Fluid Mechanics and Hydraulic Machinery Miscellaneous
 Oil (kinematic viscosity, υ _{oil} = 1.0 × 10^{6} m^{2}/s) flows through a pipe of 0.5 m diameter with a velocity of 10 m/s. Water (kinematic viscosity, v_{w} = 0.89 × 10^{6} m^{2}/s) is flowing through a model pipe of diameter 20 mm. For satisfying the dynamic similarity, the velocity of water (in m/s) is _______.

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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 =?
[R_{e}]_{(oil)} = [R_{e}]_{(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 =?
[R_{e}]_{(oil)} = [R_{e}]_{(w)}10 × 0.5 = V × 0.02 1.0 × 10_{5} 8.9 × 10_{6}
⇒ v = 22.25 m/s
 For a fully developed laminar flow of water (dynamic viscosity 0.001 Pas) 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 ________.

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u = 1 δP (R²  r²) 4μδx = 1 × (10)((0.05)²  (0.002)²) 4μδx
u = 6.24 m/sCorrect Option: A
u = 1 δP (R²  r²) 4μδx = 1 × (10)((0.05)²  (0.002)²) 4μδx
u = 6.24 m/s
 Air (ρ = 1.2 kg/m^{3} and kinematic viscosity, υ = 2 × 10^{5} m^{2}/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
C_{f} = 1.328 √Re_{x}
the total drag force (in N) per unit width of the plate is _________.

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C_{f} = 1.320 √Re_{x} Re_{x} = ρvd = vd. μ υ
v = 2m/s
1 = 2.5m
υ = 2 × 10^{–5} m²/s
F = 1/2 C^{f}ρAυ²
A = 2.5 × 1
On substituting we get
F = 0.0159NCorrect Option: D
C_{f} = 1.320 √Re_{x} Re_{x} = ρvd = vd. μ υ
v = 2m/s
1 = 2.5m
υ = 2 × 10^{–5} m²/s
F = 1/2 C^{f}ρAυ²
A = 2.5 × 1
On substituting we get
F = 0.0159N
 Couette flow is characterized by

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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.
 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 ______

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∴ δ = k , here ‘k’ is constant x √x ∴ δ_{1} = δ_{2} √x_{1} √x_{2} ∴ 8 = δ_{2} ∴ δ_{2} = 13.86 mm. √0.25 √0.75 ∵ δ = 0.60 x √Re_{x} or δ = 0.60 = 0.60√v x √xu_{∞}/v √x.√u_{∞}/v
∵ √v and √u_{∞} is constant in both the casesCorrect Option: B
∴ δ = k , here ‘k’ is constant x √x ∴ δ_{1} = δ_{2} √x_{1} √x_{2} ∴ 8 = δ_{2} ∴ δ_{2} = 13.86 mm. √0.25 √0.75 ∵ δ = 0.60 x √Re_{x} or δ = 0.60 = 0.60√v x √xu_{∞}/v √x.√u_{∞}/v
∵ √v and √u_{∞} is constant in both the cases