Figure 105 — Streamlines around a circular 



cylinder in translation and with circulation 



around it; the fluid is at rest at infinity. 



See Section 70. (Copied from 



Reference 1.) 



Figure 106 - Same as Figure 105 but with 

 the circulation four times as strong. 



Since, however, it is necessary that r ^ a, a stagnation point can occur only if |r| = 2na\U\, 

 If r = 2naU, it lies on the surface of the cylinder. 



Streamlines for F = 3n-at//4r and F = Sn-aC are shown in Figures 105 and 106. 



The pressure and the lift on the cylinder are as in the last section. 



Changing the sign of F changes the diagram as if by reflection in the a;-axis. Chang- 

 ing the signs of both F and U merely reverses all velocities. 



If the direction of motion of the cylinder mai<es an angle y with the positive a;-axis, 

 from [69j] with z^ = 0, 



a^U 



2;r 



In — . 



[70h] 



a^U F a^U T r ^ ^ 



4, = ^=— cos (9 - y) - — e, 0= sin(6'-y)+— In—; [70i,]] 



T 2ff r 2tt a 



a'^V a^U F 



? = — cos (6» - y), qQ = sin (6/ - y) + -— 



,2 ,2 2Trr 



[70k,l] 



(Reference 1, Article 69; Reference 2, Section 9.60.) 



157 



