Desai and Lieber 



The normal and the tangential components of velocity are given by 



u„ = -u^ 1 



v^ = +u„|l + -^ 1 sin 6 , u^ = a constant. 



The corresponding pressure is given by 



Po = ~ P^'^^ — ( 2 COS 2£^ - — I + p„ 



where ?„ is a constant. 



As r -► CO , 



At r - a, 



Uq = , Vq = 2u„ sin 61 , Pq "" 7 P^od^ ( 2 cos 20-1) + p„ 



We can construct Table 1, supposing = 45°. From the table it can be 

 seen that the magnitudes of the components of the velocity vector evaluated at 

 various finite distances along the line d = 45° and away from the cylinder ap- 

 proach very rapidly those evaluated at infinity. Even at a distance as close as 

 r = 10a their difference is only 1% of the magnitudes at infinity. And at a dis- 

 tance r = 50a this reduces to only 0.04% of the magnitudes at infinity. 



Table 1 

 Measurement of Physically Finite Distance, with = 45° 



Uq - lim Ug 



r-xB 



10 



0.0100 



4=u„(l- 0.0100) 



V2 



+ — G„(l + 0.0100) 



yf2 



+ 0.0100 



V2 



+ 0.0100 



v^ 



25 



0.0016 



— G„(l- 0.0016) 



y/2 



+ -^ujl + 0.0016) 



+ 0.0016-^ 



x/2 



+ 0.0016 



v^ 



50 



->( 



0.0004 



— G„(l- 0.0004) 



V2 



1 - 



V2 



+ -^G„(1 + 0.0004) 



V2 



^ _1_ -^ 



V2'''" 



+ 0.0004 



\/2 



+ 0.0004 



x'2 



512 



