GATE 2023 AE – Question 35
A ramjet vehicle flies at 1000 m/s, burns hydrogen of heat value 120 MJ/kg, and has overall efficiency 40% (propulsive power/heat release). With $g_0=10\ \mathrm{m/s^2}$, specific impulse (nearest integer seconds) is ___________.
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Correct answer: 4800
Explanation
**Definitions.**
- Overall efficiency: $\eta_o=\dfrac{\text{propulsive power}}{\text{heat release rate}}=\dfrac{F\,V}{\dot m_f\,Q}$.
- Specific impulse: $I_{sp}=\dfrac{F}{\dot m_f\,g_0}$.
**Eliminate the thrust.** From the first, $\dfrac{F}{\dot m_f}=\dfrac{\eta_o\,Q}{V}$, so
$$I_{sp}=\frac{\eta_oQ}{V\,g_0}.$$
**Numbers.**
$$I_{sp}=\frac{0.4\times120\times10^6}{1000\times10}=\frac{48\times10^6}{10^4}=\mathbf{4800\ s}.$$