GATE AE (Aerospace Engineering) Rockets previous year questions from the Propulsion section, with figures and the official answer key where available.
Propulsion - Rockets
An ideal rocket has characteristic exhaust velocity of 1200 m/s, mass flow rate of 75 kg/s, thrust coefficient of 1.5, and nozzle throat area of 0.025 m$^2$. The chamber pressure in kPa and the specific impulse due to gravity in seconds are ________, respectively. Assume that the acceleration due to gravity is 9.8 m/s$^2$.
Official answer: A
Propulsion - Rockets
Consider a launch vehicle of mass 10 tons being launched vertically. The vehicle has 8 tons of propellant, which burns completely at a constant rate over 50 s. If the engine specific impulse is 250 s, and the acceleration due to gravity at sea level is $g_0$, the acceleration experienced by the vehicle at lift-off is ________.
Official answer: C
Propulsion - Rockets
An ideal two-stage rocket has identical specific impulse and structural coefficient for its two stages. For an optimized rocket, the two stages have identical payload ratio as well. The payload is 2 tons and the initial mass of the rocket is 200 tons. The mass of the second stage of the rocket (including the final payload mass) is ____ tons.
Official answer: C
Propulsion - Rockets
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).
Official answer: 430.0 to 442.0
Propulsion - Rockets
A chemical rocket with an ideally expanded flow through the nozzle produces $5 \times 10^6$ N thrust at sea level. The specific impulse of the rocket is 200 s and acceleration due to gravity at the sea level is 9.8 m/s$^2$. The propellant mass flow rate out of the rocket nozzle is _________ kg/s (rounded off to the nearest integer).
Official answer: 2500 to 2600
Propulsion - Rockets
Two missiles $A$ and $B$ powered by solid rocket motors have identical specific impulse, liftoff mass of 5600 kg each, and burn durations of $t_A = 30$ s and $t_B = 70$ s, respectively. The propellant mass flow rates, $\dot{m}_A$ and $\dot{m}_B$, for missiles $A$ and $B$, respectively, are given by $$\dot{m}_A = 120\ \text{kg/s},\quad 0 \le t \le 30$$ $$\dot{m}_B = 70\ \text{kg/s},\quad 0 \le t \le 70$$ Neglecting gravity and aerodynamic forces, the relationship between the final velocities $V_A$ and $V_B$ of missiles $A$ and $B$, respectively, is given by
Official answer: C
Propulsion - Rockets
The region of highest static temperature in a rocket engine and the region of highest heat flux are ____________, respectively.
Official answer: B
Propulsion - Rockets
A rocket operates at an absolute chamber pressure of 20 bar to produce thrust, $F_1$. The hot exhaust is optimally expanded to 1 bar (absolute pressure) using a convergent-divergent nozzle with exit to throat area ratio $\left(\dfrac{A_e}{A_t}\right)$ of 3.5 and thrust coefficient, $C_{F,1} = 1.42$. The same rocket when operated at an absolute chamber pressure of 50 bar produces thrust $F_2$ and the thrust coefficient is $C_{F,2}$. Which of the following statement(s) is/are correct?
Official answer: B, D
Propulsion - Rockets
A rocket has an initial mass of 150 kg. After operating for a duration of 10 s, its final mass is 50 kg. If the acceleration due to gravity is 9.81 m/s$^2$ and the thrust produced by the rocket is 19.62 kN, the specific impulse of the rocket is
Official answer: C
Propulsion - Rockets
For a given chamber pressure, the thrust of a rocket engine is highest when
Official answer: B
Propulsion - Rockets
A launch vehicle has a main rocket engine with two identical strap-on motors, all of which fire simultaneously during the operation. The main engine delivers a thrust of 6300 kN with a specific impulse of 428 s. Each strap-on motor delivers a thrust of 12000 kN with specific impulse of 292 s. The acceleration due to gravity is 9.81 m/s$^2$. The effective (combined) specific impulse of the vehicle is _______ s.
Official answer: 310 to 315
Propulsion - Rockets
In a particular rocket engine, helium propellant is heated to 6000 K and 95% of its total enthalpy is recovered as kinetic energy of the nozzle exhaust. Consider helium to be a calorically perfect gas with specific heat at constant pressure of 5200 J/kgK. The exhaust velocity for such a rocket for an optimum expansion is _____ m/s.
Official answer: 7690 to 7710
Propulsion - Rockets
A rocket, with a total lift-off mass of 10000 kg, moves vertically upward from rest under a constant gravitational acceleration of 9.81 m/s$^2$. The propellant mass of 8400 kg burns at a constant rate of 1200 kg/s. If the specific impulse of the rocket engine is 240 s, neglecting drag, the burnout velocity in m/s is
Official answer: C
Propulsion - Rockets
A small rocket having a specific impulse of 200 s produces a total thrust of 98 kN, out of which 10 kN is the pressure thrust. Considering the acceleration due to gravity to be 9.8 m/s$^2$, the propellant mass flow rate in kg/s is
Official answer: C
Propulsion - Rockets
A stationary two stage rocket with initial mass of 16000 kg, carrying a payload of 1000 kg, is fired in a vertical trajectory from the surface of the earth. Both the stages of the rocket have same specific impulse, $I_{sp}$, of 300 s and same structural coefficient of 0.14. The acceleration due to gravity is 9.8 m/s$^2$. Neglecting drag and gravity effects and considering both the stages with same payload ratio, the terminal velocity attained by the payload in m/s is __________________.
Official answer: 6050 to 6250
Propulsion - Rockets
A cryogenic rocket has a specific impulse of 455 s and characteristic velocity of 2386 m/s. The value of thrust coefficient for this rocket is
Official answer: C