GATE 2025 AE – Question 64
An ideal ramjet with an optimally expanded exhaust is travelling at Mach 3. The ambient temperature and pressure are 260 K and 60 kPa, respectively. The inlet air mass flow rate is 50 kg/s. Exit temperature of the exhaust gases is 700 K. Fuel mass flow rate is negligible compared to air mass flow rate. Gas constant is $R$ = 287 J/kg/K, and specific heat ratio is $\gamma$ = 1.4. The thrust generated by the engine is ___ kN (rounded off to one decimal place).
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Correct answer: 30.9 to 31.2
Explanation
The flight speed is $V_0 = 3\sqrt{1.4 \times 287 \times 260} = 969.6$ m/s. In an ideal ramjet the total pressure is conserved, and with an optimally expanded exhaust $p_e = p_0$, so the exit Mach number is also 3. With the exit temperature of 700 K, $V_e = 3\sqrt{1.4 \times 287 \times 700} = 1591.0$ m/s. The thrust is $T = \dot m(V_e - V_0) = 50 \times (1591.0 - 969.6) = 31.07$ kN.
Official GATE 2025 answer key: https://gate2026.iitg.ac.in/doc/download/2025_Key/AE_Keys.pdf