Question

X-component of velocity in a 2-D incompressible flow is given by $u=y^2+4xy$. If Y-component of velocity 'v' equals zero at y = 0, the expression for 'v' is given by

• A. 4y
• B. $2y^2$
• C. -$2y^2$
• D. 2xy

Answer 1

The correct option is C -$2y^2$

Given, $u=y^2+4xy$
$v=0aty=0$
For a 2-D incompressible flow the continuity equation is
$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0$
$\Rightarrow 4y+\frac{\partial v}{\partial y}=0$
$\Rightarrow \int \partial v=-\int 4y.\partial y$
$\Rightarrow V=\frac{-4y^2}{2}+C$
$\Rightarrow V=-2y^2+C$
Now at $y=0,V=0$
$\Rightarrow 0=0+C$
$\Rightarrow C=0$
$\therefore$ $v=-2y^2$
i.e. y-component of velocity is $-2y^2$