The flow of a fluid towards a solid wall generates a stagnation-point flow (figure). Somebody claims that this flow has a velocity potential ø(x,y) = C(x2 + By2), with constants

C and ß. (a) If it exists, compute the stream function v (x,y) (b) If C = 3 s-1, how large is the flow rate (per unit length in the z-direction) through the square of edge length 1 m depicted in figure (a) (with the origin as its lower left corner)? (c) By adding a point source of strength m > 0 at (0, 0), a wavy interface with a "bump" can be modeled {figure (b)}, as the stagnation point shifts to (0, h). (d) Determine this bump height h as a function of (general) C and m! If m = 4 m2/s, how large must Cbe in order to position the bump at h = 1m?