## Fluid Mechanics and Hydraulic Machinery Miscellaneous

#### Fluid Mechanics and Hydraulic Machinery

1. 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. NA

##### Correct Option: D

NA

1. 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. 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
FB ≥ (mg)block
ρfgVfd ≥ (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
FB ≥ (mg)block
ρfgVfd ≥ (ρV)block× g
1000 × 0.1 × h ≥ 800 × 0.1 × 0.1 × 0.1
h ≥ 0.08 m
h ≥ 80 m

1. For the stability of a floating body the

1. NA

##### Correct Option: D

NA

1. For a floating body, buoyant force acts at the

1. 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.

1. A spherical balloon with a diameter of 10 m, shown in the figure below is used for advertisements. The balloon is filled with helium (RHe = 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 (Rair = 0.289 kJ/kgK) is_______.

1.  Vbaloon = 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, Mallowable = 540.64 × 9.81
= 5303.67 N

##### Correct Option: A

 Vbaloon = 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, Mallowable = 540.64 × 9.81
= 5303.67 N