Studies on the Motion of Viscous Flows— III 



3 l/d^ 1^_J_ i. ^L 



2 ^2 7*/Q2 



Bt Re \Br2 r 3 



r r ' r 



2 d 



Rer2 36* 



^^iPo'^^o 



''^0 ^0 ^^0 UgVo 



z 



3 3 ^ B 



dt '" 3r '" de 



^" Re Ur2 ^ r dr r^ ^ r^ 35^ 



+ d 



^i^)""^(2T-)^"^ '-^^'^ 



(1.31a) 



Z 



l\ / 1 3 



+ - u„ + 



dr 



r / n V r 



; 



(1.32a) 



and 



3t Re ^ "^V ^ U B^ Br 



r Bi 



E 



Bt '" Br '" B^ '" Br '" 



B(9 



- i '1 ^" 



3n 



(1.33a) 



Where 



'in = E "r 



n > 



n-l 

 1 n / i r m A 



n > 



The expressions in the following Eq. (1.34) show that a^^, b^^, etc., are 

 functions of space-time variables and the flow parameters: 



■in = E 7" "" 



> 



n- 1 . 



2n Z_i \ r r 3/9 m 



m=0 ^ °^ 



2n Z_j 



(1.34) 

 (Cont.) 



535 



