Desai and Lieber 



Bi// c " 



Thus at r = h we must have 



Z] n (c^^cosn^- C2„ sinn5)(c3^h"-i+ c^^h-"-i) - -(u„-e^) 



- -T - Z] n(Cj^sinn5+C2„cosn5)(c3^h"-i-C4^h-"-i) - + (u„ + e,) sin § . 



n= 1 



Hence we must have c^ = 0, c^^ = for all n, since n ?; 1, Cj^, c^^, c^^ must 

 be zero. Writing c^ = Cjj • Cg^, c^ = c^^ • c^^, we get 



: 'J Cj - c^h-^ = -Uco + e^ -■. , 



Moreover, the kinematic condition that the normal component of velocity at 

 r = a be zero requires that Cj + 02/3^ = 0. 



Now there are three conditions on two constants c^ and c^. In the evalua- 

 tion of the previous solution where the condition of uniform flow was demanded 

 as r ^ rx and e^ = e^ = 0, the first two of the above conditions reduce to a 

 single condition that c^ = -u^ because the term in Cj drops out. C2 is then 

 obtained from the third condition. This condition of overdeterminacy is pecu- 

 liar to the example chosen and is not generally obtained, as will be clear when 

 the actual problem of the flow of a viscous fluid around a circular cylinder is 

 considered. It is important to note that, in general, such constants like Cj, c^ 

 must be functions of h, the distance at which this condition is applied. 



The overdeterminacy determines h directly in the above case, c^, c^, and 

 h which satisfy these conditions are given by 



e + 2 / ^M + ^v\ 



U V ~ I , I 



2 / \ 2G^ 



^■■■-■-^m 



514 



