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GATE 2024 CE (CE1) – Question 42

Fluid Mechanics · Potential flow, laminar and turbulent flow · 2 marks · Multiple choice

A flow velocity field $\vec{V}: \vec{V}(x, y)$ for a fluid is represented by $\vec{V} = 3\hat{i} + (5x)\hat{j}$
In the context of the fluid and the flow, which one of the following statements is CORRECT?

  1. The fluid is incompressible and the flow is rotational.
  2. The fluid is incompressible and the flow is irrotational.
  3. The fluid is compressible and the flow is rotational.
  4. The fluid is compressible and the flow is irrotational.

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Correct answer: (A) The fluid is incompressible and the flow is rotational.

Explanation

The divergence is $\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0 + 0 = 0$, so the flow satisfies the incompressible continuity equation. The z-component of the curl is $\frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} = 5 - 0 = 5 \ne 0$, so the flow is rotational.