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GATE 2016 ME (ME3) – Question 24

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

An incompressible two-dimensional flow has velocity $2xy\hat i-y^2\hat j$. Its streamlines are ______.

  1. $x^2y^2=\text{constant}$
  2. $xy^2=\text{constant}$
  3. $2xy-y^2=\text{constant}$
  4. $xy=\text{constant}$

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Correct answer: (B) $xy^2=\text{constant}$

Explanation

A streamline satisfies dy/dx=v/u=−y/(2x), away from zero denominators. Integrating2dy/y=−dx/x gives ln(xy²)=constant, hence **xy²=constant, B**. The limiting coordinate-axis streamlines are consistent with the velocity field.