Figure 75 - Streamlines past a grating of 



nearly circular cylinders; see Section 47. 



(Copied from Reference 253.) 



all 



Figure 76 — Row of line dipoles with axes 

 longitudinal but alternating in direction. 



On the lines y = - a/2, i{/ =Q. Hence parallel plane walls may be inserted along these 

 lines. Then the flow is represented due to a dipole placed midway between walls a apart, with 

 its axis perpendicular to the walls; see Figure 76. 



nb nx nx 



On the a;-axis, m = 0, v = - — coth — csch — 



[48g] 



, , TzB nX ttX 



On the walls at y = i a/2, u = - — tanh — sech — 



[48h] 



ffD nx rrx 



On the y-axis, v = — cot — est; — 



[48i] 



(For notation and method, see Section 34.) 



49. LINE SOURCE, VORTEX OR DIPOLE ANYWHERE 

 BETWEEN PARALLEL WALLS 



If the line singularity between walls, as considered in Sections 44, 45, 46, and 48, is 

 at a distance b from the median plane between the walls, the complex potential is modified as 

 follows: 



Line source: 



= - i4 Mn sinh — 



2 -ih) 



2a 



+ In sinh 



7t(2 + ib -ia)~\ 

 2a ^J 



[49a] 



Line vortex: 



ir r . , n(z-ib) n(B+ib-ia)l 



= — lln sinh - In sinh 149dJ 



2j7 L 2a 2a J 



115 



