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.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1951
Accession Number
ADA800273

Entities

People

  • L. Landweber

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Aircrafts
  • Axisymmetric Flow
  • Bodies Of Revolution
  • Civil Engineering
  • Computational Science
  • Engineers
  • Equations
  • Fluid Dynamics
  • Hydrodynamics
  • Integral Equations
  • Mechanical Engineering
  • Naval Architecture
  • Physics Laboratories
  • Pressure Distribution
  • Sequences
  • Ship Model Basins
  • Stagnation Point

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Mathematical Modeling and Probability Theory.