List of top Questions asked in GATE AE

A supersonic aircraft has an air intake ramp that can be rotated about the leading edge \(O\) such that the shock from the leading edge meets the cowl lip as shown. Select all the correct statement(s) as per oblique shock theory when flight Mach number \(M\) increases.

A perfect gas stored in a reservoir exhausts through a convergent nozzle. The jet emerges at choked conditions with average velocity $u$. If reservoir pressure $p_0$ increases while $T_0$ remains constant, determine effect on $M, u, T, p, \rho$.

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.

Given vectors \[ \vec{A} = 9\hat{i} - 5\hat{j} + 2\hat{k}, \vec{B} = 11\hat{i} + 4\hat{j} + \hat{k}, \vec{C} = -7\hat{i} + 14\hat{j} - 3\hat{k} \] which of the following statements are TRUE?

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? 

Consider the International Standard Atmosphere (ISA) with $h$ being the geopotential altitude (in km) and $\dfrac{dT}{dh}$ being the temperature gradient (in K/m). Which of the following combination(s) of $\Big(h, \dfrac{dT}{dh}\Big)$ is/are correct as per ISA?

A rigid bar $AB$ of length 3 m is subjected to a uniformly distributed load of $100 \,\text{N/m}$. The bar is supported at $A$ (pin) and by rod $CD$ connected at $D$. The rod $CD$ has axial stiffness $40 \,\text{N/mm}$, and $C$ is pinned. Find the vertical deflection at point $D$ (in mm). 

A cantilever beam of length $2a$ is loaded at the tip with force $F$. The beam is supported in the middle by a roller (pin). Find the reaction moment at the built-in end of the beam as $\alpha Fa$, where $\alpha =$ ....................... (round off to one decimal place). 

The shear flow distribution in a single cell, thin-walled beam under a shear load $S_y$ is shown in the figure. The cell has horizontal symmetry with booms marked $1$ to $4$. The shear modulus $G$ is same for all walls, and the area of the cell is $135000 \,\text{mm}^2$. With respect to point $O$, find the distance of shear centre $S$ (in mm). (round off to nearest integer) 

An airplane with wing planform area $S=20\,\text{m}^2$ and weight $W=8\,\text{kN}$ is flying straight and level with a speed of $V=100\,\text{m/s}$. The total drag coefficient is $C_D=0.026$ and the air density is $\rho=0.7\,\text{kg/m}^3$. The total thrust required to introduce a steady climb at angle $\gamma=0.1$ radians is ............. N. (round off to the nearest integer)
The maximum permissible load factor and the maximum lift coefficient for an airplane are $n_{\max}=7$ and $C_{L,\max}=2$, respectively. For a wing loading $W/S=6500\ \text{N/m}^2$ and air density $\rho=1.23\ \text{kg/m}^3$, the speed yielding the highest possible turn rate in the vertical plane is .............. m/s. (round off to the nearest integer)
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)
Given $G=6.67\times10^{-11}\ \text{N\,m}^2\text{/kg}^2$, planet mass $M=6.4169\times10^{23}$ kg and radius $R=3390$ km, find the escape velocity (km/s). (round off to one decimal place)
A satellite is in a circular orbit around Earth with period $T=90$ minutes. Take Earth's radius $R_E=6370$ km, Earth's mass $M_E=5.98\times10^{24}$ kg, and $G=6.67\times10^{-11}\ \text{N\,m}^2\text{/kg}^2$. Find the altitude above mean sea level (km).
A centrifugal air compressor has inlet root diameter $D_1=0.25\,\text{m}$ and outlet impeller diameter $D_2=0.6\,\text{m}$. Pressure ratio $\pi_c=p_{02}/p_{01}=5.0$. Air at rotor inlet: $p_{01}=1\,\text{atm}$, $T_{01}=25^\circ\text{C}=298\,\text{K}$. Polytropic efficiency $\eta_p=0.8$, slip factor $\sigma=0.92$. Take $C_p=1.004\,\text{kJ/kg-K}$ and $\gamma=1.4$. Find the impeller speed (RPM). (round off to the nearest integer)
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 single degree-of-freedom spring–mass–damper system has viscous damping ratio $\zeta = 0.1$. The mass has initial displacement of $10$ cm without velocity. After exactly two complete cycles of damped oscillation, find amplitude of displacement (in cm, round off to two decimals).
A thin-walled cylindrical pressure vessel of yield strength $300$ MPa has radius-to-thickness ratio $R/t = 100$. Using von Mises yield criterion, find internal pressure at failure. (round off to two decimals)
Solve differential equation: \[ x^2 \frac{d^2y}{dx^2} + 4x \frac{dy}{dx} + 2y = 0, x \geq 1 \] with initial conditions $y=0, \; y'(1)=1$ at $x=1$. Find $y$ at $x=2$. (round off to two decimals)
The operating characteristics of a pump are measured as $C_p = a \Phi^2$, where \[ C_p = \frac{P}{\rho \omega^3 D^5}, \Phi = \text{flow coefficient}, a=\text{constant}. \] If $\omega$ increases by 25% (i.e. $\omega \to 1.25\omega$) and the flow coefficient $\Phi$ is constant, determine $\alpha$ such that $P$ becomes $\alpha P$. (round off to two decimal places)
A thin cambered airfoil has lift coefficient $C_l=0$ at angle of attack $\alpha=-1^\circ$. Estimate $C_l$ at $\alpha=4^\circ$, assuming stall occurs at much higher $\alpha$. (round off to two decimal places)
In potential flow, a uniform stream of strength $U$ flows along x-axis. Line sources of strength $\pi/2, -\pi/3, \pi/4, -\pi/5$ are placed at $x=0,1,2,3$ respectively. Find strength of an additional line source at $x=4$ such that a closed streamline encircles all five sources. (round off to two decimal places)
Enstrophy is defined as square of magnitude of vorticity. For velocity field \[ \vec{V} = (4x - 1.5y + 2.5z)\hat{i} + (1.5x - 1.5y)\hat{j} + (0.7xy)\hat{k}, \] find enstrophy at $(1,1,1)$. (round off to two decimal places)
For an airfoil, which of the relations about the critical Mach number $M_{cr}$ and drag divergence Mach number $M_{dd}$ are correct?
Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?