Question

The y-component of velocity for a certain 2-D flow field is given as u = 3xy + x2 . Determine the x-component of velocity if the flow is incompressible.

Answer 1

`-(3x^(2))/(2)`

Step-by-step explanation:

It is given that y component is

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

`\Rightarrow (\partial v)/(\partial y)= 3 x`

For an incompressible flow, the continuity equation is written in differential form as

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

`\Rightarrow (\partial u)/(\partial x)= -(\partial v)/(\partial y)`

`\Rightarrow (\partial u)/(\partial x)= - 3x`

Now solving for x component of velocity is

u = -
`\int 3x.dx`

= -
`(3x^(2))/(2)`

Therefore, x component of velocity is -
`(3x^(2))/(2)`