GATE Overflow for GATE XE - Recent activity in Fluid Mechanics

Answer reshown: GATE XE 2022 | Question: 15

Thu, 21 May 2026 09:57:47 +0000

Option C , Since dynamic viscoscity doen't depent on temperature.It realted with velocity gradient (Rate of shear strain ) and the shear stress

Edited: GATE XE 2026 | Question: 187

Thu, 02 Apr 2026 11:25:04 +0000

The useful heat gain in Watt (rounded off to one decimal place) of a solar flat plate collector using Hottel-Whillier-Bliss equation is $\_\_\_\_$.

Assume:
Collector heat removal factor $=0.85$
Absorber plate area $=1.5 \mathrm{~m}^{2}$
Absorbed solar flux by the absorber plate $=600 \mathrm{Wm}^{-2}$
Overall loss coefficient $=4 \mathrm{Wm}^{-2} \mathrm{~K}^{-1}$
Water inlet temperature $=60^{\circ} \mathrm{C}$
Ambient temperature $=25^{\circ} \mathrm{C}$

Edited: GATE XE 2026 | Question: 176

Thu, 02 Apr 2026 11:10:09 +0000

A hydro turbine works under a head of $20$ $\mathrm{m}$ and has a maximum volume flow rate of $4 \mathrm{~m}^{3} \mathrm{~s}^{-1}$ and a speed of $750$ $\mathrm{rpm}$. Determine the speed (in $\mathrm{rpm}$) in order to operate the same turbine at approximately the same efficiency under a head of $5 \mathrm{~m}$.

$375.0$
$187.5$
$750.0$
$524.5$

Edited: GATE XE 2026 | Question: 166

Thu, 02 Apr 2026 10:58:48 +0000

The luminous efficacy of an electric light bulb is measured in which one of the following units?

lumen $\mathrm{W}^{-1}$
lumen $\mathrm{W}^{-1} \mathrm{~h}^{-1}$
lumen $\mathrm{m}^{-2}$
Candela $\mathrm{W}^{-1}$

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: 152

Thu, 02 Apr 2026 10:25:56 +0000

The mass (in $\mathrm{kg}$) of dry air in a room, measuring $10 m \times 7 m \times 3 m$, is $\_\_\_\_$. (rounded off to two decimal places)

[Density of dry air is $1.029 \times 10^{-3} \mathrm{~g} \mathrm{~cm}^{-3}$]

Edited: GATE XE 2026 | Question: 149

Thu, 02 Apr 2026 10:22:55 +0000

In a stable atmosphere, the change in pressure (in kilo Pascal) at a height of $100 \mathrm{~m}$ from the mean sea level is $\_\_\_\_$. (rounded off to three decimal places)

[Density of air is $1.029 \mathrm{~kg} \mathrm{~m}^{-3}$ and acceleration due to gravity is $9.81 \mathrm{~m} \mathrm{~s}^{-2}$]

Edited: GATE XE 2026 | Question: 146

Thu, 02 Apr 2026 10:15:32 +0000

What is the approximate value of annual-mean pH of seawater at the surface in the northern Indian Ocean?

$4.5$
$5.0$
$8.0$
$11.0$

Edited: GATE XE 2026 | Question: 137

Thu, 02 Apr 2026 09:34:52 +0000

For a given temperature difference between the top and bottom surfaces of a flat metal plate, Fourier's law of heat conduction implies that

temperature gradient increases with increase in heat transfer area
heat flux is proportional to the thermal conductivity of the metal
heat flux increases with increase in thickness of the metal plate
temperature gradient decreases with increase in thickness of the metal plate

Edited: GATE XE 2026 | Question: 129

Thu, 02 Apr 2026 09:09:42 +0000

Water is flowing at $100$ $\mathrm{litres}/ \mathrm{min}$ through a pipe with a diameter of $5$ $\mathrm{cm}$. Assume the coefficient of viscosity of water to be $0.001$ $\mathrm{Pa}.\mathrm{s}$ and the density to be $1000 \mathrm{~kg} / \mathrm{m}^{3}$. The Reynolds number for this flow is $\_\_\_\_$ (Round off to nearest integer)

Edited: GATE XE 2026 | Question: 95

Thu, 02 Apr 2026 06:11:10 +0000

A stream of moist air enters an adiabatic saturator at $45^{\circ} \mathrm{C}$ and $101$ $\mathrm{kPa}$ and leaves as a saturated mixture at $30^{\circ} \mathrm{C}$. Make-up water to the saturator is supplied at $30^{\circ} \mathrm{C}$. The amount of make-up water (in grams per kg of dry air) supplied is $\_\_\_\_$ (rounded off to two decimal places).

Use the following data:

Specific heat capacity of water is $4.2 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$

Specific heat capacity of air at constant pressure is $1 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$

Saturated water properties:

At $30^{\circ} \mathrm{C}$ : specific enthalpy of saturated water vapor is $2556 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, specific enthalpy of saturated liquid water is $125.7 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, and saturation pressure is $4.25$ kPa

At $45^{\circ} \mathrm{C}$ : specific enthalpy of saturated water vapor is $2582 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, specific enthalpy of saturated liquid water is $188.4 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, and saturation pressure is $9.60$ kPa

Edited: GATE XE 2026 | Question: 33

Tue, 31 Mar 2026 08:00:44 +0000

Air flows through a pipe of diameter $D$ with an average velocity of $3 \mathrm{~m}. \mathrm{s}^{-1}$. The Darcy friction factor of the pipe is $0.02$. Assume acceleration due to gravity as $10 \mathrm{~m}. \mathrm{s}^{-2}$. If the head loss per meter is $0.05$, the diameter (in m) of the pipe is $\_\_\_\_$. (rounded off to two decimal places)

Edited: GATE XE 2026 | Question: 32

Tue, 31 Mar 2026 07:59:14 +0000

The axial velocity profile of a laminar, incompressible, and fully-developed flow in a circular pipe of radius $R$ is given as $v_{z}=\dfrac{1}{4 \mu} \dfrac{d p}{d z}\left(r^{2}-R^{2}\right)$, where $\mu, p, z$, and $r$ are dynamic viscosity, pressure, axial coordinate, and radial coordinate, respectively. If the magnitude of shear stress at the pipe wall is given as $\mid \tau_{w}\mid=\dfrac{R}{K} \dfrac{d p}{d z}$, then the value of $K$ is $\_\_\_\_$. (answer in integer)

Edited: GATE XE 2026 | Question: 30

Tue, 31 Mar 2026 07:57:08 +0000

A rectangular block (density $=600 \mathrm{~kg} \cdot \mathrm{~m}^{-3}$ ) with base area of $0.06 \mathrm{~m}^{2}$ and height $15$ cm is partially submerged in water (density $=1000 \mathrm{~kg} \cdot \mathrm{~m}^{-3}$), as shown in the figure. Assume acceleration due to gravity as $10 \mathrm{~m}. \mathrm{s}^{-2}$. The submerged depth, $h$ (in $\mathrm{m}$) of the block in the water is $\_\_\_\_$. (rounded off to two decimal places)

Edited: GATE XE 2026 | Question: 29

Tue, 31 Mar 2026 07:55:31 +0000

A ship is designed to sail at a speed of $8 \mathrm{~m} \cdot \mathrm{~s}^{-1}$. A designer makes a $1/10$ scaled model to test the ship in a water tunnel. The model and the ship satisfy the dynamic similarity. The speed (in $\mathrm{m} . \mathrm{s}^{-1}$) of the model is $\_\_\_\_$. (rounded off to two decimal places)

Edited: GATE XE 2026 | Question: 28

Tue, 31 Mar 2026 07:54:54 +0000

A gas is pressurized in a vertical frictionless piston-cylinder device, as shown in the figure. The piston has a mass of $4$ kg and a cross-sectional area of $40 \mathrm{~cm}^{2}$. A metallic block of $13$ kg is placed on the piston. The atmospheric pressure ( $p_{a}$ ) is $1$ bar. Assume acceleration due to gravity as $10 \mathrm{~m} . \mathrm{s}^{-2}$. The pressure inside the cylinder, $p_{i}$ (in bar) is $\_\_\_\_$ . (rounded off to three decimal places)

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: 25

Sat, 28 Mar 2026 10:51:04 +0000

Consider a steady, laminar, and incompressible flow over a flat plate, as shown in the figure. With freestream velocity $U_{\infty}$ and kinematic viscosity $v_{1}$, the boundary layer thickness at a distance $x_{1}$ from the leading edge is $\delta_{1}$. If the kinematic viscosity of the fluid is increased by a factor of four $\left(v_{2}=4 v_{1}\right)$, the boundary layer thickness $\left(\delta_{2}\right)$ at $x_{1}$ with same $U_{\infty}$ will be equal to

$\dfrac{\delta_{1}}{2}$
$\delta_{1}$
$2 \delta_{1}$
$4 \delta_{1}$

Edited: GATE XE 2026 | Question: 24

Sat, 28 Mar 2026 10:49:46 +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

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

Edited: GATE XE 2026 | Question: 23

Sat, 28 Mar 2026 10:48:15 +0000

Consider two different cases of water flowing through a smooth pipe of $50$ $\mathrm{cm}$ diameter. The mass flow rates for the two cases are $\text{(i)}$ $0.25 \mathrm{~kg}. \mathrm{s}^{-1}$, and $\text{(ii)}$ $0.8 \mathrm{~kg}. \mathrm{s}^{-1}$. Assume the density and dynamic viscosity of water as $1000 \mathrm{kg}\cdot\mathrm{m}^{-3}$ and $10^{-3} \mathrm{~Pa}. \mathrm{s}$, respectively. Which one of the following options is correct?

The flow is laminar for both $\text{(i)}$, and $\text{(ii)}$.
The flow is laminar for $\text{(i)}$, and turbulent for $\text{(ii)}$.
The flow is turbulent for $\text{(i)}$, and laminar for $\text{(ii)}$.
The flow is turbulent for both $\text{(i)}$, and $\text{(ii)}$.

Edited: GATE XE 2026 | Question: 22

Sat, 28 Mar 2026 10:46:32 +0000

An incompressible fluid flows between a pair of infinite plates separated by a distance $L$. The top plate is moving with a constant velocity $U$, whereas the bottom plate is stationary, as shown in the figure. The difference of the stream functions $\left(\psi_{T}-\psi_{B}\right)$ at the two plates for a laminar and fully-developed flow is equal to

$\dfrac{U L}{2}$
$U L$
$2 U L$
$4 U L$

Edited: GATE XE 2026 | Question: 21

Sat, 28 Mar 2026 10:45:31 +0000

A steady, laminar, and incompressible flow between a pair of infinite parallel plates is driven by a constant pressure gradient $(-d p / d x)$. The plates are separated by a distance $2 h$, as shown in the figure. The fully-developed velocity profile of the flow is

$$u(y)=-\frac{d p}{d x} \frac{h^{2}}{2 \mu}\left(1-\frac{y^{2}}{h^{2}}\right), $$

where $\mu$ is the dynamic viscosity.

The values of $y$, for which the local flow velocity is equal to the average flow velocity, are

$\pm \dfrac{h}{2}$
$\pm \dfrac{h}{\sqrt{2}}$
$\pm \dfrac{h}{3}$
$\pm \dfrac{h}{\sqrt{3}}$

Edited: GATE XE 2026 | Question: 20

Sat, 28 Mar 2026 10:39:42 +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)

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 2026 | Question: 17

Sat, 28 Mar 2026 10:37:10 +0000

The basic dimensions, i.e., mass, length, and time are represented by $M, L$, and $T$, respectively. The correct dimension of dynamic viscosity is

$M L T^{-2}$
$M^{0} L^{2} T^{-1}$
$M L^{-1} T^{-1}$
$M^{0} L^{-2} T^{2}$

Edited: GATE XE 2026 | Question: 16

Sat, 28 Mar 2026 10:36:41 +0000

Consider the following statements:

Assertion (a)

Surface tension acts along the interface of two fluids.

Reason (r)

The pressure of the fluid inside a bubble is higher than that of the fluid outside the bubble.

Which one of the following options is correct?

Both (a) and (r) are true, and (r) is the correct explanation of (a).
Both (a) and (r) are true, however (r) is not the correct explanation of (a).
(a) is true, but (r) is false.
(a) is false, but (r) is true.

Edited: GATE XE 2026 | Question: 15

Sat, 28 Mar 2026 10:34:29 +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.

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

Edited: GATE XE 2026 | Question: 14

Sat, 28 Mar 2026 10:33:09 +0000

Consider a steady, and incompressible flow over a body with characteristic length $\text{L}$. The boundary layer thickenss at a distance $x$ from the leading edge is $\delta$. Which one of the following assumptions is correct for deriving the prandtl boundary layer equations?

$\delta \approx L$
$\delta>L$
$\delta \gg L$
$\delta \ll L$

Edited: GATE XE 2026 | Question: 13

Sat, 28 Mar 2026 10:32:42 +0000

Air flows with a freestream velocity $U$ over four different bodies having same frontal area facing to the flow direction, as shown in the figure. Which one of the following bodies has the lowest pressure (form) drag force for Reynolds number, $\operatorname{Re} \geq 10^{4}$?

Body $\text{P}$
Body $\text{Q}$
Body $\text{R}$
Body $\text{S}$

Edited: GATE XE 2026 | Question: 12

Sat, 28 Mar 2026 10:31:34 +0000

For a laminar, incompressible, and fully-developed flow through a circular pipe, the ratio of the maximum velocity to the average velocity of the flow is

$1.5$
$2$
$3$
$4$

Edited: GATE XE 2025 | Question: 172

Mon, 30 Jun 2025 16:28:12 +0000

A floating hot air balloon with volume $1000 \mathrm{~m}^{3}$ and gross mass (excluding the air in the balloon) $100 \: \mathrm{kg}$ is in hydrostatic balance where the external air temperature is $10^{\circ} \mathrm{C}$ and density is $1 \mathrm{~kg} \mathrm{~m}^{-3}$. The temperature of the air inside the balloon is $\_\_\_\_\_\_$ ${ }^{\circ} \mathrm{C}$. (Round off to the nearest integer.)

Edited: GATE XE 2025 | Question: 168

Mon, 30 Jun 2025 16:24:15 +0000

Which of the following is the correct form of the mass divergence form of the continuity equation for a compressible fluid?

[In the given equations, $\rho$ is the density and $\mathbf{V}$ the three dimensional velocity vector of the fluid.]

$\frac{\partial \rho}{\partial t}+\nabla \times(\rho \mathbf{v})=0$
$\frac{\partial \rho}{\partial t}+\nabla \cdot(\rho \mathbf{v})=0$
$\frac{\partial \mathbf{v}}{\partial t}+\rho \cdot \nabla \mathbf{v}=0$
$\frac{\partial \rho}{\partial t}+\mathbf{v} \cdot \nabla \rho=0$

$\textsf{(i)}$ and $\textsf{(ii)}$
$\textsf{(ii)}$
$\textsf{(i)}$ and $\textsf{(iv)}$
$\textsf{(iii)}$

Edited: GATE XE 2025 | Question: 161

Mon, 30 Jun 2025 16:13:46 +0000

Accumulated rainfall is often measured in $\mathrm{mm}$. If the density of rain water is $1000 \: \mathrm{kg} \mathrm{m}^{-3}$ then, one mm of rain is equal to $\_\_\_\_\_\_ \: \mathrm{kg} \mathrm{m}^{-2}$ of rain. (in integer).

Edited: GATE XE 2025 | Question: 139

Mon, 30 Jun 2025 16:12:19 +0000

The true density and bulk density of wheat grains are $1280 \mathrm{~kg} / \mathrm{m}^{3}$ and $740 \mathrm{~kg} / \mathrm{m}^{3}$, respectively. The porosity of the grains is $\_\_\_\_\_\_$ ( rounded off to $2$ decimal places)

Edited: GATE XE 2025 | Question: 43

Sun, 29 Jun 2025 12:56:17 +0000

An oil of density $870 \mathrm{~kg} / \mathrm{m}^{3}$ and viscosity $0.036 \: \mathrm{Pa.s}$ flows through a straight pipe of $10 \: \mathrm{cm }$ diameter and $1.5 \: \mathrm{km}$ length at the flow rate of $250$ liters per minute under the steady and incompressible flow conditions. To control the flow rate of oil, a valve is fixed at the middle of the pipe causing no change in the total length of the pipe. The total head loss measured across the two ends of the pipe is $11.60 \: \mathrm{m}$. Using gravitational acceleration as $10 \mathrm{~m} / \mathrm{s}^{2}$, the minor head loss contributed by the presence of the valve in $\mathrm{m}$ (rounded off to $2$ decimal places) is $\_\_\_\_\_\_$

Edited: GATE XE 2025 | Question: 42

Sun, 29 Jun 2025 12:55:34 +0000

Water flows through a pipe of diameter $20 \mathrm{cm}$ at a flow rate of $0.025 \mathrm{~m}^{3} / \mathrm{s}$. A pitotstatic tube is placed at the centre of the pipe and indicates the pressure difference of $5 \: \mathrm{ cm}$ of water column. Theoretical velocity measured through pitot-static tube when multiplied with velocity coefficient $C_{V}$ gives the actual velocity of the flow. If the mean velocity in the pipe is $90 \%$ of the actual velocity at the centre of the pipe and the gravitational acceleration is $10 \mathrm{~m} / \mathrm{s}^{2}$, the value of $C_{V}$ (rounded off to $2$ decimal places) is $\_\_\_\_\_\_$

Edited: GATE XE 2025 | Question: 41

Sun, 29 Jun 2025 12:54:46 +0000

A ship is to be operated in a fluid medium with kinematic viscosity $0.032 \times 10^{-3} \mathrm{~m}^{2} / \mathrm{s}$. A one-tenth scale model of the ship is built for testing. Consider, inertia, viscous and gravity forces are dominant for the ship and its model during the operation. The required kinematic viscosity of the liquid for testing the model is $P \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}$. The value of $P$ (rounded off to $2$ decimal places) is $\_\_\_\_\_\_$

Edited: GATE XE 2025 | Question: 40

Sun, 29 Jun 2025 12:54:01 +0000

A fixed control volume has four one-dimensional boundary sections $(1,2,3$, and $4$). For a steady flow inside the control volume, the flow properties at each section are tabulated below:

$$\begin{array}{|l|l|l|l|l|l|} \hline \textbf{Boundary} & \textbf{Type} & \textbf{Density} & \textbf{Surface Normal} & \textbf{Cross-sectional} & \textbf{Specific} \\ \textbf{Section} && (\text {kg}/{m}^3) & \textbf{Velocity} & \textbf{Area} & \textbf{Energy} \\ &&& (\mathrm{m} / \mathrm{s}) & (\mathrm{m}^{2}) & (\mathrm{J} / \mathrm{kg} ) \\ \hline 1 & \text{Inlet} & 1000 & 10 & 0.5 & 200 \\ \hline 2 & \text{Inlet} & 1000 & 2 & 3.0 & 50 \\ \hline 3 & \text{Outlet} & 1000 & 5 & 1.0 & 100 \\ \hline 4 & \text{Outlet} & 1000 & 4 & 1.5 & 80 \\
\hline \end{array}$$

The rate of change of energy of the system which occupies the control volume at this instant is $E \times 10^{6} \mathrm{~J} / \mathrm{s}$. The value of $E$ (rounded off to $2$ decimal places) is $\_\_\_\_\_$

Edited: GATE XE 2025 | Question: 39

Sun, 29 Jun 2025 12:51:30 +0000

Consider, a kite weighing $100$ grams as essentially a rigid flat plate making an angle $8^{\circ}$ with the horizontal and having a planform area of $0.045 \mathrm{~m}^{2}$ when exposed to horizontal parallel wind of $60 \mathrm{~km} / \mathrm{h}$. The thread string of the kite makes an angle $45^{\circ}$ with the horizontal. A tension of $450$ grams in the thread is necessary to float the kite steadily. Take air density as $1.2 \mathrm{~kg} / \mathrm{m}^{3}$ and gravitational acceleration as $9.81 \mathrm{~m} / \mathrm{s}^{2}$. The lift coefficient $\left(C_{L}\right)$ associated with the air flow around steadily floating kite (rounded off to $2$ decimal places) is $\_\_\_\_\_\_$

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: 37

Sun, 29 Jun 2025 12:50:07 +0000

Driven by a pressure gradient of $100 \mathrm{kPa} / \mathrm{m}$, a fluid of dynamic viscosity $0.1 \mathrm{~Pa.s}$ flows between two fixed infinitely large parallel plates under steady, incompressible, and fully developed laminar conditions. The average velocity of the flow is $2 \mathrm{~m} / \mathrm{s}$. The gap between the parallel plates in mm (rounded off to $2$ decimal places) is $\_\_\_\_\_\_$

Edited: GATE XE 2025 | Question: 35

Sun, 29 Jun 2025 12:48:26 +0000

A liquid flows under steady and incompressible flow conditions from station $1$ to station $4$ through pipe sections $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, and $\mathrm{S}$ as shown in figure. Consider, $d, V$, and $h$ represent the diameter, velocity, and head loss, respectively, in each pipe section with subscripts ' $P$ ', ' $Q$ ', ' $R$ ', and ' $S$ '. $\Delta h$ represents the head difference between the inlet (station $1$) and outlet (station $4$). All the pipe sections are placed on the same horizontal plane for which the figure shows the top view.

Which one of the following options is correct for the given flow loop?

$\Delta h=h_{P}+h_{Q}+h_{R}+h_{S} \quad$ and $\quad V_{P} d_{P}^{2}=V_{Q} d_{Q}^{2}=V_{R} d_{R}^{2}=V_{S} d_{S}^{2}$
$\Delta h=h_{P}+h_{Q}+h_{R} \quad$ and $\quad V_{P} d_{P}^{2}=V_{Q} d_{Q}^{2}=V_{R} d_{R}^{2}=V_{S} d_{S}^{2}$
$\Delta h=h_{P}+h_{Q}+h_{R} \quad$ and $\quad V_{P} d_{P}^{2}=V_{Q} d_{Q}^{2}=V_{R} d_{R}^{2}+V_{S} d_{S}^{2}$
$\Delta h=h_{P}+h_{Q}+h_{R}+h_{S} \quad$ and $\quad V_{P} d_{P}^{2}=V_{Q} d_{Q}^{2}=V_{R} d_{R}^{2}+V_{S} d_{S}^{2}$

Edited: GATE XE 2025 | Question: 34

Sun, 29 Jun 2025 12:46:38 +0000

Figure shows the steady and incompressible flow of a fluid in the direction of arrow from section $A$ to section $D$. Three pipe connectors are to be placed between sections at $A$ and $D$ having Total Energy Line $\textsf{(TEL)}$ and Hydraulic Grade Line $\textsf{(HGL)}$ as depicted in the figure. Consider, $\mathrm{g}, \mathrm{P}, \mathrm{Q}, \mathrm{V}, \gamma$, and $\mathrm{Z}$ denote gravitational acceleration, pressure, volume flow rate, velocity, specific weight, and elevation of centerline of the pipe connectors from the datum, respectively.

Which one of the following options, in sequence, indicates the correct nature of connectors between sections $A$ and $B$, $B$ and $C$, and $C$ and $D$ in the direction of flow?

Converging, Constant area, Diverging
Diverging, Constant area, Converging
Constant area, Constant area, Constant area
Constant area, Converging, Diverging

Edited: GATE XE 2025 | Question: 33

Sun, 29 Jun 2025 12:44:37 +0000

A solid body of uniform specific gravity floats in a deep liquid pool. Take $B, G$, and $M$ as the centre of buoyancy, centre of gravity, and metacentre of the body, respectively.

Which one of the following options is correct for the stable floatation of the body in the pool when the body is given a small tilt angle?

$\overline{M G}$ is the metacentric height and $G$ should lie below $M$
$\overline{M G}$ is the metacentric height and $B$ should lie above $M$
$\overline{M B}$ is the metacentric height and $B$ should lie below $M$
$\overline{M B}$ is the metacentric height and $G$ should lie above $M$

Edited: GATE XE 2025 | Question: 32

Sun, 29 Jun 2025 12:43:37 +0000

$\textbf{Group-I}$ shows different two-dimensional bodies and $\textbf{Group-II}$ mentions their total drag coefficient $\left(C_{D}\right)$ based on frontal area while facing parallel flow of fluid having Reynolds number $R e \geq 10^{4}$ along the direction of arrow. The bodies are placed symmetrically with respect to the flow direction.

Which one of the following options identifies the correct match between $\textbf{Group-I}$ and $\textbf{Group-II}$, as per the concept of degree of streamlining?

$\mathrm{P}-3, \mathrm{Q}-2, \mathrm{R}-1, \mathrm{~S}-4$
$\mathrm{P}-3, \mathrm{Q}-2, \mathrm{R}-4, \mathrm{~S}-1$
$\mathrm{P}-2, \mathrm{Q}-3, \mathrm{R}-1, \mathrm{~S}-4$
$\mathrm{P}-3, \mathrm{Q}-1, \mathrm{R}-2, \mathrm{~S}-4$

Edited: GATE XE 2025 | Question: 31

Sun, 29 Jun 2025 12:41:41 +0000

Figure shows two parallel plates (upper plate at $x=b$ and lower one at $x=-b$ ) of length $L$ (aligned in $z$ direction) and infinite width (in $y$ direction, normal to the plane of the figure). Two immiscible, incompressible liquids are flowing steadily in the $z$ direction through the thin passage between the plates under the influence of horizontal pressure gradient $\left(P_{0}-P_{L}\right) / \mathrm{L}$. During the flow, the passage is always half-filled with denser fluid $I$ (viscosity $\mu^{I}$ ) at the bottom and rest is occupied by lighter fluid $II$ (viscosity $\mu^{I I} ; \mu^{I I}<\mu^{I}$ ). Considering exactly planar interface between the fluids and no instabilities in the flow, the shear stress, $\tau_{x z}$ is expressed as:
$$\tau_{x z}=\frac{\left(P_{0}-P_{L}\right) b}{\mathrm{~L}}\left[\left(\frac{x}{b}\right)-\frac{1}{2}\left(\frac{\mu^{I}-\mu^{I I}}{\mu^{I}+\mu^{I I}}\right)\right]$$

Which one of the following options correctly identifies the location of the point having maximum velocity of the flow?

Above the interface
Below the interface
At the interface
At the top plate

Edited: GATE XE 2025 | Question: 30

Sun, 29 Jun 2025 12:40:09 +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

Edited: GATE XE 2025 | Question: 29

Sun, 29 Jun 2025 12:36:30 +0000

Consider the steady, incompressible, and fully developed laminar flow of a fluid through a circular pipe. Here, $\Delta P$ is the pressure drop in the direction of the flow and $V$ is the average axial velocity of the fluid at any cross-section. The relation between $\Delta P$ and $V$ is:

$$\Delta P=K \: V^{n}$$

Here, $K$ and $n$ are constants.

Which one of the following options is the correct value of $n$ ?

$1$
$2$
$1.75$
$0.5$