Studies on the Motion of Viscous Flows — III 



NONDIMENSIONAL EQUATIONS AND BOUNDARY CONDITIONS 



Let us introduce the following nondimensional variables, as it is convenient 

 to work with them. 



P - Po 



p = 



U 1 "^ 2 



(1.11) 



P 1 ^ 

 t = t 



The Reynold's number based on radius is Re = u^a/i^. We note that u„ and p„ 

 are constant magnitudes of velocity and pressure recorded by the instruments 

 at and beyond some finite distance away from the cylinder. The symbol a is 

 retained in the sense of the idea of a physically infinite distance. 



Using Eqs. (1.11), we get from Eqs. (1.1), (1.2), (1.3), and (1.7) the following 

 nondimensional equations: 



Bu 3u_ y^_xl-_l^ J- /l^ 1 lii ii JL if^ _ A izVl 12) 



Bt'^^Br^rgg, r" 23r^Re\Br2"^'"3r~r2^r2 35 2 ^2 -^gj^ ' 



3v 3v v3v uv _ J_ ^ 1 / B^v 1 3v _v_ J_ ^_^ 2 Bu\/. ,o\ 



~t ^ ^^ ^ ^w ^ ~ ' ~ 'Tr'de ^ R^ \b72 "^ r b7 ~ 7^ ^ T^ de^ ^ T^ Je) 



— +-+ = (1.14 



. Br r r 361 . ■ 



BVV^ ^B^BVV_ 1BV;3VV_ J_^,^^ Q ^ ^ (1.15) 



where 



and 



Bt r 3(9 3r »" Br B^ Re 



,32 IB 1 B2 



V - + + 



Br2 •■ Br r2 B02 



l<r<co, < 9 < 2iT 



The corresponding nondimensional boundary conditions obtained from Eqs. 

 (1.10) are: , ,., .... 



517 



