## Fluid Mechanics and Hydraulic Machinery Miscellaneous

#### Fluid Mechanics and Hydraulic Machinery

1. Water flows through a pipe of diameter 0.30 m. What would be the velocity V for the conditions shown in the figure below?

1.  h = x 1 − ρmano ρpipe

 = 0.3 1 − 800 1000

= 0.06 m of water
V1 = √2gh = √2 × 9.8 × 0.6
= 1.084 m/s

##### Correct Option: D

 h = x 1 − ρmano ρpipe

 = 0.3 1 − 800 1000

= 0.06 m of water
V1 = √2gh = √2 × 9.8 × 0.6
= 1.084 m/s

1. In a hand operated liquid sprayer (figure shown below) the liquid from the container rises to the top of the tube because of

1. NA

##### Correct Option: C

NA

1. An incompressible fluid (kinematic viscosity, 7.4 × 10–7 m²/s, specific gravity, 0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates: the shear stress in Pascals on the surface of top plate is

1. Given:
υ = 7.4 × 10–7 m2 /s
ρ = 0.88 × 1000 = 880
v = 0.5 m/s

 Shear stress,   τ = μ⋅ du = (υ × ρ) × du dy dy

 = 7.4 × 10–7 × 800 × 0.5 = 0.6512. (0.0005)

##### Correct Option: B

Given:
υ = 7.4 × 10–7 m2 /s
ρ = 0.88 × 1000 = 880
v = 0.5 m/s

 Shear stress,   τ = μ⋅ du = (υ × ρ) × du dy dy

 = 7.4 × 10–7 × 800 × 0.5 = 0.6512. (0.0005)

1. The velocity profile in fully developed laminar flow in a pipe of diameter D is given by u = u0 (1– 4r²/D²), where r is the radial distance from the center. If the viscosity of the fluid is ρ, the pressure drop across a length L of the pipe is

1. By Hagen – Poiseuille law, for steady laminar flow in circular pipes

 τ = –μ ∂u ∂r

 τ = –∂p . r ∂x 2

 μ ∂u = ∂P ⋅ r ∂r ∂x 2

 μu0 −8r = P . r D² L 2

 .... ∵  u = u0 1 − 4r² D²

 = –16μLu0 D²

[(–) sign is due to drop]

##### Correct Option: D

By Hagen – Poiseuille law, for steady laminar flow in circular pipes

 τ = –μ ∂u ∂r

 τ = –∂p . r ∂x 2

 μ ∂u = ∂P ⋅ r ∂r ∂x 2

 μu0 −8r = P . r D² L 2

 .... ∵  u = u0 1 − 4r² D²

 = –16μLu0 D²

[(–) sign is due to drop]

1. Consider steady laminar incompressible axisymmetric fully developed viscous flow through a straight circular pipe of constant crosssectional area at a Reynolds number of 5. The ratio of inertia force to viscous force on a fluid particle is

1.  Reynold’s number = Inertia force = 5 Viscous force

##### Correct Option: A

 Reynold’s number = Inertia force = 5 Viscous force