TABLE 64

RADIATION FROM COVERED AND UNCOVERED STEAM PIPES

CALCULATED FOR 160 POUNDS PRESSURE AND 60 DEGREES TEMPERATURE

+ -+ + + -+ + + + -+ -+ -+ Pipe 1/2 3/4 1 1-1/4 1-1/2 Inches Thickness of Covering inch inch inch inch inch Bare + + -+ + + + -+ -+ -+ B. t. u. per lineal foot per hour 149 118 99 86 79 597 B. t. u. per square foot per hour 240 190 161 138 127 959 2 B. t. u. per square foot per hour per one degree difference in temperature .770 .613 .519 .445 .410 3.198 + + -+ + + + -+ -+ -+ B. t. u. per lineal foot per hour 247 193 160 139 123 1085 B. t. u. per square foot per hour 210 164 136 118 104 921 4 B. t. u. per square foot per hour per one degree difference in temperature .677 .592 .439 .381 .335 2.970 + + -+ + + + -+ -+ -+ B. t. u. per lineal foot per hour 352 269 221 190 167 1555 B. t. u. per square foot per hour 203 155 127 110 96 897 6 B. t. u. per square foot per hour per one degree difference in temperature .655 .500 .410 .355 .310 2.89 + + -+ + + + -+ -+ -+ B. t. u. per lineal foot per hour 443 337 276 235 207 1994 B. t. u. per square foot per hour 196 149 122 104 92 883 8 B. t. u. per square foot per hour per one degree difference in temperature .632 .481 .394 .335 .297 2.85 + + -+ + + + -+ -+ -+ B. t. u. per lineal foot per hour 549 416 337 287 250 2468 B. t. u. per square foot per hour 195 148 120 102 89 877 10 B. t. u. per square foot per hour per one degree difference in temperature .629 .477 .387 .329 .287 2.83 + + -+ + + + -+ -+ -+ + -+

Covering—Magnesia, canvas covered.

For calculating radiation for pressure and temperature other than 160 pounds, and 60 degrees, use B. t. u. figures for one degree difference.

Radiation from Pipes—The evils of the presence of condensed steam in piping systems have been thoroughly discussed above and in some of the previous articles. Condensation resulting from radiation, while it cannot be wholly obviated, can, by proper installation, be greatly reduced.

Bare pipe will radiate approximately 3 B. t. u. per hour per square foot of exposed surface per one degree of difference in temperature between the steam contained and the external air. This figure may be reduced to from 0.3 to 0.4 B. t. u. for the same conditions by a 1-1/2 inch insulating covering. Table 64 gives the radiation losses for bare and covered pipes with different thicknesses of magnesia covering.

Many experiments have been made as to the relative efficiencies of different kinds of covering. Table 65 gives some approximately relative figures based on one inch covering from experiments by Paulding, Jacobus, Brill and others.

TABLE 65

APPROXIMATE EFFICIENCIES OF VARIOUS COVERINGS REFERRED TO BARE PIPES + + + -+ + Covering Efficiency + -+ + Asbestocel 76.8 Gast's Air Cell 74.4 Asbesto Sponge Felt 85.0 Magnesia 83.5 Asbestos Navy Brand 82.0 Asbesto Sponge Hair 86.0 Asbestos Fire Felt 73.5 + -+ + + +

Based on one-inch covering.

The following suggestions may be of service:

Exposed radiating surfaces of all pipes, all high pressure steam flanges, valve bodies and fittings, heaters and separators, should be covered with non-conducting material wherever such covering will improve plant economy. All main steam lines, engine and boiler branches, should be covered with 2 inches of 85 per cent carbonate of magnesia or the equivalent. Other lines may be covered with one inch of the same material. All covering should be sectional in form and large surfaces should be covered with blocks, except where such material would be difficult to install, in which case plastic material should be used. In the case of flanges the covering should be tapered back from the flange in order that the bolts may be removed.

All surfaces should be painted before the covering is applied. Canvas is ordinarily placed over the covering, held in place by wrought-iron or brass bands.

Expansion and Support of Pipe—It is highly important that the piping be so run that there will be no undue strains through the action of expansion. Certain points are usually securely anchored and the expansion of the piping at other points taken care of by providing supports along which the piping will slide or by means of flexible hangers. Where pipe is supported or anchored, it should be from the building structure and not from boilers or prime movers. Where supports are furnished, they should in general be of any of the numerous sliding supports that are available. Expansion is taken care of by such a method of support and by the providing of large radius bends where necessary.

It was formerly believed that piping would actually expand under steam temperatures about one-half the theoretical amount due to the fact that the exterior of the pipe would not reach the full temperature of the steam contained. It would appear, however from recent experiments that such actual expansion will in the case of well-covered pipe be very nearly the theoretical amount. In one case noted, a steam header 293 feet long when heated under a working pressure of 190 pounds, the steam superheated approximately 125 degrees, expanded 8-3/4 inches; the theoretical amount of expansion under the conditions would be approximately 9-35/64 inches.



FLOW OF STEAM THROUGH PIPES AND ORIFICES

Various formulae for the flow of steam through pipes have been advanced, all having their basis upon Bernoulli's theorem of the flow of water through circular pipes with the proper modifications made for the variation in constants between steam and water. The loss of energy due to friction in a pipe is given by Unwin (based upon Weisbach) as

f 2 v*v W L E_{f} = —————- (37) gd

where E is the energy loss in foot pounds due to the friction of W units of weight of steam passing with a velocity of v feet per second through a pipe d feet in diameter and L feet long; g represents the acceleration due to gravity (32.2) and f the coefficient of friction.

Numerous values have been given for this coefficient of friction, f, which, from experiment, apparently varies with both the diameter of pipe and the velocity of the passing steam. There is no authentic data on the rate of this variation with velocity and, as in all experiments, the effect of change of velocity has seemed less than the unavoidable errors of observation, the coefficient is assumed to vary only with the size of the pipe.

Unwin established a relation for this coefficient for steam at a velocity of 100 feet per second,

/ 3 f = K 1 + - (38) 10d /

where K is a constant experimentally determined, and d the internal diameter of the pipe in feet.

If h represents the loss of head in feet, then

f 2 v*v W L E_{f} = Wh = —————- (39) gd

f 2 v*v L and h = ————- (40) gd

If D represents the density of the steam or weight per cubic foot, and p the loss of pressure due to friction in pounds per square inch, then

hD p = —- (41) 144

and from equations (38), (40) and (41),

D v*v L / 3 p = - x K 1 + - (42) 72 g d 10d /

To convert the velocity term and to reduce to units ordinarily used, let d_{1} the diameter of pipe in inches = 12d, and w = the flow in pounds per minute; then

[pi] / d_{1} w = 60v x - ^{2} D 4 12 /

9.6 w and v = ——————— [pi] d_{1}^2 D

Substituting this value and that of d in formula (42)

/ 3.6 w^{2} L p = 0.04839 K 1 + - - (43) d{1} / D d{1}^{5}

Some of the experimental determinations for the value of K are: K = .005 for water (Unwin). K = .005 for air (Arson). K = .0028 for air (St. Gothard tunnel experiments). K = .0026 for steam (Carpenter at Oriskany). K = .0027 for steam (G. H. Babcock).

The value .0027 is apparently the most nearly correct, and substituting in formula (43) gives,

/ 3.6 w^{2} L p = 0.000131 1 + - (44) d{1}/ D d{1}^{5}

/ pDd{1}^{5} w = 87 ^{.5} (45) / 3.6 1 + L d{1}/ /

Where w = the weight of steam passing in pounds per minute, p = the difference in pressure between the two ends of the pipe in pounds per square inch, D = density of steam or weight per cubic foot,[80] d_{1} = internal diameter of pipe in inches, L = length of pipe in feet.

TABLE 66

FLOW OF STEAM THROUGH PIPES + -+ Initl Diameter[81] of Pipe in Inches, Length of Pipe = 240 Diameters Gauge -+ Press .75 1 1.5 2 2.5 3 4 5 6 8 10 12 15 18 Pound -+ /SqIn Weight of Steam per Minute, in Pounds, With One Pound Loss of Pressure + -+ -+ 1 1.16 2.07 5.7 10.27 15.45 25.38 46.85 77.3 115.9 211.4 341.1 502.4 804 1177 10 1.44 2.57 7.1 12.72 19.15 31.45 58.05 95.8 143.6 262.0 422.7 622.5 996 1458 20 1.70 3.02 8.3 14.94 22.49 36.94 68.20 112.6 168.7 307.8 496.5 731.3 1170 1713 30 1.91 3.40 9.4 16.84 25.35 41.63 76.84 126.9 190.1 346.8 559.5 824.1 1318 1930 40 2.10 3.74 10.3 18.51 27.87 45.77 84.49 139.5 209.0 381.3 615.3 906.0 1450 2122 50 2.27 4.04 11.2 20.01 30.13 49.48 91.34 150.8 226.0 412.2 665.0 979.5 1567 2294 60 2.43 4.32 11.9 21.38 32.19 52.87 97.60 161.1 241.5 440.5 710.6 1046.7 1675 2451 70 2.57 4.58 12.6 22.65 34.10 56.00 103.37 170.7 255.8 466.5 752.7 1108.5 1774 2596 80 2.71 4.82 13.3 23.82 35.87 58.91 108.74 179.5 269.0 490.7 791.7 1166.1 1866 2731 90 2.83 5.04 13.9 24.92 37.52 61.62 113.74 187.8 281.4 513.3 828.1 1219.8 1951 2856 100 2.95 5.25 14.5 25.96 39.07 64.18 118.47 195.6 293.1 534.6 862.6 1270.1 2032 2975 120 3.16 5.63 15.5 27.85 41.93 68.87 127.12 209.9 314.5 573.7 925.6 1363.3 2181 3193 150 3.45 6.14 17.0 30.37 45.72 75.09 138.61 228.8 343.0 625.5 1009.2 1486.5 2378 3481 + -+

This formula is the most generally accepted for the flow of steam in pipes. Table 66 is calculated from this formula and gives the amount of steam passing per minute that will flow through straight smooth pipes having a length of 240 diameters from various initial pressures with one pound difference between the initial and final pressures.

To apply this table for other lengths of pipe and pressure losses other than those assumed, let L = the length and d the diameter of the pipe, both in inches; l, the loss in pounds; Q, the weight under the conditions assumed in the table, and Q_{1}, the weight for the changed conditions.

For any length of pipe, if the weight of steam passing is the same as given in the table, the loss will be,

L l = —— (46) 240d

If the pipe length is the same as assumed in the table but the loss is different, the quantity of steam passing per minute will be,

Q_{1} = Ql^{.5} (47)

For any assumed pipe length and loss of pressure, the weight will be,

/240dl Q_{1} = Q - ^{.5} (48) L /

TABLE 67

FLOW OF STEAM THROUGH PIPES LENGTH OF PIPE 1000 FEET

+ Discharge in Pounds per Minute corresponding to Drop in Pressure in Drop in Pressure on Right for Pipe Diameters Pounds per Square Inch corresponding in Inches in Top Line to Discharge on Left: Densities and corresponding Absolute Pressures per Square Inch in First Two Lines + Diameter[82] Discharge Density Pressure Drop + 12 10 8 6 4 3 2.5 2 1.5 1 .208 .230 .284 .328 .401 .443 .506 .548 In In In In In In In In In In 90 100 125 150 180 200 230 250 + - + 2328 1443 799 371 123. 55.9 28.8 18.1 6.81 2.52 18.10 16.4 13.3 11.1 9.39 8.50 7.44 6.87 2165 1341 742 344 114.6 51.9 27.6 16.8 6.52 2.34 15.60 14.1 11.4 9.60 8.09 7.33 6.41 5.92 1996 1237 685 318 106.0 47.9 26.4 15.5 6.24 2.16 13.3 12.0 9.74 8.18 6.90 6.24 5.47 5.05 1830 1134 628 292 97.0 43.9 25.2 14.2 5.95 1.98 11.1 10.0 8.13 6.83 5.76 5.21 4.56 4.21 1663 1031 571 265 88.2 39.9 24.0 12.9 5.67 1.80 9.25 8.36 6.78 5.69 4.80 4.34 3.80 3.51 1580 979 542 252 83.8 37.9 22.8 12.3 5.29 1.71 8.33 7.53 6.10 5.13 4.32 3.91 3.42 3.16 1497 928 514 239 79.4 35.9 21.6 11.6 5.00 1.62 7.48 6.76 5.48 4.60 3.88 3.51 3.07 2.84 1414 876 485 226 75.0 33.9 20.4 10.9 4.72 1.53 6.67 6.03 4.88 4.10 3.46 3.13 2.74 2.53 1331 825 457 212 70.6 31.9 19.2 10.3 4.43 1.44 5.91 5.35 4.33 3.64 3.07 2.78 2.43 2.24 1248 873 428 199 66.2 23.9 18.0 9.68 4.15 1.35 5.19 4.69 3.80 3.19 2.69 2.44 2.13 1.97 1164 722 400 186 61.7 27.9 16.8 9.03 3.86 1.26 4.52 4.09 3.31 2.78 2.34 2.12 1.86 1.72 1081 670 371 172 57.3 25.9 15.6 8.38 3.68 1.17 3.90 3.53 2.86 2.40 2.02 1.83 1.60 1.48 998 619 343 159 52.9 23.9 14.4 7.74 3.40 1.08 3.32 3.00 2.43 2.04 1.72 1.56 1.36 1.26 915 567 314 146 48.5 21.9 13.2 7.10 3.11 0.99 2.79 2.52 2.04 1.72 1.45 1.31 1.15 1.06 832 516 286 132 44.1 20.0 12.0 6.45 2.83 0.90 2.31 2.09 1.69 1.42 1.20 1.08 .949 .877 748 464 257 119 39.7 18.0 10.8 5.81 2.55 0.81 1.87 1.69 1.37 1.15 .97 .878 .769 .710 665 412 228 106 35.3 16.0 9.6 5.16 2.26 0.72 1.47 1.33 1.08 .905 .762 .690 .604 .558 582 361 200 92.8 30.9 14.0 8.4 4.52 1.98 0.63 1.13 1.02 .828 .695 .586 .531 .456 .429 +

To get the pressure drop for lengths other than 1000 feet, multiply by lengths in feet / 1000.

Example: Find the weight of steam at 100 pounds initial gauge pressure, which will pass through a 6-inch pipe 720 feet long with a pressure drop of 4 pounds. Under the conditions assumed in the table, 293.1 pounds would flow per minute; hence, Q = 293.1, and

_ _ 240x6x4 Q_{1} = 293.1 - ^{.5} = 239.9 pounds _ 720x12_

Table 67 may be frequently found to be of service in problems involving the flow of steam. This table was calculated by Mr. E. C. Sickles for a pipe 1000 feet long from formula (45), except that from the use of a value of the constant K = .0026 instead of .0027, the constant in the formula becomes 87.45 instead of 87.

In using this table, the pressures and densities to be considered, as given at the top of the right-hand portion, are the mean of the initial and final pressures and densities. Its use is as follows: Assume an allowable drop of pressure through a given length of pipe. From the value as found in the right-hand column under the column of mean pressure, as determined by the initial and final pressures, pass to the left-hand portion of the table along the same line until the quantity is found corresponding to the flow required. The size of the pipe at the head of this column is that which will carry the required amount of steam with the assumed pressure drop.

The table may be used conversely to determine the pressure drop through a pipe of a given diameter delivering a specified amount of steam by passing from the known figure in the left to the column on the right headed by the pressure which is the mean of the initial and final pressures corresponding to the drop found and the actual initial pressure present.

For a given flow of steam and diameter of pipe, the drop in pressure is proportional to the length and if discharge quantities for other lengths of pipe than 1000 feet are required, they may be found by proportion.

TABLE 68

FLOW OF STEAM INTO THE ATMOSPHERE ___________ Absolute Velocity Actual Discharge Horse Power Initial of Outflow Velocity per Square per Square Pressure at Constant of Outflow Inch of Inch of per Square Density Expanded Orifice Orifice if Inch Feet per Feet per per Minute Horse Power Pounds Second Second Pounds = 30 Pounds per Hour __ ___ __ __ ___ 25.37 863 1401 22.81 45.6 30. 867 1408 26.84 53.7 40. 874 1419 35.18 70.4 50. 880 1429 44.06 88.1 60. 885 1437 52.59 105.2 70. 889 1444 61.07 122.1 75. 891 1447 65.30 130.6 90. 895 1454 77.94 155.9 100. 898 1459 86.34 172.7 115. 902 1466 98.76 197.5 135. 906 1472 115.61 231.2 155. 910 1478 132.21 264.4 165. 912 1481 140.46 280.9 215. 919 1493 181.58 363.2 __ ___ __ __ ___

Elbows, globe valves and a square-ended entrance to pipes all offer resistance to the passage of steam. It is customary to measure the resistance offered by such construction in terms of the diameter of the pipe. Many formulae have been advanced for computing the length of pipe in diameters equivalent to such fittings or valves which offer resistance. These formulae, however vary widely and for ordinary purposes it will be sufficiently accurate to allow for resistance at the entrance of a pipe a length equal to 60 times the diameter; for a right angle elbow, a length equal to 40 diameters, and for a globe valve a length equal to 60 diameters.

The flow of steam of a higher toward a lower pressure increases as the difference in pressure increases to a point where the external pressure becomes 58 per cent of the absolute initial pressure. Below this point the flow is neither increased nor decreased by a reduction of the external pressure, even to the extent of a perfect vacuum. The lowest pressure for which this statement holds when steam is discharged into the atmosphere is 25.37 pounds. For any pressure below this figure, the atmospheric pressure, 14.7 pounds, is greater than 58 per cent of the initial pressure. Table 68, by D. K. Clark, gives the velocity of outflow at constant density, the actual velocity of outflow expanded (the atmospheric pressure being taken as 14.7 pounds absolute, and the ratio of expansion in the nozzle being 1.624), and the corresponding discharge per square inch of orifice per minute.

Napier deduced an approximate formula for the outflow of steam into the atmosphere which checks closely with the figures just given. This formula is:

pa W = —— (49) 70

Where W = the pounds of steam flowing per second, p = the absolute pressure in pounds per square inch, and a = the area of the orifice in square inches.

In some experiments made by Professor C. H. Peabody, in the flow of steam through pipes from 1/4 inch to 1-1/2 inches long and 1/4 inch in diameter, with rounded entrances, the greatest difference from Napier's formula was 3.2 per cent excess of the experimental over the calculated results.

For steam flowing through an orifice from a higher to a lower pressure where the lower pressure is greater than 58 per cent of the higher, the flow per minute may be calculated from the formula:

W = 1.9AK ((P - d)d)^{.5} (50)

Where W = the weight of steam discharged in pounds per minute, A = area of orifice in square inches, P = the absolute initial pressure in pounds per square inch, d = the difference in pressure between the two sides in pounds per square inch, K = a constant = .93 for a short pipe, and .63 for a hole in a thin plate or a safety valve.



HEAT TRANSFER

The rate at which heat is transmitted from a hot gas to a cooler metal surface over which the gas is flowing has been the subject of a great deal of investigation both from the experimental and theoretical side. A more or less complete explanation of this process is necessary for a detailed analysis of the performance of steam boilers. Such information at the present is almost entirely lacking and for this reason a boiler, as a physical piece of apparatus, is not as well understood as it might be. This, however, has had little effect in its practical development and it is hardly possible that a more complete understanding of the phenomena discussed will have any radical effect on the present design.

The amount of heat that is transferred across any surface is usually expressed as a product, of which one factor is the slope or linear rate of change in temperature and the other is the amount of heat transferred per unit's difference in temperature in unit's length. In Fourier's analytical theory of the conduction of heat, this second factor is taken as a constant and is called the "conductivity" of the substance. Following this practice, the amount of heat absorbed by any surface from a hot gas is usually expressed as a product of the difference in temperature between the gas and the absorbing surface into a factor which is commonly designated the "transfer rate". There has been considerable looseness in the writings of even the best authors as to the way in which the gas temperature difference is to be measured. If the gas varies in temperature across the section of the channel through which it is assumed to flow, and most of them seem to consider that this would be the case, there are two mean gas temperatures, one the mean of the actual temperatures at any time across the section, and the other the mean temperature of the entire volume of the gas passing such a section in any given time. Since the velocity of flow will of a certainty vary across the section, this second mean temperature, which is one tacitly assumed in most instances, may vary materially from the first. The two mean temperatures are only approximately equal when the actual temperature measured across the section is very nearly a constant. In what follows it will be assumed that the mean temperature measured in the second way is referred to. In English units the temperature difference is expressed in Fahrenheit degrees and the transfer rate in B. t. u.'s per hour per square foot of surface. Pecla, who seems to have been one of the first to consider this subject analytically, assumed that the transfer rate was constant and independent both of the temperature differences and the velocity of the gas over the surface. Rankine, on the other hand, assumed that the transfer rate, while independent of the velocity of the gas, was proportional to the temperature difference, and expressed the total amount of heat absorbed as proportional to the square of the difference in temperature. Neither of these assumptions has any warrant in either theory or experiment and they are only valuable in so far as their use determine formulae that fit experimental results. Of the two, Rankine's assumption seems to lead to formulae that more nearly represent actual conditions. It has been quite fully developed by William Kent in his "Steam Boiler Economy". Professor Osborne Reynolds, in a short paper reprinted in Volume I of his "Scientific Papers", suggests that the transfer rate is proportional to the product of the density and velocity of the gas and it is to be assumed that he had in mind the mean velocity, density and temperature over the section of the channel through which the gas was assumed to flow. Contrary to prevalent opinion, Professor Reynolds gave neither a valid experimental nor a theoretical explanation of his formula and the attempts that have been made since its first publication to establish it on any theoretical basis can hardly be considered of scientific value. Nevertheless, Reynolds' suggestion was really the starting point of the scientific investigation of this subject and while his formula cannot in any sense be held as completely expressing the facts, it is undoubtedly correct to a first approximation for small temperature differences if the additive constant, which in his paper he assumed as negligible, is given a value.[83]

Experimental determinations have been made during the last few years of the heat transfer rate in cylindrical tubes at comparatively low temperatures and small temperature differences. The results at different velocities have been plotted and an empirical formula determined expressing the transfer rate with the velocity as a factor. The exponent of the power of the velocity appearing in the formula, according to Reynolds, would be unity. The most probable value, however, deduced from most of the experiments makes it less than unity. After considering experiments of his own, as well as experiments of others, Dr. Wilhelm Nusselt[84] concludes that the evidence supports the following formulae:

[lambda]{w} w c{p} [delta] a = b - ^{u} d^{1-u} [lambda]

Where a is the transfer rate in calories per hour per square meter of surface per degree centigrade difference in temperature, u is a physical constant equal to .786 from Dr. Nusselt's experiments, b is a constant which, for the units given below, is 15.90, w is the mean velocity of the gas in meters per second, c{p} is the specific heat of the gas at its mean temperature and pressure in calories per kilogram, [delta] is the density in kilograms per cubic meter, [lambda] is the conductivity at the mean temperature and pressure in calories per hour per square meter per degree centigrade temperature drop per meter, [lambda]{w} is the conductivity of the steam at the temperature of the tube wall, d is the diameter of the tube in meters.

If the unit of time for the velocity is made the hour, and in the place of the product of the velocity and density is written its equivalent, the weight of gas flowing per hour divided by the area of the tube, this equation becomes:

[lambda]{w} Wc{p} a = .0255 - ^{.786} d^{.214} A[lambda]

where the quantities are in the units mentioned, or, since the constants are absolute constants, in English units,

a is the transfer rate in B. t. u. per hour per square foot of surface per degree difference in temperature, W is the weight in pounds of the gas flowing through the tube per hour, A is the area of the tube in square feet, d is the diameter of the tube in feet, c{p} is the specific heat of the gas at constant pressure, [lambda] is the conductivity of the gas at the mean temperature and pressure in B. t. u. per hour per square foot of surface per degree Fahrenheit drop in temperature per foot, [lambda]{w} is the conductivity of the steam at the temperature of the wall of the tube.

The conductivities of air, carbonic acid gas and superheated steam, as affected by the temperature, in English units, are:

Conductivity of air .0122 (1 + .00132 T) Conductivity of carbonic acid gas .0076 (1 + .00229 T) Conductivity of superheated steam .0119 (1 + .00261 T)

where T is the temperature in degrees Fahrenheit.

Nusselt's formulae can be taken as typical of the number of other formulae proposed by German, French and English writers.[85] Physical properties, in addition to the density, are introduced in the form of coefficients from a consideration of the physical dimensions of the various units and of the theoretical formulae that are supposed to govern the flow of the gas and the transfer of heat. All assume that the correct method of representing the heat transfer rate is by the use of one term, which seems to be unwarranted and probably has been adopted on account of the convenience in working up the results by plotting them logarithmically. This was the method Professor Reynolds used in determining his equation for the loss in head in fluids flowing through cylindrical pipes and it is now known that the derived equation cannot be considered as anything more than an empirical formula. It, therefore, is well for anyone considering this subject to understand at the outset that the formulae discussed are only of an empirical nature and applicable to limited ranges of temperature under the conditions approximately the same as those surrounding the experiments from which the constants of the formula were determined.

It is not probable that the subject of heat transfer in boilers will ever be on any other than an experimental basis until the mathematical expression connecting the quantity of fluid which will flow through a channel of any section under a given head has been found and some explanation of its derivation obtained. Taking the simplest possible section, namely, a circle, it is found that at low velocities the loss of head is directly proportional to the velocity and the fluid flows in straight stream lines or the motion is direct. This motion is in exact accordance with the theoretical equations of the motion of a viscous fluid and constitutes almost a direct proof that the fundamental assumptions on which these equations are based are correct. When, however, the velocity exceeds a value which is determinable for any size of tube, the direct or stream line motion breaks down and is replaced by an eddy or mixing flow. In this flow the head loss by friction is approximately, although not exactly, proportional to the square of the velocity. No explanation of this has ever been found in spite of the fact that the subject has been treated by the best mathematicians and physicists for years back. It is to be assumed that the heat transferred during the mixing flow would be at a much higher rate than with the direct or stream line flow, and Professors Croker and Clement[86] have demonstrated that this is true, the increase in the transfer being so marked as to enable them to determine the point of critical velocity from observing the rise in temperature of water flowing through a tube surrounded by a steam jacket.

The formulae given apply only to a mixing flow and inasmuch as, from what has just been stated, this form of motion does not exist from zero velocity upward, it follows that any expression for the heat transfer rate that would make its value zero when the velocity is zero, can hardly be correct. Below the critical velocity, the transfer rate seems to be little affected by change in velocity and Nusselt,[87] in another paper which mathematically treats the direct or stream line flow, concludes that, while it is approximately constant as far as the velocity is concerned in a straight cylindrical tube, it would vary from point to point of the tube, growing less as the surface passed over increased.

It should further be noted that no account in any of this experimental work has been taken of radiation of heat from the gas. Since the common gases absorb very little radiant heat at ordinary temperatures, it has been assumed that they radiate very little at any temperature. This may or may not be true, but certainly a visible flame must radiate as well as absorb heat. However this radiation may occur, since it would be a volume phenomenon rather than a surface phenomenon it would be considered somewhat differently from ordinary radiation. It might apply as increasing the conductivity of the gas which, however independent of radiation, is known to increase with the temperature. It is, therefore, to be expected that at high temperatures the rate of transfer will be greater than at low temperatures. The experimental determinations of transfer rates at high temperatures are lacking.

Although comparatively nothing is known concerning the heat radiation from gases at high temperatures, there is no question but what a large proportion of the heat absorbed by a boiler is received direct as radiation from the furnace. Experiments show that the lower row of tubes of a Babcock & Wilcox boiler absorb heat at an average rate per square foot of surface between the first baffle and the front headers equivalent to the evaporation of from 50 to 75 pounds of water from and at 212 degrees Fahrenheit per hour. Inasmuch as in these experiments no separation could be made between the heat absorbed by the bottom of the tube and that absorbed by the top, the average includes both maximum and minimum rates for those particular tubes and it is fair to assume that the portion of the tubes actually exposed to the furnace radiations absorb heat at a higher rate. Part of this heat was, of course absorbed by actual contact between the hot gases and the boiler heating surface. A large portion of it, however, must have been due to radiation. Whether this radiant heat came from the fire surface and the brickwork and passed through the gases in the furnace with little or no absorption, or whether, on the other hand, the radiation were absorbed by the furnace gases and the heat received by the boiler was a secondary radiation from the gases themselves and at a rate corresponding to the actual gas temperature, is a question. If the radiations are direct, then the term "furnace temperature", as usually used has no scientific meaning, for obviously the temperature of the gas in the furnace would be entirely different from the radiation temperature, even were it possible to attach any significance to the term "radiation temperature", and it is not possible to do this unless the radiations are what are known as "full radiations" from a so-called "black body". If furnace radiation takes place in this manner, the indications of a pyrometer placed in a furnace are hard to interpret and such temperature measurements can be of little value. If the furnace gases absorb the radiations from the fire and from the brickwork of the side walls and in their turn radiate heat to the boiler surface, it is scientifically correct to assume that the actual or sensible temperature of the gas would be measured by a pyrometer and the amount of radiation could be calculated from this temperature by Stefan's law, which is to the effect that the rate of radiation is proportional to the fourth power of the absolute temperature, using the constant with the resulting formula that has been determined from direct experiment and other phenomena. With this understanding of the matter, the radiations absorbed by a boiler can be taken as equal to that absorbed by a flat surface, covering the portion of the boiler tubes exposed to the furnace and at the temperature of the tube surface, when completely exposed on one side to the radiations from an atmosphere at the temperature in the furnace. With this assumption, if S^{1} is the area of the surface, T the absolute temperature of the furnace gases, t the absolute temperature of the tube surface of the boiler, the heat absorbed per hour measured in B. t. u.'s is equal to

/ T / t 1600 ^{4} - ^{4} S^{1} 1000/ 1000/

In using this formula, or in any work connected with heat transfer, the external temperature of the boiler heating surface can be taken as that of saturated steam at the pressure under which the boiler is working, with an almost negligible error, since experiments have shown that with a surface clean internally, the external surface is only a few degrees hotter than the water in contact with the inner surface, even at the highest rates of evaporation. Further than this, it is not conceivable that in a modern boiler there can be much difference in the temperature of the boiler in the different parts, or much difference between the temperature of the water and the temperature of the steam in the drums which is in contact with it.

If the total evaporation of a boiler measured in B. t. u.'s per hour is represented by E, the furnace temperature by T{1}, the temperature of the gas leaving the boiler by T{2}, the weight of gas leaving the furnace and passing through the setting per hour by W, the specific heat of the gas by C, it follows from the fact that the total amount of heat absorbed is equal to the heat received from radiation plus the heat removed from the gases by cooling from the temperature T{1} to the temperature T{2}, that

/ T / t E = 1600 ^{4} - ^{4} S^{1} + WC(T{1} - T{2}) 1000/ 1000/

This formula can be used for calculating the furnace temperature when E, t and T_{2} are known but it must be remembered that an assumption which is probably, in part at least, incorrect is implied in using it or in using any similar formula. Expressed in this way, however, it seems more rational than the one proposed a few years ago by Dr. Nicholson[88] where, in place of the surface exposed to radiation, he uses the grate surface and assumes the furnace gas temperature as equal to the fire temperature.

If the heat transfer rate is taken as independent of the gas temperature and the heat absorbed by an element of the surface in a given time is equated to the heat given out from the gas passing over this surface in the same time, a single integration gives

Rs (T - t) = (T_{1} - t) e^{- —} WC

where s is the area of surface passed over by the gases from the furnace to any point where the gas temperature T is measured, and the rate of heat transfer is R. As written, this formula could be used for calculating the temperature of the gas at any point in the boiler setting. Gas temperatures, however, calculated in this way are not to be depended upon as it is known that the transfer rate is not independent of the temperature. Again, if the transfer rate is assumed as varying directly with the weight of the gases passing, which is Reynolds' suggestion, it is seen that the weight of the gases entirely disappears from the formula and as a consequence if the formula was correct, as long as the temperature of the gas entering the surface from the furnace was the same, the temperatures throughout the setting would be the same. This is known also to be incorrect. If, however, in place of T is written T_{2} and in place of s is written S, the entire surface of the boiler, and the formula is re-arranged, it becomes:

WC T{1} - t R = - Log[89] - S T{2} - t

This formula can be considered as giving a way of calculating an average transfer rate. It has been used in this way for calculating the average transfer rate from boiler tests in which the capacity has varied from an evaporation of a little over 3 pounds per square foot of surface up to 15 pounds. When plotted against the gas weights, it was found that the points were almost exactly on a line. This line, however, did not pass through the zero point but started at a point corresponding to approximately a transfer rate of 2. Checked out against many other tests, the straight line law seems to hold generally and this is true even though material changes are made in the method of calculating the furnace temperature. The inclination of the line, however, varied inversely as the average area for the passage of the gas through the boiler. If A is the average area between all the passes of the boiler, the heat transfer rate in Babcock & Wilcox type boilers with ordinary clean surfaces can be determined to a rather close approximation from the formula:

W R = 2.00 + .0014 - A

The manner in which A appears in this formula is the same as it would appear in any formula in which the heat transfer rate was taken as depending upon the product of the velocity and the density of the gas jointly, since this product, as pointed out above, is equivalent to W/A. Nusselt's experiments, as well as those of others, indicate that the ratio appears in the proper way.

While the underlying principles from which the formula for this average transfer rate was determined are questionable and at best only approximately correct, it nevertheless follows that assuming the transfer rate as determined experimentally, the formula can be used in an inverse way for calculating the amount of surface required in a boiler for cooling the gases through a range of temperature covered by the experiments and it has been found that the results bear out this assumption. The practical application of the theory of heat transfer, as developed at present, seems consequently to rest on these last two formulae, which from their nature are more or less empirical.

Through the range in the production of steam met with in boilers now in service which in the marine type extends to the average evaporation of 12 to 15 pounds of water from and at 212 degrees Fahrenheit per square foot of surface, the constant 2 in the approximate formula for the average heat transfer rate constitutes quite a large proportion of the total. The comparative increase in the transfer rate due to a change in weight of the gases is not as great consequently as it would be if this constant were zero. For this reason, with the same temperature of the gases entering the boiler surface, there will be a gradual increase in the temperature of the gases leaving the surface as the velocity or weight of flow increases and the proportion of the heat contained in the gases entering the boiler which is absorbed by it is gradually reduced. It is, of course, possible that the weight of the gases could be increased to such an amount or the area for their passage through the boiler reduced by additional baffles until the constant term in the heat transfer formula would be relatively unimportant. Under such conditions, as pointed out previously, the final gas temperature would be unaffected by a further increase in the velocity of the flow and the fraction of the heat carried by the gases removed by the boiler would be constant. Actual tests of waste heat boilers in which the weight of gas per square foot of sectional area for its passage is many times more than in ordinary installations show, however, that this condition has not been attained and it will probably never be attained in any practical installation. It is for this reason that the conclusions of Dr. Nicholson in the paper referred to and of Messrs. Kreisinger and Ray in the pamphlet "The Transmission of Heat into Steam Boilers", published by the Department of the Interior in 1912, are not applicable without modification to boiler design.

In superheaters the heat transfer is effected in two different stages; the first transfer is from the hot gas to the metal of the superheater tube and the second transfer is from the metal of the tube to the steam on the inside. There is, theoretically, an intermediate stage in the transfer of the heat from the outside to the inside surface of the tube. The conductivity of steel is sufficient, however, to keep the temperatures of the two sides of the tube very nearly equal to each other so that the effect of the transfer in the tube itself can be neglected. The transfer from the hot gas to the metal of the tube takes place in the same way as with the boiler tubes proper, regard being paid to the temperature of the tube which increases as the steam is heated. The transfer from the inside surface of the tube to the steam is the inverse of the process of the transfer of the heat on the outside and seems to follow the same laws. The transfer rate, therefore, will increase with the velocity of the steam through the tube. For this reason, internal cores are quite often used in superheaters and actually result in an increase in the amount of superheat obtained from a given surface. The average transfer rate in superheaters based on a difference in mean temperature between the gas on the outside of the tubes and the steam on the inside of the tubes is if R is the transfer rate from the gas to the tube and r the rate from the tube to the steam:

Rr ——- R + r

and is always less than either R or r. This rate is usually greater than the average transfer rate for the boiler as computed in the way outlined in the preceding paragraphs. Since, however, steam cannot, under any imagined set of conditions, take up more heat from a tube than would water at the same average temperature, this fact supports the contention made that the actual transfer rate in a boiler must increase quite rapidly with the temperatures. The actual transfer rates in superheaters are affected by so many conditions that it has not so far been possible to evolve any formula of practical value.



INDEX

PAGE

Absolute pressure 117 Absolute zero 80 Accessibility of Babcock & Wilcox boiler 59 Acidity in boiler feed water 106 Actual evap. corresponding to boiler horse power 288 Advantages of Babcock & Wilcox boilers 61 Stoker firing 195 Water tube over fire tube boilers 61 Air, composition of 147 In boiler feed water 106 Properties of 147 Required for combustion 152, 156 Specific heat of 148 Supplied for combustion 157 Vapor in 149 Volume of 147 Weight of 147 Alkalinity in boiler feed water 103 Testing feed for 103 Altitude, boiling point of water at 97 Chimney sizes corrected for 248 Alum in feed water treatment 106 A. S. M. E. code for boiler testing 267 Analyses, comparison of proximate and ultimate 183 Proximate coal, and heating values 177 Analysis, coal, proximate, methods of 176 Coal, ultimate 173 Determination of heating value from 173 Analysis, Flue gas 155 Flue gas, methods of 160 Flue gas, object of 155 Anthracite coal 166 Combustion rates with 246 Distribution of 167 Draft required for 246 Firing 190 Grate ratio for 191 Semi 166 Sizes of 190 Steam as aid to burning 191 Thickness of fires with 191 Arches, fire brick, as aid to combustion 190 Fire brick, for 304 Fire brick, laying 305 Automatic stokers, advantages of 195 Overfeed 196 Traveling grate 197 Traveling grate, Babcock & Wilcox 194 Underfeed 196 Auxiliaries, exhaust from, in heating feed water 113 Superheated steam with 142 Auxiliary grates, with blast furnace gas 228 With oil fuel 225 With waste heat 235 Babcock, G. H., lecture on circulation of water in Boilers 28 Lecture on theory of steam making 92 Babcock & Wilcox Co., Works at Barberton, Ohio 7 Works at Bayonne, N. J. 6 Babcock & Wilcox boiler, accessibility of 59 Advantages of 61 Circulation of water in 57, 66 Construction of 49 Cross boxes 50 Cross drum 53 Cross drum, dry steam with 71 Drumheads 49 Drums 49 Durability 75 Evolution of 39 Fittings 55 Fixtures 55 Fronts 53 Handhole fittings 50, 51 Headers 50, 51 Inclined header, wrought steel 54 Inspection 75 Life of 76 Materials entering into the construction of 59 Mud drums 51 Path of gases in 57 Path of water in 57 Rear tube doors of 53, 74 Repairs 75 Safety of 66 Sections 50 Set for utilizing waste heat 236 Set with Babcock & Wilcox chain grate stoker 12 Set with bagasse furnace 208 Set with Peabody oil furnace 222 Supports, cross drum 53 Supports, longitudinal drum 52 Tube doors 53 Vertical header, cast iron 58 Vertical header, wrought steel 48 Babcock & Wilcox chain grate stoker 194 Babcock & Wilcox superheater 136 Bagasse, composition of 206 Furnace 209 Heat, value of 206 Tests of Babcock & Wilcox boilers with 210 Value of diffusion 207 Barium carbonate in feed water treatment 106 Barium hydrate in feed water treatment 106 Barrus draft gauge 254 Bituminous coal, classification of 167 Combustion rates with 246 Composition of 177 Distribution of 168 Firing methods 193 Semi 166 Sizes of 191 Thickness of fire with 193 Blast furnace gas, burners for 228 Combustion of 228 Composition of 227 Stacks for 228 Boiler, Blakey's 23 Brickwork, care of 307 Circulation of water in steam 28 Compounds 109 Development of water tube 23 Eve's 24 Evolution of Babcock & Wilcox 39 Fire tube, compared with water tube 61 Guerney's 24 Horse power 263 Loads, economical 283 Perkins' 24 Room piping 108 Room practice 297 Rumsey's 23 Stevens', John 23 Stevens', John Cox 23 Units, number of 289 Units, size of 289 Wilcox's 25 Woolf's 23 Boilers, capacity of 278 Care of 291 Efficiency of 256 Horse power of 265 Operation of 291 Requirements of steam 27 Testing 267 Boiling point 86 Of various substances 86 Of water as affected by altitude 97 Brick, fire 304 Arches 305 Classification of 304 Compression of 303 Expansion of 303 Hardness of 303 Laying up 305 Nodules, ratio of 303 Nodules, size of 303 Plasticity of 302 Brick, red 302 Brickwork, care of 307 British thermal unit 83 Burners, blast furnace gas 228 By-product coke oven gas 231 Natural gas 231 Oil 217 Oil, capacity of 221 Oil, mechanical atomizing 219 Oil, operation of 223 Oil, steam atomizing 218 Oil, steam consumption of 220 Burning hydrogen, loss due to moisture formed in 261 By-product coke oven gas burners 231 By-product coke oven gas, combustion of 231 By-product coke oven gas, composition and heat value of 231 Calorie 83 Calorific value (see Heat value). Calorimeter, coal, Mahler bomb 184 Mahler bomb, method of correction 187 Mahler bomb, method of operation of 185 Calorimeter, steam, compact type of throttling 132 Correction for 131 Location of nozzles for 134 Normal reading 131 Nozzles 134 Separating 133 Throttling 129 Capacity of boilers 264, 278 As affecting economy 276 Economical loads 283 With bagasse 210 With blast furnace gas 228 With coal 280 With oil fuel 224 Capacity of natural gas burners 229 Capacity of oil burners 221 Carbon dioxide in flue gases 154 Unreliability of readings taken alone 162 Carbon, fixed 165 Incomplete combustion of, loss due to 158 Monoxide, heat value of 151 Monoxide, in flue gases 155 Unconsumed in ash, loss due to 261 Care of boilers when out of service 300 Casings, boilers 307 Causticity of feed water 103 Testing for 105 Celsius thermometer scale 79 Centigrade thermometer scale 79 Chain grate stoker, Babcock & Wilcox 194 Chemicals required in feed water treatment 105 Chimney gases, losses in 158, 159 Chimneys (see Draft). Correction in dimensions for altitude 248 Diameter of 243 Draft available from 241 Draft loss in 239 For blast furnace gas 253 For oil fuel 251 For wood fuel 254 Height of 243 Horse power they will serve 250 Circulation of water in Babcock & Wilcox boilers 57, 66 Of water in steam boilers 28 Results of defective 62, 66, 67 Classification of coals 166 Fire brick 304 Feed water difficulties 100 Fuels 165 Cleaners, turbine tube 299 Cleaning, ease of, Babcock & Wilcox boilers 73 Closed feed water heaters 111 Coal, Alaska 169 Analyses and heat value 177 Analysis, proximate 176 Analysis, ultimate 173 Anthracite 166 Bituminous 167 Cannel 167 Classification of 165, 166 Combustion of 190 Comparison with oil 214 Consumption, increase due to superheat 139 Distribution of 167 Formation of 165 Lignite 167 Records 293 Semi-anthracite 166 Semi-bituminous 166 Sizes of anthracite 190 Sizes of bituminous 191 Code of A. S. M. E. for boiler testing 267 Coefficient of expansion of various substances 87 Coke 171 Oven gas, by-product, burners 231 Oven gas, by-product, combustion of 231 Oven gas, by-product, composition and heat value of 231 Coking method of firing 195 Color as indication of temperature 91 Combination furnaces 224 Combustible in fuels 150 Combustion 150 Air required for 152, 156 Air supplied for 157 Combustion of coal 190 Of gaseous fuels 227 Of liquid fuels 212 Of solid fuels other than coal 201 Composition of bagasse 205 Blast furnace gas 227 By-product coke oven gas 231 Coals 177 Natural gas 229 Oil 213 Wood 201 Compounds, boiler 109 Compressibility of water 97 Compression of fire brick 303 Condensation, effect of superheated steam on 140 In steam pipes 313 Consumption, heat, of engines 141 Correction, stem, for thermometers 80 For normal reading in steam calorimeter 131 For radiation, bomb calorimeter 187 Corrosion 101, 106 Coverings, pipe 315 Cross drum, Babcock & Wilcox boiler 52, 53, 60 Dry steam with 71 Draft area as affecting economy in Babcock & Wilcox boilers 70 Available from chimneys 241 Draft loss in chimneys 239 Loss in boilers 245 Loss in flues 243 Loss in furnaces 245 Draft required for anthracite 246 Required for various fuels 246 Drums, Babcock & Wilcox, cross 53 Cross, boxes 50 Heads 49 Longitudinal 49 Manholes 49 Nozzles on 50 Dry steam in Babcock & Wilcox boilers 71 Density of gases 147 Steam 115 Dulong's formula for heating value 173 Ebullition, point of 86 Economizers 111 Efficiency of boilers, chart of 258 Combustible basis 256 Dry coal basis 256 Increase in, due to superheaters 139 Losses in (see Heat balance) 259 Testing 267 Test _vs._ operating 278 Variation in, with capacity 284 With coal 288 With oil 224 Ellison draft gauge 254 Engine, Hero's 13 Engines, superheated steam with 141 Equivalent evaporation from and at 212 degrees 116 Eve's boiler 24 Evolution of Babcock & Wilcox boiler 39 Exhaust steam from auxiliaries 113 Expansion, coefficient of 87 Of fire brick 303 Of pipe 315 Pyrometer 89 Factor of evaporation 117 Fahrenheit thermometer scale 79 Fans, use of, in waste heat work 233 Feed water, air in 106 As affecting capacity 279 Boiler 100 Feed water heaters, closed 111 Economizers 111 Open 111 Feed water heating, methods of 111 Saving by 110 Feed water, impurities in 100 Lines 312 Method of feeding 110 Feed water treatment 102 Chemical 102 Chemical, lime and soda process 102 Chemical, lime process 102 Chemical, soda process 102 Chemicals used in lime and soda process 105 Combined heat and chemical 105 Heat 102 Less usual reagents 106 Firing, advantages of stoker 195 Methods for anthracite 190 Bituminous 193 Lignite 195 Fittings, handhole in Babcock & Wilcox boilers 50, 51 Pipe 311 Superheated steam 145 With Babcock & Wilcox boilers 55 Fixtures with Babcock & Wilcox boilers 55 Flanges, pipe 309 Flow of steam into pressure above atmosphere 317 Into the atmosphere 328 Through orifices 317 Through pipes 317 Flue gas analysis 155 Conversion of volumetric to weight 161 Methods of making 160 Object of 155 Orsat apparatus 159 Flue gas, composition of 155 Losses in 158, 159 Weight per pound of carbon in fuel 158 Weight per pound of fuel 158 Weight resulting from combustion 157 Foaming 102, 107 Fuel analysis, proximate 176 Ultimate 173 Fuel calorimeter, Mabler bomb 184 Tests, method of making 186 Fuels, classification of 165 Gaseous, and their combustion 227 Fuels, liquid, and their combustion 212 Solid, coal 190 Solid, other than coal 201 Furnace, bagasse 209 Blast furnace gas 228 By-product coke oven gas 231 Combination wood and oil 225 Efficiency of 283 Natural gas 229 Peabody oil 222 Webster 55 Wood burning 201, 202 Galvanic action 107 Gas, blast furnace, burners 228 Combustion of 228 Composition of 227 Gas, by-product coke oven, burners 231 Combustion of 231 Composition of and heat value 231 Gas, natural, burners 229 Combustion of 229 Composition and heat value of 229 Gases, chimney, losses in 158, 159 Density of 163 Flue (see Flue gases). Path of in Babcock & Wilcox boilers 57 Waste (see Waste heat) 232 Gaskets 312 Gauges, draft, Barrus 254 Ellison 255 Peabody 255 U-tube 254 Gauges, vacuum 117 Grate ratio for anthracite 191 Gravity of oils 214 Grooving 102 Guerney's boiler 24 Handhole fittings for Babcock & Wilcox boilers 50, 51 Handholes in Babcock & Wilcox boilers 50, 51 Hardness of boiler feed water 102 Permanent 102 Temporary 102 Testing for 105 Hardness of fire brick 303 Heat and chemical methods of treating feed water 105 And its measurement 79 Balance 262 Consumption of engines 141 Latent 84 Of liquid 120 Sensible 84 Specific (see Specific heat) 83 Total 86 Transfer 323 Heat value of bagasse 205 By-product coke oven gas 231 Coal 177 Heat value of fuels, determination of 173 Determination of Kent's approximate method 183 High and low 174 Heat value of natural gas 229 Oil 215 Wood 201 Heat waste (see Waste heat) 232 Heaters, feed water, closed 111 Economizers 111 Open 111 Heating feed water, saving by 110 Hero's engine 13 High and low heat value of fuels 174 High pressure steam, advantages of use of 119 High temperature measurements, accuracy of 89 Horse power, boiler 265 Evaporation (actual) corresponding to 288 Rated boiler 265 Stacks for various, of boilers 250 Hydrogen in flue gases 156 Ice, specific heat of 99 "Idalia", tests with superheated steam on yacht 143 Impurities in boiler feed water 100 Incomplete combustion of carbon, loss due to 158 Injectors, efficiency of 112 Relative efficiency of, and pumps 112 Iron alum in feed water treatment 106 Kent, Wm., determination of heat value from analysis 183 Stack table 250 Kindling point 150 Latent heat 84, 115 Laying of fire brick 305 Red brick 305 Lignite, analyses of 181 Combustion of 195 Lime and soda treatment of boiler feed 102 Used in chemical treatment of feed 105 Lime treatment of boiler feed water 102 Liquid fuels and their combustion 212 Loads, economical boiler 283 Losses due to excess air 158 Due to unburned carbon 158 Due to unconsumed carbon in the ash 261 Losses in efficiency (see Heat balance). In flue gases 158, 159 Low water in boilers 298 Melting points of metals 91 Mercurial pyrometers 89 Moisture in coal, determination of 176 In fuels, losses due to 259 In steam, determination of 129 Mud drum of Babcock & Wilcox boiler 51 Napier's formula for flow of steam 321 Natural gas, burners for 229 Combustion of 229 Composition and heat value of 229 Nitrate of silver in testing feed water 105 Nitrogen, as indication of excess air 157 In air 147 In flue gases 157 Nodules, fire brick, ratio of 303 Size of 303 Normal reading, throttling calorimeter 131 Nozzles, steam sampling for calorimeter 134 Location of 134 Oil fuel, burners (see Burners). Capacity with 224 Combustion of 217 Comparison with coal 214 Composition and heat value of 213 Efficiency with 224 Furnaces for 221 Gravity of 214 In combination with other fuels 224 Stacks for 251 Tests with 224 Open hearth furnace, Babcock & Wilcox boiler set for utilizing waste heat from 236 Open heaters, feed water 111 Operation of boilers 291 Optical pyrometers 91 Orsat apparatus 160 Oxalate of soda in feed water treatment 106 Oxygen in air 147 Flue gases 155 Peabody draft gauge 255 Formulae for coal calorimeter correction 188 Furnace for oil fuel 221, 222 Oil burner 218 Peat 167 Perkins' boiler 24 Pfaundler's method of coal calorimeter radiation correction 187 Pipe coverings 315 Data 308 Expansion of 315 Pipe fittings 311 Flanges 309 Flow of steam through 317 Radiation from bare and covered 314 Sizes 312 Supports for 315 Piping, boiler room 308 Pitting 102 Plant records, coal 293 Draft 294 Temperature 294 Water 293 Plasticity of fire brick 302 Pressed fuels 171 Priming in boilers 102 Methods of treating for 107 Properties of water 96 Proximate analyses of coal 177 Proximate analysis 173 Method of making 176 Pulverized fuels 170 Pump, efficiency of feed 112 Pyrometers, expansion 89 Mercurial 89 Optical 91 Radiation 90 Thermo-electric 90 Quality of steam 129 Radiation correction for coal calorimeter 187, 188 Correction for steam calorimeter 131 Effect of superheated steam on 140 From pipes 314 Losses in efficiency due to 307 Pyrometers 90 Ratio of air supplied to that required for combustion 157 Reagents, less usual in feed treatment 106 Records, plant, coal 293 Draft 294 Temperature 294 Water 293 Requirements of steam boilers 27 As indicated by evolution of Babcock & Wilcox 45 Rumsey's boiler 23 Safety of Babcock & Wilcox boilers 66 Salts responsible for scale 101 Solubility of 101 Sampling coal 271 Nozzles for steam 134 Nozzles for steam, location of 134 Steam 134 Steam, errors in 135 Saturated air 149 Saving by heating feed 110 With superheat in "Idalia" tests 143 With superheat in prime movers 140, 142 Scale (see Thermometers) 101 Sea water, composition of 97 Sections, Babcock & Wilcox boiler 50 Selection of boilers 277 Sensible heat 84 Separating steam calorimeter 132 Sizes of anthracite coal 190 Bituminous coal 191 Smoke, methods of eliminating 197 Smokelessness, relative nature of 197 With hand-fired furnaces 199 With stoker-fired furnaces 199 Soda, lime and, treatment of feed 103 Oxalate of, in treatment of feed 106 Removal of scale aided by 300 Silicate of, in treatment of feed 106 Treatment of boiler feed 103 Space occupied by Babcock & Wilcox boilers 66 Specific heat 83 Specific heat of air 148 Ice 99 Saturated steam 99 Specific heat of superheated steam 137 Various solids, liquids and gases 85 Water 99 Spreading method of firing 193 Stacks and draft (see Chimneys) 237 Stacks for blast furnace gas 228 Oil fuel 251 Wood 202, 254 Stayed surfaces, absence of, in Babcock & Wilcox boilers 69 Difficulties arising from use of 67 Steam 115 As aid to combustion of anthracite 191 As aid to combustion of lignite 195 Consumption of prime movers 289 Density of 115 Flow of, into atmosphere 320 Flow of, into pressure above atmosphere 318 Flow of, through pipes 317 High pressure, advantage of 119 History of generation and use of 13 Making, theory of 92 Moisture in 129 Properties of, for vacuum 119 Properties of saturated 122 Properties of superheated 125 Quality of 129 Saturated 115 Specific heat of saturated 99 Specific heat of superheated 137 Specific volume of 115 Superheated 137 Superheaters (see Superheated steam). Steaming, quick, with Babcock & Wilcox boilers 73 Stem Correction, thermometer 80 Stevens, John, boiler 23 Stevens, John Cox, boiler 23 Stokers, automatic, advantages of 195 Babcock & Wilcox chain grate 194 Overfeed 196 Smokelessness with 199 Traveling grate 197 Underfeed 196 Superheated steam 137 Additional fuel for 139 Effect on condensation 140 Effect on radiation 140 Fittings for use with 145 "Idalia" tests with 143 Specific heat of 137 Variation in temperature of 145 With turbines 142 Superheater, Babcock & Wilcox 136 Effect of on boiler efficiency 139 Supports, Babcock & Wilcox boiler 52, 53 Tan bark 210 Tar, water gas 225 Temperature, accuracy of high, measurements 89 As indicated by color 91 Of waste gases 232 Records 294 Test conditions _vs._ operating conditions 278 Testing, boiler, A. S. M. E. code for 267 Tests of Babcock & Wilcox boilers with bagasse 210 Coal 280 Oil 224 Theory of steam making 92 Thermo-electric pyrometers 90 Thermometer scale, celsius 79 Thermometer scale, centigrade 76 Fahrenheit 79 Reaumur 79 Thermometer scales, comparison of 80 Conversion of 80 Thermometer stem correction for 80 Thermometers, glass for 79 Throttling calorimeter 129 Total heat 86, 115 Treatment of boiler feed water (see Feed water) 102 Chemicals used in 105 Less usual reagents in 106 Tube data 309 Doors in Babcock & Wilcox boilers 53 Tubes in Babcock & Wilcox boilers 50 Ultimate analyses of coal 183 Analysis of fuels 173 Unaccounted losses in efficiency 261 Unconsumed carbon in ash 261 Units, boiler, number of 289 Size of 289 Units, British thermal 83 Unreliability of CO_{2} readings alone 162 Vacuum gauges 117 Properties of steam for 119 Valves used with superheated steam 312 Variation in properties of saturated steam 119 Superheat from boilers 145 Volume of air 147 Water 96 Volume, specific, of steam 115 Waste heat, auxiliary grates with boilers for 235 Babcock & Wilcox boilers set for use with 236 Boiler design for 233 Curve of temperature, heat absorption, and heating surface 235 Draft for 233 Fans for use with 233 Power obtainable from 232 Temperature of, from various processes 232 Utilization of 232 Water, air in boiler feed 106 Boiling points of 97 Compressibility of 97 Water feed, impurities in 100 Methods of feeding to boiler 132 Saving by heating 110 Treatment (see Feed water). Water-gas tar 225 Heat of the liquid 120 Path of, in Babcock & Wilcox boilers 57 Properties of 96 Records 293 Specific heat of 99 Volume of 96 Weight of 96, 120 Watt, James 17 Weathering of coal 169 Webster furnace 55 Weight of air 147 Wilcox boiler 25 Wood, combustion of dry 202 Wet 203 Composition and heat value of 201 Furnace design for 201 Moisture in 201 Sawmill refuse 202 Woolf s boiler 24 Zero, absolute 81



FOOTNOTES

[Footnote 1: See discussion by George H. Babcock, of Stirling's paper on "Water-tube and Shell Boilers", in Transactions, American Society of Mechanical Engineers, Volume VI., Page 601.]

[Footnote 2: When one temperature alone is given the "true" specific heat is given; otherwise the value is the "mean" specific heat for the range of temperature given.]

[Footnote 3: For variation, see Table 13.]

[Footnote 4: Where range of temperature is given, coefficient is mean over range.]

[Footnote 5: Coefficient of cubical expansion.]

[Footnote 6: Le Chatelier's Investigations.]

[Footnote 7: Burgess-Le Chatelier.]

[Footnote 8: For accuracy of high temperature measurements, see Table 7.]

[Footnote 9: Messrs. White & Taylor Trans. A. S. M. E., Vol. XXI, 1900.]

[Footnote 10: See Scientific American Supplement, 624, 625, December, 1887.]

[Footnote 11: 460 degrees below the zero of Fahrenheit. This is the nearest approximation in whole degrees to the latest determinations of the absolute zero of temperature]

[Footnote 12: Marks and Davis]

[Footnote 13: See page 120.]

[Footnote 14: See Trans., A. S. M. E., Vol. XIV., Page 79.]

[Footnote 15: Some waters, not naturally acid, become so at high temperatures, as when chloride of magnesia decomposes with the formation of free hydrochloride acid; such phenomena become more serious with an increase in pressure and temperature.]

[Footnote 16: L. M. Booth Company.]

[Footnote 17: Based on lime containing 90 per cent calcium oxide.]

[Footnote 18: Based on soda containing 58 per cent sodium oxide.]

[Footnote 19: See Stem Correction, page 80.]

[Footnote 20: See pages 125 to 127.]

[Footnote 21: The actual specific heat at a particular temperature and pressure is that corresponding to a change of one degree one way or the other and differs considerably from the average value for the particular temperature and pressure given in the table. The mean values given in the table give correct results when employed to determine the factor of evaporation whereas the actual values at the particular temperatures and pressures would not.]

[Footnote 22: See page 117.]

[Footnote 23: Ratio by weight of O to N in air.]

[Footnote 24: 4.32 pounds of air contains one pound of O.]

[Footnote 25: Per pound of C in the CO.]

[Footnote 26: Ratio by volume of O to N in air.]

[Footnote 27: Available hydrogen.]

[Footnote 28: See Table 31, page 151.]

[Footnote 29: This formula is equivalent to (10) given in chapter on combustion. 34.56 = theoretical air required for combustion of one pound of H (see Table 31).]

[Footnote 30: For degree of accuracy of this formula, see Transactions, A. S. M. E., Volume XXI, 1900, page 94.]

[Footnote 31: For loss per pound of coal multiply by per cent of carbon in coal by ultimate analysis.]

[Footnote 32: For loss per pound of coal multiply by per cent of carbon in coal by ultimate analysis.]

[Footnote 33: The Panther Creek District forms a part of what is known as the Southern Field; in the matter of hardness, however, these coals are more nearly akin to Lehigh coals.]

[Footnote 34: Sometimes called Western Middle or Northern Schuylkill Field.]

[Footnote 35: Geographically, the Shamokin District is part of the Western Middle Mahanoy Field, but the coals found in this section resemble more closely those of the Wyoming Field.]

[Footnote 36: See page 161.]

[Footnote 37: U. S. Geological Survey.]

[Footnote 38: See "Steam Boiler Economy", page 47, First Edition.]

[Footnote 39: To agree with Pfaundler's formula the end ordinates should be given half values in determining T", i. e., T" = ((Temp. at B + Temp. at C) / 2 + Temp. all other ordinates) / N]

[Footnote 40: B. t. u. calculated.]

[Footnote 41: Average of two samples.]

[Footnote 42: Assuming bagasse temperature = 80 degrees Fahrenheit and exit gas temperature = 500 degrees Fahrenheit.]

[Footnote 43: Dr. Henry C. Sherman. Columbia University.]

[Footnote 44: Includes N.]

[Footnote 45: Includes silt.]

[Footnote 46: Net efficiency = gross efficiency less 2 per cent for steam used in atomizing oil.

Heat value of oil = 18500 B. t. u.

One ton of coal weighs 2000 pounds. One barrel of oil weighs 336 pounds. One gallon of oil weighs 8 pounds.]

[Footnote 47: Average of 20 samples.]

[Footnote 48: Includes H and CH_{4}.]

[Footnote 49: B. t. u. approximate. For method of calculation, see page 175.]

[Footnote 50: Temperatures are average over one cycle of operation and may vary widely as to maximum and minimum.]

[Footnote 51: Dependant upon length of kiln.]

[Footnote 52: Results secured by this method will be approximately correct.]

[Footnote 53: See "Chimneys for Crude Oil", C. R. Weymouth, Trans. A. S. M. E., Dec. 1912.]

[Footnote 54: To determine the portion of the fuel which is actually burned, the weight of ashes should be computed from the total weight of coal burned and the coal and ash analyses in order to allow for any ash that may be blown away with the flue gases. In many cases the ash so computed is considerably higher than that found in the test.]

[Footnote 55: As distinguished from the efficiency of boiler, furnace and grate.]

[Footnote 56: To obtain the efficiency of the boiler as an absorber of the heat contained in the hot gases, this should be the heat generated per pound of combustible corrected so that any heat lost through incomplete combustion will not be charged to the boiler. This, however, does not eliminate the furnace as the presence of excess air in the gases lowers the efficiency and the ability to run without excess air depends on the design and operation of the furnace. The efficiency based on the total heat value per pound of combustible is, however, ordinarily taken as the efficiency of the boiler notwithstanding the fact that it necessarily involves the furnace.]

[Footnote 57: See pages 280 and 281.]

[Footnote 58: Where the horse power of marine boilers is stated, it generally refers to and is synonymous with the horse power developed by the engines which they serve.]

[Footnote 59: In other countries, boilers are ordinarily rated not in horse power but by specifying the quantity of water they are capable of evaporating from and at 212 degrees or under other conditions.]

[Footnote 60: See equivalent evaporation from and at 212 degrees, page 116.]

[Footnote 61: The recommendations are those made in the preliminary report of the Committee on Power Tests and at the time of going to press have not been finally accepted by the Society as a whole.]

[Footnote 62: This code relates primarily to tests made with coal.]

[Footnote 63: The necessary apparatus and instruments are described elsewhere. No definite rules can be given for location of instruments. For suggestions on location, see A. S. M. E. Code of 1912, Appendix 24. For calibration of instruments, see Code, Vol. XXXIV, Trans., A. S. M. E., pages 1691-1702 and 1713-14.]

[Footnote 64: One to two inches for small anthracite coals.]

[Footnote 65: Do not blow down the water-glass column for at least one hour before these readings are taken. An erroneous indication may otherwise be caused by a change of temperature and density of the water within the column and connecting pipe.]

[Footnote 66: Do not blow down the water-glass column for at least one hour before these readings are taken. An erroneous indication may otherwise be caused by a change of temperature and density of the water within the column and connecting pipe.]

[Footnote 67: For calculations relating to quality of steam, see page 129.]

[Footnote 68: Where the coal is very moist, a portion of the moisture will cling to the walls of the jar, and in such case the jar and fuel together should be dried out in determining the total moisture.]

[Footnote 69: Say 1/2 ounce to 2 ounces.]

[Footnote 70: For methods of analysis, see page 176.]

[Footnote 71: For suggestions relative to Smoke Observations, see A. S. M. E. Code of 1912, Appendix 16 and 17.]

[Footnote 72: The term "as fired" means actual condition including moisture, corrected for estimated difference in weight of coal on the grate at beginning and end.]

[Footnote 73: Corrected for inequality of water level and steam pressure at beginning and end.]

[Footnote 74: See Transactions, A. S. M. E., Volume XXXIII, 1912.]

[Footnote 75: For methods of determining, see Technologic Paper No. 7, Bureau of Standards, page 44.]

[Footnote 76: Often called extra heavy pipe.]

[Footnote 77: See Feed Piping, page 312.]

[Footnote 78: See Superheat Chapter, page 145.]

[Footnote 79: See Radiation from Steam Lines, page 314.]

[Footnote 80: D, the density, is taken as the mean of the density at the initial and final pressures.]

[Footnote 81: Diameters up to 5 inches, inclusive, are actual diameters of standard pipe, see Table 62, page 308.]

[Footnote 82: Diameters up to 4 inches, inclusive, are actual internal diameters, see Table 62, page 308.]

[Footnote 83: H. P. Jordan, "Proceedings of the Institute of Mechanical Engineers", 1909.]

[Footnote 84: "Zeitschrift des Vereines Deutscher Ingenieur", 1909, page 1750.]

[Footnote 85: Heinrich Grober—Zeit. d. Ver. Ing., March 1912, December 1912. Leprince-Ringuet—Revue de Mecanique. July 1911. John Perry—"The Steam Engine". T. E. Stanton—Philosophical Transactions, 1897. Dr. J. T. Nicholson—Proceedings Institute of Engineers & Shipbuilders in Scotland, 1910. W. E. Dally—Proceedings Institute of Mechanical Engineers, 1909.]

[Footnote 86: Proceedings Royal Society, Vol. LXXI.]

[Footnote 87: Zeitschrift des Vereines Deutscher Ingenieur, 1910, page 1154.]

[Footnote 88: Proceedings Institute of Engineers and Shipbuilders, 1910.]

[Footnote 89: Natural or Hyperbolic Logarithm.]

THE END