A Computer Solution of the Buckingham Pi Theorem Using SYMBOLANG, A Symbolic Manipulation Language.

摘要

Among the theories of similitude, application of the Buckingham Pi Theorem allows one to find meaningful relationships among variables, check the formulation of a system of equations, and allow prediction from scaled parameters. Simply stated, the Pi Theorem asserts that if there are n variables involving N fundamental units, these may be combined to form n-N dimensionless parameters each containing N+1 variables. SYMBOLANG is a FORTRAN-based symbol manipulator using a list structure. Symbol manipulators operate on strings of symbols rather than numbers. As an example, a symbol manipulator allows multiplication of N+1 by N-1 to obtain (N sup 2)-1. A list structure allows data to be stored and manipulated by relationships rather than sequentially or by some other scheme.