Two-dimensional potential flow theory - Aerodynamics - Aerospace Engineering Previous Year Questions

1

2007 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2007

A circular cylinder is placed in a uniform stream of ideal fluid with its axis normal to the flow. Relative to the forward stagnation point, the angular positions along the circumference where the speed along the surface of the cylinder is equal to the free stream speed are

A

30, 150, 210 and 330 degrees

B

45, 135, 225 and 315 degrees

C

0, 90, 180 and 270 degrees

D

60, 120, 240 and 300 degrees

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2

2008 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2008

Consider 2-D flow with stream function \(\psi = \frac{1}{2} \ln (\sqrt{x^2 + y^2})\). The absolute value of circulation along a unit circle centered at \((x=0, y=0)\) is

A

0

B

1

C

\(\pi/2\)

D

\(\pi\)

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3

2009 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2009

For two-dimensional irrotational and incompressible flows

A

Both potential and stream functions satisfy the Laplace equation.

B

Potential function must satisfy the Laplace equation but the stream function need not.

C

Stream function must satisfy the Laplace equation but the potential function need not.

D

Neither the stream function nor the potential function need to satisfy the Laplace equation.

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4

2010 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2010

If \(\phi\) is the potential function for an incompressible irrotational flow, and u and v are the Cartesian velocity components, then which one of the following combinations is correct?

A

\(u = \frac{\partial \phi}{\partial x} , v = \frac{\partial \phi}{\partial y}\)

B

\(u = -\frac{\partial \phi}{\partial y} , v = \frac{\partial \phi}{\partial x}\)

C

\(u = -\frac{\partial \phi}{\partial y} , v = \frac{\partial \phi}{\partial y}\)

D

\(u = \frac{\partial \phi}{\partial x} , v = \frac{\partial \phi}{\partial y}\)

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5

2016 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2016

The maximum value of coefficient of lift (\( C_l \)) for a 2D circular cylinder, provided at least one stagnation point lies on the cylinder surface, is predicted by the potential flow theory to be

A

\(\pi/2 \)

B

\(\pi \)

C

\(2\pi \)

D

\(4\pi \)

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6

2018 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2018

In a low-speed wind tunnel, the angular location(s) from the front stagnation point on a circular cylinder where the static pressure equals the free-stream static pressure, is

A

\(\pm 38^0 \)

B

\(\pm 30^0 \)

C

\(\pm 60^0 \)

D

\(0^0 \)

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7

2020 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2020

A pair of infinitely long, counter-rotating line vortices of the same circulation strength \( \Gamma \) are situated a distance \( h \) apart in a fluid, as shown in the figure. The vortices will

A

rotate counter-clockwise about the midpoint with the tangential velocity at the line vortex equal to \(\frac{\Gamma}{2\pi h} \)

B

rotate counter-clockwise about the midpoint with the tangential velocity at the line vortex equal to \(\frac{\Gamma}{4\pi h} \)

C

translate along \(+y \) direction with velocity at the line vortex equal to \(\frac{\Gamma}{2\pi h} \)

D

translate along \(+y \) direction with velocity at the line vortex equal to \(\frac{\Gamma}{4\pi h} \)

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8

2022 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2022

Consider a two-dimensional potential flow over a cylinder. If the freestream speed is $U_\infty$, the maximum speed on the cylinder surface is

A

\(\frac{U_\infty}{2}\)

B

\(\frac{3U_\infty}{2}\)

C

2U_\infty

D

\(\frac{4U_\infty}{3}\)

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9

2023 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2023

In a two-dimensional potential flow, the doublet is a limit of the superposition of

A

a uniform stream and a source

B

a source and a sink of equal strength

C

a uniform stream and a sink

D

a source and a vortex

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10

2023 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2023

In a potential flow, a uniform stream of strength \(U\) directed along the x-axis and four line sources (2-dimensional) of strengths \(\frac{\pi}{2}\), \(-\frac{\pi}{3}\), \(\frac{\pi}{4}\), \(-\frac{\pi}{5}\) are placed along the x-axis at \(x = 0, 1, 2, 3\), respectively. The strength of an additional line source to be placed at \(x = 4\) such that a closed streamline encircles all five sources is _____. (round off to two decimal places).

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11

2024 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2024

In the context of steady, inviscid, incompressible flows, consider the superposition of a uniform flow with speed \( U \) along the positive x-axis (from left to right), and a source of strength \( A \) located at the origin. Which one of the following statements is NOT true regarding the location of the stagnation point of the resulting flow?

A

It is located to the left of the origin

B

It moves closer to the origin for increasing \(A \), while \(U \) is held constant

C

It moves closer to the origin for increasing \(U \), while \(A \) is held constant

D

It is located along the x-axis

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12

2025 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2025

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?

A

The vortices translate downwards together with a velocity \(\frac{\Gamma}{2\pi a}\)

B

The vortices translate upwards together with a velocity \(\frac{\Gamma}{2\pi a}\)

C

The vortices rotate clockwise around each other about their centroid O.

D

The vortices rotate counter-clockwise around each other about their centroid O.

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13

2025 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2025

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/m³. The circulation around the cylinder is ____ m²/s (rounded off to two decimal places).

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14

2026 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2026

In fluid dynamics, d’Alembert’s paradox refers to which one of the following?

A

Deviation of drag from \(D \propto v^2 \) at very low speeds

B

Deviation of drag from \(D \propto v^2 \) at high subsonic speeds

C

Prediction of zero drag by potential flow theory

D

Presence of shocks in transonic flows

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15

2026 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2026

The velocity potential function \( (\varphi) \) given below represents which one of the following? \[ \varphi = 5x - 12y \]

A

Doublet

B

Irrotational vortex

C

Source

D

Uniform flow

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16

2026 · Aerospace Engineering · Aerodynamics · Two-dimensional potential flow theory

Aerospace Engineering (AE) 2026

Consider the flow over an oval modeled using the elementary potential flows as shown below. U represents uniform flow velocity and Γ represents circulation around an irrotational line vortex.

Which of the following statements is/are TRUE for this model?

A

Increasing U enlarges the oval

B

Increasing Γ enlarges the oval

C

Interchanging the sense of the two vortices does not alter the oval

D

Moving the vortices too far apart causes the oval to break up

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