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27pa/ Ta, where pa is the air pressure, in lb / in2 abs (kPa abs), and Ta the temperature, in F abs ( C abs) The true pressure of the air is pa B hpv, where B is the barometer pressure (in same units as p), h the relative humidity, and pv the vapor pressure for saturation at Ta This is the value given in steam tables The weight of water vapor, lb / ft3 (kg / m3), is wv h / Vs, where Vs is the speci c volume of dry saturated steam at Ta
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25 Density of Air The weight of dry air, lb / ft3 (kg / m3), is given by wa
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The weight of the moist air is w wa wv The quantity w is the actual weight per cubic foot (m3) that is handled by the compressor At 65 F (183 C), 147 lb / in2 (1013 kPa) barometer, and 70 percent humidity, w 00752
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26 Free Air By free air is meant air at the pressure and temperature of the place from which the compressor draws its supply Its volume may be obtained from the volume at any other set of conditions by the equation pV / T constant 27 Gas Laws If a perfect gas is compressed or expanded, it follows the law
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pVn constant If the process is isothermal, n 1 If it is adiabatic, n k, which for air is approximately 14 In a piston compressor, n is usually from 13 to 135, and in a centrifugal compressor very nearly 14 The temperature change during compression or expansion is determined by the relation T2 T1 V1 V2
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(1345)
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28 Volumetric Ef ciency This term is really a capacity factor, as it represents
the relationship between the actual capacity of a machine and its physical size, and in an air compressor has but small effect upon true ef ciency It is de ned as the ratio of the volume of free air actually delivered by the compressor to its displacement volume In Fig 1376, the compressed air in the clearance space at the end of the stroke expands down to 4 before the suction valve can open The volume of air drawn into the machine is only V1, while the displacement volume is Vp If c Vc / Vp, or the percent of clearance divided by 100, then V1 Vp 1 c c p2 p1
(1346)
To reduce the volume V1 to that of free air, multiply it by ( p1 / pa) (Ta / T1) The effect of the clearance and the value of p1 / pa can be obtained from an indicator card, but the temperature of the air in the cylinder at the end of the suction stroke is not known For piston compressors, clearance is usually from 2 to 6 percent, the larger values being found with smaller machines The actual volumetric ef ciencies of
FIGURE 1376
CHAPTER THIRTEEN
single-stage compressors are from 50 to 85 percent, depending upon the clearance and the pressure
29 Multistaging For high pressures, compressors are built in two or more
stages, thus reducing the pressure range within each cylinder and hence maintaining a reasonable volumetric ef ciency If the air is also cooled, between stages, to the initial temperature, there is a saving of power as shown in Fig 1377, where ABC is the compression line for a single cylinder and AD is an isothermal For minimum work with perfect intercooling, the intermediate pressures are 3 2 3 2 p1 p2 for a two-stage compressor; p p1 p2 and p p1 p2 for given by p a three-stage machine If there were no pressure drops in the intercoolers, the cylinder volumes would be inversely proportional to these pressure and to p1 Owing to the higher volumetric ef ciency with the lower pressure, the volume of the low-pressure cylinder will be less than that of a single-stage compressor of the same capacity
30 Compressor Ef ciencies The mechanical ef ciency is the work done in the air cylinders as given by the actual indicator card divided by the indicated work in the engine cylinders, if driven by a direct-connected engine, or by the work delivered by a belt, if it is belt-driven For piston compressors, mechanical ef ciencies are about 90 percent for direct-connected machines and a few percent higher for the belt-driven types The compression ef ciency is the ratio of the work required to compress and deliver the gas, as given by an ideal cycle with isothermal (or adiabatic) compression, to the work done on the air, as shown by actual indicator cards Values of isothermal compression ef ciency are usually from 65 to 70 percent and nearly independent of the pressure, while adiabatic compression ef ciencies are: 64 percent for p2 / p1 1; 76 percent for p2 / p1 2; 87 percent for p2 / p1 3; and about 90 percent for all higher ratios
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