Desai and Lieber 



!1^ + ii^ "o , 1 ^^"o 2 ^^0 ^ Q 



■2 r2 3^2 r2 



^'^0 1 ^ _ ^ J. !!l^ _l!^ 

 Br2 ^ r ^r r2 ^ r2 3^2 ^ ^2 ^^ 



^'^0 l^>Ao 1 ^Vc 



- (1.22) 



3r2 r Br r2 3^2 



The boundary conditions satisfied by u^, Vq and p^ are: 

 At r = 1, 



As r — > 



Po(l,0) = 2 cos 25 - 1 



lim uJr,0) = 



cos 9 



^0o\ (1-23) 



lim v^(T,d) = ( = +sin5 



r->oo \ Br / 



r->oo 



lim Po(r,0) = - 



The set of Eqs. (1.21) consists of the Euler equations and the continuity 

 equation in two dimensions. The Euler equations are equations of equilibrium 

 for an idealized fluid which is assumed to be nonviscous. Historically, Eqs. 

 (1.17), (1.18), (1.19), and (1.20) are obtained as solutions to Eqs. (1.21) and 

 (1.23) when the flow is further assumed to be irrotational. However, in view of 

 Eqs. (1.21) and (1.22), it follows that v/zq, Uq, v^, and Pg as given by Eqs. (1.17), 

 (1.18), (1.19), and (1.20) satisfy Eqs. (1.12), (1.13), (1.14), and (1.15) for a 

 real viscous fluid. We emphasize that this is due to the condition of irrotation- 

 ality which implies that the velocity field can be derived from a potential. A 

 comparison of the kinematical conditions in Eqs. (1.23) with the conditions in 

 Eqs. (1.16) shows that these solutions satisfy all but the no- slip condition for a 

 real fluid. 



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