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?

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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/m^{3}. Liquid of densit y 1000 k g/m^{3} 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.

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Given, side of cube (a) = 100 m
Density of material of cube = 800 kg/m^{3}
Poured liquid density = 1000 kg/m^{3}
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_{f}gV_{fd} ≥ (ρV)_{block}× g
1000 × 0.1 × h ≥ 800 × 0.1 × 0.1 × 0.1
h ≥ 0.08 m
h ≥ 80 mCorrect Option: A
Given, side of cube (a) = 100 m
Density of material of cube = 800 kg/m^{3}
Poured liquid density = 1000 kg/m^{3}
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_{f}gV_{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

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NA
Correct Option: D
NA
 For a floating body, buoyant force acts at the

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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_______.

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V_{baloon} = 4 πr^{3} = 4 × 3.14 × 5^{3} = 523.33m^{3} 3 3 ρHe = P = 100 × 10_{3} = .1669 kg/m^{3} RT 2080 × 288
Total mass = .1669 × 523.33 = 87.36 kg mass of air:ρ = P = 100 × 10^{3} = 1.2 kg/m^{3} 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 NCorrect Option: A
V_{baloon} = 4 πr^{3} = 4 × 3.14 × 5^{3} = 523.33m^{3} 3 3 ρHe = P = 100 × 10_{3} = .1669 kg/m^{3} RT 2080 × 288
Total mass = .1669 × 523.33 = 87.36 kg mass of air:ρ = P = 100 × 10^{3} = 1.2 kg/m^{3} 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