A two-dimensional flow field has velocities along the x and y directions given by u = $x^{2} t$ and v = -2xyt respectively, where t is time. The equation of streamline is

x^{2} y = c o n s t a n t

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x y^{2} = c o n s t a n t

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xy = constant

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not possible to determine

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Solution

The correct option is A $x^{2} y = c o n s t a n t$
Equation of streamline,

$\frac{d x}{u} = \frac{d y}{v}$

$\frac{d x}{x^{2} t} = \frac{d y}{- 2 x y t}$

$\frac{d x}{x} = \frac{d y}{- 2 y}$

$2 \frac{d x}{x} + \frac{d y}{y} = 0$

$2 l o g_{e} x + l o g_{e} y = l o g_{e} c$

$l o g_{e} y x^{2} = l o g_{e} c$

$x^{2} y = c$

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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)

\frac{\partial u}{\partial x}, i s e q u a l t o

(i i i) \frac{d x}{u} = \frac{d y}{v} = \frac{d z}{w}

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