Figure 54 — Flow net for equal line source and sink, or for a pair of equal and 



opposite line vortices, or, in Section 42(A), for the circulating flow 



around and between two circular cylinders. 



(Copied from Reference 1.) 



positive source is at (c,0). The streamlines run from the source to the sink, and the stream 

 function <// is many-valued. There is flow symmetry about the a;-axis, mere geometrical sym- 

 metry about the y-axis. 



Vortex Pair 



In the conjugate flow, it is the potential (f>' = ifj that is many-valued in the manner just 

 described; the stream function ib' = - cf) is single-valued. Consequently there is circulation 

 of magnitude 



r = - ^(^'=27r/l 



around any curve encircling (c,0) once, or of magnitude -^nA if the curve encircles (-c,0) 

 once, whereas the circulation vanishes around curves encircling both points the same number 

 of times. A simple line vortex may be supposed to exist at (c,0) and another of equal strength 

 but opposite sign at (-c,0); these are called a vortex pair. The components of velocity for 

 this case are m'= - -y, v' = u, where u and v are given by [41d,ej. There is flow symmetry with 

 respect to the y-axis, geometrical symmetry with respect to x. 



