Answer:
Velocity component in x-direction [tex]u=-\frac{3}{2}x^2-\frac{1}{3}x^3[/tex].
Explanation:
v=3xy+[tex]x^{2}[/tex]y
We know that for incompressible flow
[tex]\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0[/tex]
[tex]\frac{\partial v}{\partial y}=3x+x^{2}[/tex]
So [tex]\frac{\partial u}{\partial x}+3x+x^{2}=0[/tex]
[tex]\frac{\partial u}{\partial x}= -3x-x^{2}[/tex]
By integrate with respect to x,we will find
[tex]u=-\frac{3}{2}x^2-\frac{1}{3}x^3[/tex]+C
So the velocity component in x-direction [tex]u=-\frac{3}{2}x^2-\frac{1}{3}x^3[/tex].
