Question

Velocity components in an incompressible flow are: v = 3xy + x^2 y: w = 0. Determine the velocity component in the x-direction.

Answer 1

Answer:

Velocity component in x-direction $u=-\frac{3}{2}x^2-\frac{1}{3}x^3$.

Explanation:

   v=3xy+$x^{2}$y

We know that for incompressible flow

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

$\frac{\partial v}{\partial y}=3x+x^{2}$

So   $\frac{\partial u}{\partial x}+3x+x^{2}=0$

$\frac{\partial u}{\partial x}= -3x-x^{2}$

By integrate with respect to x,we will find

$u=-\frac{3}{2}x^2-\frac{1}{3}x^3$+C

So the velocity component in x-direction $u=-\frac{3}{2}x^2-\frac{1}{3}x^3$.