A steady velocity field is V=(-x2+3y) i+2xy j. Find the magnitude of particle acceleration at (1,-1).

GATE 2017 ME (ME1) – Question 42

Fluid Mechanics · Control-volume analysis of mass, momentum and energy · 2 marks · Multiple choice

A steady velocity field is $\mathbf V=(-x^2+3y)\hat{\mathbf i}+2xy\hat{\mathbf j}$. Find the magnitude of particle acceleration at $(1,-1)$.

2
1
$2\sqrt5$
0

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Correct answer: (C) $2\sqrt5$

Explanation

At the point, $u=-4$ and $v=-2$. For steady flow, $a_x=uu_x+vu_y$ and $a_y=uv_x+vv_y$. Derivatives there are $u_x=-2,u_y=3,v_x=-2,v_y=2$. Thus $a_x=8-6=2$, $a_y=8-4=4$, and $|\mathbf a|=\sqrt{2^2+4^2}=2\sqrt5$, C.

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