Question $2.[80$ pts $.]$ The velocity components in a two$-$dimensional flow are

$u=\frac{Kx}{x^2+z^2}$ and $w=\frac{Kz}{x^2+z^2}$

where $K$ is constant. For the given velocity field:

$($i$)$ Determine whether the flow is incompressible.

Question $2.[80$ pts$.]$ The velocity components in a two$-$dimensional flow are

$u=\frac{Kx}{x^2+z^2}$ and $w=\frac{Kz}{x^2+z^2},$

where $K$ is constant. For the given velocity field:

$($i$)$ Determine whether the flow is incompressible.

$($ii$)$ Determine whether the flow is irrotational.

$($iii$)$ Obtain the function for the velocity potential.

$($iv$)$ Noting that streamlines are normal to the isopotential curves, plot the streamlines over $x-z$

planes