THE AXIALLY SYMMETRIC POTENTIAL FLOW ABOUT 

 ELONGATED. BODIES OP REVOLUTION 



by 

 L. Landweber 



ABSTRACT 



An iteration formula for Fredholm integral equations of the first kind is ap- 

 plied in two new methods for obtaining the steady, irrotational, axisymmetric flow of 

 an inviscid, incompressible fluid about a body of revolution. In the first method a 

 continuous, axial distribution of doublets is sought as a solution of an integral equa- 

 tion of the first kind. A method of determining the end points and the initial trends 

 of the distribution, and a first approximation to a solution of the integral equation are 

 given. This approximation is then used to obtain a sequence of successive approxima- 

 tions whose successive differences furnish a geometric measure of the accuracy of an 

 approximation. When a doublet distribution has been assumed, the velocity and pres- 

 sure can be computed by means of formulas which are also given. 



In the second method the velocity is given directly as the solution of an inte- 

 gral equation of the first kind. Here also a first approximation is derived and applied 

 to obtain a sequence of successive approximations. In contrast with the first method, 

 which, in general, can give only an approximate solution, the integral equation of the 

 second method has an exact solution. 



Both methods are illustrated in detail by an example. The results are com- 

 pared with those obtained by other well-known methods. 



