Figure 102 — Streamlines around a 



circular cylinder in translation. 



(Copied from Reference 1.) 



Thus on the cylinder q = \U\. There are no stagnation points, but at the points 6 = Q and 

 d - 180° the fluid is simply moving with the cylinder. 



The distribution of pressure on the cylinder is the same as in the last section, and the 

 net force on it vanishes if the motion is uniform. 



The kinetic energy of the fluid per unit of length of the cylinder is 





q'^rdd =- pa^V" 



[68i] 



(For notation; see Section 34; Reference 1, Article 68; Reference 2, Section 9.20). 



69. FLOW WITH CIRCULATION PAST A CIRCULAR CYLINDER 



To introduce circulation around the cylinder, it is only necessary to add appropriate 

 terms from Section 40. Then [67a,e,f] are replaced by 



w = v{z + ~]+ — \n-, 2 = re'^, [69a,b] 



\ z / 2n a 



/ a2\ r f a^\ r r 



d, = U [r + —]cos d -^ — d, il; = U [r-—}Bin d + — In—. [69c,d] 



^ \ rj 2n \ r/ 2n a 



Here r, d are polar coordinates with origin on the axis of the cylinder, whose radius is a, and 

 with 6 measured from the positive a;-axis, as in Figure 99; U and F are real constants. 

 The velocity components are 



y, = f/ ^-1+^cos^, ?0 = ^(l^yj^'"^+^ 



[69e,f] 



152 



