Velocity Potential and Elementary Flows - Potential Flows - Engineering Sciences Previous Year Questions

1

2007 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2007

If the source and sink are placed in a uniform approach stream, the resulting external flow corresponds to that

A

of a doublet

B

over a circular cylinder

C

over a Rankine half-body

D

over a Rankine oval

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2

2007 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2007

A uniform stream of an ideal fluid with velocity \( U \) and pressure \( p_\infty \) flows past a circular cylinder as shown in the figure below. The fluid velocity on the cylinder wall is given by \( V_\theta = 2U \sin \theta \). The pressure coefficient is defined as \( C_p = \frac{p - p_\infty}{0.5 \rho U^2} \). The minimum value of \( C_p \) on the surface of the cylinder is

A

1

B

-1

C

-3

D

-4

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3

2008 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2008

A potential function can be defined for a flow if and only if it is

A

laminar

B

incompressible

C

steady

D

irrotational

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4

2008 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2008

What is the radius of the cylinder?

A

\(R = \sqrt{\frac{\mu}{2\pi U}} \)

B

\(R = \sqrt{\frac{2\pi U}{\mu}} \)

C

\(R = \sqrt{\frac{\mu}{\Gamma - 2\pi U}} \)

D

\(R = \sqrt{\frac{\Gamma - 2\pi U}{\mu}} \)

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5

2008 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2008

Where are the stagnation points located?

A

\(\theta = 0 \) and \(\theta = \pi \)

B

\(\theta = \sin^{-1} \left( \frac{\Gamma}{4\pi U R} \right) \) and \(\theta = \pi - \sin^{-1} \left( \frac{\Gamma}{4\pi U R} \right) \)

C

\(\theta = \frac{\pi}{2} \) and \(\theta = -\frac{\pi}{2} \)

D

\(\theta = \cos^{-1} \left( \frac{\Gamma}{4\pi U R} \right) \) and \(\theta = 2\pi - \cos^{-1} \left( \frac{\Gamma}{4\pi U R} \right) \)

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6

2008 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2008

The stream function for a potential flow around a corner is given by ψ(x, y) = kxy, where k is a constant. The slopes of the streamline and the potential line passing through the point (1,1) are respectively

A

1 and -1

B

-1 and 1

C

1 and 1

D

-1 and -1

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7

2009 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2009

Common Data for Questions 19 and 20:
A long cylindrical object submerged in still water is moving at a constant speed of 5 m/s perpendicular to its axis, as shown in the figure. Neglect viscous effects and assume free stream pressure to be 100 kPa.
The fluid velocity at point P with respect to the cylinder will be approximately

A

3.5 m/s

B

5 m/s

C

7 m/s

D

10 m/s

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8

2010 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2010

Consider an ideal fluid flow past a circular cylinder shown in the figure below. The peripheral velocity at a point P on the surface of the cylinder is

A

0

B

\(U_\infty\)

C

\(U_\infty \sin \theta\)

D

\(2 U_\infty \sin \theta\)

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9

2011 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2011

The drags due to potential flow past a cylinder of diameter D cm and a slender airfoil of chord length D cm are compared. Assuming unit depth for both the bodies, which one of the following would be TRUE?

A

The drag on the cylinder is greater

B

The drag on the airfoil is greater

C

Both the drags are equal

D

Additional data is needed to compare the drags

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10

2011 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2011

The velocity potential \(\phi(x, y)\) for the flow is

A

\(2x - 2y + \text{const}.\)

B

\(2xy + \text{const}.\)

C

\(x^2 + y^2 + \text{const}.\)

D

\(x^2 - y^2 + \text{const}.\)

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11

2012 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2012

In a potential flow, the superposition of the stream functions of a uniform flow and a line source gives rise to a dividing streamline representing

A

Rankine’s half-body

B

infinite circular cylinder

C

infinite rotating circular cylinder

D

infinite elliptical cylinder

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12

2013 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2013

Flow past a circular cylinder can be produced by superposition of the following elementary potential flows:

A

Uniform flow, doublet

B

Uniform flow, vortex

C

Source, vortex

D

Sink, vortex

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13

2013 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2013

The stream function for a potential flow field is given by \(\psi = x^2 - y^2\). The corresponding potential function, assuming zero potential at the origin, is

A

\(x^2 + y^2\)

B

\(2xy\)

C

\(x^2 - y^2\)

D

\(x - y\)

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14

2014 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2014

Flow around a Rankine half-body is represented by the superposition of

A

source and vortex flows.

B

source and uniform flows.

C

vortex and uniform flows.

D

source, vortex and uniform flows.

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15

2014 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2014

A source with a strength of \(k_1\) and a vortex with a strength of \(k_2\) are located at the origin. The resultant velocity at a radial distance \(r\) from the origin due to the superposition of the source and vortex is expressed as

A

\(\frac{k_1 + k_2}{r}\)

B

\(\frac{\sqrt{k_1^2 + k_2^2}}{r}\)

C

\(\frac{\sqrt{k_1^2 - k_2^2}}{r}\)

D

\(\frac{k_1 - k_2}{r}\)

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16

2014 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2014

In a steady state two-dimensional potential flow field due to a point source, the acceleration of a particle at a distance \( r \) from the point source is

A

proportional to \(r^{-1} \).

B

proportional to \(r \).

C

a constant.

D

proportional to \(r^{-3} \).

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17

2015 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2015

Consider a combined forced-free vortex. The central region with radius \(R\) and angular velocity \(\omega\) is the forced vortex and the rest is the free vortex. The pressure at the edge of the combined vortex is \(p_o\). If the density of the fluid is \(\rho\), the pressure at the center of the combined vortex is

A

\(p_o - \rho \omega^2 R^2\)

B

\(p_o - \frac{1}{2} \rho \omega^2 R^2\)

C

\(p_o + \frac{1}{2} \rho \omega^2 R^2\)

D

\(p_o + \rho \omega^2 R^2\)

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18

2015 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2015

Consider a two-dimensional potential flow field with the radial and tangential velocity components, \(v_r = \frac{m}{2\pi r}\) and \(v_\theta = \frac{k}{2\pi r}\), respectively, where \(m\) and \(k\) are constants. The stream function is such that it increases along the direction of traverse of a line in the flow field if the flow is from left to right across that line. The stream function \(\psi\) for this flow field, with \(\psi = 0\) at \(r = a\) and \(\theta = 0\), is

A

\(\frac{m\theta}{2\pi} + \frac{k}{2\pi} \ln \frac{r}{a}\)

B

\(\frac{m\theta}{2\pi} - \frac{k}{2\pi} \ln \frac{r}{a}\)

C

\(\frac{m\theta}{2\pi} + \frac{k}{2\pi} \ln \frac{r}{a}\)

D

\(\frac{m\theta}{2\pi} - \frac{k}{2\pi} \ln \frac{r}{a}\)

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19

2016 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2016

Velocity potential and stream function in polar coordinates ( \( r \), \( \theta \) ) for a potential flow over a cylinder with radius \( R \) is given as \( \phi = U_{\infty} (r+\frac{R^2}{r})\cos\theta \) and \( \psi = U_{\infty} (r-\frac{R^2}{r})\sin\theta \), respectively. Here, \( U_{\infty} \) denotes uniform freestream velocity, and \( \theta \) is measured counter clockwise as shown in the figure. How does the velocity magnitude, \( q \), over the surface of the cylinder will vary?

A

\(q=2U_{\infty}\cos\theta \)

B

\(q=2U_{\infty}\sin 2\theta \)

C

\(q=U_{\infty}\cos 2\theta \)

D

\(q=2U_{\infty}\sin\theta \)

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20

2016 · Engineering Sciences · Potential Flows · Velocity Potential and Elementary Flows

Engineering Sciences (XE) 2016

If \(\phi(x, y)\) is velocity potential and \(\psi(x, y)\) is stream function for a 2-D, steady, incompressible and irrotational flow, which one of the followings is incorrect?

Check answer

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