Question

In an air compressor air flows steadily at the rate of 0.5 kg/s through an air compressor. It enters the compressor at 6 m/s with a pressure of 1 bar and a specific volume of 0.85 m³/kg and leaves at 5 m/s with a pressure of 7 bar and a specific volume of 0.16 m³/kg. The internal energy of the air leaving is 90 kJ/kg greater than that of the air entering. Cooling water in a jacket surrounding the cylinder absorbs heat from the air at the rate of 60 kJ/s. Calculate : 

(i) The power required to drive the compressor ; 

(ii) The inlet and output pipe cross-sectional areas

Answer 1

Air flow rate through the compressor, m = 0.5 kg/s

Velocity of air at the inlet to compressor, C₁ = 6 m/s

Velocity of air at the outlet of compressor, C₂ = 5 m/s

Pressure of air at the inlet to the compressor, p₁ = 1 bar

Pressure of air at outlet to the compressor, p₂ = 7 bar 

Specific volume of air at inlet to the compressor, v₁ = 0.85 m3/kg 

Specific volume of air at outlet to the compressor, v₂ = 0.16 m3/kg 

Difference of internal energy at the outlet and inlet of the compressor

(u₂ – u₁) = 90 kJ/kg

Heat rejected by air (to cooling water),

Q = – \(\cfrac{60}{0.5}\) = – 120 kJ/kg.

(i) Power required to drive the compressor : 

Using the steady flow energy equation,

(Note that the change in kinetic energy is negligibly small in comparison with the other terms). 

Work input required = 237 kJ/kg = 237 × 0.5 kJ/s = 118.5 kW 

Hence, power required to drive the compressor = 118.5 kW.

(ii) Inlet and outlet pipe cross-sectional areas, A₁ and A₂ : 

Using the relation,

Inlet pipe cross-sectional area, A₁ = 0.0708 m₂.

Again,

Outlet pipe cross-sectional area, A₂ = 0.016 m².

Comments

Thanks for the solution