Figure 118 — Streamlines past a circular arc 

 with no circulation about it. 



Figure 119 — Noncirculatory streamlines about a semicircular arc. 

 (Copied from Reference 113) 



The lift per unit length on the lamina, in the direction perpendicular to the direction of 

 the steady stream at infinity, is in any case L = pTV, by the Kutta-Joukowski theorem. The 

 torque about the origin of coordinates or the center of the chord, from Equation [77g], in which 

 here y = -o, 77 = 90 deg, A = c tan j3, is, in any case, 



N ^2npc'^ U^ s\r\ 2a - pcT V t&n ^ sina -' [78k] 



Here p is the density of the fluid. 



The lift and torque will be the same if the lamina is itself moving through fluid which 

 is at rest at infinity; the lift is then perpendicular to the direction of motion of the lamina, 

 and a is the angle between the direction of motion and the chord of the lamina, as shown in 

 Figure 120. 



180 



