Question

The centrifugal air compressor of a gas turbine receives air

from the ambient atmosphere where the pressure is 1 bar and

the temperature is 300K. At the discharge of the compressor,

the pressure is 4 bar and the temperature is 480K and the

velocity is 100 m/s. The mass flow rate of air is 15kg/s. (a)

Determine the power required to drive the compressor and

(b) Explain why the given air exit temperature is more or less

than the reversible adiabatic compression temperature.

Answer 1

Solution:

$$Q−W=Δh+ΔK$$ $$Δh=(1)(480−300)=180 \frac{kJ}{kg} ​$$

$$ΔK=0.5(100) ^2 =5000 \frac{J}{kg} ​ =5 \frac{kJ}{kg}$$

$$W=−180−5=−185 \frac{kJ}{kg} ​$$ $$P=−185(15)=−2775 kW$$