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GATE 2020 AE – Question 16

Aerodynamics · Two-dimensional potential flow: sources, sinks, doublets, point vortex and Bernoulli's equation · 1 mark · Multiple choice

Two infinitely long counter-rotating line vortices, each of circulation magnitude Γ, are separated by h in a fluid as shown. They will

Diagram for GATE 2020 AE question 16
  1. Rotate counterclockwise about the midpoint at speed $\Gamma/(2\pi h)$.
  2. Rotate counterclockwise about the midpoint at speed $\Gamma/(4\pi h)$.
  3. Translate along +y at speed $\Gamma/(2\pi h)$.
  4. Translate along +y at speed $\Gamma/(4\pi h)$.

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Correct answer: (C) Translate along +y at speed $\Gamma/(2\pi h)$.

Explanation

At distance h, one point vortex induces speed $\Gamma/(2\pi h)$. The drawn opposite circulation senses make the induced velocity at each vortex point upward. Since both have equal induced translational velocities, their separation stays h and the pair translates in +y, rather than rotating about the midpoint. Select C.

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