49 



SUMMARY 



Two new methods for computing the steady, irrotational, axisymmetric 

 flow of a perfect, incompressible fluid about a body of revolution are 

 presented. 



In the first method a continuous, axial distribution of doublets 

 which generates the prescribed body in a uniform stream is sought as a solu- 

 tion of the integral equation 



f 6 m(t) 



Ja ~3 



dt =-±- 



where r is the distance from a point (t, 0) on the axis to a point (x, y) on 

 the body, r 2 = (x - t) 2 + y 2 (x). 



A method of determining the end points of the distribution and the 

 values of the distribution at the end points is given. If the equation of the 

 body profile, with the origin of coordinates at one end, is 



y^x) = a x x + 



a x + a x° + 



a very good approximation for the distribution limit a at that end, when the 

 coefficients a , a , ... are small, is given by 



^ = 4 + a 2+ l^i7 



if a 3 ^ 0. If a is negative, the term containing it is neglected. The cor- 

 responding value of the doublet strength at this point is 



1 / a 3 2 a i\ 



i(a) =-g-(l +y> +— lo S IT/ a2 Ka A 



Formulas and tables for determining a and m(a), which may be used when the 



above procedure is insufficiently accurate, are also given. The values a, b, 



m = m(a), m, = m(b), f = y^a) and f. = y^b) are then used to obtain the 

 approximate solution of the integral equation 



b-x f. x-a ;, \ , b-x _ , x-a _ 



m. 



/ \ nl j2 b-x ~ x-a « \ . b-x „ 



1 (X) = CflT - r f - r — • f, + r m + 



i v ' V b-a a b-a b^ b-a a 



b-a a b-a b 



