power necessary One way to decrease the power needed to compress a gas using a c
ID: 1857788 • Letter: P
Question
power necessary
One way to decrease the power needed to compress a gas using a compressor is to encompass the compressor in a water jackct which serves to cool the gas as it is being compresscd. Air enters the compressor at a pressure and temperature of 0.2 MPa and 400 K, respectively and exits at a pressure of 2 MPa. a) Calculate the power necessary to compress the air isentropically in this compressor without the water jacket if the mass flow rate of the air is 2.5 kg/s. If the cooling water enters at a temperature of 20 degree C and exits at a temperature of 25 degree C and has a mass flow rate of 1 kg/s, determine the minimum power input of the compressor.Explanation / Answer
= T1 (P2/P1)^(k-1/k) This is from Isentropic equation PV^k = constant ---------------- where k is equal to 1.4 for air (Cp/Cv) ------------------------------------------------------------ Given T1 = 400K , P1 = 0.2MPa and P2 = 2MPa ----------------------------------------------- Therefore T2 = 772.28 K ----------------------------------------------------------------------------- Power = {mass flow * R *(T2-T1)} / ( k-1) = {2.5 *287*(772.28-400)}/0.4 = 667.8 KW --------------------------------------------------------------------------------------------------------- When Cold water is passed the heat released by air is carried by cold water -----------------------------Therefore, Power = mass flow *Cp*delta(T) = 1.5*1.004*10^3 *5 =7.53 KW
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