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GATE 2018 ME (ME1) – Question 44

Fluid Mechanics · Differential equations of continuity and momentum, velocity potential · 2 marks · Multiple choice

A Lagrangian particle trajectory is $x=x_0e^{-kt}$, $y=y_0e^{kt}$, where $x_0,y_0,k$ are constants. The flow is ______.

  1. unsteady and one-dimensional
  2. steady and two-dimensional
  3. steady and one-dimensional
  4. unsteady and two-dimensional

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Correct answer: (B) steady and two-dimensional

Explanation

Differentiate the particle coordinates: $u=-kx_0e^{-kt}=-kx$ and $v=ky_0e^{kt}=ky$. In Eulerian form these depend on position but not time. The flow is steady and two-dimensional (B).