Transformations of the Hodograph Flow Equation and the Introduction of Two Generalized Potential Functions
Abstract
It has been shown that the hodograph equations of motion can be derived in a symmetrical form by the choice of the velocity and the mass velocity as independent variables. The equations obtained by the use of the velocity potential, the stream function, or their transforms as the unknown function are of the same general form and therefore can be treated in the same manner. Particular sets of solutions have been studied independently of the gas law adopted and some properties of the series obtained by means of these sets have been discussed. Approximate gas laws for which the solutions of the holograph equations can be easily found have been briefly discussed. The equations have been further transformed so as to have as independent variables the complex velocity and the complex mass velocity. Two new generalized potential functions can then be introduced that satisfy very compact equations. From these functions, all the quantities concerned with the representation of the motion can be derived by means of formulas independent of the gas law adopted. By means of the generalized potential functions some developments have been performed with the approximate Chaplygin-Von Karman-Tsien law. An approximate transonic method has also been suggested.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1951
- Accession Number
- ADA382131
Entities
People
- Luigi Crocco
Organizations
- National Aeronautics and Space Administration