Question

X-component of velocity in two dimensional incompressible flow is given by$u=2y^2+6xy$. If the Y-component of velocity v is zero at y =0, the expression for Y-component of velocity is given by

• A. $v=3y^2+f\left(y\right)$
• B. $v=3y^2+f\left(x\right)$
• C. $v=-3y^2+f\left(y\right)$
• D. $v=-3y^2+f\left(x\right)$

Answer 1

The correct option is D

$v=-3y^2+f\left(x\right)$

(d)

$u=2y^2+6xy$

From continuity equation

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

$\Rightarrow -6y=\frac{\partial v}{\partial y}$

$\Rightarrow v=-3y^2+C$

At y = 0, v =0

$\therefore v=-3y^2+f\left(x\right)$