For a two$-$dimensional flow the velocity function is given by the expression, $=$

x$2-$ y$2$

$($i$)$ Determine velocity components in x and y directions.

$($ii$)$ Show that the velocity components satisfy the conditions of flow continuity

and irrotationality.

$($iii$)$ Determine stream function and the flow rate between the stream lines $(2,0)$

and $(2,2).$

$($iy$)$ Show that the streamlines and potential lines intersect orthogonally at the

point $(2,2).$