GATE CE 2024 Set 1 — Question 42
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Engineering Mathematics → Fluid Kinematics & Dynamics → Continuity Equation
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Question
A flow velocity field for a fluid is represented by In the context of the fluid and the flow, which one of the following statements is CORRECT?
Correct answer
(A) The fluid is incompressible and the flow is rotational.
Solution
Given the velocity field .
1.Check for Incompressibility:
For a flow to be incompressible, the divergence of the velocity field must be zero:Since , the fluid is incompressible.2.Check for Rotationality:
For a flow to be irrotational, the curl of the velocity field must be zero. In 2D, the vorticity is given by:Since , the flow is rotational.Therefore, the fluid is incompressible and the flow is rotational.Continue learning with Success Tracker
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