Name (25 pts) Air is compressed at steady state from 14.7 lbf/in2 and 60 F to a

Question

Name (25 pts) Air is compressed at steady state from 14.7 lbf/in2 and 60 F to a final pressure of 150 lbf/in2. As the air passes through the compressor, it is cooled at a rate of 10 Btu per lb. of air. The volumetric flow rate of air at the inlet is 5000 ft/min and the power input to the compressor is 700 hp. The air behaves as an ideal gas. Neglecting kinetic and potential energy effects, determine the 3) a) Mass flow rate of the air, in lb/s b) Temperature of air at the compressor exit, in °F. 5 pts] 20 pts

Explanation / Answer

Initial pressure of air, Pinitial = 14.7 lbf/in2

Final pressure of air, Pfinal = 150 lbf/in2

Initial temperature of air, Ti = 60 0F

Volumetric flow rate, Q = 5000 ft3/min = 2.35 m3/s

Power input to the compressor, P = 700 hp = 521990 W

(b) Temperature of air at the compressor exit which will be given by -

using a Gay-Lussac's law, we get

P1 / T1 = P2 / T2

T2 = (P2 / P1) T1

T2 = [(150 lbf/in2) / (14.7 lbf/in2)] (60 0F)

T2 = (10.2) (60 0F)

T2 = 612 0F

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