The velocity field of an incompressible flow is given by
$V = (a_{1} x + a_{2} y + a_{3} z) i + (b_{1} x + b_{2} y + b_{3} z) j + (c_{1} x + c_{2} y + c_{3} z) k,$ where $a_{1} = 2$ and $c_{3} = - 4$ . The value of $b_{2}$ is______
2

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Solution

The correct option is A 2
From continuity equation

$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$

$a_{1} + b_{2} + c_{3} = 0$
$2 + b_{2} - 4 = 0$
$o r b_{2} = 4 - 2 = 2$

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