## Fluid Mechanics and Hydraulic Machinery Miscellaneous

#### Fluid Mechanics and Hydraulic Machinery

1. Oil (kinematic viscosity, υ oil = 1.0 × 10-6 m2/s) flows through a pipe of 0.5 m diameter with a velocity of 10 m/s. Water (kinematic viscosity, vw = 0.89 × 10-6 m2/s) is flowing through a model pipe of diameter 20 mm. For satisfying the dynamic similarity, the velocity of water (in m/s) is _______.

1. oil water
v = 1.0 × 10–5 m²/s v = 0.89 × 10– 6 m²/s
d = 0.5 m
d = 0.02 m
v = 10 m/sec
v =?
[Re](oil) = [Re](w)

 10 × 0.5 = V × 0.02 1.0 × 10-5 8.9 × 10-6

⇒ v = 22.25 m/s

##### Correct Option: C

oil water
v = 1.0 × 10–5 m²/s v = 0.89 × 10– 6 m²/s
d = 0.5 m
d = 0.02 m
v = 10 m/sec
v =?
[Re](oil) = [Re](w)

 10 × 0.5 = V × 0.02 1.0 × 10-5 8.9 × 10-6

⇒ v = 22.25 m/s

1. For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through a pipe radius 5 cm, the axial pressure gradient is –10 Pa/m. The magnitude of axial velocity (in m/s) at a radial location of 0.2 cm is ________.

1.  u = -1 δP (R² - r²) 4μδx

 = -1 × (-10)((0.05)² - (0.002)²) 4μδx

u = 6.24 m/s

##### Correct Option: A

 u = -1 δP (R² - r²) 4μδx

 = -1 × (-10)((0.05)² - (0.002)²) 4μδx

u = 6.24 m/s

1. Air (ρ = 1.2 kg/m3 and kinematic viscosity, υ = 2 × 10-5 m2/s) with a velocity of 2 m/s flows over the top surface of a flat plate of length 2.5 m. If the average value of friction coefficient is
 Cf = 1.328 √Rex

the total drag force (in N) per unit width of the plate is _________.

1.  Cf = 1.320 √Rex

 Rex = ρvd = vd. μ υ

v = 2m/s
1 = 2.5m
υ = 2 × 10–5 m²/s
F = 1/2 CfρAυ²
A = 2.5 × 1
On substituting we get
F = 0.0159N

##### Correct Option: D

 Cf = 1.320 √Rex

 Rex = ρvd = vd. μ υ

v = 2m/s
1 = 2.5m
υ = 2 × 10–5 m²/s
F = 1/2 CfρAυ²
A = 2.5 × 1
On substituting we get
F = 0.0159N

1. Couette flow is characterized by

1. Couette flow is steady incompressible, laminar flow between one fixed plate and other moving with constant velocity.

##### Correct Option: D

Couette flow is steady incompressible, laminar flow between one fixed plate and other moving with constant velocity.

1. Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of 0.25 m from the leading edge of the plate is 8 mm, the boundary layer thickness (in mm), at a distance of 0.75 m, is ______

1.  ∴ δ = k , here ‘k’ is constant x √x

 ∴ δ1 = δ2 √x1 √x2

 ∴ 8 = δ2 ∴ δ2 = 13.86 mm. √0.25 √0.75

 ∵ δ = 0.60 x √Rex

 or δ = 0.60 = 0.60√v x √xu∞/v √x.√u∞/v

∵ √v and √u is constant in both the cases

##### Correct Option: B

 ∴ δ = k , here ‘k’ is constant x √x

 ∴ δ1 = δ2 √x1 √x2

 ∴ 8 = δ2 ∴ δ2 = 13.86 mm. √0.25 √0.75

 ∵ δ = 0.60 x √Rex

 or δ = 0.60 = 0.60√v x √xu∞/v √x.√u∞/v

∵ √v and √u is constant in both the cases