Part 45 (1/2)
The table h a pipe of a given dia froht headed by the pressure which is theto 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 | |____________|_____________|____________|____________|_____________| | | | | | | | 2537 | 863 | 1401 | 2281 | 456 | | 30 | 867 | 1408 | 2684 | 537 | | 40 | 874 | 1419 | 3518 | 704 | | 50 | 880 | 1429 | 4406 | 881 | | 60 | 885 | 1437 | 5259 | 1052 | | 70 | 889 | 1444 | 6107 | 1221 | | 75 | 891 | 1447 | 6530 | 1306 | | 90 | 895 | 1454 | 7794 | 1559 | | 100 | 898 | 1459 | 8634 | 1727 | | 115 | 902 | 1466 | 9876 | 1975 | | 135 | 906 | 1472 | 11561 | 2312 | | 155 | 910 | 1478 | 13221 | 2644 | | 165 | 912 | 1481 | 14046 | 2809 | | 215 | 919 | 1493 | 18158 | 3632 | |____________|_____________|____________|____________|_____________|
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 forth of pipe in dias 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 tith equal to 40 diath equal to 60 diaher 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 stateed into the ature, the atreater 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 at taken as 147 pounds absolute, and the ratio of expansion in the nozzle being 1624), and the corresponding discharge per square inch of orifice per minute
Napier deduced an approximate formula for the outflow of steaures just given This formula is:
pa W = ---- (49) 70
Where W = the pounds of stea per second, p = the absolute pressure in pounds per square inch, and a = the area of the orifice in square inches
In some experiments h pipes fro and inch in diareatest difference from Napier's formula was 32 per cent excess of the experi through an orifice froreater than 58 per cent of the higher, the flow per minute may be calculated from the formula:
W = 19AK ((P - d)d){} (50)
Where W = the weight of steaed 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
[Illustration: Vesta Coal Co, California, Pa, Operating at this Plant 3160 Horse Power of Babcock & Wilcox Boilers]
HEAT TRANSFER
The rate at which heat is transas to a coolerhas 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 infor and for this reason a boiler, as a physical piece of apparatus, is not as well understood as it ht be This, however, has had little effect in its practical development and it is hardly possible that aof 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 teth 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 aas is usually expressed as a product of the difference in te surface into a factor which is conated the ”transfer rate” There has been considerable looseness in the writings of even the best authors as to the way in which the gas teas varies in teh which it is assumed to flow, and most of them seem to consider that this would be the case, there are two as temperatures, one the mean of the actual temperatures at any time across the section, and the other thesuch a section in any given time Since the velocity of floill 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 telish units the terees 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 teas 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 Voluests 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 teas 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 for the facts, it is undoubtedly correct to a first approximation for small temperature differences if the additive constant, which in his paper he assuiven a value[83]
Experi 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 e the transfer rate with the velocity as a factor The exponent of the power of the velocity appearing in the for to Reynolds, would be unity The most probable value, however, deduced from most of the experi experiments of his own, as well as experiments of others, Dr Wilhelm Nusselt[84] concludes that the evidence supports the following formulae:
_ _ [lambda]_{ c_{p} [delta] | a = b ------------ | --------------- |{u} d{1-u} |_ [lambda] _|
Where a is the transfer rate in calories per hour per square rade difference in temperature, u is a physical constant equal to 786 from Dr Nusselt's experiiven below, is 1590, w is the as in as at its rarams per cubic meter, [lambda] is the conductivity at the mean temperature and pressure in calories per hour per square rade 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 teh the tube per hour, A is the area of the tube in square feet, d is the diaas at constant pressure, [laas 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