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GATE 2020 CE (CE2) – Question 25

Fluid Mechanics · Potential flow, laminar and turbulent flow · 1 mark · Multiple choice

An incompressible flow has $u=-5+6x$, $v=-(9+6y)$. Find the streamline equation.

  1. $(-5+6x)-(9+6y)=C$
  2. $(-5+6x)/(9+6y)=C$
  3. $(-5+6x)(9+6y)=C$
  4. $(9+6y)/(-5+6x)=C$

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Correct answer: (C) $(-5+6x)(9+6y)=C$

Explanation

Streamline slope is $dy/dx=-(9+6y)/(-5+6x)$. Integrate $dy/(9+6y)=-dx/(-5+6x)$ to obtain $\ln|9+6y|+\ln|-5+6x|=C$. Therefore **$(-5+6x)(9+6y)=C$, C**.