Question

Air is compressed by a rotary compressor in a steady flow process at a rate of 1.5 0 kg/s. At entry, the air has a specific volume of 0.900 m3/kg and has a velocity of 80.0 m/s. At exit, the air has a specific volume of 0.400 m3/kg and has a velocity of 45.0 m/s. In its passage through the compressor, the specific enthalpy of the air is increased by 110.0 kJ/kg and it experiences a heat transfer loss of 20.0 kJ/kg.

Answer 1

Air is compressed by a rotary compressor in a steady flow process at a rate of 1.5 0 kg/s. At entry, the air has a specific volume of 0.900 m3/kg and has a velocity of 80.0 m/s. At exit, the air has a specific volume of 0.400 m3/kg and has a velocity of 45.0 m/s. In its passage through the compressor, the specific enthalpy of the air is increased by 110.0 kJ/kg and it experiences a heat transfer loss of 20.0 kJ/kg. Determine: a. The inlet and exit areas of the compressor in m2 b. The power required to drive the compressor in kW

a.

$m=ρ_1A_1V_1 \\ 1.5 = \frac{1}{0.9} \times A_1 \times 80 \\ A_1 = 0.01687 \;m^2 \\ m=ρ_2A_2V_2 \\ 1.5 = \frac{1}{0.4} \times A_2 \times 45 \\ A_2 = 0.0133 \;m^2$

b. Using ateady flow energy equation:

$h_1 + \frac{c_1^2}{2} -Q = h_2 + \frac{c^2_2}{2} + w \\ \frac{80^2}{2000} -20 =110 + \frac{45^2}{2000} + w \\ w= -127.81 \;kJ/kg \times 1.5 \;kg/s \\ w = -191.72 \;kW$