ASSIGNMENT $2$

Briefly explain the following terms:

$($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.

$3.$ A two$-$dimensional flow is described by the velocity components:

$u=5x^3$

$v=-15x^{2}y$

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