The Axially Symmetric Potential Flow About Elognated Bodies of Revolution
Abstract
An interation formula for Fredholm integral equations of the first kind is applied 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 equation 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 approximations whose successive differences furnish a geometric measure of the accuracy of an approximation. When a doublet distribution has been assumed, the velocity and pressure 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 integral 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 compared with those obtained by other well-known methods.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1951
- Accession Number
- ADA800273
Entities
People
- L. Landweber