

y ^ V 



A 



^Y"^^/ 





1 " 





 -cC 



A\' 







Figure 86 — Vortex pair in a 

 transverse stream. 



See Figure 86. Also - 



/6in e^ sin fljX ^2 + 



u = -A[ } - U = 2 Ac 



V r, r„ / ,2 



c^-y^ 



2 ^2 

 1 '^2 



■, 0, = tan~^ 



-U, 



V = A 



\ r r / 2 .2 



1 ^ r^ Tj 



t55d] 



[55e] 



On the ar-axis, u = - V + 2Ac/(x'^ + c^); on the y-axis, u = - V + 2Ac/ (c^ - y'^). Hence, 

 stagnation points occur; they are on the a;-axis at a; = ^ ojq if A/V > c/2, or on the y-axis at 

 y = i y^ if A/U < c/2, where 



]/2A l/ 2A 



[55f,g] 



If A/U = c/2, there is a single stagnation point at the origin. 



The a;-axis represents a plane of flow symmetry, the y-axis, a plane of geometrical 

 symmetry for the flow net. 



A dividing surface S always occurs, passing through the stagnation points. If 

 A/U ^ c/2, it consists of two loops, each surrounding one vortex. If A/U > c/2, it consists 

 of a single loop surrounding both vortices, defined by the equation. 



A '"2 



y = — In — , or a;-^ + y'^ + c^ = 2cy coth (Uy /A). 



U T^ 



[55h,i] 



128 



