Implementation of Buckingham's Pi theorem using Python. (November 2022)

• Record Type: Journal Article
• Authors: Dumka, Pankaj; Chauhan, Rishika; Singh, Ayush; Singh, Gaurav; Mishra, Dhananjay
• Is Part Of: Advances in engineering software. Volume 173(2022)
• Publication Date: 2022-11
• Subjects: Buckingham's Pi theorem -- Fluid mechanics -- Dimensional analysis -- Physical similarity analysis -- Python programming; RV, rv repeating variables -- nrv nonrepeating variables -- BuPi Buckingham's Pi function -- SI International System; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2022.103232
• Languages: English
• ISSNs: 0965-9978

Abstract

Highlights: The process of dimensional analysis has been automated. A detailed algorithm has been given to program Buckingham's pi theorem. Python programming has been used to develop the functions. Developed python code has been presented. The results of computer program are in very good agreement with the typical hand calculations. 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.