GATE ME 2017 Set 1 — Question 7
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Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations
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Question
Consider the two-dimensional velocity field given by , where and are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?
Correct answer
(B) a₁ + b₂ = 0
Solution
For an incompressible flow, the divergence of the velocity field must be zero:Given , where:
The continuity equation for incompressible flow is:Calculating the partial derivatives:Substituting these into the continuity equation:Thus, the correct option is (B).
The continuity equation for incompressible flow is:Calculating the partial derivatives:Substituting these into the continuity equation:Thus, the correct option is (B).
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