ve have 



iv 





V B * 0) - Yq (s + q) 





iv 



I. 



*.(».o) - Y ( . + q) 



q { (s -k Q ) 2 K_(-q) 



On y ■ 0, x > we know from (8.7) what <f> should be, and this can be 

 confirmee' from the expression for ♦ . Ony-0, x<0we close the inverse 

 Fourier integral path in the upper half-plane. The pole s - -q lies 

 outside the contour and makes no contribution, so that we only need to 

 examine the second contribution to *_ as s ■* o° in R_. For this contri- 

 bution 



_ 3 



*_(s,0) - s" T 

 and so 



<|>(x,0) - (-x) 2 



(times some coefficient) as x * 0-. Thus the pressure and the pressure 



l 

 jump both vaninh like (-x) near the plate edge. Note that although 



the pressure jump does vanish at the plate edge (which would be regarded 



in aerofoil theory as the satisfaction of a Kutta condition), the 



velocity is nonetheless infinite at the edge. 



In summary, the least singular solution has 



<j> - 0(x T ) 



i f (8.27) 



V* - 0(x T ) ) 



near the edge, and conditions of this kind are often imposed et the 

 outset as edge conditions . It seems preferable not to anticipate the 

 edge behavior in advance, but to follow the W-H method through as far 



59 



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