GATE 2021 AE – Question 53
A turbojet has flight speed 270 m/s, inlet static enthalpy 260 kJ/kg, fuel/air ratio 0.019, fuel heating value 44.5 MJ/kg, heat loss 25 kJ/kg air and exhaust static enthalpy 912 kJ/kg. Its exhaust speed is ___ m/s.
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Correct answer: 603.80 to 609.86
Explanation
Apply the **steady-flow energy equation** to the engine (inlet to exit), per kg of air:
$$h_1+\frac{V_1^2}{2}+f\,Q_{fuel}-q_{loss}=(1+f)\left(h_e+\frac{V_e^2}{2}\right).$$
Here the fuel flow is $f=0.019$ per kg of air, the fuel adds $fQ_{fuel}=0.019\times44.5\times10^6=845\,500$ J, the heat loss is 25 000 J, the inlet static enthalpy is 260 000 J/kg and the flight speed is 270 m/s. (The fuel's own enthalpy is neglected.)
**Left side:**
$$260\,000+\frac{270^2}{2}+845\,500-25\,000=260\,000+36\,450+845\,500-25\,000=1\,116\,950\text{ J/kg air}.$$
**Per kg of exhaust gas** (divide by $1+f=1.019$):
$$h_e+\frac{V_e^2}{2}=\frac{1\,116\,950}{1.019}=1\,096\,124\text{ J/kg}.$$
**Exhaust speed**, with $h_e=912\,000$ J/kg:
$$\frac{V_e^2}{2}=1\,096\,124-912\,000=184\,124\;\Rightarrow\;V_e=\sqrt{368\,248}=\mathbf{606.8\ m/s}.$$