For a solution in which the pressure on the free surface is different from that at 

 infinity; see Reference 7, page 134. 



(For notation and method; see Section 34; Reference 1, Article 76; Reference 2, 

 Section 12.20.) 



114. INFINITE STREAM OBLIQUE TO A PLANE LAMINA. 



The solution of the last section is easily modified so as to allow the stream to imping 

 at an angle oi with the plane of the lamina, as illustrated in Figure 186. Let a be measured 

 from the positive a;-axis. As before, let the velocity on the free streamlines and at infinity 

 be unity. 



Figure li 



— Plate in a stream incident obliquely, with a wake behind it. 

 See Section 114. 



The dividing streamline will now meet the lamina perpendicularly at a stagnation 

 point C that is displaced from the center. The transformations from (^ to In i^ and t are 

 unaltered; but, at the point corresponding to infinity in the approaching stream, the vector 

 representing ^, having the direction of the velocity, must lie on the radius, 6 =a - n, and 

 the corresponding value of t will lie to the right of the origin, as shown in Figure 187. When 

 ^ = e'^" ~ '^^ = - cos a - i sin a , then t = cos a by Equation [113b]. The flow on the ^-plane 

 is easily displaced so as to transfer its central point from the origin to t - cos a ; in place of 

 Equation [113c], let 



285 



