A turboprop engine consists of a diffuser, compressor, combustor, turbine, and nozzle. The turbine drives a propeller as well as the

compressor. Air enters the diffuser with a volumetric flow rate of $63\mathrm{.}7\frac{m^3}{s}$ at $40$kPa,$240K,$ and a velocity of $180\frac{m}{s},$ and

decelerates essentially to zero velocity. The compressor pressure ratio is $9$ and the compressor has an isentropic efficiency of $85\%.$

The turbine inlet temperature is $1140$ K $,$ and its isentropic efficiency is $85\%.$ The turbine exit pressure is $50$ kPa and the nozzle exit

pressure is $40$ kPa $.$ Flow through the diffuser and nozzle is isentropic$.$ Use an air$-$standard analysis and neglect kinetic energy except at

the diffuser inlet and the nozzle exit.

Step $1$

Determine the power delivered to the propeller, in MW$.$

$W_{\text{p}\text{r}\text{o}\text{p}}^{}=$