Hand written solution required

Advanced Physics 9.89. (a) Show that the complex potential for fluid flow past the elliptic cylinder of Fig. 9-49 is given by 1 (2) = Vous+ (a+b)= ] where 5 = !(z + vz -c2) and c? = a - b2. 316 CHAPTER 9 Physical Applications of Conformal Mapping (b) Prove that the fluid speed at the top and bottom of the cylinder is Vo(1 + b/a). Discuss the case a = b. [Hint. Express the complex potential in terms of elliptic coordinates (5, n) where z = x + iy = ccosh(5 + in) = ccosh 5.] Fig. 9-49