Question

. A steam turbine operates between 500°C and 3.5 MPa to 200°C and 0.3 MPa. If the turbine generates 750 kW and the heat loss is 100 kW, what is the flow rate of steam through the turbine?

Answer 1

Answer:

1.757 kg/s

Explanation:

According to the First Law of Thermodynamics, the physical model for a turbine working at steady state is:

$-\dot Q_{out} - \dot W_{out} + \dot m \cdot (h_{in}-h_{out})=0$

The flow rate of steam is:

$\dot m = \frac{\dot Q_{out}+\dot W_{out}}{h_{in}-h_{out}}$

Water enters and exits as superheated steam. After looking for useful data in a property table for superheated steam, specific enthalpies at inlet and outlet are presented below:

$h_{in} = 3451.7 \frac{kJ}{kg} \\h_{out} = 2967.9 \frac{kJ}{kg}$

Finally, the flow rate is calculated:

$\dot m = \frac{100 kW + 750 kW}{3451.7 \frac{kJ}{kg} - 2967.9 \frac{kJ}{kg}}\\\dot m =1.757 \frac{kg}{s}$