"L'l B R A RY OF THE U N I VERS ITY OE ILLI NOIS Digitized by the Internet Archive in 2017 with funding from University of Illinois Urbana-Champaign Alternates # https://archive.org/details/practicaltreatisOOboxt A PEACTICAL TEEATISE ON HEAT, AS APPLIED TO THE USEFUL AETS, FOR THE USE OF ENHINEERS, ARCHITECTS, Etc. By THOMAS BOX, AUTHOR OF ‘PRACTICAL HYDRAULICS.’ E. & F. N. SPOX, 48, CHARING CROSS. 1868. J.ONDON: I'K/KTKD IJY W. CLOWES AND SONS, STAMIOIID STltHKT AND CIIAIIING CROSS. 536, 1 13 * PREFACE. The object of the following work is to give Data, Rules, and Tables to facilitate the practical application of the Laws of Heat to the Useful Arts. The subject has throughout been largely illustrated by Examples worked out in detail, and this has led to calcu- lations more or less complicated ; but the author’s special desire to make the ^^principles’’ of the subject clear to the reader could not be so well attained by any other means. The authorities from whom the Experimental Data, &c., are derived, are for the most part given as they occur ; but Peclet’s great work, ^ Traite de la Chaleur,’ should be more particularly mentioned. Bath, August, 1868. 90S ERRATA. Page 41, line n,/or 812 read *812 » 74 , }f 28 2 X L2 »» “s' „ 74, ff oi (2 X 3? j} 2 2 X 32 ” 2 “ „ 91 . tj 13, „ 37 CO CONTENTS. CHAP. I. — General Principles and Facts in the Theory of Heat. Paragraph Unit of Heat 1 Specific Heat of Solids, &c 2 „ Air 3 Latent Heat of Liquefaction 6 „ Vapourization 7 Boiling point of Liquids 10 Expansion of Solids, &c 11 „ Liquids 12 „ Gases, &c 14 „ Moist Air 17 Thermometers 18 Frigorific Mixtures 21 Temperature of the Globe, &c 22 CHAP. II. — On Combustion. Chemical Composition of Combustibles 23 Heat evolved in Combustion by Theory 25 to 31 „ direct Experiment 32 to 48 Air required for Combustion 49 to 59 Products of ,, 61 to 71 Mode of giving out Heat usefully 72 to 74 Combustion in Brick Furnaces 76 Temperature of the Air as it leaves the Fire 78 Kadiating Power of Combustibles 82 to 88 Combustion in Steam-boilers 89 Temperature in different Parts of Flue 94 Distribution of the Heat in a Pound of Coal 96 Kelative effect of Ijong and Short Boilers 97 Effect of Forcing the Fire 100 „ too much Air 101 „ too little Air .. .. 103 Proper Begulation of the Fire 106 CHAP. III. — On Steam-boilers. Heating Surface, effective 108 Horse-power of Boilers 114 Furnaces and Consumption of Fuel 119 VI CONTENTS. ParnfO’aph Fire-bars, &c., &c 121 Steam-cliests 122 Safety-valves 123 Dampers 128 Arrangement of Flues 129 Strength of Boilers for Internal Pressure 132 ,, External Pressure 134 „ Elliptical Tubes 137 CHAP. IV.— On the Efflux of Am, &c. Analogy of Efflux of Water, &c . . 140 Velocity of Air, Steam, and Gas into a Vacuum 142 „ into Air 145 Coefficients of Contraction 148 Discharge of Steam into the Atmosphere 149 Friction of Air, &c., in Long Pipes 153 Square and Rectangular Channels 160 Effects of Repeated Enlargements and Contractions 161 Steam-pipes to Engines 163 CHAP. V. — On Chimneys. Chimneys to Steam-boilers 166 Round Chimneys 167 Square Chimneys 168 Effect of Long and Short Flues .. .. 170 CHAP. VI.— On Vapocr. Density and Weight of Vapour 172 Mixtures of Air and Vapour 174 CHAP. VII. — On Evaporation. Evaporation in Open Air, &c 177 „ at Higli Temperatures 182 Refrigerators for Breweries, &c 189 Evaporating Pans 190 Evaporation at Boiling Point 191 Condensation Reservoirs to Engines 193 Cold Produced by Evaporation 196 Dryness of Air, increased by Heat 197 Evaporation Vessel for Stoves 199 „ by Current of Air 200 CHAP. VIII. — On Distillation. Principle of the Process ^ 201 Pro])oriionH of Ai)paiatus 203 Condensing Apparatus 207 CONTENTS. Vll CHAP. IX.— On Drying. Paragraph Drying in Open Air 209 ,, by Heated Air 210 Proper Position of Outlet Openings, &c 212 Drying Closet for Linen, &c. 214: Size of, for Schools, Asylums, &c 226 CHAP. X. — On Heating Liquids. Heating Liquids by Fire Direct 227 „ Steam in Cased Vessel 231 ., a Worm 232 „ Vertical Tubes 236 ,, Steam Direct 238 CHAP. XI. — On Heating Air. Heating Air by Stoves, &o .. ,. 240 Effect of Stove-pipes, Sheet-iron 241 ,, Cast-iron 244 ,, Earthenware 245 Horizontal Flues 246 Height of Chimney for Stoves 248 Heating Air by Steam-pipes 249 „ Enclosed Steam-pipes 249 Air Cocks 250 Apparatus for Condensed Water 251 Supply of Water to Boiler, &c 254 Expansion of Pipes by Heat . . . . . . ‘ . . ‘ . . . . 255 Heating Air by Hot-water Pipes . . 257 Position of the Fire in Hot-water Apparatus 2.58 Velocity of Current necessary 260 Circulation with the Fire above the Pipes . . . . 264 CHAP. XII. — On the Transmission of Heat and Laws of Cooling. Loss of Heat by Eadiation . . ... 266 „ Contact of Air 270 „ Conduction 274 „ Buildings 279 „ Ceiling and Ground .. .. 279 „ the Walls 280-292 „ Glass in Windows 293 ,, Glass Houses, &c 295 Phenomena of Heated Booms, &c 297 Vlll CONTENTS. CHAP. XIII. — Laws of Cooling at High Temperatures. Paragraph Loss by Radiation, Dulong’s Formula 299 „ Contact of Air „ 301 „ Steam-pipes 302 „ Enclosed Steam-pipes 303 „ Polished Metal and other Surfaces 304 „ Thick Cast-iron Pipes, &c 305 „ Steam Pipes cased in bad Conductors 307 CHAP. XIV. — On the Transmission of Heat by Conduction. Law of Cauchy, &c., 310 Transmission by Water 311 CHAP. XV. — On Ventilation, &c. Air required for Respiration, &c 312 Heat produced by „ 314 Modes of effecting Ventilation 315-320 Summer and Winter Ventilation 321 Natural Ventilation 322 Mechanical Ventilation 323 Heating and Ventilation of Schools 326-336 „ ' „ Chapels 337-351 „ „ Hospitals 352-358 CHAP. XVI. — Examples of Heating and Ventilation. Prison Mazas 359 „ Provins 364 Church of St. Roch, particulars of 366 „ Temperature of Walls, &c 367 ,, Volume of Air 368 „ Time to Heat the Building 371 „ Time to Cool the Building 379 „ Heating-apparatus, &c 380 CHAPTER XVII. — On Wind, and its Effects on Ventilation, &c., &c. Principle of the Influence of Wind 383 Force and Velocity of Wind 384 Cowl for Chimneys 386 Form of Vane for Chimneys 387 Stability of Buildings in Storms 389 / \ - , , f PRACTICAL TREATISE ON HEAT. CHAPTEE I. GENERAL PRINCIPLES AND FACTS. (1.) ‘‘ Unit of Heat . — It is necessary to Have a standard for measuring the amount of heat absorbed or evolved during any operation : in this country the standard unit is the amount of heat necessary to raise the temperature of a pound of water Fahr. This amount is not quite uniform at all temperatures, as is shown by the experiments of Eegnault : thus from 32^ to 212° we have, by a uniform rate, 212 — 32 = 180 units, but Eegnault gives 180*9 units; and from 32° to 446, instead of 446 — 32 = 414 units, Eegnault gives 422*4 units; but for practical purposes we may in most cases assume it to be uniform. (2.) “ Specific Heat '" — Different bodies require very different quantities of heat to effect in them the same change of tempera- ture. The capacity of a body for heat is termed its “ Specific Heat,” and may be defined as the number of units of heat necessary to raise the temperature of 1 lb. of that body 1° Fahr. Table 1 gives its value for most of the solid, liquid, and gaseous bodies commonly met with in practice. . The specific heat of all bodies (except gases) appears to increase with the temperature, as we have seen to be the case with water. This is shown by Table 2, from the experiments of Dulong and Pouillet, but at ordinary temperatures the departure from uniformity is not great, and in most cases we may admit a uniform rate, having the value given by Table 1. Thus, to heat 200 lbs. of cast iron 120°, would require 200 X 120 x *12983 = 3116 units of heat; the same weight of water requiring 200 x 120 = 24000 units, or nearly eight times the heat required for cast iron. The specific heat of air is a more intricate matter. (3.) “ Specific Heat of Airf ^c . — When air, &c., is heated in a closed vessel, the capacity or volume remaining constant, the B 2 SPECIFIC HEAT. Table 1. — Of the Specific Heat of Solid, Liquid, and Gaseous Bodies, being the number of Units of heat necessary to heat One Pound of the Body 1° Fahrenheit. Specific Heat. I Authority. Iron (wrought) •11379 Kegnault. Ditto (cast) •12983 J > Copper •09515 9 J Tin (English) •05695 9 9 Zinc •09555 9 9 Brass •09391 9 9 Lead •03140 9 9 Mercury •03332 9 9 i Gold •03244 J 9 Silver v. •05701 9 9 Platina •03243 9 9 Bismuth •03084 9 9 Glass •19768 9 9 Marble ^ white) •21585 9 9 Chalk (white) •21485 9 9 Burnt Clay (white) •18500 Gadolin. Coal •2777 Crawford. Sulphur •20259 ' Kegnault. Spermaceti •3200 Irvine. Wood Tpine) •650 Mayer. Ditto (birch) •480 » » Gadolin. Bees-wax •450 Ice •504 Person. Water 1-0000 — Olive Oil •3096 Lavoisier. Alcohol (s. g. • 793) •622 Dalton. Oil of Turpentine •472 Despretz. Gases under constant Pressure of 30 in. Mercur} . Oxygen Gas •2182 Kegnault. Hydrogen Gas 3-4046 9 9 Nitrogen Gas •2440 9 9 Carbonic Acid Gas •2164 9 9 Sulphuretted Hydrogen •2423 9 9 Vapour of Water .. •4750 9 9 Air •2380 9 9 pressure is increased ; if, on the other hand, the air be suffered to expand freely, by increase of temperature, the pressure may remain constant. Now the specific heat of air is different under these two different conditions. Considering first the specific heat under constant pressure, which is the case most generally SPECIFIC HEAT OF GASES. 3 Table 2. — Of the Vakiation in the Specific Heat of Bodies at different Temperatures. Between Between Between 32° and 212°. 32° and 392° 32® and 572° Mercury (Dulong) , , •0330 •0350 Silver •0557 •0611 Zinc •0927 .. •1015 Copper 5» y •• •0940 •1013 Iron •1098 •1150 •1218 Platina *0335 •0355 Antimony ’0507 •0547 Glass •1770 •• •1900 At 2120 At 5720. At 9320. 1 At 12920. At 18320. At 21920. Platina (Pouillet) . . •03350 •03434 •03518 •03600 •03718 •03818 met with : imagine a gas-holder so well-balanced as to exert no pressure on the enclosed gas, and let it contain one pound of air at 62°, with the barometer at 29*92, or say 30 inches of mercury; its capacity (Table 32) would be 13*14 cubic feet. If heat be applied, so as to raise the temperature 1°, or to 63°, the air would be expanded slightly (14), and the gas-holder would rise to allow for it. The amount of heat required under these circumstances, according to Eegnault’s experiments, would be *238 units, or the amount which would have raised the same weight of water *238 of a degree, and this is equal •238 to ; = *01817 units per cubic foot. If the gas under con- sideration were hydrogen, the capacity of the gas-holder, capable of holding one pound, would have been 189*7 cubic feet, and to effect a change of 1° in the temperature would require, according to Kegnault, 3*4046 units of heat, or 3*4046 =*018 units per cubic foot, practically the same as a cubic foot of air. Table 1 gives the specific heat of air, gases, and vapour, under these conditions. (4.) If the pressure were other than 30 inches (but still constant), the specific heat would be different, as is shown by the experiments of Clement and Desormes in Table 3. Here the specific heats are given for equal volumes instead of equal weights, B 2 1 4 SPECIFIC HEAT OF GASES. Table 3. — Of the Specific Heat of Air, from the Experiments of Clement and Desormes. Total Pressure in inches of ' Mercury. Ratio of Specific Heat at the different Pressures for equal Volumes. Error. Experiment. Calculations. 39-G 1*215 1*152 - *063 29*84 1*000 1*000 *000 14*92 *692 *706 -f *013 7*44 *540 *499 - *041 3*74 • *368 *387 + *019 and this appears to vary directly as the square root of the pressure, as is shown by column 3 which is calculated by the rule VT? X '183 = E, in which P = the pressure in inches ol mercury, and E = the ratio of specific heat of air at that pres- sure, the specific heat at 29*84 being 1*000, Table 4 has been Table 4. — Of the Variation in the Specific Heat of Air, at different Densities. Total Pressure above a Vacuum in inches of Mercury. Relative Density. Specific Heat of 1 equal Volumes. Specific Heat with Pressure Constant- Specific Heat with Volume Constant and Temperature 62°. Cubic feet in 1 lb. of Air at 62° Fahr. Units per Pound at any Tem- perature. Units per Cubic foot at 62°. Units per Pound at 62°. Units per Cubic foot at 62°. 120 4 1 1 *476 *119 *03634 *0837 *02556 3*275 60 2 ^ *336 •168 *02690 *1184 *01808 6*55 30 1 *238 *238 *01817 *1674 •01280 13*1 15 1 2 *168 *336 *01284 *2367 *00903 26*2 7*5 1 4 *119 *476 *00908 *3348 *00639 52*4 3*75 "8 *084 *672 *00642 *4734 *00452 104*8 (1) i (2) (3) I (4) (5) (6) (7) (8) calculated on the same principles, thus the (col. 3) has been obtained by multiplying *238, tlic specific heat at atmospheric pressure, by the square root of the density in col. 2, which again is simply proportional to the pressure in col. 1. The col. 4 is ob- tained by dividing col. 3 by col. 2, and col. 5 by dividing col. 4 SPECIFIC HEAT OF GASES. by col. 8. The general formula for the specific heat of gases with constant pressure, is = S', in which S = the a/ P specific heat at 30 inches of mercury, as in Table 1 and in col. 1 of Table 5, P = the total pressure in inches of mercury, and S' = the specific heat under that pressure. For air this becomes - = S', and col. 2 in Table 6 has been thus calculated. V P Table 5. — Of the Specific Heat of Gases and Yapour. Specific Heat of 1 lb. of Gas under a Constant Pressure of 29*92 inches of Mercury (Regnault). Ratio of the Specific Heat under Constant Pressure, to the Specific Heat with Constant Volume (Dulong). Specific Heat of 1 lb. of Gas taken with the Barometer at 29 * 92 inches, the Volume remain- ing Constant. Oxygen Gas •2182 1-415 •1542 Hydrogen Gas 3-4046 1-407 2-4200 Nitrogen Gas •2440 , , •1717 Carbonic Acid Gas •2164 1-338 •1617 Carbonic Oxyde Gas .. •2479 1-427 •1737 Sulpliuretted Hydrogen •2423 •1825 Yapour of Water •4750 •3624 Atmospheric Air -2380 1-421 •1674 (1) (2) (3) (5.) When air and gases are heated in closed vessels, expan- sion being prevented, the pressure is increased, and the specific heat is less than when the pressure is constant and expansion permitted. The experiments of Dulong give the ratio of specific heat under these two different conditions for several of the most important gases, as per col. 2 in Table 5 ; thus for air the ratio . 238 is 1’421 to 1, and we have - — = *1674 for the specific heat 1*421 of air in a closed vessel, and under a pressure of 30 inches of mercury. The general rule for the specific heat of gases with constant volume is ~ x — = = S", in which K is the ratio, as P V P per col. 2 in Table 5, S" = the specific heat with constant volume, and S and P the same as before. For air the rule •917 becomes — 7=- = S" V P thus with a pressure of 120 inches of 6 LATENT HEAT OF LIQUEFACTION. mercury, the specific heat of air in a closed vessel would be •917 -917 Vllo’ 10 • 95 ^ 0 in Table 4, and col. 3 in Table 6. We may deduce the specific heat under constant Table 6.— Of the Specific Heat of Air at different Pressures. Total Pressure in inches of Mercury. Specific Heat with Total Pressure ! in inches 1 of Mercury. Specific Heat with Pressure Constant, and Volume Variable with Change of Temperature. Volume Con- stant, and Pres- sure Variable with Change of Temperature. Pressure Constant, and Volume Variable with Change of Temperature. Volume Con- stant, and Pres- sure Variable with Change of Temperature. 1 1*303 •9170 70 •1558 •1096 5 •5827 •4101 75 •1504 •1059 10 •4121 •2900 80 •1457 •1025 15 •3360 •2367 85 •1413 •0995 20 •2914 •2050 90 •1374 •0967 25 •2606 •1834 100 •1306 •0919 110 •1242 •0874 30 •2380 •1674 120 •1190 •0837 130 •1143 •0804 35 •2203 •1550 140 •1101 •0775 40 •2061 •1450 150 •1064 •0749 45 •1943 •1367 180 •0971 •0684 50 •1843 •1297 210 •0899 •0633 55 •1757 •1236 240 •0841 •0592 60 •1680 •1184 270 •0793 •0558 65 •1616 •1138 300 •0752 •0529 volume from that under constant pressure by the rule S" = S' __ in which G = the specific gravity of the gas, air being 1* 0, and S' and S" the same value as before and thus in Table 5 we have obtained the numbers, in col. (3), for gases, &c., whose ratio is not given by the experiments of Dulong. This rule is given by Bunsen. (6). ‘^Latent Heat of Liquefaction '' — When a body passes from the solid to the liquid state, it absorbs a large amount of heat without changing its own temperature, the heat thus ab- sorbed becoming latent, and insensible to the thermometer. This is termed the “ latent heat of liquefaction,” and may be defined as the number of units of heat absorbed by one pound of the solid, in passing to the liquid state. When the process is LATENT HEAT OF VAPOURIZATION. 7 reversed, the liquid congealing, freezing, or passing back again to the solid state, the same amount of heat is emitted or restored. Thus when ice is heated to 32°, it begins to melt, the tempera- ture remaining fixed until the last particle of ice is melted ; and during this process 142*4 units are absorbed, being the amount that would have raised the same weight of water 142° • 4 ; but the ice itself, having, by Table 1, a specific heat of *504, would have had its temperature raised = 281° if the heat *504 had not become latent. The “ latent heat,’’ however, is not 281, but 142*4 units. Table 7 gives the latent heat of liquefaction. Table 7.— Of the Latent Heat of Liquefaction, being the number of Units of Heat absorbed by One Pound of different Bodies in changing their state from Solid to Liquid. Increase of Temperature 1 Latent Heat in Units. in the Body if Heat had not been absorbed in melting. Authority. Ice to Water . . 142-4 o 281 Person. Sulphur . . 16-8 83 > > Tin 25-6 450 9 9 Lead 9-7 ■ 309 9 9 Zinc 50-6 530 9 9 Bismuth . . 22-8 740 9 9 Silver 38-0 665 9 9 Cast Iron . . 233-0 1574 Clement. Beeswax . . 78-7 175 Irvine. Spermaceti 46-4 145 » > 1 the col. 3 being obtained by dividing the latent heat by the specific heat. (7) “ Latent Heat of Vapourization .^^ — When a liquid changes its state to the gaseous or vapourous state, another large amount of heat becomes latent, and this is termed the “latent heat of vapourization;” and it may be defined as the number of units of heat absorbed by one pound of a liquid in the act of passing to the gaseous state. Thus a pound of water at 212°, passing to steam at 212°, absorbs, according to Eegnault, as much heat as would have raised the temperature of the water 966° if it had not become latent. Again, a pound of alcohol absorbs 8 LATENT HEAT OF VAPOURIZATION. 457 units in the act of vapourization, or tlie amount of Lcat that would have raised a pound of water 457 ; hut alcohol having by Table 1 a specific heat of * 622, its own temperature 457 would have been raised = 735° if heat had not become * o22 latent. Table 8 gives the latent heat of vapourization for a few of the liquids most eommonly met with in practice. Table 8 . — Of the Latent Heat of Vapourization, being the number of Units of Heat required to convert Liquids from their respective Boiling-points to Vapour, under a ]n'essure of 30 in. Mercury. Increase of Temperature Latfn t Heat of Liquid if in Units. Heat had not become Latent, Water 9GG 96G Eegnault. Alcohol i 457 735 Ure. Ether ' 313 473 9 9 Oil of Turpentine i 184 390 9 9 Naphtha 1 184 9 9 (8) Table 9 shows that the temperature of the boiling-point of water, varies with the pressure; and it has been found by experiment, that the amount of heat which becomes latent during vapourization, varies with the temperature at which it is effected. Table 9. — Of the Boiling Points of Liquids, at Atmospheric Pressure. j Temp. i Fahr. Ether, Sulphuric, sp. gr. • 73G5 o 100 G. Lussac. Alcohol ,, *813 173 Ure. Muriatic Acid , , 1 • 047 222 Dalton. Nitric Acid ,, I’lG 220 9 9 Sulphuric Acid , , 1 • 3 240 9 9 ,, 1-85 G20 9 9 Oil of Turj)entine 31G Ure. Nafhtha 30G > > Sulphur 570 • » > Tdnsccd Oil GOO — Mercury G52 Mean of G. Water 212 LATENT HEAT OF VAPOURIZATION. 9 but that the total amount of heat necessary to raise the liquid from a low temperature and then evaporate it, is constant. Thus the heat required to raise a pound of water from 0° to 212° and then evaporate it, is212-|-966 = 1178 units. Table 10 shows Table 10 . — Of the Temperature of the Boiling-Point of Various Liquids under different Pressures, deduced from the Experiments of Kegnault. Liquid Pressure in inches of Mercury. 80 15 10 5 Temperature of Ebullition. o o o o Water 212 180 162 134 Alcohol 173 146 127 101 Ether 100 62 55 17 Oil of Turpentine 316 271 248 210 See also Tables 12, 22, &c. that if the atmospheric pressure were reduced to 15 inches of mercury in the barometer, water would boil at 180° instead of 212°, but the units of heat from 0° would still be 1178 ; and, as 180° only were required to raise the water to its new boiling- point, the latent heat of vapourization must be 1178 — 180 = 998 units, instead of 966. Again, at a pressure of 60 lbs. per square inch above the atmosphere. Table 11 shows that water must be heated to 307° before ebullition commences ; but the latent heat of vapourization will be proportionately diminished, and will in that case become 1178 — 307 = 871 units, instead of 966 units. For convenience of calculation in other parts of this work, it is assumed in the above that water could be reduced to 0° without passing to the solid state, or to ice, where, as we have seen, its specific heat is altered. This, of course, is fictitious : the real amount of heat required to convert a pound of ice at 0° to steam at 212° is 1304; 5 units, as follows : — A pound of ice at 0° to ice at 32°, = 32 x ’ 504 = „ ice at 32° to water at 32° . . = „ water at 32° to water at 212° = „ „ 212° to steam at 212° = 16*1 142*4 180*0 966*0 units ?5 Total = 1304-5 10 VOLUME OF STEAM, Table 11, — Of the Temperature and Volume of Steam at different Pressures, calculated from the Experiments of Regnault, &c. Pressure above the Atmos- phere in lbs, per square in. Temp. Fahr. Cubic feet of Steam from one Cubic foot of Water. Pressure above the Atmos- phere in lbs. per square in. Temp. Fahr. ! Cubic feet of Steam from one Cubic foot of Water. Pressure above the Atmos- phere in lbs. per square in. Temp. Fabr. Cubic feet of Steam from one Cubic foot of Water. 0 o 212 1640 44 o 291 446 88 330 264 1 215 1544 45 292 439 89 » » 261 2 219 1456 46 294 432 90 331 258 3 222 1378 47 295 426 91 332 256 4 224 1310 48 296 419 92 333 254 5 227 1247 49 297 413 93 » > 252 6 230 1190 50 298 407 ; 94 334 250 7 232 1138 51 299 401 95 9 9 248 8 235 1089 52 300 394 96 335 246 9 237 1048 53 301 387 97 336 244 . 10 239 1008 54 302 384 98 9 9 242 11 241 969 55 303 379 99 337 240 12 244 936 56 304 374 100 338 238 13 246 904 57 305 369 102 339 234 14 248 875 58 9 9 364 104 340 230 15 250 846 59 306 360 105 341 228 16 252 820 60 307 355 106 342 226 17 253 796 61 308 350 108 343 223 18 255 774 62 309 346 110 344 220 19 257 743 63 310 342 115 347 212 20 259 732 64 311 338 120 350 203 21 260 713 65 312 334 125 353 197 22 262 694 66 313 330 130 355 190 23 264 676 67 314 326 135 358 184 24 265 660 68 9 9 322 140 361 179 25 267 644 69 315 319 145 363 174 26 268 630 70 316 315 150 366 169 27 270 615 71 317 312 160 370 159 28 271 602 1 72 318 309 170 375 151 29 272 589 ; 73 9 9 306 180 380 144 30 274 576 I 74 319 302 190 384 138 31 275 564 75 320 299 200 388 132 32 277 553 76 321 296 210 392 126 33 ; 278 542 77 322 293 220 396 121 34 279 532 78 9 9 290 230 399 116 35 281 521 79 323 287 240 403 112 36 282 512 80 324 284 250 406 108 37 283 503 81 325 282 260 409 104 38 284 494 82 9 9 279 270 413 101 3>9 285 485 83 326 276 280 416 98 40 286 476 84 327 273 290 419 95 41 288 4(>8 85 328 271 300 422 91 42 289 4(;o 8(> 9 9 268 43 290 453 87 329 266 ELASTIC FORCE OF VAPOUR. 11 Table 12, — Of the Elastic Force of Yapour of Water in inches of Mercury, calculated from the Experiments of Eegnault. I'emp. Fahr. Force in inches. Temp. Fahr. Force in inches. Temp. Fahr. Force in inches, j Temp. Fahr. 1 Force in 1 inches. Temp. Fahr. 1 Force in 1 inches. <5 o o 1 o ! o 0 •044 46 •311 92 1 1-501 138 5-565 184 16-68 1 •046 47 •323 93 1-548 : 139 5-710 185 17-05 2 •048 48 •335 94 1-596 1 140 5-858 186 17-42 3 •050 49 •348 95 1-646 141 6-010 187 17-81 4 •052 50 •361 96 1-697 i 142 6-165 188 18-20 5 •054 51 •374 97 1-751 i 143 6-324 189 18-60 6 •057 52 •388 98 1-806 144 6-488 190 19-01 7 •060 53 •403 99 1-862 145 6-655 191 19-42 8 •062 54 •418 100 1-918 146 6-825 192 19-83 9 •065 55 •433 101 1-976 147 7-000 193 20-26 10 •068 56 •449 102 2-036 148 7-177 194 20-68 11 •071 57 •465 103 2-098 149 7-360 195 21-12 12 •074 58 •482 ! 104 2-162 150 7-546 196 21-57 13 •078 59 •500 105 2-227 151 7-736 197 22-03 14 •082 60 •518 106 2-293 152 7-930 198 22-50 15 •086 61 .537 107 2-361 153 8-128 199 22-97 16 •090 62 •556 108 2-431 154 8-330 200 23-46 17 •094 63 •576 109 2-503 155 8-536 201 23-95 18 •098 64 •596 1 110 2-577 156 8-746 202 24-45 19 •103 65 •617 i 111 2-653 157 8-960 203 24-95 20 •108 66 •639 ' 112 2-731 : 158 9-177 204 25-47 21 •113 67 •661 113 2-811 I 159 9-400 205 26-00 22 •118 68 •685 114 2-893 1 160 9-628 206 26-53 23 •123 69 •708 115 2-977 161 9-861 207 27-08 24 •129 70 •733 116 3-063 162 10-099 208 27-64 25 •135 71 •759 117 3-151 163 10-342 209 28-19 26 •141 72 •785 ! 118 3-241 1 164 10-590 210 28-76 27 •147 73 •812 1 119 3-333 i 165 10-843 .211 1 29-34 28 •153 74 •840 ! 1 120 3-427 i 166 11-101 212 29-92 29 •160 75 •868 ! 121 3-523 167 11-36 213 ! 30-52 30 •167 76 •897 1 122 3-621 168 11-63 214 i 31-13 31 •174 77 ! -927 1 1 123 3-721 i 169 11-90 1 215 1 31-75 32 •181 78 •958 1 124 3-824 170 12-18 1 216 1 32-38 33 •188 79 •990 125 3-930 , 171 12-46 217 i 33-02 34 •196 80 1-023 ! 126 4-039 172 12-75 i 218 33-67 35 •204 81 1-057 ' 127 1 4-151 173 13-05 i 219 34-33 36 •212 82 1-092 ' 128 4-265 ! 174 13-35 i 220 35-01 37 •220 83 1-128 129 4-382 175 13-66 221 35-68 38 •229 84 1-165 j 130 4-502 176 13-96 j 222 1 36-37 39 •238 85 1-203 1 131 4-625 177 14-28 i 223 37-08 40 •247 86 1-242 ! 1 132 4-752 ' 178 14-60 1 224 37-80 41 •257 87 1-282 133 4-881 j 179 1 14-93 1 225 38-53 42 •267 88 1-323 134 5-012 I 180 15-27 ' 226 39-27 43 •277 1 89 1 - 366 , 135 5-146 ' 181 1 15-61 1 i 227 40-02 44 •288 1 90 1-401 ; 136 5-283 i 182 1 15-96 1 228 40-79 45 •299 i 1 91 1 j 1-455 I 1 137 5-423 i 183 1 16-32 229 41-56 12 ELASTIC FORCE OF VAPOUR. Table 12 — continued. Temp. ' Fahr. Force in inches. Temp. Falir. Force in inches. Temp. Fahr. Force in indies. i Temp, j Fahr. Force in inches. I’emp. Fahr. P’orce in j inches. o 280 42-34 o 274 91-18 o 1 318 177-9 o 362 320-5 o i 406 539-5 231 43-14 275 92-67 i 319 180-5 363 324-6 407 545-5 232 43-95 276 94-18 ' 320 183-1 1 364 328-7 j 408 551-6 233 44-78 277 95-72 321 ' 185-7 ‘ 365 332-8 1 409 557-7 234 45-62 278 97-27 322 188-3 366 336-9 ' 410 563-9 235 46-47 279 98-84 323 191-0 367 341-2 1 411 570-1 236 47-32 280 100-4 324 193-7 368 345-4 ' 412 576-4 237 48-20 281 102-0 325 196-4 369 349-7 1 413 582-8 238 49-08 282 103-6 326 199-2 370 354-0 1 414 589-2 239 49-98 283 105-3 327 201-9 371 358-4 415 595-7 240 50-89 284 107-00 328 204-8 372 362-8 416 602-2 241 51-83 285 108-7 329 207-6 373 367-2 417 608-8 242 52-77 286 110-4 330 210-5 374 371-8 418 615-4 243 53-72 287 112-1 331 213-4 375 376-3 419 622-1 244 54-69 288 113-9 332 216-4 376 380-9 420 628-8 245 55-68 289 115-7 333 219-4 377 385-5 421 635-6 246 56-68 290 117-5 I 334 222-4 378 390-2 422 642-5 247 57-69 291 119-3 ! 335 225-4 379 394-9 423 649-4 248 58-71 292 121-2 ' 1 336 228-5 380 399-6 i 424 656-3 249 59-75 293 123-05 337 231-6 381 404-4 i 425 663-3 250 60-81 294 124-9 1 338 234-7 382 409-3 426 670-4 251 61-89 295 126-8 i j 339 237-8 383 414-1 427 677-5 252 62-98 296 128-8 I 340 241-1 384 419-0 428 684-7 253 64-09 297 130-7 ! ; 341 244-3 385 424-0 429 691-9 254 65-21 298 132-7 342 247-6 386 429-0 430 699-2 255 66-35 299 134-7 343 250-9 387 434-1 431 706-5 256 67-50 300 136-8 344 254-3 388 439-2 ; 432 713-9 257 1 68-66 301 138-9 345 i 257-6 389 444-4 433 721-4 258 1 69-85 302 141-0 346 1 261-1 390 449-6 434 728-9 259 71-05 303 143-1 ! 347 264-5 i 391 454-9 435 736-5 260 I 72-27 304 145-2 1 348 1 268-0 392 460-2 ! 436 744-1 261 73-50 305 147-4 1 349 271-5 393 465-5 ; 437 751-8 262 ' 74-76 306 149-6 1 350 275-0 394 470-9 1 438 759-6 263 , 76-03 307 151-8 351 278-6 395 476-4 439 767-4 264 77-31 308 154-0 352 282-3 1 396 1 481-9 440 775-3 265 78-62 309 156-3 353 285-9 397 487-4 441 783-2 266 79-!)3 310 158-6 ! 354 289-6 ! 398 1 493-0 ! 442 791-2 267 ; 81-27 311 160-9 355 293-4 1 399 498-7 i 443 799-3 268 ' 82-63 312 163-2 35 () 297-1 1 400 504-4 i 444 807-4 269 84-01 313 165-6 357 300-9 1 401 510-1 445 1 815-6 270 85-41 314 168-0 358 304-7 402 515-9 446 ! 823-9 271 8(;-83 315 170-5 359 308-6 ! 1 403 521-7 447 1 832-2 272 88-26 316 1 172-9 i 3()0 312-6 404 527-6 ! 448 1 840-6 273 ' 89-72 1 1 3 J 7 J 75-4 3{)1 1 316-5 405 533-5 1 449 1 849-0 BOILING-POINTS OF LIQUIDS. 13 But this difference will not affect the correctness of our calculation ; for instance, the amount of heat to convert water at 32 to steam is by the above, 180 -j- 966 = 1146 units, and by the other method, 1178 — 32 = 1146 units also. (9.) These results, however, will be slightly modified by the fact that the latent heat of water itself varies with the tem- perature (1), and the total heat from 32° will be more accurately given, according to the experiments of Kegnault, by the for- mula, H = 1081*4 j-f- *305 /, in which H = the total heat from 32°, at the temperature t ; thus at 212° we have 1081 *4 -|~ (•305 X 212) = 1146*06 units. The heat that becomes latent will be given precisely by the formula Z = 1115*2 — *708 Z being the latent heat at the temperature t (10.) ‘‘ Boiling-point of Liquids ^’ — When the temperature of any liquid is raised to a certain point, the liquid passes off in a state of vapour, and the temperature remains constant. This temperature varies however, with the pressure of the atmosphere or vapour on the surface of the liquid. Table 9 gives the boiling-points of liquids at ordinary atmospheric pressures, and Table 10 the variation in temperature with reduced pres- sure. Tables 11 and 12 give the temperatures with increased pressure. The boiling-point is not affected by foreign bodies in the water, &c., so long as the body does not combine chemically with the water ; but a great number of salts, &c., do so combine, and the boiling-point is raised, as shown by Table 13, from the experiments of M. Legrand and others. It has been found that the vapour produced at the surface of a saline solution is that of pure water, and has the same temperature of 212° under 30 inches of mercury, although the temperature of the solution itself may be much higher. (11.) “Expansion .'' — All bodies, whether solid, liquid, or gaseous, are expanded or increased in volume by heat, but in very different proportions, as shown by Table 14. In the case of solids the expansion may be estimated by the increase in length, or by the increase in volume. Let us imagine a very expansible solid, such that by a given change of temperature its length would be doubled, say from one foot to two feet ; now if the body were a cube, expansion taking place equally in all directions, it is obvious that, while before expansion it measured one cubic foot, it would, after expansion, measure 2 x 2 x 2 = 8 cubic feet. Estimating by length, therefore, we should say that 14 EXPANSION. Table 13 — Of the Boiling-Points of Solutions of Various Salts, at ordinary Atmospheric Pressure, from the Experiments of M. Legrand and others. Temperature of Ebullition. Weight of Salt in 100 lbs. of Water. o lbs. Saturated solution of Chlorate of Potassa 210 -.56 61-50 9 9 Carbonate of Soda 220-28 48-50 » ♦ 9 9 Phosphate of Soda 221-0 113-30 5 » 9 9 Chloride of Potassium 226-94 50-40 » » 9 9 , , Soda . . 227-12 41-20 9 9 Neutral Tartrate of Potassa . . 238-40 296-20 » » 9 1 Nitre, or Saltpetre 240-62 335-10 J » 9 9 Nitrate of Soda 249-80 224-80 5 » 9 9 Acetate of Soda . . 255-00 209-00 5 > 9 9 Carbonate of Potash 275-00 205-00 9 9 9 9 Nitrate of Lime .. 303-80 362-20 9 9 9 9 Acetate of Potassa 336-20 798-20 9 V 9 9 Cidoride of Calcium 355-10 325-00 9 9 9 9 Nitrate of Ammonia 356-00 Tritinite 9 9 9 9 Common Salt 226-0 36-37 Not saturated solution of Common Salt 224-0 33-34 9 9 9 9 9 9 • • 223-7 30-30 9 9 9 9 9 9 • • 222-5 27-28 9 9 9 9 9 9 • • 221-4 24-25 9 9 9 9 9 9 • • 220-2 21-22 9 9 9 9 9 9 219-0 18-18 9 9 9 9 9 9 • • 217-9 15-15 9 9 9 9 9 9 • • 216-7 12-12 9 9 9 9 9 9 • • . . . . 215-5 9-09 9 9 9 9 9 9 • • 214-4 6-06 9 9 9 9 9 9 . . . . 213-2 3-03 9 9 9 9 9 9 • • .. .. j 212-0 0-00 the comparative lengths at the two temperatures were as 1 to 2, but by volume as 1 to 8, and in all cases the increase in volume is the cube of the increase in length. For the very small dilatation of solids, such as are met with by experience, the expansion in volume may without sensible error be taken at three times the linear dilatation, for a cube has three dimensions, length, breadth, and height, and if each of these dimensions be increased by a very small amount, it is evident that the expansion of the cube in volume is very nearly three times the linear expansion. “ Contraction of Metals in Casting , — The contraction which EXPANSION. 15 Table 14 . — Of the Expansion of Bodies by Heat for 1° Fahrenheit, being the expansion per degree between 32° and 212°, the Volume at 32° being 1*0. Fire Brick Marble (black) White Deal Brick, stock Marble (Carrara) Granite ( Aberdeen grey) Glass tube Platina Slate (Penrhyn) Cast Iron Steel, rod Wrought Iron Iron Wire Roman Cement Copper Brass, cast , , plate , , wire Silver Tin Lead Zinc, hammered Mercury , , (in glass) *Water (40° to 212°) ,, ,, (in glass) Alcohol (30° to 100°) Linseed Oil (32° to 212°; (in glass) .. Expansion for 1° Fahrenheit. No. of Authori- ties. In Length. In Volume. •000002349 •000007047 1 •000002407 •000007420 1 •000002556 •000007669 2 •000003057 •000009170 1 •000003633 •000010900 1 •000004386 •000013157 1 •000004567 •000013701 5 •000004835 •000014506 2 •000005764 •000017290 1 •000006167 •000018501 3 •000006441 •000019324 4 •000006689 •000020067 4 •000007430 •000022290 2 •000007972 •000023915 1 •000010088 •000030264 4 •000010417 •000031250 1 •000010450 •000031350 3 •000010723 •000032170 1 •000011121 •000033364 6 •000013102 •000039307 4 •000015876 •000047628 2 •000017268 •000051806 1 •000100540 7 •000086839 1 •0002517 1 •0002380 1 •0006318 1 •0004030 1 metals experience in cooling down from their melting points to ordinary temperatures is very considerable, and allowance has to be made for it in fixing the size of the pattern. Table 15 gives the result of practical observations on this subject; thus a cast-iron girder, 20 feet long, must have a pattern •1246 x 20 = 2*492 inches longer than itself; but a pattern 20 feet long would give a casting *1236 x 20 = 2*472 inches shorter than itself. For practical purposes Jth of an inch to a foot is a good approximation. * See Table 18. 16 CONTRACTION OF METALS. Table 15. — Of the Contraction of Metals in Casting. Contraction. Length Per foot. of Total Pattern. in inches. Of Of 1 Pattern. Casting. ft. in. iiu'iies. in( hes. Cast-iron girder 21 8i ^10 •1236 •1246 » ) 1 > • • Gun-metal bar 1(3 9 2-05 •1225 •1236 5 4f 1-0 •185()8 •1886 Maximum. •936 •1653 •1(376 (3 ’bi •97 1 •1713 • 1737 9 9 • • • • • • 1-0 , •1(3(>1 •1(384 99 •• •• •• .5 6 -^- •92 I •1671 •1(395 9 9 • • • • • • 9 9 •90 •1635 •1657 99 •• #• •• 9 9 •88 •1598 •1(320 9 9 • • • • • • 9 9 •84 •1526 •1545 Minimum. 9 9 • • • t • . •1607 •1632 Mean of 8. Copper and Tin, Copper) 113, Tin 10 / 5 C* •895 •1623 •1645 Maximum. •880 ; •1595 •1617 9 > ? 9 9 9 •880 •1595 •1617 9 9 9 9 9 9 •855 •1550 •1570 Minimum. 9 9 9 9 9 9 .. •1591 •1612 Mean of 4. Yellow Brass 2 91- •5 •1811 •1839 Copper 7 10^ 1-54 •1948 •1980 Minimum. 7 51 1-465 •1972 •2005 9 9 1-465 •1972 •2005 Maximum. 9 9 • • • • • • • • Lead •1964 •1996 Mean of 4. 2 ’b •*21 •1050 •1059 Zinc, cast in iron mould . . •455 •2257 •2301 Minimum. 9 9 9 9 • • 9 9 •465 •2307 •2352 Maximum. 9 9 9 9 •• •2282 •2326 Mean of 2. The contraction of wheels is anomalous, as is shown by Table 16. The great irregularities in the apparent contraction arise in great part from the practice of “ rapping ” the pattern in the sand, to make it an easy fit, and enable it to be drawn out with facility. This is most influential in small heavy wheels, of great width of face : in some cases, and in rough hands, the casting of a small and heavy pinion may be quite the full size of tlie pattern. Tlie allowance to be made is, therefore, not uniform, but must be fixed by judgment. But besides this, a wheel, &c., is not so free to contract as a straight bar, and in any case its contraction will be rather less. EXPANSION OF LIQUIDS, 17 Table 16. — Of the Contraction in Casting Spur Wheels in Cast Iron. Extreme Width Contraction. Pitch diameter ol of Pf»r fnnf Wheel in Teeth in Total Casting. inches. inches. in inches. Of Of Casting. Pattern. ft. in. inches. inches. 10 2| 3i 12 1*08 •1059 •1040 6 2^ 9 •54 •0893 •0886 6 1| 3J 11 •375 •0613 •0610 5 5^ Si 11 •345 •0631 •0628 2 Hi Si 12 •11 •03896 •03884 2 4if 3i 9 •115 •0397 •0396 (12.) “ The Ex^pansion of Liquids .^' — The expansion of liquids must be estimated by the increase in volume. Eeferring to the former illustration (11), we may suppose that a cubic foot of the liquid is contained in a vessel that does not itself expand with heat, but of such a height as to allow the liquid to expand in that direction only. When, by expansion,^ the cubic foot of liquid becomes 8 cubic feet, it is obvious that the vessel, whose length and breadth is fixed, must be 8 feet high to hold the ex- panded liquid, and thus the linear dilatation is in fact the actual expansion in volume. But if the vessel is itself expansible, the observed expansions are apparent only, not real and absolute, being in fact the Table 17. — Of the Variation in the Expansions of Bodies at different Temperatures, from the Experiments of Dulong. Iron . . Copper Glass 32° to 212°. 32° to 392°. 32° to 572°. Linear Expansion for Fahrenheit. •000006567 •000009545 •000004785 •000005125 •000008158 •000010462 •000005616 Mercury .. Expansion in Volume for 1° Fahrenheit. •0001001 •00010241 •00010482 A 0 18 EXPANSION OF WATER. difference between the expansion of the liquid and that of tlie vessel containing it. Thus from Table 14 the expansion of glass in volume is *000013701, and the absolute expansion of mercury is *00010054, the apparent expansion of mercury in a glass vessel (such as a thermometer bulb, &c.) will therefore be * 00010054 - '000013701 = *000086839, as per Table 14. The expansion of water is exceptional and anomalous. It attains a minimum volume and a maximum density at dO*", and a departure from that temperature, in either direction, is accom- panied by expansion, so that 8® or 10® of cold produces Table 18. — Of the Volume, Specific Gravity, Expansion, and Weight of Water at different Temperatures. Temp. Fahr. Volume. Specific Gravity. Weight of a Cubic foot Expansion for 1° between the different in pounds. Temperatures. o 20 1*0012000 -99880 62 -.33 •0000822 • 0000.378 •0000129 •0000486 •0000895 •0001216 •0001516 •0001758 •0002010 •0002239 •000246 •000266 •000287 •000306 •000323 •000345 •000360 *000378 •000396 •000411 •000434 •000464 •000498 •000562 •000573 •000656 •000718 •000780 •000866 30 1*0003780 *99962 62 -.38 40 1-0000000 1-00000 62-408 42 1-0000258 *99997 62*406 52 1-0005123 *99950 62-377 62 1-0014070 -9986 62-321 72 1-002627 -9974 62*25 82 1-004143 *9959 62*15 92 1-005901 *9941 62-04 102 1-007911 -9921 61-92 112 1-010150 *9900 61-78 122 1-01261 *9875 61*63 132 1-01527 -9850 61-47 142 1-01814 -9822 61-30 152 1-02120 •9792 61*11 162 1-02443 •9761 60-92 172 1-02788 •9729 60-72 182 1-03148 -9695 60-5 192 1-03526 •9659 60-28 202 1-03922 •9622 60-05 212 1*04333 *9585 59-82 230 1*05115 •9513 59-37 250 1-06043 •9430 58-85 275 1-07289 • 9.321 58-17 300 1-08693 •9200 57*42 350 l - n .560 •8963 55-94 400 1-14840 •8708 54-34 4.50 1-18430 •8444 52-70 500 1-22330 •8175 51-02 600 1-30990 •7634 47-64 EXPANSION OF GASES. 19 about the same amount of expansion as 8° or 10° of heat. This is shown by Table 18, which is calculated by Tredgold’s rule — log. (t — 40) -j- 6*910909 = the log. of the Expansion. (13.) The expansions of solids and liquids are not equal for equal increments of heat, but increase with the temperature, as is shown by Table 17, from the experiments of Dulong ; but for practical purposes we may in most cases admit a uniform rate, having the value given by Table 14. (14.) ‘^Expansion of Gases'' — It has been found by experi- ment that all the gases, dry air, and even vapours out of contact with their generating fluids expand alike, with the same change of temperature, or very nearly so. Eegnault’s experiments give the expansion from 32° to 212° at *00367 of the bulk at 32°. The general formula becomes V' = V X 458*4 + 458*4 + ^ ’ in which Y = volume of gas, &c., at the temperature /, and V' = „ at the new temperature t\ Thus air whose volume at 32°= 1*0000 will have at 2500° a volume of 1*0000 x ^ ^ t = 6*032. Table 19 has 458*4 + 32 been caculated by this rule, and Table 20 gives a comparison of its results with the experiments of Dulong and Petit. (15.) When the pressure is not constant, the volume may be calculated by the law of Marriotte, namely, that the volume of any gas varies in the invey^se ratio of the pressure^ the temperature remaining constant The pressure here meant is the total pres- sure above a vacuum. Thus a cubic foot of air, in ordinary cases, has the pressm*e of the atmosphere upon it to begin with, say 15 lbs. (nearly) per square inch, and its volume, under a pressure of say 45 lbs. per square inch above atmosphere, will 15 1 X = *25 cubic foot. Practical men have generally 15 4- 45 & j to deal with pressures above the atmosphere, and are apt to forget to add the pressure of the atmosphere itself, and thereby make serious errors in calculation. (16.) When there is a change both in temperature and pressure, the rule becomes V' = V X which V, P, P' 458*4 + t and t are the Volume, Pressure, and temperature in one case? and V', P', and t the Volume, Pressure, and temperature in another case. Thus 10 cubic feet of air at ordinary atmospheric G 2 20 VOLUME, &C., OF DRY AIR. Table 19. — Of the Volume and Weight of Dry Air at Different ^J'emperatures under a constant Atmospheric Pressure of 29’02 inches of Mercury in the Barometer, the Volume at ^2° being 1. Temp. Volume. Weight of a Cubic foot in pounds. Temp. Volume. Weight of a Cubic foot in pounds. o 0 •935 •0864 o h.lO 1 i 2- 056 •0384 12 •960 •0842 600 2-158 •0376 22 •980 •0824 650 2-260 •0357 32 1-000 •0807 700 2-362 •0338 42 1-020 •0791 1 750 2-464 •0328 52 1-041 •0776 1 800 ! 2-566 •0315 62 1061 •0761 1 850 1 2-668 •0303 72 1-082 •0747 1 1 900 i 2-770 •0292 82 1-102 • 078 :! 1 950 2-872 •0281 92 1-122 •0720 1000 2-974 • 026 ^ 102 1-143 •0707 1100 3-177 •0254 112 1-163 •0694 1200 3-381 •0239 122 1-184 •0682 1300 3-585 •0225 132 1-204 •0671 1400 3-789 •0213 142 1-224 •0660 1500 3-993 •0202 152 1-245 •0649 1600 4-197 •0192 162 1-265 •0638 1700 4-401 •0183 172 1-285 •0628 1800 4-605 •0175 182 1-306 •0618 1900 4-809 •0168 192 1-326 •0609 2000 5-012 •0161 202 1-347 •0600 1 2100 5-216 •0155 2 J 2 1-367 •0591 2200 5-420 •0149 230 1-404 •0575 2300 5-624 •0142 250 1-444 •0559 2400 5-828 •0138 275 1-495 •0540 2500 6-032 •0133 300 1-546 •0522 2600 6-236 •0130 325 1-597 •0506 2700 6-440 •0125 350 1-648 •0490 2800 6-644 •0121 375 1-689 •0477 2900 6-847 •0118 400 1-750 •0461 3000 7-051 •0114 450 1-852 •0436 3100 7-255 •0111 500 1-954 •0413 3200 7-459 •0108 Table 20. — Of the Expansion of Dry Air by Heat. 1 Tempera- ture. Volume by Experiment. Dulong and Petit. Volume by Calculation. 1 Tempera- ture. Volume by iKxperiment. Dulong and Petit. Volume by Calculation. o - 32-8 •8650 •8678 o 392 1-7389 1 - 7,34 + 32 1 -0000 1-0000 i 482 1-9198 1-918 212 1-3750 1-367 1 .572 2-0976 2-101 302 1 -5576 1-551 1 680 2-3125 2-322 EXPANSION OF MOIST AIR, &C. 21 pressure, say 15 lbs. per square inch, and temperature 60°, would, if heated to 200°, and under a pressure of 40 lbs. per square inch above the atmosphere, or 15 -f- 40 = 55 lbs. above a vacuum, become 10 x X - 7 — — =3*7 cubic feet. 55 458*4+ 60 (17.) Expansion of Moist Air ” — When the vapour of water or other liquid, is present in the air or gas, another element becomes necessary in the calculation of its bulk at different temperatures, namely the elastic force of the vapour at the given temperature, which is given for water by Table 12. The rule then becomes Y' = V x X 4^0 ^ 5 which V, P, P + F 458-4 + F, and t represent the Volume, Pressure, elastic Force of vapour, and temperature in one case, and V', P', F', and i’ in another case. The principle of this rule will be best understood by reasoning out an example. Imagine a vessel containing 1000 cubic feet of air at 0°, saturated with vapour, and having a barometer enclosed indi- cating say 32*18 inches of mercury as the pressure of the mixture of air and vapour. Now it is an axiom that the pressure of such a mixture is the sum of the separate pressures or elasti- cities of the air and the vapours ; and as the elastic force of vapour at 0° is *044, it follows that the pressure of the air alone is in our case 32*18 — *044 = 32*136 inches. If the mixture be heated to say 112 °, it will behave exactly as dry air or gas if no water be present to supply vapour ; and the pressure remaining the same, the volume would become 1000 x ^ I n— = 1244 cubic feet. If now a little water be added 458*4+ 0° to saturate the heated air, the tension of vapour at 112 ° being 2*731, the pressure would in a closed vessel be increased to 32*136 + 2*731 = 34*867 ; and if the vessel be enlarged until that pressure be reduced to its normal state of 32*18 inches, its capacity would become 1244 x = 1348 cubic feet. oA * lo Putting this in the form of the formula already given, we have 1000 X 2-731 458-4 + 112 _ X . = 1348 cubic feet, as 32*136+ *044 458*4+0 before. General Eoy made some experiments on the expansion of moist air at a pressure of 32*18 inches. His results are given in Table 21. Col. 4 is calculated by the formula. 22 EXPANSION OF MOIST AIR, &C. Table 21. — Of the Expansion of Moist Air, at a pressure of 32T8 in. of the Barometer, from the Experiments of General Boy. Elastic force Tempera- of Vapour, Volume by Volume by ture. inches of Mercury. Experiment. Calculation. O 0 •044 1000-00 1000-0 32 •181 1071-29 1074-5 52 •388 1123-05 1125-1 72 •785 1182-50 1183-7 92 1-501 1255-14 1255-0 112 2-733 1353-75 1348-3 132 4-752 1491-06 1476-4 152 7-931 1689-00 1657-0 172 12-752 1929-78 1918-3 192 19-837 2287-44 2291-0 / 212 30-000 2672-00 2824-0 If the vapour present is other than that of water, of course the elastic force of that particular vapour must be taken, from Table 22. Table 22.--0f the Elastic Force of the Yapour of Alcohol, Ether, &c. &c., in inches of Mercury, from the Experiments of Kegnault. Temp. Fahr. j Water. Alcohol. Ether. Oil of Tur- pentine. Sulphuret of Carbon. Chlorofonn. o - 4 •036 •130 2-724 + 14 •082 •256 4-457 . . 3-110 32 •181 •500 7-177 •082 5-012 50 •361 •949 9-311 •091 7-846 5-133 68 •685 1-732 17-118 •169 11-740 7-488 86 1-242 3-087 25-079 •276 17-110 10-870 104 2-162 5-279 35-968 •441 24-311 14-331 122 3-621 8-673 49-921 •677 33-571 20-642 140 5-858 13-780 68-122 1-059 45-772 29-055 J 58 9-177 21-228 90-925 1-649 60-982 38-433 176 i 13-962 32-000 116-031 2-409 88-941 53-850 194 20-687 47-866 j 153-504 3-583 112-035 71-319 212 29-921 66-338 193-717 5-311 130-760 92-701 230 ' 42-337 92-591 246-024 7.374 162-846 118-913 248 58-712 126-291 • • \ 10-118 201-638 150-315 26 f ; 7 il -! 13,2 170-520 13 - 6(51 246-480 185-866 284 107-000 221 -957 18-201 , , 302 111-000 285-740 23-799 • • •• THERMOMETERS. 23 (18.) Thermometers .^^ — The expansion of bodies by heat has afforded the most convenient method of measuring temperatures. In the common thermometers mercury is used for medium tem- peratures, say from 0^ to 600° ; for lower temperatures alcohol is used, because it always remains fluid, even with the greatest cold which can be produced by artificial means ; for high tem- peratures metals are commonly used. There is an imperfection in all these bodies as measurers of heat, for as we have seen (13) their expansions are not equable for equal increments of heat ; but in the case of the mercurial thermometer it most fortunately happens that the variations of expansion in glass and mercury almost exactly compensate each other, so that mercury in glass has an expansion nearly equable at medium temperatures. Table 23, calculated from the refined experiments of Kegnault, Table 23. — Of the Error of the Common Mercurial Thermometer in Glass Tube, from the Experiments of Kegnault. Temperature by an Air Thermometer. 1 Error of Mercurial Thermometer in Degrees Fahr. Temperature by an Air Thermometer. Error of Mercurial Thermometer in Degrees Fahr. Temperature by an Air Thermometer. Error of Mercurial Thermometer in 1 )egrees Fahr. o 212 •000 o 374 -•630 536 + -936 230 -•036 392 -•550 554 + 1-440 248 -•090 410 “•450 572 + 1-944 266 -•162 428 -•360 590 + 2-610 284 -•270 446 -•270 608 + 3-240 302 -•360 464 - -180 626 + 4-320 320 -•468 482 + •090 644 + 5-400 338 -•576 500 + •360 662 +7-200 356 -•666 518 + • 684 gives the error of the mercurial thermometer in common glass, such as is ordinarily used for thermometers, and it shows that, for temperatures under 640°, the error is less than 1° Fahr. ; above that temperature the error becomes rapidly greater, and amounts to 7*2° at 662°. The amount of error seems to vary greatly with the kind of glass employed : with fine crystal glass the error at 662° was found by Eegnault to be as much as 19°. Thermometers '' — Air offers the great advantage as a measurer of heat, that its expansions are equal for equal incre- ments of heat, and it is particularly valuable at high tempera- tures, where the departures of solids from uniformity become very serious : this is strikingly shown by Tables 24 and 25, from 24 MELTING POINTS OF METALS, &C, Table 24. — Of the Melting Point of Metals, &c., according to tlie Experiments of Poiiillet; the temperatures above dull red heat were measured by au Air Thermometer. Wrought Iron, English, hammered . . Fahr. 29^10 M. Pouillet. , , French, soft 2730 9 9 Steel, maximum 2550 9 9 , , minimum 2370 9 9 Cast Iron, grey, 2nd fusion 2190 9 9 , , , , very fusible 2010 9 9 , , white, maximum 2010 9 9 , , , , minimum 1920 9 9 Gold, very pure 2280 9 9 , , standard coin Silver, very pure . . 2156 1830 9 9 Brass 1650 9 9 Antimony 810 9 9 Zinc 793 9 9 1 Lead 630 9 9 Bismuth 518 • 9 Tin 455 9 9 Sulphur 239 9 9 Wax, white 154 9 9 , , unbleached 143 Spermaceti 120 9 9 Stearine 109° to 120 9 • Phosphorus 109 9 9 Tallow 92 9 9 Oil of Turpentine 14 9 9 Mercury -40 9 9 Bismuth, 4 ; Tin, 1 ; Lead 1 201 9 9 ,, 8 5>3 ,, 5 212 9 9 ,, 5 ,, 3 ,, 2 212 9 9 ,, 5 ,, 4 ,, 1 .. .. 246 9 9 ,, 1 ,, 1 ,, 0 .. .. 286 9 9 ,, 1 ,, 2 ,, 0 .. .. 334 9 9 ,, 0 ,, 3 ,, 1 334 9 9 ,, 0 ,, 3 ,, 1 367 9 9 ,, 0 ,, 4 ,, 1 .. .. 372 9 9 ,, 0 ,, 5 ,, 1 .. .. 381 9 9 ,, 0 ,, 2 ,, 1 .. .. 385 9 9 ,, 1 ,, 3 ,, 0 .. .. 392 9 9 0 ,, 1 ,, 1 .. .. 466 9 9 ,, 0 ,, 1 ,, 3 .. .. 504 9 9 Common Salt, 1 ; Water, 3 4 Dr. Ure Sulpliuric Acid, sp. gr., -45 ’ * i , , J^hlier -46 ,, Ice 32 1 TEMPERATURE OF FURNACES, &C. 25 Table 25. — Temperatures corresponding to various Degrees of Light in Heated Metal, Furnaces, &c. M. Pouillet. Eed, iust visible , , dull , , cherry, dull , , , , full Fahr. o 977 1290 1470 1650 1830 2010 2190 2370 2550 2730 , , , , clear Orange, deep , , clear White heat , , bright , , dazzling . . ' tlie experiments of Pouillet and others with air thermometers, which exhibit glaring errors in the old tables of Wedgwood, Morveau, and Daniell. The scale of the thermometer is arbitrary ; in this country the scale of Fahrenheit is used, the distance between the freezing and boiling point of water being divided into 180 degrees, and Zero or 0° is fixed 32° below the freezing-point. On the continent the Centigrade scale is commonly used : here 0° is the freezing- point of water, and 100° the boiling-point. The readings of these two scales are easily convertible by the rules (C x 1*8) (F - 32) 4- 32 = F and “yrg — ^ = C, in which F and C represent degrees in the respective scales, Fahrenheit and Centigrade. Plate 12. gives a direct comparison of these scales to all useful temperatures. Table 26. — Of the Mean Temperature of the Air, in various parts of the Globe, at different Seasons of the Year. Height above the Mean Temperature. Sea in Feet. Year. Spring. Summer. Autumn. Winter. Irkutsk, Siberia o 14-5 17G 63° 0 o 20-1 o -38 Nain, Labrador 25-5 21-6 45*7 36-0 - 1-3 St. Bernard, Alps . . 15*890 30-2 28-4 43-0 31*3 18-0 St. Gothard, Alps . . 6873 30-6 27*1 44*1 32-0 18-3 Petersburgh 38-3 35-1 60-3 40’5 16-7 Moscow 480 38-5 43-3 62-6 34-9 13-5 2G ME.V:N TEMrERATURE OF THE AIR. Table 26 — continued. Height above the Sea in Feet. Mean Temperature. Year. Spring. Summer, Autumn. Winter. Christiana o 41*7 39 2 o 59 5 o 42-4 o 25 2 Stockholm 134 421 38 3 61 0 43-7 25 5 M[ontreal 43-7 44 2 69 1 47*1 17 5 Warsaw 397 45-5 44 6 63 5 46-4 27 5 Berne 1918 46*0 45 8 60 4 47*3 30 4 Stromness ( Orkney) 46-4 43 7 54 5 48-2 39 2 Copenhagen , , 46-8 43 7 63 0 48-7 31 3 Dresden 397 47-3 47 1 62 9 47-1 31 3 Edinburgh 288 47-5 45 7 57 9 48-0 38 5 Berlin 128 47-5 46 4 63 1 47-8 30 6 Nicolaief .. 48-7 49 3 71 2 50-0 25 9 Vienna 512 50-2 50 9 68 5 50-9 33 4 London 50-7 49 1 62 8 51*3 39 6 Paris 210 51-4 50 5 64 6 52-2 37 9 Penzance 52-0 49 8 61 7 53*8 43 9 Hobart Town 52-3 52 9 63 1 51-6 42 1 Turin 915 53-1 53 1 71 6 53-8 33 4 Trieste 288 55-8 53 8 71 5 56-7 39 4 Constantinople 56-7 51 8 73 4 60-4 40 6 Montpellier , , 57-4 56 8 75 9 61-0 44 5 Madrid 2175 57-6 57 6 74 1 56-7 42 1 Rome 174 59-7 57 4 73 2 61-7 46 6 Nice 60-1 55 9 72 5 63-0 48 7 Quito 9560 60*1 60 3 60 1 63-5 59 7 Naples 180 61-5 59 4 74 8 62-2 49 6 Lisbon 236 61-5 59 9 71 1 62*6 52 3 Buenos Ayres 62-5 59 4 73 0 64-6 52 5 Palermo 180 63-0 59 0 74 3 66-2 52 5 Algiers 64-0 63 0 74 5 70-5 54 0 Paramatta (Australia) .. 64-6 66 6 73 9 64-8 54 5 Madeira f Funchal) 65*7 63 5 70 0 67-6 61 3 Cape of Good Hope 66 ’4 65 5 74 1 66-9 58 6 Canton ,, 69-8 69 8 82 0 72-9 54 8 Cairo 72-3 71 6 84 6 74-3 58 5 Ceylon (Candy) 1683 72-9 74 3 73 0 72*3 72 1 Rio Janeiro 73*6 72 5 79 0 74-5 68 5 Calcutta .. 78-4 82 6 83 3 80-0 67 8 Jamaica •• 79-0 78 3 81 3 80-0 76 3 Note. — 'Flie Seasons in this Table are (for the Northern Hemisphere) : Sprinf^ — March, April, and May; Suininer — June, July, and August; Autumn — Sef)tcmber, October, and November ; and Winter — December, January, and February. TEMPEKATURE OF COMPRESSED AIR. 27 (19.) The law of Marriotte (15) is true only so long as the temperature remains constant ; but every change of pressure, and its accompanying change of volume, is simultaneously accompanied by a change of temperature, compression causing increase, and dilatation decrease. Thus if we take air at 60° and suddenly compress it to one-fourth of its volume as in (15), we should, by the law of Marriotte, have increased the pressure 60 to = 4 atmospheres; but we shall see presently that the compression causes an increase in temperature of 394° Fahr., as in col. 7 of Table 27, which will cause, in a closed vessel, a further increase of pressure, and instead of 4 atmospheres, we should have 7, as per col. 1, which, however, would subside to 4 when the temperature was reduced by the dissipation of heat to the normal temperature of 60°. Table 27. — Of the Heat produced by the Compression, and of the Cold produced by the Dilatation of Air, the Volume at Atmos- pheric Pressure being 1*0 at the Temperature of 59° Fahrenheit. Pressure Volume. Tempera- ture of the Air through- out the Process. Total Increase or Decrease of Tempera- ture. Above a Vacuum. Above the Atmosphere in pounds per Sq. in. Atmos- pheres. Inches of Mercury. Pounds per Square in. •167 5 - 2-45 3-56 - 151-6 - 210-6 •333 10 - 4-9 2-18 - 82-8 - 141-8 •5 15 * 7-35 1-634 - 35-7 - 94-7 •667 20 - 9-8 1-333 + 1-4 - 57-6 •833 25 - 12-25 1-137 + 32-0 - 27-0 1-000 30 - 14*7 o*-ooo 1-000 59-0 0-0 11 33 - 16-17 1-47 •9346 73-58 14-58 1-25 37-5 18-37 3-67 •838 83-84 24-84 1-5 45-0 22-05 7-35 •726 105-08 46-08 1-75 52-5 25-81 11-11 •6724 150-62 91-62 2-0 60 - : 29-4 14-7 •6116 175-00 116-0 3-0 90 - 44-1 29-4 •4588 255 - 196 - 4*0 120 - 58-8 44-1 •374 317 - 258 - 5-0 150 - 73-5 58-8 •320 369 - 310 - 6-0 180 - 88-2 73-5 •2807 414 - 355 - 7-0 210 - 102-9 88-2 •2515 453 - 394 * 8-0 240 - 117-6 102-9 •2290 490 - 431 - 9-0 270 - 132-3 117-6 •2062 524 - 464 - 10-0 300 - 147-0 132-3 •1953 553 - 494 - (1) ( 2 ) (3) (4) (5) (6) (7) 28 TEMPERATURE OF COMPRESSED AIR. The general relations between volume, pressure, and tempera- ture, are expressed bj the following formula) : — T.. (J.) -“x + T.) - 273, „a X in which Yi and T^are the pressure, volume, and temperature in Centigrade degrees in one case, and Pg Vg and Tg in another case ; P^ and P 2 are total pressures above a vacuum. Table 27 has been calculated by these rules. (20.) The heat thus evolved by the compression of air is found very troublesome in some cases, such as where air-pumps are used to supply air to diving-bells, and pneumatic piles for bridges, &c., being destructive to the lubricating oil, and to the valves, &c. It is usual in such cases to surround the barrels with cold water, continually changed by a current passing through the cistern, and we can calculate the quantity of water necessary in any particular case. Say we take the case of a set of double-acting pumps, having two barrels, each 12 inches diameter and 18 inches stroke, which, working against 100 feet of water, with 35 revolutions per minute, and about 15 horse- power, would discharge 165 cubic feet of air, taken at the ordinary atmospheric pressure per minute. The weight of the air is 165 x *076], = 12*6 lbs., and as it is compressed with a pressure of four atmospheres, the heat generated will be 258^ by col. 7 in Table 27, not 394°, as it would have been if the extra pressure generated by the temperature had not been Table 28 . — Of Frigorific Mixtures for the Artificial Proportional Parts, by Water 16 16 1 1 1 Sal Ammoniac 5 5 4 Nitre 6 5 2 . . i . . Common Salt 1 .. Nitrate of Ammonia 1 1 5 6 .. 1 3 Sulphate of Soda 8 3 6 6 8 5 1 Carbonate of Soda i . . 1 . . Phosphate of Soda 9 9 Potash Muriate of Lime i Crystallized Lime Snow or pound(!d Ice . . 1 . . Muriatic Acid 5 Diluted Nitric Acid .. .. 2 4 4 4 4 Jhluted Sulphuric Acid. . 4 . . 'J’ernp(!rature of Jngredients . . +r.o + 60 + 50 + 50 +50 + 50 +50 + 50 + 50 + 50 + 50 + 32 0 'J’emperaiure of the Mixture + 10+4 + 4 -1 — 10 — 14 -12 -21 0° + 3 0 —34 Cold produced 40° 46° 46° 57 jr.3 60 1 64 62 1 50 47 32 34 Note.— 'J’ o obtain these results the temperature of the ingredients must be reduced previously temperatures given, whatever may be the rRIGORIFIC MIXTURES. 29 allowed to escape. In our case the outlet valve of the pump opens when the pressure becomes equal to four atmospheres, which happens when the volume has become *374 or nearly (col. 5) and not *25, which would have been the volume if the temperature had not increased by the compression of the air. The specific heat of the air varies every moment with the pressure, as may be seen by Table 6 ; at the commencement of the stroke the air being at the ordinary pressure of 30 inches, its specific heat in a closed vessel is *1674; at the end of the compression, the pressure having increased to 120 inches of mercury, the specific heat is • 0837, and it varies every moment between those extremes. Taking a mean of all the pressures in Table 6, we find the mean specific heat to be *1154 ; the heat developed by the air will therefore be 12*6 x 258 x *1154 = 375 units ; and if it be allowed that the water may be heated 375 20°, the quantity necessary would be = 18*75 lbs. or 1 * 875 gallons per minute. The temperatures given by Table 27 will seldom be fully realized in practice, because the heat generated is rapidly dissipated by radiation and contact of cold air, &c. (21.) Frigorific Mixtures ” — The mixture of many salts with water, snow, or acids is productive of cold, and by this means a very low temperature may be obtained at all seasons and in all climates. The best experiments we have are the old ones of Mr. Walker, whose results are given by Table 28. Production of Cold, from the Experiments of Mr. Walker. Weight, in the Mixture. to the given temperature by some of the other mixtures. The four last compounds yield the previous temperatures of the ingredients. 30 HEAT OF THE GLOBE, &C. Cold may also be produced by the dilatation of air, as shown by col. 7 in Table 27. If compressed air be deprived by cold water or otherwise of the heat naturally developed by compres- sion, and then suffered to return to its normal volume by the relief of the pressure, a very low temperature may be obtained. Cold is also produced by evaporation (196). (22.) ‘^The Temperature of the Air at the Surface of the GloheT — The temperature of the air varies not only with geographical position, but also with the height above the sea level, and with local circumstances, so that observation alone can determine the mean temperature of any place. Table 26 gives the mean for the year, and for the four seasons, from the table of M. Mahl- mann in Humboldt’s great work on Central Asia, &c. Table 63 gives the mean temperature of every tenth day throughout the year in this country. The influence of elevation above the sea is very considerable, but seems to vary with the climate, the season, and the contour of the ground. Where the slope is gradual, the cold produced is Fahr. for about 430 feet; on steep mountain slopes about 355 feet ; and in balloon ascents about 330 feet. The temperature of the surface of the ground, follows pretty closely that of the air, but at a certain depth we come to a stratum whose temperature is invariable throughout the year, and is equal to the mean temperature of the air at that place. This depth varies, being in this country about 20 feet ; in tropical America the depth is only 2 feet. Below this stratum of uniform temperature the heat increases at about the rate of 1° Fahr. for every 58 feet of depth, so that if we assume 62° for the temperature of the surface, water would boil at melt at (212 - 62) X 58 5280 (2012 - 62) X ~5280 = 1*647 miles, and cast-iron would 58 = 2T4 miles. COMBUSTION. I CHAPTEE ON COMBUSTION. (23.) Combustion consists in the combination of bodies with oxygen, the result being usually the development of heat and light. The combustibles used in the arts are principally com- posed of carbon and hydrogen, as shown by Table 29. The Table 29. — Of the Chemical Composition of Combustibles, according to Peclet, &c. Elements. Coal. Coke. Wood. Peat. Perfectly dry. Ordinary state. Char- coal. Perfectly dry. Ordinary state. Carbon •812 •850 •510 •408 •930 •580 •464 Hydrogen •048 •053 •042 •060 •048 Oxygen •054 • « •417 •334 •310 •248 Nitrogen and Sulphur •031 • • . * Water •*200 •200 Ashes •055 •150 •020 •016 •070 •050 •040 Total . . 1-000 1-000 1 1-000 1 O O O 1-000 i 1-000 1-000 Elements. Oil of Tur- pentine. Alcohol. Olive Oil. Sulphuric Ether. Tallow. Bees- wax. Carbon •884 •5198 •7721 •6531 •790 •816 Hydrogen •116 •1370 •1336 •1333 •117 •139 Oxygen •3432 •0943 •2136 •093 •045 Nitrogen and Sulphur • • . . . . . . Water . . , , , , Ashes •• •• •• •• •• Total . . 1-000 1-000 1-000 1-000 1-000 1-000 carbon, combining with oxygen derived from the air, forms car- bonic acid, and the hydrogen similarly combining, forms water. Carbonic acid is composed of one equivalent of carbon (or 75), and two equivalents of oxygen (or 200), therefore a pound of car- 75 200 bonic acid consists of ^ = *2727 carbon, and — = 75+200 75+200 •7273 oxygen. 32 POWER OF COMBUSTIBLES. Water is composed of one equivalent of oxygen (or 100), and one of hydrogen (or 12*5), therefore a pound of water consists 100 -^- 12 ^-= 100 -^ W oxygen. Table 30. — Of the Calorific Power of Combustibles, by Experiment. Units of Heat Units of per lb. of Fuel, by Experi- ment. Authorities. Heat per lb. of Fuel, by 1 Theory. Hydrogen, burning to Water . . G2535 Dulong. » » j » .... G2032 Favi-e & Silbermann. » » > > .... 42120 1 Laplace. 39807 Clement. J 5 ? » .... Carbon, burning to Carbonic Acid , . 42552 ' Despretz. 12906 Dulong. , , from wood, burning to Car-l bonic Acid j 14544 Favre & Silbermann. Carbon, burning to Carbonic Acid . . 14040 Despretz. , , , , Carbonic Oxyde 2495 Dulong. 4453 Favre & Silbermann. Carbonic Oxyde, burning to Car-\ bonic Acid j 4478 Dulong. > » J » » » 1 lb. Carbon in the form of Carbonic 'I Oxyde, burning to Carbonic Acid / 4325 10411 Favre & Silbermann. Dulong. Wood, perfectly dried by artificial! heat / 6480 Kumford 6582 Wood, in ordinary state of dryness . . 5040 , , . . . . Dulong 5265 OUveOil 17752 17482 16279 Kumford. Colza Oil . . 20153 Lavoisier. 16753 Kumford. Alcohol 12339 Dulong 12593 ,, •• •• •• •• •• •• Sulphuric Ether 11151 Kumford. 16974 Dulong . . 15095 , , density .728 at G8° 14454 Kumford. Ttillnw 15550 16792 ,, ** •• •* •• •• •• Oil i29:ir) 99 #• •• •• Laplace. 19505 Dulong 18663 Na[)lit])a, density *827 13208 Kumford. Sulpliur 4()82 Dulong. 4032 Favre & Silbermann. PliOHpliorus Laplace. Pecs’ Wax, widte , 18900 18873 » » > » 17422 Kumford. THEORETICAL POWER OF COMBUSTIBLES. (24.) The experiments of Dulong, as given in Table 30, show that one pound of carbon, combining with the necessary quantity of oxygen, develops 12906 units of heat ; ,and one pound of hydrogen, similarly combining, yields 62535 units. The unit of heat is the amount necessary to heat one pound of water rFahr, See(l.) (25.) When a combustible contains hydrogen and oxygen in the proportion required to form water, they combine during the process of combustion, but give out no useful heat. If hydrogen alone is present, it yields usefully the full amount of heat due to it. When oxygen is present, but in too small a proportion to combine with the whole of the hydrogen, there remains an excess of hydrogen, which yields its due proportion of heat as before. (26.) Taking as an illustration, first, a body containing no oxygen — say oil of turpentine, which is shown by Table 29 to be composed of *884 carbon, and *116 hydrogen — then one pound will give — Carbon .. *884 x 12906 = 11409 units of heat Hydrogen .. *116 x 62535 = 7254 „ 18663 , (27.) Alcohol will serve to illustrate the effect of oxygen in a combustible, it being composed, as per Table 29, of *5198 carbon, *137 hydrogen, and *3432 oxygen. We have seen in (23) that oxygen requires one-eighth part of its weight of hydrogen to form water; the oxygen in alcohol will require •3432 — — = *0429 hydrogen ; whereas the combustible contains o •137 of hydrogen: there remains, therefore, -137 — •0429 = •0941 hydrogen in excess to develop its heat, and we have — Carbon *5198 x 12906 = 6708 units Hydrogen in excess ^ .. ^0941 x 62535 = 5885 „ 12593 „ Similarly for Olive Oil, composed of -7721 carbon, *1336 hydrogen, and *0943 oxygen, we have — Carbon ’7721 x 12906 = 9965 units Hydrogen (-1330 - — g— J = -1218 x 62535 = 7517 „ 17^2 „ D 34 THEORETICAL POWER OF COMBUSTIBLES. Tallow, composed of *79 carbon, *117 hydrogen, and *093 oxygen, will give — Carbon *79 x 12906 = 10195 units Hydrogen (^-117 - 1^- j = -1055 x 02535= 6597 „ 1G792 „ Sulphuric Ether, composed of carbon *6531, hydrogen *1333, and oxygen *2136, will give — Carbon *6531 x 12906 = 8429 units Hydrogen ^*1333 — = *1066 x 62535 = 6666 „ 15095 „ Beeswax, composed of carbon *816, hydrogen *139, and oxygen * 045, will give — Carbon *816 x 12906 = 10531 units ^ = *1334 X 62535 = 8342 „ Hydrogen ^ *139 — — ^ 18873 (28.) From the Government experiments on Coal, bylTayfair and He la Beche, we find, as a mean of 17 ditferent kinds of English, Welsh, and Scotch coals, the composition to be as per Table 29, and from this we have — Carbon *812 x 12906 = 10480 units ’ Hydrogen (-048 - = -041 x 62535 = 2564 „ 13044 „ Coke, containing * 85 carbon, without any hydrogen or oxygen, will yield *85 x 12906 = 10970 units of heat. (29.) Wood, perfectly dry, contains not only *51 carbon, but also *47 liydrogen and oxygen, but as these are in the pro- ])ortion j)r()j)er for forming water, they combine without yielding any useful lieat, and we have *51 x 1290G = 6582 units per pound of dry wood. Wood in its ordinary state of dryness contains 20 per cent, of water, its (;arbon is tliere])y reduced to *51 x *8 = *408, and its calorific 2 )ower to *408 x 12906 = 5265 units per pound. EXPERIMENTS ON FUEL. 35 Charcoal from wood, containing *93 carbon, will give *93 x 12906 = 12002 units per pound. (30.) Peat, artificially dried, contains *58 carbon, *06 hy- drogen, and • 31 oxygen. The oxygen in the fuel will combine . oi with — = *04 hydrogen, leaving *06 — *04 = *02 hydrogen 8 in excess, to develop its share of heat ; and we have — Carbon *58 x 12906 = 7485 units Hydrogen in excess .. *02 x 62535 = 1251 „ 8736 „ Peat in its natural state of dryness contains *464 carbon, *048 hydrogen, and *248 oxygen. The oxygen will combine with — = *031 hydrogen, leaving *048 — *031 = *017 hy- 8 drogen in excess, and we have — Carbon *464 x 12906 = 5988 units Hydrogen in excess .. *017 x 62535 = 1163 „ Charcoal of peat contains *818 carbon, and yields *818 x 12906 = 10557 units per pound. (31.) The heating power of combustibles, as found by the preceding calculations, is the maximum effect they are capable of producing. When we come to apply it to practice we shall see (96) that there are sources of unavoidable loss which reduce their useful effect considerably. (32.) The heating power of combustibles may also be deter- mined by direct experiment this has been done by calorimeters specially designed for the purpose, such as Kumford^s and others. But perhaps the most valuable experiments are those that have been made on the large scale on steam-engine boilers in practice ; we then obtain the heating power of fuel, in a form directly applicable to cases analogous to the experimental ones. (83.) Some care is necessary in applying experimental data to particular cases, to be certain that the circumstances are identical with the experimental ones. For instance, if we make experiments on a steam-boiler in full work, with steam up and fire in good order, and observe for some hours the quantity of fuel consumed, leaving off the experiment with steam up to the same pressure and fire in good order, &c., we get a certain result. 30 EFFECT OF WATER IN COMBUSTIBLES. but one that cannot be applied without correction to ordinary cases where a boiler is worked only 10 or 12 hours per day, and where there are losses during stoppages and at night, for which allowance must be made. (34.) Eumford’s apparatus consisted of a shallow vessel of copper filled with water ; the fuel to bo experimented on is burnt beneath it, and the products of combustion being collected by a hood or inverted funnel, are caused to pass by a worm cir- culating through the mass of the water, and the calorific power is estimated by the increase in temperature of the water and the vessel. To avoid loss of heat by the apparatus during the expe- riment, the mean temperature is arranged to be the same as the temperature of the air ; thus if the air was at 60° and the range of temperature 20°, the water would be taken at 50° to begin with, and would be 70° at the end of the experiment. With such an apparatus we should not obtain the total heating power in the fuel ; some of the heat would be lost by direct radiation from the burning fuel, and some would pass off with the air issuing from the apparatus after passing through it, which would always have a temperature higher than the water it was intended to heat. (35.) Say we had an apparatus like Eumford’s, made of sheet copper, weighing 10 pounds and holding 60 pounds of water at 50°, which became heated to 70° by of a pound or 4 ounces of dry wood. The specific heat of copper (Table 1) being * 095 by Eegnault’s experiments, the amount of heat absorbed by the vessel heated 20° will be 10 x.20 x *095 = 19 units, and the water absorbs 60 x 20 = 1200 units. The \ lb. of fuel has thus given out 19 -|- 1200 = 1219 units, which is equal to 1219 — = 4876 units per pound. Table 30 gives the calorific power of combustibles by Eumford and others. (36.) “ Effect of Water in a ComhustihleJ ' — When a combustible contains water, with which it is more or less saturated, the effect is twofold ; say we take wood in its ordinary state, containing 20 per cent, of water ; the really combustible matter is reduced to 80 per cent, of the amount contained in the same weight of wood j)erfectly dry, and of necessity the calorific power is reduced in tlie same proportion. The second effect is, that part of tlie lieat in tlic residue is consumed uselessly in evaporating tlie water. Wood ])orfectly dry gives by Table 30, 6480 units, which for wood in the ordinary state containing 20 per cent, of HEATING POWER OF COMBUSTIBLES. 37 water, is reduced to G480 x *8 = 5184 units, but tlie *2 water, say at 62^, will require for its evaporation (1178 — 62) x •2 = 223 units, so that the useful heat is reduced to 5184 — 223 = 4961 units : this correction may be neglected in many cases, the amount being small in proportion to the heat given out by the fuel. (37.) The experiments of Eumford have shown that the heat- ing power of wood varies only with the state of dryness ; that is to say, all the different kinds of wood in the same state of dryness yield sensibly the same amount of heat. (38.) The best experiments on the heating power of wood, on the large scale, are given by Peclet. In one case with a hot- water boiler in a public bath, 15,800 lbs. of water were heated 153^ by 440 lbs. of wood in the ordinary state of dryness. containing 20 per cent, of water ; this gives 15800 X 153 440 = 5494 units per pound of wood. This is an exceptionally good result, arising no doubt from the fact that the apparatus was so well arranged that the smoke left it at the temperature of the atmosphere, or nearly so, the whole of the heat given out by the wood being thus utilized. (39.) In another experiment on a steam-boiler, 3*24 lbs. of water were evaporated per pound of wood : the air passed into the chimney at 480°, and retained half of its oxygen, or 10 per cent, unconsumed (60). The temperature of the feed- water is not given, but assuming that it was 100°, the calorific power of the wood is 3-24 X (1178 — 100) = 3493 units per pound of fuel. (40.) This is a low result, but it is w^hat might be expected under the circumstances. The wood used contained 25 per cent, of water, therefore a pound of such wood contained only ’75 lb. of real combustible; the water would require *25 x (1178 — 62°) = 279 units to evaporate it, and there would be a further loss of heat by the air in the chimney which departs highly heated. We shall see in (55) and (60) that dry wood requires 80*5 x 2 = 161 cubic feet of air when the oxygen is only half consumed, as in our case ; therefore wood containing 25 per cent, of water requires 161 x *75 = 120 cubic feet; or 120 X *0761 = 9*1 lbs. of air, which, heated 4*20°, or say from 60 to 480, the temperature of the air in the chimney will carry off 9*1 x 420 x *238 = 910 units. Adding these together, we obtain 3493 -(- 279 4682 units per 38 HEATING TOWER OF COALS. pound of damp wood. Eumford’s experiments in Table 30 give 5040 units, the difference arises no doubt from loss of lieat by radiation from the boiler, &c., &c., which, as we have seen in (34) was avoided in the apparatus of Ilumford. The circumstances under which this experiment was made are analogous to most practical cases, and the heating power of wood in its ordinary state of dryness may be taken at about 3500 units per pound of fuel. (41.) Experiments were made upon the zree/cZy consumption of coals by two Elephant or French boilers, composed of a body of large diameter, connected by necks with three smaller ones about 20 inches diameter : the furnaces were Juckes’ self-acting. The experiments were made with two kinds of coal, one a kind of Welsh coal, and the other small coal, or screenings from Yorkshire coals; each kind was experimented on for 6 days, from Monday to Saturday, and the result includes, therefore, loss by radiation during the night, &c., &c., and in getting up steam each morning. The water evaporated was measured in a vessel from which the feed pump was supplied. (42.) With the Welsh coals 193876 lbs of water were 193876 evaporated by 28160 lbs. of coals, or ^ of water per pound of coal, about 80^, and hence we have The water had a temperature of (1178 - 80) X 193876 28160 = 7560 units per pound of Welsh coals. (43.) With the Yorkshire small coals, 167526 lbs. of water 1 G752G were evaporated by 29802 lbs. of coal, or ~ 29 gQ>> = 5*621 lbs. of water per pound of coal, or (1178 ^ 80) X 167526 29802 = 6172 units of heat per pound of Yorkshire small coal. (44.) Both these results are low, as might bo expected, but they apply without correction to analogous cases, which are very numerous. The engine icorlced about 12 hours per day. (45.) There is a source of error in such experiments, fre- rpiently overlooked, arising from priming^ in which water passes over with the steam, and is not evaporated to steam at all. In the two following exjierimcnts this was avoided by taking off tlie man-liole and allowing the steam to escape into the atmos- pliere ; the water was measured in by hand with a two-gallon S 2 >irit measure. HEATING POWER OF COALS. 39 Experiment with Cater’s patent tubular boiler, in which the fire is placed beneath the body, passes along the bottom, return- ing to the front by a set of 4 -inch tubes, and again to the back by another set of 3-inch tubes, thus traversing the length of the boiler thrice ; the temperature of the air as it left the boiler was 320°. In six hours, 628 lbs. of Duffryn Welsh coals evaporated 5140 lbs. of water at 52° to steam at 212°, and we have therefore (1178 - 52) X 5140 p , = 9220 units per pound oi coal. (46.) This boiler was full 20-horse power, but could not be worked up to more than 10 -horse in the experiment, because it primed or boiled over at the man-hole, when the fire was kept up to its prpper intensity. This is what might have been expected; by Table 11, each pound of water evaporated, formed 1640 cubic feet of steam, whereas with say 45 lbs. pressure, only 439 cubic feet would have been formed, and the tendency to boil over would be proportional to the volume of steam to be extricated from the water in a given time. To produce the same amount of priming with 45 lbs. steam, this boiler would require to be worked up to 10 x 1640 439 37-horse power. The result was, that the fire-grate could not be kept covered with fuel, and the economic result was not as good as it might have been if the boiler could have been worked up to its full power. (47.) A similar experiment was made with a Cornish boiler, the fire being inside as usual. In six hours, 361 lbs. of Dulfryn coals evaporated 2600 lbs. of water at 58° to steam at 212°, and we have therefore ^ 2600 ^ 3055 units per pound gf coal. (48.) In the extensive experiments made by H.M. Government, a Cornish boiler was used ; the results obtained are given with others in Table 31, which gives a general view of the preceding ex- jierimental results ; we have added in the third column the quan- tity of fuel required per horse-power, taking that to be equal to a cubic foot of water evaporated to steam, which is a good general practical rule. The quantity of heat required to raise the tem- perature of water from 60°, and to evaporate it is by ( 8 ) equal to 1178 — 60° = 1118 units per pound, or 1118 x 62*32 = 69674 units per cubic foot ; thus in the case of Newcastle coal. , 69674 we have 8 • 46 lbs. of coal per cubic foot of water, as per Table 31, and it is the same at all tcmperatui*es. 40 AIR REQUIRED FOR COMBUSTION. Table 31 . — Of the Heating Power of Combustibles from cases in ])racticc. Units of ' 1 leat or ' Pounds of Water at 2120 to Steam at any Pres- Pounds of Fuel to Pounds of evaporate Kind of Boiler, &c. Authorities. Kind of Fuel. Water iCulMcfoot heated 1° of Water by 1 lb. of Fuel. sure per Pound of Phiel. at 6<)0, to Steam. Hot- water boiler Peclet . . . . AV'ood (‘2 water) .^)49t 5-687 12-68 Steam-boiler . . . . 99 AVood (‘25 water) 3500 3-62 19-90 Steam, Elephant, boiler ) (weekly result) . . f Easton & Amos AVelsh Coals '75* *0 7-62 9-21 99 99 99 99 99 Yorkshire, small 6172 6-40 11-28 Steam-boiler, Cater's > J’atent 'I'ubular . , s 99 99 Duffryn Coals . . 9220 9-52 7-55 Steam-boiler, Cornish ) single Sued . . . . j 99 99 8066 8-35 1 8-64 99 99 99 ( H. ]\r. Com - 7 \ missioners < AVelsh Coals 9080 9-40 7-67 >9 99 99 99 99 Newcastle Coals 8230 8*52 8-46 99 99 99 99 99 l^ancashire Coals 7612 7-H8 9-15 99 99 99 99 99 Scotcli Coals 7515 7-80 9-24 Steam-boiler . . . . James Watt . . Staffordshire Coals 65'i0 6-72 1 10-70 99 99 . • • • 'I’redgold Peat (Dartmoor) 2400 2-48 ! 29-00 1 (49.) Air required to support Comhustion .^' — A knowledge of the quantity of air necessary for different combustibles is important, in order to determine the sizes of flues, &c. (50.) We have seen in (23) that carbonic acid is composed of *2727 carbon, and *7273 oxygen; and as atmospheric air is composed of two equivalents (or 350) of nitrogen ; and one equivalent (or 100) of oxygen, it follows that one pound of air consists of 100 350 + 100 = *222 lbs. of oxygen, and 350 350 + 100 = *778 lbs. of nitrogen. A pound of carbon will require • 7273 *2727 ~ 2*67 lbs. of oxygen, which is the amount con- 2 67 tained in 7 ^22 ~ 12 *03 lbs. of air; and as a cubic foot of air 1203 at 62"^ weighs, by Table 19, *0761 lbs., this is equal to = 158 cubic feet of common air at ordinary temperatures. Tliis is tlic minimum amount necessary for the combustion of a pound of carbon. (51.) Water being composed of '111 hydrogen and *889 AIR REQUIRED FOR COMBUSTION. 41 oxygen, one pound of hydrogen requires oxygen, which is the amount contained in •889 •111 8 •222 8 Ihs. of 30 lbs., or - j - = 473 cubic feet of common air at 62% and this is the minimum amount necessary for the combustion of a pound of hydrogen. (52.) From these elements we can easily calculate the quantity of air required for any combustible whose composition is known. (53.) The average composition of coal is given by Table 29 at ^812 carbon, and *048 hydrogen, which last is, by (28), re> duced to *041 hydrogen in excess, and we shall require (812 X 158) + (*041 X 4:73) = 147 • 6 cubic feet of air at 62°. (54.) Coke, by Table 29, contains ^85 carbon, and will require ^85 x 1^8 = 134*3 cubic feet of air at 62° per pound. (55.) Wood perfectly dried by artificial means, contains *51 carbon, and will require *51 x 158 =80*5 cubic feet of air at 62° per pound. (56.) Wood in its ordinary state of dryness contains, by Table 29, about 20 per cent, of water, and the carbon is thereby reduced to • 408 per pound of wood, which will require * 408 X 158 = 64*5 cubic feet of air per pound. (57.) Charcoal, of wood, contains *93 carbon, which will require • 93 x 158 = 147 cubic feet of air at 62° per pound. (58.) Peat, perfectly dried by artificial means, contains • 58 carbon, *06 hydrogen, and •31 oxygen. The oxygen will com- * 31 bine with -^th of its weight of hydrogen, or -^ = * 04, leaving • 06 — * 04 = • 02 hydrogen in excess, and the air required will be (*58 X 158) + (‘02 x 473) = 101*1 cubic feet of air at 62° per pound of dry peat. (59.) Peat, in its ordinary state of dryness, produced by long exposure to the air, contains 20 per cent, of water, and its carbon is reduced to * 464, the hydrogen to • 048, and oxygen to *248. The oxygen will combine with ^th of its own weight of •248 hydrogen, or = *031, leaving thus *048 — •031 = *017 hydrogenin excess, and the air required will be (*464 x 158) 42 PRODUCTS OF COMBUSTION. + (‘017 X 473) = 81 ‘3 cubic feet of air at G2° per pound of ordinary peat. (60.) The quantities of air, as found by tlie preceding calcu- lations, is the minimum absolutely necessary to furnish the oxygen required to support the combustion. Practice has led to the use of a much larger quantity of air than the theory indicates, the reason being, no doubt, to avoid the formation of carbonic oxyde instead of carbonic acid^ which would be the result if the supply of oxygen were too small, see (103). Analyses of the air that has passed through the fires of well- arranged steam-boilers, &c., show that the air retains 10 per cent, of oxygen unconsumed, so that in such cases double the quantity of air has been used ; and we may admit as a practical rule, that the quantity of air used should be double the minimum theoretical quantity. The effect of varying the quantity of air on the useful result will be seen by (101). THE VOLUME OF GAS, &C., PRODUCED BY THE DIFFERENT COMBUSTIBLES. (61.) If combustibles were formed of pure carbon, the only product would be carbonic acid : this is the case with some kinds of fuel, such as charcoal and coke. When a combustible contains hydrogen, it combines with 8 times its own weight of oxygen, derived from the oxygen in the fuel, or from the air which supports the combustion ; in either case water is formed, which again becomes vapour. (62.) When a combustible contains water already formed, and with which it is more or less saturated, vapour is formed from it, and is added to the products of combustion. By (col. 5) in Table 32 we find that a pound of vapour of water at ordinary atmospheric temperature and pressure has a volume of 21*07 cubic feet. Carbonic acid gas occupies 8*59 cubic feet, and oxygen 11*88 cubic feet. When oxygen and carbon combine, the volume of the carbonic acid gas is nearly the same as that of the oxygen from which it is formed; we have seen (23) that a pound of carbonic acid gas contains *7273 lb. of oxygen, wliicli will have a volume of *7273 x 11*88 = 8*64 cubic feet, being nearly tlie same as the volume of the carbonic acid gas formed, which, as we have seen, is 8*59 cubic feet ; so that when a combustible contains carbon only, the volume of gas in the chimney is the same a^J the volume of aii’ entering VOLUME OF AIR, ETC., IN CHIMNEY. 48 Table 32. — Of the Density of Gases and Vapours, Air at the same Temperature and Pressure being 1*0 ; also the Weight of a Cubic foot at 62°, under an Atmospheric Pressure of 29*92 inches of Mercury. Density, Air at the same Temp, and Pressure being 1 (Regnault). Specific Gravity or Density, Water at 62° being 1 * * 0. Weight of a Cubic foot in Pounds. Cubic feet at 62° in lib. Air (atmospheric) . . 1-COOOO •001221 or •07610 13*14 Hydrogen Gas •06926 •0000846 „ *00527 189*70 Oxygen Gas 1*10563 •001350 „ ,1^ *08414 11*88 Nitrogen Gas *97137 •001185 „ *07383 13*54 Carbonic Acid Gas . . 1 *.52901 •001870 „ *11636 8*59 Vapour of Water • 6235 •0007613 „ TaVs •04745 21-07 , , Alcohol . . 1*589 •00194 „ •12092 8’27 , , Sulphuric Ether 2 *.586 •00316 „ •19680 5*08 , , Oil of Turpentine 4*760 •00581 „ ^ •36224 2*76 , , Mercury . . 6*976 •00850 „ •52987 1*88 (1) (2) (3) (4) (5) Note.— The densities of the vapours in column (2^, &c., are reduce S • C 5 CC <05 CO CO ^ r, y 0 ao CO <05 (M ICO 0 S ? 0 / --H ^ O -.J ^ CQ.-;: ^ (M t— i I-H rH CC r-t rH CO rH CM rH CM rr rH rH "O) 'd t-, 0 o p< .B t*o’ eis CO cio CC CM CM CC CM s 0 CO -H 00 CC CM • 0 o 3 « CO 0 CO CM JO CO o O f- . SO, rH <05 rH cp CO .o :3 QJ P,«o -- ^ oS 05 I Ci (M • rH (CO g rH rH rH o ti . *^0 IQ C 05 rH <05 CM CO - 0 ^^ (05 0 CO (M <05 0 CO g p C CM (M rH rH &• to CO lO 0 '<±1 CO r^^ CO be w ' u Cj B o c 0 0 0 »o 0 0 s OJ CM O U o no <0 nO 0 <0 •pH c3 CQ >> f-l d •9 O cS O TEMPERATURE OF AIR FROM FURNACES. 47 (77.) Supposing that the fuel used was coal, one pound of coal yields 18,000 units of heat (28), and requires 147*6 cubic feet of air (53) at 62°; and allowing double, as per (60), we have 147*6 x 2 = 295 cubic feet, or 22*44 lbs. of air per pound of coal. Thus a pound of coal will heat a pound of water 13000 degrees ; and as the specific heat of air by Eegnault’s experi- ments is • 238, an equal weight of water being 1, it follows that a pound of coal will heat a pound of air ~ 54600°; and as we have 22*44 pounds of air to carry off this heat, the increase of temperature will be 54600 22*44 = 2434°, and as the air enters the fire at 62°, it must depart at 62° -f 2434° = 2496°. (78.) We assumed, for the purpose of illustration, that the fire- brick of which the furnace was constructed was a perfect non- conductor, which is not a fact — a considerable portion of the heat will be transmitted to the outer surface, and dissipated by radiation there. Allowing that 10 per cent, of the heat is dissipated by radia- tion, &c., in the case Fig. 4, the heat carried off by the air is reduced to 13000 x *9 = 11700 units, and the temperature of the air to (2434° x *9) + 62 = 2252°. The other kinds of fuel, yielding their respective quantities of heat to the air required for their combustion, will give different temperatures to that air as per (col. 11), Table 33, allowing throughout 10 per cent, for loss by radiation. (79.) The temperature of the air will also vary with the volume admitted : in the case we have investigated the oxygen was half consumed. Table 34 gives the variation of temperature for coal with different volumes of air. Table 34. — Of the Temperature of the Air from a Fire-brick Furnace, showing the effect of using different volumes of Air. State of the Oxygen. Cubic feet. lbs. Increase of Temp. Temp, of Atmosphere. Temp, of Air as it leaves the Fire. Half burnt Quarter bum t .. Onc-fifth burnt . . 295 = 22-44 590 = 44-88 737 = 56-10 000 2190 + C2 = 2252 1095 + 02 = 1157 876 -f 62 933 48 EADIATING POWER OF COMBUSTIBLES. (80.) It should be observed that the quantity of air cannot be reduced below a certain amount, for obviously the temperature of the air cannot be higher than the temperature of the fire itself. Now the temperature of a fire at white lieat, according to Pouillet’s Table 25, is 2370°; a cubic foot of air lieated from G2° to 2370° requires *0701 x (2:i70 - 62) x *238 = 41*8 units of heat; and the least quantity of air to carry off 11700 . . 11700 , units IS = 280 cubic feet. (81.) We will now investigate the phenomena of combustion in cases analogous to I’ig. 3, where the fuel is more or less siu*- rounded by surfaces of low temperature which absorb the radiant heat. By studying our three illustrations, it will be evident that the amount radiated will vary with the temperature of the absorbing surface, for if, as in Fig. 2, the walls were of the same temperature as the fire, no radiant heat would be given out or re- ceived, and generally the lower the temjierature of the absorbent, the more radiant heat would be received by it. THE RADIATING POWER OF COMBUSTIBLES. (82.) Peclet’s apparatus for ascertaining the radiating power of combustibles is shown in Fig. 5 : it consisted of an annular vessel of tin plate, the interval between the two cylinders being filled with water, the temperature of which was given by two thermometers with long bulbs, whose stems pass through corks. The internal cylinder was open at both ends, its surface was coated with lamp-black, and in its centre was suspended a cage of wire containing the fuel. In using this apparatus a given weight of fuel in a state of ignition is introduced and consumed, the radiant heat and that alone is absorbed, and raises the tem- perature of the water and the vessel itself : knowing the weight of the water, and of the vessel, also the increase of temperature with a given weight of fuel, we can calculate the heat given out by radiation. But a correction is necessary here, for evidently witli this form of apparatus we only obtain 'part of the heat i*adiated, because radiation takes place equally in all directions^ and part of it must escape by the open ends of tlie cylinder, and be lost. In Peclet’s apparatus the internal cylinder was 8 inches diameter and 12 inches high, and the ratio of the total radiant heat to tlie portion absorbed was in that case as 1*2 to 1, as shown ])y the following investigation. RADIATING POWER OF COMBUSTIBLES. 49 (83.) The principles on which this correction is made are illustrated by Fig. 6, in which A is the radiant body, say at 600°, placed in the centre of a hollow sphere, C D E F, at 100°. The body. A, will send out radiant heat equally in all directions, which will be absorbed by the sphere, but if two segments, C D and E F, be cut out and removed, the radiant heat that would have fallen on them passes out into the atmosphere and is lost ; but knowing the proportion which those two segments bear to the whole sphere, we can estimate the amount lost by their removal. The rules of mensuration show that the surface of any sphere or segment of a sphere, is given by multiplying the circumference of the sphere by the diameter, or by the height of the segment. The distances C E and C D are given, in our case 12 in. and 8 in. respectively, and the angle C E F being a right angle, we get the diameter C F of the circumscribing sphere = V 12^ -|- 8*^ = 14 ’4 inches or 45*2 inches circumference, and 45*2 X 14*4 = 650 total surface. The area of the two segments is 45 •2x 1*2x2 = 108, leaving in the apparatus 650 — 108 = 542 square inches to absorb the heat, the ratio of which to 650 the surface of the whole sphere is = 1 ' 2 to 1. (84.) With this apparatus the weight of water was 23 * 84 lbs., and the vessel itself which was made of tin plate weighed 4 • 9 lbs. The combustion of * 1232 lbs. of wood charcoal raised the tem- perature 25° *2, the water received 23 84 x 25*2 = 600*7 units of heat, and the vessel whose specific heat (2) was -11 received 4*9x25'2x *11 =13 6 units, altogether 600*7 -j- 13*6 = 614*3 units, which with a completely surrounding surface would have been 614*3 x 1*2 = 737 units, or 737 1232 = 5983 units per pound of fuel, and the total heating power being as we have 5983 shown (29) 12000 units, the radiant heat is ^2006 ~ nearly, so that 50 per cent is given out by radiation, and 50 per cent to the air passing through the fuel. (85.) The temperature of the ignited fuel would be about 2200°, and the mean temperature of the absorbing surface being 70° in the above experiment, the difference of temperature was 2200 — 70 = 2130°, whereas if the absorbing surface had been at 300°, as in high pressure steam-boilers, the difference would ’ have been 2200 — 300 = 1900° and the heat lost by radiation^. 50 RADIATING TOWER OF COMBUSTIBLES. ,,, ^ 5983 x 1900 . 5337 would have hecn 2130 “ 5337 units which is y2000 ~ •445, or say 45 per cent of the heat in the fuel, leaving 55 per cent, to pass off in the air. (86.) In another experiment with oak wood, made witli tlie same apparatus, -2145 lbs. of wood raised 23 *84 lbs. of water and 4' 9 lbs. of tin-plate 9^, which is equal to 23*84 -f- (4-9 X *11) X 9 X 1*2 -.^qq •. ^ = 1228 units per pound, •2145 ^ and the total heating power of ordinary wood being (29) as 1228 wo have shown 5265 units, the radiant heat is = *233 — 5265 say 23 per cent. ; leaving 77 per cent, to pass off with the air. (87.) In another experiment with peat charcoal, by the com- bustion of *0858 lbs. of fuel the temperature was raised 15° 3, which is equal to 23:_8^+(4_:9_x ^ 11) x • 2 ^ units per pound, and as the total heating power is by (30) 10557 units, the radiant heat is 5217 = *5 nearly, or 50 per cent, of 10557 the total heat ; leaving 50 per cent, to heat the air. Peclet estimates the radiant power of peat itself to be 50 per cent, also, the same as peat charcoal. (88.) The radiant power of coal, coke, &c., could not be satisfactorily determined by this apparatus, from the difficulty of keeping a small quantity of fuel ignited ; but by comparison Peclet estimates them as rather more than wood charcoal, which we found to be 45 per cent. (85) ; we may therefore estimate the radiant power of coal and coke at 50 per cent. (89.) We have shown (77) that the air leaving a fire of coals, when all loss by radiation was avoided, had the temperature of 2496° ; but when 10 per cent, was radiated the temperature was reduced to 2252°. When the fire is surrounded by cool surfaces 50 per cent, is radiated, and the temperature of the air is greatly reduced, the same weight having to receive only half the amount of heat. In the case of coals, the air leaves the fire at 13000 X ^ 02° = 1279° ; with wood in the ordinary state 22 44 X -238^ ’ ^ of dryness, •7^— 4-62° = 1797°; and so on with the ^ ’ 9*817 X *238 ' rest., COMBUSTION IN STEAM-BOILERS. 51 Table 33 gives a general and collected statement of tbe facts arrived at in the foregoing investigations. (90.) We may now apply all this to the case of a steam boiler, &c. We may assume that with ordinary firing about 5 per cent, more of the combustible matter in the fuel falls unconsumed from the grate, than in the experiments from which the data are derived, the useful heat being reduced to 13000 x *95 = 12350 units; we will also assume that each pound of coals requh’es 300 cubic feet, or 22 * 83 lbs. of air at 62°. (91.) Let Fig. 7 be a boiler or fire-box — not of a practical form, but such as to serve for the illustration of the case in which the fire being completely surrounded by an absorbing surface, will lose none of its radiant heat. In such a case 50 per cent, of the total heat in the fuel will be given out by radiation, and 50 per cent, to the air by which the combustion is supported ; the first, or 6175 units, is absorbed by the side, &c., of the fire-box, and 6175 units pass off with the air into the chimney and is lost. The temperature of the air as it departs may be found as before; the heat carried off by it would heat one pound of water 6175°, therefore a pound of air. 6175 •238 25950^, and as we have 22 *83 lbs. of air the increase of temperature will be 25950 22-83 1138°, and the final temperature 1138° -|- 62° = 1200°. (92.) This temperature will vary with the quantity of air admitted, as is shown by Table 35. Table 35. — Of the Effect of Different Volumes of Air in Steam- boiler Furnaces. state of the Oxygen. Cubic feet. Pounds. Increase of Temp. Temp, of Atmosphere. Temp, of Air as it Paves the Fire. o o O ' Half burnt 300 22-83 1138 + 62 = 1200 Quarter burnt .. 600 = 45-66 568 + 62 = 630 One-fiftli burnt . . 750 = 57-00 455 62 = 517 (93.) We have seen that a boiler like Fig. 7, in which the air escapes immediately out of the furnace, 50 per cent, of the heat in the fuel is lost. Part of this may be recovered by causing the heated air to pass in contact with the surface of the boiler, through a long circuit, on its way to the chimney. In Fig. 8 we have a . fire-box as in Fig. 7, and, for the purpose of e 2 52 COMBUSTION IN STEAM-BOILERS. illustration, we will suppose the boiler to have no return flue, but to be of great length, with the cliinincy at the end. It is found by observation of well-arranged boilers, that the air passes into the chimney at about 550°, — a high tem})crature is necessary to obtain the proper draught, as will aj)pcar herejifter (16G) ; we have seen that as it leaves the fire-box it is at 1200°, while from end to end the absorbiug surface in the case of a bigh-pressure boiler is at 300°. (94.) The amount of heat abstracted from the air at each point will be in proportion to the difference between the tem- perature of the air at that point and the temperature of the boiler ; at the fire-box end the difference is 1200° — 300° = 900°, while at the chimney end it is only 550° - 300° = 250°. Say we assume that one-tenth of this difference of temperature is parted with from point to point throughout, then the first diflference being 900°, one-tenth of that is 90°, and the next point will have a temperature of 1200° — 90° = 1110°. The difference is now, therefore, 1110° — 300° = 810°, and the tem- Ol A perature of the second point will be 1110° — ~ = 1029°, and thus we have calculated the successive temperatures in Fig. 8. (95.) The air departing into the chimney at the high tem- perature of 552°, carries off a considerable amount of heat, namely the amount required to heat 22*83 pounds of air 490° (or 552° — 62°) ; and this is equal to 22 * 83 x 490 x ’ 238 = 2663 units, or about 20 per cent, of the total heat in the coals. (96.) There is also another source of loss of heat, namely by radiation and contact of cold air with the outside of the boiler and its brickwork, whereby the boiler-house is kept at a high temperature. The loss from this cause will vary very greatly with the greater or less exposure, &c. ; but for ordinary Cornish boilers, set in brickwork in the usual way in a closed boiler- house, we may take this loss at 12 per cent. Collecting these results we have the total heat in one pound of coal (13,000 units) distributed as shown by Table 36. Table 36. — Of the Distribution of the Heat in One Pound of Coals, by an ordinary Boiler, with internal fire. In Afiltes, left unhnrnt IROOO x 5% = 050 units. Lost by Air in Ciiiinney IROOO x 20% = 2600 , , Lo.st hy Jiadiation, &e., in Boiler-house .. IfiOOO x 12% = 1560 ,, Utilized in production of Steam .. .. 13000 x 63% = 8100 ,, Total 13000 EFFECT OF “ LENGTH ” IN BOILEKS. 53 (97.) “ Efficiency of Long mid Short Boilers ^ — We have stated (93) that a high temperature of the air in the chimney is necessary in order to obtain a good draught ; but if it were not so, an extreme length of boiler would be necessary to secure even a small portion of the heat wasted. Say we doubled the length of our boiler, Fig. 8, continuing the calculation of the successive temperatures, we obtain the series given by Fig. 9. The heat lost by the chimney in this case would be the amount necessary to heat 22*83 lbs. of air 307^ (or 369° — 62°), or 22*83 X 307 x *238 = 1668 units. With the ordinary length of boiler the loss from the same cause was (95) 2663 units ; so that by doubling the length we obtain 2663 — 1668 = 995 units only, or 12 per cent, increase on the useful effect (8190 units). (98.) But even this would not be realized. In Table 36 we have allowed 1560 units as the loss in the boiler-house, &c., by a boiler of ordinary length : with double the length, the loss from the same cause would be greater, and would dissipate much of the extra heat obtained by the extra length. Indeed, it is obvious that beyond a certain point we should, by increasing the length, lose more from one cause than we should gain from the other. If we assume that in a boiler of ordinary length one half of the loss by radiation, &c., is due to the exposed front and furnace, and the other half to the body of the boiler, we shall be conducted to the results shown by Table 37. Table 37. — Of the Heat Lost by Long and Shokt Boilers, &c. Propor- tional length of Boiler. Tempera- ture of Air in the Chimney Heat lost by Air in Chimney. Heat lost by Radiation, &c. Left in the Ashes. Heat utilized. Ratio of Economy. Gain or Loss per cent. By Front, &c. By Body. Total. o Units. Units. Units. Units. Units. Units. i 778 3890 780 + 390 = 1170 650 7290 897 - 10*3 3 4 648 3184 780 + 585 = 1365 650 7802 960 - 4*0 1 552 2663 780 + 780 = 1560 650 8127 1000 0*0 IJ 432 2010 780 + 1170 =: 1950 650 8390 1032 + 3*2 2 369 1668 780 + 1560 = 2340 650 8342 1026 4 - 2*6 This would show that by reducing the boiler to half the usual length we should only lose 10 per cent. ; one, half as long again as usual, would give only 3 * 2 per cent, more useful heat ; and by increasing the length to double we should actually lose rather than gain. These results are not given as absolutely correct, EFFECT OF FORCED FIRING. r>4 but will at least serve to sliow approximately tlie relative clTcct of long and short boilers. (99.) We have so far supposed that a certain fixed quantity of fuel was used with a certain fixed volume of air, but with a powerful chimney and a regulated draught, the velocity of the current of air might be so adjusted that the volume was, say, reduced to one half or doubled, c^c., c^c. Say we admit a double volume, producing in our case a double velocity, if a double quantity of coals were burnt in the same time, we should have the common case of a fire forced beyond its proper intensity ; if, on the other hand, the quantity of fuel was not increased, then twice the necessary quantity of air would be used. In both cases a loss of useful effect would ensue, the amount of wliich we will proceed to investigate. (100.) ‘‘Effect of Forced Firing^ — Taking the first case of a forced fire, and referring again to Fig. 8, we shall observe that with double velocity, the air which in a given time moved half the length of the boiler from A to B, will in our new case have moved from A to C ; and as the amount of heat lost by it is a question of time, it follows that instead of being reduced to 652^, as at C, it will be reduced to 778° only, as at B, and will pass ofi* into the chimney at this last temperature, bearing off with it 778° — 552° = 226° more heat than in the former case ; so that by forced firing we lose for each pound of coal 226 x 22*83 x • 238 = 1228 units of heat ; and as with ordinary firing we obtained 8190 units (Table 36), we nov/ obtain only 8190 — 1228 = 6962 units, showing a loss of nearly 15 per cent, by forcing the fire to the extent of a double consumption of fuel. (101.) “Effect of too much AirT — When more air is used than is necessary to effect the proper combustion, a great loss occurs. We shall have as before 6175 units given out by radiation to the fire-box surrounding the fuel, and 6175 units to be carried off by the air ; but, instead of 22 * 83 lbs. of air per lb. of coal, we shall now have 45 ‘ 66 lbs. of air, its temperature will therefore 1)0 raised -^1 - — = 569°, and the atmospheric tem- 45*66 X *238 peraturc being 62°, it will leave the fire at 569°-[-62° = 631° ijistead of 1200°. Then, calculating as before with Fig. 8 and (94), wo liavo 631° — 300° = 331 for the first difference, and ‘>‘>1 = 33 for the decrease between the first and second points, 10 the second point will therefore be 631° — 33° = 598°, &c., &c. ; EFFECT OF TOO MUCH, AND TOO LITTLE AIR. 55 and thus we obtain the series of numbers in Fig. 10. It will be observed that as the velocity is double, the distances between point and point will be doubled, and the air will pass into the chimney at 475°, or 475° — 62° = 413° above the tem- perature of the atmosphere ; and the amount of heat lost thereby will be 45*66 x ^13 X ‘238 = 4488 units, and we have — In ashes left unburnt 650 units. Lost by air in chimney 4488 „ Ditto by radiation, &c., in boiler-house .. 1560 „ Utilized in production of steam .. .. 6302 „ _13000 „ With the proper quantity of air, 8190 units were utilized per lb. of coal (Table 36), whereas now we have only 6302 units, showing a loss of 23 per cent, of useful effect, by the admission of double the necessary quantity of air. (102.) This is a fruitful source of loss of fuel in very many cases : an ignorant stoker delights in a roaring fire and sharp draught, unconscious of the loss of fuel incurred ; in all cases the damper should be regulated so as to produce a moderate draught, and this is especially important where there is a tall or powerful chimney. (103.) Ejfect of too little Air ^ — Care must be taken on the other hand not to curtail the supply of air too much, as in that case also a great loss would arise from the formation of carbonic oxyde instead of carbonic acid ; carbonic oxyde being formed of one equivalent of carbon and one oxygen, whereas carbonic acid is formed of carbon 1 and oxygen 2. The experiments of Favre and Silbermann in Table 30 show that a pound of carbon burning to carbonic oxyde yields only 4453 units of heat, whereas it would yield 12906 units in burn- ing to carbonic acid by the experiments of Dulong. The coal we have been considering (28), which is composed of * 812 carbon and *041 hydrogen in excess, will give — In carbon burning to carbonic oxyde *812 x 4453 = 3616 units. „ hydi-ogen in excess to water • 041 x 62535 = 2564 „ 6 l 80 „ The same coal with a proper quantity of oxygen (28) gave 13044 units, we have therefore in our case ]^q ~|4 = *46, or 46 per cent, of the available heat which the fuel could supply. 56 TROPEU REGULATION OF THE FIRE, &C. (104.) We have here taken an extreme case, the quantity of air being only half the amount absolutely necessary for proj)cr combustion, and by (60) ^th of the amount usually consumed in well-regulated furnaces. Where the air is curtailed, but to a less degree, part of the carbon will he tianformcd into carbonic acid, and part into carbonic oxyde, and the result will be inter- mediate between the extremes we have given. Say we have oxygen to 1 carbon ; in that case they will still combine only in the proper proportions to form one or other of the two pro- ducts, that is to say, 1 to 1, or 1 to 2, but they may arrange themselves thus : we have 1^- oxygen which will divide itself into two unequal portions, 1 oxygen combining with carbon, forming l.j carbonic acid, and ^ oxygen combining with ^carbon forming 1 carbonic oxyde, and in that case the coals we have considered would give — In carbon burning to carbonic acid *406 x 12906 = 5240 units. „ „ „ oxyde *406 x 4453 = 1808 „ „ hydrogen „ water ’Oil x 62535 = 2564 „ In this case we should have therefore j ^4 = '73, or 73 per cent, of the heat due to the best condition with the proper quantity of air. (105.) This will explain the anomalous fact that where there is a bad draught, not only is there difficulty in keeping up the steam, &c., but that there is a great consumption of fuel for the work done ; it might be expected that with a slow dull fire few coals would be burnt, or if by dint of forcing, fuel was largely consumed, it must yield the heat due to it, but it will be evident that it is possible for there to be a dull fire, a large consumption of fuel, and little useful result at one and the same time, and all this arising from insufficient draught. (108.) It will also be seen that in every case the proper regulation of the damper is a matter of extreme importance, and that nice adjustment is necessary to produce the best effect, too much or too little air causing a great loss of fuel ; an intelligent stoker, without any knowledge of the theory, finds by experience the height of damper with which he can do the work with least fuel ; if tlie work varies he watches and adjusts the damper accordingly, and sucli a man should have more consideration and better wages than he usually receives. ON STEAM-BOILERS. 57 CHAPTEE III. ON STEAM-BOILERS. Having in the preceding chapter investigated the phenomena of combustion, drc., we may apply the results to steam-boilers in practice, checking and, if needs be, modifying our deductions by the dictates of experience. We found in (98) that in all cases the most economical size of boiler was a medium one, and that a departure therefrom in either direction was followed by a loss of effect, an excessively long and a very short boiler giving less duty for the fuel used than a medium-sized one, properly pro- portioned to the work to be done. (108.) When heated air is in contact with a surface much colder than itself, the amount of heat given out is not only a question of time, but also (A position^ of the receiving surface. Let A, Fig. 16, be a square vessel full of cold water, and let heated air pass along the four flues BODE; the four sur- faces F G H J will absorb very different quantities of heat, although they are all of the same area, &c. The surface F will receive the most, for two reasons : the hottest of the heated air will occupy the upper portion of the flue, in immediate contact with the bottom of the boiler; and the water when heated becomes lighter there, and immediately ascends, and is replaced by colder v/ater ; and so the hed-t received is rapidly distributed through the mass of the water. But the surface H is in the worst possible position, for if the water in contact with it is heated, it becomes lighter and remains persistently in contact with the surface, refusing to communicate heat downwards ; thus it has been found by experiment that alcohol or turpentine, &c., suffi- cient to boil a given mass of water, may be ignited and burnt when floating on the surface of the water without increasing its temperature 1°. We may therefore admit that the surface H is useless, receiving no heat whatever. The surfaces G and J are in an intermediate position, and we may assume that they absorb a quantity of heat, a mean between F and H, or ^ ; the whole boiler therefore receives only half the amount of heat that it would have received if its whole surface had been as effective as F. We have thus to consider, not only the real surface of a boiler, but the effective surface, in estimating the result to be obtained. 58 “ EFFECTIVE ” HEATING SURFACE OF BOILERS. (109.) Tn Fig. 17 wc have an octagonal boiler, and by the same principles we find that if the surface F absorbs an amount of beat represented by 1, B will receive 0, and C D E the respective quantities and as in the figure. (110.) Let Fig. 18 be a cylindrical boiler filled with water for illustration, as before, we have the effective surface repre- sented by a scries of numbers, as in the figure from 0 at A to 1 at B, &c. ; and in all the three forms it will be seen that the effective surface is half tlie real surface where the whole is exposed to the heated air. (111.) In an internal flue, as Fig. 19, the same series of numbers occur, but in inverted order, the most effective surface being at the top, decreasing to 0 at the bottom as in the figure. (112.) With cylindrical boilers, heated outside, the lower half of the cylinder only is usually made available as in Fig. 19, in ill which case the effective surface is (Fig. 18) i A real surface exposed to the heated air, but where the whole surface is exposed, as in flues heated internally, the effective surface is half the real, as we have seen (HO). (113.) In determining the area necessary for doing a given amount of work, we must be guided by practical experience. There is great latitude here, for we have seen by (100) that a boiler, nominally of a certain power, may be forced up to double or more, with a certain loss of economy ; and also that a slight increase of efficiency may be obtained by a great increase in size, up to a certain point. Besides, the area necessary per horse-power, &c., varies somewhat with the size of the boiler ; a small boiler is not so effective in proportion to the area as a large one (see 98), the loss by radiation, &c., being much greater in proportion to the power. It is found by experience that a 4-horse boiler requires about 18 effective square feet of surface per horse-power; 10- horse, about 14 square feet; 20-horse, about 12; and 50-horse, about 11. The best rule we can give is an empirical one, II -|- ( V II X 2 • 5) X 8 = A, in which H = the horse-power, and A = tlic effective area of the boiler in square feet. Table 38 is calculated by this rule. (114.) The term horse-power is so indefinite that it is pre- ferable to estimate the power of a boiler by the cubic feet of water evaporated to steam per hour ; but fortunately, a common high-pressure engine of fair size, working without expansion, HORSE-POWER OF BOILERS. 59 Table 38 . — Of the Area of Surface for Steam Boilers and their Fire Grates. Nominal Horse- power of Boiler. “ Effective ” area of surface of Boiler in Square feet. Area of Fire Grate in Square feet. Total. Per Horse- power. Total. Per Horse- power. 3 59 19*60 3*28 1*09 5 85 17*00 4*72 *94 10 143 14*32 7*94 *79 15 198 13*20 11*0 *74 20 249 12*45 13*8 *69 25 300 12*00 16*7 •67 30 350 11*67 19*4 •65 40 446 11*16 24*8 *62 45 494 10*98 27*4 *61 50 542 10*83 30*1 •60 60 635 10*58 35*3 •59 except a small amount obtained by lap of the slide, consumes about a cubic foot of water evaporated to steam per hour. Thus an engine of 12-horse power — say with 12^-inch cylinder, 24- inches stroke, cutting off steam at 17 inches by lap of slide, with 40 revolutions per minute and 40 lbs. steam — would have 118 inches area of cylinder, and by Table 11 the volume of steam 476 for water 1, and would consume 118 X 17 X 2 X 40 X 60 1728 X 476 11*98 cubic feet of water per hour, or very nearly a cubic foot per horse-power. (115.) The term horse-power is convenient, and we shall use it therefore with this limitation. We can qualify the result, for application to other kinds of engines, afterwards. By (48) it will be seen that we have assumed 60° for the temperature of the feed water, therefore a cubic foot of w^ater at 60° evaporated to steam is equal to 1-horse power. Table 31 gives, in col. 6, the number of pounds of different kinds of fuel per cubic foot of water or per horse-power. (116.) When a boiler is applied for working a steam-engine, its power is usually estimated by that of the engine which it supplies, and as different kinds of engines require different quantities of steam to do the same work, it is necessary to consider that fact in fixing the size of the boilers. If we know GO HORSE-rOWER OF BOILERS. the particulars of the engine, we can calculate approximately tlio amount of water it will require as in (114). »Say we liave a 10-horsc high-pressure expansive engine, with a 12-inch cylinder, 2-feet stroke, 60 revolutions per minute, and by a double slide, cutting off its steam at ^rd. The area of the cylinder 1 foot diameter is *7854 of a square foot, and hence we have •7854 X 4 X 60 3 63 cubic feet of steam per minute, or 3780 cubic feet per hour. The bulk of steam at say 45 lbs. per square inch is, per Table 11, 439 times the bulk of water, we have therefore 378 ^ 439 8 * 7 cubic feet of water evaporated per hour, and the size of the boiler may be calculated for that quantity, instead of 10 horses, the power of the engine. Calculating in this way, we find by extensive observation on engines of various powers, that a common high-pressure engine, non-condensing and non-expansive, except by the slide lap, requires 1 cubic foot of water per horse-power per hour, a similar engine cutting off at ^rd, about * 87 of a cubic foot ; and a double-cylinder condensing-engine about the same. The safest course, however, is to calculate in each particular case by the capacity of the cylinder, &c., &c., and it is advisable in all cases to allow ample boiler power, see (100). (117.) As an illustration of the application of the rule in (113), &c., say we take the case of the 20-horse boiler. Fig. 39. The tube has an effective area of 3*14 x 3 x *5 x 21 = 98 square feet, and the body having the lower half only exposed to 3*14 X b * 5 the heated air gives ^ X *75 x 21 = 136 square feet effective area; so that we have a total of 98 -f 136 = 234 234 square feet, or = 11*7 square feet per horse-power. Table 39 gives the proportions of Cornish boilers from 3 to 55 horse power, and Figs, 36 to 43 other particulars ; the thickness of plates is in accordance with the best London practice, being rather stronger than the theory indicates. For convenience, we have given with each particular boiler 3 or 4 different lengths and tlie corres 2 )onding horse-power. (118.) Cornish boilers have become so common as almost to 8 U 2 )ersede all otliers, but the same rules a2)2>ly to the many forms of tubular and other boilers occasionally used, and do not require S 2 )ecial illustration, but it will be observed that a tube PROPOETIONS OF CORNISH BOILERS, 61 W. in O lO 0^ aJ S H o +-> C o3 w « W O PQ !I! 02 l-H >5 O O o oT K N O a CO >A « a> :Q ■£ T B .2 ,1^ CO c 3 ^ .• ■**! _S COCDCD':DTti(M'^(M irHrHOoa5G«oi-i^L'-t-L^L-t^t>cDcr>':D:ocox)':o':i:)CD'X)COOco (M lO *0 lO CD >r5 lO *jiOJOOOCDt^COi-Ht^>COOOO a, dCO^iOiOiOCDCOt-GOL'^asO^O'MCOiO-wiCCOOiCOCvlOt^OCO t— Ir— li— (r— IrHr—lT— (r— Ir-HrHp-HC^lOIC^COCO c o CO CD Ci O CD O o o o ft. 2 (M (M CO tH io CD CD CD t- ^ V' fg = ^ easMCDcocoocoocoascoaicocDocoococoocoaiCDocDocD 4^rH(^^(^q(^^(^^^D(^^C0C0(^lC0C0T^lC0r^^•rt^^O(:0(:0'^T^lC0r^^lOTJ^l^:»iO »o ^T^iT-ICO»0»0'HHOOQOrHCCCDrHOOO^GOt^CDCD^-iOCO'^OGOQOGOOO Cj-Oi OC^:^CDCOTt^COCOCOCOCOCCC^lI-Hl-H^— (T— IrHrHrHrHr-tr-HOOOO (y r-tr—Kr— IpHr— (rHr— (r— IrHrHT-HrHrHi—IrHrH)— IrHi-HrHi-Hr— (f— (i-Hr-H tC!*- C o , (M r-H TtH 00 to J^CC (MCD(Mai>OOOOI>-COCOTiH-Ha5C 0 DGCaii— IrHCO'COOCOa, Ol^--HCO»Oi-COOi— lIO-t-GOOtGOrdHOS I— It-Hi— (!— ir— li-Hi— I >trHCOCOt^OCO r— IrHrHr-Hr— li— li— HrHi-Hr— IrHG^irHi— IC< 1 C CD ' lO r-l . .CD . .00 . ; CO I 1 1 cn t ' ; rH i ; : oo ! *. o * * ThlTH'^rt^ CO COtJh’ Thick- ne.ss of Plate. 1 “"j® * I «i« I *. ^[® 1 1 ►'j® I 1 I ^]® I : hn : : : hn : : oj® : : Diame- 1 ter , inside. i CCOOCDO CD O CDCD ^•COrflrttiO iO CD CDt- •80UlSu\f OAlSUndxS -uo(ij njnB8ud-n“i(| Ul JOMOd-OBJO) ( pilK ‘j’no|| jad uji!ai> tn J31«A\ JO Jo*y OIHOJ ... CO Tfl JO lO CD 00 X O OI 0'C0 O ICO 1— (T— (r-1r-(rHr-lrHr-ject ion able, because tlie valve may be leaky, or by care- less firing tlie pressure may frequently bo allowed to get up too SAFETY-VALVES FOR STEAM-BOILERS. 67 Table 42 .— Of the Sizes of Safety Valves for Steam Boilers. Diameter of Pressure of Steam in Pounds per Square Inch above the Atmosphere. 7 25 45 I 65 100 Valve. '^Effective" area of Boiler surface in Square Feet. In. 1 7 17 27 38 54 15 39 61 84 123 2 27 67 108 149 218 42 105 170 235 343 3 61 151 243 335 491 83 205 331 457 668 4 108 268 432 596 873 137 329 547 755 1105 5 169 418 675 932 1363 203 505 814 1123 1644 6 243 603 972 1341 1963 Velocity of discharge in Feet per Second. 1090 1560 1704 1784 1872 Note. — The effective area meant in this Table is explained in (108-113) ; see also Table 38 for the connection between the effective area and the horse-powers of boilers, &c. high, and blow off, without attracting attention. The open- topped form is preferable, and with ordinary care in firing should seldom be found blowing off. In adjusting the weight, allowance should be made for the weight of the lever and valve ; this can be done by the application of a Salter’s balance at B. Say we had a 3-inch valve for 45 lbs. steam, and that the effective weight at B was 12 lbs., and we had to determine the weight at C, the distances AB and AC being 31 and 19*5 inches respectively, or 1 to 6. The area of 3 inches being 7*06, wc ( t-qs x 45) - 12 ID'S 6 ■ “ 51 lbs. at C. The seat of the valve should not be wide, as in Fig 22, but very narrow, as in Fig. 26 ; with a wide seat, there is considerable uncertainty in estimating the actual or effective diameter, which is usually intermediate between the large and small diameters of the cone ; with a narrow seat this is avoided, F 2 G8 DAMPERS FOR BOILERS. {incl if well executed it is more easy to grind true and keep steam-tight. (128.) “Dampers .'^ — The area of a damper depends on tliat of the chimney, and where there is only one boiler it may have tlie same area as the chimney, if that is properly jiroportioned to the power of the boiler. Thus for a chimney, as per Table 55, 40 feet high, 12 inches square, we have =17*7 inches per horse-power, but for a chimney 150 feet high, and 2 feet 6 inches square, = 8*4 inches per horse-power only. As an approximate 108 rule, we may give no V H = A, in which H = the height of the chimney in feet, and A = the area of the damper in square inches per horse-power ; thus for a chimney 100 feet high we have =11 inches per horse-power. The form of damper is arbitrary, and must often be varied to suit the form of the flue, but for ordinary cases we may adopt standard sizes, a convenient proportion being 3 to 1, and thus we have the sizes and powers given in Table 43. The powers .of other sizes may be easily Table 43. — Of the Sizes of Dampers to Steam Boilers, with different Heights of Chimney. Height of Chimney in Feet. Size of the 40 60 80 100 ! 120 150 Damper in Square Inches of Damper per Horse-power. Inches. 17-4 14-2 12-4 11-0 10-0 9-0 1 Horse-power of the Boiler. 6 X 18 6-2 7-6 8*7 9-9 10-8 12 7 X 21 8*5 10 12 IB 15 16 8 X 24 11 16 18 19 22 0 X 27 14 ! 17 20 22 24 27 10 X yo 17 21 25 28 30 34 12 X 8() 25 HI 85 40 43 48 14 X 42 ;m 41 47 5B 59 65 10 X 48 44 54 62 70 77 85 ARRANGEMENT OF FLUES. GO calculated by tlie numbers in the fourth line of the table ; thus, say we required the size for a large damper to a set of boilers 300-horse power for a chimney 100 feet high ; the table gives 11 inches per horse-power, and we have 300 x 11 = 3300 square inches for the area required, and if the height was fixed at 6 feet, or 72 inches, the width must be 3300 “ 72 ~ = 46 inches. &c., &c. (129.) Area and Arrangement of Flues !"* — The volume of heated air which has to pass along a boiler flue is proportional to the horse-power, and as in order to give out a given amount of heat, or to be cooled to a fixed temperature, it must be in contact with the boiler a certain time, it follows that the velocity of the current should be proportional to the length of the boiler, so that a particle of air traverses it in the same time, whether the boiler be long or short, and departs into the chimney cooled down to the same temperature in all cases. Let us take three boilers, say 10, 20, and 30 feet long, and 4, 16, and 50-horse power, as per Table 39; the velocities should therefore be in the ratios 1, 2, 3, and the volumes of air in the ratios 4, 16, 50, or 1, 4, 12 nearly ; the areas must therefore be in the ratio of Volume Qp 1 _ 2 4 _ 2 ^ 4 go that the 50-horse Velocity 1 ’ 2 ’ 3 boiler requires a flue only four times the area of a 4-horse one with the length of boilers we have taken. If the volume of air is proportional to the horse-power, and the velocity proportional to the length, the area of flue would be in the ratio of Horse-power Length (130.) But we have seen (113) that the volume of air is not exactly proportional to the horse-power, small boilers consuming more fuel than large ones, and requiring more air. The area of flue must therefore be made proportional to the effective area of the boiler, rather than its horse-power, and the rule becomes X 47 = a, in which A = the effective area of the boiler in Li square feet, as in (108), &c., L = the length of boiler in feet, and a = the area of flue in square inches. Thus in our cases the 4-horse boiler requires 72-4 10 ” X 47 = 348 square inches, or 87 inches per horse-power; the 16 -horse 204 ~ 20 ' X 47 = 480 inches 70 8T11ENGTH OF STEAI^I-BOILEilS. 54 2 or 30 indies per liorsc-i)ower ; and tlie SO-Iiorsc \ x 47 = 851 indies, or 17 indies per horse-power. (131.) There are three principal ways in whidi the flues of a Cornish boiler may be arranged. Fig. 27 shows tlie best plan : the fire proceeding along the tube to the back of the boiler descends and returns beneath the body to the front, where it splits and passes on both sides to the chimney. This mode of setting is preferable to any other, because the bottom of the boiler is more effectively heated, and thereby a better circulation of the water is effected ; it requires, however, rather more lengtli in the house than other modes. Fig. 28 is another arrangement, in which the fire splits at the back, returning on both sides to the front, where it descends, and proceeds by one flue to the chimney. Fig. 29 shows a “ wheel ” draught, and is the most common form of any. The fire returns to the front on one side, passes under the boiler by an opening in the dividing-wall, and passes to the chimney on the other side. The flues which receive the first part of the heat should be lined with fire-brick ; the boiler should be fixed at such a level that the fire-bars are about 2 feet 6 inches above the stoke-hole floor. (132.) “ The Strength of Steam BoilersT — For almost all our knowledge of the strength of steam boilers we are indebted to the venerable Mr. Fairbairn. From his experiments the mean strength of boiler-plate is 23 tons, or 51520 lbs. per square inch, but the strength with ordinary single-riveted joints is 66 per cent, of the strength of a solid plate, or 34000 lbs. per square inch, and this has commonly been taken as a standard in cal- culating the strength of boilers ; but Staffordshire plates, which are extensively used by the best makers, bear only 20 tons per square inch, or 20 x *66 = 13*2 tons, or say 30,000 lbs. per square inch with single-riveted joints. Hence 30000 X 2 1 ~d P, in which t = thickness of plate in inches, d = the internal diameter of the boiler in inches, and P the bursting-pressure in pounds per square inch. Table 44 has been calculated by this rule for the thickness in the first column. The worhing -pressure may be taken at one- sixth of the bursting-pressure. STRENGTH OF STEAM-BOILERS, 71 bO •S 'S. a cS P-l o O ^ ^ 2 0*0 W ^ H O W « m o W >A < C O £ GO C CO 2 ^ if i> CO CO .2 .2 ^ d >o .2 d o .2 ^ d^ .2 d CO .2 ' 0 > dco .2^ d .2 dcq cCO CO GO t- CO 1-0 H-* CO 04 o 05 CO CO rH JO 05 CO rH JO 05 GN CO tH rH 04 CO CO CO TH rH cq CO »o l> CO O oq -■H lO I> CO o tM GO (M CO O JO 05 CO 4-- JO o rH GN 04 C 04 I:- rH CO tH JO Tfl 00 CO t> 04 co rH JO O Hq 0:5 CO r— 1 rH c-q 04 CO CO TH rH tH JO 00 CO oq o 00 JO CO rH (O; C5 tH C5 tH 00 CO 00 CO 00 04 t> rH tH 04 oq CO CO TH JO JO CM t-H CO GO O oq CO 00 O 04 tH iO O O O CO r-H CO rH CO 04 G^4 1— ( W rH 1 — 1 Ol 04 CO CO Th tH JO JO CO l> o t- HH rH l> tH tH CO JO rH iO rH oq 00 -H (05 JO rH CO 04 GO O’ CO rH Ol oq CO CO hH iO JO CO CO Ph w p-l (M »o o o oq JO I:- O oq JO o CO CO oq 00 lO rH CO O CO G^ GO JO Q rH I— 1 oq CO CO JO JCP CO CO C- 'A P (2 C5 05 00 t> CO CO JO tH tH CO CO !3 CO CO o t- "H r-H 00 JO 04 05 CO CO rH (M oq CO rd JO CO CO l> 00 p M P 'Si 00 CO "tH oq O 00 CO rH oq o GO CO p f-i 1> »o CO rH 05 CO -(f 04 o CJO JO CO P 6 A r— 1 ON CO CO JO CO c- 00 05 02 Cb 00 1> CO JO hH rH CO 04 rH o P 00 CO o hH CO 04 o 05 GO L- P I— 1 oq CO ttI uo CO I> CO 00 05 o pq rH 00 oq CO o tH 00 04 CO o GO o o 1—1 oq oq 04 CO CO ’H rH (M CO tM ir5 CO 4> 00 G5 o rH G^ rH rH rH uo o uo o JO o JO o JO O JO O (M lO o G'q lO c- o 04 JO O rH (M CO iQ CO t- 00 o T— I C^4 CO JO rH rH rH rH rH CO oq 00 o CO 04 00 -H O CO 04 lo r— t o oq 00 CO C5 -H O CO tH l- rH CO CO 05 o 04 rH ir5 1- GO rH rH rH rH r-H rH GO CO oq o 00 CO 04 O CO CO O y—> oq JO 'tH -H JO CO 4^ CO oo 05 0^ CO 00 o 04 HH CO 00 o 04 rH rH rH rH rH iH GM 04 1 o^* 5 S 3 1 6 Hl-il "|h eol'» Hlcq »12 w|co 1 1 1 0 «|hi M'a t-ico Ph i . o *2 O O "IS rHl» h|hi «!» -IS HICI -is io;x) 1 1 iti H 72 STRENGTH OF STEAM-BOILERS. (133.) Tills rule shows, that in theory the thickness of boilers of different diameters, for the same pressure, should vary simply with the diameter ; for instance, a 6-ft. boiler for high-jiressiire steam of 50 lbs. might be as per Table, ^ thick, a 3-ft. one being and an 18-in. one, &c., hut these strengths would in practice he considered much too light, especially for the small diameters, in fact such boilers would he apt to collapse with their own weight. For this and other reasons it is advis- able to add, say ^ of an inch, to all the thicknesses given by the Table, which is done in column 2, by which we find that for 50 lbs. safe, or 300 lbs. bursting-pressure, a 6-feet boiler should be i in. thick, 4 ft. = f , 3 ft. = and 2 ft. = in., &c. But even with this correction the thicknesses come out too light with very low pressures, and in such cases the engineer must be guided rather by his judgment. Our Table gives the theoretical strength in any case, thus, with the sizes now given the bursting-strain is 416, 468, 520, and 624 lbs. per square inch respectively. (134.) “ Strength of Boiler Tubes to resist External Pressure,'' — From the experiments of Fairbairn it appears that the strength of cylindrical tubes of boiler-plates to resist external pressure varies directly as the 2*19 power of the thickness, and inversely as the diameter and length, and he gives the following rules, in Vv^hich p = the collapsing Pressure, in pounds per square inch. L = the Length of the boiler, in feet. D = Diameter of ditto, in inches t = thickness of plate, in inches ^ 2-19 then p = 806300 x A convenient modification of this rule is p = 33* 61 X ( 1000 ^ LD or logarithmically 1*5265 -j- 2*19 (log. 100^) — log. (L x F) = log. p. It apjicars from this that p X L X D is constant for the same thickness of plate, and its value will be given by the rule 33*61 X (100 = p X L X D, or by logarithms. 1*5265+ 2*19 X (log. 100 t) = log. p x L x D. By this rule Table 45 has been calculated, and from it we can easily calculate the strength of a tube by the simple rules STllENGTH OF STEAM-BOILERS . 73 of aritlimetic, thus, a tube 30 in. diameter, f in. thick, and 12 ft. 94110 long, will collapse with ^ ^ = 261 lbs. per square inch; and again, to ascertain the proper thickness for a flue say 33 inches diameter, 20 feet long, to sustain a working-pressure of 45 lbs. per inch, or say 45 x 6 = 270 lbs. collapsing pressure, then p X X Dis in our case 270 x 20 x 33 = 178200, the nearest number to which in Table 45 is opposite ^ inch, the thickness required. Table 45. — For the Strength of Boiler Tubes to resist External or Collapsing Pressure. Thickness Value of Thickness Value of of Plate. 1 i? X L X D. of Plate. X L X inch. inch. 1 1 6 1860 9 1 6 228700 1 8 8484 5 g 288000 3 1 6 20620 1 1 1 6 354900 1 4 38720 3 4 429500 5 1 6 63130 1 3 1 6 511700 3 8 94110 ■g 601800 7 1 6 131900 1 5 1 6 700100 1 2 176700 1 806300 (135.) From experiments on the large scale it would appear that lap-jointed tubes, such as are commonly used in practice, resist a collapsing strain more powerfully than the small expe- rimental tubes from which the constants in the formula are derived. Fairhairn gives two experiments on large boilers, one 35 feet long with 3 feet 6 inch tubes, f thick, which gave way with 97 lbs. per square inch, but by rule and Table it should , , 94110 have borne — 64 lbs. only. The other experiment was on a tube 25 feet long, 3 feet 6 inches diameter, and f thick, which collapsed with 127 lbs. per square inch, but whose strength by Table, &c., was 94110 42 X 25 = 89*6 lbs. only. This is only what might be expected, the double thickness at the joint acts partially like a series of rings, and increases the strength in the same way ; the rules therefore give a minimum and safe strength, in fact only about 70 per cent, of the strain which ordinary boiler tubes seem to be capable of bearing. 74 STllENGTII OF STEA]\I-BOILKUS. (136.) An obvious and easy mode of increasing tlic strength of a boiler tube is by adding strong rings at intervals, so as (in eifect) to divide it into short lengths, and Mr. Fairbairn j)rop()se8 to do this by making the tube butt-jointed and using J_ iron for the junctions ; but a butt-joint cannot easily be made tiglit, and it is better to make the tube lap-jointed as usual, and add ~Y or L rings where required. Even this is objectionable from the great thickness of metal where the rings are riveted on, the metal there being in consequence unduly heated. An ingenious plan of Mr. Bramwell, C.E., of London, promises well to get over this objection : — let Fig. 30 be a cylindrical tube A B C D, compressed into the ellipsis E F G H. This change of form may be resisted in two ways, namely, by preventing E and F from giving in, or G H from giving out ; if G H be prevented from bulging out, E and F will be effectually prevented from collapsing. This is effected by putting on the tube, thin deep rings of iron, say f X 3 inches deep, as J in Fig. 31, such rings are free (from their small thickness) to the objection of in- creasing the thickness of the metal exposed to the fire, &c., &c., to which _L iron rings are liable. (137.) Elliptical tubes are exceeding weak for resisting an external pressure. Experiments were made by Mr. Fairbairn on such tubes, one 14 in. x 10^ in. diameter, 5 feet long and *043 thick, collapsed with 6-^ lbs. per square inch; another 205 in. X 15^ in. x 5 ft. 1 in. long and *25 thick, collapsed with 127-^ lbs. per square inch ; from which it appears that in elliptical tubes the diameter to be taken in calculating the strength is - ^ — , in which L = the major and S the minor axis of the ellipse; thus in Fig. 30, L = 3 feet and S = 2 feet, and the flattest part of the ellipse at E or F is part of a circle whose (2 X 3)^ ~ ^ collapsing pressure will diameter is be that due to a tube 9 feet diameter ; this will show the ex- cessive weakness of elliptical, or oval tubes. (138.) The French Government and Mr. Fairbairn assume the safe working-strain on a boiler at one-sixth of the bursting (;!• collapsing pressure, and we may admit this to be a safe rule for all ordinary cases in practice. (139.) The flat ends of boilers require to bo well stayed with longitudinal rods, or gusset stays to tlie body as in the Figures, tliese latter are every way the best and most convenient. EFFLUX OF COMPllESSED CHAPTEE IV. ON TUE EFFLUX OF COMPRESSED AIR, GAS, AND STEAM. (140.) “ Efflux of Compressed Ah\ dc ” — Wlien water or other liquid escapes from an orifice in the side of a vessel into the air as at A, Fig. 32, the velocity of efflux is the same as that of a body falling freely by gravity from the height S A. Similarly when a liquid escapes from one vessel into another, by a sub- merged orifice B, the velocity of efiiux is that due to the height S T, or the difference of level of the liquids in the two vessels, and it is not affected by the depth T B, at which the orifice is placed. (141.) We have here supposed that one and the same liquid was being dealt with, but if one compartment were filled with a liquid of different specific gravity to that in the other, we have a different case. Say in Fig. 33 we have a vessel with two compartments, C and D, filled to the same level with two fluids, whose specific gravity (for the sake of illustration) was as 3 to 1, C being the denser of the two. The conditions of pressure at E are precisely the same as would arise with one and the same fluid in both compartments, by columns having the respective heights F E and H E, that is to say, the velocity of efflux will be that of a falling body, with the height G H, and of course it is the denser fluid which escapes with that velocity. (142.) “ Velocity into a Vacuum ” — Applying this reasoning to elastic fluids, we are met by the difficulty that we have no real surface level to calculate from ; in the case of air, for instance, the density diminishes as we leave the earth in geometric ratio, and the limit is in infinity. But for the purpose of calculation, we may find what the height of the atmosphere would be, if it had throughout the same density as it has at the surface of the earth. Assuming that the barometer was at 30 inches, we find from Table 46 the density of mercury to be 13 *596, water being 1 ; and from Table 32 air has a density of *001221, water being 1, the height of a homogeneous column of air equal 13*596 X 30 to 30 inches of mercury is therefore . qqi221 12 “ and although this is fictitious, we may use it for the purposes of calculation without error. We shall now find the velocity into a vacuum by the rule for falling bodies to be V2T838 x 3 = 1344 feet per second. 76 VELOCITY OF AIR, &C., INTO A VACUUM. Table 46, — Of the Specific Gravity and Weight of Materials, Water at 62° being 1*000. Weight of a Weight of No. of Specific Cubic Fool a Cubic Culuc Feet Gravity. in Pounds. Inch in Pounds. in one Ton. Mercury 817*3 *4003 2*341 Lead 11*352 707*5 *4004 3*133 Copper, sheet 8*785 517*5 *3138 4*001 Gun Metal, cast 8*370 510*3 *3127 4*145 Copper, cast 8*307 533*4 *3104 4*173 Brass, ,, 8*303 523*1 *3027 4*282 Wrought Iron 7*788 485*3 *2800 4*315 Tin, cast 7*201 454*4 *2330 4*030 Zinc, sheet Cast Iron, British, mean 7*100 448*1 *2503 4*000 7*087 441*3 *2553 5*07 Zinc, cast 3*831 427*3 *2474 5*24 Slate 2*835 173*7 *1022 12*38 Glass 2*73 172*0 *0005 13*02 Granite, Cornish 2*332 135*0 *0030 13*50 Sandstone, Yorkshire j 2*503 153*2 *0004 14*34 Brick, London Stock 1*811 114*7 *0334 19*52 Sand, River 1*513 03*35 *0558 23*25 Coal, British, mean 1*313 81*83 *0474 27*37 Water, distilled 1*000 32*321 *03303 35*95 Ice, at 32° *03 57*03 •03354 38*65 Alcohol *813 50*37 *02032 44*21 Oil, Olive •0153 57*04 *03301 39*27 Oak, seasoned •777 48*42 *02802 46*26 Elm, „ •588 33*35 *0212 61*13 IMahogany, Honduras, seasoned . . •530 34*0 *0202 64*18 Pine, Yellow, seasoned •483 30*1 *01742 74*41 Coke, Gas, in measure •353 22*0 *01273 101*8 Cork •24 14*03 *00833 149*7 (143.) The velocity of steam at atmospheric pressure into a vacuum, may be calculated in the same way : taking its density from Table 32 at • 0007613, we have Tq ^ ^ 3^x* ~ 44648 feet for the height of a column of steam equivalent to 30 inches of mercury, and the velocity into a vacuum V 44648 x 8 = 1690 feet, per second. (144.) Applying these rules to air, steam, &c., of other than ordinary densities and pressures, we are conducted to the re- markable fact that the velocity into a vacuum is constant, wliatcver the jiressure may be ; for instance, air of double the VELOCITY OF DISCHARGE OF AIR, &C. 77 atmosplieric pressure would have a double height of column, and thereby an increased velocity, if the density remained the same, but the density being of necessity double also, the height of column remains the same, and hence the velocity which is due to that height remains the same also. It follows from this, that if we filled a vessel with air compressed to any number of atmospheres and allowed it to escape into a vacuum, the velocity would be the same from first to last, although the pressure would be continuously reduced by the escape of the compressed air ; but the quantity or weight of air which escapes would not be the same at all pressures, but would vary with the density of the air, which varies every moment with the pressure. (145.) Velocity into Air ,'^ — This uniformity of velocity at all pressures does not hold when the discharge is made into air. Let Fig. 33 represent the discharge into rarefied air, say of one- third the ordinary density (made so by heat or otherwise), we have then a case analogous to (141), in which we found the velocity to be that due to the difference of height of the two columns. Thus in Fig. 33 we have two columns of the same height, or 27,838 feet, but the pressure exerted at the orifice E by the column G E is the same as that of a column of ordinary air of one-third the height, or 27838 ‘ 3 = 9279 feet, and, as in (141) the velocity of efflux will be that due to the difference, or 27838 - 9279 = 18559 feet head, namely, x 8 = 1090 feet per second. Again, the velocity of steam of 20 lbs. pressure per square inch into the atmosphere may be calculated in the same way. By Table 41 we find that 20 lbs. per square inch is equal to 46*22 feet of water-pressure, and by Table 11 the volume of 20-lb. steam is 732 for water 1, hence the height of the column of steam generating the velocity is 46*22 x 732 = 33833 feet, and the velocity of efflux V 33833 X 8 = 1472 feet per second. (146.) It will be seen from this, that for finding the velocity of efflux in any case, we require only the difference of pressure at the two sides of the orifice and the density of the issuing gas or steam ; this is further illustrated by (123), &c. (147.) When the pressure varies very slightly^ as is usually the case in most questions of ventilation, discharge of coal- gas, &c., we may admit, without sensible error, that the density is constant, and the velocity of discharge will then be governed 78 VELOCITY OF DISCnARGE OF AIR. by tlie square root of the pressure simply, and we Lave the rule VPx6G*l = Vfor air, and V P X 102 = V for coal-gas of density * 42 for air 1 ; P being the pressure in inclies of water, and V = velocity in feet per second. Cols. 3 and G in Table 47 have been calculated by these rules. These rules may be modi- Table 47. — Of the Velocity of Discharge of Common Air and of Coal-Gas, at ordinary Temperature and Pressure, with small differences of Pressure. Common Air at 62° under 30 inches of the Barometer. Coal Gas, specific gravity -42, that of Air being 1 • 0. ±ieaa or JJitterence of Pressure in Coefficient of Discharge. Coefficient of Discharge. Inches of Water. Pounds per 1*0 *93 * 65 1*0 •93 *65 Square foot. Velocity in feet per second. Velocity in feet per second. •005 •026 4*67 4*,34 3*03 7*2 6*70 4*68 •01 •052 6*61 6*14 4*29 10*2 9*48 6*63 •02 ‘ -104 9*35 8*69 6*07 14*4 13*4 9*36 •03 •156 11*4 10*6 7*41 17*6 16*3 11*4 •04 •208 13*2 12*3 8*58 20*4 19*0 13*3 •05 •260 14*8 13*7 9*62 22*8 21*2 14*8 •07 •363 17*4 16*2 11*3 27*0 25*1 17*5 •10 •519 20*9 19*4 13*6 32*3 30*0 21*0 •15 •779 25*6 23*8 16*6 39*5 36*7 25*7 •2 1*038 29*5 27*4 19*2 45*6 42*4 29*6 •25 1-298 33*1 30*8 21*5 51*0 47*4 33*1 •3 1*558 36*2 33*6 23*5 55*8 51*9 36*2 •35 1-818 39*1 36*3 25*4 60*3 56*1 39*2 •4 2*077 41*8 38*8 27*2 64*5 60*0 41*9 •45 2*337 44*3 41*2 28*8 68*4 63*6 44*5 •5 2*597 46*7 43*4 30*3 72*1 67*0 46*8 •G 3*116 51*2 47*6 33*3 79*0 73*4 51*3 •7 3*635 55*3 51*4 35*9 85*4 79*4 55*5 •8 4*155 59*1 54*9 38*4 91*2 84*8 59*3 •9 4*674 62*7 58*3 40*7 96*8 90*0 62*9 1-0 5*193 66*1 61-4 42*9 102 95 66*3 1-5 7*790 80*9 75*2 52*5 125 116 81 2-0 10*38 93*5 86*9 60*7 144 134 94 2-5 12*98 104 96*7 67*6 161 149 104 3*0 15 *.58 114 106 74*1 176 163 114 3 *5 18*18 124 115 80*6 191 177 124 4*0 20*77 132 123 85*8 204 190 133 D 5 23*37 140 130 91*0 216 201 140 5*0 25*97 148 138 96*2 228 212 148 c-o 31*16 162 151 105*3 250 232 162 COEFFICIENT OF CONTRACTION. 79 fied so as to give the quantity discharged instead of the velocity. Thus for round apertures with air we have d^xVPx 21*64 = C ; and for coal-gas x ^ P X 33* 4 = C, in which C = cubic feet discharged per minute, d = diameter of orifice in inches, and P = pressure in inches of water. (148.) “ Coefficient of Contraction !' — But the quantities dis- charged will vary considerably with the form of the orifice, for the issuing vein of air, &c., suffers contraction, as in the case of water, and as shown by Fig. 34, where with a thin plate, an orifice 1 inch diameter has the jet reduced to *8 diameter, and the area to *8^ = *64, that of the orifice being 1. The experi- ments of Daubuisson give the following coefficients of discharge for air : — *65 for an orifice in a thin plate. *93 for a very short cylindrical pipe, say two diameters long. *95 for a similar pipe slightly enlarged outward, or trumpet- shaped. (149.) Velocity of Steam !' — With steam of a fixed pressure (say 45 lbs. per square inch on one side of an orifice and 44 lbs. on the other side) we have a difference of 1 lb. per square inch, which by Table 41 is equal to 2 * 3 feet head of water ; and by Table 11 we find the volume of 45 lbs. steam to be 439 times that of water, and hence the height of column of 45 lbs. steam, equivalent to 11b. pressure, is 2*3 x 439 = 1010 feet; and the velocity due to that height is V 1010 x 8 = 254 feet per second, which is the velocity at the most contracted part of the issuing jet (C, Fig. 34) ; but with a pipe taking * 93 for the co-efficient this becomes 254 x *93 = 236 feet per second over the full area of the orifice at B. From this we obtain the general rule Vp X 236 =y, in which p = the loss of pressure in pounds per square inch, and V = the velocity of the discharge over the full area of the orifice in feet per second. Table 48 has been calcu- lated by these rules. (150.) The discharge of steam maybe sometimes conveniently estimated by the horse-power instead of cubic feet. Taking the case of 45 lbs. steam, and admitting that one cubic foot of water evaporated to steam represents 1-horse power (115), we find by Table 11 that a cubic foot of water is equal to 439 cubic feet of steam at that pressure, and to pass that quantity through an orifice 1 inch diameter we should require a velocity of 439 X 144 7854 X 60 X 60 = 22 '36 feet per second, which with a 80 VELOCITY OF DISCHARGE OF STEAM. Table 48 . — Of the Velocity of Discharge of 45 Ihs. Steam, with given differences of Pressure at tlie two sides of an orifice. Loss of Pressure in Pounds per Square inch. Co-efficient of Discharge. Loss of Pressure in Pounds per Square inch. Coefficient of Discharge. 1-0 •93 •65 1-0 •93 1 -65 Velocity in feet per second. Velocity in feet per second. •01 25-4 23-6 16-5 •6 197 183 128 •02 35-9 33-4 23-3 •7 213 198 138 •03 44-0 40-9 28-6 •8 228 211 148 •04 50-8 47-2 33-0 •9 241 224 157 •05 56-9 52-9 37-0 1-0 254 236 165 •1 80-4 78-4 52-3 1-1 267 248 173 •15 98-5 91-6 64-0 1-2 279 259 181 •2 114 106 74-1 1-3 290 270 188 •3 139 129 90-3 1-4 301 280 195 •4 161 150 105 1-5 311 289 202 •5 180 167 1 117 pipe becomes 22-36 •93 = 24 feet per second, the bead due to wbicb by the rule for falling bodies ^namely ~ ^ ) 24\2 Q becomes in our case = 9 feet head of steam, or 439 *0205 feet of water, which again by Table 41 is equal to *0205 X *4327 = • 00887 lbs. pressure per square inch. (151.) From this we get for circular apertures, or rather for short pipes discharging 45 lbs. steam, the general rule — x Oj • 00887 = p, in which H = horse-power of steam, estimated in cubic feet of water ; d = diameter of short pipe, say two dia- meters long, in inches ; p = the difference of pressure at the two ends of the short pipe, in pounds per square inch. Thus, a short 3-inch pipe, say 6 or 8 inches long, discharging 120 120 horse-power of steam, would require — o X 00887, or 14400 81 X *00887 = 1*57 lbs. per square inch, so that the pressure at the exit end of the pipe is reduced from 45 to 45 — 1 * 57 = 43-4311)8. per square inch. Table 49 has been calculated by this rule. VELOCITY OF DISCHARGE OF STEAM, 81 o of CL> pH B cS «4-< o ‘o o cc cc c »-q o bO C *E 'bb -Ji H CZ2 CO jQ IP O pc-l a w p fa H CO CO £ lO tH CO iH|N CM (M GO CO CM JO CO JO CM o GO c05 rH HH CM OO GO CO CO CM O rH CO JO CM rH OO CO JO JO !>• O o o O rH CM 'H CO CO CJ5 rH O o o o o O O o rH rH CO CO CO t- CM o CM JO 00 rH CO 05 CM C5 O CO CO o 1-H CO JCO Cj5 o CO CO r> o CM o o o o O o CM CO 00 rH CO CO 05 o o o O o o O o rH CM CO JO CO rH CO JO rH o l> JO rH Oi rH rH rH 05 CO JO o CM CO O l> GO 00 CO CO l> JO rH o o O rH CO CO JO CM rH CJ5 o o O o O o o rH CM rH CO O rH CM a CO 00 CM o t> rhi CO t- JO OO o O O JO r- C CO JO CM CM JO O o o O O o o rH CO JO 00 CM CM rH CM I> GO Oi CM JO l> CM O CO CO r-H JO CO JO o 00 GO o o CO JO OO CJ5 rH OO 00 CO • • o o o o o o rH CO CO rH • • rH CM l> CP JO CO rH rH JO rH CM o rH CO 00- ■ rH CM CO o rH CM rH CO) l> t- rH 05 JO • • • • O o O O o rH CM CO O • • • • rH CM !>• rH CO CO CM JO lo CM rH O rH JO t- CO o o CM JO 05 O CO CO o O o O CM CO JO CM CM rH CM GO rH CO CO CO rH CO lO rH rH 00 CO JO CO T— ^ iO CM CM 05 00 OO rH O O i-H CM rH OO CO rH rH CO lO O JO O JO l> Oi o t— O t- o tH CO t> JO OO co CM rH CM t> CM CO O rH • (M GO o JO • • • CM iO O JO O o o O CO rH a cc 00 t— CO JO t- o JO o JO O O rH rH CM CO rH CO 05 CO 00 CM CO rH rH CM CM CO GO JO rH CO JO l> rH JO GO r> JO CO CO a (M 05 JO rH l> CO JO C5 rH JO rH CM CO rH CO 05 CM JO a:. JO ' rH rH rH (M lO o iO o O o o JO o o O O o o tH rH CM CO rH JO o JO o JO o o rH rH CM CM CO rH ■T3 c3 «> Tc O) p a ^ r/, -s g 'Sc 3 O a o 3 p WO- C3 -2 p 2 bo P .2 P 3 bC 2 P3 r :S. o « l> 'P 3 »«- '5 "p p> 82 VELOCITY OF DISCHAIIGE OF 8TEA]\r. For 7 lbs. steam, the rule becomes tbis we have calculated Table 50. X •0231 = p; and by -M >> -4-s ‘o o a o o ;=i o P CO cc o to CO O CO 0 p, 1 o O} rP fcD > < H EH 02 CO O 6 fcO w p p -Ij H CO H^ 04 fH o H^ O (M rH 04 CD rH 1(0 HH o CD rH o o O rH 04 HH o 4^ 1 o o O o o O H rH (04 CO o* (20 o o rH o HI o oi CO 1(0 CO CO 04 (M CO o CO o o o rH 04 1(0 CO o 1- 4- o o o o O o o 04 CO no tH t— CO o HH tH CD ao oo CM CM o o o O 1— ( CO 1(0 CO G, 1(0 CO rH 1- CO o O O o o o »— 1 CO rH CD CO w o o o o o o o rH CO no CO o lb 'cc~ 04 w 04 o o HH Gi Cfl Ol lO CO rH CD CD no GO 04 • 00 <3 o o o rH CO no 04 (M o O • 5 P Cl* CO o o o o o O rH 04 no CO 2 Ci CD lO CD K) rH GO CD -H I— I o 04 00 w p4 (M CO 00 KO HH H^ CD HI no CD • . P t> o o o rH 04 1(0 (02 CO oo o • • Q o o o O O O O rH CO (X) w § w (2 CO H 00 o 04 04 GO o L- o 1-H O 'H lo rH CO lO o o CD rH t- CD GO -H O GO o 04 • • w o o o rH 04 HH o 4^ o iH • • CJ g o o o o O O rH rH Tt! I td ;< cej Ch l> CO 00 CO (04 no hH O o Q CO GO HH CO CO (04 CD O 04 • • o &c o o r-i CO lO (CO rH 1- CO • • O o o o o o o CM CO oo o o o CO rH 04 CO iO CO o Oi o CD 1— ( HH no t- 04 • • • • Tin 1 o C'l CO GO HH (04 o o • • [ o o O O rH CM no (J2 uo rH o lO o no CO 1 00 CD CD CM 1 (M CD r-l lO lO rH 1 o O rH 04 HH l> O CD (M lO t> (M t- tH CO lO !/J "73 CO ^ OJ QJ M rCl M g .S P 0-6 iO CO o 00 O O CD O no CD rH O lo o o o o ^ OJJ p eg M QU 5^ d rH I— ( (04 CO CD CO CO 00 o no wo^ § tH iH 04 CO c4 w 1(0 is rH 1(0 00 l> no 2 Yoy.g CD CO oi Gi 1(0 T— ( CO lO r- rH no CO w .5 B a rH tH 04 CO HH CD (J2 (M CO no CO g CO c/2 O) 1 rH rH CM CO a o 1(0 O o o o 1(0 o O O O O o o ^ ► o rH rH CN CO HH no o lO O O O o iH rH (04 CO tJH no p> FEICTION OF AIR AND STEAM PIPES. 83 (152.) Tlie pressure varies as the fourth power of the dia- meter of the orifice, as shown by the preceding rules, for this reason : — the area of an orifice, and consequently the velocity of efflux with a given quantity, varies as d®; and as the pressure varies as V^, the ratio becomes x or more simply as For instance, if in any particular case we reduce the diameter of an orifice to one half, the velocity would be increased in the ratio of 1 to 4, and the pressui^e from 1 to 16. (153.) ^‘Friction of Long Pi^es ” — We have so far considered only the head or pressure necessary to give any required velocity with an orifice, or a pipe so short that the friction was inappreciable ; but where the length is considerable, there is a second loss of pressure due simply to the friction of the air or steam against the sides of the pipe ; and in all such cases the head due both to velocity and to friction must be separately calculated and the sum total taken. (154.) The head due to friction alone may be calculated by the follovdng rules — C^XL ^(3-7d)^xH p, C-^xL ^ ^ = L = C,_^=(o 7 cZ),^-^xH=L, in which d = the diameter of the pipe in inches, L = the length of pipe in yards, C = cubic feet per minute, and H = the head (or difference of pressure at the two ends of the pipe) in inches of water. These rules cannot be easily worked without the use of logarithms ; but we have calculated by them Table 51, for the use of which we have the following rules : — (155.) 1st. Having the diameter, length, and discharge given, to find the head, take from Table 51, opposite the given dia- meter, the number in column 2 or 3 (according to the terms in which the head is desired), and multiply it by the square of the given discharge in cubic feet, and by the length in yards ; and the product is the head in inches of water, or in pounds per square inch, due to friction alone, to which the head due to velocity has to be added from Tables 47 or 48, &c. (156.) 2nd. Having the head, diameter, and length given, to find the discharge, assume a discharge and calculate the head for that as in (155) ; divide the assumed discharge by the square root of the head due to it, and multiply by the square root of the given head ; and the quotient is the true discharge sought. (157.) In order to facilitate calculation, the Table 51 is so arranged, that for diameters under one inch the discharge must 84 FRICTION OF AIR AND STEAM FIRES. Table 51. — Of the Friction of Am, Steam, and Gas in Long Pipes. Diameter of Pipe in inches. Head, or difference of Pressure at the two ends of a Pipe one yard long, in Inches of Water. Pounds per Square Inch. Head for 1 Cubic Foot per Minute, 1*477 •05317 , 3 . •1945 •00700 .1 •0185 •000666 3 . •000077 •0002187 1 •001442 •0000519 Head for 10 Cubic Feet per Minute. H •04725 •001701 •01899 •000684 i| •00878 •000326 2 •00451 •000162 •00250 •000090 2i •00148 •0000532 Head for 100 Cubic Feet per Minute. 3 •0594 •00214 •0740 •000989 4 •0141 •000507 4V •00782 •000281 5^ •00462 •000166 6 •00186 •0000668 7 •000858 •0000309 8 •000440 •0000158 Head for 1000 Cubic Feet per Minute. 9 ■02442 •000879 10 •01442 •000519 12 •00579 •000209 15 •00189 •0000681 18 •000763 •0000275 21 •000353 •0000127 24 •000181 •00000653 Head for 10,000 Cubic Feet per Minute. 30 •00593 •000214 3>3 •00368 •000133 30 •00238 •0000858 42 •001103 •0000398 48 •000566 •0000204 54 •000314 •0000113 (iO •000185 •00000667 DISCHAKGE OF AIR, ETC., BY PIPES. 85 be taken in cubic feet, as in (155), &c., but from inch to inches in tens, from 3 inches to 8 inches in hundreds, from 9 inches to 24 inches in thousands, and from 30 to 60 inches in tens of thousands of cubic feet. Thus a |-inch pipe, 20 yards long, discharging 2 cubic feet of air per minute, requires * 006 x 2'^ X 20 = ’48 inch head of 144 X 2 water for friction, and the velocity being 74 4 ^ ~ 0 Q = per second, the head for that velocity by Table 47 is • 03 inch of water, making *48-1- *03 = *51 inch total. A 2^-inch pipe, 40 yards long, with 38 cubic feet of air, will require *00148 x X 40 = *85 inch head for friction. 144 X and the velocity being — 38 = 18*6 feet per second, or by X 60 Table 47 = * 1 inch head, we have a total of * 85 -|- * 1 = * 95 inch head. A 4-inch pipe, 10,560 yards long, discharging 852 cubic feet of gas per hour, or 14*2 cubic feet per minute, will requii’e / 14 * 2\2 *0141 X ( qQQ j X 10,560 = 3*002 inches head for friction. With so small a discharge, the head for velocity will be in- appreciable ; Clegg found by experiment, that the head with a pipe having these conditions was 3 inches of water. A 9-inch pipe, 30 yards long, discharging 500 cubic feet of gas / 500 \ per minute, will require * 02442 x ( ) head for friction, and the velocity being X (^IQOO j X 144 X 500 6 X 60 = 18*8 feet per second, the head for that velocity by Table 47 is * 04 inch, or *183 -f *04 = *223 inch total. (158.) Again, say we require to know the discharge of 45 lbs. steam by a 4-inch pipe, 150 yards long, with a loss of 1 lb. in pressure, the steam at the exit end being reduced to 44 lbs. per square inch. Let us assume, say 400 cubic feet for the discharge, /400\^ and calculating as in (156), we have *000507 x ( Jqq ) X 150 = 1*22 lb. per square inch, as the head due to friction alone. the velocity will be 144 X 400 12*6 X 60 = 76*2 feet per second, which. by Table 48, with *93 co-efficient, requires about *1 lb. ]per 8G DISCHAEGE OF AIR, ETC., BY SQUARE PIPES. square incli, so that for our assumed quantity, tlic total licacl is 1*22 q- *1 = 1*32 lb. per square inch, instead of 1 lb., tlio j)ressurc allowed in our case. The true discharge (15G) witli the given head is therefore — - x V 1 = cubic feet of y 1 * 32 steam per minute. (159.) This last result is obtained by the application of a useful general law, which may be stated thus : the discharge of any pipe or system of pipes, apertures, &c., &c., is proportional to the square root of the head ; and conversely, the head is pro- portional to the square of the discharge. (160.) “ Square and Rectangular Channels , — The case of square and other rectangular channels may be assimilated to that of round pipes, and then the velocity, &c., may be calcu- lated by the rules and tables given for the latter. The velocity of discharge, whatever may be the form of the pipe or channel, is in all cases proportional to the sectional area divided by the periphery or circumference. In round pipes, this is always one- fourth of the diameter : thus a pipe 1 inch diameter has an area • 7854 of *7854, and a circumference of 3 * 142, and a 4-inch pipe gives 12-57 12*57 - 1 . Square Pi^esJ ' — Square pipes give the same uniform ratio : thus a pipe one inch square will have an area of 1, and a periphery of 4 inches, and ^ = ’25 as with a circular pipe : again, a pipe 4 inches square has an area of 16 square inches, and a periphery of 16 inches also, and as with the round pipe { f = 1, it follows that the velocity of discharge with a square pipe is the same as with a round one, with the same length and head, &c. ; but of course the quantity discharged will be greater with a square pij)e in the same proportion, as the area of a square is greater than that of a circle, or as 1 to *7854. “ Rectangular Ripes.^' — The same laws apply to rectangular pipes : thus a pipe 6 inches by 3 inches has an area of 18, and a i)erij)hery of 18 also, and J f = 1, which is the same as a 4-inch pipe, as we have seen ; therefore a round pipe 4 inches diameter will liave the same velocity of discharge as a pipe 4 inches square, or as another 6 in. x 3 in., and tlie quantities dis- (•liarged will be in proportion to the areas, or 12*57, 16, and 18 respectively. 8.ay we liave a rectangular channel, 40 yards long, 36 inches EFFECT OF ENLARGEMENTS, ETC., IN AIR-CHANNELS. 87 wide, and 18 indies deep, and we require to know the head or pressure for a velocity of 6 feet per second. The area is 36 x 18 = 648, and the periphery 108, and we have = 6, which is the same as a pipe 6 x 4: = 24 inches diameter, and we can calculate the head as for a round pipe of that diameter. A round 24-inch or 2-feet pipe, discharging at the rate of 6 feet per second, would deliver 3*14 x 6 x 60 = 1130 cubic feet per /1130Y VioooJ minute, requiring *000181 x X 40 = * 0077 inch head for friction alone. The head for 6 feet velocity by Table 47 with *93 for co-efficient, is *01 inch of water; the total head is therefore *0077 -J- *01 = *0177 inch of water, and this is also the head for a pipe 36 inches by 18 inches, as in our case. (161.) Effect of Itepeated Enlargements and Contractions — It might be supposed, that the effect of enlarging the channel would be to diminish friction in discharging a fixed quantity of air, and this is true where the -velocity has not to be got up again ; but where there are repeated and successive contractions and enlargements, the head saved in friction by each enlarge- ment, may be more than compensated by that required for getting up the velocity at the next contraction. Let Fig. 113 represent the rectangular pipe 40 yards long, the head for which with a velocity of 6 feet per second we have just calculated to be *0177 inches of water. Let Fig. 114 be a similar pipe, but one having two chambers or rooms, A and B, in its course, by which the length of the pipe or channel itself, C F, is reduced to one-half or 20 feet. The velocity of the air passing through the two rooms is so very small, that there will practically be no friction there, so that the friction is thus reduced to one-half also. But we found that the head at C, due to the air entering the pipe with 6 feet velocity, was * 01 ; when the air enters the room A, that velocity is lost, and must be got up again for the air entering the next contraction at D, to be again lost in B, and got up again at E. The head for friction in this case is *0077 2 *00385, and the head for the velocity at 3 places *01 x 3 = *03, making a total of * 00385 -j- *03 = *03385, or about double the head for a uniform pipe ; so far therefore from diminishing the head by enlarging the channel at A and B, we have really doubled it in 1 ABLE 52.— Of tlic Friction of Steam-Pipes for 45 lbs. Steam, being the head lost by a length of one yard of Pii)e. 88 FRICTION OF HIGH-PRESSURE STEAM-PIPES. CO CO CO (M (M >o CO 1— • 1- -f QO C5 rH OI (M -H CO C5 CO OI CO JO O o o CO JO CO o o o o o o o rH o o o o o o o o CO r—i (M JO O CO t- CO CO 00 o o rH CO CO o -tH CO o o o o o rH OI o o o o o o o o 03 rH CO 03 CO o CO JO CO o JO o CO CO 03 rH n o o o 03 CO GO -f 03 03 l- o o o o o o O 03 CO JO rn o o o o o O o O o o u QO CO D '+1 CO O' JO CO 03 03 CO CO t- -H 03 o Oi O JO GO o o rH 03 JO OD o JO JO CO 03 K w o o O o o O 03 CO JO Pi o o o o o O o o o o rH GO b o CO CO 03 JO p CO o CO 03 ft o rH 03 -H CO JO l> rH CO CO CO 03 o o o o o I— t 03 CO o CO CO o o o o o o O O rH rH 03 tH CO CO CO -H rH JO JO 03 03 JO M 03 rtH o GO GO -fH CO CO CO CO • K o o O rH rH 03 CO JO JO rH 03 • o o O O O O o 03 o M rH O rH CO CO tH o a t- QO CO CO JO tH o l> fc? O 03 CO rH JO JO rH 05 05 CO • « • t) cc Ui o O CO rH 03 rfl JO GO CO CO • • o o o O o O o rH 03 CO rH u rH HH CO CO QO r+H rH CO tH CO CO CO JO 03 GO CO rff t> 00 CO 3> CO • • • • O O rH CO t- CO rH 00 CO 30 • • • • o O o o o rH 03 GO 05 rH rH JO o JO O JO CO CO 03 CO GO TtH 03 03 o CO GO 03 00 rH JO o O O rH CO JO 05 o 03 CO l> CO CO CO CO 03 o a o 03 CO rH rH 03 Two Engines, Coupled Cranks at right angles. 4*5 9-0 13-5 18-0 27*0 36-0 45-0 67-6 90-1 135 180 225 270 360 Single Steam- engine. 1 CO t> rHCO»OI>rHJOGOl>l>JO C0CO05O305 JOrHl>C0JOl>O5THJO rHrH03CO^C005 C3J005JO rH rH rH 03 1 JOOJOOOOOJOOOOOOO O ^ rHrH03COTl^JOt>OJOOJOOO ^ ^ rH rH 03 03 CO 53 r' FEIOTION OF LOW-PEESSUEE STEAM-PIPES. 89 lO CO CM »o O CM O -H t— O 00 rH 05 (M O o rH CO CO CM OO O o O o o ?-H rH o o O o o o O io GO CM CM o CO CM o 05 rH o O O rH rH rH tr. CO o L- o o O O o rH CO rH o o O o o o o O bO rH 05 tH 00 lO . lO l> rH rH l> CO 05 iO '"P a O o rH CO t- CM GO O 05 O o O O o rH CM lO w O o o o o O O o o o i=! o Es] (M (>J Tt^ lO rH cc Ah « lO 05 t}H CM t> 05 o t> GO GO < o O rH CO lO CM CO r— 1 rH rH P o o O o O rH CM iO 05 rH s o o O o o o o o o rH Ph s u Pi h— 1 Ph O rH 05 o CO ■Hh o t- 00 CO CM 00 GO t> 5«^i O rH CN CO rH lO rH O 05 O o o o o o rH CM rH O t> 00 rH O o o o o o O O O rH rH CM bXD P w t> 00 l> o ai JO 05 rH GO o CO CM lO GO m CO q o O (M CO CO CO rH rH CO 00 t> • cd o P o o O O o rH CM JO 05 rH GO • • Ph pi o o O O o o O o O CM CO .W H W Q < <1 W w (M CO pt* O CO (M c/i ft o CO CO tH CO rH o CM • • lO o 1-H (M lO 05 lO rH O CO rH CM • • • w o o o o O rH CO CO CO rH rH CO Pi tj o o o o O O O O rH CM iO So CO W £ riH tH CO CO o GO rH CO o tIh CO 1— ( -HH t- CO 05 CO rH rH CO • • • O o o rH (M Ttn o 00 rH CO • • • o o o o O O O rH rH rH t— ( H O tH rH CO CO JlO 05 CO GO CO r> o 05 CO CO lO rH • • • • • o o rH CO CO 05 CO t- • • • • • o O o o rH rH rH *H-H o GO CO 1 00 (M GO 1 i cj CO o i> rH lo GO r> t> lO P 1 t rH rH CM CO c 5^ si o O O o o o o O O o o o c'" <2 o rH rH (M CO o t- o iO O o o o ^ ‘c ’oJ rH t-H CM CO rH iO y;> 90 DISCnATlGE OF STEAM-FirES. tins case. It is important to keep tliis fact in view in cases of ventilation, &c. ; in large buildings, the changes of area in tlui passages are numerous and unavoidable, they are also too com- plicated to be calculated, but in the case of the Prison Mazas (862), we found that the velocity was thus reduced to ’423 of tlie theoretical velocity, and in the Prison of Provins (3G5), to •322. (162.) “ Steam Pipes — Pepresenting 1-horso power by one cubic foot of water evaporated to steam, we have, by Table 11, for 45 lbs. pressure, 439 cubic feet of steam per horse-power per hour, or 7*3 cubic feet per minute, and for a pipe 1 inch diameter, 1 yard long, and 10-horsc power, we have by the rule C^XL (7*3xl0y^xl ( 3 • 7c?)' ~ (3 • 7 X 1 )' 7-685 = 7*685 inches head of water, or 12 ^ 4327 = *277 lb. per square inch, and thus we have calculated Table 52. With 7 lbs. steam we have by Table 11, 1138 cubic feet of steam per horse-power per hour, or 19 cubic feet per minute, and for 10-horse power and a pipe 1 inch diameter we require 190^ X 1 = 52*06 inches head of water, or (3*7 xiy = 1*88 lb. per square inch, as in Table 53. 52*06 X -4287 12 (163.) “ Steam-Pipes to Engines — In applying these rules to pipes for steam-engines, it must be observed that the supply of steam to an ordinary engine is intermittent, being 0 when passing the centre, and a maximum when at the middle of the stroke, and that the maximum velocity should be taken in calcu- lating the size of steam-pipe. Thus, an engine of 5-feet stroke and 22 revolutions per minute has a mean velocity of 5 x 2 x 22 = 220 feet per minute ; but when at the centre of the stroke, the piston is moving with the velocity of the crank pin, or 5 x 3*14 X 22 = 345 feet per minute, instead of 220. It will be found that in a common double-acting engine the maximum velocity is 1*57 times the mean velocity, and with a pair of engines having their cranks at right angles the ratio is 1*11 to 1 : so that, for instance, one engine of 100-horse power takes steam at the maximum rate of 157-horse power, and a pair of eugines, each of 50 -horse power, combined at right angles, takes 1 1 1-liorse power of steam at the maximum speed. From this we have columns 2 and 3 in Tables 49, 52, &c. STEAM-PIPES TO ENGINES. 91 (164.) The following examples will illustrate the use of these Tables : — Example 1. A single engine of 25-horse power, with a 2^-inch steam-pipe, 50 yards long and 45 lbs. steam, will by Table 49 require * 365 lb. pressure for velocity of entry, and by Table 52 • 0454 lb. per yard for friction, or in our case • 0454 x 50 = 2*27 lbs. per square inch, making a total of *365 -f- 2’27 = 2*635 lbs., so that the available pressure for working the engine is reduced to 45 — 2*635 = 42*365 lbs. per square inch. Example 2. A single low-pressure engine of 250-horse power, with 7 lbs. steam, 10-inch pipe, 20 yards long, will require by Table 53 (say 255-horse power) *0301 x 20 = * 6021b. for friction, and by Table 50, 37 lbs. for velocity, making a total loss of *602 -f- *37 = *972 lb. per square inch, thus reducing the effective pressure at the engine to 7 — *972 = 6*028 lbs. per square inch. Example 3. A pair of engines, of the collective power of 180 horses, with a 5-inch pipe, 40 yards long and 45 lbs. steam, would require by Table 52, *0355 x 40 = 1*42 lb. for friction, and by Table 49, ‘568 for velocity, giving a total loss of 1*42 -j- *568 = 1*988 — say 2 lbs. per square inch. Example 4. Say that the steam of a 20-horse boiler is used for evaporating pans or similar work where the velocity is uniform, then with 45 lbs. steam and 100 yards of 2-inch pipe, we should have a loss of (*03464 x 100) -j- ‘2216 = 3 *6856 lbs. per square inch. (165.) With steam of other pressures than 45 or 7 lbs. per square inch, the pressure lost must be calculated by Table 51, &c. Thus, say we have an engine with a 15-inch cylinder, 3 feet stroke, making 40 revolutions per minute, and that the steam-pipe is 3 inches diameter and 30 yards long, the pressure of steam in the boiler being 25 lbs. per square inch. The maxi- mum velocity of the piston is 3 x 3*14 x 40 = 377 feet per minute, or 6*3 feet per second, which with a 3-inch pipe becomes ^ =157 feet per second, or with *93 for co- o 157 efficient, = 168 feet per second, in the contraction at entry I/O (148), the head due to which is = 441 feet of steam, and the volume of 25 lbs. steam, being by Table 11 = 644 92 CHIMNEYS TO STEAM-BOILERS. times tliat of water, we have = * G84 feet of water, or 644 ’ •684 X *4327 = *296 lb. per square inch, as the pressure due to velocity only. Then the area of the piston being 1*227 feet, we have 1'227 X 377 = 462 cubic feet of steam per minute as the maximum quantity passing through the pipe; and by Table 51 we shall have for friction alone * 00214 x ^ 30 = 1 * 38 lb. per square inch, which added to the head due to velocity makes the total loss of pressure *296 -(- 1*38 = 1.676 lb. per square inch, and the effective pressure at the engine is reduced to 25 — 1*676 = 23 ’324 lbs. per square inch. CHAPTER V. CHIMNEYS. (166.) The case of a chimney is analogous to that in (141) and (145), where we had two columns of equal height but unequal density, and we found that the velocity was that due to the reduced difference of the two columns. It has been shown in (93) that the temperature of the air, &c., in well-arranged steam-boiler chimneys is about 550®, and by Table 19 it will be found that at that temperature the density of air is almost exactly one-half of the density at 62®, and we have, as in Fig. 35, a column of air in the chimney, say 80 feet high, weighing only half as much as the same height of external air, and motion will ensue as in (145) with a velocity due to 80 — 40 = 40 feet head. For the purposes of calculation this [head may be represented in inches of water, thus the density of air at 62^ being g^th that of water, and at 552° i^th a column 80 feet or 960 inches high will be equal to g 2 Q = 1*17 and = * S85 inch re- spectively, and the difference is 1*17 — *585 = *585 inch of water, see (221). Assuming a fixed or standard temperature for the chimney at 552°, we have in Table 54 the equivalent differences of pressure in inches of water, by which we may calculate the velocities, &c., by the rules and Tables 47, 51, &c., &c. ROUND CHIBINEYS. 93 Table 54. — Of the Draught Powers of Chimneys, &c., with the Internal Air at 552°, and External Air at 62°, and with the Damper nearly closed. Height of Chimney ill Feet. Draught Power in Inches of Water. Theoretical Velocity in Feet per Second. Height of Chimney in Feet. Draught Power in Inches of Water. Theoretical Velocity in Feet per Second. Cold Air entering. Hot Air at exit. Cold Air entering. Hot Air at exit. 10 •073 17*8 35-6 80 •585 50-6 101-2 20 •146 25-3 50-6 90 •657 53-7 107-4 30 •219 31-0 62-0 100 •730 56-5 113-0 40 •292 35-7 71-4 120 •876 62-0 124-0 50 •365 40-0 80-0 150 1-095 69-3 138-6 60 •438 43-8 87*6 175 1-277 74-8 149-6 70 •511 47*3 94-6 200 1-460 80-0 160-0 We allowed in (90) 300 cubic feet of air at 62° per pound of coal ; in passing through the fire this is highly heated and it leaves at 1279° (89) and is expanded to about 3^ times its former volume (Table 19); from thence to the chimney it is pro- gressively cooled to 652°, and becomes reduced to double its normal volume, or to 600 cubic feet. If we allow 10 lbs. of coal per horse-power, we have to pass 6000 cubic feet up the chimney per horse-power per hour. (167.) “ Bound Chimney s ,''' — Say we require the power of a chimney 80 feet high, 2 feet 9 inches diameter, attached to steam- boilers 30 feet long, having flues the same area as the chimney, and say 100 feet long in circuit from furnace to chimney. It will be seen that we have to determine the discharge of a pipe 180 feet or 60 yards long, 2 feet 9 inches diameter, with a head of *585 inch of water by Table 64 and (166). We must assume a discharge as in (166), say 100-horse power or = 10000 cubic feet per minute, which will require 10000 ^ 00 by the rule in (164) ^3.7 ^ 33) 5 = *2211 inch of water for friction alone ; we have to add to this the head due to velocity. The diameter being 2-76 feet, we have an area of 6*94 feet, and as we have = 167 cubic feet per second, the velocity will 167 be 6*94 = 28 feet per second, which by Table 47, with * 93 co- 94 SQUARE CHIMNEYS. efficient, is due to a head of • 2 inch of water, and tlio total liead for 100-horse 2 )ower is *2211 -|- *2 = -4211 inch of water. We have, however, *585 inch at disposal, and hy (15G) or (159) this will be equal to or ^ ' 4211 118-horse power. A chimney of these dimensions is working well at Dartford, the consumjition of coal being 10 cwt. per hour, which allowing 10 lbs. per horse-power, as we assumed in (166), is equal to - - = 112-horse power. 100 X *765 •649 (168.) Square Chimneys ” — If the chimney we have just con- sidered had been square, the horse-j^ower would have been greater in the simple proportion of the areas of a square to a circle, see (160). The velocity of discharge is the same in both cases, and the quantity discharged is proportional to tlie respective areas, or as ’7854 to 1 ; in our example (167), a square chimney 118 would have been equal to = 150-horse power. (169.) We shall assume a constant length of circuit of flues at 100 feet, this will be too great for small boilers, but the only effect will be to make the chiimiey rather too powerful for such cases. It is expedient to allow a margin for unforeseen contingencies, and to give an excess of power in all cases ; the damper can be regulated so as to obviate any mischievous results from the admission of an excess of air (101). We have calculated. Table 55, on these principles, giving the power throughout at 75 per cent, of the maximum calculated power, thus allowing 25 per cent, for margin. Figs. 44 to 46 give elevations of common chimneys of 40, 60, and 80 feet height ; care should be taken not to contract the channel at the points B, C, D, to less area than the outlet A at the top. Mortar should be used for the most part, because cement is destroyed by a strong heat, the 4^-inch work at the top, however, should be in good cement ; with so thin a wall the heat is rapidly carried off by the external air, and the cement will not be injured. With steam-boilers the heat of the air should not exceed GOO'^ ordinary stock-bricks will stand that temperature well, but with reverberatory and other l)rick furnaces (78), the air is at a temperature of about 2250°, and for such cases the chimney should be lined with fire-brick tliroughout, and as tlic cohesion of mortar is soon destroyed with such liigh tciiq)eraturcs, there should be wrought-iron bands Table 55.— Of ths Poweb of Chimneys to Steam-boilees, having flues 100 feet long, in circuit from Furnace to Chimney. table of chimneys to steam-boilees, 95 Note — The power of the chimneys in this Table is three-fourths of their absolute maximum power: thus the ^ 150 X 4 maximum power of a chimney 3 ft. Gin. diameler, 80 fe;.t high, is ^ = 200-horse power, &c. 96 EFFECT OF LENGTH OF FLUES TO CHIMNEYS. round the outside at regular distances from top to bottom. In ordinary chimneys hoop-iron should be built into the brickwork every few courses to form a bond ; and a lightning conductor should not be omitted. (170.) Effect of Long and Short Flues f — The effect of dif- ferent lengths of flue is shown by Table 56, in which we have Table 56, — Of the Power of a Chimney 60 ft. high, 2 ft. 9 in. square, with Flues of different Lengtlis. Ivength of Flue in Feet, Horse-power. Length of Flue in Feet. Horse-power. 50 107-6 800 56-1 100 100-0 1000 51-4 200 85-3 1500 43-3 400 70-8 2000 35-9 600 62-5 taken as an example a chimney 60 feet high and 2 feet 9 inches square, which by Table 65 with an ordinary flue 100 feet long, is equal to 100-horse power ; it will be seen that with a flue of one-half the length, or 50 feet, the power is increased to 107* 6-horse power only, and that with a flue 1000 feet long, the power is reduced to one-half nearly. This may be applied to other cases, say we required a chimney of 150-liorse power, mth a flue 1000 feet long (from furnace to chimney), this would 150 be equal to = 300-horse power in Table 55, and might be 120 feet high and 4 feet square. Again, a chimney of 50-horse 50 power, with a flue 400 feet long, must be equal to = 70-horse power, in Table 55, and may be 80 feet high and either 2 feet 6 inches round, or 2 feet 3 inches square, &c., &c. (171.) Peclet has given rules for the calculation of chimneys, by which we have calculated Table 57 ; but we have certainly Imown chimneys doing nearly double the work assigned by that Table, for instance the chimney at Dartford (167) would be by this Table about 60-horse power, whereas our calculation gives its maximum j)()wer at 118 horses, and as we have shown it is really doing 112-horso power satisfactorily. ON VAPOUR. 97 Table 57. — Of the Power of Chimneys to Steam Boilers, according to the rules of Peclet. Horse-power of Chimuey. Assumed Length of circuit of Flues In Height of the Chimney in Feet. 20 40 60 80 100 125 150 Square. Round. Feet. Minimum Size of Chimney in Inches. 10 7-8 45 18-40 14-12 12-95 20 16 65 23-30 19-73 18-12 17-07 35 27 85 30-73 26-10 23-83 22-39 50 39 105 36-76 31-17 28-41 26-06 25-45 75 59 110 37-96 34-56 32-39 i 30-88 100 78 110 39-63 37-11 ’ 35-35 34-52 150 118 110 48-34 44-19 43-03 41-00 39-57 200 157 110 55 '55 51-95 49-40 47-04 45-38 300 235 120 , , 60-23 .57-33 55-20 400 315 130 65-97 63-48 500 390 150 •• •• •• •• 70-85 See Table 55, which agrees better with experience. CHAPTEE VI. ON VAPOURS. (172.) Let Fig. 57 be a barometer with a large chamber A, one cubic foot in capacity, and let the bore of the tube be very small, so that its capacity may be regarded as infinitely small compared with that of the chamber ; the space A will then be a perfect vacuum and the height of the column of mercury at ordinary atmospheric pressure will be say 30 inches. Now if a few drops of water be introduced into A, vapour will instantly be formed from it, filling the chamber and depressing the column B say to G, the amount of this depression will depend on the temperature of A ; by adding mercury at 0 until that column is raised say to D, the column B may be restored to its former level. Now the height of the column C B was the measure of the atmospheric pressure, and as that is supposed to be constant, it is evident that a pressure equal to 0 D is exerted by the vapour in the chamber A, thus if C D is 1 inch, D B will then be 29 inches H 98 MIXTURES OF VAFOUR AND AIR. only, and as 30 is required to balance the atmosj)licric pressure, the rest must have been made up by the pressure of tlie vaj)()ur in A, and is equal in this case to 1 inch of mercury. Tlie ex- periments of Eegnault give the elasticities or pressure of vapour of water at different temperatures as in Table 12 and in column 4 of Table 58, thus at 212® the boiling-point of water, column C, would have been raised to E, at the same level as B, showing that at that temperature the elastic force of va 2 )our is equal to that of the atmosphere. (173.) The weight of water contained in the vapour may now be calculated ; the experiments of Eegnault and Despretz have shown that the weight of a given volume of vapour of water is * 623, or nearly f the weight of the same volume of air at the same temperature and pressure. (See Table 32.) Thus at 132®, the weight of a cubic foot of dry air at atmospheric pressure is given by column 3 of Table 58 at *0671 lb., but the force of vapour at 132® is 4 - 752 inches of mercury, under which pressure air would weigh 0671 X 4*752 = *010656 lb. only, therefore 29 * 921 a cubic foot of vapour will be *010656 x ‘623 = *006639 lb., and thus has been calculated column 7 of Table 58. (174.) By opening the cock at E we may admit the atmos- pheric air ; if the space A, Fig. 57, had been a vacuum we should of course have then a cubic foot of dry air there, whose weight is given by column 2 in Table 58, but vapour being present, less than a cubic foot will be required. Say we take the case in which the elastic force of the vapour is 15 inches, or about half that of the atmosphere. If we assume that the relative volumes and densities of vapour follow the law of Marriotte (15) as dry air and gases do (which is not a fact, but the correctness of our deduction will not be affected in this case), we shall have a cubic foot of vapour at 15 inches pressure or elastic force, and if a piston were fitted into the cube, as at Fig. 58, and forced to descend from A to B, the pressure would increase from 15 inches at A to 30 inches at B, and the cubic foot of vapour would of course be reduced to half a cubic foot, its density being doubled and its elastic force increased to that of tlie atmosphere, also the space C above the piston would be a vacuum ; if now the cock F were opened the air would fill the vacant half cubic foot, and the piston being removed the two would intermix with one another, but the relative weights would not be altered, the vapour would return to its normal volume and jiressure of 15 inches of mercury, and the air being dilated Table 58. — Of the Weight of Air, Vapour of Water, and Mixtures of Air saturated with Vapour, at different Temperatures, under the ordinary Atmospheric Pressure of 29*921 inches in the Barometer. mixtures of vapour and air. 99 ‘t-i 2 a> J-, M .2 ^ o ^ ^ h'S :2 § ” • Q-. a. o > CO io (M CD GO t- rH OSiMJO^OaiO’^TfHCO'-HrHGOCO^aiQOOCifMt^ P' Qciooicoi— lOTHcoociOi— tait^iOTjHccccc O T-ICOr>C5TiHJOOOOa5iOCr5GO»OlOCDOi-li.OO QOr-irHt>lOCOTHO^a5CDTflr-lTHrHr-l'<±iaOCOO COGODq'^ai(MOi— ilOr-HGOCD^COtMrH CDL■-(^^OOlOTt^CO(^^^H^H C<1 rH T— I 'P B rA a .a to O O o a5i-^05D50rHCy5l>COTH>-HOiOCOOOOCOOO l:-CDrHL--.OOCDOOrh'iOOCt>L^<:Di— iCOOTjHCO.-a COiOGOr-icr)COC < 1 ^ a o I (u . « -o 5 , 03 ^ 0.i!g>gS O 03 -I- ^ 2 ® •sS?3 THOl>i-HrHl:^Ol>CD(Ma5C0CD»O(MCD(M»0O O'rhCNGODqCDrHCi'^H^COI^i— iT-HQOCO'^rtHtM lOQOCqiOcr^CQt^GOOOOGOTfit^CDCOCD^CO OGOt>OCOCqOGOI:^OCOOGOiODI05»0-^CD CO l>- l> CO CO CD CD CD lO »0 lO ^ tM rfH CO ooooooooooooooooooo r+OI>CDCr-i^OOCOTtHrH(M CO-^CDQODqCDOlCCaii— iCDTHt>THCDiOrHiOGO OOOO^r-ioqcMCOiOCDQOOCOCDOiCO'O OOOOOOOOOOOOi— IrHrHCMDlCOCO OOOOOOOOOOOOOOOOOOO (MrHCDt^tr^CDTiHOT-lOTt^HHt^COOGOlOOO OGOCD'o^iO^OOOiOCOOCDCNOCMCDGCOOO GOt^t^t^t^t^CDCDCDiOiOiO^^CODqcMi— lO OOOOOOOOOOOOOOOOOOO OrHCOiOCDOOiOOOOCDrHDqcOrHCOi-HO rfiOCOCDCOiMDQGOOOCDiOOcMCDCDOt^O t^OiOCOr-lOO'+IGOrHCOrHt^aJGOrHOOTHO (OOOOOGOGOt-t-CDiOCCi— iail>COOiOO (M(MCCOCDiO(Mr-lCDrHT-H(MlOOa5COOGOOrH GOCDQOiOGCOOCOCOCMiOCDCCOiOCDDliODq r-(DqCOiOt>OiOOt>CDt>i— lOiOr^OOOrHO r^^^<^^(^^COT^^CD^>OC<^lOairHO r-i i-H rH rH C<1 C<1 53 o 2 . o o t-i fl -i-a 2 g-sts S,cg r-O fH t>T— (CDi— lt>COOt^THC-CD^CO(Mi— lOOO O GOt^t^l>t-t-t>l:^CDCDCDCDCDCDCDCDCDCD10 OOOOOOOOOOOOOOOOOOO o . 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The value of 11 for water hy Table 71 is 1*0853, and by the simple rule (2G7) tlie loss would be 1*0853 x (122 — 32) = 97*G77 units, but applying the correction of Table 80, as explained in (299), we find the ratio with 122 — 32 = 90° excess to be 1* 1G3, and the true loss becomes 97*G77 X 1*1G3 = 113* G units per hour, as in (col. G) Table 59. Tlie heat lost by radiation during the 1’8G hour is therefore 113*6 X 1*86 = 211 units as per (col. 7). There is another loss by the air which carries off the vapour, for that air has to be raised from 32° to the temperature of tlie water, or to 122°. Table 58 shows (col. 10) that each pound of water requires at that temperature 11*G5 lbs. of air; the heat thus lost will therefore be 11*65 x (122 — 32) x *238 = 250 units, as per (col. 8) in Table 59. (188.) Collecting these results, we have 1119-|-211-j-250 = 1580 units of heat to evaporate 1 lb. of water at 122 (col. 10), 1580 or = ^4:9 units per square foot per hour : this varies with the temperature of the water, as shown by (col. 11). It will also be seen from (col. 10) that the heat required to evaporate a pound of water is not constant, but attains a maximum at about 62°. Table 59 may be applied to the solution of many practical questions, as we shall proceed to show. (189.) “ Befrigerators ” — In the refrigerators commonly used in breweries, &c., a very large surface is necessary, and we can calculate the area for any particular case : say we have to cool 20 barrels, of 36 gallons each, from 202° to 82° in an hour. The work to be done is to dissipate 360 x 20 x 120° = 864000 units per hour. At the commencement, each square foot will lose (col. 11) at the rate of 4465 units, but at the last, 319 units only : taking the loss for each temperature between the extremes, we obtain the average of 1511 units per square foot per hour; so that we require an area of 864000 1511 = 570 square feet. This is the maximum area for calm air; with a very moderate breeze, such as may mostly be reckoned on, the area might be reduced (182) to ^ = 397 square feet. There must be free passage allowed for the dry air to enter, and the vapour to depart, &c. ; the volume of dry air required is very great ; taking a mean from 82° to 202° (col. 12), we find EVAPORATING PANS. 107 tliat we require 142 cubic feet per pound of water evaporated, tlie mean quantity evaporated is 1*283 lb. per square foot per bour, in our case 1*283 x ^70 = 731 lbs. is evaporated, which will require 731 x 1^2 = 103802 cubic feet of air. (190.) “ Evaporating Pans '' — In concentrating syrups, and in many chemical operations, it is frequently essential that evapo- ration should be carried on at low temperatures, because high temperatures would injure the product operated on. For such cases the evaporating pan must expose a large area, and must have no cover (179), the depth is unimportant; say we had to evaporate to one-half 10 gallons per hour, that is to say, 5 gallons or 50 lbs. had to be evaporated at a temperature not exceeding 152°, Table 59 shows (col. 3) that at 152° the loss is 1*1783 lb. per square foot per hour; we shall therefore 50 require = ^2 square feet, say 6 feet x 7 feet, or, if circular, about 7 feet 6 inches diameter. The heat required to do the work is by (col. 10) 1392 x 50 = 69600 units, which may be obtained by a fire beneath, consuming 69600 6000 = 11-6 lbs. of coal, and a fire-grate about 1 foot square, allowing 6000 units per pound of coal, which is about the economic value of coals for such a case. (See Table 31.) (191.) “ Evaporation at the Boiling-point ," — ^When a liquid is not injured by a high temperature. Table 59 shows that evapo- ration by boiling is the most economical of all ; thus water requires only 1209 units per pound, if the surface is exposed ; but if a cover be used, to avoid the loss by radiation, and to which there is no objection as at lower temperatures, the heat is reduced to 1209 — 63 = 1146 units. In this case a large sur- face is not necessary, the pan may have any convenient form, such as Figs. 59 or 60. Say we take a pan like Fig. 60, with a double or steam case, &c., containing 100 gallons of water, and having the dimensions given by Table 64 ; the area in contact with the water is about 17 square feet, and with 25 lbs. steam, having by Table 11 a temperature of 267°, the difference of temperature between the steam and boiling-water would be 267 — 212 = 55°. Say we require to know the quantity of water at 212°, that would be evaporated in 15 minutes. By (237) we may admit the evaporative power of a steam- cased vessel to be 330 units for 1° difference in temperature per square foot, and the latent heat of steam at 212° being 966, we 108 CONDENSATION RESERVOIRS TO STEAM-ENGINES. shall therefore evaporate — — ^ = 320 lbs. of water 9GG 320 per hour, or ^ = 80 lbs., or 8 gallons in 15 minutes. (192.) We have here supposed that the water was at 212*^, or the boiling-point, to begin with: if it had a low temperature, the case would have been different. Say that tlie water was at 42^, and we require to know what quantity of water would he evaporated from that temperature in an hour. To raise 100 gallons, or 1000 lbs., of Tvater from 42° to 212 °, will require 1000 X (212 — 42) = 170000 units of heat; tlie 7nean tempera- ture of the water while being heated will be 42 + 212 = 127°, and the difference between the temperature of the steam and the water will be2G7 — 127 = 140°, and with 17 square feet of area the time to raise the water to 212 ° would be 33 ++J 4 Q ^ if = •21G hour, so that only 1 — *210 = *784 hour would be left to do the evaporation work, and the quantity evaporated would be 330 X 55 X 17 X -784 9GG gallons evaporated to steam. Other forms of apparatus would give different results : see (231), (237), &c. ^ (193.) ‘^Condensation Beservom to Steam-engines, cfc.” — Say, we take the case of an engine working 24 hours per day, and assume that the temperature of the water for condensation shall be 82°, and the air at 32°. Admitting that a cubic foot of water evaporated is equal to one horse-power, and that the temperature of that water taken from the hot well of the air- pump is 40° higher than the condensation water, or 122°, we shall have (1178 — 122) x62*3 = G5789 units of heat per hour per horse-power to consume or dissipate. The water enters at one end of the reservoir at 122 ° and departs to the engine at the other end at 82°, and is gradually cooled down 40° in its passage ; by (col 11) of Table 59, the rate of loss at 82°, 92°, 102°, 112°, and 122°, are respectively 319, 415, 533, G71, and 849 units per hour, the mean is 557 units, and we shall therefore require G5789 “557~ 118 square feet of surface per horse- power for an engine working night and day. The depth in such a case is quite unimportant ; but if the engine is to work only 12 hours per day, the surface area might be reduced. CONDENSATION KESERVOIRS TO STEAM-ENGINES. 109 because the water would cool during the night, and in that case depth or capacity becomes a necessity, as we will proceed to show. (194.) Let us assume that 82^ shall still be the mean temperature of the condensation water ; this however will not be uniform, it will be lowest in the morning, after cooling down all night, rising all day till it reaches its maximum at the end of the day’s work. If we admit a variation of 10° each way, we shall have 72° and 92° for the minimum and maximiun temperatures of the condensation water. The difference of the temperatures of the water entering from the engine, and departing to it, will still be 40°, for if the engine receives the water 10° colder, it will return it 10° colder also, so that in the morning at starting the water in the reservoir will be 72° at one end, and 112° at the other, and at night, 92° and 132°. The mean loss per square foot by (col. 11) Table 59, from 72° to 112°, is 435 units, and from 92° to 132° it is 707 units ; the mean loss during 4-35 I 707 the day is therefore = 571 units. During the night end, being the temperature will be uniform from end to 92 + 132 = 112° at first, and 72 + 112 = 92° at last ; the loss 2 “ 2 per square foot is, by (col. 11), 239, 319, and 415 units, the mean being 324 units per square foot per hour. The total heat given out by the engine in the 12 working hours, or 65789 x 12 = 789468 units, has to be divided into two unequal parts, having the ratio of 571 and 324, hence we 789468 X 571 have — 57L+r324^ “ 503600 units to be dissipated during the day, or — 503600 shall = 42000 units per hour, and we 42000 "" require =73 square feet of surface per horse-power. The question now is, what must be the capacity of the reservoir, or the quantity of water to hold the heat which accumulates during the day, or 789468 — 503600 = 285868 285868 units. The water being raised 20”, we shall require — 20 14293 14293 pounds, or ■02.‘3' = 232 cubic feet of water, and as we 110 COOLING BY EVArORATION. 232 have an area of 73 square feet, the depth would 1)0 J,. 3*2 feet, i o if the reservoir has vertical sides, &c. ; with sloping sides of course the depth would be greater, which is a matter of cal- culation. (195.) We find from this investigation that when an engine works day and night the depth is unimportant, and that we require 118 square feet of surface per horse-power; when the engine works only 12 hours per day, 73 square feet will suffice, but in that case the depth must be such as to give 232 cubic feet of water per horse-power. There will be some advantage in making the reservoir larger than these dimensions where convenient, the water will be cooler in that case and a better vacuum obtained. The following Table gives the particulars of reservoirs in practice, and it shows that reservoirs are frequently made larger than are absolutely necessary for the temperatures, &c., we have assumed. Nominal Horse- power. Surface Actual. Area in Square feet. Calculated. Capacity in Cubic feet for 12 hours per Day. 24 hours. 12 hours. Actual. Calculated. Brighton 100 14464 11800 14600* 87884 46400* Sutton . . 40 4500 4720 2900 14742 9280 Ramsgate 30 3240 3540 2190 9228 6960 Sevenoaks 20 2240 2360 1460 7152 4640 (196.) “ Cold produced hy Evaporation ” — If we cover the bulb of a thermometer with muslin, &c., saturated with water, a considerable amount of cold will be produced, varying with the temperature of the air and the dryness of the atmosphere : see Table 60. Say we take the case of a summer day, with air and water at 72°, and that the wet bulb shows 62°, or 10° of cold. This shows that the film of water is cooled 10°, and the air which carries off the vapour must be reduced to the same temperature as the vapour, and tlms it supplies the greater part of tlie heat required to vapourize the water. The heat whicli becomes latent in vapourizing a pound of water at 62® is by the ordinary rule, 1178 — 62 = 1116 units, * One ciigiiio working 21 liours per day, or two 12 hours. COOLING BY EVAPORATION. Ill Table 60 . — Of the Indications of the Hygrometer (Dry and Wet-bulb), from Mr. Glaisher’s Observations at Greenwich. Degrees of Cold m the Wet-bulb Thermometer. Temperature 1 2 3 4 5 6 7 8 9 10 11 of the Air. Degrees op Humidity, Saturation being 100. o 32 .. .. 42 .. .. 87 92 75 85 78 72 66 60 54 49 44 40 36 33 52 .. .. 93 86 80 74 69 64 59 54 50 46 42 39 62 .. .. 94 88 82 77 72 67 62 58 54 50 47 44 72 .. .. 94 89 84 79 74 69 65 61 57 54 51 48 82 .. .. 95 90 85 80 76 72 68 64 60 57 54 51 Temperature of the Air. Degrees of Cold in the Wet-bulb Thermometer. 13 14 15 16 17 18 19 20 21 22 1 23 Degrees of Humidity, Saturation being 100. o 32 42 30 27 52 36 33 30 27 25 62 41 38 35 32 30 28 26 72 45 42 39 36 34 32 30 28 26 24 23 82 48 45 42 40 38 35 33 31 29 27 26 and as the water itself only yields 10 units, the air must supply the rest, or 1106 units, and the specific heat of air being -238, . . .A I. we shall require = ^650 lbs., or 4650 0747 = 62250 cubic feet of air cooled 10® per pound of water. Each cubic foot bears off only = *000016 of a pound of water, or about ^i_th part of the vapour required to saturate it, and hence it may happen that air after having passed over a large surface of water is only slightly charged with moisture. The quantity of air thus required is so great, that except with a wind, the process of evaporation proceeds very slowly; the observations of Mr. Miller give on an average of six years a yearly evapora- tion of 30 inches and a maximum of 4 • 5 inches in a month, as per Table 61. 112 DRYNESS OF AIR INCREASED BY HEAT. Table 61 . — Of the Evaporation TUBES, from observations at Inches. January *880 February 1 * 042 March 1*770 April 2*535 May 4 * 146 June 4*547 July 4*200 Note. — T he above is the mean of fall was 45 * 255 inches. F Water at Natural Tempera- Vliiteiiaven by Mr. Miller. Inches. August 3 * 308 September 3*174 October 1*030 November 1*322 December 1 * 087 Total 30*032 years, during which the mean rain- (197.) “ Dryness of Air increased hy Heat ’' — The capacity of air for carrying vapour increases very rapidly with the tempe- rature, as is shown by Table 58, so that, for instance, if air at 82 ^ saturated with moisture, and holding in suspension * 0037 9 lb. of vapour jier lb. of air, be suddenly heated to 42^, it will no longer be saturated, because at this latter temperature it could hold *00561 lb.; it has therefore only 00379 00561 = cent, of the vapour that would saturate it, and would show by Table 60, about 37°, or 42 — 37 = 5° of cold on the wet-bulb thermometer. The whole philosophy of drying and evaporation by heated air turns on this fact ; in our dwellings too the damp air entering them is not only warmed, but is at the same time converted from damp to dry air, and our sense of comfort arises from both causes. If air at 32° and saturated with moisture be successively raised as per Table 62 to 72°, we should obtain the given indications Table 62 . Temp, of Air. Temp, of Wet Bulb. Cold. Degree of Saturation. 0 32 o 32 1*00 Saturated. 42 37 5 •68 Dry. 52 42 10 •46 Very dry. 62 46 16 •32 72 49 23 •23 Intensely dry. of the liygrometer, and the corresponding dryness ; but to obtain this result the air must bo prevented from absorbing EVAPORATING VESSEL FOR STOVES. 113 moisture from surrounding objects, wbicli it would do with gmat avidity. (198.) Witli open fires, such as are commonly used in this country, we seldom get an objectionable degree of dryness, the air itself is seldom raised to a high temperature, because the only useful heat given out by an open fire is radiant heat, which passes through the air without’ raising its temperature (268) (298), and is absorbed by the walls, which afterwards heat the air moderately. Besides, the quantity of air drawn in by the open throat of the chimney is so great, that the dryness is kept down by the large volume of damp air passing through the room. But with close stoves, the air becomes much more highly heated, and * the quantity used is diminished, and a very objectionable amount of dryness would ensue, if means were not taken to prevent it. This is usually done by placing a vessel of water on the stove, where it becomes heated, and gives out vapour copiously, (199.) “ Evaporating Vessels for Stoves^ — Say we take the case of a stove in which 40 lbs. of coals are burnt per 10 hours, and that we have a vessel half a square foot in area placed on it, and maintained at 122°, while the air in the room was 62°, and external air at 32° : 4 lbs. of coals per hour will require 4 X 300 = 1200 cubic feet, or 91*3 lbs. of air, which at 32° will contain by Table 58, •00379 x 91*3 = *346 lb. of vapour. But during the hour, the small evaporating vessel will add by Table 59 (col. 3), *538 x *5 = *269 lb. of vapour, and we shall then have •346-j- *269 = *615 lb. of vapour, whereas 91 3 lbs. of air at 62° would require by Table 58 (col. 9), •01179 X 91*3 = 1*0764 lb. to saturate it; it therefore holds •615 i • 0764 *57 or 57 per cent, instead of *32 only as per Table 62, which last would be extremely and very uncomfort- ably dry. With a vessel of double area, we should have had *538 lbs. P . .n . . . *346 + -538 01 vapour, and the air would then have contained — 1^764^ = *82 or 82 per cent., which would have been too damp, &c. The same result might have been obtained by placing the small vessel in a position where it would have been more highly heated, until its evaporating power was doubled, which by Table 59 would have been at about 152°. With an open fire, each pound of coal consumes and passes I 114 DISTILLATION. iiiiconsumccl up the open chimney, about G times the amount of air that coal burnt in a stove requires, and the dryness is thereby reduced. (200.) “ Evaporation hy an Artificial Current of Ah \^^ — We have seen that a draught or wind causes a more raj)id evapora- tion, the reason for which is explained in (179), &c. ; Dalton supposes, that in a very strong current, the rate of evaporation would be double that in calm air. The movement of the air might be effected by a fan, or other mechanical means, or the air used by the fire under the evaporating pan, where that mode of heating is adopted, might be made to pass over the surface before it enters the fire. Taking the case of evaporation at 142% Table 59 shows (col. 12) that at tliat temperature, 77 cubic feet of air and 1445 units of heat are required, and admitting that a pound of coals requires 300 cubic feet of air, we shall require 1445 for the evaporation of a pound of water at 142'^ about = *241 lb. of coal, and *241 x 300 =72 cubic feet of air, so that in this case the air required for combustion and for evapor- ation, is nearly the same. But at lower temperatures. Table 59 (col. 12) shows that a much greater volume of air is necessary ; for instance, at 92° about 5 times as much as at 142°, while the quantity of heat and of coals varies within very narrow limits ; so that for temperatures above 152° this plan would answer, but not for lower temperatures. If we allow that the air in passing over the surface of the water should be only Aa^Z-saturated, 162° would be the limit, for at that temperature by (col. 12), 39 feet of saturated, or39x2 = 78 feet of half-saturated air, would suffice for the evaporation, being the same as the amount for combustion, which we found to be 72 cubic feet. CHAPTEE VIII. DISTILLATION. (201.) It will be seen by Table 9, that the boiling-point of liquids differs considerably, for instance, water boils at 212°, and alcoliol at 173° ; if a mixture of these two fluids is heated to 173°, tlie alcohol in it would rise in vapour, leaving the water beliind, and thus in theory the whole of the alcohol might DISTILLATION OF ALCOHOL. 115 be separated, and tlie whole of the water remain. But practi- cally, it is found that part of the water becomes entangled witli the alcoholic vapour, and passes away with it ; by repeating the process, however, the alcohol may be obtained almost pure. (202.) The vapour thus evaporated is conducted into a refrigerator, where it is condensed and restored to the liquid state again. The distilling apparatus consists therefore essen- tially of a closed evaporating vessel, and a condensing vessel, connected together by a pipe to conduct the vapour. The evaporator might be heated direct by the fire, or by steam-pipes circulating through the liquid to be evaporated, &c. (203.) The quantity of heat necessary to evaporate a given quantity of alcohol may be easily calculated ; say we required the quantity of coals necessary to evaporate 30 gallons of alcohol from 62°. A gallon of water weighs 10 lbs., and by Table 46 v/e see that the specific gravity of alcohol is *813, therefore in our case the weight of alcohol is 30 x 10 X *813 — 244 lbs., which will require by Table 1, 244 x *022 x (173° — 62°) == 4646 units of heat to raise it from 62° to 173°, the boiling-point ; to evaporate it we shall require by Table 8, 244 x 457 = 111508 units more, or altogether, 4646 -j- 111508 = 116154 units, and taking the economic value of a pound of coals at 6000 units, we shall require 1101 ^1 6Q0Q ~ “ whole work ; and if it had to be done in an hour, the fire-grate should have an area (120) of about 1^ square foot, and the work being about 2-horse power with that consumption of fuel, we should require (113) about 20 feet effective heating surface in the boiler, or body of the still exposed to the fire, &c. This calculation is for the distillation of alcohol, when it is mixed with foreign bodies, from which we desire to separate it. (204.) In this country, alcohol is commonly distilled from wort made by the infusion of barley, it contains about 10 per cent, of alcohol ; by the evaporation of this to one-half, nearly the whole of the spirit passes over, the liquor thus obtained being composed of ^th spirit and fths water. Say we had a still containing 100 gallons of wort, we should obtain by the first distillation 50 gallons of liquor, composed of 10 gallons of alcohol and 40 gallons of water. The heat required and the size of the apparatus may be easily calculated, the work to be done being composed of three portions, namely, to raise 10 gallons of alcohol from 60° and evaporate it ; to raise 40 gallons of water ’vvhich passes over with it, from 60° and evaporate it, — and 116 DISTILLATION CONDENSING ArrARATUS. to raise tlio 50 gallons wliicli remain in the still at tlie end of the operation from 60° to 212°. We will assume tliat this work has to be done in an hour. (205.) The alcohol will weigh 10 x 10 X *813 = 81*3 lbs., and the sum of the latent and sensible heats being always the same (8), a pound of alcohol at 60° will require (173 — 60) x *622 4- 457 = 527 units, and in our case we have 527 x 81*3 = 42845 units for the alcohol. A pound of water requires 1178 — 60 = 1118 units, or in our case, 1118 x 400 = 447200 units; and the water remaining in the still (212 — 60) x 500 = 76000 units, giving a total of 42845 -(- 447200 -|- 76000 = 566045 units. We may fix the size of the boiler, &c., by analogy, with a steam-boiler doing the same amount of work. By (48), we see that about 70000 units are required per horse-power, the work in . , ^ 566045 ^ ^ our case is therefore = 8-horse power, we must therefore have by (113) and Table 38, say 16 x 8 = 128 square feet of 128 effective fire-surface ; the fire-grate by (120) must be =7*1 square feet, and the consumption of fuel will be 7*1 x 14 = 99*4 lbs. of coals. (206.) The fuel may be economized by heating the wort beforehand by the heat given out in the refrigerator, where the alcoholic vapours are condensed. Assuming the boiling tem- perature at 200°, to raise the 10 gallons of alcohol from 60° will require (200 — 60) x *622 x 81*3 = 7080 units, and to heat 90 gallons of water requires (200 — 60) x 900 = 126000 units, altogether 7080 -|- 126000 = 133080 units, which is equal by proportion to 133080 X 99*4 566045 = 24 lbs. of coals nearly, the consumption being thereby reduced to 99*4 — 24 = 75*4 lbs. (207.) “ Condensing Apparatus ” — It is obvious that the apparatus we have described in (230), &c., for heating liquids by vapour, may be applied equally for the condensation of vapour in the process of distillation, and the sizes necessary in any particular case may be determined by the same rules. The most common form of condenser is the worm in a tub of cold water, as in Fig. 61 and (232) ; taking the case (205) we iriay detcioiiine the lengtli and diameter of the helix, and the (quantity of cold water necessary to effect the condensation. The tem})erature of the water used will be about the same as that of tlie atmoHpliere, taking the hottest month we find, by Table 63, DISTILLATION — WATER FOR CONDENSING. 117 Table 63. — Of tbe Mean Temperature of every Tenth Day in the Year in the Central District of England. 1st. 11th. 21st. 1st. nth. 21st. o o o o o o January 36-5 35-6 37*1 July .. .. 61-2 Gl-5 62-0 February .. 37*2 37*5 38*5 August 62-5 01*7 CO-6 March .. 40-1 41*0 41*9 September . . 58*8 57*4 55*5 April . . 43-6 45-0 47*0 October 53-5 51-4 49-0 ]May 50-0 51-3 53*8 November . . 46*4 44-0 42-0 June . . 56-4 57*5 59*8 December .. 41*7 40*2 38-4 ference, we should have = 6*35 coils. the mean temperature of July and August to be say 62° ; it may depart at 102°, its mean temperature therefore is 82°, and that of the vapour being say 202°, the difference is 202° — 82° = 120°. Admitting 320 units per square foot of smfface per hour for 1° difference as in (232), we have in our case 320 x 120 = 38400 . . . .... . 42845+ 447200 _ ^ units for 120 , and shall require = 12 ‘7 square feet of surface ; if the pipe is 1 j diameter outside, its circum- 12*7 ference is *325 foot, and the length must be = 4:0 feet, and the diameter of the helix being say 2 feet or 6*3 feet circum- 6-3 (208.) If the temperature of the water in the tub was the same throughout the mass, namely, 82°, we should evidently requii’e 42845 + 447200 (8 2° — 62°) X 6 0 ~ 4:0*8 gallons of cold water per minute. But the water would not naturally have a uniform temperature, indeed it would require continued stirring to make it so, the water at the bottom (where it should enter) will be nearly cold or 62°, in the middle it v/ill be 82° as we have assumed, and therefore at the top it must be about 102, and if the outlet pipe be taken from that part, as it ought to be, we . .. . . 42845 -h 447200 should only require ^4 q 2 _ 02) x 60 ~ 204 lbs., or 20 *4 gallons per minute. There is a further advantage too by this arrange- ment, the alcohol departing from the lowest coil, is cooled down almost to atmospheric temperature, and accidental losses of alcoholic vapour are reduced in amount. 118 DIlYINa IN OPEN ATK, &C. CHAPTER IX. ON DRYING. (209.) “ Drying in 0]pcn AirT — Tliis is the commonest and clicapest mode of all, but in our climate it is too uncertain to be depended on for many manufacturing purposes ; it is fre- q^uently used however in drying paper, glue, whiting, &c. In such cases a covered building is used to keep off the rain, the sides being open to admit the air freely, but shutters are pro- vided to keep out the air as much as possible on damp days. The rate of drying varies exceedingly, see (177) to (181) ; generally the air is only about half- saturated with humidity, and drying proceeds rapidly, especially with a wind; but in v/inter it is often completely saturated, and the drying process is comjffetely suspended. The laws by which drying is governed are explained in the chapter on evaporation. (210.) ‘^Drying hy Heated AirT — The capacity of air for moisture increases rapidly with the temperature, as we have shovm in (197), and the efficacy of hot-air drying depends on that fact. The philosophy of the process will be best under- stood by an illustration. Let Fig. 67 be a drying-closet, in which the air entering at the bottom becomes highly heated by contact with the steam- pipes, and rising through the closet, finally escapes by the chimney at the top. Say we had 10 lbs. of water to evaporate from 42^ ; that the external air of a November day was 42° (see Table 63) and completely saturated with moisture, the exit temperature being say 102°, and let us admit for illustration that the air at exit is only ^aZ/’-saturated with moisture. Now every pound of air at entry and at 42°, is by col. 9 of Table 58 charged with ’00561 lb. of water, and at its exit at • 04547 102° with -04547 lb. if saturated, but in our case — k — = -02273 lb. only ; it tlierefore takes up in its passage *02273 — •00561 = *01712 lb. of water, and to carry off* 10 lbs. we shall 10 require ~ (21 1.) To evaporate; 10 lbs. of water from 42° requires by (8) 1178 — 12 X 10 = 11360 units of heat, or tlie amount that would raise 11360 11)H. of water 1°, and the specific heat of air DRYING-CLOSET FOR LINEN, &C. 119 1 1 360 (3) being *238, tliis is equal to = 47731 lbs. of air 1°. But we have only 584 lbs. of air to do tbe work required, it 47731 must therefore be heated = 82°, and the air must enter the closet at 102 -(- 82 = 184°. Thus we have 584 lbs. of air, heated from 42° to 184°, which coming in contact with the wet clothes is cooled down to 102°, the heat thus parted with serving to evaporate the 10 lbs. of water. The total quantity of heat expended in the process is not only the 11360 units required to evaporate the water, but also that required to raise 584 lbs. of air from 42° to 102°, which is equal to 584 x (102 — 42) = 8340 units, making a total of 11360+ 8340 = 19700 units. (212.) “ Position of Outlet-opening, deJ ^ — In Fig. 67 we have shown the common mode of arranging the inlet and outlet openings, but the plan is a very bad one, as may be seen in the chapter on ventilation (317, &c.); the heated air takes the shortest course to the chimney, and escapes only partially saturated v/ith moisture, and in those parts of the drying-room out of the course of the current the drying process proceeds very slowly. If instead of entering by numerous openings uniformly distri- buted as in the Figure, the air entered at one place, the case would be still worse. (213.) The best position for the outlet opening is near the floor, the requisite draught being obtained by a chimney, which may be made of light wood- work. The heated air rises in a body to the roof of the closet as in (320), whence it is gradually drawn down by the action of the chimney ; all the horizontal layers of' air will have the same temperature throughout, as in Fig 93, and the drying in every part of the room will be equally effective. (214.) Figs. 68 to 70 give a good arrangement of a drying- closet for linen ; the horses are sometimes made of wrought iron, but well-seasoned deal is the lightest, cleanest, and best material in all respects ; they are formed with a back and front plate, A B, about 12 inches wide, connected together by hori- zontal rails, on which the linen is suspended. They are su23- ported by two flanged wheels, running on JL iron rails C, which are prolonged outside the closet, far enough to allow the horse to bo drawn out, which is done by the handle D, the 120 DllYTNG-CLOSET FOR LINEN, &C. Tipper part being guided by a long wooden rail E E, wliicli Ik also prolonged outside the closet. Tlie openings, F, are al)out an inch narrower than A B, and say 2 inches less in lieight, so that when the horse is in its place, the opening is closed by the plate B, and when drawn out, by the plate A. Tlie air entering from without by the channel G, fills the cl i amber IT, and rises by a series of holes into the chamber J, containing 21 — 9 feet lengths of 4-inch steam-pipes. Tlie floor of the closet is closed all over, except from L to M, whicli is covered by an open grating of cast iron, the full width of the room, and through this the heated air rises in a body to the roof, where it is distributed, and descends at the back part of the room to the opening N, by which it escapes into the chimney O, and thence into the atmosphere. (215.) The length of steam-pipes including bends is about 210 feet of 4-inch pipe; if we take the pressure of steam at 10 lbs., its temperature by Table 11 will be about 240^, and at that temperature an enclosed pipe as in our case will yield by Table 66 , 314 units per foot run, or in our case 314 x 210 = 65940 units per hour, admitting that 10 per cent, is lost by radiation, &c., from the walls of the closet, we shall have 65940 X *9 = 59346 units available for drying purposes. (216.) We will assume that the air leaves the steam-pipes and enters the closet at 172° and dejDarts at 82° ; it is first heated by the steam-pipes 130°, or from 42° to 172°, and the available 59346 heat is sufficient to raise 3^39 ^ >23 8 = 1 ^ 1 ^ of air to the required temperature. (217.) By Table 58, a pound of air at 42° saturated with moisture contains *00561 lb. of water, and at 82, *02361 Id.; it therefore takes up in passing through the closet *02361 — *00561 = *018 lb. of air, and we have in our case *018 X 1914 = 34*5 lbs. of water absorbed from the linen per hour. If the wet linen is introduced at 50°, each pound of water in it will require 1178 — 50 = 1128 units of heat to evaporate it, and in our case 1128 x 34*5 = 38923 units per hour. This licat has to be supplied by the air in the act of cooling from 172^^ to 82°, and we must see that it is capable of doing it; it will yield 1914 x (172 — 82) x *238 = 41000, or rather more tlian is necessary. (218.) If we liad assumed 162° for the temperature at entry, we sliould tlien liave had 59346 120 X *238 = 207 8 lbs. of air heated DRYING-CLOSET FOR LINEN, &C. 121 which would carry off * 018 x 207 8 = 37*4 lbs. of water requiring 37*4 X 1128 = 42187 units of heat. The air in cooling from 162^ to 82° would yield 2078 x (162 - 82) x *238 = 39565 units only, being 42187 — 39565 = 2622 units too little. The conditions assumed in (216) are therefore correct, and the power of the closet may be taken at 34 ' 5 lbs. of water per hour. (219.) Air-chimney, ^ — We have in our case 1914 lbs. of air per hour, or *55 lb. per second, and by Table 19, this is *55 equal at 42° to = 6*95 cubic feet at entry from external 55 air, and at 82° to = 7*5 cubic feet at exit. But to this 0733 last has to be added the 34 • 5 lbs. of vapour taken up in the 34*5 closet: this is only = *0096 lb. per second, or *0096 x 21*07 = *2 cubic feet (63) and the volume of air at exit is increased by it to 7 * 5 -j- * 2 = 7*7 cubic feet per second. (220.) The mean temperature of the air in the closet is 172 -i- 82 — = 127°, the air in the chimney is at 82°, and both are saturated with moisture. It is necessary to remember this last fact, because the relative weights are affected by the presence of vapour, and the draught-power of the chimney is affected thereby. We assumed in (210) for the sake of varying the illustration, that the air departed only ^aZ/’-saturated, but it is a necessary condition where economy is considered that the air should be saturated. (221.) The condition of the chimney and closet with reference to the creation of a draught current is peculiar, and must be understood before we can calculate the necessary sizes of openings, &c. Let Fig. 71 be an outline diagram, in which A is the chimney and B the closet both of the same height, the air being at 82° in the chimney, and 127° in the closet. The air in B being lighter than in A in consequence of its higher temperature would ascend, and motion would ensue in the direction shown by the arrows being the reverse of what is required. Let Fig. 72 be a similar diagram, with a chimney twice the height of the closet, the column in the chimney is now opposed not only by the column in the closet, but also by another one in the imaginary chamber C, which makes up the height of the chimney with air at the external temperature of 42°. The mean T3]lAUaiIT-CTIIMNJ:Y TO DllYING-CLOSET. I 0 0 tompcrature of tlie combined column B C is tliercforc 12 4- 127 2 = 84° • 5, tliat in A remaining at 82° ; with tins height we sliouhl therefore still have a reverse drauglit. In Fig. 73 we have a chimney three times the height of the closet, and the column in the chimney is now op2)osed ])y a column of equal height composed of B, C, D, whose mean tem- 127 4-42 + 42 perature will be ^ = 70°, or 12° colder than the air in the chimney, and wo shall now obtain a draught in the right direction. (222.) We can now calculate the power of the chimney in our case, and will assume for it a height of 28 feet, or four times the height of the closet. The fact that the air at 42°, 82°, and 127°, is all saturated with moisture complicates the case, and it .will not be quite correct to take a mean temperature for the columns B, C, D, &c., as we have done with dry air in (221). The weight of air saturated with vapour is given by (col. 8) of Table 58 ; for 127° we must interpolate between 122° and .0^0 , *065042+ *063039 132°, and we have ^ = * 06404 lb. per cubic foot, and for the closet 7 feet high *06404 x 7 = *44828, the weight of the column in B; for C, D, &c., we have *07884 x 21 = 1*65564, and together *44828 + 1*65564 = 2*104. The air in the chimney at 82° weighs (as a column 1 foot square) *07226 X 28 = 2*023 lbs. Then by (145), &c., the 28 feet of the lighter air is equal to 28 X 2-023 — 2 +04 — “ 26*92 feet of the denser, leaving 28 — 26*92 = 1*08 feet to produce velocity, which by the laws of falling bodies will give /v/1‘98 x 8 = 8*3 feet per second theo- retically. Admitting that the loss of effect by friction, change of direction, and successive enlargements and contractions of the air-passages through the closet (161) which it would be impos- sible to calculate, this velocity is reduced to half (362) (365), we shall have 4*15 feet per second in the chimney and openings generally ; that througli the closet would be less, because of the greatly increased area there. (223.) The chimney 0 and the opening N having to pass, as we liave seen in (219), 7*7 cubic feet of air per second, must DRYING-CLOSETS FOR SCHOOLS. 123 7*7 have an area of = 1*85 square feet, and may be 1 * 5 x 1*25 feet ; the channel G and the holes in the top of the 6 ' 95 chamber H must be ^^^5 = 1*67 square feet, &c., &c. (224.) To facilitate the establishment of the draught when the closet is first heated, it will be well to have an opening P, by which the heated air can pass direct from the steam-pipes into the chimney ; when the draught is well established this must be closed, otherwise we should have a waste of heat, and the drying operation would be retarded. A sliding door worked by a rod outside would be the most convenient mode of regu- lating the size of the opening. (225.) It will be seen, that with damp air, the chimney must not be less than four times the height of the closet. Where such a height is impracticable from local reasons, a low one may be made to answer by keeping the opening P permanently open, the effect being to increase the temperature of the air in the chimney ; but this is an expensive mode of effecting the pur- pose, and where possible, a high chimney should always be secured. (226.) In Asylums, Schools, and similar establishments, the size of the drying-closet must be fixed by experience ; it will vary considerably with the character of the inmates, &c.. Lunatic and Pauper Asylums requiring of course a larger washing and drying apparatus than others. Generally, we may allow 1 square foot of drying-horse for children, say 1 ^ for men, and 2 for women, estimating the area of the horse by its length multiplied by its height ; thus in our case Fig. 68, &c., we have 8*5x6 X 5 = 255 square feet of surface, which would suffice for say 255 255 250 children; or ^7^ = 170 men; or = 128, say 130 women. In the case of a school for 1200 pauper children of both sexes near London, the work had to be done with thirteen horses, each 9*5 X 6*5 feet, which by our rule would have sufficed for 9 * 5 x 6 '5 X 13 = 802 children only. It was therefore much too small, and to compensate for that fact, very long hours had to be worked ; in damp weather when the whole of the work had to be done by the closet, from 6 a.m. to 9 p.m. for six days per week scarcely sufficed to accomplish it. An ordinary blanket weighing 3^ lbs. when dry contains 124 ON HEATING LIQUIDS. about lbs. of water wlicn wrung as dry as possible ; tlio closet Fig. 68 would contaiu five such blankets, and to evaporate 32 • 5 tlie 32 * 5 lbs. of water in tliem, we sliould req^uire hour, say one hour. A common sheet, weighing 1^ lbs. dry, contains 2 lbs. water, and 5 such, holding 10 lbs. of water. would be dried in 10 34-5 *29 hour, or rather more than a quarter of an hour, &c. CHAPTER X. ON THE HEATING OF LIQUIDS. (227.) “ Heating of Liquids hy Fire direct ^ — Liquids may be heated directly by a fire, or by steam which may be applied in several ways. When water is heated by a fire the best position for the fire is immediately beneath the vessel, and the worst possible position is the top, for when water is heated it expands, becomes lighter, and ascends, being replaced by colder water which in its turn is heated, and so on until the whole mass is raised at once to the required temperature, but if heat be applied at the top the heated water remains at the top, and may be even boiled there while the water beneath receives no heat whatever, (108) and (311). (228.) The form of the vessel is unimportant, only it must be such as to receive the heat of the fire readily. Figs. 69 and 60 are common and convenient forms, and for convenience of calculation the dimensions given are for a capacity of 1 gallon, and the dimensions for any other capacity may be found by multiplying by gall, required; thus if a copper to hold 125 gallons was required, the ^ of 125 is 5 and the sizes would be given by multiplying all the dimensions in the Fig. 59 or 60 by 5. (229.) The quantity of water which can be evaporated to steam depends on the area exposed to the action of the fire, and for a vessel of this form we may estimate that each square foot will evaporate 4 lbs. of water at 212° to steam, which is equal to 966 X = 3864 units of heat, or to = 2 *14 gallons. HEATING LIQUIDS BY STEAM. 125 of water at 62° heated 180° (or to 212°) per hour per square foot. The quantity of coals will be about ^th of the weight of water evaporated, and the size of the grate may be determined by allowing about 10 lbs. of coal per square foot per hour. Table 64 gives the sizes for coppers up to 300 gallons calcu- lated by these rules. Table 64. — Of the Pkoportions of Boiling and Evaporating Pans. Capacity of Copper Dimensions of Shallow Copper as per Fig. 59. Dimensions of Deep Copper as per Fig. 60. Area of Fire- grate Coals burnt per Pounds 1 ofWater at 212° to Gallons of Water heated from 62° in Gallons, A B C D E F G H J M N in Square feet. Hour in lbs. Steam per Hour. to 21 2 ^ per Hour. 20 in. 5J in. 8i in. li in. 151 in. 241 in. ! 4 in. in. ij in, 1 '20 ! in. 22 in. 201 1 2 5 29 15*5 50 |lli li 201 34 6 20 fi ,271 30 261 1 10 56 30*0 100 9| 14 li 25 42 7 25 11 331 37 33 15 87 46*5 150 11 16 2 29 48 8 28 2 38 42 38 2 21 124 66*2 200 12 18 2 32 53 9 31 2 42 47 42 2i 24 144 77*0 250 13 19 2 34 57 91 33 2 441 51 45 2i 29 173 92*3 300 14 21 2 37 60 10 36 2 48^ 54 48 3 31 185 98*8 (230.) “ Heating Liquids hy Steam J ’ — There are three methods commonly used for heating liquids by steam : by forming a steam-jacket, or double vessel, as in Fig. 60 ; by a worm circu- lating through the liquid and filled with steam, as in Fig. 61 ; and by blowing the steam by a pipe direct into the liquid to be heated. (231,) xeclet gives an experiment with an apparatus of the form like Fig. 60, in which 1980 lbs. of liquid (beet-root juice) at 39° was raised to 212° in 16 minutes, the steam being at 30 lbs. per square inch (above the atmosphere) and consequently at 274°, and the surface exposed to its action, 25*8 square feet. , . 1980 X (212° -- 39°) x 60 per hour is The work done 16x25*8 50000 units nearly per square foot. The mean temperature of = 125°, and the difference the water in this case was of temperature between that and the steam, 274° — 125° = 149°; and we have therefore from this experiment — = 335 units 149 ° per square foot per hour for a difference of 1^ 12G APPAHATUS FOR HEATING LIQUIDS. (232.) An experiment was also made witli a worm ajiparatus like Fig. Gl, the pipe was 138 feet long and 1*35 incli diametor outside, having a surface of 48 square feet, and was filled with steam at 274°. The vessel contained 880 lbs. of water at 4G which was heated to 212° in 4 minutes, and in 11 minutes more 550 lbs. of water were evaporated. (233.) In the first case the work done per hour in heating the , 880 X (212" - 4G°) X GO . water was ^4 ^48 ~ 45G50 units per square /212 + 4G°' for 1° we have j = 145°, and 315 units, agreeing pretty well with the foot for a mean difference of 274° — ( 456 ^ 145 former experiment. (234.) In the second part of the operation the work done was 550 X OGG X GO . 1 1 X 1 8 ~ G0400 units per lioui* per square foot ; the difference between the temperatures was constant, and equal to 274° — 212° = 62°, therefore for 1° difference we have = 974 units, which is a very high result, and differs unaccount- ably from (233) deduced from the same apparatus. (235.) In another experiment with a similar apparatus two worms were used, each 49 feet long, 1 ' 35 inch diameter inside, presenting altogether a total exterior surface of 39*5 square feet, filled with 15 lbs. steam having a temperature of 250°, and 132 lbs. of water were evaporated in 5 minutes. The dif- ference of temperature being 250° — 212° = 38°, we have ~ 1020 units for 1° difference per square foot per hour ; a still higher and incredible result, especially when compared with the following. (236.) An experiment was made, by Easton and Amos, of London, with a thin welded tube of wrought iron 1^ inch diameter outside and about y\r inch thick, fixed vertically in a vessel of water 12 inches square and 3 ft. 7 in. deep in water as in Fig. G2, steam was turned gently on at A, and the cock B was kept a little open to carry off any water that primed from the boiler, &c. ; an air- vent was left open constantly at E, and tlie water condensed was discharged by an (q)en nozzle at C, r.nd collected in a vessel, 1). We can estimate the amount of licat transmitted in two different ways, namely, by the rise in APPARATUS FOR HEATING LIQUIDS. 127 tlie temperature of tlie water in F, and by tbe weight of water condensed, and there should he perfect agreement between tlie two. The weight of the water in F was 223 lbs., and it was stirred well to produce uniformity of temperature, the surface of the tube in contaet with the water was 1’4 square foot. In one experiment the water was raised from 65° to 110°, or 45° in 15 minutes, and 10*218 lbs. of water were collected at D, the quantity at D, calculated from the rise in temperature of the 223 X 45 water, should have been — — = 10*38 lbs., agreeing very nearly with the experimental quantity. The mean temperature 65 -j- 110° of the water was ~ ^ difference between that and the steam 212° — 87° *5 = 124°* 5 ; and we have there- ^ 223 X 45 X 12 X 124-5 X a difference of 1°. Two other experiments gave 207 and 210 units respectively, and calculating from' the water collected, rather less in all three cases. Table 65 gives the collected results. 60 = 230 units per square foot per hour. for Table 65. — Of the Heating Powers of a Vertical Tube with Steam. Weight of AVater in the Vessel. Temperature of the AVater. Water collected at D in 15 minutes. Error. Units per Square foot per Hour for 1° difference of Internal and External Temperature. Min. Max. Mean. Increase. Actual. Calculated. lbs. o o o o lbs. lbs. lbs. 2*23 65 110 87i 45 10*218 10*38 *082 230 223 60 1021 81J 42*5 8*67 9*81 1*14 207 223 69 109i 89i 40*5 8*95 9*35 *4 210 (237.) It is difficult to see a reason for the great discrepancy between these results and those given in (234) ; a great source of error in such cases is that the air is not expelled, but in the case Fig. 62 the air could escape at hoth ends of the tube, and the difference could not have arisen from that cause. It is almost incredible that in (232) 55 gallons of water could be evaporated in 11 minutes; these results require confirmation, and in the present state of our knowledge we may take the value of a square foot of surface for 1° difference at 230 units per hour for a vertical tube, 330 for a double-bottomed vessel. 128 ON HEATING AIR. and say 430 for a horizontal tube or worm. The work done is governed by tbe outside diameter, for witii good conductors, sucb as tbe metals, tbe outside of pipes will bave sensibly tbe same temperature as tbe steam witbin, see (305) and Table 84. (238.) Tbe third method of beating fluids with steam, by blowing it direct into tbe water to be heated, is commonly used for rough purposes, there are some objections to it for reflned use; where tbe steam-boiler is connected with a steam-engino particles of grease may prime over with tbe steam ; tbe volume of liquid is augmented by the steam condensed to a considerable extent, thus to heat 100 gallons of water from 62° to 212° (or 180°) will require 100 x 10 X 180 = 180000 units of beat, to 180000 obtain which we must condense ^0^ “ =186 lbs. of steam, or nearly 19 gallons, which will of course be added to tbe water to be heated. Another objection is tbe loud noise with which this method is accompanied, this may be partially obviated by placing tbe end of tbe steam-pipe in a small vessel full of small fragments of broken granite, &c., a cover of coarse wire gauze being stretched over tbe mouth of tbe vessel to prevent tbe stone being scattered by tbe steam. CHAPTER XL ON HEATING AIR. (239;) Heating Air^ y tlie rules in (147) and (153), CHIMNEYS TO STOVES, 133 Thus with the stove we considered in (243), we found that we required 44 square feet of surface in the pipe, and if we assume 6 inches for the diameter, a 6 -inch pipe having an area of 1 ’ 57 square feet per foot run, we shall require for sheet-iron 44 a length of yrgy = 28 feet, or 9 • 3 yards. Then 450 lbs. of air 450 at 800° by Table 19, is equal to Tq ^]_ 5 x 60 ~ cubic feet per minute, and the area of a 6 -inch pipe being *196 square 240 feet, the velocity will be . ]^90 ^ 00 ~ 20*3 feet per second, the head for which by Table 47, with a co-efficient of * 93 will be about *55 lb. per square foot for velocity alone. The head for friction, by (153) and Table 51, with a 6 -inch pipe 9*3 yards long and 240 cubic feet per minute, will be /240Y" 0000668 X ^ lob j X 9*3 = *00357 lb. per square inch, or * 00357 X 144 = * 514 lb. per square foot, which added to that required for velocity, makes a total of *55 -j- *514 = 1*064 lb. per square foot. Now a cubic foot of air at 62° weighs by Table 19 *0761 lb., and at 400° (which is the temperature of the air in the chimney at the end of the flue) *0461 lb., so that each foot in height gives an unbalanced pressure of *0761 ■— *0461 = *03 lb. per square foot; we shall therefore require ^ 03 “ = 35 ‘5 feet, as the height of the chimney, which is greater than the length ! With a slight increase in the diameter of the flue, the height of the chimney would be greatly reduced. Thus a 7-inch pipe having a circumference of =1*83 feet, the length 44 would be = 24 feet or 8 yards, and the head for friction is 0000309 X /240Y Viooj X 8 X 14:4 = * 205 lb. per square foot. The area of 7 inches being * 267 of a square foot, the velocity with 240 cubic feet is — = 15 feet per second, which by Table 47 is *31 lb. per square foot. The total is *205-f- • 515 *31 = *515 and the height of chimney “ 03 = 17 feet, instead 134 HEATING AIR BY STEAM-riBES. (if 35*5 feet, wliicli we found to be necessary with a G-incli pipe. (249.) Heating Air hy Steam-pipes, — We sliall see by (302) that the amount of heat given out by heated pities to the surrounding air per square foot of surface, is not constant, but varies with the diameter, small pipes being most effective, and that 2, 3, 4 and 6-inch pipes yiehl respectively 327, 303, 291, and 279 units per square foot per hour, when the temperature of the pipe is 210^, and of the external air, (fee., 60^. With thin metal such as is commonly used in practice, we may admit that the outside surface has sensibly the same temperature as the steam within, see Table 84 and (305), and assuming and f inch for the respective thicknesses, we obtain *654, *95, 1*21, and 1*767 as the area or surface of the different pipes per foot run. Taking the 4-inch as an example, we find the loss of heat per foot run to be 291 x 1*21 = 352 units per hour ; the specific heat of air (3) being * 238, this is equal to heating 352 * 238 “ Table 19 a cubic foot 1479 of air at 62° weighs *0761 lb., we have = 19435 cubic feet of air at 62®, heated 1° per foot run of 4-inch pipe per hour. Table 66 has been calculated in this way, the loss per square foot for the different temperatures having been calculated as in (302). ‘‘ Pipes enclosed in Narrow Gliamhers or Channels!^ — When pipes are enclosed in small chambers, whose sides being very near them, become highly heated, they emit very much less heat than when freely exposed to air and distant walls, having a low temperature. This case is investigated in (303) and (382), from which it appears that the loss in the case of an enclosed pipe is about 70 per cent, of the loss when freely exposed ; and thus we obtain the numbers in the second part of Table 66. “ Effect of Variations in Internal and External Temperature,’’^ — The Table 66 is calculated for pipes freely exposed in a room with air at 62°, but sometimes for drying and other purposes the air is at a much higher temperature, and at other times the temperature is much below 62°. The effect of these changes on tfie amount of heat emitted is given by Table 67 for a gi’cat range of external and internal temperatures ; thus say that we recpiired 1000 cubic feet of air per minute, or 60000 HEATING AIR BY STEAM AND HOT-WATER PIPES, 135 a -4-3 o a QJ H ■4^ CD -1-3 a . c/3 O W O fL, 3 M O Ph =i bD ^ .a H O ^ O K ^ 3 a '-d 3 o r:3, g H a> CO >» CD Eh CO CO w « Eh o B o =s W O) ^ .2 ^ Oi-H(M-HO:i»^t^COQOOOO iX>C i-'-ioaiio'XiTiHOtiOcocococo rHiOCTi-tHGil' ^(MOCjOCD-H lOTtiC0C0CJG005(MI'-(C^dHl^(C^GC-t^O CD — ( t' H O (05 »0 -H Dt — ( O C0(C0C.T+iJoococo>ooo i-iQOG<1^00COO0(Ml^t^O3)r-l OSCO-Ht^r- i-Ht^-— IIOOIOCM OC^IGO-H-— iCit^CO-HCO'— lO COCOCNC1 CND4— (— (— (rH— (— (rH 5l O g in. 3 COOCOCTSf-Hh-f^COOOt^i-H 1— lOdCOOSt^THOOStM-HGOCO L-^rHtM-HCqcr. lOi— lOlt^-tHCO GCCOCOOt^iOT+HCOi— (00500 CCDO (04 — ( — ( rH — ( rH rH ■§a o .2 iocqoocooocoior-oooo (^0 00 T— 1 lO (M L-^ CO LO t ^ (MiO(M(03Q000t^r>-0005Or-( (M05t^Tt(C^nHOa500t>t^O CM 1 — 1 r-l T— 1 1 — ( rH rH o‘ 00 i—< -HI:^C0(MC000CCDCD»0rh(^ rH — ( — ( rH >1 . 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This may be very incor- rect ; but the extreme rapidity with which a body at white-heat cools down to orange and cherry red, &c., seems to indicate that at extreme temperatures the loss of heat is exceedingly rapid. (300.) The application of Table 80 is very simple. Say we have a mass of wrought-iron heated to 600° in a chamber whose walls are at 190°. By Table 71, the radiant power of an ordi- nary surface of wrought-iron is ’5662, and by the simple rule we have *5662 x (600 — 190) = 232 units per square foot per hour ; but by Table 80, the nearest number to the temperature of the absorbent is 194°, and to the difference or (600 — 190 = 410°), is 414°, and the ratio for those two numbers is by the Table = 6*26, and the true loss by radiation in our case is therefore 232 x 5*26 = 1220 units per square foot per hour. (301.) Loss bij Contact The researches of Dulong show that the loss by contact of cold air is independent of the absolute temperature of the heated body, differing in this respect from radiant heat ; but he found that the heat lost increases more rapidly than the simple ratio of excess of temperature. Putting his formula, with the constants given by the experi- ments of Peclet, in such a form as to give us a ratio for the *652 X different temperatures, we have the rule ^ = K'", in which t = the difference of temperature of the body and the air in contact with it in degrees centigrade, and K'" = the ratio of loss of heat with that difference ; and thus we obtain the numbers in Table 81 and in col. 5 of Table 82. It will be observed that the departures from the simple law are much less than with radiant heat; at the extreme temperature of 2580°, and with air at 59°, the loss is only 2*985 times the amount given by the simple rule. Applying this to the case in (300), say that the heated body was a vertical plane 4 feet high. Table 74 gives *478 for the value of A, and with the air at 190°, we have by the simple rule *478 x (600 — 190) = 196 units; but for a difference of 410°, the nearest number in Table 81 is 414°, for which the ratio is 1*96, and hence we have 196 x 1’96 = 384 units per square foot per hour. Adding the respective losses by radiation and contact of air together, we obtain 1220 -(- 384 = 1604 units as the total loss per square foot per hour. (302.) We may apply these rules to the case of a steam-pipe. Say the air of the room and the walls are at 60°, and the steam- IGG LOSS OF HEAT AT HIGH TEMrEIlATURES — STEAM-PI I'ES. Table 81. — Of the Piatio of Heat Emitted or Absorbed hy Contact of Air with ^iven Differences of 'J emperature. DiffercncG of Temperature of the Air and ihe Body in Contact. Ratio of Heat. 1 Difference of Temperature of the Air and tlie Body in Contact. Ratio of Heat. o 18 •94 o 252 1-742 30 1*11 270 1-774 54 1-22 288 1-800 72 1-305 300 1-827 90 1-372 324 1-852 108 1-433 342 1-874 120 1-480 300 1-897 144 1-533 378 1-920 102 1-575 390 1-940 180 1-015 414 1-900 198 1-050 432 1-980 210 1-084 450 2-000 234 1-720 1 pipe at 210°, or 150° difference. Then the correction for radiant heat hy Table 80 is say 1 * 5, and for contact of air by Table 81 = 1 • 55. Table 7 6 gives for horizontal cylinders of 2, 3, 4, and 6 inches diameter, the respective values of A at *728, *6256, *5745, and *523, and we have Units per By By Sq. Ft. R. Diff. Ratio. Radiation. A. Diff. Ratio. Contact, per Hour. For 2in.diam.(-7xl50xl*5) = 157 Vndr*728xl50y 1*55)= (69*5 = 327 3 „ „ „ (-6256 X 150 X 1*55) = 145-5 = 303 4 „ „ „ (-5745 X 150 X 1-55) = 133*5 = 291 G „ „ „ (-523 X 150 X 1-55) = 121-5 = 279 The v/eight of steam condensed to water at 212° per hour will be found by dividing the units of heat by 9G6 (the latent heat of steam), and we thus obtain *338, *312, *301, and *289 lb. of water per square foot per hour. (303.) “ Enclosed Pi^pes, dtcP — It should be observed that these calculations apply strictly to the case of a pipe freely exposed to air and radiant walls, &c., both of the same tempera- ture, and this is nearly true where pipes are fixed in the room to be heated ; but where they are enclosed in small channels under the floor, the case is very different, for in that case the walls enclosing the pipe become highly heated, and were they not continuously cooled by the air passing through them, they would soon take the same temperature as the pipe itself, LOSS OF HEAT AT HIGH TEMPERATUllES — ENCLOSED FIFES. 1G7 Table 82 .— Of the ItATio of Loss of Heat at very High Tempera- tures, by the Formula? of Dulong. Temperature of the Heated Temperature of the Air in Contact with the Body, and of all Surrounding Objects. Difference of Temperature of the Body, and of the Ratio of Heal lost at different Temperatures by Body. Air, and Surrounding Objects. Radiation. Contact of Air. 490 o 60 430 3*10 1-980 600 » 5 540 4-19 2-085 780 9 » 720 7-17 2*230 960 Red, just visible . . 9 9 900 12-68 2-348 1140 9 9 1080 23-01 2-450 1320 Dull red . . . . 9 9 1260 42-70 2-540 1500 Dull clierry red . . 9 9 1440 80-67 2-620 1680 Glierry red .. 9 9 1620 154-5 2-693 1860 Clear red 9 9 1800 299-7 2-760 2220 Clear orange . . 9 9 2160 1159-0 2-880 2580 White, bright 9 9 2520 4604-0 2-985 Note. — For the loss at lower Temperatures, see Tables 80 and 81. radiation from the pipe would cease altogether, and it would give out only about half the amount of heat. Taking the 4 -inch pipe as an example from the cases just calculated, the loss by radiation is *7 x 150 x 1’5 = 157*5 units, or rather more than half of the total heat emitted, which was 291 units. But the heat received by radiation from the pipe is given out again by the wall to the air, and the temperature of the wall rises only until the two are equal to one another. This tem- perature we find by trial to be about 158^. The wall will then be 210 — 158 = 52° colder than the pipe, and the ratio by Table 80 being 1*83 for a recipient at 158°, and the absorbent powers of brickwork being by Table 71 *736, we have *736 x 52 X 1*83 = 69*7 units received from the pipe. The amount given out by the wall to the air may be found by taking the value of A for a wall say 2 feet high from Table 74 at *528 and the ratio from Table 81 for 158° — 60° = 98° difference at say 1*39, and we have *528 x 98° x 1*39 = 71*9 units, or nearly the same amount as was received, showing that the temperature of 158° is nearly correct. The pipe at 210°, exposed to absorbing walls at 158°, and air at 60°, will lose ( *7 X 52 x 1*83) + (*5745 X 150 x 1*55) = 200*2 units instead of 291 units, as we found for the case of air and walls of the same 1G8 LOSS OF HEAT BY POLISHED METAL SURFACES, &C. temperature; the ratio is = *088, or say 70 per cent.; see also (382.) (304.) Effect of Polished Metal Surfaces^ dec’' — The amount of heat lost by contact of air is not affected by the nature of the surface of the body, but that lost by radiation varies ex- ceedingly, and the sum total is modified considerably. This may be illustrated by taking the case of a horizontal pipe 4 inches diameter outside, as in the last examples, heated at 210°, with air at 60°, &c., but with varying character of radiating surface. Taking the values of E from Table 71, and A as before from Table 76, at *5745, we have the results shown by Table 83. It will be observed, that the difference between a pipe in its ordinary state and a whitewashed one is very small indeed ; blackening with lamp-black increases the loss about 11 per cent. ; and a blackened pipe loses 317-97 139-55 2'27 times as much heat as one of silvered copper highly polished like a mirror. Where it is desired to lose as little heat as possible, tinned iron (or common tin-plate) is a very effective and cheap material, losing less than half the amount of a blackened surface. (305.) Effect of Thichness of Metal in Pipes heated internally,” — We have assumed in the preceding calculations, and elsewhere throughout the work, that the outside of a steam-pipe has the same temperature as the steam, &c., inside, and this is practi- cally true with thin pipes, such as are commonly used. With great thicknesses, however, the external temperature becomes sensibly less than that of the internal steam ; it will be in- teresting to investigate the case generally. We cannot calculate the loss of heat by the ordinary rules (274), because the surface dissipating the heat has a greater area than the surface receiving it ; the ordinary rules suppose the wall, &c., transmitting heat to have parallel plain surfaces and to have a very large (or infinite) area, so that the heat may be considered as travelling in parallel lines from surface to surface, but in a thick pipe the heat travels in radial lines, and the amount transmitted cannot be calculated in the common way. Let r = the radius of the inside of the pipe, in inches. r' = „ outside „ E = the radiant power of the outside surface. Table 71. Table 83. — Of the Loss of Heat by a Horizontal Pipe 4 inches outside Diameter, heated to 210° and exposed to Air, &c., at 60°, showing the effect of different kinds of Kadiating Surface. LOSS OF HEAT BY POLISHED METAL SURFACES. 169 c 3 ^ o 2 u 0)0)0 « g P O ‘5 a o >» pq o S 5 •!I2 pq « .2 « ^ •4860 •5325 •5373 •9971 1-0000 1-1070 iO 05 i> o i> iO 00 cq cq rH 05 05 CD f- CO iO lO 00 00 rH rH r-H »o lO CO CD GO CD CD lo cq 00 CD <05 cq GO 05 MJ C3 GO 1— t rP G<1 ICO Cm .8^ a ^ 0 C5 .& 2 o3 d jd, p Sj p O 'd 05 rd ^ 2 „ o w TO -d 03 P -§ SSS 3 H-j5 ^ 1 e c3 I. c3 t4_, g ^ P P S3 g g pS S 05 .P Cd 05 ‘Sj^ "S 170 LOSS OF HEAT BY THICK METAL riBES. Let A = the loss of horizontal cylinder by contact of air (273), and Table 76. Q = E + A. C = conducting power of the material of the pipe, Table 77. N = (log. / — log. r) X 2*3. i — temperature of the steam, &c., and of inside surface. T' = „ external air, and radiant objects. U = units of heat lost per square foot per hour. U' = „ per foot run per hour. . *5233 X Q X r' X C X (^ - T') _ th C + (Qx/xN) . ’ . . Taking the case of a pipe 4 inches bore, 4 inches thick in cast-iron, 12 inches outside diameter, with steam at 212° and air, &c., at 60° or 152° difference, we may take E at *7, A at •4722, Q at 1*1722, and C at 233, for N we have log. of 6 = •778, and log. of 2 = *301, and N = (-778 - -301) x 2*8 = . .07 1 L •5233 X 1-1722 X 6 x 233 X 152 1-097, and the rule becomes ”233 + (1- 1722 x 6^x 1 - 097 )“ = 541 • 5 units per foot run ; and a pipe 12 inches or 1 foot diameter, having an area of 3 * 14 square feet per foot in length, 541*5 this is equal to "oTJJ' = 172*4 units per square foot per hour. (306.) But with a good conductor of heat, such as cast-iron, the external temperature of the pipe will be high, and these numbers will require correction (299) (301) by Tables 80 and 81, and to apply these we require to know the temperature of the external surface. U By the rule in (286) U = Q x (^ — T'), and hence q = 172*4 (I — T'), which in our case becomes above the atmosphere ; the temperature of the outer surface must therefore be 147 -(- 60 = 207°, or 5° less than that of the inside of the pipe. With that temperature, the correction by Table 80 is 1*48, and for A by Table 81 1*535, and calculating the true loss as in (302) we have (*7 x 1*48) -f- (*4722 x 1*535) x 147 = 258*8 units per square foot per hour, or 258*8 x 3*14 = 812*6 units per foot run. With a pipe infinitely thin in metal: A becomes *5745, Q 1*2745, C is cut out, and N being 0, the expression (Qxr'xN) vanishes, and the rule becomes *5233 X Q X X (^ — T'), or LOSS OF HEAT BY THICK METAL BIPES. 171 in our case ’5233 x 1*2745 x 152 = 202*77 units per foot 3*14 X 4 run, or the area of a 4-incli pipe being 1*0467 202*77 square foot, the loss is = 193*7 units per square foot. This might have been calculated by the common rule, Q x (t — T') = U, or in our case 1*2475 x 152 = 193*7 units per square foot per hour, or the same as by the other rule. Correcting these numbers by Tables 80 and 81, we have the true loss for 152*" difference = (*7 x 1*5) + (*5745 x 1*55) X 152 = 294*9 units per square foot, or 294*9 x 1*0467 = 308*7 units per foot run per hour; so that the pipe 4 inches 812 * 6 thick loses gQ+y = 2*6 times as much heat per foot run, as one infinitely thin. Table 84 . — Of the Loss of Heat by a Hoeizontal Cast Ikon Pipe, 4 inches bore, with different Thicknesses of Metal, heated with steam inside at 212°, and freely exposed to air, &c., at 60°. Diameter of the Pipe in inches. Thick- Loss of Heat per Hour. Temperature. ness of Metal in inches. Per foot run. Per Square Of the External Surface. Of the Internal Surface. Difference. Inside. Outside. Units. Ratio. Foot. Units. 4 4 0 308*7 00 294*9 o 212 o 212 °000 4 6 1 441*17 1*4291 281*0 211*022 212 *978 4 8 2 571*4 1*851 273*0 210 212 2*0 4 12 4 812*6 2*600 258*8 207 212 5*0 4 16 6 1021*6 3*300 244*0 191 212 21*0 Table 84 has been calculated in this way ; we find that even with the great thickness of 4 inches, the external temperature is only 5° less than that of the steam ; with a thickness of 1 inch the difference is less than 1°, and of course with a pipe of the ordinary thickness of ^ inch, the external temperature Avill be sensibly the same as the internal, and the assumption that the heat lost is proportional to the external diameter is practically correct. (307.) Steam Pipes, &c., cased in Bad Conductors of Heat,’’ — The loss of heat by naked pipes to steam-engines, &c., is very considerable, and where the length is great it becomes serious, 172 LOSS OF HEAT BY PIPES CASED IN BAD CONDUCTORS. not only from the waste of fuel, but from the formation of water by condensation, which is obstructive to the working of the engine. Thus, with 35 lbs. steam, having by Table 1 1 a tem- perature of about 280°, the loss of heat by Table G6 with a 4-inch pipe would be 587 units per foot run per hour, and as by (48) a horse-power requires about 70,000 units, we find that a 4-inch steam -pipe, 4| diameter outside and 100 feet long, would lose — ^70^00 “ * 84-horse power. This loss may bo greatly reduced by casing the pipes in a material which con- ducts heat badly : see Table 77. The woollen,^ felt which is made for this special purpose is the best and cheapest material. Adopting the same notation as before (305), but putting C for the conducting power of the casing, and r" for its outer radius, N will be (log. r" — log. r') X 2*3, and the rule becomes •5233 X Q X X C X - T') C + (Qx»"'xN)" For illustration of the effect of casing with different materials, we will take the case of a pipe 4 inches outside diameter, heated to 212°, the casing being covered in all cases with canvas, so as to give the same radiating power to the outer surface, and thus exhibit the variation in loss of heat due to conducting power alone. = U'. Thickness of Casing in Inches. C. Tinch. 1 inch. j2 inches. 4 inches. 6 inches. Woollen Felt, or Cotton) Wool j •323 79-5 52-4 34 22-5 18-1 Sawdust •523 108 76-7 52 35-6 28-92 Fir-wood (transmission) perpendicular) . . . . j •748 131 99 71 49-6 40-7 Coal Ashes (coke pul-) verized) / 1 •29 165 138 108 80-6 67-6 Plaster 3 •86 216 216 209 189-0 172-0 Stone 13 •G8 244 272 316- 367-0 388-0 Marble, grey, fine . . 28 •00 250 287 352 452-0 519-0 Thus, for instance, with a casing of fir-wood, 1 inch thick, the outer diameter becomes G inches, r" = 3 inches, E by Table 71 for canvas or calico = •74G1, A by Table 7G = ‘523, therefore Q = 1-2G91, and C = *748 by Table 77. For N we have log. 3 = -477 and log. 2 = *301, and N = (‘477 - *301) x 2*3 = •405. Tlieii tlie rule becomes — LOSS OF HEAT BY PIPES CASED IN BAD CONDUCTORS. 173 5233 X 1-2691 x 3 x *748 x 152 = 98-9, or say 99 units •748+ (1*2691 X 3 X -405) per foot run per hour. Calculating in this way with the different conducting powers and thicknesses, we obtain the numbers in the preceding Table. (308.) With low conductors such as woollen felt, and con- siderable thicknesses such as 4 or 6 inches, these numbers are correct enough for practice, but with thin casings and better conductors, the external temperature will be high, and they require correction by Tables 80 and 81. We must first find the temperature : continuing the case with fir-wood, in which we have a loss of 99 units per foot run, the area of a 6 -inch cylinder is — ^12^ =1*57 square foot, and the loss of heat per square . 99 IS foot U 1*57 63 units, and the excess of temperature being 63 Q = (^ — T'), becomes in our case p”. 2691 ~ above the ex- ternal air, and the temperature of the external surface is 50 + 60 - 110°. With 50° excess, the correction of E by Table 80 is 1*2, and of A by Table 81 = 1*22, and the true loss of heat is (*7461 x 1*2) + (*523 x 1*22) x 50 = 76 units per square foot, or 76 x 1*57 = 119 units per foot run per hour. Comparing this with the loss by a 4-inch pipe uncased, but still covered with thin canvas, the corrections for 15 2° difference by Tables 80 and 81 are respectively 1 * 5 and 1*55 as in (302), and we have (*7461 x 1-5)+ (*5745 x 1*55) x 152 = 305*4 units per square foot, or 305*4 x 1*0467 = 320 units per 119 foot run, the ratio is = * 372, the uncased pipe being 1 • 0. Table 85 has been calculated in this way throughout : it will be observed that with low conductors, such as woollen felt, the loss becomes rapidly less with increase in thickness, but with such good conductors as stone and marble, the loss with all thicknesses is greater than by an uncased pipe, and the thicker the casing, the greater the loss ; it is therefore worse than useless to use even moderately good conductors for such a purpose, and it is to illustrate this fact that such materials are introduced in the Table. (309.) The effect of a given thickness of casing is not quite the same for all diameters of pipe ; Table 86 gives the loss of heat by horizontal pipes of different diameters from 2 to 12 174 LOSS OF HEAT BY PIFES CASED IN BAD CONDUCTORS. Table 85. — Of the Loss of Heat by a Horizontal Pipe 4 inches Outside cased in different Thicknesses of various Materials and covered with Tliiii the Loss Thk^kness of Casing on a Material of the Casing. Con- ducting Power of the Casing (C.) 5 -inch thick. 1 inch thick. l CD o\ cn 05 CO -tH I- CD CM 05 CO f- -H t- CD ^ CO CM o CD >0 CM O) CM 10 t- »0 rH CD t> 10 05 CO -H l> >o ^ 10 i-H >0 rH rH CM "1^ CO' O CM CO CM 05 O CD 00 CM rH_ ^cd' tH CD 00 o CO CM l> CO CO 00 rH CM CM O 00 CM 00 CO CO co_ o o CO GO 10 CO o CM CD iQ CM 10 Ttt • CD bo .2 ‘S J's r§ ^ a r/) § ^ o 2 ^ 2 ® 3 CL. O 'Ph^ f which being 4*35 x 3*14 = 13*7 feet, we shall require for 11*8 feet per second, or 700 feet per minute. 300 13*7 = 50 revolu- tions per minute. With so slow a speed there would be no objectionable noise with well-fitted wheels ; the pitch should be fine and the re((uisitc strength obtained by width on the face. The strength and sizes of the wheels must vary with the weight HEATING AND VENTILATION OF CHAPELS. 195 to be carried (see Table 88) ; the style of worlmiansliip should be like that of a church clock, &c. (348.) ‘^Air-passages^ (fc.” — The air from the fan descends below the floor of the boiler-house, and branching right and left, enters the channels in which the hot-water pipes are fixed, A, B, C, Fig. 104, from which it is conveyed by branch chan- nels D, E, &c., into four other channels, G, H, J, K, which deliver the air by apertures under the seats in each pew, as at L, M N, 0, &c. The arrangement of these openings is a matter of importance to avoid objectionable draughts. Figs. 101 and 102 illustrate two modes of doing it, which may be varied to suit local circumstances, &c. The plan 102 is much the best. To supply air to the galleries, channels are taken from G and K, as at P, P, P, &c., and are continued by other channels, K, E, &c., in the walls, and thence into the pews by branches S, S, S, &c. To prevent the accumulation of heated air under the galleries, short channels are made at intervals, as at T, T, T, &c., covered with ornamental open gratings. The heated air passes away out of the building by channels W,W, &c., which deliver into the roof, where it finally escapes by the cowl V. In winter the heated air escapes by openings at Y. The reason for placing it at so low a level is that the heat may be retained as long as possible, for the purpose of heating the building. In summer the air may escape by openings near the ceiling at X. These openings, Y and X, must be closed by sliding registers, which should be connected together, so that when one is open the other is closed, &c. For summer ventilation the openings might be made through the ceiling at Z Z, which must be closed in winter. For the inlet of air to the fan a permanent provision should be made by a louvred window, U, having a free area of about 10 or 12 square feet, and well-fitted shutters should be provided to close it completely while the walls are being heated (341.) (349.) The area of the channels should be proportional to the volume of air passing through them. With a velocity of 5 feet per second, or 300 feet per minute, allowing 220 feet of air per head, each of the main air-channels as they leave the ^ 1 -, 1 . 220 x 400 lan should have an area oi o — oTTa 2 X oO X 300 = 2 • 5 square feet. A section of these channels is given in Fig. 107. The pipes are carried by rollers on cross-timbers, H, built at intervals across the channel, and they should coincide with the branch-channels o 2 196 HEATING AND VENTILATION OF HOSPITALS. D, SO that the contraction occurs at one jilace ; and then to obviate it and preserve the area, the bottom should dip in a curve, as in Fig. 108. The hot-water pipes are enclosed com- pletely in a wooden casing ; the air is admitted by a row of holes, say 1^ inch diameter, whose total area must he ecpial to the area of the two main channels, or 5 square feet, or 144 x 6 = 720 square inches. With *8 for coefficient of contraction (148), the area of 1^ is 1*22 x *8 = *976, and we shall require 720 = 740 holes, which distributed on a length of 214 feet 2568 , or 2568 inches, must = 3^ inches, centre to centre. (350.) In fixing the area of the branch-channels, we may 720 allow = 1*8, say 2 square inches per head. Each pew for four persons requires 2x4 = 8 square inches, and there would he no loss of effect here if it were made much larger, say double. Loss of power arises from loss of velocity only where that velocity has to be regained, which is not the case when the air is finally discharged (161). The galleries may contain 90 people, and the 8 channels, P, E, and S, supplying each 11 people, must have an area of 11x2 = 22 square inches ; the 7 channels, D D, have to supply 110 people, or 16 each, including P, E, and S, and must be 16 x 2 = 32 inches area ; the others, E, E, have only eight to supply, and must be 8 x 2 = 16 inches area. (351.) The eight exit openings Y and channel W should 720 have an area of at least -g- = 90 square inches ; but here also there will be no loss by using a larger area. Allowance should also be made for the obstructions of the grating, and the con- traction (148) which a fluid experiences in passing by a thin- lipped orifice. With *65 for coefficient, each opening must 90 have a free area of Tgg = 140 square inches; the bars of the grating may probably occupy -^th of the total area, which should 140 X 5 therefore be r — =175 square inches, say 15 x 12 inches. (352.) “ Hospitals ” — The ventilation of a hospital must be more perfect, powerful, and uniform than any other ; the state of health of the inmates necessitates a larger volume of fresh air than is necessary for persons in good health, and the venti- lation must be continuous night and day without intermission. HEATING AND VENTILATION OF HOSPITALS. 197 For perfect comfort, the walls should be at least as hot as the air in the room, which as we have seen (297 ) is impossible, where they have to be heated by the air in the room. Mecha- nical ventilation by a fan is not admissible, because in most cases hospitals are too large to be thus ventilated without an engine, to work which night and day is expensive ; besides, as the work to be done cannot be remitted even for an hour, we should require a duplicate set of apparatus in case of repairs. A chimney in which a draught is maintained by a fire is the best plan, because the mass of brickwork in the chimney retains so much heat as to maintain a fair draught for hours after the fire has been suffered to die out : see (365). (353.) Figs. 109-112 represent a small hospital, or the wing of a large one, in which heated air is supplied in winter by a cockle or hot-air stove, and the ventilation is maintained at all seasons by a draught chimney. A is the hot-air apparatus, con- sisting of a collection of pipes, B, open at both ends and built into the side-walls, which are retained in position by clamp plates and bolts, the fire from the furnace at C circulates among the pipes in its passage to the chimney D, which serves for the escape of the smoke, &c., as well as the foul air from the rooms. The air to be heated enters the pipes at E, and passes through them into the chamber F, from which it proceeds by the channels G G, which run longitudinally the whole length of the building. Other channels, H H, are made in the main walls by which the highly-heated air passes to the top of the building, thence descending by the channels J J to the bottom again, imparting the requisite heat to the walls in its passage. From the channels J J, branch-pipes, N N, are laid, discharging the heated air (which by this time is cooled down to the proper temperature) into other long channels, 0 0, and thence into the room by openings under each bed and at suitable places in the offices, &c., &c., in the ground floor. (354.) The air thus received into the rooms passes through and ventilates them, escaping by orifices, K K, &c., in the ceiling, into foul air channels, L L, which conduct it to the end of the building, where it enters the descending shafts, M M, which communicate with the chimney D, by which it is finally dis- charged into the atmosphere. The heated air enters the walls at a much higher temperature than is desirable for the rooms, but the walls absorb its surplus heat, and become heated perfectly throughout their mass, the 198 HEATING AND VENTILATION OF HOSPITALS. air having for the most part to traverse tlie height of tlie Imild- ing twice, before it escapes into the rooms. Tlie direction of the currents is shown by arrows, and it will he observed that the vitiated air moves off directly into the atmosphere, without mixing with the rest of the air in the room. (355.) “ Loss of Heat hy the Building, dc ” — Allowing 1000 cubic feet of air per head per hour, and that we have 50 x 3 = 150 inmates, we shall require 150000 cubic feet of air at G0°, or •076 X 150000 = 11400 lbs. of air per hour. If we assume that the interior smffacc of the walls is at 60°, with a thickness of 2 ft. 3 in., we shall have (288) by the formula U = Q X (t - T') 1 “f" Q E C or in our case 1-134 X (60 - 30) 27 = 4*63 units per square foot per hour, and as 4-83, we have 11790 square feet of wall surface (windows excepted), the heat dissipated by them will be 11790 x 4*63 X 54567 units of heat per hour. This heat has to be supplied by the 11400 lbs. of air entering the building, and to 54567 do that, it must be cooled ^ ^ 7775 ^ = 20 °, and as it leaves the walls to enter the rooms at 60°, it must enter them at 80°. mean temperature of the air in the walls is thus — ^ The = 70°, and the internal surface would be rather more than 60°, as we assumed. The windows contain 1440 square feet of surface, and will dissipate (293) 1440 x *53 x 30° = 22896 units per hour, the greater part of which will have to be supplied by the air in the rooms. (356.) “ CocTde, or Air-stove ^ — It will be seen by (355) that we require 11400 lbs. of air per hour for ventilation, which air has to be heated from 30° to 80°, and will require therefore 11400 X 50° X *238 = 135660 units of heat. With a cockle such as A in Eig. 112, we should not expect perhaps more than 6000 units usefully from a pound of coals, and in that case the 135660 consumption would be = 23 lbs. of coal per hour. = 2 6000 square feet of fire-grate. . . 23 requiring through the cockle, would be heated to 80' The air passing and would become HEATING AND VENTILATION OF HOSPITALS. 199 by Table 12, 150000 X 1*102 ro6i 156000 cubic feet per hour, or 2600 per minute, and the velocity given by tlie chimney (357) being 5 feet per second, or 300 feet per minute, the combined area of the pipes in the cockle, through which the air has to be 2600 drawn, must not be less than =8*7 square feet. A pipe heated externally as in our case gives out no radiant heat to the air within (268), but only by contact. For such a case it is advisable to use a larger volume of air than usual, in order to keep down its temperature as it leaves the furnace, &c., and there will be no loss of effect if we admit a double quantity, the case being quite different to a steam-boiler, &c., where we have shown (101) that a great loss would arise with an extra large volume of air. Then by Table 34, with a double quantity of air, the temperature as it leaves the fire would be 1157°, say 1200° ; as it leaves the apparatus it would probably be reduced to 400°, the mean temperature is therefore about 800°, and allowing that the air passing through is heated to 80°, we have a difference of 800 — 80 = 720°, the ratio for which by Table 82 is about 2 • 2, and taking the value of A from Table 76 at * 5, we have *5 x 2*2 x 720 = 792 units per square foot of surface, 135G60 and the internal area must be — = 171 square feet ; but with pipes arranged on one another as in Fig. 112, the full external surface is not effectively exposed, probably not more than -frds can be reckoned on, and hence we require — = 256 square feet. The size of the pipes must therefore be such as to expose an area to the fire of 256 square feet, and a cross-sectional area of 8 * 7 square feet for the passage of the air to be heated. These conditions are nearly fulfilled by 8-inch pipes, the cross-sectional area of 8 inches is * 36 square foot, and with 25 pipes we should have *36 x 25 = 9 square feet. With pipes 9 feet long, allowing that 18 inches is built into the side- walls, the effective length is reduced to 6 feet, and the circum- ference of 8 inches being about 2 feet, we have 6 x 2 x 25 = 300 square feet, instead of 256 feet as required. (357.) “ Ventilation ” — The proportions of the ventilating apparatus must be fixed with reference to summer requirements, when a fire has to be maintained specially for that purpose, and when the air in the draught-chimney, not being so highly heated 200 HEATING AND VENTILATION OF IIOSriTALS. as in winter, when it receives the waste heat from the cockle, the draught is more feeble. For summer ventilation the damper P is closed, and a fire is maintained night and day in the furnace E at the base of the chimney ; this has a closed ash-pit, so that the air feeding the fire is drawn from the body of foul air enter- ing the base of the chimney. The air in the chimney becomes heated, say 50° higher than the atmosphere, and the cliimney being 60 feet high, we have by Table 19 a column of hot air say at 82° and 60 feet high, which is counterbalanced by a column at 32° — 2 Vj^Q2 4 ^Gct high, giving 60 — 54*4 = 5*6 feet to produce motion, and which by the rule for falling bodies VH X 8 = V, is in our case V5 * 6 x 8 = 18 * 92 feet per second. This is the theoretical velocity, which is greatly reduced by the friction of the air in long passages, and by changes of velocity which in practice are unavoidable. These losses, however, cannot be calculated but by many experiments on such chimneys. Peclet finds that where the circuit is long, the real velocity is only ‘ 25 or * 3 of the theoretical, and even where the circuit is short, not more than *4 (362) (365). Taking the velocity at * 3 in our case we have 18 * 92 x ' 3 = 150000 5*6, say 5 feet per second, and as we have to pass = 41*7 cubic feet per second, the chimney and main air-passages 41*7 must have an area of = 8*34 square feet, or 144 x 8*34 = 1200 square inches, and the chimney may be, say 3 feet square. The area of the channels G will each be 600 square inches ; 1200 , . 1200 ^ 1200 11= = 67 square inches; N = ^ ^ = 22; L = — g— = 200 square inches, &c., &c. (358.) The cost of maintaining the ventilation in winter is nothing, the waste heat from the heating cockle being used ; in summer, as we have seen, it is 23 lbs. of coal per hour, or 5 cwt. per day. The ventilation in summer can be adjusted by regu- lating the fire in E ; in winter it may be necessary to regulate the draught by dampers S S, in the main channels G G. EXAMPLES OF HEATING AND VENTILATION — PRISON MAZAS. 201 CHAPTER XVI. EXAMPLES OF BUILDINGS HEATED AND VENTILATED. As illustrations of the application of the rules given in Chap. XV. for calculating the loss of heat by buildings, and to show how far they agree with observed facts, we may take the following examples which are given by Peclet. (359.) Prison Mazas ” — This great prison is situated in Paris, and contains cells for the solitary confinement of 1200 prisoners. These cells are arranged in six long buildings, which radiate from a centre, and occupy nearly two-thirds of a circle. The walls are of stone, about 36 feet high, averaging 24 inches thick, and exposing an exterior area of 140000 square feet ; the area of the windows is 23400 square feet. For the seven months of the year, during which the building was heated, the mean temperature of the exterior air was 44°, and the interior air 58°, being a difference of 14°, and from these particulars we can calculate the weight of coals required by the building, &c. The ventilation was maintained constantly by a chimney with a fire at its base, as in Fig. 112; this chimney was cylindrical, 7 feet internal diameter and 95 feet high, the mean quantity of air passing through the building was 1059600 cubic feet per hour, and this air had to be heated 14°, from the external to the internal temperatures, and required a further quantity of fuel. (360.) The conditions of the building are similar to those in (290) and Fig. 84, with one face exposed, and by Table 79 we find that a wall of stone 24 inches thick loses * 284 unit per square foot for 1° difference of internal and external tempera- ture of the air. In our case, therefore, the walls will lose •284 X II X 140000 = 556640 units per hour. The windows were for the most part only 2 feet high, and by the rule in (293) lose ’56 unit per square foot for 1°. The loss in our case is *56 X 14 X 23400 = 183456 units per hour. By Table 19 the weight of air at say 42° is *079 lb. per cubic foot; we have therefore 1059600 x *079 = 83708 lbs. of air to bo heated 14°, and the specific heat of air being *238, this is equal to 83708 X * 238 x H = 278910 units per hour. Collecting these three results we have a total loss of 556640 -f- 183456 -j- 278910 202 HEATING AND VENTILATION PLISON MAZA8. = 1019006 units per hour. But part of tliis heat will ho siip- jilied hy the animal heat of the prisoners, as explained in (^>14), where we find that each man will yield 191 units per hour, and we have 191 x 1200 = 229200 units per hour from this source, leaving 1019006 — 229200 = 789806 units to be supplied by the heating-apparatus. Allowing for intermittent firing as in (41), we may take the economic value of coals from Table 31 at 6000 units per pound, and shall require 789806 6000 ^ 24 = 3160 lbs. of coal per day. The experimental quantity was found to be 3564 : the difference may arise from losses in the vaults, &c., not included in the calculation.* (361.) During the cold weather of winter it was found that 5280 lbs. of coal were consumed per 24 hours, to maintain the internal air at 59° *3 while the external air was 39°, the We found that for 14° difference the the loss with 20*3 will therefore be difference being 20° -3. loss was 1019006 units 1019006 X 20-3 = 1477560, and deducting the heat emitted by the prisoners, we have 1477560 -- 229200 = 124836 units to be supplied by the fuel, requiring 124836 6000 ^ X 24 = 4994 lbs. of coal, instead of 5280 as per experiment. (362.) ‘‘Ventilation ^ — For maintaining the ventilation it was found that the mean consumption of coals by the fire at the foot of the chimney was 770 lbs. per day in winter, and 880 lbs. per day for the rest of the year ; but for the ventilation, equal to 1059600 cubic feet per hour, the consumption was 44 lbs. per hour in winter, and 55 lbs. in summer. The temperature of the air in the chimney was not observed, but we can calculate it from the consumption of fuel. By (28) the total heat in a pound of coals is 13044 units, nearly the whole of this will be given out to the air passing up the chimney ; allowing that 5 per cent, falls from the grate uncon- sumed as in (90), and that 5 per cent, more is lost by radiation, &c., we have from 44 lbs. of coals 13044 x *9 x 44 = 516544 * Peclot brinp:s out the calculated quantity mucli nearer the experimental quantity than in the above, but he assumes that the temperature of the in- ternal Hiirfacc of the walls is the same as that of the internal air. This is not a fact, tlie wall receiving heat from the air, must of necessity be much colder than that air in order to do so. We have shown hy Fig. 84 that the wall is about 00 — 54‘3G = 5°'04 colder than the internal air. HEATING AND VENTILATION — PEISON MAZAS. 203 units of heat per hour, and as this is carried off by 83708 lbs. of air, and the specific heat of air being *238, we have 516544 . ~*~^ 38 X 83708 ~ increase oi temperature, and the air entering at 58° (the temperature of the building) becomes 58°-|- 26° = 84° in the chimney, or 84 — 44 = 40° warmer than the exterior air. A 95-feet column of air at 44° is equal by (14) to 95 x 458-4 + 44 — i — ov = 88-feet column of air at 84°, and we have 95 — 458*4 + 84 ’ 88 = 7-feet head to generate velocity, which will give ^7 x 8 = 21*1 feet per second. The chimney was 7 feet diameter, having an area of 38*5 square feet ; but the centre of it was occupied by the iron chimney from the steam-boilers, which was 2 feet 8 inches diameter, having an area of 5 * 5 square feet. The acting area of the air-shaft was thus reduced to 38*5 — ■ 5*5 = 33 square feet, and when discharging 1059600 cubic feet per hour, the velocity of the air entering the chimney must be 33 ^ 0 Q ^ 0 Q = 8*92 feet per second. The real velocity 8 * 92 is therefore only ^ ~ **^23 of the theoretical velocity, this loss arising from friction, change of velocity by frequent con- tractions and enlargements in the air-channels, &c., &c., which are practically unavoidable in long circuits; see (161). The mechanical work done by the chimney being proportional to the square of the velocity, is thus reduced to *423’^ = *179. (363.) Mechanical and Chimney Ventilation compared ^ — We may compare mechanical ventilation with that produced by heat, and ascertain the relative economy of the two systems, by calcu- lating the power of an engine and fan capable of doing the same work and the consumption of fuel in the two cases. By (362) we have seen that with the standard quantity of air the consumption of coals was 44 lbs. per hour during the seven cold months of the year, and 55 lbs. per hour for five months. We have therefore (44 x 24 x 30 x 7) + (55 x 24 x 30 x 5) = 419760 lbs. of coals per year, with a heated chimney. By a high-pressure engine the work in winter costs nothing^ because the steam after working the engine is used for heating the building. The mechanical work done is 83708 lbs. of air per hour, or 1228 lbs. per minute, at a velocity of 8*92 feet per second, the . 204 HEATING AND VENTILATION — TIIISON OF FIIOVINS. head due to which, by the law of falling bodies, is 1’243 feet; we have therefore 1228 X 1*243 3’3000 = *0463 liorsc- jiower. But we have seen that by friction, &c., &c., in the passages the work is reduced to *179 of the power employed; and as a low-jiressure fan and gearing will probably yield only one-third of the force ex 2 )ended on it, we should re(]^uire *046 3 xj *179 = *776 horse-power. If v/e allow 10 lbs. of coal per horse-power, this is equal to 7*76 lbs. of coal per hour for seven months of the year only, and the yearly consumption would be 7*76 x 24 x 30 x 7 = 39110 lbs. of coal, instead of 419760 lbs. as required by a draught-chimney; the ratio is 1 to 9 * 3. This is a favourable case for mechanical ventilation, being a very large one. By the ordinary allowance of 350 cubic feet per head, the air dealt with would suffice for “^ 350 ^ = 3000 persons, and even for this large number we require an engine of only three-fourths of a horse-power. For small, and even for ordinary cases, the engine would be excessively small, the fric- tion proportionally much greater, and the relative economy of the system less. There is also the practical objection that the engine must work day and night, requiring an extra man for the night-work, &c., and a duplicate engine in case of repairs, &c. (364.) ^‘Prison of PromnsT — This prison was arranged in the same manner as the prison Mazas, but was very much smaller, consisting of one range of buildings for 39 prisoners. The walls were of stone, 24 inches thick, and exposed 11340 square feet of surface. The windows had an area of 1157 square feet, and the air used for ventilation was 120090 cubic feet per hour. Experiments were made on the consumption of fuel from the 15th of March to the 6 th of April, the mean temperature of the day was 43° by observation, that of the night was not observed, but is reported to have been very cold, probably it was 8 ° colder than the day, or 35° ; the mean temperature of the exterior air would therefore be 39°, and the internal air being maintained at 59°, the difference would be 20°. The consumption of fuel under these circumstances was found to be 807 lbs. of peat per day. The loss by the walls 24 inches thick will be * 284 units for HEATING AND VENTILATION — PRISON OF PROVINS. 205 1° by Table 79, and we have *284 x 20 x 11340 = 64411 units per hour lost by the walls. The windows by (360) will lose * 56 X 20 X 1157 = 12958 units, and the air 120090 X ‘079 x * 238 X 20 = 45348 units ; collecting these three losses, we have 64411 + 12958 + 45348 = 122717 units per hour. The prisoners will yield 191 x 39 = 7449 units, leaving 115268 to be supplied by the fuel. By (28) and (30) we find the total heat in coals and peat to be 13044 and 7151 units respectively, and the economic value of coals being as we have assumed 6000 units, that of peat will be 6000 X 7151 — — = 3290 units per lb., and thus we shall require 115268 — X 24 = 840 lbs. of peat per day, whereas experiment gave 807 lbs. (365.) “ Ventilation .^^ — The draught or air chimney was 59 feet high, and 2 feet diameter at the top, its area being 3*14 square feet. An experiment was made when all the fires had been extinguished six hours, the temperature of the air in the chimney would be about the same as that in the building, which was 16° higher than the external air, which being taken at 39 ° that in the chimney would be 55°. The observed discharge of air under these circumstances was 40052 cubic feet per hour, , . , 40052 and the velocity oi discharge must therefore be g^QQ gTJJ = 3 * 54 feet per second. For calculating the theoretical velocity we have a column of air 59 feet high at 39°, which is equal in 458*4 4-39 weight to a column 59 x 453 . 4 ^ 5 ~5 = 57*11 feet high at 55°, and we have 59 57*11 = 1*89 foot head to generate velocity, which will give Vl'39 x 8 = 11 feet per second, whereas the real velocity was only 3 * 54 feet per second. The ratio in this 3 * 54 case is — = *322 to 1, and the mechanical work of the chimney, only * 322^ = * 104 of its theoretical value : see (362). (366.) “ Church of St. Boch .’’ — This church was about 377 feet long, 92 feet wide, and from 50 to 60 feet high. The walls were of stone, 20 inches thick, exposing a surface of 37674 square feet ; the windov/s were about 13 feet high, and exposed an area of 9257 square feet. When the interior air was maintained at 29° above the exterior air, the consumption of coals was 88 lbs. per hour. 206 HEATING AND VENTILATION — CHURCH OF ST. ROCH. The conditions of this building arc similar to Fig. 80, the walls being exposed on all sides to cooling influences. The loss of heat for this case is given by Table 78, which for stone walls 20 inches thick may be taken at * 2 for 1° ; in our case the loss will be *2 x 29 x 37674 = 218510 units per hour. By (294) the windows lose *4 unit for 1% or in our case *4 x 29 X 9257 = 107385 units, and the loss from both sources is 325895 units per hour. There will also be another loss of heat by a large but unknown volume of air, which enters through the heating apparatus by openings in the floor, and passes out by innumerable crevices in the leaden casements, the glass being very loosely fitted ; it will therefore escape at the temperature of the glass, and if we know that temperature we can calculate the volume of air which passes through the building. (367.) ‘‘Temperature of the Walls and Glass in Windows '' — To give distinctness to the question, we will assume that the internal air is at 59°, and the external air at 30°, or 29° difference. We can now calculate the temperatures of the two surfaces of the walls by the rules in (282) and (283). Taking the value of K from Table 71 at *736, of A from Table 74 at *398, and of C from Table 77 at 13*7, Q will be 1’ 134 and the rule Q (E A T + C T') + A C T ■ C(2 A + E)+(E AQ) = ^ becomes in our case 1*134 (20 X *398 X 59 -f 13*7 x 30) + *398 x 13*7 X 59 13*7 X (2 X *398) + (*736) + (20 x *398 x 1*134) = 44° which is the temperature of the interior surface of the wall. The temperature of the exterior surface may now be C ^ + Q E T' found by the rule — q q p ] — = l\ which in our case becomes (13 7 x 44) + (1-134 x 20 x 30) _ 13-7 + (1-134 X 20) - The temperature of the glass in the windows will be given by (T - t) X A ^ — - j - 1 [ T the rule in (294) ^ — which in our case becomes (59 - 44) X -43 -43 + -5948 + = 40° *15, and this is also the temperature of the air at exit. “ Volume of Air ." — We can now calculate the volume cf air passing through the building, for as it departs at 40° * 15, HEATING AND VENTILATION — CHUKCH OF ST. EOCH. 207 it must have been cooled by the walls from 59° to 40*15 = 18^*85, and the weight of air which in doing that would yield to the walls and windows the required quantity of 325895 units, must be 325895 18*85 X -238 70342 70342 lbs., or ."q^^ = 88930 cubic feet at 42^. This air departing at 40° *15, or 10° *15 above the external air, will carry off 70342 x 10*15 x *238 = 170000 units of heat, which added to the amount lost by the walls and windows gives a total of 325895 -|- 170000 = 495895 units per 495895 hour, requiring “ 0 QQQf =82*6 lbs. of coal, instead of 88 lbs. as per experiment. (369.) But we might have calculated approximately both the volume of air and its temperature at exit, and therefore of the glass in the windows from the known quantity of coals con- sumed. 88 lbs. of coals give 88 x 6000 = 52800 units of heat, and as the whole of this heat is given out to the air as it passes the hot-water pipes and enters the building, and that air being heated 29°, its weight must be ^ = 76500 lbs. This air has to yield 325895 units to the walls, &c., and to do that must be cooled down 325895 76500 X -238 17° * 9, it therefore departs from the building at 59° — 17° *9 = 41° *1, and this is also the temperature of the glass. The volume of air and temperature of the glass as thus calcu- lated, differs but little from those found by the former method, which no doubt is the more correct of the two. (370.) Taking the volume of air at 88930 cubic feet per hour, and allowing as in (312) 215 cubic feet per head, this would 88930 suffice for - ^ • = 4100 people ; the ordinary numbers present are 2000 to 4000 ; on fete-days, 4000 to 6000 ; and on grand occa- sions, 6000 to 8000. The capacity of the church is about 113000 cubic feet of air ; it is therefore renewed about 8 times per hour. (371.) “ Time required to heat the Building to the Standard Temperature.^^ — It was found that to heat the building to the standard temperature of 29° above the external air, required eight days of continuous firing day and night, and it will be in- structive to see how far this agrees with calculation. The walls contain 63576 cubic feet of stone, weighing by Table 46 about 156 lbs. per foot, or 63576 x 156 = 9917856 lbs., 208 HEATING AND VENTILATION — CHURCH OF ST. ROCH. and tlie specific licat by Table 1 being about *21585, tliey will require 9917856 x *21585 = 2140770 units of beat to raise their temperature 1° We found in (367) tliat when the standard temperature was attained, the two surfaces arc 44° and 35° *27 respectively, the mean tem 2 )crature of the wall is there- fore 44 + 35*27 39° *625, or 9° *625 above the external tem- perature, and this is the amount of heat which the walls must receive before the standard temperature can be attained. We found that for 1° they required 2140770 units, they will tliere- fore require 2140770 x 9*625 = 20626320 units to bring them up to the standard. (372). The time in which this quantity can be supplied is in our case governed by the maximum power of the heating-apparatus. This was proved with an external temperature of 21°, for in that case the internal temperature could not be maintained higher than 50°, being a difference of 29°, or the same as at the standard in- ternal temperature of 59°, with external air at 30°. The appa- ratus could therefore yield only 218510 units per hour to the walls as in (366), and to do that, the temperature of the walls must be 15° colder than the air as we have seen in (367), where the respective temperatures were 59° and 44°. This difference would be constant throughout, so that the walls being 30° at the commencement, the internal air would be heated by the apparatus to 45°, when further increase of temperature would be arrested by the walls absorbing the heat, and as their tempe- rature increased, so would that of the air be progressively and simultaneously increased, and the difference of 15° would be maintained throughout. (373.) But while heat was thus received by the internal surface, a considerable amount would be dissipated by the external surface. At the commencement, when the walls had the same temperature as the external air, the loss would be 0, progressively increasing to 218510 units per hour when the walls were heated to the standard temperature ; for when that is attained, the external surface dissipates the same amount as the internal surface receives, and the temperature remains sta- 218510 + 0 t ionary. The mean loss is therefore ^ = 109255 units per liour, so that while 218510 units were received by the interior surface, 1 09255 units would be dissipated by the external surface, and 109255 units would be stored up in the walls ; and HEATING AND VENTILATION — CHURCH OF ST. ROCH. 209 to obtain 20626320 units, tbe time required to bring them to the standard temperature would be 20626320 109255 X 24 “ practically tbe same as by experiment, which, as we have stated, was eight days. (374.) With a powerful heating-apparatus this time might be shortened ; but if the maximum temperature of the internal air be limited to 59° (the standard temperature), which is almost a practical necessity, as a higher temperature would be intoler- able, the time will be governed by the absorbing power of the walls, irrespective of the power of the apparatus beyond a cer- tain point. With the apparatus we have considered, the air could not be heated more than 15° above the temperature of the walls ; but with one of greater power the difference might be 29° or 59° — 30°, so that the air could be raised at once to the standard temperature of 59°, and the walls would then absorb 218510 X 29 15 = 422424 units ; but as the temperature of the walls increased, that of the air being fixed at 59°, the difference would become less and less, until when the standard temperature was attained, it would be reduced to 15°, and the amount of heat received to 218510 units per hour, the mean is therefore 422424 4- 218510 ^ = 320467 units per hour. The outer surface would still lose at a mean rate of 109255 units, and the amount stored in the walls being thus 320467 — 109255 = 211212 . n. . 20626320 units per hour, we should require 211212 x 24 “ ^ ^ attain the standard temperature. (375.) If the building is not to be occupied during the time its walls are being raised to the standard temperature, the maxi- mum temperature of the internal air need not be limited to 59°, and in that case the time might be still further shortened. For instance, with air at 88°, the difference at the commence- ment would be 88 — 30 = 58°, or double that in the last case, which was 29°, and the walls would absorb at first 422424 x 2 = 844848 units per hour ; the mean heat received would then 844848 + 218510 be o = 531679, and the mean amount dissipated being as before 109255, the amount stored in the walls would be 531679 -- 109255 = 422424 units, and the time re- quired to bring the building up to the standard temperature p 210 HEATING AND VENTILATION — CHURCH OF ST. ROCH. 2062G320 T22424: 24 “ ^ flays. In this case the fire would have to be put out some time before the hour of worsliip, to allow the air to cool down to 59°, and the time for this may be approxi- mately calculated. (37G.) The church contained 113000 cubic feet of air, or 113000 X ’0733 = 82829 lbs. of air, which in cooling down 29° from 88 ° to 59°, would yield 82829 x 29 x ‘238 = 571G8 units. The hot- water apparatus contained 1588G lbs. of water at 248°, and in cooling that down 189°, or to 59°, we shall have 1588G X 189 = 3002454 units ; so that to cool down to the standard temperature we must absorb 571G8 -f- 3002454 = 3574140 units. During the cooling process the mean temperature of the internal air is _ 730 - 5 ^ being 73*5 — 30 = 43° *5 colder than the external air. With 29° difference, we found (3GG) the loss by the windows to be 107385 units, the temperature of the glass being 40° *15, or 10° *15 colder than the external air; but with 43° *5 difference, as in our case, the temperature of the glass by the rule in (294) is 43° *2, or 13° *2 colder than the external air, and the loss by the windows and the air in the two cases will be proportional to those differences. In the former case these losses were 107385 -f- 170000 = 277385; in our present case it 277385 X 13*2 will therefore be 10 ^T 5 “ 3 G 0730 units per hour. The walls at this time are absorbing their standard quantity of 218510 units ; so that altogether the cooling influences are equal to 3G0730 4 - 218510 = 579240 units per hour, and the time in which the internal air, &c., will be cooled down is 3574140 . . , 6 * IT” hours. If the heating apparatus had consisted of s/eam-pipes instead of hot- water pipes, we should not have had the body of water to cool down, and the air alone would 571G8G have been cooled to the standard temperature in ^^924 9 = 1 hour nearly. (377.) It should be observed that the time required to bring the walls up to the standard temperature is simply proportional to the power of the heating-apparatus, but that the mean heat consumed, and consec^uently the consumption of fuel, follows a mucli lower ratio. The maximum power of the apparatus in tlie tliree cases we have considered was 218510, 422424, and 814848 units per houi* res 2 )ectively, the ratio being 1.2.4 HEATING AND VENTILATION CHUIICH OF ST. KOCH. 211 nearly, but the mean heat given out in the three cases was 218510, 320467, and 531679, the ratio being 1, 1*46, and 2*43. (378.) We have assumed in the foregoing that the area of the internal surface absorbing heat was equal to that of the external surface dissipating it ; and this is nearly true in our case, the internal area being increased by massive stone pillars, buttresses, &c., supporting the roof. (379.) ‘‘Time required to Cool the Building T — When once heated, a considerable time would be required to cool the whole building down to the external temperature. If the air passing through it be stopped by closing the inlet-openings, heat would be dissipated only by the walls and windows, and we should lose 325895 units at first, which would be progressively reduced to nothing at the end of the time. The mean loss would therefore be 325895 + 0 = 162947 units per hour, and the heat of the V n ^ • 20626320 building would be dissipated in I 02947 ^ 24 “ ^ ^ ' days. If the circulation of air be permitted as usual, the mean rate of loss would be — = 264000 units per hour, and the building would cool down to the external temperature in 20626320 264000 X 24 “ (380.) “ Heating- Apparatus” — The heating-apparatus con- sisted of a boiler about 12 -horse power, with hot- water pipes 5^ and 4f inches diameter. They were laid in channels with brick sides, under the floor of the church in the usual way. The total area of the hot- water pipes was 1774 square feet, they 495875 therefore gave out = 279*5 units per square foot: (see (368.) The temperature of the water as it left the boiler was 248% and as it returned 216% its mean temperature was therefore 232% or 232°— 29° = 203° above the external air. By Table 66 , a 6 -inch enclosed pipe yields 286 units per square foot, for 200° difference. The case of a pipe enclosed in a channel is quite different to that of a pipe freely exposed. (381.) When a pipe is enclosed, the walls receive radiant heat from it, and their temperature is raised until they give out to the air in contact the same amount as they are receiving from the pipe, when further increase of temperature is arrested, p 2 212 EFFECT OF WIND ON VENTILATION. and it remains stationary. With brick walls and a steam-pi po at 232° the temperature of the walls would he 158°. At that tcmj)erature, being 232 — 158 = 74° colder than the pipe, the ratio (299) of heat lost by radiation is, by Table 80, 1*9, and the value of E from Table 71 being for bricks *730, the walls will receive *736x 74x 1*9 = 103 units per square foot per hour. Then by (301) a wall, say 2 feet high, will have *528 for the value of A by Table 74, and the difference of temperature of the air and of the wall being 158 — 30 = 128°, the ratio by Table 81 is 1*486, and the loss by contact of air is *528 x 128 X 1*486 = 100*3 units per hour, nearly the same amount as was received by radiation, and showing that the temperature of 158° is very nearly correct. (382.) A steam-pipe 5 inches diameter, heated to 232°, exposed to radiant walls at 158°, and to air at 30° (see 302), R, Diff, Ratio. A. Diff. Ratio. will lose (* 7 X 74° X 1 * 9) + (• 544 x 202° x 1 * 65) = 279 * 7 units per square foot per hour, which by an accidental coincidence is almost exactly the amount found by experience, which we have seen to be 279*5 units. If this same pipe had been freely exposed to air and radiant objects both at 30°, the difference of temperature would have R. Diff. been 232° — 30° = 202° in both cases, and the loss (*7 x 202 Ratio. A. Diff. Ratio, xl*5i) -(- (*544 X 202 x 1*65) = 394*8 units, and an en- 279 * 7 closed pipe therefore gives only = *708, or say 70 per cent, of the amount lost by a pipe freely exposed (303). CHAPTER XVII. WIND, FORCE OF, AND EFFECT ON VENTILATION, ETC. (383.) “ Influence of the Wind in Ventilation^ ^cV — The effect of the wind on the draught-power of chimneys to furnaces, &c., is well-known by experience. Let ABC, Fig. 13, be a tube freely exposed to the action of the wind, A B being vertical ; if now the wind moves in the direction C to B, it will enter at C and pass out at A ; but if the wind moves from B to 0, it will enter at A and pass out at C. EFFECT OF WIND ON VENTILATION. 213 It will be seen, that this is analogous to the case of a boiler- house on a plane, with a chimney at one end, as in Fig. 15, the whole being freely exposed to the wind on all sides, and air admitted by openings at the end C ; but here the air in the chimney is highly heated, and a powerful upward draught thereby created, still it will be retarded when the wind sets from B to C, and assisted and accelerated when in the contrary direction. Table 54 shows the draught-power of chimneys in calm air, in inches of water pressure, by which we can compare the power of the draught, with that of the wind. (384.) According to the experiments of Hutton, the force of wind at moderate velocities varies as the 2 * 04 power of the velocity : he also found that a plane 32 square inches in area, and moving at a velocity of 12 feet per second, experiences a resistance from the wind of * 841 ounce. From these data we obtain the formulae. Y 2 C4 ^ -001487 = P and in which V = the velocity in feet per second, and P = the pressure in lbs. per square foot ; Table 89 has been calculated by these rules. (385.) Taking as an illustration a chimney 80 feet high, we find by Table 54 that the draught-power is equal to *585 inch of water, and by Table 89 this is equal to a wind having a velocity of about 42 feet per second, which is a very brisk breeze, and if the boiler-house is freely exposed to its force, the draught of the chimney would be destroyed when the wind was blowing with that strength in the direction B C, and doubled when in the direction C B. In such a case the doors or other openings at the end C should be closed, and others opened at the end B or or at the side D. (386.) To obviate the adverse action of the wind, and to utilize its power of increasing the draught, we may use a movable cowl, whose action and principle may be illustrated by Fig. 14, in which we have a tube like Fig. 13 surmounted by a cowl, movable round the centre of the tube A B by the action of the wind itself, which is assisted by the vane E. When the wind is in the adverse direction B C, the cowl A D opposes and balances the effect of the wind on the lower branch, and if both are equally exposed to its action, the one would simply neutralize the other, and there would be no internal current in either direction, but if, as is usually the case in practice, B C is sheltered by adjacent buildings, &c., and A D is fully exposed, the cowl will always be the controlling power, creating in all 214 FORCE OF WIND AND EFFECT ON VENTILATION, cases an upward current, irrespective of tlie action of heat on the internal air, and the adverse action of the wind is not only annulled, but reversed and made to augment the draught. Table 89. — Of the Force and Velocity of Wind, according to Hutton’s Experiments. Pressure. Velocity. Character of the Wind according to Itouse and Lind. In lbs. per square Foot. In Inches of Water. In Feet per Second. In Miles per Hour. •1 •01926 7-87 5-37 Gentle Wind. •25 •0481 12-90 8-79 Pleasant ditto. •5 •0963 16-18 11-03 Fresh Breeze. 1 •193 24-33 16-60 Brisk Gale. 2 •385 34-17 23-30 Very brisk ditto. 3 •578 41-69 27-77 4 •770 48-00 32-73 5 •963 53-55 36-51 High Wind. 6 1-155 58-55 39-92 7 1-348 63-15 43-06 8 1-541 67-43 45-97 9 1-733 71-43 48-70 Very high ditto. 10 1-926 75-22 51-28 11 2-118 78-82 53-74 12 2-311 82-20 56-07 13 2-504 85-54 58-32 14 2-696 88-70 60-48 Storm or Tempest. 15 2-889 91-76 62-56 16 3-081 94-70 64-57 17 3-274 97-56 66-52 18 3-467 100-30 68-41 19 3-659 103-00 70-25 20 3-852 105-70 72-03 Great Storm. 25 4-815 117-80 80-36 30 5-778 128-9 87-97 Hurricane. 35 6-741 139-0 94-77 40 7-704 148-7 101-4 Very great ditto. 45 8-667 157-2 107-2 50 9-630 165-6 112-9 Most violent ditto. 55 10-593 177-5 118-3 60 11-556 181-0 123-4 (387.) The effect of the vane E may be greatly augmented by making it with double blades, as in Fig. 99 ; the experiments of Hutton show that the force of wind acting obliquely on a plane, is given by the rule (Sine and he gives a table calculated by that rule, from which we obtain with a single FORCE OF WIND AND EFFECT ON VENTILATION. 215 blade, tlie forces *003, 006, &c., &c., as per Table 90, tbe force at a right angle or 90° being 1*0. It has been found by the numbers in this Table, that the best angle for the blades is 38° with the axis, or 76° with each other, as in Fig. 100. To show the superior efficacy of a double-bladed vane, say that the wind was at an angle of 1 ° with the axis, then with a vane having blades at the best angle instead of impinging on both blades at 38°, we should evidently have it at 37° on one, and 39° on the other, and by Hutton’s Table the forces with these angles would be *507 and *555, and the force tending to turn the vane *555 — • 607 = * 048 instead of * 003, as with a single blade of the same area, or •048 •003 16 times greater. Table 90 .— Of the Eelative Power of Wind- vanes, with Single and Double Blades. Angle of Wind'with the Axis. 1° 2° 3° 40 5° 10° 20° 30° Ratio of the Turning Force. Single Blade Double Blades, 1 angle 38° withi axis . . . . ) Katio of effect, j single blade be- > ingl .. •003 •048 16 •006 •095; 15-8 •010 •141 14-1 •014 •185 13-2 •018 •228 12-7 •046 •431 9-4 •156 •739 4.7 •347 •910 2-6 • (388.) Table 90 shows that the superiority of the double blade over the single is greatest at small angles, where in fact it is most wanted. Such a vane would not only be more sensitive but also more steady, or less subject to oscillation. Angles greater or less than 38° are not so effective, the turning power at 15° would be about i, and at 5° about ^th of that at 38°. (389.) “ Maximum Force of the TFmd.” — In this country, the force of the wind seldom exceeds 50 lbs. per square foot even in our great storms ; it has been known, however, occasionally to exceed that amount. In the great hurricane of January, 1868, the anemometer at Birmingham, which was graduated up to 60 lbs., had its pencil driven far beyond that pressure, the maximum force was estimated at 70 or 80 lbs. per square foot. 216 FORCE OF WIND IN OVERTURNING BUILDINGS, &C. (390.) Wc will calculate the force of the wind capable of overturning the chimney 80 feet high, shown hy Fig. 44. There are two forces which resist the wind, namely, tlie weight of the whole chimney and the cohesion of the mortar. The chimney contains 1747 cubic feet of brickwork, which weighs hy Table 46 115 lbs. per foot, giving a total weight of 200000 lbs. The cohesion of good old mortar (14 years old) is 60 lbs. i)er square inch, and the area of the section of base being 81^ — 36^ = 5265, the resistance of the cohesion of the mortar will be 5265 x 60 = 315900 lbs., which added to the weight of the chimney makes a total of 200000 + 315900 = 515900 lbs. If the materials were incapable of crushing, the chimney would turn on that edge of its base remote from the wind, but in truth that point would bo somewhere between the centre and the edge, and the chimney would resist fracture, partly by the crushing strain and partly by the cohesion assisted by the weight. By analogy with other materials broken transversely, we know that the result is very nearly the same as if the neutral axis coincided with the edge, and the force of cohesion only came into play. Admitting this, the force of 515900 lbs. acts with a leverage equal to half the diameter of the base, or 40*5 inches. The centre of effort of the wind is at the centre of gravity of the surface exposed to it ; the easiest way of finding the centre of gravity in our case, is by cutting out an outline of the chimney in drawing paper, &c., of equable thickness, and balancing it on the point of a needle. We thus find the centre of effort in our case to be 36 feet, or 432 inches above the base, and the surface area of one side of the chimney being 440 square feet, the force of the wind that would overturn it would be 515900 X 40-5 432 X 410 110 lbs. per square foot, which as we have seen is greater than any wind in this country. With very bad mortar, the force would be much less, for instance, without mortar altogether, the force of the wind would be 200000 X 40;^5 '' 432 ^ 440 ^ = 42*6 lbs. per square foot. LONDON : nciNTED HY W. CLOWKS & SONS, STAMI'OUD STillCET AND ClIAUING CROSS. PLATE 1 E & F N Sjion, 48, Char ing Gross, Loncli PIATK 2. £ &: ? 1^1 . Spoil, 4-8, Qia.rin^ Cross,Lonclon Pl.ATK 3, PMT}; 4 Z.6 i'n- irf) c^nd ^tO K P. S^.f. PiMii Fig. 38. Zl Hovsa- Pomj- ZZ.O irufidt -. > 1^ ''9i , 2 3 . .. F i g. 3.8. ZO Horse Power J , .Z G-. -, /4 Horsey Power V ' V ^ 'ci r — '8 i : /' Low Moor s 1 . 9 ' ^ Z.d x 5 ". H ^ ^ ^ ^ ^ IS . 0 insioU. ' f ^ “i.e J Fig. 4 - 1 . W Horse Power ^ 6 - ^ - -- /] .CVS Moor t 3 , 0 " * 3 , 4 . _yi— <- - 75.(7 inside ^ Fig. 4 r 2 IZ.O ills L tor 4 U.P. Sety PI(Aie J AVw bo y .t 4lea/7/iPr hrii ■iS/nstlp.'> ‘ffo/id E Si F N . Spon^ 48 , Charing Crost,, London so /«€/■ PLATT. 5 PI-ATi: 6 E &. F N Spoil, 48. Charing, Cro.st;. London PIATE 7 t- PLATE 8. pi.atf: 9, Pi g. 80 . 81 , l i 82 , Interna, i Air T= GO r-T — - External Air T^30’ External A O' 7=30“ t3S’d Air T‘G0" t Air T=30 t’OS'O NmO) y&Ale/niiuiu: lijlij'l' ./■^lU'.S^mbor:^ r. Sc V M Spon, 48, Qiai'lng Cross, Loniion, Fig. 87. F i g. 08 . Fi^. 90. E &. F "N . Spoil, 48, Cha.rinA CrosS; London. . ' plate; .11 Z &. F.N. Spon, 48, Qidiinfe G-oss, London. i^IATZ 12 CROSS SECTION. PLATE 14.. 4^zrv \ ;i V I i- 113. 40 yar(L>>\ - F i 1M-. c A s -h £ » — ♦ E s 70 10 10 ScaZe. Irvchy = 1 Foot. Pi 10 9. PLAN. 3C . CZ]« E it F N Spon, 4-8, Charing G-oss, London / S' ii UNIVERSITY OF ILLINOI8-URBANA 3 0112 067649993