GATE 2021 AE – Question 31
A point vortex of strength 5 m²/s lies outside the shown polygonal closed contour. The circulation around the contour is ___ m²/s.
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Correct answer: 0
Explanation
The **circulation** around a closed contour is $\Gamma=\oint\vec V\cdot d\vec s$.
For a point vortex of strength $K$, the flow is irrotational everywhere except at the vortex itself. By Stokes' theorem, the circulation around a closed contour equals the total vorticity enclosed.
- If the vortex is **inside** the contour, $\Gamma=K$.
- If the vortex is **outside** the contour, the contour encloses no vorticity, so $\Gamma=0$.
The vortex of strength 5 m²/s lies outside the polygonal contour, so the circulation is **0 m²/s**.