GATE ME 2020 Set 1 — Question 26
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Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations
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Question
The velocity field of an incompressible flow in a Cartesian system is represented byWhich one of the following expressions for is valid?
Correct answer
(B) -4xy - 4xz
Solution
For an incompressible flow, the divergence of the velocity field must be zero:Given , we have:
Substituting these into the continuity equation:Integrating with respect to :Checking the options:
(A)
(B) . This is valid.
(C)
(D)
Thus, option (B) is the correct expression.
Substituting these into the continuity equation:Integrating with respect to :Checking the options:
(A)
(B) . This is valid.
(C)
(D)
Thus, option (B) is the correct expression.
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