2. (a) Consider a single horseshoe vortex of strength I composed by a bound vortex (- b/2<y<b/2) and two semi-infinite trailing vortex, as shown in the figure below. Obtain an expression for the induced velocity w(y) along the bound vortex. (10 %) C Bound vortex Trailing vortex Hint: 0B 1/2 Ꮎ . h = P Trailing varies a single horseshoe vortex 4 PA =8 Induced velocity of a straight vortex segment AB at Point P is г г V= (cose-cose,)=- (cosp+cos p₂) 4th 4th Bound vortex T1 Trailing vortex D E T2 P Trailing vortex B A A> A 8 F A pair of horseshoe vortex (horseshoe vortex ACDF & horseshoe vortex ABEF) (b) Consider a pair horseshoe vortex composed by two horseshoe vortex ACDF and ABEF). The strength of the bound vortex CD for horseshoe vortex ACDF is I₁ and the strength of the bound vortex BE for horseshoe vortex ABEF is T2. BCDE is a square and point P is at the center of the square. Obtain an expression for the induced velocity at Point P. (10%)