The velocity components in the x and y directions of a two dimensional potential flow are u and v, respectively. Then
$\frac{\partial u}{\partial x}, i s e q u a l t o$

\frac{\partial v}{\partial x}

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- \frac{\partial v}{\partial x}

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\frac{\partial v}{\partial y}

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- \frac{\partial v}{\partial y}

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Solution

The correct option is D $- \frac{\partial v}{\partial y}$

For two dimensional flow, continuity equation should be satisfied.
i.e.,

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

$∴ \frac{\partial u}{\partial x} = - \frac{\partial v}{\partial y}$

Suggest Corrections

Similar questions

T h e c o n t i n u i t y e q u a t i o n i s \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}

T h e a c c e l e r a t i o n i n x - d i r e c t i o n i s a_{x} = \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y}

T h e c o n d i t i o n o f i r r o t a t i o n a l i t y i s \frac{\partial u}{\partial y} = \frac{\partial v}{\partial x}

u = \frac{x}{T_{1}}, v = \frac{- y}{T_{2}} a n d w = 0

T_{1} (\neq 0) a n d T_{2} (\neq 0)

x^{2} t

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