GATE Overflow for GATE XE - Recent questions and answers in Bernoulli’s Equation and its Applications, Potential Flows

GATE XE 2026 | Question: 15

Tue, 24 Feb 2026 15:49:03 +0000

Three different siphons steadily discharge water at velocities $V_{\mathrm{I}}, V_{\mathrm{II}}$, and $V_{\mathrm{IIII}}$, as shown in the figure. The tubes of the siphons are of same diameter. If the frictional losses are neglected, which one of the following options is correct?

In the figure, $g$ is acceleration due to gravity; $a, b$, and $h$ are different heights.

$V_{\mathrm{I}}>V_{\mathrm{III}}>V_{\mathrm{II}}$
$V_{\mathrm{II}}>V_{\mathrm{II}}>V_{\mathrm{III}}$
$V_{\mathrm{I}}=V_{\mathrm{II}}=V_{\mathrm{III}}$
$V_{\mathrm{II}}>V_{\mathrm{III}}>V_{\mathrm{I}}$

GATE XE 2026 | Question: 20

Tue, 24 Feb 2026 15:48:41 +0000

A piezometer and a Pitot tube are tapped into a horizontal water pipe, as shown in the figure, where $h_{1}=4 \mathrm{~cm}, h_{2}=6 \mathrm{~cm}$ and $h_{3}=5 \mathrm{~cm}$. Consider the flow to be steady, laminar, and incompressible. Assume the density of water as $1000 \mathrm{~kg} \cdot \mathrm{~m}^{-3}$ and acceleration due to gravity as $10 \mathrm{~m} \cdot \mathrm{~s}^{-2}$. The water velocity $V$ (in $\mathrm{m} . \mathrm{s}^{-1}$) at the center of the pipe is $\_\_\_\_$. (rounded off to one decimal place)

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: 32

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

Consider the incompressible, steady and irrotational flow through a concentric reducer in a horizontal pipeline. The pipe diameter reduces from $d_{1}=12 \mathrm{~cm}$ to $d_{2}=4 \mathrm{~cm}$ as shown in figure. The pressure at position 1 and position 2 of the reducer is $p_{1}=55 \mathrm{kPa}$ and $p_{2}=27 \mathrm{kPa}$, respectively. The specific weight of fluid is $7 \mathrm{kN} / \mathrm{m}^{3}$. Acceleration due to gravity is $10 \mathrm{~m} / \mathrm{s}^{2}$.

Neglecting frictional effects, the mass flow rate $\text{(in $\mathrm{kg} / \mathrm{s}$, rounded off to two decimal places)}$ of the fluid through the reducer is ____________.

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: 16

Wed, 14 Feb 2024 18:10:05 +0000

Consider steady incompressible flow over a flat plate, where the dashed line represents the edge of the boundary layer, as shown in the figure. Which one among the following statements is true?

Bernoulli's equation can be applied in Region I between any two arbitrary points.
Bernoulli's equation can be applied in Region I only along a streamline.
Bernoulli's equation cannot be applied in Region II.
Bernoulli's equation cannot be applied in Region I.

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 2023 | Question: 30

Wed, 14 Feb 2024 18:09:52 +0000

Q. 40 Water (density $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ ) flows steadily with a flow rate of $0.05 \mathrm{~m}^{3} / \mathrm{s}$ through a venturimeter having throat diameter of $100 \mathrm{~mm}$. If the pipe diameter is $200 \mathrm{~mm}$ and losses are negligible, the pressure drop (in $\mathrm{kPa}$, rounded off to one decimal place) between an upstream location in the pipe and the throat (both at the same elevation) is

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: 21

Fri, 17 Feb 2023 06:52:23 +0000

Consider an inviscid flow through a smooth pipe which has a pitot-static tube arrangement as shown. Find the centre-line velocity in the pipe.

Consider that the density of the fluid is $1000 \mathrm{~kg} / \mathrm{m}^3$, acceleration due to gravity is $10 \mathrm{~m} / \mathrm{s}^2$, and the specific gravity of the manometric fluid is $11$.

$2 \text{m/s}$
$3 \text{m/s}$
$5 \text{m/s}$
$7 \text{m/s}$

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 $a a^{\prime}$.

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