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GATE 2021 ME (ME2) – Question 23

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

A two dimensional flow has velocities in $x$ and $y$ directions given by $u=2xyt$ and $v=-y^2t$, where $t$ denotes time. The equation for streamline passing through $x=1$, $y=1$ is

  1. $x^2y=1$
  2. $xy^2=1$
  3. $x^2y^2=1$
  4. $x/y^2=1$

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Correct answer: (B) $xy^2=1$

Explanation

At fixed time, streamline slope is $dy/dx=v/u=-y/(2x)$. Separate variables: 2 dy/y=−dx/x.

Integration gives ln(xy²)=constant. Through(1,1), **xy²=1 (B)**. The common time factor cancels for nonzero t.