Question

the centrifugal compressor of a gas turbine receives air at 1 bar and 300k. At the discharge of the compressor, the pressure is 4 bar, temperature is 480k and velocity is 100m/s. The mass rate of flow into the compressor is 15kg/s. Determine the power required to drive the compressor?

Answer 1

$$Q-W=\Delta h+\Delta K\\\Delta h=(1)(480-300)=180\frac{kJ}{kg}\\\Delta K=0.5(100)^2=5000\frac{J}{kg}=5\frac{kJ}{kg}\\W=-180-5=-185\frac{kJ}{kg}\\P=-185(15)=-2775\ kW$$