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GATE 2024 AE – Question 21

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

In the context of steady, inviscid, incompressible flows, consider the superposition of a uniform flow with speed $U$ along the positive x-axis (from left to right), and a source of strength $\Lambda$ located at the origin. Which one of the following statements is NOT true regarding the location of the stagnation point of the resulting flow?

  1. It is located to the left of the origin
  2. It moves closer to the origin for increasing $\Lambda$, while $U$ is held constant
  3. It moves closer to the origin for increasing $U$, while $\Lambda$ is held constant
  4. It is located along the x-axis

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Correct answer: (B) It moves closer to the origin for increasing $\Lambda$, while $U$ is held constant

Explanation

The stagnation point is where the uniform stream cancels the source velocity, $U = \frac{\Lambda}{2\pi r}$ on the negative x-axis, so $x_s = -\frac{\Lambda}{2\pi U}$. It lies on the x-axis to the left of the origin (A and D true). It moves closer to the origin as $U$ grows (C true) but farther away as $\Lambda$ grows, so B is not true.