Consider a turbojet engine flying at Mach $0\mathrm{.}9$ at an altitude of $11$ km$.$ The mass flow rate of air coming in the inlet is of $29\mathrm{.}17$ kg$/$s$.$ The nozzle is such that it is made of a converging section only which is designed such that it leads to the largest thrust. We know that the compressor efficiency is of $85\%,$ that the turbine efficiency is of $90\%,$ and that the stagnation pressure drops by $2\%$ in the combustor. We also know that the compressor stagnation temperature ratio is of $2\mathrm{.}512,$ that the stagnation temperature at the combustor exit is of $1650$ K$,$ that the heating value of the fuel is of $44$ MJ$/$kg$,$ and that the fuel$-$air ratio is of $0\mathrm{.}03.$ Do the following:

$($a$)$ Find the freestream temperature, and the stagnation pressure and temperature at the inlet entrance.

$($b$)$ Find the power input to the flow by the compressor.

$($c$)$ Find the burning efficiency in the combustor.

$($d$)$ Find the stagnation pressure at the nozzle exit.

$($e$)$ Find the stagnation temperature at the nozzle exit.

Assume that the gas constant R$=287$

J$/$kgK$,$ the specific heat ratio $\backslash$gamma $=1\mathrm{.}4$

$,$ and the specific heat at constant pressure cp$=1000$

J$/$kgK throughout.

Answers

$1.217$ K$,252$ K$,38\mathrm{.}39$ kPa, $11\mathrm{.}11$ MW$,0\mathrm{.}808,248\mathrm{.}9$ kPa, $1280$ K$.$