Figure 155 — Streamlines, above the plane of symmetry, due to two equal line dipoles 

 with transverse axes. See Section 93(A). (Copied from Reference 124.) 



B. Flovb Past One or Between and Around Two Similar Cylinders of Special Shape. 

 Assume U/fi > 0, so that the dipole axes are oppositely directed to the stream at infinity, 

 whose velocity is U toward negative x. 



The streamline for = consists of the a;-axis and also of the curve S defined by 



iy 



r2 ,2 



[93j,k] 



provided c > 86 . If c is large, S approximates a circle enclosing both dipoles. As c 

 decreases, S becomes compressed along the a;-axis; when c^ = 86^^, S consists of two cir- 

 cular arcs defined respectively by r^ = 26 and r - 26 and meeting at the stagnation points, 

 which are then at (-\/3 b, 0). This is a special case, for n = 2/3, of the flow considered 

 in Section 89. As c^ becomes less than 86'^, the curve defined by 93(j) disappears, ami the 

 dividing surface splits along the a;-axis to form two separate curves, each of which surrounds 

 one dipole and carries two stagnation points. The curves can be found by setting u=v = in 

 93(f, g) in order to find the stagnation points and then calculating the value of ip at these points 

 from 93(c); with this constant value of ip, 93(c) defines the curves. They soon approximate to 

 circles, whose radius, for small c/b, approximates c/\/2"= \Jfi/U. 



The dividing surface may represent a cylinder, or two cylinders, of a certain shape, 

 immersed in a uniform stream. The limiting form of S for c^ = 86^ and a larger oval are 



230 



