It is now necessary to develop expressions for the velocity at large 

 distances (|r^| ^ °°) and In the Immediate vicinity of the singularity 

 (r-r -> 0). For convenience, the velocity may be regarded as the sum of 

 three terms, 



V(r) = V + V^(^) + V^(f) 



I ♦ I 



Free Body Singularity 



Stream Induced Induced 



Velocity Velocity 



The body velocity, V (r ) , is given by 

 B 



rr— r 

 a(^ ) 5-^ dS(r^ ) 

 B |-_i -J I J B 



As r -> 



where 



As r -> r , 



where 



-^ ~^-R 1 3rCy -r) 



4iT r r 



ii^ 



^B = / '^V "^B -^^(^b) 



^b(^>~^B^V - -^•y^\<-\'> ^ O ieh 



en = r^ - r 



71 



