A flow has velocity potential function given by $\phi=x^3-3xy^2$. Verify whether it represents valid flow fluid. If it does, then determine the stream function and also calculate the velocity and pressure at (1,-3) given that the pressure at (4,1) is 14 kPa and the fluid is water.

Data:-

$\phi = x^3-3xy^2,$ $P_{(4,1)}=14kPa,$ $w=9810\frac{N}{m^3}$.........(water)

To find:-

i) To verify valid fluid flow

ii) $\psi=?$

iii) Velocity and pressure at (1,-3)=?

Solution:-

i) In velocity potential function,

velocity component in x-direction 'u' is given by

$u=-\frac{\partial \phi}{\partial x}$

and

velocity component in y-direction 'v' is given by

$v=-\frac{\partial \phi}{\partial …