On the given surface we have, from [6l ], 



f &m (t) 1 ipAx) 



J„ r 3 2 y2(x) 



where now 



r 2 = (x-t) 2 + f(x) [65: 



Differentiating [64] with respect to x gives 



r »- t .„. w , tf-[U) 2<Mx)y'(x) 

 3 f t-x-yy (t)dt = _i . _i 



Ja r 5 i y^x) y 3 (x) 



Hence, from [62] and [64] we obtain 



f(x) 



and, from [63], [66], and [67], 



[66; 



/•rni.(t) 2^ (x) 



Ja t> 5 f(vl 



^ (x) 



v = uy'(x) + -^ [68] 



y(x) 



where the primes denote differentiation with respect to x. Equations [67] 

 and [68] are the desired expressions for u and v. If the approximation m. (t\ 

 is very good, the contributions of the error function &Ax) should be very 

 small. It is interesting to note that the form of Equation [68] shows the 

 deviation of the resultant velocity from the tangent to the given body. 



Bernoulli's equation for steady, incompressible, irrotational flow 

 with zero pressure at infinity now gives the pressure distribution p, 



|= 1 - (u 2 + v 2 ) [69] 



where q is the stagnation pressure. 



