GATE AE 2026 • Q43
MCQ • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
An experimental study is planned to map out the low-Reynolds number incompressible steady two-dimensional aerodynamic characteristics of a promising novel airfoil. The operational parameters of the problem are the speed, density and viscosity of the freestream, the chord of the airfoil and its angle of attack. If the objective is to achieve this with the minimum number of test runs Nmin while taking 10 equally-spaced test values of each independent parameter of the problem in a suitable range, then Nmin is ________.
Official Key: B ➔
GATE AE 2025 • Q18
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
For a NACA 4415 airfoil, the location of maximum camber, as a fraction of the chord length from the leading edge, is ______.
Official Key: B ➔
GATE AE 2025 • Q19
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
A positively cambered airfoil is placed in a uniform flow (velocity, U∞) at its zero-lift angle of attack. M is the corresponding pitching moment. Which one of the following representations accurately describes this scenario?
Official Key: A ➔
GATE AE 2025 • Q20
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Consider a pair of point vortices with clockwise circulation $\Gamma$ each. The distance between their centers is a, as shown in the figure. Assume two-dimensional, incompressible, inviscid flow. Which one of the following options is correct?
Official Key: C ➔
GATE AE 2025 • Q34
NAT • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m^3. The circulation around the cylinder is ____ m^2/s (rounded off to two decimal places).
Official Key: 0.165 ➔
GATE AE 2025 • Q36
MCQ • 2M
Subtopic: Finite Wing Theory & Induced Drag
A lifting surface has a spanwise circulation distribution of $\Gamma(\theta) = A \sin 3\theta$ (where $A \neq 0$) over its span $-\frac{b}{2} \le y \le \frac{b}{2}$, and $y = -\frac{b}{2} \cos \theta$ is the spanwise coordinate. Furthermore, the downwash varies along the span as $w(\theta) = V_\infty \left(\frac{3A \sin 3\theta}{\sin \theta}\right)$, where $V_\infty$ is the freestream velocity. Which one of the following options represents the total lift ($L$) and induced drag ($D_i$)?
Official Key: B ➔
GATE AE 2025 • Q47
NAT • 2M
Subtopic: Finite Wing Theory & Induced Drag
A rectangular wing of 1.2 m chord length and aspect ratio 5 is tested in a wind tunnel at an air speed of 60 m/s. The density and the dynamic viscosity of air are 1.3 kg/m3 and 1.8×10-5 kg/m-s, respectively. A second rectangular wing of the same span, but with an aspect ratio of 6, is to be tested in the same tunnel at the same Reynolds number. The air speed at which the second test should be performed is _______ m/s (answer in integer).
Official Key: 72.0 ➔
GATE AE 2025 • Q52
NAT • 2M
Subtopic: Finite Wing Theory & Induced Drag
A jet-powered airplane is steadily climbing at a rate of 10 m/s. The air density is 0.8 kg/m^3, and the thrust force is aligned with the flight path. Using the information provided in the table below, the airplane's thrust to weight ratio is ______ (rounded off to one decimal place). Airplane speed 80 m/s Lift coefficient, CL 0.8 Aspect ratio 6 Oswald efficiency factor 0.8 Zero-lift drag coefficient 0.02
Official Key: 0.2 ➔
GATE AE 2024 • Q24
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Consider steady, incompressible, inviscid flow past two airfoils shown in the figure. The coefficient of pressure at the trailing edge of the airfoil with finite angle, shown in figure (I), is CPI while that at the trailing edge of the airfoil with cusp, shown in figure (II), is CPII. Which one of the following options is TRUE?
Official Key: C ➔
GATE AE 2024 • Q63
NAT • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
The figure (not to scale) shows a control volume to estimate the forces on the airfoil with elliptic cross-section. Surfaces 2 and 3 are streamlines. Velocity profiles are measured at the upstream end (surface 1) and at the downstream end (surface 4) of the control volume. The drag coefficient for the airfoil is defined as Cd = D 1 2 $\rho$ U∞ 2 c , where D is the drag force on the airfoil per unit span and is the density of the air. The static pressure, p , is constant over the entire surface of the control volume. Assuming the flow to be incompressible, two -dimensional and steady, the Cd for the airfoil is _________ (rounded off to 3 decimal places).
Official Key: 0.02 ➔
GATE AE 2024 • Q64
NAT • 2M
Subtopic: Finite Wing Theory & Induced Drag
An airplane of mass 1000 kg is in a steady level flight with a speed of 50 m/s. The wing has an elliptic planform with a span of 20 m and planform area 31.4 m^2. Assuming the density of air at that altitude to be 1 kg/m 3 and acceleration due to gravity to be 10 m/s^2, the induced drag on the wing is _________ N (rounded off to 1 decimal place).
Official Key: 64.0 ➔
GATE AE 2023 • Q17
MCQ • 1M
Subtopic: Finite Wing Theory & Induced Drag
An ideal glider has drag characteristics given by 0D D D i C C C=+ , where 2 DLi C KC= is the induced drag coefficient, LC is the lift coefficient, and K is a constant. For maximum range of the glider, the ratio 0DD i CC is
Official Key: A ➔
GATE AE 2023 • Q18
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
The figures shown in the options are schematics of airfoil shapes (not to scale). For a civilian transport aircraft designed for a cruise Mach number of 0.8, which among them is aerodynamically best suited as a wing section?
Official Key: D ➔
GATE AE 2023 • Q30
NAT • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
For studying wing vibrations, a wing of mass M and finite dimensions has been idealized by assuming it to be supported using a linear spring of equivalent stiffness k and a torsional spring of equivalent stiffness k as shown in the figure. The centre of gravity (CG) of the wing idealized as an airfoil is marked in the figure. The number of degree(s) of freedom for this idealized wing vibration model is _________. (Answer in integer)
Official Key: 2.0 ➔
GATE AE 2022 • Q40
MCQ • 2M
Subtopic: Finite Wing Theory & Induced Drag
Consider a conventional subsonic fixed-wing airplane. $e$ is the Oswald efficiency factor and $AR$ is the aspect ratio. Corresponding to the minimum $\left( \frac{C_D}{C_L^{3/2}} \right)$, which of the following relations is true?
Official Key: B ➔
GATE AE 2022 • Q51
NAT • 2M
Subtopic: Finite Wing Theory & Induced Drag
Consider a circulation distribution over a finite wing given by the equation below: $\Gamma(y) = \begin{cases} \Gamma_0 \left(1 - \frac{2y}{b}\right) & \text{if } 0 \le y \le \frac{b}{2} \\[6pt] \Gamma_0 \left(1 + \frac{2y}{b}\right) & \text{if } -\frac{b}{2} \le y \le 0 \end{cases}$ The wingspan $b$ is $10\text{ m}$, the maximum circulation $\Gamma_0$ is $20\text{ m}^2/\text{s}$, density of air is $1.2\text{ kg/m}^3$ and the free stream speed is $80\text{ m/s}$. The lift over the wing is ______ $\text{N}$ (rounded off to the nearest integer).
Official Key: 9650.0 ➔
GATE AE 2020 • Q43
NAT • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
The ratio of tangential velocities of a planet at the perihelion and the aphelion from the sun is 1.0339. Assuming that the planet's orbit around the sun is planar and elliptic, the value of the eccentricity of the orbit is _________ (round off to three decimal places).
Official Key: 0.017 ➔
GATE AE 2020 • Q45
NAT • 2M
Subtopic: Finite Wing Theory & Induced Drag
For a general aviation airplane with tail efficiency n = 0.95, horizontal tail volume ratio Vu = 0.453, downwash angle slope de = 0.35, wing lift curve slope C*a = 4.8 rad"', horizontal tail lift curve slope CLa= 4.4 rad"', shift in neutral point location as a percentage of mean aerodynamic chord is (round off to two decimal places).
Official Key: 1.0 ➔
GATE AE 2019 • Q15
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
The Mach number increases and the static temperature decreases. (C) The Mach number decreases and the static temperature increases. (D) Both the Mach number and the static temperature decrease. Q.7 For a NACA2415 airfoil of chord length c, which of the following is true?
Official Key: B ➔
GATE AE 2019 • Q48
NAT • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
For a symmetric airfoil at an angle of attack of $10^\circ$, assuming thin airfoil theory, the magnitude of the section lift coefficient $C_l$ is _________ (round off to 2 decimal places).
Official Key: 0.27 ➔
GATE AE 2019 • Q49
NAT • 2M
Subtopic: Finite Wing Theory & Induced Drag
The span-wise distribution of circulation over a finite wing of span $b = 10$ m is given by $\Gamma(y) = \Gamma_0 \sqrt{1 - (2y/b)^2}$. If $\Gamma_0 = 20$ m$^2$/s and the freestream velocity is 50 m/s at an air density of 1.2 kg/m$^3$, the induced drag (in N) on the wing is _________ (round off to 1 decimal place).
Official Key: 18.6 ➔
GATE AE 2019 • Q51
NAT • 2M
Subtopic: Finite Wing Theory & Induced Drag
Consider an airplane with a weight of 8000 N, wing area of 16 m$^2$, wing zero-lift drag coefficient of $C_{D0} = 0.02$, Oswald efficiency factor $e = 0.8$, and wing aspect ratio $AR = 8$. At sea level with $\rho = 1.225$ kg/m$^3$, the maximum lift-to-drag ratio $(L/D)_{\max}$ divided by 10 is _________ (round off to 2 decimal places).
Official Key: 1.34 ➔
GATE AE 2018 • Q40
MCQ • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
An aircraft with mass of 400,000 kg cruises at 240 m/s at an altitude of 10 km. Its lift to drag ratio at cruise is 15. Assuming g as 9.81 m/s^2, the power (in MW) needed for it to cruise is _______ (accurate to two decimal places).
Official Key: C ➔
GATE AE 2018 • Q43
MCQ • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
A pitot probe on an aircraft in a steady, level flight records a pressure of 55,000 N/m^2. The static pressure and density are 45,280 N/m2 and 0.6 kg/m^3, respectively. The wing area and the lift coefficient are 16 m2 and 2, respectively. The wing loading (in N/m^2) on this aircraft is _________ (accurate to one decimal place).
Official Key: B ➔
GATE AE 2017 • Q38
NAT • 2M
Subtopic: Finite Wing Theory & Induced Drag
An aircraft model was tested in a low speed wind-tunnel (Reynolds number based on mean chord $Re = 10^6$). The lift curve slope of the wing is $C_{L\alpha} = 4.5$ rad$^{-1}$. If the aspect ratio of the wing is 6 and Oswald efficiency factor is 0.9, the profile drag coefficient $C_{D0}$ is 0.015. At $C_L = 0.6$, the total drag coefficient $C_D$ of the wing is _________ (round off to 3 decimal places).
Official Key: 0.036 ➔
GATE AE 2017 • Q44
NAT • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
A conventional aircraft was analyzed to estimate the contribution of the vertical tail to the directional stability derivative $C_{n\beta}$. The vertical tail area is 2 m$^2$, moment arm is 5 m, wing area is 20 m$^2$, and wing span is 10 m. If the lift curve slope of the vertical tail is 4.0 rad$^{-1}$ and tail dynamic pressure ratio is 0.9, the contribution of the vertical tail $C_{n\beta, v}$ is _________ rad$^{-1}$ (round off to 2 decimal places).
Official Key: 0.18 ➔
GATE AE 2016 • Q17
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
The vector u is defined as y xeˆx eˆy u , where xeˆ and yeˆ are the unit vectors along x and y directions, respectively. If the vector is defined as u , then u ______.
Official Key: C ➔
GATE AE 2016 • Q31
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
The rate of change of moment coefficient with respect to the angle of attack, d dC m , at half chord point of a thin airfoil, as per approximations from the thin airfoil theory is
Official Key: C ➔
GATE AE 2016 • Q46
MCQ • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
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 Key: A ➔
GATE AE 2015 • Q12
MCQ • 1M
Subtopic: Finite Wing Theory & Induced Drag
For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing, with thin cambered airfoil section at small angles of attack, leads to
Official Key: A ➔
GATE AE 2014 • Q34
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
For inviscid, compressible flow past a thin airfoil, shown in the figure, free-stream Mach number and pressure are denoted by 𝑴𝑴∞ and 𝒑𝒑∞respectively. Ratio of pressure at point A and 𝒑𝒑∞is 0.8 and specific heat ratio is 1.4. If the Mach number at point A is 1.0 and rest of the flow field is subsonic, the value of 𝑴𝑴∞is
Official Key: B ➔
GATE AE 2014 • Q36
MCQ • 2M
Subtopic: Finite Wing Theory & Induced Drag
Induced velocity w at a point zz = zz1 along the lifting line can be calculated using the formula ww(zz1) = - 1 4$\pi \pi$ ∫ dd$\Gamma$ ddzz ss -ss 1 zz-zz1 ddzz. Given $\Gamma$2 $\Gamma$oo2 + zz2 ss2 = 1, wherezz, $\Gamma$oo and sare given in figure below. For theabove semi-elliptic distribution of circulation, $\Gamma$, the downwash velocity at any point zz1,for symmetric flight can be obtained as, ww(zz1) = $\Gamma$oo 4$\pi \pi$ss [$\pi \pi$ + zz1II], where II = zz1 ∫ ddzz �ss2-zz2�zz-zz1� ss -ss . Which of the following options is correct if the induced drag is DDii (given ∫ �1 - zz2 ss2 ss -ss ddzz = $\pi \pi$ss 2 )
Official Key: A ➔
GATE AE 2013 • Q17
NAT • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
The channel section of uniform thickness 2mm shown in the figure is subjected to a torque of 10 Nm. If it is made of a material with shear m odulus of 25 GPa, the twist per unit length in radians/m is _________ 300mm 600mm 300mm A 2013 AEROSPACE ENGINEERING - AE AE 8/19
Official Key: 0.125 ➔
GATE AE 2013 • Q30
NAT • 1M
Subtopic: Finite Wing Theory & Induced Drag
A glider is launched from a 500m high hilltop. Following data is available for the glider: Zero lift drag coefficient 0 0.02DC , aspect ratio 10AR and Oswald efficiency factor e = 0.95. The maximum range of the glider in km is _________
Official Key: 9.5 ➔
GATE AE 2013 • Q32
NAT • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Consider an airplane with rectangular straight wing at dihedral angle 010 . Lift curve slope of wing airfoil section (constant over the whole span of the wing) is 5.4 / .lcr a d The roll stability derivative, lC in per radian is __________
Official Key: -0.235 ➔
GATE AE 2013 • Q40
MCQ • 2M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
A horizontal rectangular plate ABCD is hinged at points A, B and C. AC and BD are diagonals of the plate. Downward force P is applied at D. The upward reactions RA, RB, and RC at points A, B and C, respectively, are
Official Key: B ➔
GATE AE 2012 • Q19
MCQ • 1M
Subtopic: Finite Wing Theory & Induced Drag
For a wing of aspect ratio AR, having an elliptical lift distribution, the induced drag coefficient is (where CL is the lift coefficient)
Official Key: B ➔
GATE AE 2012 • Q28
NAT • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
An airfoil generates a lift of 80 N when operating in a freestream flow of 60 m/s. If the ambient pressure and temperature are 100 kPa and 290 K respectively (specific gas constant is 287 J/kg-K), the circulation on the airfoil in m^2/s is ____.
Official Key: 1.15 ➔
GATE AE 2010 • Q46
MCQ • 2M
Subtopic: High-Lift Devices & Flaps
Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work sllently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause. Which of the following statements best sums up the meaning of the alive passage:
Official Key: A ➔
GATE AE 2009 • Q26
MCQ • 1M
Subtopic: Finite Wing Theory & Induced Drag
A symmetrical airfoil section produces a lift coefficient of 0.53 at an angle of attack of 5 degrees measured from its chord line. An untwisted wing of elliptical planform and aspect ratio 6 is made of this airfoil. At an angle of attack of 5 degrees relative to its chordal plane, this wing would produce a lift coefficient of
Official Key: D ➔
GATE AE 2007 • Q17
MCQ • 1M
Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
A 1 kg mass attached to a spring elongates it by 16mm. The mass is then pulled from its equilibrium position by 10mm and released from rest. Assuming the acceleration due to gravity of 9.81 m/s', the response of the mass in mm is given by
Official Key: B ➔