Figure 71 — Row of equal line dipoles with 

 transverse axes. 



-— -{ 



y 



._ 





(1) Dipole Between Walls 



On the lines y =- a/2, lA = 0. Walls may be inserted along these lines, which are 

 drawn broken in Figure 71. Then the flow is represented due to a dipole placed midway 

 between parallel walls separated by a distance a; the axis of the dipole is parallel to the walls. 



On the walls at y = - a/2, -y = 0, u = cosh + 1 



a \ a I 



On the a;-axis, t» = 0, u - cosh - 1 



On the y-axis, -y = 0, u = - 



27tB 



1 - cos 



'-?r 



[46g] 



[46h] 



[46i] 



(2) Dipole in a Stream Between Walls 



If a uniform stream at velocity U toward negative x is superposed, terms Uz, Ux, Uy 

 are added in w, (p, ij/, respectively, and a term - U in u. Assume that B/U > 0. Then lA = 0, 

 not only on the a;-axis or median plane between the walls, but also on an oval cylindrical 

 surface S whose equation is 



,, B . 2rry 

 Uy =— sin 

 2 



rryJ 



a \ 



sinh^ 



ny 



[46j] 



See Figure 72. The semidiameters of S, r , and r^, in the x and y directions, are given by 



nT. I fnB B nr^ 



= 1/ „ ' ^ =77Cot -^ [46k, 1] 



a f ail 



sinh 



r. = — cot 

 2 U 



109 



