a$.$ Show that both the stream function and the velocity potential satisfy Laplace equation: $gra{d}^{2}f=0.(5\%)$

b$.$ What is the relationship between the velocity potential and the stream function of the same flow? $(3\%)$

c$.$ A certain irrotational flow field in the $xy$ plane has the stream function $=Bxy,$ where $B=0\mathrm{.}3s^{-1},$ and the coordinates are measured in meters. Determine the rate of flow between points $(x,y)=(2,4)$ and $(3,5).$ Find the velocity potential for this flow. $(12\%)$