GATE 2025 AE – Question 63
A monopropellant liquid rocket engine has 800 injectors of diameter 4 mm each, and with a discharge coefficient of 0.65. The liquid propellant of density 1000 kg/m$^3$ flows through the injectors. There is a pressure difference of 10 bar across the injectors. The specific impulse of the rocket is 1500 m/s. The thrust generated by the rocket is _____ kN (rounded off to one decimal place).
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Correct answer: 436.11 to 440.49
Explanation
The flow through one injector is $\dot m_1 = C_dA\sqrt{2\rho\Delta p} = 0.65 \times \pi(0.002)^2 \times \sqrt{2 \times 1000 \times 10^6} = 0.3653$ kg/s. For 800 injectors $\dot m = 292.2$ kg/s. The specific impulse is given as an effective exhaust velocity, 1500 m/s, so $T = \dot m I_{sp} = 292.2 \times 1500 = 4.383 \times 10^5$ N = 438.3 kN.