Example using the Control Volume Energy Equation Given: A large air compressor takes in air at absolute pressure P1= 14.0 psia, at temperature T1= 80oF (539.67 R), and with mass flow rate = 20.0 lbm/s. The diameter of the compressor inlet is D1= 24.5 inches. At the outlet, P2= 70.0 psia and T2= 500oF (959.67 R). The diameter of the compressor outlet is D2= 7.50 inches. The shaft driving the compressor supplies 3100 horsepower to the compressor. m±(a) To do: Calculate the average velocity of the air entering the compressor. Solution: At the inlet, mV1, avg1, avg1111AVAρ≈=±where the subscripts “avg” have been dropped for convenience. Thus, 11211442RTmmmADPDρπρπ===±±±V, where we have used the ideal gas law PRT=to calculate the density of the air. Substitution of the values yields 2ft lbf53.34539.67 Rlbm Rlbf14.024.5in⋅⋅VV2P1V1P2Compressor D1D2Input shaft power ωV2()1122lbm420.04fts87.229sinRT mPD=≈ft87.2s±(b) To do: Calculate the average velocity of the air leaving the compressor.
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