Air_compressor_example

Air_compressor_example - Example using the Control Volume...

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Example using the Control Volume Energy Equation Given : A large air compressor takes in air at absolute pressure P 1 = 14.0 psia, at temperature T 1 = 80 o F (539.67 R), and with mass flow rate = 20.0 lbm/s. The diameter of the compressor inlet is D 1 = 24.5 inches. At the outlet, P 2 = 70.0 psia and T 2 = 500 o F (959.67 R). The diameter of the compressor outlet is D 2 = 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, mV 1, avg 1, avg 1 1 1 1 A V A ρ ≈= ± where the subscripts “avg” have been dropped for convenience. Thus, 1 1 2 11 4 4 2 RTm mm ADP D ρπρ π == = ± ±± V , where we have used the ideal gas law PR T = to calculate the density of the air. Substitution of the values yields 2 ft lbf 53.34 539.67 R lbm R lbf 14.0 24.5 in    V V 2 P 1 V 1 P 2 Compressor D 1 D 2 Input shaft power ω V 2 () 1 1 2 2 lbm 4 20.0 4 ft s 87.229 s in RT m PD = ft 87.2 s ± (b) To do : Calculate the average velocity of the air leaving the compressor.
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