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GATE 2018 ME (ME1) – Question 19

Fluid Mechanics · Differential equations of continuity and momentum, velocity potential · 1 mark · Multiple choice

For two-dimensional incompressible velocity $\mathbf u=A(x\hat i-y\hat j)$, A > 0, which is FALSE?

  1. It satisfies continuity.
  2. It is unidirectional as $x\to0$, $y\to\infty$.
  3. Its streamlines are x = y.
  4. It is irrotational.

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Show answer and explanation

Correct answer: (C) Its streamlines are x = y.

Explanation

Continuity holds because $u_x+v_y=A-A=0$. Curl is zero. Streamlines satisfy $dy/dx=-y/x$, hence $xy=C$, not x = y. Therefore C is false.