A turbojet powered aircraft is flying at Mach number 0.8 at an altitude of10 km. What is the thrust of the 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?
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
\[T=\dot{m}_{a}\left [ \left ( u_{e}-u_{\infty } \right )+\left ( P_{e}-P_{\infty } \right ) \right ]A_{e}\]
\[\Rightarrow T=69.27 \left [ \left ( 500-239.6 \right )+\left ( 60-26.5 \right ) \right ]\times 10^{3}\times 0.4\]
\[=31.44\;kN\]
