Chapter XVII: Part 17

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 | 2½| 2 | 1½| 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

_ _
| 240×6×4 |
Q_{1} = 293.1 | ------- |^{½} = 239.9 pounds
|_ 720×12_|

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 ¼ inch to 1½ inches long and ¼ 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)^{½} (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
Réaumur 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.]