Fluid Mechanics - Fluid Mechanics and Marine Hydrodynamics - Naval Architecture & Marine Engineering Previous Year Questions

1

2022 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2022

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

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

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2

2022 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2022

A 1:20 scaled model of a surface ship is tested in a towing tank. The model is towed at 3 m/s and drag force measured is 10 N. The velocity of the prototype and the drag force acting on the prototype, respectively, are ______ m/s and ______ kN.

A

60.4 and 80

B

13.4 and 80

C

13.4 and 4

D

60.4 and 4

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3

2022 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2022

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

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4

2022 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2022

Consider a steady flow through a horizontal nozzle. The nozzle inlet area is 1 m² and the outlet area is 0.05 m². At the outlet, the flow discharges to atmosphere. Assuming the flow to be incompressible and frictionless, and the density of the fluid as 1 kg/m³, the gauge pressure required at the nozzle inlet to produce an outlet speed of 100 m/s is _____ N/m² (rounded off to nearest integer).

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5

2022 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2022

Consider a steady incompressible laminar flow between two parallel long plates separated by a distance \(h = 1\) 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.
If the upper plate has a velocity of \(U = 10\) m/s, the kinematic viscosity of the fluid is \(10^{-5}\) m²/s and the density of the fluid is \(10^3\) kg/m³, then the shear stress at the bottom plate is __________ N/m² (correct to two decimal places).

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6

2023 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2023

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 ρ kg/m³ and the acceleration due to gravity is g m/s². The magnitude of the resultant hydrostatic force per unit width acting on AB in N/m lies between

A

190ρg and 200ρg

B

210ρg and 220ρg

C

230ρg and 240ρg

D

250ρg and 260ρg

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7

2023 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2023

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

A

4x^2 t y \, \hat{i} + (x^2 + 4xy^2 t) \, \hat{j}

B

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

C

4x^2 t y \, \hat{i} + x^2 \, \hat{j}

D

x^2 \, \hat{j}

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8

2023 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2023

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

A

\(\nabla^2 \varphi = 0\) and \(|\nabla \psi|^2 = |\nabla \varphi|^2\)

B

\(\nabla^2 \varphi = 0\) and \(\nabla \psi \cdot \nabla \varphi \neq 0\)

C

\(\nabla^2 \psi = 0\) and \(|\nabla \psi|^2 \neq |\nabla \varphi|^2\)

D

\(\nabla^2 \psi = 0\) and \(\nabla \psi \times \nabla \varphi = 0\)

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9

2023 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2023

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

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

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10

2024 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2024

Which one of the following is the mass conservation equation?

A

\(\frac{D}{Dt}\iiint_V \rho \vec{v} \cdot \hat{n} \, dV = 0\)

B

\(\frac{\partial}{\partial t}\iiint_V \rho dV = 0\)

C

\(-\frac{\partial}{\partial t}\iiint_V \rho dV = \iint_S \rho \vec{v} \cdot \hat{n} \, ds\)

D

\(-\frac{D}{Dt}\iiint_V \rho dV = \iint_S \rho \vec{v} \cdot \hat{n} \, ds\)

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11

2024 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2024

Identify the type of flow from the time series plots of instantaneous fluid velocity (u) at a point.

A

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

B

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

C

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

D

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

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12

2024 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2024

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 m³/s. The ratio of the velocity at the outlet to that at the inlet is _____ (rounded off to one decimal place)

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13

2024 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2024

A 100 m long ship has a cruising speed of 25 knots. A geometrically similar model of 4 m length is used for resistance prediction in a towing tank. The corresponding speed of the model is _____ knots.

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14

2024 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2024

Consider a fluid between two horizontal parallel flat plates 5 mm apart as shown in the figure. The top plate of dimensions 0.5 m × 2 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 (μ) of the fluid is 0.89 × 10⁻³ N-s/m², then the towing velocity of the top plate is ______ m/s (rounded off to three decimal places).

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15

2024 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2024

Consider model testing where \(\lambda\) is the prototype to model length scale ratio. Let \(v_p\) and \(v_m\) 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

\(v_m = \lambda^{-3/2}v_p\)

B

\(v_m = \lambda^{3/2}v_p\)

C

\(v_m = \lambda^{2/3}v_p\)

D

\(v_m = \lambda^{-2/3}v_p\)

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16

2024 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2024

Consider the following momentum equation. 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?
\[ \rho \left[ \frac{\partial \boldsymbol{V}}{\partial t} + grad \left( \frac{|\boldsymbol{V}|^2}{2} \right) + (curl \boldsymbol{V}) \times \boldsymbol{V} \right] = -grad(P + \rho gz) + \mu \nabla^2 \boldsymbol{V} \]

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.

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17

2025 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2025

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

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18

2025 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2025

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 << 1

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19

2025 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2025

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

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20

2025 · Naval Architecture & Marine Engineering · Fluid Mechanics and Marine Hydrodynamics · Fluid Mechanics

Naval Architecture & Marine Engineering (NM) 2025

Match the non-dimensional numbers in Column 1 with the corresponding definitions in Column 2

Column 1	Column 2
I. Froude number	P. Ratio of inertial force to surface tension force
II. Reynolds number	Q. Ratio of inertial force to gravitational force
III. Euler number	R. Ratio of inertial force to viscous force
IV. Weber number	S. 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

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