Dimensional Analysis: A Centenary Update

TL;DR

This paper revisits dimensional analysis, proposing a generalized approach that considers multiple invariants and relations simultaneously, revealing richer information than traditional methods.

Contribution

It introduces a generalized framework for dimensional analysis that accounts for multiple invariants and relations, expanding its analytical power.

Findings

More invariants and relations can be considered simultaneously.

Generalized dimensional analysis provides deeper insights.

Potential for improved modeling accuracy.

Abstract

It is time to renew old ways of thinking about dimensional analysis. Specifically, more than $n-r$ invariants and more than one functional relation between invariants need to be considered simultaneously. Thus generalized, dimensional analysis can yield more information than previously recognized.