Question

A two stage single acting air compressor with complete intercooling takes in air at 1 bar and 288k at rate of 360kg/h.The delivery pressure is 16 bar. Calculate the power required,the isothermal efficiency ,FAD and the net heat transferred in each cylinder and the intercooler . Take the index of compression and expansion for both stages is 1.3. The speed of the compressor is 420rpm. If the clearance ratios for the LP and HP cylinders are 0.06 and 0.08 respectively , calculate the swept and clearance volumes for each cylinder.

Answer 1

$P_1= 1 bar = 1×10^5N/m²\\ n= 1.3kJ/kg K\\ T_1= 288K\\ \\ P_3= 16bar = 16×10⁵N/m²\\ r= 360kg/h\\ \omega = 420rpm= 14π \ rad/s\\ r_{LP} = 0.06\\ r_{HP}=0.08$

$R=287J/kg K$

we know that for complete intercooling. the intercooler pressure$P_2= \sqrt{P_1P_3} = \sqrt{1×16}= 4 bar\\ = 4×10⁵ N/m²$

$V =\dfrac{mRT_1}{P_1} = \dfrac{1.3×287×288}{1×10⁵}\\ = 1.075\textsf{ m}³$