A two-stage air compressor with inter-stage cooling is shown in Figure P3.23. The dry air enters the first compressor stage at 1 atm, 25°C, a volumetric flow rate of 3500 cfm, and is compressed to 5 bar. The air then passes through a heat exchanger with no appreciable drop in pressure, after which, it is compressed in the second stage to 10 bar. The isentropic efficiency of both compression stages is 83%. The heat exchanger is a counter flow heat exchanger where the air is being cooled by water. The water enters the heat exchanger at 20°C and exits at 75°C. The pinch point temperature difference of the heat exchanger is 4 K and the pinch point occurs on the cold end.
Determine the following,

a. The volumetric flow rate of the cooling water entering the heat exchanger (gpm)

b. The total power draw of both compressors (kW)

c. Investigate the effect of the intermediate pressure P2 by constructing a plot that shows the total power draw as a function of P2 for the range, 2 bar ≤ P2 ≤ 5 bar d. One reason for multistage compression with intercooling is to reduce the total power requirement in an overall compression process. Verify that this idea is correct by calculating the power draw for a single compressor used to compress 3500 cfm of air from 1 bar to 10 bar with an isentropic efficiency of 83%.

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T = 75C 6 Compressor 1 2 + P =5 bar ATX = 4 K www www P = 1 atm -T = 25C + = 3500 cfm 1e1=1e27 = 0.83 FIGURE P3.23 Two-stage air compressor with inter-stage cooling. Cooling water + T = 25C 5 Pinch point 3 P = P Compressor 2 + W P = 10 bar