$($a$)$ Stream function.

$($b$)$ Velocity potential.

The velocity components of the fluid flow are:

u$=$x$^(2)+$z$^(2)+5$

v$=$y$^(2)+$z$^(2)-3$

$($a$)$ Show that the flow is rotational flow.

$($b$)$ If the flow is a three dimensional and incompressible fluid flow,

determine the velocity in z$-$direction.

A two$-$dimensional flow is described by the velocity components:

u$=5$x$^(3)$

v$=-15$x$^(2)$y

Determine the velocity and stream function at P$($x$,$y$)=(1,2).$