# Determine the thrust of the turbojet engine.

A turbojet powered aircraft is flying at Mach number $$0.8$$ at an altitude of $$10\; km$$.The inlet and exit areas of the engine are $$0.7\; m^{2}$$ and $$0.4\; m^{2}$$ respectively.The exhaust gases have velocity of $$500\; m/s$$ and pressure of $$60\;kPa.$$ The free stream pressure,density and speed of sound are $$26.5\; kPa,0.413\; kg/m^{3}$$ and $$299.5 \;m/s$$ respectively.What is the thrust of the engine?

Asked on 10th October 2019 in

Mach number is given as (velocity of the aircraft / speed of the sound).

$M=\frac{V}{a}$

Speed of sound is given as $U_{\infty }={M}{a} \\=0.8\times 299.5 \\=239.6\;m/s$

Mass flow rate of air through the inlet is $\dot{m}_{a}=\rho _{\infty }u_{\infty}A_{i} \\=0.413\times 239.6\times 0.7 \\=69.27\;kg/s$

Thrust of the engine is given as

$T=\dot{m}_{a}\left [ \left ( u_{e}-u_{\infty } \right )+\left ( P_{e}-P_{\infty } \right ) \right ]A_{e}$
$\Rightarrow T=69.27 \left [ \left ( 500-239.6 \right )+\left ( 60-26.5 \right ) \right ]\times 10^{3}\times 0.4$

$=31.44\;kN$