Wang 



-S^.'^^^- 



(6) 

 where 



The flow region In various planes can also be found In Fig, 2. For 

 points on the plate AB, we may deduce from (6) 



X = y (sin 29 - 4 cos e - TT - 29) , (8) 



where 9 = Arg t,, when t, is on the circular arc ACB, and 



- TT < 9 S . (9) 



III. UNSTEADY PERTURBED FLOW 



It is shown in W that by eliminating h between (1) and (2) 

 and transforming (s,n) and R to the variables f© and Wq a 

 single free surface boundary condition in complex variable form can 

 be obtained, which is 



Re [L(f,)] =0, (10) 



where 



f, = <!>,+ ivf, (11) 



is the complex perturbation potential, and the linear differential 

 operator L is 



It is also shown in W that the boundary condition (3) on the 

 solid body can be transformed into 



i-lTi=-i7[lr^^<'ioh)], (13) 



192 



