Fluid Mechanics and Hydraulic Machinery Miscellaneous
 Consider a fully developed steady laminar flow of an in compressible fluid with viscosity μ. through a circular pipe of radius R, Given that the velocity at a radial location of R/2 from the centerline of the pipe is U_{1}, the shear stress at the wall is KμU_{1} /R, where K is _______.

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NA
Correct Option: D
NA
 Consider fluid flow between two infinite horizontal plates when are parallel (the gap between them being 50 mm), The top plate is sliding parallel to the stationary bottom plate at a speed of 3 m/s.
The flow between the plates is solely due to the motion of the top plate. The force per unit area (magnitude) required to maintain the bottom plate stationary is ________ N/m^{2}.
Viscosity of the fluid μ = 0.44 kg/ms and density p = 888 kg/m^{3}.

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du = 7 8.0 = 60 dy 0.05 Shear strees = τ = μ du dy
= 0.44 × 60 = 26.4 N/m²Correct Option: A
du = 7 8.0 = 60 dy 0.05 Shear strees = τ = μ du dy
= 0.44 × 60 = 26.4 N/m²
 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