GATE Overflow for GATE XE - Recent questions in Elementary Potential Flows

GATE XE 2026 | Question: 24

Tue, 24 Feb 2026 15:48:27 +0000

A two-dimensional source flow (with stream function, $\psi_{1}=m \tan ^{-1} \dfrac{y}{x}$ ) is placed at the origin in a uniform flow (with stream function, $\psi_{2}=U y$ ). Here, the strength of the source is $m$ and the freestream velocity is $U$. The velocity components $u$ and $v$ of the combined flow in $x$ - and $y$-directions, respectively, are

$u=U+\dfrac{m x}{x^{2}+y^{2}} ; v=\dfrac{m y}{x^{2}+y^{2}}$
$u=\dfrac{m x}{x^{2}+y^{2}} ; v=U+\dfrac{m y}{x^{2}+y^{2}}$
$u=U+\dfrac{m x}{x^{2}+y^{2}} ; v=-\dfrac{m y}{x^{2}+y^{2}}$
$u=\dfrac{m x}{x^{2}+y^{2}} ; v=U-\dfrac{m y}{x^{2}+y^{2}}$

GATE XE 2025 | Question: 30

Sun, 04 May 2025 19:08:03 +0000

A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together.

Which one of the following options correctly represents the nature of the product of the strength and the distance between them during approach?

Remains always constant
Continuously decreases
Continuously increases
First increases and then continuously decreases after reaching a maximum

GATE XE 2024 | Question: 31

Sun, 21 Jul 2024 16:42:21 +0000

The velocity potential function in a two-dimensional flow field is given by $\phi(x, y)=-\left(a x y+b x^{2}-b y^{2}\right) \mathrm{m}^{2} / \mathrm{s}$ where $\mathrm{a}=2$ per second and $\mathrm{b}=0.5$ per second. The magnitude of the velocity $\text{(in $\mathrm{m} / \mathrm{s}$, answer in integer)}$ at $x=2 \mathrm{~m}$, $y=1 \mathrm{~m}$ is ____________.

GATE XE 2023 | Question: 17

Wed, 14 Feb 2024 18:10:04 +0000

An inviscid steady incompressible flow is formed by combining a uniform flow with velocity $U_{\infty}$ and a clockwise vortex of strength $K$ at the origin, as shown in the figure. Velocity potential $(\phi)$ for the combined flow in polar coordinate $(r, \theta)$ is

$\phi=\frac{K \theta}{2 \pi}-U_{\infty} r \cos \theta$
$\phi=\frac{K \theta}{2 \pi}-U_{\infty} r \sin \theta$
$\phi=K \ln r+U_{\infty} r \cos \theta$
$\phi=-K \ln r+U_{\infty} r \sin \theta$

GATE XE 2023 | Question: 23

Wed, 14 Feb 2024 18:09:58 +0000

\begin{tabular}{l|l}
Q. 33 & For a potential flow, the fluid velocity is given by $\vec{V}(x, y)=u \hat{\imath}+v \hat{\jmath}$. The slope \\
of the potential line at $(x, y)$ is \\
\hline

& $\frac{u}{v}$ \\
\hline
& $\frac{v}{u}$ \\
\hline
& $-\frac{u}{v}$ \\
& $-\frac{v}{u}$
\end{tabular}

GATE XE 2022 | Question: 18

Fri, 17 Feb 2023 06:52:25 +0000

A flow has a velocity potential given by $\phi=A x^{3}$ where ' $A$ ' is a non-zero constant. Which of the following statement(s) is/are true about the flow?

The flow is incompressible.
The flow is irrotational.
The flow has local acceleration.
The flow has convective acceleration.

GATE XE 2022 | Question: 23

Fri, 17 Feb 2023 06:52:21 +0000

A two-dimensional flow field is described by a combination of a source of strength $m$ at the origin and a uniform flow, $U$, in the positive $x$-direction such that the velocity potential is given by
$\phi=U x+\frac{m}{2 \pi} \ln \sqrt{x^{2}+y^{2}}$

The stagnation streamline is shown in the figure. Find the distance $a a^{\prime}$.

$\quad \frac{m}{U}$
$\quad \frac{2 m}{U}$
$\quad \frac{8 m}{U}$
$\quad \frac{m}{2 U}$