GATE 2020 CE (CE1) – Question 24

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

Uniform flow of speed U makes angle θ with the y-axis as shown. Find velocity potential φ.

Diagram for GATE 2020 CE (CE1) question 24

$\pm U(x\sin\theta+y\cos\theta)$
$\pm U(y\sin\theta-x\cos\theta)$
$\pm U(x\sin\theta-y\cos\theta)$
$\pm U(y\sin\theta+x\cos\theta)$

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Correct answer: (A) $\pm U(x\sin\theta+y\cos\theta)$

Explanation

Velocity components are $u=U\sin\theta$ and $v=U\cos\theta$. Integration gives $\phi=U(x\sin\theta+y\cos\theta)+C$. A negative sign applies to the alternate velocity-potential convention. **A**.