P−V and T−S diagrams for multistage compression are shown in Figure 10.6.
Figure 10.6 ρ−V and T−S Diagrams for Multistage Compressor
If P1, T1 and delivery pressure P3 are fixed, the optimum value of the intermediate pressure P2 for minimum work can be obtained by setting the derivative dW/dP2 = 0.
For perfect cooling, 
In general, if there are N stages, the pressure ratio for each stage will be given by,
Heat Rejected During Compression Process
Mean Effective Pressure, pm
Example 10.3: A single-stage, single-acting air compressor has intake pressure of 1 bar and delivery pressure of 12 bar. The compression and expansion follows the law pV1.3 = constant. The piston speed and rotations of shaft is 180 m/min and 350 rpm, respectively. Indicated power is 30 kW and volumetric efficiency is 92%. Determine the bore and stroke.
Solution:
The indicating power of single-acting reciprocating compressor is
Example 10.4: An air compressor has eight stages of equal pressure ratio of 1.35. The flow rate through compressor and the overall efficiency are 50 kg/s and 90%, respectively. If the air enters compressors at a pressure of 1.0 bar and temperature of 313 K. Determine
- State of air at the exit of compressor.
- Polytropic of small stage efficiency.
- Power required to drive the compressor.
Solution:
Example 10.5: A double acting, single cylinder, reciprocating air compressor has a piston displacement of 0.015 m3 per revolution, operates at 500 rpm and has a 5% clearance. The air is received at 1 bar and delivered at 6 bar. The compression and expansion are polytropic with n = 1.3. Determine
- The volumetric efficiency.
- The power required.
- The heat transferred and its direction during compression if inlet temperature of air is 293 K.
Solution:
V = 0.015 m3 per revolution; N = 500 rpm; ∈ = 5%; n = 1.3; P1 = 1 bar; and P2 = 6 bar.
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