The GATE Grind

GATE 2022 AE – Question 15

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

For two-dimensional potential flow over a cylinder at free-stream speed $U_\infty$, the maximum cylinder-surface speed is

  1. $U_\infty/2$
  2. $3U_\infty/2$
  3. $2U_\infty$
  4. $4U_\infty/3$

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Show answer and explanation

Correct answer: (C) $2U_\infty$

Explanation

For the 2-D potential flow of a uniform stream $U_\infty$ past a circular cylinder of radius $a$ (uniform flow plus a doublet), the velocity components at the surface $r=a$ are
$$u_r=0,\qquad u_\theta=-2U_\infty\sin\theta .$$

The speed on the surface is therefore
$$|u_\theta|=2U_\infty|\sin\theta| .$$

It is largest at $\theta=\pm90^\circ$ (top and bottom of the cylinder), where $\sin\theta=\pm1$:
$$V_{max}=2U_\infty\quad(\text{option C}).$$

(At the stagnation points, $\theta=0^\circ$ and $180^\circ$, the speed is zero.)