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Irina18 [472]
3 years ago
12

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.
Engineering
1 answer:
Maslowich3 years ago
8 0

Answer:

-\frac{3x^{2}}{2}

Explanation:

It is given that y component is

v = 3xy + x^{2}

\Rightarrow \frac{\partial v}{\partial y}= 3 x

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

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

\Rightarrow \frac{\partial u}{\partial x}= -\frac{\partial v}{\partial y}

\Rightarrow \frac{\partial u}{\partial x}= - 3x

Now solving for x component of velocity is

u = - \int 3x.dx

  = - \frac{3x^{2}}{2}

Therefore, x component of velocity is - \frac{3x^{2}}{2}  

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