An airplane is flying at an altitude of \(10,000\,m\) with a turbojet engine at a velocity of \(900\, km/h\). The inlet and exit areas of the turbojet engine are \(0.9\,m^2\) and \(1.3\,m^2\). Find the thrust produced by the engine if the exhaust velocity and pressure are \(500\,m/s\) and \(32500\,N/m^2\).
An airplane is flying at an altitude of \(10,000\,m\) with a turbojet engine at a velocity of \(900\, km/h\). The inlet and exit areas of the turbojet engine are \(0.9\,m^2\) and \(1.3\,m^2\). Find the thrust produced by the engine if the exhaust velocity and pressure are \(500\,m/s\) and \(32500\,N/m^2\).
Thrust produced by a turbojet engine is given as
\[T = \dot m\left( {{V_e} – {V_\infty }} \right) + \left( {{P_e} – {P_\infty }} \right){A_e}\]
At an altitude of \(10 000\,m\) ,
\[{P_\infty } = 2.65 \times {10^4}\,N/{m^2}\]
\[{\rho _\infty } = 0.41351\,kg/{m^3}\]
\[{V_\infty } = \,900\,km/h = \,250\,m/s\]
\[\dot m = {\rho _\infty }{A_i}{V_\infty } = \,0.41351 \times 0.9 \times 250 = 93.04\,kg/s\]
Therefore , Thrust
\[T = 93.04\left( {500 – 250} \right) + \left( {32500 – 26500} \right)1.3 = 31060 \,N\]
