197] FLOW AROUND CORNER. 527 



128) y 



and if we know the values of qp on the circumference of a circle 

 with center at the origin, we may find the coefficients by the method 

 of Fourier as in 140 a, 83). 



Let us examine the motion in a segment between two walls 

 making an angle 2 a at the origin and reaching to infinity. If we 

 use the value of cp given by equation 128), the coefficients and the 

 values of n admissible are to be determined by the condition 



along each wall. But since dn = rda), we have 



129) - ^ 



which must vanish for to = + a. If 



a*-f-i 



na = ~ n, 



and if 



ncc = nit, sin (+ no) 0, 



3c being any integer. Therefore if we put when n is an odd multiple 

 of 9 A n = and B n = C^x+i and for even multiples, B n = and 

 An = C^x, we shall have as a solution of the problem 



n 2 a /2x-fl n V-.--AT /* 



C 2 y. + ir sm (- ^ ') + ft^ cos ^ o 



The tangential velocity at the wall is given by 

 131) 



The exponent of the lowest power of r is ^ -1. If this is negative, 

 that is if a > --> the velocity is infinite for r = 0, that is at the 

 corner, unless C^ = 0. 



The pressure is given by the equation 



p = const. -| 2 , 



so that at a sharp projecting edge around which the water flows 

 there would be an infinite negative pressure. This being impossible, 

 around such an edge the motion is discontinuous, so that instead of 



