Figure 41 — Definition of U and a in 

 Equation [35a]. 



Figure 42 — Flow net in a right angle: 



36. HYPERBOLIC FLOW 



w = Az'^ 

 where A is a real constant. Then (ji + z i/f = A (a; +iy)'^. 



[36a] 



[36b,c] 



Both the equipotential curves and the streamlines are rectangular hyperbolas, the former with 

 asymptotes inclined at 45 degree to the x- y-axes, the latter with the axes themselves as 

 asymptotes. 



In the conjugate flow 



0'=24a;y, rfj' = A{y'^ -x'^) [36d,e] 



In both cases 9 = «= at infinity, 7 = at the origin. 



The flow net is the same in all quadrants. One quadrant is shown in Figure 42. It may 

 be used to give an approximate idea of the flow past a square corner. 



The two conjugate flows differ only in that the flow pattern is rotated through 45 degree. 

 (For notation and method; see Section 34; Reference 1, Article 63; Reference 2, Section 4.70.) 



37. LINEDIPOLE 



w) = — , // is a real constant, 



+ iip = 



tj.(x-iy) 



flX 



i^y 



x + iy {x+iy){x-iy) x^+y^ 



fix p-y 



•^ " ~2 2 ' "^ "^ 2 2 



2 2 

 X +y^ 



[37a] 



[37b,c] 



75 



