GATE Overflow for GATE XE - Recent activity in Internal Flows

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: 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: 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: 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: 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: 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: 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: 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: 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: 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 $n$ ?

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

Recategorized: GATE XE 2024 | Question: 18

Mon, 05 May 2025 14:40:53 +0000

For incompressible, laminar, fully-developed flow through a circular pipe, Darcy friction factor and Fanning friction factor are represented as $f$ and $C_{f}$, respectively. Which one of the following options is correct?

$f=0.25 C_{f}$
$f=0.5 C_{f}$
$f=2 C_{f}$
$f=4 C_{f}$

Recategorized: GATE XE 2024 | Question: 17

Mon, 05 May 2025 14:40:51 +0000

The hydraulic diameter for a circular pipe of radius $R$ is

$0.5 R$
$R$
$2 R$
$4 R$

Recategorized: GATE XE 2024 | Question: 21

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

A thin film of an incompressible, Newtonian liquid $\text{(density $\rho$, viscosity $\mu$)}$ with an uniform thickness $(h)$ is flowing down on a vertical plate. The flow is driven by gravity $(g)$ alone. Assume zero shear stress condition at the free surface.

The maximum velocity is given by

$\frac{1}{2 \mu} \rho g h^{2}$
$\frac{1}{4 \mu} \rho g h^{2}$
$\frac{1}{\mu} \rho g h^{2}$
$\frac{1}{8 \mu} \rho g h^{2}$

Recategorized: GATE XE 2024 | Question: 29

Mon, 05 May 2025 14:40:15 +0000

Consider the steady, incompressible flow of water in a horizontal pipe of constant diameter $1$ m with an inlet velocity of $12 \mathrm{~m} / \mathrm{s}$.

As shown in figure, water is lost through a circular hole of diameter $0.6$ $m$ at the rate of $4.53 \mathrm{~m}^{3} / \mathrm{s}$. The outlet velocity $\text{(in $\mathrm{m} / \mathrm{s}$, rounded off to two decimal places)}$ of water in the pipe is ____________.

Recategorized: GATE XE 2024 | Question: 30

Mon, 05 May 2025 14:40:13 +0000

The axial velocity profile of a laminar, incompressible and fully-developed flow in a circular pipe of radius $(R)$ is given as $u_{z}=-\frac{1}{4 \mu} \frac{\partial p}{\partial z} R^{2}\left(1-\frac{r^{2}}{R^{2}}\right)$, where $r, z, \mu$, and $p$ are radial direction, axial direction, fluid viscosity, and pressure, respectively. If the average velocity of the flow is given by $u_{z, a v g}=\frac{1}{K}\left(-\frac{R^{2}}{\mu} \frac{\partial p}{\partial z}\right)$, then the value of $K$ $\text{(answer in integer)}$ is ____________.

Recategorized: GATE XE 2022 | Question: 13

Mon, 05 May 2025 12:43:54 +0000

The figure shows the developing zone and the fully developed region in a pipe flow where the steady flow takes place from left to right. The wall shear stress in the sections $\mathrm{A}, \mathrm{B}, \mathrm{C}$, and $\mathrm{D}$ are given by $\tau_{A}, \tau_{B}, \tau_{C}$, and $\tau_{D}$, respectively. Select the correct statement.

$\tau_{A}>\tau_{B}$
$\tau_{B}>\tau_{A}$
$\tau_{C}>\tau_{B}$
$\tau_{C}>\tau_{D}$

Recategorized: GATE XE 2022 | Question: 16

Mon, 05 May 2025 12:43:48 +0000

Which of the following statement(s) regarding a venturimeter is/are correct?

In the direction of flow, it consists of a converging section, a throat, and a diverging section.
In the direction of flow, it consists of a diverging section, a throat, and a converging section.
It is used for flow measurement at a very low Reynolds number.
Pressure tappings are provided just upstream of the venturimeter and at the throat.

Recategorized: GATE XE 2022 | Question: 26

Mon, 05 May 2025 12:43:18 +0000

Consider steady fully developed flow of a liquid through two large horizontal flat parallel plates separated by a distance of $2 \mathrm{~mm}$. One of the plate is fixed and the other plate moves at a speed of $0.5 \mathrm{~m} / \mathrm{s}$. What is the magnitude of the pressure gradient in $\mathrm{Pa} / \mathrm{m}$ in the direction of the flow required to ensure that the net flow through the plates is zero?

Dynamic viscosity of the liquid is $5 \times 10^{-4} \mathrm{Ns} / \mathrm{m}^2$
$\text{(Round off to the nearest integer)}$

Recategorized: GATE XE 2022 | Question: 25

Mon, 05 May 2025 12:43:15 +0000

Identify the configuration(s) in which steady two-dimensional internal flow may show boundary layer separation if the flow direction is left to right.

Recategorized: GATE XE 2022 | Question: 27

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

Consider two-dimensional turbulent flow of air over a horizontal flat plate of length $1 \mathrm{~m}$. Skin friction coefficient at a length $x$ from the leading edge of the plate is obtained as:
\[
c_{f}=\frac{0.06}{\left(\operatorname{Re}_{x}\right)^{0.2}}
\]
where, $\mathrm{Re}_{x}$ is the local Reynolds number.
Find out the drag force per unit width in $N / m^{2}$ on the plate if the free stream air velocity is $10 \mathrm{~m} / \mathrm{s}$.

Density and dynamic viscosity of air are given as $1.2 \mathrm{~kg} / \mathrm{m}^{3}$ and $1.83 \times 10^{-5} \mathrm{~N}-\mathrm{s} / \mathrm{m}^{2}$, respectively.

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

Recategorized: GATE XE 2023 | Question: 21

Mon, 05 May 2025 12:21:19 +0000

Consider steady fully-developed incompressible flow of a Newtonian fluid between two infinite parallel flat plates. The plates move in the opposite directions, as shown in the figure. In the absence of body force and pressure gradient, the ratio of shear stress at the top surface $(y=H)$ to that at the bottom surface $(y=0)$ is

$1$
$\frac{U_{1}}{U_{2}}$
$\frac{U_{1}-U_{2}}{U_{2}}$
$\frac{U_{1}+U_{2}}{U_{2}}$

Recategorized: GATE XE 2023 | Question: 32

Mon, 05 May 2025 12:20:46 +0000

Q. 42 Axial velocity profile $u(r)$ for an axisymmetric flow through a circular tube of radius $R$ is given as,
\[
\frac{u(r)}{U}=\left(1-\frac{r}{R}\right)^{1 / n}
\]
where $U$ is the centerline velocity. If $V$ refers to the area-averaged velocity (volume flow rate per unit area), then the ratio $V / U$ for $n=1$ (rounded off to two decimal places) is

Recategorized: GATE XE 2023 | Question: 127

Mon, 05 May 2025 12:15:48 +0000

\begin{tabular}{l|l}
Q. 137 & Which of the following statements is NOT correct? \\
\hline

& \begin{tabular}{l}
As the shear rate increases, the apparent viscosity decreases for a pseudoplastic \\
fluid.
\end{tabular} \\
\hline
& As the shear rate increases, the apparent viscosity increases for a dilatant fluid. \\
\hline
& A Bingham fluid requires application of yield stress prior to any response. \\
\hline
& Rheopectic and thixotropic are two time independent fluids. \\
\hline
\end{tabular}

Recategorized: GATE XE 2024 | Question: 142

Mon, 05 May 2025 10:52:53 +0000

The surface temperature of a hot plate is $175^{\circ} \mathrm{C}$. The ambient air temperature is 25 ${ }^{\circ} \mathrm{C}$. The rate of heat transfer per unit area in $\mathrm{kW} . \mathrm{m}^{-2}$ from the plate to the ambient air is _________ $\text{(Answer in integer)}$. Assume the convective heat transfer coefficient is $20 \mathrm{~W} \cdot \mathrm{m}^{-2} \cdot \mathrm{K}^{-1}$.