The steady velocity field is v=2 i+(x+y) j+xyz k. Find fluid acceleration at (1,1,2).

GATE 2019 CE (CE2) – Question 23

Fluid Mechanics · Continuity, momentum and energy equations · 1 mark · Multiple choice

The steady velocity field is $\vec v=2\hat i+(x+y)\hat j+xyz\hat k$. Find fluid acceleration at (1,1,2).

$2\hat j+10\hat k$
$4\hat j+12\hat k$
$\hat j+\hat k$
$4\hat j+10\hat k$

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Correct answer: (D) $4\hat j+10\hat k$

Explanation

The field is steady, so $\vec a=(\vec v\cdot\nabla)\vec v$. The i component is zero. The j component is $2+(x+y)=4$ at (1,1,2). The k component is $2yz+(x+y)xz+(xyz)xy=4+4+2=10$. Therefore **4ĵ + 10k̂, D**.