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QUESTION: 1

Apart from inertia force, which of the following forces is most important in motion of submarines underwater?

Solution:

QUESTION: 2

Assuming that the thrust T of a propeller depends on the diameter D, speed of advance V, angular velocity ω, dynamic viscosity μ and mass density ρ, which of the following ’non -dimensional parameters can be derived ‘by dimensional analysis?

Solution:

Number of variables = 6

Number of dimensions = 3

Dimensionless parameters = 6 - 3 = 3.

Take D, V, and ρ as repeating variables.

VD/μ will not be dimensionless- number as its dimension is [M^{-1}L^{3}].

QUESTION: 3

Which of the following could be a π-parameter of the function f(F, V, r, m, L) = 0 when V, r and L are taken as repeating variables?

Solution:

A π parameter is constant and has zero dimensional unit i.e. M°L°T°.

QUESTION: 4

Match List-I (Flow problem under study) with List-ll (Model law) and select the correct answer using the codes given below the lists:

List-I

1. Rise of gas bubbles in liquid

2. Flow of gas in a pipe

3. Flow over a spillway dam

4. Flight of supersonic jet

List-II

A. Euler number

B. Froude number

C. Mach number

D. Reynold’s number

E. Weber’s number

Solution:

QUESTION: 5

A ship’s model of scale 1 : 100 had a wave resistance of 1 kg at its design speed. The corresponding wave resistance in prototype will be

Solution:

Froude model is applicable here because of influence of gravity force using froude model law,

or, F_{p} = 1000000 kg

QUESTION: 6

If the velocity, bulk modulus of elasticity and the mass density of a fluid are denoted by U, K and ρ respectively, then the Mach number is given by

Solution:

Mach number U/C =

QUESTION: 7

Euler’s equation of motion

Solution:

ma_{x} = (fg)_{x }+ (f_{p})_{x} + (f_{n})_{x} + (f_{t})_{x}

→ Reynold’s equation

f_{g} → Due to gravity

f_{p} → Due to pressure

f_{n} → Due to viscosity

f_{t} → Due to turbulence

ma_{x} = (fg)x_{ }+ (f_{p})_{x} → Euler’s equation

(Neglected viscous force vand force due to turbulence)

QUESTION: 8

A model of reservoir is emptied in 10 minutes. If the model scale is 1:25, the time taken by the prototype to empty itself, would be

Solution:

∴ t_{p} = 5t_{m} = 5 x 10 = 50 min

QUESTION: 9

When Mach number is more than 6, the flow is called

Solution:

when the Mach number in flow region is slightly less to slightly greater than 1, flow is transonic flow.

QUESTION: 10

A harbour model has a horizontal scale of 1/150 and a vertical scale of 1/60. The interval between successive high tides in the model will be nearly

Solution:

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