Desai and Lieber 



At r = 1, 



^ ^^ '^ u(l,6,t) ={-—-] =0 for all t 



\ ^ ad I 



r= 1 



30 

 v(l,^, t) = I 1 =0. for all t 



Br 



r= 1 



At r = h% 



u(h*,9,t) = I i — ) =0 for t = O' 



r = h* 



(1 - e^) cos for t > 

 v(h*,0,t) =1 ) =0 for t=0 



(1.16) 



= +(1 + e^) sin 6 for t > 



p(h*,^,t) = Cp . for t > 



£^, e^, and ep fall within the limits of accuracy of the measuring instruments 

 and hence are not registered. For the purposes of calculations they are to be 

 regarded as negligible. The physically infinite distance is h*, determined as 

 discussed earlier. 



It is interesting to note that the condition at h* requires that dip/dO be 

 equal to zero, because h* is a finite distance. The conventional boundary con- 

 dition at infinity requires 



lim I- ^U . 



This appears a much weaker condition on d^/dd than the previous one. That 

 this is not so can be seen when we take into consideration how the idea of a 

 physically infinite distance h* is based on the requirement that all physical 

 disturbances should attenuate with distances away from the source of disturb- 

 ances and on the manner in which it is to be found mathematically. 



To complete the formulation of the problem, we should add to the boundary 

 conditions an initial condition, depicting the state of the whole fluid at t = 0. If 

 we neglect the initial and the boundary conditions at time t = and look for a 

 time -independent solution, the problem becomes simpler. The boundary condi- 

 tions as stated correspond to the idealized problem of flow past a cylinder 

 started impulsively from rest. The idealization consists in the discontinuous 

 variation of the velocity at t = o. A realistic formulation may need to alter this 

 by allowing for a very rapid but continuous variation of the velocity at t = 0. In 



518 



