and the lift is 



L ^ pTU = in paU^ sin (a + (3), 



[78p] 



where a = c/cos ^. The lift in this case is directed away from the convex side of the lamina 

 provided a > - /3, and it is a maximum for a = 90 deg - ft. 



The flow net around such an arc-shaped lamina, with the circulation adjusted to make 

 the velocity finite at the trailing edge, is shown in Figure 121. The stream approaches from 

 the left at an angle of 10 deg to the chord. Because of the presence of circulation, the 

 apparent directions of approach and departure differ in the figure by a few degrees. The 

 theoretical pressure-differences on both surfaces of the lamina are plotted in Figure 122, 

 drawn vertically from the arc as a base; the numbers represent millimeters of water in an 

 airstream of 10 meters per second. The broken line represents old measurements by Eiffel. 



2 6L • ? 7 ' -fh '\ 6V— -^\ O' -'d. "6^^0.2', ' -0.6C?l.2~Cro:2i0.4i0.6i0.8a,0'.1.2 .1.44:^:8 2.07.2 



Figure 121 — Flow with finite trailing velocity around an arc-shaped lamina. 



The kinetic energy of the fluid when the lamina moves in translation is easily found. 

 Let it move at velocity U at the angle a with the direction of its chord, with no circulation 

 around it, and with the fluid at rest at infinity. From Equation [78h], in which the term in 

 e"^ represents the uniform stream and is to be dropped, the appropriate potential is 



a' U 

 z-ih 



c?- Ve~'^ ih a^U 



with a measured downward from the positive real axis. The transformation Equation [77a] 

 can be written in descending powers of 2 'as 



182 



