LINE SINGULARITIES IN COMBINATION 

 41. LINE SOURCE AND SINK; LINE VORTEX PAIR 



Or, 



w = .4 [In (3 + c) - In (3 -c)] 

 z = c cotli 



2A 



For simplicity, let the constants A and c be real. 

 Writing 



z-c = T^e , 2-^ c = Tr^e 



as illustrated in Figure 53, and a = a; + zy, 



w = + z lA = 4 In— s + z .4(^2 ~^i)' 



= 41n-^, xi, = - A{d^-Q^^- A\^x^ — 



2cy 



2^ + y -c 



- M + it; = — = 4 

 dz 



/cos (9, cos 0-\ x^-y^-c^ 

 w= 4 1 i ^1 = 2/lc — 5—- 



-y = 4 



sin 0j sin 6^ iAc xy 



,2 ^2 

 1 2 



Circle 2 



[41a] 



[41b,c] 



[41d] 



[41e] 



Figure 53 — Illustrating the variables for Sections 41-42. 



