Implementation of Buckingham's Pi theorem using Python

Abstract

Buckingham's Pi theorem plays an important role in engineering, applied mathematics, and physics for dimensional analysis. From the given variables, it will be utilised to evaluate the set of dimensionless parameters. It indicates that the validity of the physical law is independent of the specific unit system, and it can be expressed as an identity incorporating only dimensionless variables associated with the law. A python-based function has been developed and reported in this manuscript, which can be utilised to evaluate Pi terms (commonly called π terms) for any fluid flow problem. Smaller moderation in the written function can make it capable of solving any fundamental dimensions. Different fluid mechanics problems are utilised to test and validate the reported function, five of which are presented in this manuscript along with code. Obtained results are in good agreement with the theoretically obtained results.