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

Velocity component in x-direction
`u=-(3)/(2)x^2-(1)/(3)x^3`.

Explanation:

v=3xy+
`x^(2)`y

We know that for incompressible flow

`(\partial u)/(\partial x)+(\partial v)/(\partial y)=0`

`(\partial v)/(\partial y)=3x+x^(2)`

So
`(\partial u)/(\partial x)+3x+x^(2)=0`

`(\partial u)/(\partial x)= -3x-x^(2)`

By integrate with respect to x,we will find

`u=-(3)/(2)x^2-(1)/(3)x^3`+C

So the velocity component in x-direction
`u=-(3)/(2)x^2-(1)/(3)x^3`.