Fluid Mechanics and Hydraulic Machinery Miscellaneous
 Match the following pairs:
Equation Physical Interpretation P. ∇ × v̄ = 0 I. Incompressible continuity equation Q. ∇ . v̄ = 0 II. Steady flow R. ∆v̄/∆t = 0 III. Irrotational flow S. δv̄/δt = 0 IV. Zero acceleration of fluid particle

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PIII, QI, RIV, SII
Correct Option: C
PIII, QI, RIV, SII
 For an incompressible flow field, V, which one of the following conditions must be satisfied?

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In compressible flow condition
∇.v̄ = 0Correct Option: A
In compressible flow condition
∇.v̄ = 0
 For the continuity equation given by∆ . V̄ = 0 to be valid, where V̄ is the velocity vector, which one of the following is a necessary condition?

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The basic equation of continuity for fluid flow is given by
ρu ρv ρw ρ u y z t
Now if ρ remains constant, then only we can write
∇.v̄ = 0i.e. δu + δv + δw = 0 δx δy δz
hence incompressible flowCorrect Option: D
The basic equation of continuity for fluid flow is given by
ρu ρv ρw ρ u y z t
Now if ρ remains constant, then only we can write
∇.v̄ = 0i.e. δu + δv + δw = 0 δx δy δz
hence incompressible flow
 Which combination of the following statements about steady incompressible forced vortex flow is correct?
P: Shear stress is zero at all points in the flow.
Q: Vorticity is zero at all points in the flow.
R: Velocity is directly proportional to the radius from the centre of the vortex.
S: Total mechanical energy per unit mass is constant in the entire flow field.
Select the correct answer using the codes given below:

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Clearly zero shear stress and vortex.
Correct Option: B
Clearly zero shear stress and vortex.
 The 2D flow with, velocity
V̄ = (x + 2y + 2) î + (4 – y) ĵ is

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v̄ = (x + 2y +2)î + (4  y)ĵ
u =x + 2y + 2, v = 4 – y∴ δv = 1, δv =  1 δx δy ∴ δv + 1, δv = 0 δx δy
hence in compressible.Again, ω = 1 δv  δv 2 δx δy = 1 (0  2) =  1. 2
hence not irrotational.Correct Option: D
v̄ = (x + 2y +2)î + (4  y)ĵ
u =x + 2y + 2, v = 4 – y∴ δv = 1, δv =  1 δx δy ∴ δv + 1, δv = 0 δx δy
hence in compressible.Again, ω = 1 δv  δv 2 δx δy = 1 (0  2) =  1. 2
hence not irrotational.