Question

An air compressor compresses 15 L/s of air at 120 kPa and 20°C to 800 kPa and 300°C while consuming 6.2 kW of power. How much of this power is being used to increase the pressure of the air versus the power needed to move the fluid through the compressor?

Answer 1

Gas constant $R = 0.287 kPa.m^3/kg.K$

Specific volume of the air at the compressor inlet is:

$v_1=\frac{RT_1}{P_1}\\ v_1=\frac{0.287\times 293}{120} =0.7008 m^3/kg$

The air mass flow rate:

$\dot m=\frac{\dot V_1}{v_1}\\ \dot m = \frac{15\times 10^{-3}}{0.7008} = 0.0214 kg/s$

The flow work:

$\dot W_{flow}=\dot m R(T_2-T_1)\\ \dot W = 0.0214\times 0.287 \times 280=1.72 kW$

Power used to increase the air pressure:

$\dot W_p=\dot W_{in}-\dot W_{flow}=6.2-1.72 =4.48 kW$