Question

Air is drawn from the atmosphere into a turbomachine. At the exit, conditions are 500 kPa (gage) and 130oC. The exit speed is 100 m/s and the mass flow rate is 0.8 kg/s. Flow is steady and there is no heat transfer. Compute the shaft power interaction with the surroundings.

Answer 1

P=- 88.41 KW

Negative sign indicates that power is given to the system.

Step-by-step explanation:

Given that

P₂=500 KPa

T₂=130°C

V₂=100 m/s

mass flow rate ,m= 0.8 kg/s

Lets take inlet condition for air

T₁=25°C

P₁=100 KPa

V₁=0 m/s

We know that

Heat capacity for air Cp=1.005 KJ/kg.k

We know that for air change in enthalpy only depends only on temperature

Now from first law for open system

`h_1+(V_1^2)/(2000)=h_2+(V_2^2)/(2000)+W`

`1.005* 298+(0^2)/(2000)=1.005* 403+(100^2)/(2000)+W`

`W=1.005* 298-1.005* 403-(100^2)/(2000)`

W=-110.52 KJ/kg

Shaft power P = m .W

P = -110.52 x 0.8

P=- 88.41 KW

Negative sign indicates that power is given to the system.