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GATE 2026 AE – Question 47

Aerodynamics · Two-dimensional potential flow: sources, sinks, doublets, point vortex and Bernoulli's equation · 2 marks · Multiple select

Consider the flow over an oval modeled using the elementary potential flows as shown below. $U$ represents uniform flow velocity and $\Gamma$ represents circulation around an irrotational line vortex.

[Figure: A uniform stream $U$ from the left, added to two line vortices a distance $a$ apart, one on top of strength $-\Gamma$ and one below it of strength $+\Gamma$.]

Which of the following statements is/are TRUE for this model?

Diagram for GATE 2026 AE question 47
  1. Increasing $U$ enlarges the oval
  2. Increasing $\Gamma$ enlarges the oval
  3. Interchanging the sense of the two vortices does not alter the oval
  4. Moving the vortices too far apart causes the oval to break up

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Correct answer: (B) Increasing $\Gamma$ enlarges the oval; (D) Moving the vortices too far apart causes the oval to break up

Explanation

The vortex pair induces a velocity opposed to the stream between and ahead of the vortices, and the oval is the region where this is balanced by $U$. A stronger pair ($\Gamma$) enlarges the oval (B), while a stronger stream shrinks it (A false). Reversing the vortices turns the induced flow the other way, so there is no closed oval (C false). When the vortices are too far apart, their induced velocity at the centre is too weak and the closed oval breaks up (D).

Official GATE 2026 answer key: https://gate2026.iitg.ac.in/doc/download/2026/Keys/AE_Keys.pdf