Ug (x,r) = C 



X 



Ug (x,r) = 

 r 



/* R /"OO 



\^^'^^ ^ ' ^ X ^/o 'o^'^'^ 'i^^'^ ''"^ '"' '^ '^ " > ° 



7 r^ dr r°° ^^ 



^ (^'^> = - 47 I ^I^ I '^ ^0(^^> ^l^^P) , dk dp X < 



X ■'^T 1 U _ K-X 



\ 



2-e 





(25) 



e^^ X < 

 '^H "^ "O " ^ 2-e-^ 



The total tangential velocity component is given by 



•R 



V-'^) = % + X =^I ^X 'o(^P> -^1^^^) {-2} ^^'^ - > 



f f R (J 



^ 



7r (r) 

 u/x,r) = - -2~ X > 0, Ry < r < R 



= elsewhere 



It follows that the steady velocity induced by a moderately loaded lifting 

 line propeller at points outside the sli-pstveam is given by 



-x^-'^) = ^ fe /' % TTG) £ '"^ V^'^ ^1^^^^ e-^ 1^1 dk dp X < 

 Rjj 1 



R^ 1 



u^(x,r) = 



16 



