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.

Question

asked Sep 15, 2020 221k views

1 Answer

Mahavir Munot · Answer 1 · 2020-09-21T08:40:36+0000

Answer:

-(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 -