The velocity components are 



H 





3(24^ + 1) cot"^ C-6C- 



e^i. 



sin w, [138p"] 



A 



l-2f/' 



^ (^2^^2)1/2 



(^2 + 1)1/2 3^cot-i <C-3 + 



c^+1 



sin cj, [138q"] 



^ / . -1 . 1 

 ^^ , = — ^ I 34 cot 4 - 3 + 1 cos &>. 



e + 1 



[138r"] 



For a circular disk, obtained by letting a-> 0, so that ^q-*0 and A-» c, >4 = 20^ n/377, 

 and on the disk itself y = c( 1-^^)1/2 ^Qg ^^ 3 = c(l-/i2)i/2 gjf, ^^ ^^^j j,^ ^ +(^2 _y2_22^l/2_ 



Thus, on the side on which fx > 0, 



377 



n2(c2-y2_32)l/2^ 



[138s"] 



and the y and 3 components of velocity tangential to the disk are 



yz 



dcf, 41} 



dy in (^2_y2_32)l/2 



[138t' 



40 y2^232_c^ 



dz 2.n (^2_y2_^2)l/2 



[I38u 



On the opposite side of the disk </> , f , and w are reversed in sign. 



Over most of the disk the fluid flows rather as if to go round the axis in the direction 

 of rotation of the disk. Close to the edge the values of u and v are such that the radial com- 

 ponent of the velocity predominates, becoming infinite at the edge, and its direction is that 

 of a flow around the edge in opposition to the rotation. 



The kinetic energy of the surrounding fluid of density p is 



45 ^ 



[I38w"] 



368 



