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Fluid Mechanics & Potential Flow Theory(32)Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing(13)

Fluid Mechanics & Potential Flow Theory

32 Questions

GATE→2026→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q1

MCQ[1 Mark]

The potential flow theory assumes that the flow is

(A)

irrotational, inviscid and incompressible

(B)

rotational, viscous and incompressible

(C)

rotational, viscous and compressible

(D)

irrotational, inviscid and compressible

Explanation

GATE→2026→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q2

MCQ[2 Marks]

The drag force on a non-lifting smooth body immersed in an incompressible, irrotational, uniform flow is

(A)

zero

(B)

finite and greater than zero

(C)

infinite

(D)

finite and less than zero

Explanation

GATE→2026→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q3

MSQ[2 Marks]

Pick the CORRECT statement(s) corresponding to the following equation: $$\frac{\partial u}{\partial t} + u \cdot \nabla u = -\frac{1}{\rho}\nabla p + g + \nu\nabla^2 u$$ where u is velocity vector, p is pressure, \rho is density, g is gravitational acceleration vector, t is time, and \nu is kinematic viscosity.

(A)

It represents the conservation of linear momentum.

(B)

It is a nonlinear partial differential equation.

(C)

It is valid for both Newtonian and non-Newtonian fluids.

(D)

It is valid for incompressible flow.

Explanation

GATE→2026→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q4

MSQ[2 Marks]

Which of the following Reynolds numbers do(es) NOT represent creeping flow?

(A)

0.01

(B)

0.001

(C)

$5 \times 10^5$

(D)

2300

Explanation

GATE→2026→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q5

NAT[2 Marks]

Water of density $1000\text{ kg/m}^3$ flows at a steady rate in a converging duct of circular cross-section. Let the areas of sections 1 and 2 be $100\text{ cm}^2$ and $50\text{ cm}^2$ respectively. The pressure and average velocity at section 1 are 110 kPa and $1\text{ m/s}$. If the centres of the two sections are at the same elevation, then the pressure at section 2 is kPa (answer in one decimal place).

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q6

MCQ[1 Mark]

The sum of the static pressure and dynamic pressure at a point in a fluid flow is called the

(A)

kinematic pressure

(B)

vacuum pressure

(C)

stagnation pressure

(D)

kinetic pressure

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q7

MCQ[1 Mark]

Identify the range of Reynolds number (Re) for a creeping flow.

(A)

$2000 < Re < 20000$

(B)

$1000 < Re < 2000$

(C)

$10 < Re < 100$

(D)

$Re \ll 1$

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q8

NAT[2 Marks]

The stream function of a two-dimensional flow field is given as $\psi = 2xy + 2y + 2x$. The coordinates of two points P and Q in the flow field are $(1, 2)$ and $(2, 5)$ respectively.\nThe magnitude of flow discharge between the streamlines passing through P and Q is (answer in integer).

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q9

NAT[2 Marks]

A tank with a constant water level of 4 m above the centreline of an opening of diameter 100 mm is shown in the figure. Neglect all losses and assume $g = 9.81\text{ m/s}^2$.\nThe discharge through the opening is litre/s (answer in integer).

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q10

NAT[2 Marks]

A negligibly thin horizontal plate PQ has a length 3 m and width 1 m. It is being pulled along its length at a speed of $1\text{ m/s}$ in between two static parallel plates as shown in the figure. The gap of 6 cm between the plates is filled with a Newtonian fluid of dynamic viscosity $\mu = 0.2\text{ N-s/m}^2$. The thin plate is located at 3 cm from the top surface. The velocity distribution between the thin plate and the static plates is linear.\nThe steady force required to pull the plate is N (answer in integer).

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q11

NAT[2 Marks]

Water of density $\rho = 1000\text{ kg/m}^3$ flows with a velocity $V = 50\text{ m/s}$ through a $180^{\circ}$ curved tube of uniform cross-section as shown in the figure. If the flow rate is $0.06\text{ m}^3/\text{s}$, the magnitude of reaction force $F_x$ required to keep it stationary is kN (rounded off to one decimal place).

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q12

MCQ[1 Mark]

Which one of the following is the integral/differential mass conservation equation (continuity equation)?

(A)

Option A

(B)

Option B

(C)

$-\frac{\partial}{\partial t}\iint_{V}\rho dV=\iint_{S}\rho\vec{v}.\hat{n}\,ds$

(D)

Option D

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q13

MCQ[1 Mark]

Identify the type of flow from the time series plots of instantaneous fluid velocity (u) at a point (I, II, III, IV).

(A)

Option A

(B)

Option B

(C)

I - steady turbulent flow; II - unsteady turbulent flow; III - steady laminar flow; IV - unsteady laminar flow

(D)

Option D

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q14

NAT[1 Mark]

A 10 m long pipe with inlet and outlet diameters of 40 cm and 20 cm respectively, is carrying an incompressible fluid with a flow rate of $0.04\text{ m}^3/\text{s}$. The ratio of the velocity at the outlet to that at the inlet is (rounded off to one decimal place)

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q15

NAT[1 Mark]

Consider a fluid between two horizontal parallel flat plates 5 mm apart as shown in the figure. The top plate of dimensions $0.5\text{ m} \times 2\text{ m}$ is towed with an applied horizontal force F of 0.01 N, while the infinitely long bottom plate is kept fixed. The horizontal velocity profile between the plates is assumed to be linear. If the dynamic viscosity ($\mu$) of the fluid is $0.89 \times 10^{-3}\text{ N-s/m}^2$ then the towing velocity of the top plate is $m/s$ (rounded off to three decimal places).

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q16

MCQ[2 Marks]

A uniform flow, a point source of strength $+\sigma$ at $(a, 0)$ and a point sink of strength $-\sigma$ at $(-a, 0)$ are shown in the figure. The velocity potential $\phi$ resulting from the superposition of these flow fields is given by

(A)

$\phi=-U_{\infty}x+\frac{\sigma}{2\pi}\ln\sqrt{(x+a)^{2}+y^{2}}-\frac{\sigma}{2\pi}\ln\sqrt{(x-a)^{2}+y^{2}}$

(B)

$\phi=-U_{\infty}x+\frac{\sigma}{2\pi}\ln\sqrt{(x-a)^{2}+y^{2}}-\frac{\sigma}{2\pi}\ln\sqrt{(x+a)^{2}+y^{2}}$

(C)

$\phi=U_{\infty}x+\frac{\sigma}{2\pi}\ln\sqrt{(x-a)^{2}+y^{2}}-\frac{\sigma}{2\pi}\ln\sqrt{(x+a)^{2}+y^{2}}$

(D)

$\phi=U_{\infty}x+\frac{\sigma}{2\pi}\ln\sqrt{(x-a)^{2}+y^{2}}-\frac{\sigma}{2\pi}\ln\sqrt{(x-a)^{2}+y^{2}}$

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q17

MSQ[2 Marks]

Consider the following momentum equation vector form terms: $\rho \left[ \frac{\partial V}{\partial t} + \text{grad}\left(\frac{V^{2}}{2}\right) + (\text{curl}\,V)\times V \right] = -\text{grad}(P + \rho gz) + \mu\nabla^{2}V$ Let A, B and C denote the first, second and third term on the left-hand side respectively and, D and E denote the first and second term on the right-hand side respectively. Which of the following statement(s) is/are correct?

(A)

If terms A, C and E vanish, then the flow is irrotational.

(B)

If term A vanishes, then the flow is steady.

(C)

If term D vanishes, then it leads to the Euler's equation.

(D)

If terms A, B, C and E vanish, then it leads to the hydrostatic equation.

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q18

NAT[2 Marks]

A circular cylinder of diameter $0.5\text{ m}$ and length $2\text{ m}$, rotating in clockwise direction in a flow of velocity $2\text{ m/s}$. Assume the density of fluid is $1.225\text{ kg/m}^3$ and $\pi = 3.14$. By Kutta-Joukowski theorem, the lift force is N (rounded off to the nearest integer).

Explanation

GATE→2023→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q19

MCQ[1 Mark]

A submerged cylinder of diameter 1 m is rotating clockwise at 100 rpm, in a flow with a free stream velocity of $10\text{ m/s}$. Assuming ideal flow, the number of stagnation points on the cylinder is

(A)

2

(B)

3

(C)

1

(D)

0

Explanation

GATE→2023→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q20

NAT[1 Mark]

A piezometer and a pitot tube measure the static and the total pressure of a fluid in a pipe flow respectively. The piezometer reads 100 kPa and the pitot tube shows 200 kPa. The density of the fluid is $1000\text{ kg/m}^3$.\nThe velocity of the flow is m/s (round off to one decimal place)

Explanation

GATE→2023→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q21

MCQ[2 Marks]

A fully filled water tank OABCD has a circular arc (AB) of radius 10 m at the bottom as shown in the following figure. The height BC is 10 m. The length OA and CD are 5 m and 15 m, respectively. The density of the water is $\rho\text{ kg}/\text{m}^3$ and the acceleration due to gravity is $g\text{ m}/\text{s}^2$.\nThe magnitude of the resultant hydrostatic force per unit width acting on AB in N/m lies between

(A)

190\rho g and 200\rho g

(B)

210\rho g and 220\rho g

(C)

230\rho g and 240\rho g

(D)

250\rho g and 260\rho g

Explanation

GATE→2023→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q22

MCQ[2 Marks]

The velocity vector of a 2D flow field is given by $\vec{V}=2y^{2}\hat{i}+x^{2}t\hat{j}$.\nThe acceleration is

(A)

$4x^{2}ty\hat{i}+(x^{2}+4xy^{2}t)\hat{j}$

(B)

$4x^{2}ty\hat{i}-(x^{2}+4xy^{2}t)\hat{j}$

(C)

$4x^{2}ty\hat{i}+x^{2}\hat{j}$

(D)

$x^{2}\hat{j}$

Explanation

GATE→2023→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q23

MCQ[2 Marks]

For a 2D ideal flow, let $\varphi$ be the velocity potential and $\psi$ be the stream function.\nWhich one of the following is TRUE?

(A)

$\nabla^{2}\varphi=0$ and $|\nabla\psi|^{2}=|\nabla\varphi|^{2}$

(B)

$\nabla^{2}\varphi=0$ and $\nabla\cdot\nabla\varphi\neq 0$

(C)

$\nabla^{2}\psi=0$ and $|\nabla\psi|^{2}\neq|\nabla\varphi|^{2}$

(D)

$\nabla^{2}\psi=0$ and $\nabla\psi\times\nabla\varphi=0$

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q24

MCQ[1 Mark]

A truck loaded with a half-filled water tank is moving at a constant horizontal acceleration a. The acceleration due to gravity is g. At steady state, the angle $\theta$ made by the free surface with the horizontal plane is

(A)

$\sin^{-1}(a/g)$

(B)

$\tan^{-1}(g/a)$

(C)

$\tan^{-1}(a/g)$

(D)

$\sin^{-1}(g/a)$

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q25

MCQ[1 Mark]

Which one of the following combinations of elementary flows will lead to an ideal flow past a deeply submerged circular cylinder with circulation?

(A)

Source, sink and uniform flow

(B)

Doublet, uniform flow and vortex

(C)

Doublet and vortex

(D)

Source and uniform flow

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q26

MSQ[1 Mark]

Which of the following flows are represented by the velocity field, $\vec{V}=(x^{2}-y^{2})\hat{i}-2xy\hat{j}$?

(A)

Incompressible flow

(B)

Compressible flow

(C)

Irrotational flow

(D)

Rotational flow

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q27

MCQ[2 Marks]

In a potential flow field, if the stream function $\psi=xy^{2}$, then the velocity potential is

(A)

$\frac{x^{2}-y^{2}}{2}$

(B)

$\frac{x^{2}+y^{2}}{2}$

(C)

$y\left(x^{2}+\frac{y^{2}}{3}\right)$

(D)

$y\left(x^{2}-\frac{y^{2}}{3}\right)$

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q28

MSQ[2 Marks]

Which of the following statements are TRUE for a fluid flow over a deeply submerged body?

(A)

D'Alembert's paradox states that a deeply submerged body in a real fluid flow experiences no drag force

(B)

D'Alembert's paradox states that a deeply submerged body in an ideal fluid flow experiences no drag force

(C)

The wall shear stress at the point of flow separation on the body is zero

(D)

Dimples/dentures on a body surface facilitate earlier transition to turbulent flow which delays the boundary layer separation

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q29

NAT[2 Marks]

A horizontal cylinder of 1.0 m diameter is placed transversely at the aft of a ship and is completely immersed in water. The cylinder rotates at 100 RPM and inflow velocity is $10\text{ m/s}$. Water density is $1000\text{ kg/m}^3$. Assuming an ideal planar flow, the lift force/unit length acting on the cylinder is kN/m (rounded off to one decimal place).

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q30

NAT[2 Marks]

Consider a steady flow through a horizontal nozzle. The nozzle inlet area is $1\text{ m}^{2}$ and the outlet area is $0.05\text{ m}^{2}$. At the outlet, the flow discharges to atmosphere. Assuming the flow to be incompressible and frictionless, and the density of the fluid as $1\text{ kg/m}^{3}$, the gauge pressure required at the nozzle inlet to produce an outlet speed of $100\text{ m/s}$ is $N/m^{2}$ (rounded off to nearest integer).

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q31

NAT[2 Marks]

Consider a point source in a uniform flow of velocity $U=4\text{ m}/\text{s}$ along the positive x-axis as shown in the figure. Assume a two-dimensional steady potential flow. The potential due to the point source is given by $\log_{e}(r)$, where $r^{2}=x^{2}+y^{2}$.\nThen the magnitude of the distance d between the point source and the stagnation point is m (rounded off to two decimal places).

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Fluid Mechanics & Potential Flow Theory

Q32

NAT[2 Marks]

Consider a steady incompressible laminar flow between two parallel long plates separated by a distance $h=1\text{ m}$ as shown in the figure. The bottom plate is fixed, and the flow is driven by the motion of the upper plate alone. No externally imposed pressure exists.\nIf the upper plate has a velocity of $U=10\text{ m}/\text{s}$, the kinematic viscosity of the fluid is $10^{-6}\text{ m}^2/\text{s}$ and the density of the fluid is $10^{3}\text{ kg}/\text{m}^{3}$, then the shear stress at the bottom plate is $N/m^{2}$ (correct to two decimal places).

Explanation

Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

13 Questions

GATE→2026→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q33

MCQ[2 Marks]

Adverse pressure gradient implies that

(A)

pressure decreases in the direction of flow

(B)

pressure increases in the direction of flow

(C)

pressure is zero everywhere within the flow field

(D)

pressure is uniform (non-zero) everywhere within the flow field

Explanation

GATE→2026→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q34

MSQ[2 Marks]

Consider a steady, two-dimensional, laminar, incompressible flow of water over a horizontal flat plate of length L with Reynolds number, $Re_L = 10^4$. The flat plate is aligned with the incoming free-stream flow. The x-axis is along the length of the plate while the y-axis is normal to the plate. The respective velocity components are u and v. Which of the following statements is/are TRUE?

(A)

For the flow within the boundary layer, $u \gg v$.

(B)

For the flow within the boundary layer, $\frac{\partial u}{\partial y} \gg \frac{\partial u}{\partial x}$.

(C)

The flow within the boundary layer is irrotational and inviscid.

(D)

The thickness of the boundary layer is much less than the length of the flat plate.

Explanation

GATE→2026→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q35

MSQ[2 Marks]

Consider the flow of water over a smooth curved wall surface. It is given that the flow separates at some location R on the surface known as the separation point. Pick the CORRECT option(s).

(A)

At R, the wall shear stress is zero.

(B)

At R, $\frac{\partial u}{\partial y} = 0$, where y is normal to the surface and u is the velocity of the flow tangential to the surface.

(C)

At R, viscosity of the fluid becomes zero.

(D)

Immediately downstream of R, the direction of flow is reversed locally.

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q36

MCQ[1 Mark]

The ratio of the magnitudes of vorticity to rate of rotation in a fluid flow is ______

(A)

2

(B)

3

(C)

$\frac{1}{2}$

(D)

1

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q37

MCQ[1 Mark]

In a laminar boundary layer, the ratio of boundary layer thickness ($\delta$) to the corresponding displacement thickness ($\delta^*$) lies between

(A)

1.5 and 2.4

(B)

2.5 and 3.4

(C)

3.5 and 4.4

(D)

4.5 and 5.4

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q38

MCQ[2 Marks]

Match the non-dimensional numbers in Column 1 with the corresponding definitions in Column 2: \nColumn 1:\nI. Froude number\nII. Reynolds number\nIII. Euler number\nIV. Weber number \nColumn 2:\nP. Ratio of inertial force to surface tension force\nQ. Ratio of inertial force to gravitational force\nR. Ratio of inertial force to viscous force\nS. Ratio of pressure force to inertial force

(A)

I-S; II-R; III-P; IV-Q

(B)

I-Q; II-R; III-S; IV-P

(C)

I-Q; II-R; III-P; IV-S

(D)

I-S; II-Q; III-R; IV-P

Explanation

GATE→2025→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q39

NAT[2 Marks]

Air flows with a velocity of $2\text{ m/s}$ over a flat plate parallel to its length of $0.5\text{ m}$. Kinematic viscosity of air $\nu$ is $1.5 \times 10^{-5}\text{ m}^2/\text{s}$.\nUsing Blasius solution, the boundary layer thickness at the trailing edge of the surface is mm (rounded off to two decimal places).

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q40

MCQ[2 Marks]

Consider model testing where $\lambda$ is the prototype to model length scale ratio. Let $\nu_{p}$ and $\nu_{m}$ denote the corresponding fluid kinematic viscosities. If Froude and Reynolds similarities are maintained between the prototype and model, then which one of the following is correct?

(A)

$\nu_{m} = \lambda^{-3/2} \nu_{p}$

(B)

$\nu_{m} = \lambda^{3/2} \nu_{p}$

(C)

$\nu_{m} = \lambda^{2/3} \nu_{p}$

(D)

$\nu_{m} = \lambda^{-2/3} \nu_{p}$

Explanation

GATE→2024→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q41

MSQ[2 Marks]

Consider the flow past a curved wall as shown in the figure. Which of the following statement(s) is/are correct?

(A)

P is the separation point.

(B)

Between T and U, the pressure gradient in the streamwise direction at the wall is positive.

(C)

U is the stagnation point.

(D)

Between T and U, the streamwise-velocity gradient in the normal direction at the wall is negative.

Explanation

GATE→2023→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q42

MCQ[1 Mark]

In dimensional analysis, according to Buckingham's \pi-theorem, if n is the total number of variables and m is the number of independent dimensions, then the maximum number of independent dimensionless \pi-groups will be

(A)

$m-n$

(B)

$mn$

(C)

$m+n$

(D)

$n-m$

Explanation

GATE→2023→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q43

MCQ[2 Marks]

Water is flowing with a free stream velocity of $0.25\text{ m/s}$ around a submerged flat plate of 2 m length (in the direction of flow) and 1 m width. The local shear stress at a distance x from the leading edge of the plate is given by $\tau = \frac{0.332\rho u^{2}}{\sqrt{Re_{x}}}$\nwhere $\rho = 1000\text{ kg/m}^3$ is the density of the water, u is the free stream velocity and $Re_{x}$ is the Reynolds number at x. Assume that the flow is laminar, and the kinematic viscosity of water is $10^{-6}\text{ m}^2/\text{s}$.\nThe drag force (in Newton) acting on one side of the plate lies between

(A)

0 and 0.05

(B)

0.05 and 0.10

(C)

0.10 and 0.15

(D)

0.15 and 0.20

Explanation

GATE→2023→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q44

MCQ[2 Marks]

A long body with elliptical cross section is held perpendicular to a 2D uniform steady flow field of horizontal velocity $U_{\infty}$ as shown in the following figure. The heights of the control volume (bounded by the dashed lines) at the inlet and outlet are 2h and 4h, respectively. The profile of the horizontal velocity far downstream is given by $U(y)=\frac{U_{\infty}y}{2h}$. The density of the fluid is $\rho$. The magnitude of the drag force per unit length acting on the body is

(A)

$\frac{2\rho{U_{\infty}}^{2}h}{3}$

(B)

$\frac{\rho{U_{\infty}}^{2}h}{3}$

(C)

$\frac{\rho{U_{\infty}}^{2}h}{2}$

(D)

$\frac{2\sqrt{2}\rho{U_{\infty}}^{2}h}{3}$

Explanation

GATE→2022→Fluid Mechanics and Marine Hydrodynamics→Boundary Layer Theory, Vorticity & Hydrodynamic Model Testing

Q45

NAT[1 Mark]

The laminar and turbulent boundary layer thickness of a flat plate are given by $\frac{0.37x}{Re_{x}^{1/5}}$ and $\frac{3x}{Re_{x}^{1/2}}$ (or similar standard correlations), where x is the distance from the leading edge and $Re_{x}$ is the Reynolds number at x-location.\nThe kinematic viscosity of the fluid is $10^{-6}\text{ m}^2/\text{s}$. A 100 m long plate is moving at a speed of $10\text{ m}/\text{s}$. The boundary layer thickness at the rear end of the plate is m (rounded off to two decimal places).

Explanation