Fluid Mechanics and Hydraulic Machinery Miscellaneous Easy Questions and Answers | Page - 22

Fluid Mechanics and Hydraulic Machinery Miscellaneous

Consider the following statements regarding streamline(s):
(i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point
(ii) There is no flow across streamlines
(iii)
dx =
dy =
dz is the differential equation of a streamline, where u, v and w are velocities in directions x, y and z, respectively
u v w

(iv) In an unsteady flow, the path of a particle is a streamline
Which one of the following combinations of the statements is true?

1. (i), (ii), (iv)
1. (ii), (iii), (iv)
1. (i), (iii), (iv)
1. (i), (ii), (iii)

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NA

Correct Option: D

NA

A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m³. Liquid of densit y 1000 k g/m³ is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is _____ mm.

1. h ≥ 80 mm
1. h ≥ 70 mm
1. h ≥ 75 mm
1. h ≥ 81 mm

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Given, side of cube (a) = 100 m
Density of material of cube = 800 kg/m³
Poured liquid density = 1000 kg/m³
Now, Minimum height to which the liquid needs to be poured into the container for the cube to just lift up, should satisfy the condition
F_B ≥ (mg)_block
ρ_fgV_fd ≥ (ρV)_block× g
1000 × 0.1 × h ≥ 800 × 0.1 × 0.1 × 0.1
h ≥ 0.08 m
h ≥ 80 m

Correct Option: A

Given, side of cube (a) = 100 m
Density of material of cube = 800 kg/m³
Poured liquid density = 1000 kg/m³
Now, Minimum height to which the liquid needs to be poured into the container for the cube to just lift up, should satisfy the condition
F_B ≥ (mg)_block
ρ_fgV_fd ≥ (ρV)_block× g
1000 × 0.1 × h ≥ 800 × 0.1 × 0.1 × 0.1
h ≥ 0.08 m
h ≥ 80 m

For the stability of a floating body the

1. centre of buoyancy must coincide with the centre of gravity
1. centre of buoyancy must be above the centre of gravity
1. centre of gravity must be above the centre of buoyancy
1. metacentre must be above the centre of gravity

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NA

Correct Option: D

NA

For a floating body, buoyant force acts at the

1. centroid of the floating body
1. center of gravity of the body
1. centroid of the fluid vertically below the body
1. centroid of the displaced fluid

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For floating body Buoyancy force acts through the center of buoyancy which is C.G for displaced volume.

Correct Option: D

For floating body Buoyancy force acts through the center of buoyancy which is C.G for displaced volume.

A spherical balloon with a diameter of 10 m, shown in the figure below is used for advertisements. The balloon is filled with helium (R_He = 2.08 kJ/kgK) at ambient conditions of 15°C and 100 kPa. Assuming no disturbances due to wind, the maximum allowable weight (in Newton) of balloon material and rope required to avoid the fall of the balloon (R_air = 0.289 kJ/kgK) is_______.

1. 5303.67 N
1. 5203.67 N
1. 5403.67 N
1. 5213.67 N

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V_baloon = 4 πr³ =
4 × 3.14 × 5³ = 523.33m³
3 3

ρHe = P = 100 × 10₃ = .1669 kg/m³
RT 2080 × 288

Total mass = .1669 × 523.33 = 87.36 kg mass of air:
ρ = P =
100 × 10³ = 1.2 kg/m³
RT 2080 × 288

Mass of displaced volume of air = 1.2 × 523.33 = 628 kg
Net Buoyant mass = 628 – 87. 36 = 540.64 kgl Allowable Mass, M_allowable = 540.64 × 9.81
= 5303.67 N

Correct Option: A

V_baloon = 4 πr³ =
4 × 3.14 × 5³ = 523.33m³
3 3

ρHe = P = 100 × 10₃ = .1669 kg/m³
RT 2080 × 288

Total mass = .1669 × 523.33 = 87.36 kg mass of air:
ρ = P =
100 × 10³ = 1.2 kg/m³
RT 2080 × 288

Mass of displaced volume of air = 1.2 × 523.33 = 628 kg
Net Buoyant mass = 628 – 87. 36 = 540.64 kgl Allowable Mass, M_allowable = 540.64 × 9.81
= 5303.67 N