Machinery's Handbook, 31st Edition
Work REQUIRED TO COMPRESS AIR 2815 P 1 = initial absolute pressure in pounds per square foot; P 2 = absolute pressure in pounds per square foot, after compression; and, V 1 = initial volume in cubic feet. The total work required for isothermal compression is: Total work in foot-pounds P 1 V 1 e = in which P 1 , P 2 , and V 1 denote the same quantities as in the previous equation, and V 2 = volume of air in cubic feet, after compression. V 1 V 2 log --- The work required to compress air isothermally, that is, when the heat of compression is removed as rapidly as produced, is considerably less than the work required for compress ing air adiabatically, or when all the heat is retained. In practice, neither of these two theoretical extremes is obtainable, but the power required for air compression is about the median between the powers that would be required for each. The accompanying table gives the average number of foot-pounds of work required to compress air. Horsepower Required to Compress Air: In the accompanying tables is given the horse power required to compress one cubic foot of free air per minute (isothermally and adiabat ically) from atmospheric pressure (14.7 pounds per square inch) to various gage pressures, for one-, two-, and three-stage compression. The formula for calculating the horsepower required to compress, adiabatically, a given volume of free air to a given pressure is: = where N = number of stages in which compression is accomplished P = atmospheric pressure in pounds per square inch P 2 = absolute terminal pressure in pounds per square inch V = volume of air, in cubic feet, compressed per minute, at atmospheric pressure n = exponent of the compression curve = 1.41 for adiabatic compression For different methods of compression and for one cubic foot of air per minute, this for mula may be simplified as follows: HP 144 NPVn 33 000 n –1 ( ) , ----------------- P 2 P --- n – 1 Nn ----------- –1 For one-stage compression: HP = 0.015 P ( R 0.29 - 1) For two-stage compression: HP = 0.030 P ( R 0.145 - 1) For three-stage compression: HP = 0.045 P ( R 0.0975 - 1) For four-stage compression: HP = 0.060 P ( R 0.0725 - 1) In these latter formulas R P 2 P = --- = number of atmospheres to be compressed The formula for calculating the horsepower required to compress isothermally a given volume of free air to a given pressure is: HP 144 PV 33000 --------- P 2 P --- e log = Natural logarithms are obtained by multiplying common logarithms by 2.30259 or by using a handheld calculator. The work and power required for air compression can be found in Table 35 to Table 38. Stress and heat are what limits the maximum compression of any single stage of a com pressor. The volumetric efficiency drops as pressure rise increases, further limiting the maximum compression of a single stage. Multi-stage compressors are used when a single stage cannot develop enough pressure. Multi-stage axial compressors use a series of axial fans to deliver very large flow rates. Perfect intercooling is impractical, so it is important to note that for every 10°F temperature increase, the horsepower requirement increases nearly 1%.
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