Problem $3$:

A gas turbine has the following component performance:

The maximum temperature of the combustor is $1,200C$ with fuel $Q_R=48,000k\frac{J}{k}g.$ The gas turbine inlet

temperature is $40C$ with air flow rate of $34k\frac{g}{s}.$ The turbine is cooled by bleeding $2\%$ of the compressor

output air. A steam power plant with thermal efficiency of $35\%$ is integrated with the gas turbine to form

a combined cycle. The air exits the boiler at $195C.$

a$)$ Determine the power output, the overall efficiency and the SFC $(k\frac{g}{k}W*hr)$ of the simple gas

turbine.

b$)$ Determine the total power output, the overall efficiency and SFC of the combined cycle.

c$)$ Find the flow rate of water if the boiler effectiveness is $75\%$ and water enters the boiler at $85C$

and $2$ MPa $.$ In the boiler, consider the water process to be isobaric and the air $Cp=1\mathrm{.}065k\frac{J}{k}g.K.$