$6\mathrm{.}31$: A double$-$spool turbofan engine; Fig. $(6\mathrm{.}66),$ is used to power an aircraft flying at speed of $250$ m$/$s at an altitude of $11,000$ m$.$ As shown in the figure below, the low$-$pressure turbine drives the fan and low$-$pressure compressor, while the high$-$pressure turbine drives the high$-$pressure compressor. The engine has the following data:

$$ Bypass ratio $=8.$

$$ Total ingested air flow rate $=180$ kg$/$s$.$

$$ Overall pressure ratio OPR $=35.$

$$ Fan pressure ratio $=1\mathrm{.}6.$

$$ Pressure ratio of high$-$pressure compressor is four times that of the low$-$pressure compressor; HPC$=4$ LPC$.$

$$ Turbine inlet temperature $=1650$ K$.$

$$ Fuel heating value $=43$ MJ$/$kg$.$

Assuming all processes are ideal and neglecting any pressure drop, it$$s required to:

$1.$ Find the thrust, TSFC$,$ and efficiencies of the engine

$2.$ Plot the velocity and temperature distribution over the engine cross section

$($rear end$).$ Figure $(6\mathrm{.}66)$ Double spool high bypass ratio turbofan engine