(x,g(x)) 



Figure 3 



df/dx = tan Y- Fo^ the irrotational flow, the velocity components in the 

 X- and y-directions will be denoted by u(x,y) and v(x,y). 



We wish to determine the source distribution M(x) such that, on 

 y = g(x), the stream function (J;(x,y) assumes the values 



ijj = U(6-6^) 



(8) 



We have 



\ 3s / g \^x ds ^y ds / g \ ds ds / 



(9) 



But 



v(x,g) = v(x,0) + g V (x,0) = ttMCx) - g u (x,0) 



y x 



u(x,g) ■= u(x,0) + g u (x,0) = u(x,0) 



(10) 



(11) 



since u (x,0) = by symmetry. Also, by (8), we have 



(lf)s = i"<«-Vi(S) 



(12) 



