List of top Propulsion Questions

For an ideal gas, the specific heat at constant pressure is \(c_p = 1147 \ \mathrm{J\,kg^{-1}\,K^{-1}},\) and the ratio of specific heats is \(\gamma = 1.33.\)
What is the value of the gas constant \(R\) in \(\mathrm{J\,kg^{-1}\,K^{-1}}\)?
 

A surrogate liquid hydrocarbon fuel, approximated as \( \mathrm{C}_{10}\mathrm{H}_{12} \), is burned with dry air (79% \( \mathrm{N_2} \) and 21% \( \mathrm{O_2} \) by volume). How many moles of dry air are required for the stoichiometric combustion of 1 mole of this fuel at atmospheric conditions?

In an airbreathing gas turbine engine, the combustor inlet temperature is \(600\ \text{K}\). The heating value of the fuel is \(43.4\times 10^{6}\ \text{J/kg}\). Assume\(c_p = 1100\ \mathrm{J\,kg^{-1}\,K^{-1}}\) for air and burned gases, burner efficiency \(=100\%\), and fuel-air ratio \(f\ll 1\). Neglect kinetic energy at inlet/exit. What fuel-air ratio is required to achieve \(1300\ \text{K}\) at the combustor exit?}

An aircraft with a turbojet engine is flying with \(V_0=250\ \text{m s}^{-1}\) at an altitude where \(\rho=1\ \text{kg m}^{-3}\). The inlet area is \(A_0=1\ \text{m}^2\). The average exhaust-gas speed at the nozzle exit, with respect to the aircraft, is \(V_{e,\text{rel}}=550\ \text{m s}^{-1}\). The exit pressure equals ambient and fuel–air ratio is negligible. Find the uninstalled thrust (rounded to the nearest integer).

A turbojet–powered aircraft flies at \(V_0=250\ \text{m s}^{-1}\). The (uninstalled) thrust is \(T=60{,}000\ \text{N}\). Fuel heating value is \(44\times 10^{6}\ \text{J kg}^{-1}\); fuel flow is \(\dot m_f=3\ \text{kg s}^{-1}\). The engine thermal efficiency is \(35\%\). Exit pressure equals ambient. What is the propulsion efficiency (in %)?

Which of the following statements is/are TRUE for an axial turbine?
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 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).
A centrifugal compressor is designed to operate with air. At the leading edge of the tip of the inducer, the blade angle is $45^\circ$, and the relative Mach number is 1.0. The stagnation temperature of the incoming air is 300 K. Consider $\gamma = 1.4$. Neglect pre-whirl and slip. The inducer tip speed is .............. m/s (rounded off to the nearest integer).
In the \(T\!-\!s\) diagram shown, several ideal–gas processes are sketched: \(aa'\), \(bb'\), \(cc'\), \(dd'\). Match each curve to the process it best represents. \begin{center} \includegraphics[width=0.7\textwidth]{04.jpeg} \end{center}

A scramjet engine features an intake, isolator, combustor, and a nozzle, as shown. Station 3 indicates the combustor entry point. Assume stagnation enthalpy is constant between Stations 1 and 3, and air is a calorically perfect gas with specific heat ratio $\gamma$. Select the correct expression for Mach number $M_3$ at the inlet to the combustor from the options given.

Consider a one-dimensional inviscid supersonic flow in a diverging duct with heat addition ($Q_{in}$). Which of the following statement(s) is/are always TRUE? 

A gas turbine combustor burns methane with air at equivalence ratio $\phi=0.5$, where $\displaystyle \phi=\frac{(F/A)}{(F/A)_{\text{st}}}$. If the air mass-flow rate is $\dot m_{\text{air}}=20\ \text{kg/s}$, find the methane mass-flow rate (kg/s). (round off to two decimal places)
A cryogenic liquid rocket engine (expander cycle) burns liquid hydrogen and liquid oxygen at stoichiometry. The hydrogen mass-flow rate is $\dot m_{H_2}=32\,\text{kg/s}$, and the oxygen mass-flow rate satisfies $\dot m_{O_2}/\dot m_{H_2}=8$. Assuming the forward reaction dominates, find the rate of formation of $\mathrm{H_2O}$ (kmol/s). (round off to the nearest integer)
A supersonic vehicle powered by a ramjet engine is cruising at \(1000~\mathrm{m/s}\). The ramjet engine burns hydrogen in a subsonic combustor to produce thrust. The heat of combustion of hydrogen is \(120~\mathrm{MJ/kg}\). The overall efficiency of the engine \(\eta_0\), defined as the ratio of propulsive power to the total heat release in the combustor, is 40%. Taking \(g_0=10~\mathrm{m/s^2}\), the specific impulse of the engine is \underline{\hspace{1cm}} seconds. \;(round off to nearest integer)
Two missiles $A$ and $B$ powered by solid rocket motors have identical specific impulse, liftoff mass of $5600 \,\text{kg}$ each, and burn durations of $t_A = 30 \,\text{s}$ and $t_B = 70 \,\text{s}$, respectively. The propellant mass flow rates $\dot{m}_A$ and $\dot{m}_B$ are given as: \[ \dot{m}_A = 120 \,\text{kg/s}, \, 0 \leq t \leq 30, \dot{m}_B = 70 \,\text{kg/s}, \, 0 \leq t \leq 70 \] Neglecting gravity and aerodynamic forces, the relation between final velocities $V_A$ and $V_B$ is:
From the options given, select all that are true for turbofan engines with afterburners.
An aircraft is cruising with a forward speed \(V_a\) and the jet exhaust speed relative to the engine at the exit is \(V_j\). If \(V_j/V_a=2\), what is the propulsive efficiency?
In a single–spool aviation turbojet engine, which of the following is the correct relationship between the total work output \(W_t\) of a 2-stage axial turbine and the total work required \(W_c\) by a 6-stage axial compressor, neglecting losses?