.4745 192.70'0.3217 167 1.2738! 119.62 0.21 41) 217 1.3751 157.76 0.2727 267 1.4766 193.39; 0.3227 168 1. 2758 j 120.41 0.2161 : 218 1.3772 158.50 0.2737 268 1.4786 194.08 0.3236 169 1.2778 J121.20 0.2173 219 1.37921159.24 0.2748 269 1.4806) 194.77 i 0.3246 170 1.2798| 121.98 0.2186 220 ' 1. 38 12 ' 159.97 0.2758 1270 1.48261195.46 0.3255 171 1.2818 122.77 0.2198 22 1.3832 160.71 0.2768 271 1.4847 196.15 0.3265 172 1.2839 1 123.56 0.2210 222 1.3853 161.45 0.2781 272 1.4867 1 196.84 ; 0.3274 173 1.2859:124.350.2222 2l-'" 1.3873 162.19 i 0.2792 273 1.4887 197.530.3284 174J1.287J i 125. 13 0.2236 224 : 1. 3893 1 162.93 0.2803 274 1.4907 198.22 0.3293 175i 1.28991125.91 0.2248 22' : 1.3913, 163.67 0.2814 275 1. 4D28 198.90 0.3302 176 1.2920! 126.69 0.2259 : 226' 1.3934 164.41 0.2824 278 1.4948 199.58 0.3310 177 1.294C ) 127.4- 0.2271 227 1 .'>1)5- 165.15 0.2*34 277 1 1.4968 200.2' 0.3319 178 1.2960 128.25 0.2283 ,228 1.3974165.880.2844 278 1.4988 200.94:0.3327 179 1.2980 129.02 0.2295 221) 1.3995 166.61 0.2854 279 1.5009201.620.3337 180 ; 1.3001; 129.80 0.2307 230i 1.4015! 167.25 0.2864 2SO 1.5029 202.30 0.3346 181 1.3021 130.57 0.2329 1231 1.4035 '167. 98! 0.2874 281 1.5049 202.98 0.3355 126 PERMANENT GASES. TABLE XXX. Physical Properties of Permanent Gases. Temp. PV T-t l-l PV T-t l-L Temp. PV L=* l_ Kahr! pv V* pv V* X Fab?. pv V* X T 282 1.5070 y 203.66 0.3363 1 X 1.6084 y _':;<;.:,.-, z 0.3781 T 382 X 1.7097 267*71 0.4150 288 1.5090 204.34 0.3372 1.6104237.19 0.3788 383 1.7118 2S.:W 0.4157 2S4 1.5110 205.02 0.3381 1 1.61 24 237.83 0.3796 :w4 1.7138 268.94 0.4164 1 2S5 2S(i 1.5131 205.70J0.3390 1.5151 206.37 0.3399 1.6144 1.6165 238.43 239.11 0.3804 0.3811 385 386 1.7158 269.551 0.417 li 1.7179 270.16 0.4179 287 1.5171 207.04 0.3407 1.6185 239.75 0.3819 387 1.71991270.77 0.4185 288 1.5192 207.71 0.3416 1.6205 240.39 0.3827 388 1.7219:271.38 0.4192 289 1.5212 208.38 0.3425 1 1.6226 241.02 0.3836 389 1. 72 10 27 1.99 0.4199 290 1.5232 209.05 0.3433 01.6246 241.65 0.3845 390 1.7260 '272.50 0.4206 291 1.5252 209.720.3442 1.6266 242.28 0.3852 391 1.7280 273.100.4212 292 1.5273 210.39 0.3458 2 1.6286 242.91 0.3859 392 1.7301 273.70 0.4219 293 1.5293 211.06 0.3459 3 1.6307 243.54 0.3868 893 1.7321 274.30 0.4226 294 1.5313 211.73 0.3468 4 1.6327 244.17 0.3875 394 1.7341 274.90 0.4232 295 296 297 1.5334 212.40 0.3476 1.5354 213.07 10.3485 1.53741213.74 0.3493 ' o 1.6347 6 1.6368 7 1.6388 244.80 245.43 246.06 0.3882 0.3889 0.3897 395 396 397 1.7361 275.49 1.7382 276.09 1.74021276.69 0.4239 0.4246 0.4252 298 1.5395 214.40 0.3501 8 1.6408 246.69 0.3906 398 1.7422i277.29 0.4259 299 1.5415 215.06 0.3510 i 91.6429 247.31 0.3913 399 1.7443 277.89 0.42155 300 1.5435 215.72'0.3518 Oi 1.6449 ! 247.93 0.3920 400 1.7463 278.48 10.4272 301 1.5455 216.38 0.3527 1 1.6469 248.56 0.3928 401 .7483 279.0810.4279 302 1.5476,217.040.3539 2 1.6490 249.19 0.3935 402 1.7504 27!Ui,S 0.428.-, 303 1.5496217.700.3548! 31.6610249.82 0.3942 403 1.7524280.27!0.4292 304 1.5516>218.36 0.3556 1 4 1.6530 250.45 0.3950 404 1.7544 280.8(5 0.4-29S' 305 306 1.5537 1.5557 219.02 ! 0.3584 219.68 0.3573 -> 1.6551 251.08 6 1.65711251.70 0.3957 0.3964 405 406 1.7564281.450.4305 1.7585 282.04 0.4314 307 1.5577 220.34! 0.3581 7 1.6591 2.32.32 0.3971 407 1.7605 2S2.M 0.4320 308 1.5597 221.000.3589 8 1.6611 252.94 0.3979 408 1.7625 283.22 0.4325 309 1.5618 221.65 0.3597 911.6632 253.56 0.3986 409 1.7646 283.81 o.4:;:;:> 310 1.5638 222.30 0.3605 01.6652 254.18 0.3993 410 1.7666 2S4.40 0.4340 311 r.5658 222.96 0.361 4 ' 1 1.6672 254.80 0.4001 411 1.7686 284.9~9 ! 0.4346 312 1.5678223.61 0.3622 2 1.6692 255.42 0.4008 412 1.7706 285.58, 0.4353 313 1.5699224.27 0.3630, 31.6713 256.04 0.4015 413 1.7727 286.17 0.4359 314 1.5719224.930.3638 4 l.()7. 4 ;:i 256.66 0.4022 414 1.7747 286.76 0.4365 315 1.5739 225.58 0.3646 5! 1.6753 257.28 0.4029 415 1.7767 287.35 0.4372 316 317 318 1.5759 1.5780 1.5800 226.23 0.3654 ; 226.880.3662; 227.530.36701 6|1.6773 7 j 1.6794 8|1.6814 257.90 258.51 259.12 0.4036 0.4043 0.4051 416 417 418 1.7787 287.94 0.4378 1.7808 288.43 0.4384 1.7828 289.01 0.4391 319 1.5820 228.28 0.3678 911.6834 259.740.4058 419 1.7848 289.59 10.4397 320 1.5840 228.83 0.3686 Oi 1.6854 260.36 '0.4065 420 1.7868 >!)() .27 0.4403 321 1.58611229.480.3694 1 1.6875 260.97 0.4072 421 1.7889 290.85 ! 0.4410 322 1.58811230.13 0.3702 21.6895261.58 0.4079 422 1.7909 291.430.4416 323 1.5901 j230.78 ( 0.3710 31.6915262.190.4085 423 1.7929292.01:0.4422 324 1.5922 '231. 42 0.37 18 i 41.6935262.800.4096 424 1.7950 292.59! 0.4428 325 326 1.5942232.060.3726! 1.5962 232.7 1 1 0.3734! 51.6956263.41 0.4103 61.6976264.020.4110 425 426 1.7970 293.17 0.4434 1.7990 293.75!0.4441 327 1.5982 233.350.3741 7 1.6996 264.63 0.4116 427 1.8010 294.33 '0.4447 328 1.6003 2:::;.;).J 0.4605 530 2.0102; 351. 26 0.5024. 1030 3.0239 573.94 0.6692 454! 1.8558 309.79 0.4611 540 2.0302 356.53 0.5073 1040 3.0441 577.73 0.6714 455 1.8579 31o..'5o 0.4617 550 2.0505 361.75 0.5120 1050 3.0644 581.530.6736 45611.8599 310.91 0.4623 560 2.0708 366.93 0.5171 1060 3.0847 585.32 0.6758 457 1.8619 311.47 458 1.8639 ! 312.03 0.4629 0.4635 570 580 2.0909 2.1113 372.06 377.16 0.5217 0.5262 1070 1080 3.1050 3.1253 589.08 0.6779 592.82 0.6799 459 1.8660312.59 0.4641 590 2.1316 382.28 0.5308 1090 3.1455 596.54 0.6820 460 1.8680 313.15 0.4647 600 2.1519 387.20 0.5353 1100 3.1658 600.24 0.6841 461 1.8700 313.71 0.4652 610 2.1721 392.18 0.5395 1110 3.1861 603.92! 0.6861 462 1 1.8720 314.27 0.4657 620 2.1924 397.13 0.5437, 1120 3.2064 607.62 0.6880 4(53 1.S741 314.83 0.4663 630 2.2127 402.03 0.5481 1130 3.2267 611.27 0.6901 464 1.8761 315.39 0.4669 640 2.-r>2!) 406.89 0.5521 1140 3.2469 614.92 0.6920 465 1.8781 315.95 0.4675 650J2.2532 411.71 0.5561 1150 3.2672 618.52 0.6938 466 1.8801 316.51 0.4681 660 2.27 34 ! 416.50 0.5601 1160 3.2875 622.13 0.6957 467 1.8822 317.07 O.l'isi; 670 2.29381421.25 0.5640 1170 3.3078 625.73 0.6976 468 469 1.8842 317.63 0.4692 1.8862 318.19 0.4697 6802.3141425.98 690 2.3343|430.67 0.5678: 0.5715' 1180 1190 3.3281 3.3484 629.32 0.6994 632.90 0.7013 470; 1.8882 31 8.75 0.4703 700 2.3545 ; 435.34 0.5752 1200 3.3687 636.38 0.7031 471 1.8903319.31 0.4709 710 2.3749 439.88 0.5789| 1300 3.5714 671.08 0.7199 472 1.89231819.87 0.4714 720 2.3952 444.52 0.5824 1400 3.7743 704.74 0.7350 473 1.8943:320.43 0.4720 730 2.4155;449.11 10.5859 1500 3.9770 737.35iO.7485 474 1.8963 320.99 0.4726 740 2.4357 453.67 0.5894 1600 4.1798 766.95 0.7608 475 1.8984 321.54 0.4731 750 2.4560 458.15 0,-><>2S 1700 4.3826 797.49 0.7768 476 ; 1.9004 322.09 0.4736 760 2.4763 462.60 0.5961 1800 4.5854 826.60 0.7818 477 1.9024 322.64 0.4742 7702.4966 467.03 0.5993 19004.7882854.450.7911 478 1.9044 323.19 0.4747 780'2.5169 471.44 0.6026 2000 4.9910 880.91 0.7996 479 1.9065 323.74 0.4752 790 2.5371 475.84 0.6058 21005.1938906.760.8074 480 1.9085 324.29 0.4758 4811.91051324.840.4764 800 2.5574 480.24 ! 0.6089 810!2.5777 I 484.56 0.6120 2200 .-.. 3966 ,931.72 0.8147 2300 5.5994 957.80 0.8213 128 PHYSICAL PROPERTIES OF AIR. COMPRESSION AND EXPANSION OF A DEFINITE WEIGHT OF AIR. 107. This subject does not yet seem to have been satisfactorily treated, either by experiments or mathematics, for which reason the following formulas and tables can be considered approximately correct only within our limit of practice. The assumption of the existence of an absolute zero at -461, and that gases are still permanent at that temperature, does not appear to agree with the experiments on the compression and expansion of a definite weight of air. In order to make the exponents of the formulas of even numbers, the temperature - 343 is herein adopted as an ideal zero, not with assumption that this is an absolute zero, but it may be the temperature about which air condenses to liquid or freezes solid and its pressure ceases. It is supposed in the following formulas that a definite weight of air is enclosed in a vessel, which volume can be increased or dimin- ished without losing or gaining any weight of the air enclosed therein, and that no heat is lost or gained by conduction or radiation to or from the sides of the vessel. V= volume and t = temperature of the air to be compressed or expanded to the volume ^ of temperature T. Thus, when the air is compressed, the small volume is ^ and the high temperature is T; but when the air is expanded, ^ means the large volume and T the lowest temperature. = (T + 343), the ideal temperature of the volume ^. t = (t + 343), the ideal temperature of the volume V. \ 108. VOLUME AND TEMPERATURE. COMPRESSION AND EXPANSION OF AIR. 129 Compression of Air. Example 3. To what volume must V= 9 cubic feet of air of t = 62 be compressed in order to increase the temperature to T=552? t = 62 + 343 = 405. C = 552 + 343 = 895. Volume, if = 9 ( Y = 1.843 cubic feet. V 895 / Example 4- A volume of air ^=5 cubic inches of t = 75 is to be compressed to ^ = 0.35 cubic inches. Required the temperature of the compressed volume ? t = 75 + 343 = 418. Temperature, C = 41 8-J - = 1607.2. 0.35 T= 1607.2 - 343 = 1264.2, the temperature required. Expansion of Air. Example 4- A volume of air %f= 12 cubic feet and of temperature t = 57 is to be expanded to ^ = 36 cubic feet. Required the temper- ature of the expanded volume ? Ideal temperature, C = 400 X / = 230.95. \ 36 343 - 231 = - 112, the required temperature. Example 3. How much must air of t = 32 be expanded in order tc reduce the temperature to T= - 80 ? C= 343 + 80 = 163 and t = 343 + 32 = 375. / S75 V Volume, ^ =( ;~ 1 = 5.293 times the primitive volume. \ 109. PRESSURE AND TEMPERATURE. p i ar s f t F i ar \ s -(T] P= pressure at temperature C or T. p = primitive pressure at temperature t or t. 130 PHYSICAL PROPERTIES OF AIR / The pressures mean above vacuum, Compression of Air. Example 6. A volume of air of p = 14.7 pounds pressure and of temperature = 52 is to be compressed until the temperature be- comes T=360. Kequired the pressure of the air at that temper- ature ? Pressure, P= 14.7/ T = 96.84 pounds. Example 7. A volume of air of pressure p = 16 pounds to the square inch and of temperature t = 45 is to be compressed to P = 80 pounds per square inch. Required the temperature of the compressed air ? t = 343 + 45 = 388. Ideal temperature, C = 388 J/ - 663.48. T= 663.48 - 343 = 320.48, the temperature required. Expansion of Air. Example 6. Air of pressure p = 14.7 pounds and t = 48 is to be expanded until the temperature becomes T= -12. Required the pressure of the expanded air ? Pressure, P- 14.7 ( - - ) =8.9181 pounds. Example 7. A volume of air of pressure p = 15 pounds and temper- ature t = SO is to be expanded until the pressure becomes P=5 pounds to the square inch. Required the temperature of the ex- panded air? t = 343 + 80 = 423. nr Ideal temperature, C - 423^1 = 293.3. \ 15 The required temperature, T= 293.3 - 343 = 49.7 below Fahr. zero. COMPRESSION AND EXPANSION OF A IE. 131 g 110. VOLUME AND PRESSURE. f# 3 /P VI ' n#7 8 9 10 Compression of Air. Example 9. A volume of air #=18 cubic feet of pressure p = 15 ffounds is compressed to P = 25 pounds to the square inch. Required the volume of the compressed air ? Volume, y => l&Jf ^ \ = 12.805 cubic feet. ' V 25 / Example 10. A volume of air #=24 cubic inches and jo = 15 pounds is compressed to "^ = 6 cubic inches. Required the pressure of the compressed volume ? // 24 V Pressure, P= 15* /( - ) = 120 pounds to the square inch. 'Me Expansion of Air. Example 9. A volume of air #=5 cubic metres and of pressure p = l atmosphere is to be expanded to P=0.25 of an atmosphere. Required the volume of the expanded air? Volume V = 5 V ( I = 12.6 cubic metres. y 0.25 / Example 10. What will be the pressure of air expanded to 5 times its original volume ? TV Pressure, ^ = \/( ) = ^-299 of the original pressure. 132 PHYSICAL PROPERTIES OF AIR. gill. WORK OF COMPRESSION. The differential work of compression will be , but P-p When W=lfr, then k=0, and P\ + c= > of which C--2pV. \ ^ The work k = 2 p \l 2 p V, Let %f and ^ be expressed in cubic feet and p = 14.7 pounds to the square inch. K= work in foot-pounds per cubic feet of V compressed to rf. 2 p = 2x!44x 14.7 = 4233.6. K= 4233.6^-^^ -A 12 , 29.4 V/ ffi A . Mean pressure, P = ~ir _^ I \IT~ * )' m P un ds per square inch. The work done by the atmospheric pressure in compressing the air is 144x14.7 (^-^, which, subtracted from the gross work of com- pression, will remain the mechanic work. *-211&*F2WJ?-lW*-tfH Example 12. Required the gross work of compressing %f=16 cubic feet of air to = 4 cubic feet ? WORK OF HEAT IN AIR. 133 Gross work, k = 4233.6 x 16 1 J3 -1\= 67737.6 foot-pounds. Of this work k = 2116.8 (16 - 4) = 25401.6 foot-pounds was done by the atmospheric pressure, leaving k - 67737.6 - 25401.6 = 4233.6 foot- pounds of mechanic work above that of the atmosphere. 112. WORK OF EXPANDING AIR. V and ^ are expressed in cubic feet. K= work in foot-pounds done of expanding V cubic feet of air to ^. *= 4233.6 V^l-^J The work done against the atmospheric pressure will be f-#). 15 Subtract Formula 14 from 15, and the remainder will be the work done in expanding the air namely, / IW \~l . 16 The following tables are calculated by the preceding formulas, as will be understood by the headings. The works K and k mean foot- pounds per cubic foot of the primitive volume V, expanded or com- pressed to ^. 134 COMPRESSION OF AIR. TABLE XXXI. % Compression of Air by External Force. Volume. tr-L Temp. Fahr. Press Atmosp. stares.' ibs. per sq. In. "Wo Gross. rks. Mechanic. t T A P K k 1.00 32. 1.000 14.7 0. 0. 0.95 41.7 1.080 15.9 110.08 4.19 0.90 52.3 1.171 17.2 229.04 17.36 0.85 63.7 1.276 18.7 358.17 40.60 0.80 76.3 1.398 20.5 499.56 76.20 0.75 90.5 1.545 22.7 660.44 131.19 0.70 105.2 1.707 25.1 826.40 191.36 0.65 122.1 1.908 28.0 1077.4 336.29 0.60 141.1 2.151 31.6 1232.0 385.28 0.55 162.7 2.452 36.0 1475.0 522.39 0.50 187.3 2.828 41.5 1753.5 694.60 0.45 216. 3.313 48.7 2075.5 910.71 0.40 250. 3.953 58.1 2460.1 1190.0 0.35 291. 4.829 71.0 2922.4 1546.4 0.33 306.5 5.196 76.4 3095.2 1684.0 0.30 341.1 6.085 89.4 3495.7 2014.0 0.25 407. 8.000 117.6 4233.6 2671.0 0.20 495.5 11.18 164.3 5232.7 3539.3 0.15 624.1 17.15 252.1 6684.9 4885.6 0.125 718. 22.63 322.7 7740.7 5888.5 0.10 843. 31.63 465. 9157.3 7252.2 0.05 1334 89.44 1315. 14700 12690 0.04 1532 125. 1837. 16934 14902 0.03 1822 192. 2828. 20209 18156 0.02 2309 353.5 5196. 25703 23629 0.01 3407 1000 14700. 38102 36006 EXPANSION OF AIR. 135 TABLE XXXIJ. Expansion of Air by External Force. Volume. V-l. Temp. Fahr. 3?res Atmosp. aiires. Ibs. per sq. in. Wo Gross. rks. Mechanic. * T A P K' V 1.0 32 1.0 14.7 0. 0. 1.1 14.6 0.8668 12.74 197.03 14.65 1.2 -0.7 0.7607 11.18 368.87 54.49 1.3 -14.1 0.6747 9.918 517.94 117.1 1.4 -26.1 0.6037 8.874 655.58 119.1 1.5 -36.8 0.5443 8. 776.86 281.6 1.6 -46.5 0.4941 7.263 886.64 383.4 1.7 -54.4 0.4512 6.632 986.60 295.2 1.8 -63.5 0.4141 6.087 1078.1 615.3 1.9 -70.9 0.3818 5.612 1162.3 742.8 2.0 -77.8 0.3535 5.196 1239.6 877.2 2.25 -93.0 0.2963 4.355 1411.2 1235 2.5 - 105.8 0.2530 3.719 1500.0 1676 2.75 -116.9 0.2193 3.223 1680.6 2024 3.0 - 126.5 0.1924 2.828 1789.7 2444 3.25 - 135.0 0.1707 2.509 1885.2 2877 3.50 - 142.6 0.1527 2.244 1970.6 3322 3.75 - 149.3 0.1377 2.024 2047.4 3774 4. -155.5 0.1250 1.837 2116.8 4234 4.5 -166.2 0.1048 1.540 2237.8 5171 5. -175.3 0.0894 1.314 2340.3 6127 6. -189.9 0.0686 1.008 2505.4 8084 7. - 201.3 0.0540 0.793* 2633.4 10067 . 8. -210.4 0.0442 0.650 2736.8 12080 9. -218.0 0.0370 0.544 - 2822.7 14112 10. -224.4 0.0251 0.369 2894.8 16157 136 PHYSICAL PROPERTIES OF AIR. CARBONIC ACID AS A PERMANENT GAS. 113. When carbonic acid is not in contact with its liquid, the relation between volume and pressure behaves like that of a per- manent gas, and its ideal zero is about - 200 centigrade. The latest and most reliable experiments on carbonic acid as a per- manent gas have been made by Dr. Andrews, from which experi- ments the following formulas are deduced both in centigrade and Fahrenheit's scales of temperature. ^ = volume of carbonic acid gas of temperature T centigrade, and of pressure A in atmospheres, compared with the volume at zero centigrade and under atmospheric pressure. t = Fahrenheit temperature, and P = pressure in pounds per square inch above vacuum. Volume, Temperature, Pressure, Formulas for Centigrade Scale. , = 1 | T-IAA ~A + 200J. ' T=A (200^-1.4) -200. T-f 200 A = 200-^ - 1.4* Volume, Temperature, Formulas for Fahrenheit Scale. 300 +t 22.45P = 22.45/^-300. The volume corresponding to T = and A = l, formula 1, should be the unit 1 instead of 0.993 as shown in the table ; but the course of Dr. Andrew's experiments indicate that the primitive volume had probably been 0.993. The error is only 0.007, which is corrected in formula 4. CARBONIC ACID. 137 TABLE XXXIII. Volume of Carbonic Acid Gas of Different Temperatures and Pressures. Tempei Fahr. atures. Cent. l 10 Pressure A 1 20 ii Atmoftpher 30 . 40 50 t T if t t t t * 32 0.993 0.093 0.0430 0.02633 0.01800 0.013 50 10 1.044 0.098 0.0455 0.02800 0.01925 0.014 68 ' 20 1.098 0.103 0.0480 0.02966 0.02050 0.015 86 30 1.148 0.108 0.0505 0.03133 0.02175 0.016 104 40 1.198 0.113 0.0530 0.03300 0.02300 0.017 120 50 1.248 0.118 0.0555 0.03466 0.02425 0.018 140 60 1.298 0.123 0.0580 0.03633 0.02550 0.019 158 70 1.348 0.128 0.0605 0.03800 0.02675 0.020 176 80 1.393 0.133 0.0630 0.03966 0.02800 0.021 '194 90 1.448 0.138 0.0655 0.04133 0.02925 0.022 212 100 1.498 0.143 0.0680 0.03400 0.03050 0.023 230 110 1.548 0.148 0.0705 0.04466 0.03175 0.024 248 120 1.598 0.153 0.0730 0.04633 0.03300 0.025 266 130 1.648 0.158 0.0755 0.04800 0.03425 0.026 284 140 1.698 0.163 0.0780 0.04966 0.03550 0.027 302 150 1.748 0.168 0.0805 0.08050 0.03675 0.028 CARBONIC ACID AS A VAPOR. 114. When carbonic acid evaporates from or condenses to liquid, the relation between temperature and pressure behaves like that of a vapor, and its ideal zero is at about - 260 Fahr. The yet most reliable experiments on carbonic acid vapor have been made by Pelouze and Faraday, from which experiments the fol- lowing formulas and table are deduced namely, T= temperature Fahrenheit of the liquid or vapor of carbonic acid. A = pressure in atmosphere. P= pressure in pounds per square inch above vacuum. Pressure atmos., A = (T+260) 4 208513600' Logarithm, 8.3191344. Pressure Ibs., P= (T+260) 4 1421700 Logarithm, 7.1527888. . 7 . 8 138 PHYSICAL PROPERTIES OF AIR. Temperature, T- 120.1 7 y'Z - 260. Temperature, T = 61.404]/ P- 260. . 9 . 10 It appears from the above formulas that liquid carbonic acid freezes to solid at the low temperature - 260. The freezing point of liquid carbonic acid is variously given by different authors, of which Olm- stead says - 85, but Faraday experimented with liquid carbonic acid at --148 without it freezing. TABLE XXXIV. Carbonic Acid Vapor, Pressure and Temperature. Fahr. Temp. T. Press Aim. A. ures. fcs.P. Fahr. Temp. T. Pre Atm.^4 ssures. fcs. P. Fahr. Temp. T Pres Amt.^4 5ii res. &s.P. -260 -85 4.5 66.15 88 70 1029 -192 0.1 1.47 -81 5 73.5 99 80 1176 -180 0.2 2.94 -72 6 88.2 110 90 1323 - 171 0.3 4.41 -65 7 102.9 120 100 1470 -164 0.4 5.88 -58 8 117.6 129 110 1617 -159 0.5 7.35 -52 9 132.3 138 120 1764 -154 0.6 8.82 -47 10 147 146 130 1911 -150 0.7 10.29 -36 12 176.4 153 140 2058 ' -146 0.8 11.76 -24 15 220.5 160 150 2205 -143 0.9 13.23 - 6 20 294 167 160. 2352 -140 1 14.7 + 9 25 267.5 174 170 2499 -127 1.5 22.05 21 30 441 180 180 2646 -117 2 29.4 32 35 514.5 186 190 2789 -109 2.5 36.75 42 40 588 192 200 2940 -102 3 41.1 51 45 661.5 197 210 3087 - 96 3.5 51.45 59 50 735 207 220 3234 - 90 4 58.8 74 60 882 212 238 35 PROPERTIES OF STEAM. 139 STEAM OK AQUEOUS VAPOR. 115. Water under atmospheric pressure evaporates at ordinary temperatures un,der the boiling point ; but that evaporation takes place only on the surface in contact with the air. When the temperature of the water is elevated to or above that of the boiling point, then evaporation takes place in any part of the water where the temperature is so elevated. The temperature of the boiling point depends upon the pressure on the surface of the water. P= pressure in pounds per square inch above vacuum on the sur- face of the water. T= temperature Fahr. of the boiling point. T=200 1 /J r -101 ...... 1 Example 1. At w T hat temperature will water boil under a pressure of P=8 pounds to the square inch? This is under a vacuum of 14.7 - 8 = 6.7 pounds to the square inch. Temperature, T= 200 1 /~8^ 101 = 181.8. Example 2. What pressure is required to elevate the temperature of the boiling point of water to T= 330 ? , / 330 + 101 Y Pressure, P=( - - =100 pounds. \ 20 / The temperatifre of the boiling point is the same as that of the steam evaporated under the same pressure. Supposing the above formulas to be correct, the ideal zero of aqueous vapor should be at -101 Fahr., or at the temperature 101 below Fahr. zero, there is no pressure of the vapor ; that is, the force of attraction between the atoms is equal to the force of expansion by heat. LATENT HEAT OF STEAM. 116. One pound of water heated under atmospheric pressure, from 32 to 212, requires 180.9 units of heat. If more heat is sup- plied, steam will be generated without elevating the temperature until all the water is evaporated, which requires 1146.6 units of heat, and 140 PHYSICAL PROPERTIES OF AIR. the steam volume will be 1740 times that occupied by the water at 32. Then, 1146.6-180.9 = 965.7 units of heat in the steam which have not increased its temperature. This is what is called latent heat, because it does not show as temperature, but is the heat consumed in performing the work -of steam. One cubic foot of water at 32 weighs 6^387 pounds, if heated to the boiling point 212, requires 62.387 x 180.9 - 11285.8 units of heat, and if evaporated to steam under atmospheric pressure, requires 62.387x1146.6^71532.9 units of heat, of which 71532.9-11285.8 = 60247.1 will be latent. It is this latent heat which generated 1740 cubic feet of steam from the cubic feet of water. The work accomplished by that latent unite of heat against the atmospheric pressure will be K= 144 x 14.7 x (1740 - 1) = 3681115 foot-pounds. 3681115 Foot-pounds per unit of heat, J = - = 61.1. The heat expended in elevating the temperature of the water from 32 to 212 is not realized as work. VOLUME OF WATER. 117. Water, like other liquids, expands in heating and contracts in cooling, with the exception that in heating it from 32 to 40 it contracts, and expands in heating from 40 upwards. The greatest density or smallest volume of water is therefore at 40 Fahr. The most reliable experiments made on this subject are probably those of KOPP, by which the greatest density of water is indicated to be between 39 and 40, or nearer 39 ; but however accurate these experiments might have been made, it is impossible without the aid of mathematics to determine correctly the temperature of the greatest density because the curve tangents the abcissa at that point. The writer has treated Kopp's experiments with very careful math- ematical and graphical analysis, the result of which located the great- est density of water at 40. The formula for volume of water deduced from Kopp's experi- ments is (t-40)* '=1 1400 t + 398500 PROPERTIES OF WATER AND STEAM. 141 The volume deduced from the same experiments, but with the as- sertion that the greatest density of water is at 39, will be (*-8)' 1 400 T+ 405400 The Formula 1 is the most correct. LATENT AND TOTAL HEAT IN WATER FROM 32. 118. When water expands it absorbs heat, which is not indicated i temperature, but remains latent. / = latent heat per pound of water heated from 32. V^ volume per Formula 1. t = temperature of the water. h = total units of heat per pound of water heated from 32. Latent heat, J-=0.1t(#-l) 3 Total heat, A = 0.1 t (#+9) -32. ... 4 Cubic Feet per Pound. e- 62.388 Pounds per Cubic foot. = 62.388 1 "'*'' is, the water indicates more temperature than units of heat imparted to it. The volume at 32 is 1.000156, and the heat required to raise the temperature of one pound of water from 32 to 40 or 88 are 0.999844 x 8 = 7.99875 units. The heat required to raise the temperature of one pound of water from 32 to 212 or 180 are 181 units. The heat required to raise water from 32 to 350 or 318 are 322 units, or 4 units more than the increase of temperature. LATENT AND TOTAL UNITS OF HEAT IN STEAM. 119. The unit of heat required to elevate the temperature of one pound of water of 32 to the boiling point and evaporate it to satu- rated steam of temperature !F is Units of heat, #=1082 + 0.305 T. .... 1 Latent heat, L = 1082 + 0.305 T - [0.1 T ( #+ 9) - 32]. L - 1114 T (0.595 -0.1 V). . . 2 142 PHYSICAL PROPERTIES OF AIR. The Formula 1 is given by Regnault. The author has reason to believe that the formula for units of heat in steam evaporated from water heated from 32 should be per cubic foot H' = 2.8 P = 2.8 r 2.8 P 2.8 IT- 101 \ per pound, *-_- (-^--J The latent heat in steam by the new Formulas 3 and 4 should be Per cubic foot, L' = 2.8 P- ^ T. .... 5 9 & P Per pound, = -T ..... 6 ? This includes also the latent heat in the water at the boiling point, which is 1 = 0.1 t(V-V). The thermo-dynamic equivalent per unit of latent heat will be 2.8 P- f T 120. The combination of the Regnault formula for units of heat with the Fairbairn formula for volume of steam does not give a con- stant thermo-dynamic equivalent of heat, which it ought to do, and therefore either or both the formulas are defective. The arith- metical ratio 0.305 T in Regnault's formula cannot be correct, for the reason that the pressure increases as the sixth power of the temper- ature, and the volume decreases nearly as the cube of the temperature. The thermo-dynamic equivalent of heat in saturated steam accord- ing to Formula 3 will be 144 P J= = 51.5, a constant number. 2.8 P That is to say, one or each unit of heat in saturated steam of any pres- sure, but without expansion, generates 51.5 foot-pounds of work. This equivalent, multiplied by 1+ hyperbolic logarithm for expan- sion, gives the thermo-dynamic equivalent, which can be realized by steam-power. It has been explained ( 10) that the steam-pressure is inversely as the expansion, which rule is sufficiently correct within our limit of practice ; but when the temperature of aqueous vapor is reduced to SUPERHEATED STEAM. 143 the ideal zero 101 Fahr. its pressure will be ; that is, the expan- sive force of the heat is equal to the force of attraction between the atoms of the vapor. The vapor at that temperature will maintain a constant volume without being enclosed in a vessel. The total heat per pound of steam, Formula 4, is nearly constant for all pressures and temperatures, differing only by the latent heat in the water heated from 32 to the boiling point under the pressure P. DRYNESS OR HUMIDITY OF STEAM. 121. We have yet no reliable means by which to determine cor- rectly the dryness or humidity of steam, the knowledge of which is of great importance in steam engineering. A steam-engine supplied with over-saturated steam does not trans- mit the full power -due to the consumption of fuel, and thus the rate of evaporation is not a correct measure of the power or steaming ca- pacity of the boiler. The best means yet at our disposal by which to measure the qual- ity of the steam working an engine is to compare the steam-volume passed through the cylinder with that due to the water evaporated in the same time, but we have yet no reliable data as to the volume of steam compared with that of its water. The experiments of Fairbairn and Tate were made on a very small scale and by apparatus which did not admit of delicate measurements, and operating so widely dif- ferent from that of a steam-boiler that we have reason to doubt the correctness of the steam-volume deduced therefrom ; nor does that volume for different pressures agree with the law of expansion of steam namely, that the volume is inversely as the pressure. We know the specific gravity of steam at 212, which, compared with that of water at 32, makes the steam-volume at 212 =1730 times that of water at 32. We also know that one volume of water at 32 resolved into its elements, oxygen and hydrogen, gases heated under atmospheric pressure to 212, makes 2610.66 volumes of gas, of which there are 870.22 volumes of oxygen and 1740.44 volumes of hydrogen. 122. When the elements are again chemically combined from gas to vapor, the volume of hydrogen takes up the volume of oxygen, leaving only 1740.44 volumes of vapor, which is probably the correct volume of steam at 212. If the volume of steam increases as the pressure increases, the steam volume at any pressure would simply be ^ = 25584.468 : P; but the decrease of volume is accompanied with an increase of temperature which expands the volume in the same 144 STEAM ENGINEERING. ratio as the volume of water is increased for the same difference of temperature. Call the volume of water ^ 1 at 40, then for any other temper- ature, according to Copp's experiments, the volume will be (t-40)' 1 400 t + 398500 At 212 the volume of water is 1.0426. Therefore the steam volume at any pressure and temperature should be 25584.468 / (T-40) 2 \ 1.0426 P \ 1400 T+ 398500 / The temperature of water and steam being alike, the 24539 # Steam volume, y = . .... 3 P TABLE XXXV. Comparison of Volume and Temperature of Steam at Different Pressures. Steam -pres- sure. Volume ( Fairbairn. f Steam. Nystrom. Temperatui Begnault. e of Steam. Nystrom. 14.7 1641.5 1740 212 212 25 984.23 1035 240.07 241.0 50 508.29 527.2 280.89 282.8 75 348.15 355.8 307.42 309.8 100 267.80 269.4 327.6 329.9 150 187.26 181.8 358.4 360.0 200 146.93 138 381.8 382.6 300 106.54 94.22 417.7 416.5 400 86.33 71.19 445.1 441.9 Comparison of Fairbairn's experiments and formulas with the author's steam volume : By Fairbairn's formula By Fairbairn's experiment By the author's formula.... Pres. P= 60.6 ^ = 428 ^ = 432 ^=437 Pres. P=8 = 3046 = 3150 Pres. P= 4.7 ^ = 4900 ^ = 4914 ^ = 5336 PROPERTIES OF WATER AND STEAM. 145 The Regnault experiments on temperature and pressure of steam gave widely different results, of which an average was adopted, and it was attempted to set up a formula to follow the average curve, which was found impossible, for which reason different formulas were set up for different parts of the irregular curve. The formula herein adopted gives a regular curve which sweeps the whole range of the Reguault experiments, and it coincides in several places with the irregular or average curve. The volume of one pound of steam in cubic feet will be 393.333 ff P The steam volume formula by Fairbairn and Tate is * fH /= inches of mercury. That is to say, the steam volume cannot be reduced below 25.62. For very high pressures we can omit the fraction 0.72 and insert 2.0372 P for J namely, When the steam-pressure is P= 24304 pounds to the square inch, the volume should be 26.62. The temperature corresponding to this pressure is T = 200 V 6/ 24304 -101= 975 Fahr. . . 6 The volume of water at this temperature will be *;_ ] + (975-40)' i 6 4 7 1400x975.+ 398500 Then 26.62 - 1.64 = 25 volumes, of steam pressure P= 24304, which cannot be materallly reduced by additional pressure, because an in- crease of pressure, would only affect the decimals of that volume. The reason why the water volume is subtracted from that of the steam, is that the water volume is considered to be the limit to which that of steam can be reduced. It will be noticed that Fairbairn's experimental numbers, 24304 and 25.62, agree nearly with the writer's numbers, 24539 and 25, which fact deserves consideration. 10 146 STEAM ENGINEERING. Messrs. Fairbairn and Tate omitted the consideration of expansion of water, for which reason they were obliged to add the empirical constant 25.62 in their formula. The above argument proves conclusively that the steam volume experiments, as well as the formula of Fairbairn and Tate, cannot be relied upon, and they do not agree with the law of expansion of vapors. The object of this paragraph is to determine the dryness or humid- ity of steam, for which purpose the volume due to the evaporation should be compared with the volume of steam passing through the steam cylinder. W= cubic feet of water at 32, evaporated during ^/"revolutions of the engine. ^ = Steam volume compared with that of its water at 32. Q = cubic feet of steam passing through the engine or cylinder at each revolution or double stroke of the piston. N= total number of revolutions of the engine in the time W cubic feet of water is evaporated. % = per centage of water in the steam. V= volume of water at the temperature of the steam. The steam-piston and valves must be perfectly tight, and the capa- city of the steam-ports and clearance of piston must be included in Q. 123. In the ordinary engine the admittance of steam is generally cut off before the piston has reached the end of the stroke, in which case the steam volume Q must be determined from the indicator diagram, as follows : Measure the steam-pressure p on the diagram where the expansion curve begins to be reg- ular. The steam volume Tfr corresponding to this pressure must be used in the formula. Measure the distance Q in feet, which, multiplied by the area of the piston in square feet, is the cubic capacity of the steam, to which add the capacity of the clear- SUPERHEATED STEAM. 147 ance and steamport, and the sura is Q. This measurement must be made for both sides of the piston. The steam-pressure should be kept as constant as possible during the experiment ; but in a long run it is difficult, if not impossible, to keep it stationary, for which a mean-pressure must be determined, as follows : The expansion being constant during the operation and the steam- pressure by gauge, noted at short and regular intervals of time, and the mean-pressure represented byjo". p' steam-pressure by gauge at the time the pressure p is taken on the diagram. p'" = mean-pressure for the volume ^ in the formula. p"' : p" =p' : p and p'" *-*. P Small steam-engines ought to be constructed for the purpose of measuring the volume, dryness or humidity of steam. The slide valve in such an engine should have no lap or lead on the steam and exhaust ports, so that the full capacity of the cylinder, including clear- ance and steamport, would be the correct measure of the steam volume for each stroke. The cylinder and short steam-pipe could be well covered with felt, so that the pressure in the boiler would correspond to the volume ^ in the engine. The exhaust steam could be condensed in a surface condenser and the water measured independent of the evaporation in the boiler. Such an engine could be temporarily attached to any boiler for the purpose of testing its quality of steam, and the properties of super- heated steam, which are yet not well understood. SUPERHEATING STEAM. 124. When steam is superheated after generated in the w r ater, the relation between temperature and pressure will remain the same as if the same steam had been evaporated at the same temperature as that to which it is superheated as long as it is in contact with the water. When steam is shut off from the water from which it is gen- erated and then superheated, the relation between temperature and pressure will still remain the same as for saturated steam, provided the volume is not increased to or over 50 per cent. When steam is superheated above the temperature and pressure due to saturated steam, and the volume is increased, the hydrogen is not 148 STEAM ENGINEERING. capable of holding all the oxygen in its own volume ; but part of the vapor is converted into gas until the volume is increased 50 per cent., when all the vapor is converted into gas. For instance, if four cubic feet of steam is superheated under constant pressure until its volume becomes six or more cubic feet, that volume will then not be vapor but a gas which maybe exploded by ignition (?) In the ordinary use of steam it is never so superheated, but is always in contact with water which prevents its conversion into gas, and it requires a tem- perature above ignition about 600 to ignite it to explosion. When the steam is superheated to gas it obeys the formulas for per- manent gases already explained. When steam is passed through and allowed to expand in iron tubes heated to a dull red heat, say 800, the steam is resolved into its elements, the oxygen being taken up by the hot iron and the hydro- gen gas passing off without explosion. A definite volume of saturated steam, superheated in a closed vessel without water, will obey the formula T= 200|/T- 101, until the primitive pressure is increased 50 per cent., when the steam becomes a gas and obeys the formulas for permanent gases above that pressure and temperature ; but being enclosed in a vessel the volume remains constant. For instance, a volume of steam of pressure P = 40 pounds to the square inch, which corresponds to a temperature of T = 200^40 - 101 - 268.87, is superheated under constant volume until the pressure becomes P- 60, the temperature will be !F= 200^60 - 101 = 294.7 ; the steam is then a gas of f volumes of hydrogen and ^ of oxygen. W= weight in pounds of the saturated steam superheated. The specific heat of steam gas at 32 under atmospheric pressure is 3.3 + 0.23 = 3.53. The units of heat h required to superheat W pounds of saturated steam of pressure p and temperature t to pressure P and temperature T will be SUPERHEATED STEAM. 149 P and p both mean absolute pressures above vacuum, and the super- he atinir accomplished without the steam being in contact with water. #= volume of the saturated steam of pressure p. tf = volume of the superheated steam of pressure P. The saturated steam becomes a perfect gas when superheated so that V ir 1.5 p IT -, or when = P 1.5V P V Example. How many units of heat are required to superheat W= 3 pounds of saturated steam of pressure p = 40 and temperature t = 268.87 to a perfect gas of pressure P=60 and temperature T= 294.7? Units of heat h = 3.53 x 3 J (294.7 - 268.87) = 223.34. ' OU The same weight -of steam raised from p = 4Q to P=60 of satu- rated steam would require -only 28 units of heat, but the steam-vol- ume which is constant in the preceding example would in this latter case be one-third less. Then 223 - 28 = 195 units of heat expended in converting the vapor into gas and in expanding the volume 50 per cent. It would therefore appear that there is no gain, but rather a loss, in superheating steam without contact with water for motive-power. The expansive property of vapor generates much more power than does that of steam-gas. But when steam is to a limited extent super- heated in contact with water, the expansive property is not impaired, and the water which may be carried along with the steam, is evaporated by the superheating ; and thus there is a considerable gain by super- heating steam, particularly when the superheating is done by the gases of combustion after having passed the water-seating surfaces. Steam- gas is very injurious to the sides and packing-rings in the cylinder; it creates more friction and is more difficult to condense than steam-vapor. NEW TABLES FOR WATER AND STEAM. 125. The following tables of properties of water and steam have been calculated by the preceding new formulas, which are considered more correct than the old ones. The meaning of each column is ex- plained in its heading. In the first two water-tables the pressure of the vapor in pounds per square inch is contained in the last column, of which + P denotes the absolute pressure above vacuum, and-p the pressure under that of the atmosphere, which is the vacuum. 150 TABLE XXXVI. Properties of Water. Tempe Centig. rat ore. Fahr. Volume. Wat. = 1 at 40. Weight >er cubic foot. Bulk, cubic feet per Ib. Units o perlb. f beat, pr. c. ft. Pressure Absol. of vapor, under at. t 0. 0.55 1.11 1.66 2.22 T 32 33 34 35 36 v . 1.000109 1.000077 1.000055 1.000035 1.000020 1.000009 1.000003 1.000001 1.000000 1.0001)03 ? 62.3871 62.3830 62.3842 62.3859 62.3868 G 0.0160304 0.0160299 0.0160295 0.0160292 0.0160290 h. 0.00000 1.00000 2.00000 3.00001 4.00003 h'. 0.0000 62.383 124.77 187.16 249.55 + P. 0.0864 0.0904 0.0946 0.0988 O.HKJ:; P- -14.614 -14.610 -14.606 -14.601 -14.597 2.77 3.33 3.88 4.44 5.00 5.55 6.11 6.66 7.22 7.77 37 38 39 40 41 62.3875 62.3876 62.3879 r,L'.:;sso 62.3878 0."tll2.2 i:;o" 62.2042 62.1952 62.1860 62.1766 0.0160632 0.0160652 0.0160673 0.0160694 0.0160716 40.01622 41.01733 42.01848 43.01968 44.02092 45.02222 46.02356 47.02495 48.02640 49.02789 2491.2 2553.2 2615.2 2677.1 2739.2 0.418S 0.4336 0.4487 0.4644 0.4804 -14.281 -14.266 -14.251 -14.236 -1 I.L'L'I) 25.00 25.55 26.11 26.66 27.22 77 78 79 80 81 1.002814 1.002956 1.003101 1.003249 1.003400 0.0160738 0.0160761 0.0160784 0.0160808 0.0160832 2S01.0 2862.8 2924.6 2985.4 3048.2 0.4970 0.5139 0.5314 0.5493 0.5677 -14.203 -14.186 -14.169 -14.151 -14.132 27.77 28.33 28.88- 29.44 30.00 30.55 31.11 31.66 82 83 84 85 86 87 88 89 1.003554 1.003711 1.003872 1.004035 1.004199 1.004370 1.004542 1.004717 62.1671 62.1574 62.1474 62.1373 62.1272 62.1166 62.1059 62.0951 0.0160857 0.0160882 0.0160908 0.0160934 0.0160960 0.0160987 0.0161015 0.0161043 50.02944 51.03104 52.03269 53.03439 54.03615 55.03797 56.03984 57.04177 3111.0 3172.8 3234.4 3296.2 3358.2 3418.7 34S0.4 3542.1 o.5sos 0.6063 0.6264 0.6470 0.6681 0.6898 0.7121 0.7351 -14.113 -14.093 -14.074 -14.053 -14.032 -14.010 -13.988 -13.965 TABLE XXXVII. Properties of Water. 151 Tempei Cen.ig. aturc. Fahr. Bulk, cub. per Ib. Units o perlb. f heat, pr. c. ft. Pressure Absol. of vapor, under at. Wat. = 1 at 40. >er cubic foot. t 32.22 32.77 33.33 33.88 34.44 35.00 35.55 36.11 36.66 37.22 T 90 91 92 93 94 V .004894 .005094 .005258 .005444 .005633 f 62.0840 62.0718 62.0617 62.0502 62.03S6 G 0.016107 0.016110 0.016113 0.016116 0.016119 h. 58.0437 59.0458 60.0479 61.0501 62.0523 h'. 3603.8 3665.0 3726.6 3788.2 3849.8 + P. 0.7586 0.7827 0.8075 0.8329 0.8590 P- -13.94 -13.91 -13.89 -13.86 -13.84 95 96 97 98 99 1.005825 .006019 .006216 .006415 .006618 Ol'. (12(17 62.0148 62.0026 61.9904 61.9779 0.016122 0.016125 0.016128 0.016131 0.016135 63.0546 64.0569 65.0593 66.0618 67.0643 3911.2 3972.6 4033.9 4095.2 4156.5 O.SS5K 0.9132 0.9609 0.9704 1.000 13.81 -13.79 -13.74 -13.73 13.70 37.77 38.33 38.88 39.44 40.00 100 101 102 103 104 .006*22 .007030 .007240 .007553 .007668 61.9653 61.9525 61.9396 61.9204 61.9133 0.016138 0.016141 0.016145 0.016150 0.016152 0.016155 ~ 0.016159 0.016162 0.016166 0.016169 68.0669 69.0696 70.0723 71.0751 72.0779 4217.7 4278.9 4340.1 4401.3 4462.5 4523.0 4585.0 4645.9 4706.8 4767.7 1.030 1.061 1.093 1.126 1.159 1.194 1.229 1.265 1.302 1.340 -13.67 -13.64 -13.61 -13.57 -13.54 40.55 41.11 41.66 42.22 , 42.77 105 106 107 108 109 .007905 .008106 .008.328 .008554 .008781 61.8987 61.8864 61.8728 61.8589 61.8450 73.0809 74.0838 75.0869 76.0900 77.0932 78.0965 79.0998 80.1032 81.1067 82.1103 13.50 13.47 -13.43 -13.40 13.36 43.33 43.88 44.44 45.00 45.55 110 111 112 113 114 ~~il5" 116 117 118 119 .0()!U32 .009244 .009479 .009718 1.009956 61.8296 61.8166 61.8022 61.7876 61.7730 0.016173 0.016177 0.016180 0.016184 0.016188 0.016192 0.016196 0.016200 0.016204 0.016208 4828.6 4889.5 4950.4 5011.3 5072.2 1.378 1.418 1.459 1.500 1.543 13.32 -13.28 -13.24 -13.20 -13.16 46.11 46.66 47.22 47.77 48.33 1.010197 1.010442 1.010688 1.010938 1.011189 61.7583 61.74:53 61.7283 61.7130 61.6977 83.1139 84.1176 85.1214 86.1252 87.1292 r>i 33.0 5193.7 5254.3 5314.9 5375.5 1.587 1.631 1.677 1.723 1.771 -13.11 -13.07 -13.02 -12.98 -12.93 48.88 49.44 50.00 50.55 51.11 120 121 122 123 124 1.011442 1.011698 1.011956 1.012216 1.012478 61.6823 61.6666 61.6509 61.6351 61.6192 0.016212 0.016216 0.016220 0.016224 0.016229 88.1332 89.1373 90.1414 91.1456 92.1500 5436.1 5496.6 5557.1 5617.6 5678.1 1.820 1.870 1.921 1.974 2.026 -12.88 -12.83 -12.78 -12.73 -12.67 51.66 52.22 52.77 53.33 53.88 125 126 127 128 129 1.012743 1.013010 1.013278 1.013550 1.013823 61.6030 61.5868 61.5805 61.5540 61.5374 61.5207 61.4355 61.3473 61.2567 (J1.16:',5 0.016233 0.016237 0.016241 0.016246 0.016250 93.1543 94.1588 95.1634 96.1680 97.1727 5738.6 5798.9 5859.2 5919.5 5979.7 2.082 2.137 2.195 2.253 2.312 2.374 2.699 3.058 3.462 3.907 -12.62 -12.56 -12.50 -12.45 -12.39 54.44 57.22 60.00 62.77 65.55 130 135 140 145 150 1.014098 1.015505 1.016962 1.018468 1.020021 0.016255 0.016277 0.016301 0.016325 0.016350 98.1775 103.2027 108.230 113.260 118.291 123.326 128.362 133.401 138.443 143.487 6040.0 6340.3 6639.6 6937.9 7215.1 -12.33 -12.00 -11.64 -11.24 -10.79 (i8.33 71.11 73.88 76.66 79.44 155 160 165 170 175 1.021619 .023262 .024947 .026672 1.028438 61.0678 60.9697 60.8695 60.7673 60.6620 0.016375 0.016401 0.016429 0.016456 0.016485 " 0.016513 0.016543 0.016573 0.016604 0.016635 0.016667 0.016799 0.016811 7531.2 7826.2 8098.1 8412.8 8704.2 4.397 4.939 5.534 6.188 6.906 -10.30 -9.761 -9.166 -8.512 -7.794 82.22 85.00 87.77 90.55 93.33 96.11 98.88 100.00 180 185 190 1 ( .l.'> 200 205 210 212 .n:;ir_>i2 .032083 .033960 .035873 1.037819 .039798 .041809 .042622 60.5567 60.4487 60.3389 60.2275 60.1146 60.0002 59.8843 59.8376 148.537 153.583 158.635 163.691 168.749 173.809 178.873 180.900 8994. 9281. 9571. 9858. 10318. 10428. 10712. 18824. 7.693 8.550 9.488 10.51 11.62 12.83 14.13 14.70 - 7.007 -6.150 -5.212 -4.19 -3.08 -1.87 -0.57 0.000 152 PROPERTIES OF WATER. TABLE XXXVIII. Water. TVmpe of the Cent. rat ure water. Fahr. ~~T~ 212. 213. Volume, water = 1 at 40. Weight. Ibs. per cubic ft. Bulk. i-iil.ir i.-<-t per pound. Units of h Tots pound. eat in wate 1 per cubic foot, r from 31 La ten pound. 10 to T. tper cubic ft. 100. 100.5 V .04262 1.04296 ? 59.838 59.819 e 0.01671 0.01671 h. 180.90 181.91 h'. 10825 10882 L 0.903 0.915 t. 54.03 54.73 102.4 216.4 1.04436 59.743 0.01674 185.36 11063 0.957 56.73 104.2 106. 107.6 219.6 222.8 225.7 1.04534 .04638 1.04785 59.668 59.594 59.520 0.01676 0.01678 0.01680 188.59 191.83 194.78 11241 11414 11583 0.994 1.033 1.082 59.31 61.56 04.40 109.1 110.6 22H.r> 231.2 1.041)4(5 1.05062 59.447 59.384 0.01682 0.01684 197.63 200.37 11749 11895 1.130 1.170 67.17 69.48 112.1 233.8 1.05175 59.322 0.01685 203.01 12037 1.209 71.72 113.6 114.8 236.3 238.7 ~24~UT 243.3 1.05284 1.05389 1.05490 1.05588 59.261 59.201 59.142 59.086 0.01687 0.01689 205.55 207.98 12175 12309 1.248 1.281 73.96 75.71 ^8J9" 80.38 116.1 117.7 0.01690 0.01692 210.32 212.66 12439 12561 1.322 1.359 118.5 119.7 120.7 T2UT 123.0 245.4 247.5 249.4 1.05683 1.05776 1.05867 59.032 0.01694 58.980 0.01695 58.930 0.01697 214.79 216.84 218.86 220.90 222.93 12678 12791 12901 1.394 1.437 1.462 82.42 84.42 86.32 251.4 253.4 1.05955 1.06042 58.881 58.832 0.01698 0.01700 13007 13113 1.496 1.532 88.09 90.02 124.0 255.3 1.06128 58.784 0.01701 224.86 13217 1.565 91.92 125.1 126.1 257.2 259.0 1.05213 1.06297 58.737 58.690 58.646 58.603 0.01702 0.01704 226.80 228.63 13318 13416 1.598 1.630 93.78 95.65 127.0 128.0 260.7 262.4 1.06380 1.06460 0.01705 0.01706 230.36 232.09 13510 13602 1.664 1.695 H7..V.) 99.37 128.9 264.1 1.06538 58.561 0.01707 233.83 13692 1.726 101.1 129.8 130.7 265.7 267.3 1.06614 1.06689 58.519 58.477 0.01709 0.01710 235.45 237.09 13780 13866 1.756 1.790 102.8 104.5 131.6 132.5 268.9 270.4 1.06761 1.06832 58.437 58.398 0.01711 0.01712 238.72 240.25 13950 14036 1.816 1.846 106.1 107.9 133.4 271.9 1.06902 58.359 0.01713 241.78 14115 1.879 109.6 134.0 134.9 273.3 274.8 1.06971 1.07039 58.321 58.284 0.01714 0.01716 243.20 244.73 14192 14267 1.905 1.935 111.2 112.7 135.6 136.4 276.2 277.6 1.07105 1.07170 58.250 58.214 0.01717 0.01718 246.16 247.59 14339 14411 1.961 1.990 114.2 115.8 137.2 279.0 1.07234 58.179 0.01719 249.02 14482 2.018 117.4 137.9 138.6 T39J5T 140.0 280.3 281.6 1.07297 1.07359 58.145 58.112 0.01720 0.01721 250.34 251.67 14551 14620 2.045 2.075 118.9 120.3 282.8 284.1 1.07421 1.07483 58.078 58.045 0.01722 0.01723 252.90 254.22 14688 14755 2.098 2.126 121.7 123.2 140.8 285.4 1.07534 58.012 0.01724 255.66 14821 2.150 124.7 141.4 142.0 286.6 287.8 1.07594 1.07653 57.980 57.948 0.01725 0.01726 256.77 258.00 14886 14951 2.175 2.202 126.2 127.7 PROPERTIES OF STEAM. 153 TABLE XXXIX. Steam. Total Ibs. persq. inch. pressure. Inches raercur. Tem- perat're Fahr. Volume water = 1 at 40. weight Ibs. per cubic ft. Bulk cubic ft. per Ib. Units Tola pound. of heat Iper cubic ft. rom 32 Latei pound. toT. t per cubic ft. lit P / T if V G H H' L L' p 14.7 15 29.92 30.55 212 213 1740 1706 0.0358 0.0365 27.897 27.347 1146.6 1147.0 41.100 41.920 965.7 965.1 34.61 35.29 .00 .3 16 32.59 216.4 1601 0.0389 25.674 1148.0 44.700 962.7 37.50 1 17 18 19 34.63 36.67 38.71 219.6 222.8 225.7 1509 1426 1353 0.0413 0.0437 0.0461 24.186 22.865 21.693 1149.0 ! 47.478 1149.950.255 1150.8 53.030 960.4 958.1 956.0 39.68 41.86 44.05 2 3 4 5 6 20 21 40.74 42.78 228.5 231.2 1288 1228 0.0484 0.0508 20.690 19.678 1151.7 1152.6 55.802 58.572 954.1 952.2 46.23 48.41 22 44.82 233.8 1173 0.0532 18.804 1153.4 61.340 950.7 50.48 7 23 24 46.85 48.89 236.3 238.7 1123 1078 0.0555 0.0579 18.005 17.272 1154.2 1155.0 64.106 66.870 948.7 946.0 52.65 54.82 8 9 25 26 50.93 52.97 241.0 243.3 1035 995.1 0.0602 0.0625 16.597 15.994 1155.7 1156.4 69.632 72.392 945.4 943.8 56.96 59.09 10 11 27 55.00 245.4 958.2 0.0648 15.422 1157.1 75.159 942.3 61.21 12 28 29 30 31 57.04 59.08 247.5 249.4 926.4 895.6 0.0672 0.0696 14.881 14.371 1157.7 1158.2 77.914 70.667 940.9 939.6 63.31 65.41 13 14 61.11 63.15 251.4 253.4 866.7 838.3 0.0720 0.0743 13.892 13.456 1158.7 1159.3 83.410 86.162 937.8 936.4 67.51 69.60 15 ! 16 32 65.19 255.3 812.0 0.076613.059 1159.9 88.913 935.1 71.68 17 33 34 67.23 69.26 257.2 259.0 787.8 765.7 0.0789 12.669 0.0812 12.313 1160.5 1161.0 91.662 94.411 933.7 932.4 73.75 75.83 18 19 35 36 37 71.30 73.34 75.38 260.7 262.4 264.1 745.8 726.9 708.8 0.0834 11.955 0.0860 11.624 0.0884 11.309 1161.5 1162.0 1162.5 97.156 99.901 102.65 931.2 929.9 928.7 77.89 79.95 82.01 20 21 22 38 39 40~ 41 77.41 79.45 265.7 267.3 691.7 675.4 0.0908 0.0930 11.013 10.745 1163.0 1163.5 105.40 108.15 927.6 926.4 84.06 86.10 23 24 81.49 83.52 268.9 270.4 654.9 640.0 0.0952 0.0974 10.498 10.262 1164.0 1164.5 110.87 113.61 925.3 924.3 88.14 90.18 25 26 42 85.56 271.9 625.4 0.0997 10.031 1164.9 116.35 923.1 92.21 27 43 44 45 46 47 87.60 89.64 273.3 274.8 611.2 597.4 0.1020 0.1044 9.8030 9.5801 1165.4 1165.8 119.09 121.83 922.1 921.1 94.24 96.26 28 29 91.67 93.71 95.75 276.2 277.6 279.0 584.1 571.9 560.1 0.1068 0.1093 0.1117 9.3617 9.1465 8.9486 1166.2 1166.7 1167.2 124.57 127.31 130.05 920.1 919.1 918.0 98.28 100.3 102.3 30 31 32 48 49 97.78 99.82 280.3 281.6 548.8 537.8 0.1141 0.1166 8.7596 8.5776 1167.6 1168.0 132.79 135.53 917.1 916.2 104.3 106.3 33 34 50 51 101.86 103.90 282.8 284.1 527.2 517.5 0.1183 0.1206 8.4504 8.2899 1168.4 1168.8 138.27 141.00 915.4 914.5 108.3 110.3 35 36 52 105.93 285.4 507.1 0.1230 8.1284 1169.2 143.73 913.6 112.3 37 53 54 107.97 110.01 286.6 287.8 498.0 489.2 0.1254 0.1278 7.9724 7.8249 1169.5 146.46 1169.8 149.18 912.7 911.8 114.3 116.3 38 39 154 PROPERTIES OF WATER. TABLE XL. "Water. Temperature Volume. Weight. Ibs. per cubic ft. Bulk, cubic feet per pound. Units of h Tola pound. eat in wate 1 per cubic foot. h'. 15014 15075 15135 15195 1 5-J.-.4 r from 31 Lateu pound. L 2.230 2.260 2.286 2.310 _'.:i: ;.-> to T. tper cubic ft. f. 129.2 130.8 132.2 133.5 134.7 Cent. Fahr. 1 at 40. ~v~~ 1.07720 1.07778 1.07835 1.07892 1.07943 142.8 143.4 144.0 144.6 145.2 T 289.0 290.2 291.3 292.4 293.6 ? 57.917 57.886 57.857 57.823 57.795 e 0.01726 0.01727 0.01728 0.01729 0.01730 h. 259.23 260.46 261.58 262.71 263.93 145.9 146.6 147.1 147.7 148.3 294.7 295.8 296.9 298.0 299.0 1.07998 1.08051 1.08104 1.08157 1.08209 f>7.7(>S 57.739 57.711 57.683 57.655 0.01731 0.01732 0.01733 0.01734 0.01735 265.05 266.18 267.30 268.43 269.45 15312 15368 15424 15480 15535 2.354 2.382 2.406 2.430 2.454 136.0 137.4 138.8 140.2 141.6 148.8 149.3 150.0 150.5 151.1 300.0 301.0 302.0 303.0 304.0 1.08259 1.08311 1.08362 1.08411 1.08460 57.629 57.604 57.579 57.546 57.522 0.01736 0.01737 0.01738 0.01738 0.01739 270.48 271.50 272.52 273.55 274.58 l.j-)SS 15641 15693 15746 15797 2.480 2.503 2.525 2.548 2.572 142.9 144.2 145.5 146.7 147.8 151.6 152.2 152.8 153.3 153.8 305.0 306.0 307.0 307.9 308.9 1.08507 1.08556 1.08604 1.08653 1.08700 57.497 57.472 57.447 57.420 57.395 57.370 57.346 57.322 57.298 57.275 0.01740 0.01740 0.01741 0.01741 0.01742 "001743" 0.01743 0.01744 0.01745 0.01745 275.60 276.62 277.64 278.56 279.58 15846 15896 15945 15995 16044 2.51)0 2.618 2.640 2.658 2.686 149.2 150.4 151.6 152.8 154.1 154.3 154.8 155.1 155.9 156.3 309.8 310.7 311.6 312.5 313.4 1.08747 1.08792 1.08838 1.08883 1.08928 280.51 281.43 282.35 283.27 284.19 16093 16140 16187 16233 16278 2.707 2.728 2.755 2.776 2.795 155.3 156.6 157.9 159.2 160.4 156.8 157.3 157.7 158.1 158.6 314.3 315.1 315.9 316.7 317.5 1.08971 1.09014 1.09057 1.09100 1.09138 T09180~ 1.09222 1.09264 1.09305 1.09346 .->7.L>.-,i> 57.230 57.208 57.186 57.164 0.01746 0.01747 0.01747 0.01748 0.01749 285.12 285.94 286.76 287.58 288.40 289.32 290.14 290.96 291.78 292.60 16324 16368 16411 16453 16493 2.K22 2.840 2.860 2.881 2.900 161.6 162.7 165.8 164.8 105.9 159.1 159.6 160.0 160.4 160.8 318.4 319.2 320.0 320.8 321.6 57.142 57.121 57.100 57.078 57.057 0.01750 0.01750 0.01751 0.01752 0.01752 16533 16574 16614 16654 16695 2.920 2.940 2.960 2.980 3.000 166.9 168.0 169.1 170.2 171.3 161.2 161.6 162.2 162.6 163.0 322.4 323.2 324.0 324.7 325.4 1.09384 1.09425 1.09465 1.09506 1.09546 57.036 57.015 56.994 56.973 56.953 0.01753 0.01754 0.01754 0.01755 0.01755 293.42 294.25 295.07 295.79 296.5 16735 16774 1C813 16852 16890 3.022 3.047 3.068 3.089 3.100 172.4 173.5 174.6 175.7 176.7 PROPERTIES OF STEAM. 155 TABLE XLI. Steam. Total i Ibs. mrsij. inch. P >ressure. Inches uiercur. Tem- jerat're Fahr. Volume water = 1 at 40. weight Ibs. per cubic ft. Bulk cubic ft. per Ib. Unite Tata pound. of heat f per cubic ft. rom32 Laten pound. toT. tper cubic ft. 111 H! / T t $ G H H' L L' p 55 56 112.04 114.08 289.0 290.2 480.6 472.1 0.1298 0.1302 7.7028 7.6774 1170.1 1170.5 151.91 154.64 910.9 910.1 118.3 120.3 40 41 57 116.12 291.3 464.0 0.1324 7.5524 1170.9 157.37 909.9 122.2 42 58 59 118.16 120.19 292.4 293.6 456.2 448.8 0.1346 0.1388 7.4277 7.2034 1171.3 1171.6 160.10 162.83 908.6 907.7 124.2 126.1 43 44 60 61 122.23 124.27 294.7 295.8 441.6 434.6 0.1422 0.1434 7.0786 6.9709 1171.9 1172.3 165.56 168.28 906.9 906.1 128.1 130.0 45 46 62 126.30 296.9 427.8 0.1456 6.8643 1172.6 171.00 905.3 131.9 47 63 64 66 128.34 130.38 298.0 299.0 421.2 414.9 0.1479 0.1502 6.7588 6.6543 1172.9 1 143.2 173.71 176.41 904.5 903.8 133.9 135.8 48 49 132.42 134.45 300.0 301.0 4 OS. -7 402.6 0.1526 0.1548 6.5510 6.4570 1173.5 1173.8 179.13 181.84 903.0 902.3 137.8 139.7 50 51 67 136.49 302.0 396.7 0.1571 6.3660 1174.1 184.53 901.6 141.7 52 63 69 138.53 140.36 303.0 304.0 391.1 385.6 0.1593 0.1616 6.2750 6.1852 1174.4 1174.7 187.24 190.00 900.9 900.1 143.6 145.6 53 54 70 71 142.60 144.64 305.0 306.0 380.4 374.7 0.1640 0.1662 6.0972 6.0162 1175.0 1175.3 192.71 195.42 899.4 898.7 147.5 149.5 55 56 72 146.68 307.0 369.5 0.1684 5.9363 1175.6 198.14 898.0 151.4 57 73 74 148.72 150.75 307.9 308.9 364.7 360.2 0.1707 0.1730 5.8576 5.7799 1175.9 1176.2 200.85 203.58 897.4 896.6 153.3 155.2 58 59 75 76 152.79 154.83 309.8 310.7 355.8 351.1 0.1753 0.1775 5.7033 5.6324 1176.5 1176.8 206.29 209.00 896.0 895.4 157.1 159.0 60 61 77 156.86 311.6 346.6 0.1798 5.5624 1177.1 211.71 895.8 160.9 62 78 79 158.90 160.94 312.5 313.4 342.3 338.1 0.1820 0.1843 5.4933 5.4251 1177.4 1177.6 214.42 217.13 894.1 893.4 162.8 164.7 63 64 80 81 162.98 165.01 314.3 315.1 334.3 330.3 0.1866 0.1888 5.3576 5.2947 1177.8 1178.1 219.84 222.55 892.7 892.2 166.6 168.5 65 66 82 167.05 315.9 326.4 0.1911 5.2327 1178.4 225.25 891.7 170.4 67 83 84 169.09 171.12 316.7 317.5 322.6 318.8 0.1926 0.1956 5.1916 5.1114 1178.7 1178.9 227.96 230.68 891.1 890.5 172.3 174.2 68 69 70 71 85 86 173.16 175.20 318.4 319.2 315.2 311.7 0.1979 0.2002 5.0522 4.9955 1179.1 1179.4 233.38 236.09 889.8 889.3 176.1 178.0 87 177.24 320.0 308.2 0.2024 4.9399 1179.7 238.79 888.8 179.9 72 88 89 179.27 181.31 320.8 321.6 304.8 301.5 0.2047 0.2069 4.8855 4.8322 1179.9 1180.1 241.50 244.21 888.1 887.5- 181.8 183.6 73 74 90 183.35 91 185.38 322.4 323.2 298.2 295.0 0.2092 0.2114 4.7803 4.7293 1180.3 1180.6 246.91 249.62 886.9 886.4 185.4 187.3 75 76 92 187.32 324.0 291.9 0.2137 4.6794 1180.9 252.33 885.9 189.2 77 93 189.46 94 191.50 324.7 325.4 288.9 285.9 0.2159 0.2182 4.6305 4.5827 1181.1 1181.3 255.04 257.75 885.3 884.8 191.0 193.2 78 79 156 PROPERTIES OF WATER. TABLE XLII. Water. Temperature of the water. Volume, water = Weight. Ibs. per Bulk, cubic feet Units of heat in wate Total per r from 32 to T. Latent per Cent. .Fahr. 1 at 40. cubic ft. per pound. pound. cubic foot. pound. cubic ft. T T V ? e h. h'. I. I'. 163.4 326.2 1.09578 56.934 0.01756 297.32 16928 3.121 177.7 163.8 327.0 1.09617 56.914 0.01756 298.14 16966 3.142 178.8 164.2 327.7 1.09655 56.894 0.01757 298.86 17004 3.163 179.9 164.6 328.5 1.09092 56.875 0.01758 299.68 17046 3.183 181.0 165.0 329.2 1.09730 56.855 0.01758 300.40 17078 S.204 182.1 165.4 329.9 1.09768 56.836 0.017.7.) 301.12 17114 3.222 ls:;.i 165.9 330.7 1.09804 56.818 0.01759 301.94 17149 3.240 184.1 166.3 331.3 1.09840 56.804 0.01760 302.56 17183 3.258 185.1 166.7 331.9 1.09876 56.786 0.01760 303.17 17217 3.276 186.0 167.0 332.6 1.09911 5(5.7(59 0.01761 ;;o:j,st) 17251 3.294 186.9 167.3 333.3 1.09949 5(5.743 0.01761 :;o 1.111 17284 3.312 187.9 167.7 334.0 1.09984 56.725 0.01762 305.33 17318 3.330 189.0 168.0 334.7 1.10019 56.706 0.01763 306.05 17350 3.349 190.0 168.4 335.4 1.10055 56.688 0.01763 306.77 17384 3.368 191.0 168.8 336.1 1.10091 56.670 0.01764 307.49 17427 3.387 192.0 169.2 336.8 1.10125 56.652 0.01764 308.21 17461 3.406 193.0 169.6 337.4 1.10159 56.635 0.01765 308.82 17493 3.425 194.0 170.0 338.0 1.10193 56.618 0.01766 309.44 17525 3.444 195.0 170.4 338.7 1.10226 56.600 0.01766 310.16 17557 3.462 196.0 170.8 339.4 1.10260 56.583 0.01767 310.88 17589 3.481 197.0 171.1 340.0 1.10292 56.566 0.01768 311.50 17(521 3.500 198.0 172.9 343.2 1.10459 56.483 0.01770 314.79 17772 3.590 202.8 174.5 346.2 1.10627 56.403 0.01773 317.88 17921 3.678 207.5 176.2 349.2 1.10787 56.326 0.01775 320.96 18068 3.763 212.1 177.7 352.0 1.10940 56.236 0.01778 :;-j:;.s.-) 18212 3.850 216.5 179.2 354.8 1.11070 56.166 0.01780 326.73 18349 3.927 220.8 180.7 357.4 1.11208 56.098 0.01782 329.41 18481 4.010 225.0 182/2 360.0 1.11344 56.031 0.01784 332.09 18607 4.090 229.0 183.7 362.5 1.11478 55.965 0.01787 334.67 18730 4.168 233.3 185.0 365.0 1.11613 55.900 0.01789 337.24 18850 4.244 237.2 186.5 367.4 1.11742 55.834 0.01791 339.72 18966 4.318 241.0 188.0 369.8 1.11869 55.770 0.01793 342.19 19080 4.390 244.6 188.5 372:0 1.11993 55.708 0.01795 344.46 19190 4.460 248.5 190.0 374.2 112109 55.648 0.01797 346.73 19296 4.530 252.1 191.2 376.4 1.12227 55.591 0.01799 349.00 19399 4.598 255.7 192.5 378.5 112343 55.534 0.01800 351.16 19501 4.666 259.1 193.7 380.6 1.12456 55.477 0.01802 353.33 19602 4.731 262.5 194.4 382.6 1.12561 55.426 0.01804 355.39 19698 4.794 265.7 197.0 386.6 1.12783 55.317 0.01807 359.54 19885 4.940 272.8 199.1 390.4 1.13000 55.211 0.01811 363.48 20068 5.0S2 279.8 PROPERTIES OF STEAM. 157 TABLE XLIII. Steam. Total i Ibs. aersq. inch. >ressure. Inches inercur. Tem- perat're Fahr. Volume water = 1 at 40. Weight Ibs. per cubic ft. Bulk cubic ft. per Ib. Units of heat Total per pound, cubic ft. Jom32 pound. to f, t per cubic ft. 1'rcssiire above at- mosphere. P 96 97 98 99 193.53 195.57 197.61 199.65 201.68 T 326.2 327.0 327.7 328.5 329.2 283.0 280.2 277.4 274.7 272.0 f 0.2204 0.2227 0.2249 0.2271 0.2294 G 4.5361 4.4902 4.4454 4.4017 4.3591 H 1181.5 1181.8 1182.1 1182.3 1182.5 H' 260.46 263.16 265.86 268.55 271.2:; L 884.2 883.8 883.3 882.6 882.1 L' 194.9 196.7 198.6 200.4 202.3 P 80 81 82 83 84 100 101 102 103 104 107 108 109 203.72 205.76 207.79 209.83 211.87 329.9 330.7 331.3 331.9 332.6 269.4 266.8 264.3 261.8 259.4 0.2316 0.2338 0.2360 0.2382 0.2405 4.:; 17ti 4.2769 4.2367 4.1970 4.1577 1182.7 1182.9 1183.1 1183.3 1183.5 273.93 276.63 279.32 282.62 284.70 881.6 881.0 880.6 880.1 879.6 204.2 206.1 208.0 209.8 211.6 85 86 87 88 89 213.91 215.94 217.98 220.02 222.06 333.3 257.0 334.0 254.6 334.7 j 252.3 335.4 250.1 336.1 247.9 0.242814.1187 0.24504.0813 0.2472 4.0444 o.2 ]'.''> 4.0081 0.2517 3.9723 1183.7 1183.9 1184.1 1184.3 1184.5 287.40 290.09 292.78 295.48 298.18 879.1 879.6 878.1 877.5 877.0 213.4 215.2 217.0 218.9 220.7 90 91 92 93 94 110 111 112 113 114 TuT 120 125 130 135 MO" 145 150 155 160 "l65~ 170 175 180 185 224.10 226.13 228.17 230.20 232.24 336.8 337.4 338.0 338.7 339.4 245.7 243.5 241.4 239.3 237.3 0.2540 3.9376 0.256H3.9036 0.258413.8701 0.2603| 3.8411 0.26283.8047 1184.7 1184.9 1185.1 1185.3 1185.5 300.87 303.56 306.26 308.94 311.65 876.5 876.1 875.7 875.1 874.6 222.6 224.4 226.3 228.1 229.9 95 96 97 98 99 234.28 244.4 254.6 264.8 275.0 340.0 343.2 346.2 349.2 352.0 235.3 226.0 217.2 209.1 201.4 0.265113.7722 0.2759 1 3.6244 0.2867 3.4875 0.2984' 3.3516 0.3098 j 3.2278 1185.7 1186.6 1187.5 1188.4 1189.3 314.33 327.89 341.44 355.00 368.55 874.2 873.8 869.6 867.4 865.5 231.8 241.0 250.1 259.0 268.1 100 105 110 115 120 285.2 295.4 305.6 310.8 325.9 354.8 357.4 360.0 362.5 365.0 194.3 187.8 181.8 176.5 171.5 0.3212,3.1139 0.3322; 3.0105 0.3432 1 2.9136 0.3534! 2.8289 0.36462.7432 1190.1 1190.9 1191.7 1192.5 1193.3 381.88 395.16 408.38 421.54 435.08 863.5 861.5 859.6 857.8 856.1 277.0 275.8 294.5 303.2 312.1 125 130 135 140 145 336.0 346.3 356.5 366.7 376.9 367.4 369.8 372.0 374.2 376.4 166.6 161.1 157.0 152.8 148.8 0.37562.6617 0.38712.5831 0.39732.5171 0.4075 2.4541 0.4182;2.3916 1194.0 1194.7 1195.4 1196.1 1196.8 448.64 462.22 475.80 488.96 502.10 854.3 852.5 851.0 849.4 847.8 321.0 329.9 338.7 347.1 355.5 150 155 160 165 170 190 378.1 195 387.3 200 407.4 210 427.8 220 '448.2 378.5 380.6 382.6 386.6 390.4 145.0 141.5 138.1 132.0 126.3 0.4292 : 2.3299 0.4409,2.2684 0.4517 2.2137 0.4719' 2.1 192 0.4935 12.0265 1197.4 1198.1 1198.7 1199.8 1201.0 515.20 528.27 542.07 568.40 574.70 846.2 844.8 843.3 840.3 837.5 363.9 372.4 381.0 398.0 414.8 175 180 185 195 205 158 PROPERTIES OF WATER. TABLE XLIV. "Water. Tt-mpe of the Cent. rature water. Fahr. Volume, water = 1 at 40. ~V~~ 1.13210 1.13301 1.13577 1.13760 1.13944 Weight. Ibs. per cubic ft. Bulk. cubic feet per pound. Unite of Tots pound. icat in wat 1 per cubic foot. er from C I.iit'-i pound. i .'/. tper cubic ft. ~l'~ 286.6 292.9 299.1 305.2 311.2 T 201.1 203.5 205.0 206.8 208.7 T 394.0 397.6 401.0 404.3 407.5 f 55.108 55.017 54.926 54.838 54.752 e 0.01814 0.01817 0.01821 0.01824 0.01826 h. 367.20 370.92 374.44 357.86 381.18 h'. 20236 20402 20561 20720 L'OSTO I. 5.200 5.318 5.437 5.558 5.679 210.2 211.9 213.6 215.1 216.7 410.6 413.5 416.5 419.2 422.1 1.14119 1.14285 1.14441 1.14589 1.14743 54.670 54.590 54.514 54.440 54.367 0.01829 0.01832 0.01834 0.01837 0.01839 liSJ.II) 387.40 390.50 393.31 3!)0.:;i 21015 21147 21273 21394 21510 5.800 5.903 6.006 6.109 6.212 317.1 324.6 332.0 339.5 346.7 ~353T 356.9 359.9 362.8 365.6 218.2 219.6 221.1 222.4 223.6 424.8 427.4 430.0 432.4 434.9 ~43L3~ 439.6 441.9 444.1 446.4 1.14897 1.15050 1.15202 1.15339 1.15481 54.299 54.230 54.161 54.093 54.024 0.01841 0.01844 0.01846 0.01849 0.01851 399.11 401.82 404.52 407.02 409.63 21622 21751 21876 21997 22114 6.315 6.418 6.521 6.624 6.727 225.1 226.4 227.7 228.9 230.2 281.4 232.5 233.6 234.7 235.9 1.15621 1.15764 1.15880 1.16003 1.16127 53.959 53.895 53.834 53.777 53.721 0.01853 0.01856 0.01858 0.01859 0.01861 412.13 414.53 416.92 419.21 421.60 22238 22347 22452 22553 22650 6.830 6.926 7.020 7.111 7.200 368.5 373.2 377.9 382.5 386.9 391.1 395.3 399.4 403.6 407.3 448.5 450.6 452.6 454.6 456.7 1.16250 1.16372 1.16494 1.16571 1.16695 53.667 53.614 53.563 53.513 53.455 0.01863 0.01865 0.01867 0.01869 0.01871 423.79 425.97 428.06 430.14 432.32 22744 22843 22938 23029 23116 7.288 7.374 7.459 7.542 7.623 237.0 238.0 239.0 241.1 244.1 ~24675~ 248.8 253.1 257.2 261.0 458.7 460.6 462.5 466.1 471.5 1.16818 1.16942 1.17066 1.17274 1.17598 53.406 53.352 53.293 53.158 53.027 0.01872 0.01874 0.01876 0.01881 0.01886 434.40 436.38 438.39 442.21 447.83 23200 23282 23363 23555 23741 7.700 7.787 7.893 8.113 8.329 411.2 415.5 423.3 433.2 442.9 475.7 479.8 487.6 494.9 501.8 1.17917 1.18231 1.18531 1.18961 1.19343 52.900 52.768 52.588 52.430 52.264 52.102 51.943 51.787 51.642 51.498 0.01890 0.01895 0.01901 0.01907 0.01913 ~aoi9~i{f 0.01925 0.01931 0.01936 0.01942 452.24 456.55 464.66 472.28 479.51 23923 24091 24436 24762 25061 8.541 8.747 9.060 9.381 9.710 452.4 461.6 476.5 491.8 507.5 263.5 268.1 271.9 273.3 277.5 508.4 514.6 521.4 526.0 531.6 1.19742 1.20131 1.20562 1.20812 1.21147 486.40 492.97 500.14 505.00 510.S4 25577 25606 25901 26079 26307 10.00 10.37 10.74 11.00 11.242 521.0 538.7 556.2 568.1 578.8 PROPERTIES OF STEAM. 159 TABLE XLV. Steam. Total Ibs. per so., inch. >ressure. Inches inercur. Tem- pi-riit're Fahr. Volume water = 1 at 40. Weight Hi-. |MT cubic fl. Bulk cubic ft. per Ib. Units of heat Total per pound, cubic ft. rom 32 Later pound. toT. t per cubic ft. m n P 230 240 250 260 270 / 468.5 488.9 509.3 529.7 550.0 T 394.0 397.6 401.0 404.3 407.5 If 120.8 116.1 111.7 107.5 103.7 A tP 0.5165 0.5364 0.5595 0.4803 0.6016 G 1.9360 1.8646 1.7874 1.7230 1.6621 H 1202.2 1203.2 1204.2 1205.2 1206.2 H' 620.96 (J47.41 673.85 700.28 726.66 L 835.0 832.3 829.8 827.4 825.0 11 431.3 447.9 464.4 480.8 497.1 P 215 225 235 245 255 280 290 300 310 320 570.4 590.8 611.1 631.5 651.9 410.6 413.5 416.5 419.2 422.1 100.2 97.01 94.22 91.13 88.21 0.6238 0.6459 0.6681 0.6896 0.7107 1.6031 1.5481 1.4967 1.4499 1.4071 l~207".2 1208.1 1209.0 1209.8 1210.6 753.04 779.40 805.74 832.96 858.36 822.8 820.7 818.6 816.5 814.4 513.3 529.4 545.4 561.4 577.3 265 275 285 295 305 330 340 350 360 370 672.3 692.6 713.0 733.4 753.8 424.8 427.4 430.0 432.4 434.9 85.44 83.19 80.99 78.84 76.74 0.7302 1.3695 0.7547 1.3250 0.7745 1.2915 0.7943 1.259U 0.81461.2275 1211.5 1212.3 1213.1 1213.9 1214.7 884.63 910.89 937.13 963.34 989.51 812.4 810.5 808.6 806.9 805.1 593.2 608.9 624.5 640.2 655.8 315 325 335 345 355 380 390 400 410 420 774.1 794.5 814.9 835.2 855.6 437.3 439.6 441.9 444.1 446.4 74.66 72.90 71.19 69.52 67.90 0.8353 0.8626 0.8745 0.8952 0.9142 1.1968 1.1597 1.1434 1.1170 1.0938 1215.5 1216.2 1217.9 1218.6 1219.3 1015.7 1041.8 1067.9 1094.0 1120.2 803.4 801.7 800.0 799.4 797.7 671.3 686.7 702.0 717.2 732.4 365 375 385 395 405 430 440 450 460 470 876.0 896.4 916.7 937.1 957.5 448.5 450.6 452.6 454.6 456.7 66.34 64.91 63.55 62.22 60.94 0.9400 1.0634 0.9599 1.0417 0.9804 i 1.0201 1.00070.9993 1.0211 jO.9793 1218.8 1219.5 1220.1 1220.7 1221.3 1146.3 1172.3 1198.3 1124.3 1150.4 795.0 793.5 792.0 790.5 789.0 747.6 762.8 777.9 792.9 807.8 415 425 435 445 455 4SO 490 500 525 550 1X5 600 650 700 750 977.8 998.2 1018.6 1069.5 1120.4 458.7 460.6 462.5 466.1 471.5 59.72 58.54 57.45 54.81 52.47 1. 0446^0.9573 1.0t552 0.9388 1.0859 0.9209 1.1381:0.8786 1.1890 0.8410 1221.9 1222.5 1223.0 1224.5 1225.8 1276.5 1302.3 1328.1 1392.6 1456.9 787.5 786.1 784.7 782.3 778.0 822.7 837.4 852.1 881.8 921.3 465 475 485 510 535 1171.4 1222.3 1324.2 1426.0 1527.9 475.7 479.8 487.6 494.9 501.8 50.32 48.35 44.75 41.70 39.05 1.2397 1.2901 1.3943 1.4961 1.5977 0.8066 0.7751 0.7172 0.6684 0.6259 1227.2 1228.3 1230.6 1232.7 1234.9 1521.0 1584.8 1709.5 1933.8 2057.7 775.0 771.8 766.0 760.4 755.4 960.4 1000 1082 1157 1234 560 585 635 685 735 800 1629.8 850 1731.6 900 1833.5 '.)>< 1935.5 1000 2037.2 508.4 514.6 521.4 526.0 531.6 36.73 34.68 32.87 31.21 29.73 1.6986 0.5887 1.7989 0.5554 1.8979 0.5269 1.9992 0.5002 2.098610.4766 1237.0 1238.9 1241.0 1242.4 1243.5 2101.2 2228.3 2355.4 2482.5 2609.6 750.6 745.9 740.0 737.4 732.3 1307 1374 1435 1490 1538 785 835 885 935 985 160 MEAN PRESSURE. TABLE XLVI. Mean Pressure of Expanding Steam. Absolute steam pressure. P 1.333 1 On 1.5 Stea t Ie of expansion of 1.6 | 2 lu cut off at I, from I * team, denoted by 3 2.666 3 beginning of strok 1 i t. 4 e. | 8 1 0.5 1 0.4826 0.9652 0.4683 0.9367 0.4587 0.9175 0.4232 0.8465 0.3713 0.7426 0.3497 0.6995 O.-J'.IS-J 0.5965 0.1924 0.3849 2 1.9304 1.8734 1.8350 1.6931 1.4482 1.3991 1.1931 0.7698 3 4 2.8956 3.8608 2.8100 3.7468 2.7524 3.6700 2.5396 3.3862 2.2280 2.8964 2.0986 2.7982 1.7897 2.3862 1.1548 1.5396 5 6 4.8262 5.7914 4.6835 5.6202 4.587;-, 5.5050 4.2328 5.0794 3.7133 4.4559 3.4977 4.1972 J.'.ix-js 3.5794 1.9246 2.3095 7 6.7566 6.5569 6.4225 5.9260 5.1966 4.8967 4.1760 2.6944 8 9 7.7216 8.6866 7.4936 8.5303 7.3400 8.2574 6.7726 7.6192 5.9413 6.6840 5.5963 6.2958 4.7726 5.3692 3.0794 3.4643 10 11 9.6524 10.617 9.3670 10.304 9.1750 10.092 8.4657 9.3123 7.4267 8.1694 6.9954 7.6949 5.9657 6.5622 :;<>:; 4.2342 12 11.583 11.240 11.010 10.159 8.9121 8.3944 7.1589 4.6191 13 14 12.548 13.513 12.177 13.113 14.050 14.987 11.927 12.845 11.005 11.852 12.69S~ 13.545 9.6548 10.397 9.0940 9.7935 7.7555 8.3520 5.0041 5.3890 15 16 14.478 15.443 13.762 14.679 11.140 11.882 10.493 11.192 8.94So 9.5451 5.7739 6.1588 17 16.408 15.923 15.597 14.392 12.625 11.892 10.141 6.5437 18 19 17.373 18.339 16.860 17.797 16.514 17.432 15.238 16.085 13.368 14.110 12.591 13.291 10.738 11.335 6.9287 7.3136 20 21 19.304 20.269 18.734 19.671 18.350 19.268 16.931 17.778 14.853 15.596 13.991 14.690 11.931 12.527 7.6986 8.0835 22 21.234 20.508 20.185 18.625 16.339 15.390 13.124 8.4684 23 24 22.199 23.165 21.545 22.481 21.103 22.020 19.471 20.318 17.082 17.823 16.089 16.789 13.720 14.317 8.8534 9.2383 25 26 24.130 25.096 23.481 24.355 J2.1C5S 23.855 21.164 22.011 18.567 19.318 17.488 18.188 14.913 15.511 9.6232 10.008 27 26.061 25.291 24.773 22.857 20.052 18.887 16.107 10.393 28 29 27.026 27.991 28.956 29.920 26.228 27.165 25.690 26.607 23.704 24.551 20.795 21.538 19.587 20.287 16.704 17.300 10.778 11.162 30 31 28.100 29.036 27.524 28.440 25.396 26.244 22.280 23.022 20.986 21.684 17.897 18.493 11.548 11.932 32 30.886 29.974 29.358 27.090 23.764 22.384 19.090 12.317 33 34 31.852 32.816 30.910 31.846 30.276 31.194 27.936 28.784 24.508 25.250 23.084 23.784 19.687 20.282 12.702 13.087 35 36 33.782 34.746 32.784 33.720 32.110 33.028 29.630 30.476 25.992 26.736 24.484 25.182 20.880 21.476 13.472 13.857 37 35.712 34.656 33.946 31.322 27.478 25.882 22.072 14.242 38 39 36.678 37.642 35.594 36.530 34.864 35.780 32.170 33.016 28.220 28.964 26.582 27.282 22.670 23.266 14.627 15.012 MEAN PRESSURE. 161 TABLE XLVII. Mean Pressure of Expanding Steam. Absolute steal n pressure. P 1.333 I On 1.5 Stea I de of expi 1.6 m cut off 1 MM. Ill Of 2 *t I, from } stc.-iin. de 2.666 beginnin 1 . loted by 3 3 j of strok i L 4 B. | 8 i 50 55 48.262 53.088 4i;.s:;.-> 51.518 45.875 50.462 42.328 46.561 37.133 40.846 34.977 38.474 2'J.H'JS 32.811 19.246 21.170 60 57.914 56.202 55.050 50.794 44.559 41.972 35.794 23.095 65 70 62.740 67.566 60.885 65.569 59.637 64.225 55.027 59.260 48.273 51.986 45.470 48.967 38.777 41.760 25.020 26.944 75 80 85 72.:):J 77.216 82.042 70.252 74.936 79.619 68.812 73.400 77.987 63.493 67.726 71.959 55.700 59.413 63.126 52.465 55.963 59.461 44.743 47.726 50.709 28.869 30.794 ; 32.718 90 95 86.866 91.699 85.303 89.986 82.574 87.163 76.192 80.425 66.840 70.553 62.958 66.456 53.692 56.675 34.643 i 36.568 ! , 100 105 96.524 101.35 93.670 98.353 91.750 S6.337 84.657 88.890 74.267 77.981 69.954 73.451 59.657 62.640 38.493 40.417 110 106.17 103.04 100.92 93.123 81.694 76.949 65.622 42.342 115 120 111.00 115.83 107.72 112.40 105.51 110.10 97.356 101.59 85.407 89.121 80.447 83.944 68.606 71.589 44.267 46.191 125 130 120.65 125.48 117.08 121.77 114.68 119.27 105.82 110.05 92.834 96.548 87.442 90.940 74.572 77.555 48.116 50.041 135 130.30 126.45 123.86 114.28 100.26 94.437 80.538 51.966 140 145 135.13 139.96 131.13 135.82 128.45 133.03 118.52 122.75 103.97 107.68 97.935 101.43 83.520 86.502 53.890 55.815 150 155 144.78 149.60 140.50 145.18 137.62 142.20 126.98 131.22 111.40 115.11 104.93 108.42 89.485 92.468 57.739 59.663 160 154.43 149.87 146.79 135.45 118.82 111.92 95.451 61.588 165 170 159.26 164.08 154.55 159.23 151.38 155.97 139.68 143.92 122.54 126.25 115.42 118.92 98.434 101.41 63.513 65.437 175 180 168.91 173.73 1 (53.02 168.60 160.55 165.14 148.15 152.38 129.96 133.68 122.42 125.91 104.40 107.38 67.362 69.287 185 178.56 173.28 169.73 156.61 137.39 129.41 110.36 71.212 190 195 183.39 188.21 177.97 182.65 174.32 178.90 160.85 165.08 141.10 144.82 132.91 136.41 113.35 116.33 73.136 75.061 200 210 193.04 202.69 187.34 196.71 1X:!..->0 192.68 169.31 177.78 148.53 155.96 139.91 146.90 119.31 125.27 76.986 80.835 220 212.34 205.08 201.85 186.25 163.39 153.90 131.24 84.684 230 240 221.99 231.65 241.30 250.96 215.45 224.81 211.03 220.20 194.71 203.18 170.82 178.23 160.89 167.89 137.20 143.17 88.534 92.383 250 260 234.18 243.55 229.38 238.55 211.H4 220.11 185.67 193.18 174.88 181.88 149.13 155.11 96.232 100.08 270 260.61 252.91 247.73 228.57 200.52 188.87 161.07 103.93 280 300 270.26 289.56 262.28 281.00 256.90 275.24 237.04 253.96 207.95 222.80 195.87 209.86 167.04 178.97 107.78 115.48 1C2 STEAM ENGINEERING. STRENGTH OF SPHERICAL, SHELLS OF STEAM-BOILERS. Addendum to 86, page 105. 126. For a spherical shell the tension or strain is equal to the area of the great circle in square inches multiplied by the steam pressure per square inch, which is resisted by the section of the shell in the great circumference. When only a part of the sphere is used, like in spherical ends of boilers or steam-drums, the same rule holds good, only that the strength must be calculated for the whole sphere. R = radius of the sphere in inches. p = steam pressure in pounds per square inch. t = thickness of shell in fraction of an inch. S = ultimate strength of the iron in pounds per square inch. Action of steam, pit R? = St2K R, the reaction of the shell. Ultimate Strength of Solid Shell in the Sphere without Riveted Joints. Steam pressure, p = 1 R f\ i O Radius of sphere, R = 2 Thickness of shell, * = ^. . . . . .3 2 S Breaking-strain, S *- 4 Example 1. The spherical end of a boiler is made of iron stamped S = 60,000 and t = 0.25 of an inch thick in one sheet without joints. What steam bursting-pressure can that spherical end stand with a radius of curvature R = 96 inches ? 2x0.25x60000 , Steam-pressure, p = = 312.5 pounds. yt) These formulas are the same as those for cylindrical shells, with the exception that the radius R of the sphere takes the place for the diameter D of the cylinder. Therefore a sphere is double as strong as a cylinder of the same diameter. The coefficient X for safety strength will therefore be the same .as for cylindrical shells, 86, page 105, namely, SPHERICAL BOILER-ENDS. 163 TABLE XXVI. Coefficients A' for Spherical Ends. Construction of Shell. X Per cent, of strength. Solid plate without joints 0.5 100 Double-riveted drilled holes 04 80 Double-riveted punched holes 0.35 70 Single-riveted drilled holes 0.3 60 Single-riveted punched holes 0.25 50 Steam-pressure, Radius of shell, Thickness of plate, p = XtS R XtS . 5 Breaking-strain, . 8 The radius E, of the spherical end, is independent of the diameter Z), of the boiler or steam-drum. Example 6. What radius is required for a spherical boiler-end of solid plate = 0.3 of an inch thick and stamped S = 64,000 to bear with safety a steam-pressure of p = 80 pounds per square inch ? Radius, 0.5x0.3x64000 80 120 inches. Example 7. The iron for a spherical boiler-end is expected to bear S= 56,000 pounds to the square inch of section, is to be curved to a radius R = 84 inches, and to have one double-riveted lap-joint with punched holes, and to bear a steam-pressure of p = 96 pounds to the square inch. Required the thickness of the iron? Thickness, 84x96 0.35x56000 = 0.411 of an inch. 164 STEAM ENGINEERING . PHYSICAL PROPERTIES OF DIFFERENT KINDS OF VAPORS. 127. The following Table 48 shows the relation between temper- ature and pressure of vapors composed of the four principal simple ele- ments namely, oxygen, nitrogen, hydrogen and carbon. The table is deduced from the experiments of Regnault, except the column for car- bonic acid, which is deduced from the experiments of Faraday and Pelouze; but those experimenters are not responsible for the formulas and tables which the writer has deduced from their experiments. The vapors of water and carbonic acid have been treated in the pre- ceding pages, and the next in order in the table is turpentine. Oil of Turpentine is distilled from resin of pine trees. It is a vola- tile spirit composed of C w HW, and boils under atmospheric pressure at a temperature of 338 Fahr. The table gives the pressure under which it boils at different temperatures. The formulas for pressure and temperatures of turpentine vapor are T=281 V 6 P-115. 281 Turpentine is a transparent liquid or gas insoluble in water, but dissolves paints and many gums and resins. Alcohol. Pure alcohol, CtH 6 2 , boils under atmospheric pressure at a temperature of 173 Fahr. The formulas for pressure and tem- perature of alcoholic vapor are T=l80yT- 108. . . . .1 The ideal zero of vapor of alcohol, according to the formula, should be -108 below Fahr. zero. The pressure of vapor of alcohol is about double that of steam of equal temperature, as will be seen in the Table. The vapor of alcohol has been tried in France as motive power, and a large pas- senger steamer named " Kabyl," built in the year 1857, was supplied with engines and boilers for the use of alcohol instead of water. The PROPERTIES OF DIFFERENT KINDS OF VAPORS. 165 " Kabyl " was running from Marseilles to ports in the Mediterranean in the year 1858 with partial success, but the alcohol was finally abandoned for the reason that its saving in fuel did not compensate for the leakage of the more expensive fluid. The vapor of the alcohol was condensed in an ordinary tubular fresh-water condenser and returned to the boiler, thus used over again perpetually. The difficulty appeared to be the leakage of alcohol, and conse- quently the expense of supplying that fluid. The writer was on board the " Kabyl " during the first trial trip, but the memorandum then made has been lost. The first trial was made with ether, which was gradually converted into alcohol that is, one atom of oxygen and one of hydrogen formed water but even with this change in the fluid the consumption of fuel proved to be very economical. One great advantage in using alcohol or ether instead of water in steam-boilers is that no incrustation is formed. > There was a very strong, but rather pleasant, odor of alcohol all over the ship, of which the passengers did not seem to complain. Ether. Pure ether, C 4 H b O, boils under atmospheric pressure at a temperature of 97 Fahr. The pressure of vapor of ether is five to six times that of steam of equal temperature, as seen in the accom- panying table. The formulas for pressure and temperature of etheric vapor are T=200v/P-216 1 The ideal zero is - 216. Benzine is a transparent liquid insoluble in water and dissolves fatty matter. It boils under atmospheric pressure at a temperature of 185 Fahr. The following Table L. shows the boiling point of benzine under different pressures. The formulas for pressure and temperature of vapor of benzine are T = 222 1 / / P-162 1 166 STEAM ENGINEERING. Ammonia, N H 3 , is a colorless vapor or liquid which boils under atmospheric pressure at about - 19.3 below Fahr. zero. The specific gravity of the liquid is about 0.76, and according to Faraday's ex- periments, freezes to a white transparent solid at - 103 Fahr., at which temperature the pressure of its vapor is about 5 pounds to the square inch. Ammonia is soluble in water, with which it generates heat, forming aqueous ammonia of great expansibility. The high tension of ammonia at low temperatures is made use of in producing cold, for which purpose liquid ammonia is kept under very high pressure in a vessel, from which a small quantity is allowed to gradually escape into another vessel or tube, where it instantly evap- orates, and the heat absorbed by that evaporation produces a very low temperature of the surrounding vessel or tube, so that water in the neighborhood will freeze to ice. This is the principle upon which ice-machines are constructed. The formulas for pressure and temperature of vapor of ammonia are Protoxide of Nitrogen, NO. This vapor is also called nitrous oxide or laughing gas, from its peculiar effect upon the mind when inhaled. The specific gravity of nitrous oxide is 1.524. The formulas for pressure and temperature of protoxide of nitro- gen are T=175 l /P~-464 ..... 1 The last column in the table shows the pressure per square inch of nitrous oxide, corresponding to the temperatures in the first columns. The Roman numbers in the table are converted from Regnault's experiments,* and the Italic numbers are calculated by the respective formulas. The object in giving this table is to show at a glance the widely different physical properties of vapors composed of only oxygen, nitro- gen, hydrogen and carbon. * Memoires de 1'Academie de France, Tome XXVI. PHYSICAL PROPERTIES OF VAPORS. 167 TABLE XLVIII. Temperature and Pressure in Pounds per Square Inch of Different Kinds of Vapor. Tempe Cent. atures. Fahr. Water, Steam. Carbonic acid. Turpen- tine. Alcohol. Ether of alcohol. Ben- zene. Ammo- nia. Protoxide of nitrogen. T T HO C0 2 CioHia C 4 H e O, C 4 H 5 Ci2H 6 NH 3 NO 40 40 164.8 0.464 8.4 202 35 31 193.4 0.626 12.0 246 30 22 0.007 225.7 0.833 0.025 16.72 270 25 13 0.012 261.8 1.092 0.049 2L4 304 20 4 0.18 302.1 0.064 1.33 0.112 26.9 340 15 + 5 0.027 346.9 0.098 l!73 0.17 33.6 381 10 14 0040 396.5 0.125 222 0.25 41.6 425 5 23 0.060 451.2 0.176 2.82 0.355 50.8 476 32 0.089 514.5 6.64" 0.245 357 0.489 61.6 530 + 5 41 0.127 577.4 0.047 0.341 4.47 0.66 74. 591 10 50 0.177 649.6 0.057 0.469 5.54 0.875 88.4 658 15 59 0.246 735.0 0.069 0.638 6.84 1.14 105. 732 20 68 0.337 814.2 0.086 0.859 8.37 1.46 123.2 813 25 77 0.456 886.6 0.105 1.15 10.2 1.85 145 903 30 86 0.61 1008 0.133 1.517 12.27 2.33 168 1000 35 95 0.808 1117 0.151 2. 14.7 2.89 195 1110 40 104 1.06 1234 0.208 2.583 17.55 3.55 223.8 1225 45 113 1.38 1362 0.257 3.33 20.8 4.34 258 1300 50 122 1.78 1471 0.328 4.25 24.42 5.24 293 1400 55 131 2.27 1644 0.405 5.38 28.7 6.3 333 1520 60 140 2.88 1817 0.511 6.78 33.33 7.54 376.5 1686 65 149 3.61 1968 0.631 8.44 38.7 8.97 425 1838 70 158 4.51 2147 0.785 10.45 45.4 10.6 476 2018 75 167 5.58 2352 0.958 12.9 51.2 12.4 534 2231 80 176 6.86 2542 1.183 15.71 58.4 14.65 596 2403 85 185 8.37 2758 1.451 19.1 66.5 16.9 664 2607 90 194 10.2 2988 1.75 23. 75.3 19.6 736 2825 95 203 12.26 32S2 2.123 27.6 77.4 22.6 816 3082 100 212 14.7 3500 2.54 32.8 95.8 26. 900 3359 105 221 17.5 3770 3.00 38.9 108 29.7 1008 3627 110 230 20.8 4060 3.59 45.75 120 33.7 1135 3926 115 239 24.5 4369 4.22 53.6 134 38.2 1268 4220 120 248 28.8 4695 4.76 62.6 149.3 43.2 1425 4558 125 257 33.8 5026 4.86 72.4 165 48.7 1572 4926 130 266 39.3 5394 6.73 83.6 194 54.6 1745 5272 135 275 45.5 5769 7.85 96. 218 61. 1934 5727 140 284 52.5 6165 8.97 109.9 245 66. 2143 6087 145 293 69.3 6586 10.35 125. 270 75.7 2364 6590 150 302 79. 7015 11.7 14L5 300 83.8 2607 7061 155 311 79. 7470 13.25 159.8 335 88.1 2879 7556 160 320 90. 7984 15. 187.1 354 96.7 3156 8128 165 329 102. 8462 16.9 214.3 409 105.9 3481 8710 170 338 115.5 9000 18.9 245.6 451 115.8 3798 9253 175 347 130. 9552 21. 283.4 497 126.2 4157 9914 180 356 146. 23.4 320 547 137.4 4545 185 365 163.5 25.9 360 601 149.3 4962 190 374 183. 28.5 401 659 162.0 5411 195 383 203.5 31.3 443 722 175.5 5892 200 392 226. 34.2 490 789 189. 6444 168 DISTILLATION OF PETROLEUM OILS. | 128. BOILING POINT UNDER ATMOSPHERIC PRESSURE. V'1477~= 1.565. Water, T = 200j> 1477 - 101 = + 21 2. Carbonic acid, T= 61.404^1477 - 260 = - 140. Turpentine, T= 281^/1477 - 115 = + 324.7. Alcohol, T= 180^1477 - 108 = +173.7. Ether, T= 200^/1477 - 216 = 4- 97. Benzine, T = 222 ^14J - 162 = + 185.4. Ammonia, T= 150^1477 - 254 = - 19.3. Protoxide of nitrogen, T = ITSjMiJ - 464 = - 190.2. BOILING POINT OR TEMPERATURE OF DISTILLATION OF PETROLEUM OILS. 129. The variety of oils distilled from petroleum boil at widely different temperatures, according to their specific gravity. The boil- ing point under atmospheric pressure varies, as the cube of the specific gravity, from the ideal zero - 215 Fahr. S = specific gravity of the oil compared with water as 1 at 32. T= temperature Fahr. at which the oil boils or distills under atmo- spheric pressure. Boiling point, T= 1150 S 3 - 215. . 1 81 f^ 2] 5' Specific gravity, S = ~~- 2 Example 1. The specific gravity of Kerosene oil is 0.808. Required its boiling point ? T= 1150 x 0.808 3 - 215 = 491.6 3 . TEMPERATURE OF INFLAMMATION OF OILS DISTILLED FROM PETROLEUM. 130. The volatility of distilled petroleum oils under atmospheric pressure ceases to exist under a certain temperature depending upon the sixth power of the specific gravity of the oil. Above that tem- perature the oil evaporates and mixes with the air, and can be ignited by a lighted match. PROPERTIES OF PETROLEUM OILS. 169 t = lowest temperature of inflammation, Fahr. S = specific gravity of the oil, water = 1. t = 1200 S 6 - 140. 1200 . 4 Undistilled or mixed oils will ignite at a lower temperature than this formula. Crude petroleum ignites at 60. Example 3. Required the lowest temperature of inflammation of Kerosene oil of specific gravity 0.805 ? t = 1200 x 0.805 8 - 140 = 180. TABLE L. Temperatures of Distillation and Inflammation of Petroleum Oils. Sp. K r. S Names of Petroleum Oils. Dist Fahr. illation. Cent. Inflam Fahr. mation. Cent. 0.6000 0.6125 0.625 0.6375 0.6500 0.6625 0.675 0.6875 0.7000 0.7125 0.7250 0.7375 0.7500 0.7625 0.7750 0.7875 0.8000 0.8125 0.8250 0.8375 0.850 0.8625 0.8750 0.8875 0.9000 34 49 63 83 101 119 139 159 180 201 219 246 270 295 320 347 375 402 424 460 490 524 555 589 623 1.11 9.44 17.22 28.33 38.33 48.33 59.44 70.55 82.22 93.88 103.8 118.8 132.2 146.1 160.0 187.7 190.5 205.5 217.7 237.7 254.4 273.3 290 304.4 328.3 -84 -76 -68 -59 -49 -38 -26 -13 2 18 35 54 74 97 121 142 176 207 240 276 314 356 399 447 498 -65 -60 -55 -51 -45 -39 -32 -25 -16 7.7 Amvlene Gasolene Toluene -t-1.66 12.2 23.3 36.1 5 49.4 61.1 79.4 97.2 115 135 156 180 204 230 259 Naphtha Naphtha or Pvridine Lutidine Paraffine Mineral Sperm Oil Lubricating Oil APPENDIX. TECHNICAL TERMS IN MECHANICS. THE science of Mechanics has heretofore been afflicted with a lan- guage of vague terms promiscuously used without definite meaning, so that different ideas have been formed from one and the same expres- sion and a variety of terms have been employed to express one and the same principle. The most crucial test of perfection of a science is precision in its vocabulary and perspicuity in its principles, so that each expression bears a definite meaning. The writer has for many years labored upon this subject namely, to expel some indefinite terms and expressions which have heretofore embarrassed the science of Mechanics. In discussing the subject he has encountered difficulties with learned men, many of whom appear to have only faith in the old dogmas, and have thus thrown obstacles in the way of success. Mr. William Dennison of East Cambridge, Mass., was the first one who understood and acknowledged the correctness of the new classifica- tion of dynamic elements and functions, and of their respective defini- tions. Mr. Dennisou addressed the author on the subject as follows : EAST CAMBRIDGE, MASS., May 12, 1874. MR. JOHN W. NYSTROM, Dear Sir In reading your pamphlet on Dynamics I have been greatly interested, as I always am on all such subjects ; .but this sub- ject should interest every one especially until its proper terms be adopted and their meaning permanently established. Except among mechanics you will seldom find any two persons to have the same ideas upon this subject, notwithstanding assertions to the contrary. The very fact that the simple question of force of a falling body was discussed by so many learned men, all with different ideas on the subject, and no two of them agreed as to which is right, is sufficient proof of ths present confusion in Dynamics, iro DENNISON'S COMMENTS. 171 Your reply to these jarring opinions, as well as to all other tions in the pamphlet, is forcible, correct and to the purpose. I consider the basis upon which you have placed this subject to be firm and well constructed, and of such a nature as never to be over- thrown or destroyed. You have also succeeded admirably in placing the subject in the most clear, comprehensive and proper light. Had there been such a treatise in our schooldays, it would have been of the greatest assistance to us all, then and since. But this sub- ject has always been in such a state of confounded conglomeration that we have been obliged to rely upon our own reasoning powers and practical understanding ; therefore but few comparatively have been able to master the subject. I have often been impressed with the idea that some scientific men like to nourish high-sounding terms, such as those you have rejected as useless and confusing. They often display extraordinary ability in Compiling highly scientific terms into heaps of phrases which may ap- pear learned to those not familiar with the subject, whilst they are sometimes mere inventions of words pretending to represent myste- rious phenomena. Yours truly, WILLIAM DENNISON. In a pamphlet on dynamical terms the writer invited institutions of learning to discuss the subject, which invitation was accepted by many, of which a few sided with the writer ; but the majority were against his views. The response of Professor Gustav Schmidt, of the Polytechnic Institute at Prague, in Bohemia, may serve as an average illustration of the present condition of the science of Mechanics in institutions of learning. The ideas on the subject held by others are substantially the same as those of Prof. Schmidt. In the following pages, the comments of Prof. Schmidt are on the left-hand and the answers on the right-hand pages, so that the num- bers of the paragraphs of the comments correspond to the numbers of the answering paragraphs. The division into paragraphs has been made by the author. 172 PROFESSOR SCHMIDT'S COMMENTS. (Translation from the German.) MR. JOHN W. NYSTROM, Dear Sir It affords me great pleasure to comply with your request for a written opinion on your work, " Principles of Dynamics," and will do so in German on account of my insufficient knowledge of the English language. 1. I have no objection to your answering me publicly in an American journal, provided you would publish an idiomatic transla- tion of this letter. 2. The term " Pferde-kraft " (horse-power) has become obsolete in Germany, and has been replaced by the term " Pferde-starke" (horse- ! strength), as proposed by Renleaux. The product ^ = F V= should consequently be called horse-strength. 3. It is customary, however, to use the word " effect," but not the word "kraft" (force), as under no circumstance would it answer for the German idiom to use the term "kraft" (power) for "effect" or " pferde-starke " (horse-strength or force). 4. The former Prussian "pferde-starke" undoubtedly had 513 second foot-pounds or 480 foot-pounds of the new weight ; this, how- ever, is not 582, but 544.8 English second foot-pounds. 5. The present German " pferde-starke " has, as in France, 75 second-metre kilogrammes = 542.5 English foot-pounds. 6. The unit proposed by you namely, 500 English foot-pounds would be 69, or nearly 70 metre kilogrammes, equal to the perform- ance of a horse at the plough. 7. As, however, the English measurement will probably give way to that of the French during this century, the 75 M. K. already adopted will most probably be retained. 8. The product F T (dynamical moment, as you call it) is never used. It could have a meaning only if the force F remains constant during the time T; then most certainly for a uniformly ac- celerated motion from a state of rest, F T would be = M V. 9. However, for a uniformly accelerated motion with an initial velocity C, F T= M ( V- (7) ; for instance, in the case of a vertical projection , then W gT=C-V and V=C-gT. NYSTROM'S ANSWER. 173 PROFESSOR GUSTAV SCHMIDT, Dear Sir It affords me great pleasure to answer your comments on my " Principles of Dynamics," and I hope the translation of your paper from German to English is satisfactory to you. 1. No American journal would publish this kind of discussion, for which reason I have concluded to append the same to this work on " Steam Engineering." 2. Both the terms "kraft" and "starke" in the German language mean " force." You have no German word for the function ^ = F V, which is power. Both your terms for horse-power mean horse-force. Strength or "starke" is the capability of resisting static force. igr F V= is power in effects. The products The term " Pferde-kraft " is more proper than " Pferde-sterke." 3. You say it is customary to use the word "effect" and give the other terms for which it is not used, but do not state for what it is used or what are its constituent elements. The term "effect" repre- sents a unit of measurement of power namely, a second foot-pound of power. Horse-power is another unit of power, consisting of 550 effects. You do not distinguish power from force in your language. 4. According to the data of Prussian weight and measure in my possession namely, 1.0297 ft. x 1.1023 Ibs. x 513 = 582.18 English foot- pounds. This, however, does not affect the correctness of the princi- ples of Dynamics. 5. I gave 542.47 English second foot-pounds per 75 second-metre kilogrammes, and did not know the new Prussian measures. 6. This unit was proposed only to accommodate the English weight and measure for the easy calculation and estimation of horse- power and practice. 7. It is yet doubtful whether the English measurement will give way for that of the French in the present century, of which only 24 years remain. 8. Because the momentum F Tis not used, is the reason why con- fusion still pervades the dynamics of matter. This momentum is there, whether it is used or not. When F is the mean force in the time T, the momentum must always be F T= M V. 174 PROFESSOR SCHMIDT'S COMMENTS. 10. For a variable force F, however, Ffit = M cv, or ,,dv W 6v , 8w F 11. Only this equation will answer for a general application ; M V F= - (force of a moving body), on the contrary, is quite super- fluous and inadmissible idea, as T, and consequently F, would be en- tirely arbitrary. 12. You entirely omit the above-mentioned highly important f\ TTT term g =- = which is the acceleration. ct M 13. For "work" in a moving body, JT=pf V* = W~, the old 9 term " lebendigo-kraft," living force, also sometimes " energie," en- ergy, is used in Germany. I have proposed for it " bervegungs arbeit," work of motion, to distinguish it from " verschriebungs arbeit," work of pushing or drawing, F S or universally / E cs. 14. We do not designate the value ^MV 1 " Grosse der Berve- gung," Quantitat der Bervegung (quantity of motion), but the pro- duct MV which you call (Bervegungs moment) moment of motion. 15. You reject the term "acting force" and "working force." If, however, the mass M is moved by a force F, which is exactly equal to the sum of all resistances F', and * te velocity V is consequently invariable, as, for instance, in the case with a train of cars, then F is a " working force " produ- cing the pushing or pulling work k = FS, which is consumed by the equally great resistance F'K' = F'S. Therefore the force F cannot cause any acceleration of speed. If the force F is greater than the resistance F', then there remains W an accelerating force f=F-F', which imparts to the mass M= the f acceleration g' = -==-r; = ~, if / is a constant quantity, or if / is inva- ^T M r\qj[ f riable it imparts the acceleration g' = = . This accelerating ct M force f=F-F' must not be mistaken for a non-accelerating but " working force " F, nor for a non-working but only " deformirender " NYSTROM'S ANSWER. 175 9. Motion and rest are only relative, for which reason the velocity V must always mean the difference of velocity caused by the action of the force F on a mass free to move, whether accelerating or retard- ing. 10. There is nothing in my treatise on Dynamics which contradicts your mathematical display. You will find these formulas in my " Ele- ments of Mechanics." 11. Your professorship is not invested with a prerogative to admit or dismiss the force of a moving body; for however arbitrary the force and time may be, they are there, in defiance of your opinion. 12. In the argument referred to there was no call for the term you say I omitted ; you will find that term in my " Elements of Me- chanics." 13. I hope you will not attempt to introduce any more confusion m Dynamics, such as the term " work of motion," which indicates that motion is a function consisting of work and something else. You have not defined the constituent elements of motion. 14. I do not designate % M F 2 as " quantity of motion," but have rejected that term in dynamics. Nor should the term "quantity of motion " designate the momentum M V. I use only one definite term for each quantity in Dynamics, but you do not appear to have a defi- nite dynamical language. 15. The term "acting force" conveys the idea that there may exist forces which do not act. The simple term "force" implies that it acts, for which reason I proposed to reject " acting." " Motive force" is the proper term for your illustration, but we may call J^the acting force and F- F' the motive force. This motive force may be wholly applied against the friction of the car moving with a uniform velocity on the road, or a part of it may be expended in accelerating the velocity of the car. It is not wrong to add the verb "acting" to the term force, but I only proposed to reject the term as superfluous in the sense in which it is often used. All your forces F F' and / are " acting forces " as well as simple " forces." You have not given any example of forces which do not act. It is necessary in Mechanics to distinguish "motive force" from " static force," but both of them are acting. The purpose for which a force is applied does not alter the nature of that force. Deforming force ! ! ! 176 PROFESSOR SCHMIDTS COMMENTS. (deforming or pressing) force. That it must not be confounded with a pull or a pressure. 16. I consider T, S, F, M as elements. or t = in general K=FS Functions. 9= 9- f Also, the mean force Fm = J - . Power, ^ = = jPm Fm. 17. It is certainly more natural to consider s and t as elements and the differential quotient V= as a derived equation than re- function. gard t and V as elements and S= \ Vf)t as a derived 18. The following are other functions. The acceleration of motion by the accelerating force, ' ~ M ~dt ~&e' 19. The " quantity of motion " = M F, and the stored-up " working F 2 force " (living force) ^MV 2 = W - . 20. You do not think it right that all authorities without excep- tion should consider " work " K= ( F 6s as independent of time. You will, however, most surely admit that in a finished building there is contained a fixed quantity of work, to do which, of course, some, but an indeterminate, time would be necessary. 21. Consequently we cannot say that the determinable work is de- pendent on the indeterminable time. 22. If the work was built in a year, it has been done " in- tensely " (intensive). If three years have been needed for the same work, then it has been done with " less intensity." NYSTROM'S ANSWER. 177 The definition of a physical element is, an essential principle which cannot be resolved into two or more different principles. Therefore an element cannot be divided by an element and the quotient become a function, as appears in your notions of elements and functions. You say time and space are elements, and then divide space by time and say the quotient is a function velocity. o When velocity F= , we have space = V T, which proves that space is a function of velocity and time. 17. Physical facts are not always natural to the mind. There was a time when matter was supposed to consist of only three simple elements namely, air, water and earth which was natural in those days. 18. No, sir. These quantities are neither elements nor functions, for they only express the numerical ratio of force and mass. 19. This has been commented on before. Working force means motive force. There is no living force in a dead body. 20. Most decidedly, because the time is included in the space $= V T. I admit that a fixed quantity of work is required for erect- ing a building ; but when you add the time necessary for it, it cannot be independent of time. If the building can be erected in no time, then that work is independent of time. 21. Work does not bear any fixed relation between its elements, IB* but the product F V T is work. You say, 2, that F V- , from which we have the work K= F V T. 22. Here you introduce a new term, which you have not defined. Is "intensity" an element or a function? If a function, of what ele- ments is " intensity " composed ? 23. In this case your formula is right, but your argument is wrong. You eliminate the time from the work in order to get the power. By the term "intensity" you mean power, and from your own formula 24. We have the work K= % T, which means that the work can be accomplished in any desired length of time, but only at the ex- pense of power. 25. Such is the case with the locksmiths namely, that one worked with double the power of the other, and consequently earned double the wages in equal lengths of time. 26. Money is equivalent to work, and you must expend F V T to earn it. There is no fixed relation between F t V and T, but can 12 178 PROFESSOR SCHMIDT'S COMMENTS. 23. Not the work but the " intensity of the work," the " arbeit- TT starke " (working-strength) = depends on the time. 24. If two locksmiths do the same work, the one, however, in half the time the other takes, then the first one has worked with twice the intensity the other did. 25. They received the same compensation for the same work, but the skillful workman received double the wages in the same time because his " arbeitstarke" (working-strength) was double as great. 26. The pay per piece in like work is independent of time, but the resulting earnings per day are in direct ratio to the arbeitstarke ( working-stren gth ) . 27. The following function may be derived from the pay per piece L and from the time used per piece : Pay in a unit of time A = . 28. According to your idea, on the contrary, the price per piece L would be a function only because it is the product of A and T, and because you will only consider a product, and not a quotient, as a derived function. 29. Such a confusion of ideas as is the case in all the articles concerning "force of falling bodies," especially on page 19 of the Scientific American of the 22d of June, 1872, occurs seldom in Ger- many. 30. There does not exist any "force of falling bodies," only a F 2 " bervegungs-arbeit " (work of motion) = MV 2 = W , stored up in the falling body, equal to the " verschiebungs-arbeit " (pushing or pulling work) WS, which was necessary to raise the weight W to F 2 a height S= . 31. This stored-up "external work of motion" is then changed into "verschiebungs-arbeit" (pushing \vork~) =Rs as a mean resist- ance, .R has been overcome through the distance s. Therefore you state correctly that ft s= WS. But E is not the force of the falling body, but rather the resistance of the down-pressing body through the distance. 32. Your equation 14 K=FVT=^, on page 21 of this treatise, is incorrect, as F is the mean velocity and F the initial force. NYSTROM'S ANSWER. 179 vary ad libitum, only that their product must correspond with the money. What you call " strength of work," intensity, or " working strength " is power f=FV. 27. The pay A per unit of time, according to the power of the workman, may be expressed as follows : Wages, ^ = f=?. 28. I have distinguished the terms "element" and "function" by proper definitions, but you use those terms promiscuously according to individual caprice. I maintain that the product of two or more elements is a function, and that a quotient is a solution of a function. 29. The confusions you allude to are written by Dr. Van der Weyde and other doctors of philosophy, for which I am not respon- sible. I do not consider your ideas of Dynamics to be much better than those of the other 'professors who have commented upon that subject. 30. Place yourself under a falling body and let it strike upon your head; and if you experience no force, then there is no force in a falling body. Please let me hear from you after you have made the experiment. 31. Is the external work of motion stored upon the surface of the body? The pushing work must then be the internal work, which leaks out when the body strikes ? No force can be experienced without an equal amount of resistance, and the force of a falling body is equal to the force of resistance it meets with. 32. Here you have really discovered an error of mine, for which I am glad to give you due credit, and thank you for calling my at- tention to it. My idea was to express the work of attraction of two bodies very far apart in space compared with the distance between their centres of gravity when in contact, in which case the force of attraction varies inversely as the square of the distance between the approaching bodies. Your formulas do not include the requisite ele- ments for that work, but merely give the work of a falling body near the surface of the earth. M and m = masses of the respective bodies. D = distance apart in feet from which the work is counted. d = any shorter distance until in contact.

a to the surface of the earth will be K= -p Vx=-mg a>**- a x x If is only larger than a by a very small quantity h, then will a_ a 1 . h a _h = = - - 1 or 1 = . x a + x 1 + h a x a Therefore, K= W a- = Wh, our well-known equation. 33. All German professors are most probably of the opinion that the professor's opinion (page 4) in the main is perfectly correct, and that your answer is composed of sophisms. 34. Willingly, however, do I acknowledge as commendable your desire to arrive at a determination of the dynamical terms, and to eradicate all superfluous ones. 35. The expression, " principle of conservation of force " (princip der erhaltung der kraft), is a very unfortunate one, and unhappily has already led many half-educated persons astray. That chosen by Professor Mach, of Prague, is more correct namely, " principle of the conversation of work" (princip der erhaltung der arbeit) and still more correct would be " principle of conversion of work." 36. I therefore say there are four kinds of work which are intro- convertible. First. External pushing or pulling work (aussere verschiebungs arbeit). Second. External work of motion (aussere bervegungs arbeit). NYSTEOM'S ANSWER. 181 K= work of attraction in foot-pounds, in drawing the bodies together. Mmd Mm/I 1 8Jr - This formula expresses the true work in foot-pounds, English measures. In the case of meteors falling on the surface of the earth we may assume D = oo and = 0. D d = 20,887,680 feet radius of the earth. M = 402,735,000,000,000,000,000,000 matte, mass of the earth. m = mass of the falling meteor expressed in matts. The work in foot-pounds of a meteor striking the earth will then be K= 671926000 m. For very small meteors the greatest part of this work may be con- verted into heat in passing through the atmosphere, and we call it shooting-stars. Assuming the mean height of the atmosphere to be 60158 feet, the radius of the atmospheric sphere is 20947018 feet = d. The velocity with which a meteor enters the atmosphere will then be 2 = 36607.46 feet per second. a 33. I consider it doubtful that all, or even a majority, and noi one of the German professors who understood the subject, would be of the opinion of the professor in question. You will no doubt say that my answers to you are composed of sophisms, but I can stand that easily, being accustomed to such charges. 34. I am very glad that you consider my labor commendable, and would state my acknowledgment in emphatic tertfis but for your em- ployment of such a conglomeration of dynamical terms, which are the worst I have met with. 35. These terms are all useless, and should never be admitted into any school or any text-book. Work in dynamics corresponds to volume in geometry, but we do not give different names to that volume according to the shape of the space it occupies. A vessel holding 100 gallons of water is a fixed volume independent of the shape of the vessel. If the vessel is cylindrical, we do not say it con- 182 PROFESSOR SCHMIDT'S COMMENTS. Third. Internal pushing or pulling work at work of pressure (Inner verschiebunga arbeit oder deformerings arbeify. As, for instance, in the bent bow, or in an extended or compressed spring, in consequence of the change in the relative position of the molecules, which is against the molecular forces. In permanent gases this is infinitely small, and in condensible vapors it is also very small. Fourth. Internal work of motion (Inner berveguns arbeit), which appears as heat. Internal (modicular) work of motion is stored up in a compressed gas or vapor, which can partly change itself into external pushing or pulling work. 37. There is likewise internal work of motion stored in hot gases, the products of combustion, which is transmitted to the water by the heating surface of the steam-boiler, and then changes itself into the internal pushing or pulling force, which must be furnished for the tearing asunder of the molecules of water, and changes also into in- ternal work of motion, which the now generated molecules of steam 38. In forging, rolling, drilling, planing, etc., the greatest part of the work is changed into internal work of motion (heat). 40. Hoping that you will not take my frank remarks on your work in an unfriendly manner, I subscribe myself Yours respectfully, GUSTAV SCHMIDT, Professor of Technical Mechanics and of Theoretical Mechanical Engineering at the K. K. German Polytechnic Institute of the King- dom of Bohemia, Austria. PRAGUE, July 1, 1875. The translation of Professor Schmidt's papers was made by Mr. P. PISTOR of Philadelphia. From the foregoing discussion it is clear that the subject of Dy- namics lacks perspicuity in the German language for the want of a definite term for the function power. The term force ought to be introduced into the German and Scan- dinavian languages, leaving the term kraft to denote power. NYSTROM'S ANSWER 183 tains 100 cylindrical gallons. So it should be with designation of work, not to give different names to the work according to the pro- portion of its constituent elements. It is customary to distinguish indoor work from outdoor work, but in Dynamics it is all F V T. 36. There exists only one kind of work in Dynamics namely, the product of the three simple physical elements, force, velocity and time. I should like you very much to go to a machine-shop and explain practically to the workmen, foremen and superintendent your nomen- clature of work ; and if you can make them understand and appreciate it without laughing at you, I am very much mistaken. Heat is convertible into work, and consequently must consist of F V T, which is actually the case. The force F is represented by the temperature of the heat and V T by the space it occupies in the gas or vapor. 37. The act of combustion is power, which multiplied by time is work ; also, the act of evaporation is power, which multiplied by time is work ; but in both cases the work of the heat is simply K=F V T. It is immaterial whether you call it external, internal or infernal work, it is still K= F V T, and nothing else. 38. Your classification of work is not accompanied with the requisite definitions to render your argument admissible. 40. I beg you to accept my sincere thanks for your frank and unsparing remarks on my work. You have liberally furnished pre- cisely what I wanted and asked for in order to test the validity of my reorganization of Dynamics. In discussions of this kind it is necessary to be frank and free the mind from fiction, for otherwise we could not rightly understand one another, and the interest of science, which we both have at heart, would suffer, notwithstanding our different and even discordant views. In conclusion let me hope that none of my expressions blynter- preted into a want of kind and courteous feeling toward your per- sonality, and I remain, with great consideration, Yours respectfully, JOHN W. NYSTROM, Civil Engineer. 1010 Spruce Street, Philadelphia, Sept. 1, 1875. 184 MECHANICAL TERMS. In -the English translation of Weisbach's Mechanics, the term and function " power," which is one of the most important functions in Dynamics, does not appear. Even the term "horse-power" is omitted, and cannot be found in the index of that book which otherwise abounds in terms and expressions like those of Professor Schmidt. On pages 15 and 16 are given a number of rejected terms, which are considered superfluous and confusing in the language of me- chanics. This kind of terms are limited only to books and schools, where they burden the student and tax his time and mind to no purpose, but only to be forgotten when he finds no equivalent for them in practice. The crowd of subjects which engross the brief years of a school career exact a severe economy of time and labor by the student. It becomes a paramount consideration, therefore, that his acquirements should in his subsequent experience be found to possess an unequivo- cal practical value, which has heretofore not been fully realized. A graduated student of Mechanics, although expected to be well versed in that subject, is, when brought to a practical test, often found wanting, as is shown in periodicals of the day, where we rarely find a sound article on Dynamics. For example, in the London Engineer lately appeared an article on Dynamics of heavy ordnance, written by an English artillery officer, stating that W V ' " The energy in vis viva in pounds = IFF 2 whereas it is not pounds, but work = This function is called "energy" by doctors of philosophy, who very often represent it as a very mysterious phenomenon. The term " energy " is not used in the English translation of Wei.<- bach, except in a note by the translator. The term " energy " is derived from the Greek tv-fyyou, of which fv means inner or within, and ipfoo means work. " Kinetic energy " (x^ro^-lp^ou} means moving energy. " Potential energy " (Latin, potentalis) means powerful energy. These terms and expressions have originated at times when the science of Dynamics was in a very clouded condition, and have since been retained with various kinds of conflicting definitions. MECHANICAL TERMS. 185 The sense in which the term " energy " is generally used, means simply " work," which consists of only F V T, and nothing more or less. WV 1 In the formula , V means the final velocity of a falling body, 19 which is double the mean velocity of the fall. W= force of gravity F, y and T= , the time in seconds of the fall, of which F=