GATE Overflow for GATE XE - Recent activity in Kinematics of Fluid Motion

Edited: GATE XE 2026 | Question: 161

Thu, 02 Apr 2026 10:50:35 +0000

For an incompressible fluid, the velocity components ( $u, v$, and $w$) are given as:
$\begin{array}{rcl}
u(x,y,z) & = & 2x + y + 2z \\
v(x,y,z) & = & ax + by + cz \\
w(x,y,z) & = & -6z
\end{array}$

The value of $b$ is $\_\_\_\_$. (Answer in integer)

Edited: GATE XE 2026 | Question: 158

Thu, 02 Apr 2026 10:40:20 +0000

Which of the following combinations of forces is/are balanced in a cyclostrophic motion?

Pressure Gradient, Coriolis, and Centrifugal
Pressure Gradient and Centrifugal
Centrifugal and Coriolis
Pressure Gradient and Coriolis

Edited: GATE XE 2026 | Question: 27

Tue, 31 Mar 2026 07:51:21 +0000

The velocity of a fluid particle in a flow is given as:

$$\vec{V}=(a-x) \hat{\imath}+(b+y) \hat{\jmath}+(c+z) \hat{k}$$

where $a, b, c$ are constants, and $\hat{\imath}, \hat{\jmath}, \hat{k}$ are unit vectors in $x$-, $y$-, $z$-directions, respectively.

Which of the following statements is/are correct?

The flow is steady for any value of $a, b$, and $c$.
At a point $(2,3,6)$, the velocity component in $x$-direction is higher than the velocity components in $y$ - and $z$-directions for $a=2, b=6$, and $c=2$.
The point $(2,3,6)$ is a stagnation point for $a=2, b=-3$, and $c=-6$.
The acceleration of the flow along the $x$-direction is not constant for any value of $a, b$, and $c$.

Edited: GATE XE 2026 | Question: 19

Sat, 28 Mar 2026 10:38:51 +0000

Which of the following statements about streamlines, pathlines, and streaklines is/are correct?

A streamline is a curve that is everywhere tangent to the instantaneous local velocity vector.
Two streamlines can intersect at a point in a flow.
A pathline is the locus of fluid particles passing sequentially through a particular point.
For steady flow, streamlines, pathlines, and streaklines are the same.

Edited: GATE XE 2026 | Question: 18

Sat, 28 Mar 2026 10:38:41 +0000

The velocity components in $x$ - and $y$-directions of a two-dimensional, incompressible flow field are $u(x, y)=2 x^{2}+y^{3}$ and $v(x, y)=x^{3}-2 x y+f(x, y)$, respectively. Here, $f(x, y)$ is a polynomial function and $g(x)$ is a polynomial function of $x$ only. Which one of the following options for $f(x, y)$ is correct?

$f(x, y)=-x y^{2}+g(x)$
$f(x, y)=-2 x+g(x)$
$f(x, y)=-2 x y+g(x)$
$f(x, y)=-2 x^{2} y+g(x)$

Edited: GATE XE 2025 | Question: 38

Sun, 29 Jun 2025 12:50:40 +0000

An incompressible fluid is flowing between two infinitely large parallel plates separated by $5 \mathrm{mm}$ distance. The bottom plate is stationary and the top plate is moving at a constant velocity of $5 \mathrm{~mm} / \mathrm{s}$ in the direction parallel to the bottom plate. The flow of the fluid between the plates is steady, two-dimensional, laminar, and the variation of fluid velocity is linear between the plates. A square fluid element of $1 \: \mathrm{mm}$ side is considered at equal distance from both the plates in the flow field such that one of its sides is parallel to the plates. The magnitude of circulation in $\mathrm{mm}^{2} / \mathrm{s}$ (in integer) along the edges of the square fluid element is $\_\_\_\_\_\_$

Edited: GATE XE 2025 | Question: 27

Sun, 29 Jun 2025 12:34:21 +0000

Conservation of mass for a steady axisymmetric flow field in the cylindrical $(r, z)$ coordinates is:

$$\frac{1}{r} \frac{\partial\left(r V_{r}\right)}{\partial r}+\frac{\partial V_{z}}{\partial z}=0 $$

Here, $V_{r}$ and $V_{z}$ are radial and axial components of velocity, respectively.

Which one of the following options is correct if $\psi$ is the stream function?

$V_{r}=\frac{\partial \psi}{\partial z}$ and $V_{z}=-\frac{1}{r} \frac{\partial \psi}{\partial r}$
$V_{r}=\frac{1}{r} \frac{\partial \psi}{\partial z}$ and $V_{z}=-\frac{1}{r} \frac{\partial \psi}{\partial r}$
$V_{r}=\frac{1}{r} \frac{\partial \psi}{\partial z}$ and $V_{z}=\frac{1}{r} \frac{\partial \psi}{\partial r}$
$V_{r}=\frac{1}{r} \frac{\partial \psi}{\partial z}$ and $V_{z}=-\frac{\partial \psi}{\partial r}$

Edited: GATE XE 2025 | Question: 24

Sun, 29 Jun 2025 12:29:54 +0000

Consider the following Statements $[1]$ and $[2]$.

Statement $[1]$: The Eulerian study focusses attention on individual particle and its motion is observed as a function of time.

Statement $[2]$: The Lagrangian study focusses attention on the motion of the particles passing through an identified point.

Which one of the following options identifies the correctness of the given statements?

Both $[1]$ and $[2]$ are correct.
Both $[1]$ and $[2]$ are NOT correct.
$[1]$ is correct, but $[2]$ is NOT correct.
$[1]$ is NOT correct, but $[ 2 ]$ is correct.

Edited: GATE XE 2025 | Question: 22

Sun, 29 Jun 2025 12:27:32 +0000

Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end.

Which one of the following options correctly represents the velocity field in the converging section in cylindrical $(r, \theta, z)$ coordinates?

Two-dimensional function of $r$ and $z$
One-dimensional function of $r$
Two-dimensional function of $r$ and $\theta$
One-dimensional function of $z$

Recategorized: GATE XE 2024 | Question: 13

Mon, 05 May 2025 14:41:05 +0000

The locus of temporary locations of all particles that have passed through a fixed point in the flow field at a particular instant is known as

streamline.
streakline.
pathline.
timeline.

Recategorized: GATE XE 2024 | Question: 14

Mon, 05 May 2025 14:40:59 +0000

Consider the velocities $u, v$, and $w$ in $x$-, $y$-, and $z$-directions, respectively. The vorticity expression in the $y-z$ plane is

$\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y}$
$\frac{\partial v}{\partial y}-\frac{\partial w}{\partial z}$
$\frac{\partial w}{\partial y}-\frac{\partial v}{\partial z}$
$\frac{\partial u}{\partial z}-\frac{\partial w}{\partial x}$

Recategorized: GATE XE 2024 | Question: 26

Mon, 05 May 2025 14:40:25 +0000

The velocity in a one-dimensional flow is given by $u(x)=\frac{a}{(b-x)^{2}} \mathrm{~m} / \mathrm{s}$, where $a=8 \mathrm{~m}^{3} / \mathrm{s}$ and $b=4 \mathrm{~m}$. The acceleration $\text{(in m/s $\mathrm{s}^{2}$, answer in integer)}$ at $x=2 \mathrm{~m}$ is ___________.

Recategorized: GATE XE 2022 | Question: 17

Mon, 05 May 2025 12:43:42 +0000

Which of the following statement(s) is/are true for streamlines in a steady incompressible flow?

Two streamlines cannot intersect each other.
Flow rate increases between two diverging streamlines.
Flow rate decreases between two diverging streamlines.
Stream function has a constant value along a streamline.

Recategorized: GATE XE 2022 | Question: 28

Mon, 05 May 2025 12:43:09 +0000

For an inviscid fluid with density } 1 \mathrm{~kg} / \mathrm{m}^{3}, \text { the Cartesian velocity field is given as:

$\mathbf{u}=(-2 x+y) t \mathbf{i}+(2 x+y) t \mathbf{j} \mathrm{m} / \mathrm{s}$
Neglecting the body forces, find the magnitude of pressure gradient in $(\mathrm{Pa} / \mathrm{m})$ at

$(x, y)=(1 \mathrm{~m}, 1 \mathrm{~m}) \text { at } t=1 \mathrm{~s}.$

$\text {(Round off to two decimal places) }$

Recategorized: GATE XE 2023 | Question: 13

Mon, 05 May 2025 12:21:48 +0000

Among the following non-dimensional numbers, which one characterizes periodicity present in a transient flow?

Froude number
Strouhal number
Peclet numbe
Lewis number

Recategorized: GATE XE 2023 | Question: 19

Mon, 05 May 2025 12:21:22 +0000

For a two-dimensional flow field given as $\vec{V}=-x \hat{\imath}+y \hat{\jmath}$, a streamline passes through points $(2,1)$ and $(5, p)$. The value of $p$ is

$5$
$5 / 2$
$2 / 5$
$2$

Recategorized: GATE XE 2023 | Question: 22

Mon, 05 May 2025 12:21:17 +0000

\begin{tabular}{|c|c|}
\hline Q. 32 & \begin{tabular}{l}
A two-dimensional incompressible flow field is defined as, \\
$\qquad \vec{V}(x, y)=(A x y) \hat{\imath}+\left(B y^{2}\right) \hat{\jmath}$ \\
where, $A$ and $B$ are constants. The dynamic viscosity of the Newtonian fluid is $\mu$. \\
In the absence of body force, which among the following expressions represents \\
the pressure gradient at the location $(5,0)$ in the concerned flow field?
\end{tabular} \\
\hline

& $\mu A(5 \hat{\imath}+\hat{\jmath})$ \\
\hline
& $\mu(-5 B \hat{\imath}+A \hat{\jmath})$ \\
\hline
& $\mu A(-\hat{\jmath})$ \\
\hline
& $\mu A(5 \hat{\imath})$ \\
\hline
\end{tabular}

Recategorized: GATE XE 2023 | Question: 25

Mon, 05 May 2025 12:21:06 +0000

\begin{tabular}{l|l}
Q. 35 & In a steady two-dimensional compressible flow, $u$ and $v$ are the $x$ - and $y$ - \\
components of flow velocity, respectively and $\rho$ is the fluid density. Among the \\
following pairs of relations, which one(s) perfectly satisfies/satisfy the definition \\
of stream function, $\psi$, for this flow? \\

& $u=\frac{\partial \psi}{\partial y}$ and $v=-\frac{\partial \psi}{\partial x}$ \\
& $u=-\frac{\partial \psi}{\partial x}$ and $v=-\frac{\partial \psi}{\partial y}$ \\
& $\rho u=\frac{\partial \psi}{\partial y}$ and $\rho v=-\frac{\partial \psi}{\partial x}$ \\
& $\rho u=-\frac{\partial \psi}{\partial y}$ and $\rho v=\frac{\partial \psi}{\partial x}$
\end{tabular}

Recategorized: GATE XE 2023 | Question: 28

Mon, 05 May 2025 12:20:57 +0000

Q. 38 The velocity and acceleration of a fluid particle are given as $\vec{V}=(-\hat{\imath}+2 \hat{\jmath}) \mathrm{m} / \mathrm{s}$ and $\vec{a}=(-2 \hat{\imath}-4 \hat{\jmath}) \mathrm{m} / \mathrm{s}^{2}$, respectively. The magnitude of the component of acceleration (in $\mathrm{m} / \mathrm{s}^{2}$, rounded off to two decimal places) of the fluid particle along the streamline is