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- Title
Determination of Pi Terms by the Method of Repeating Variables and Rayleigh Method: a Comparative Study.
- Authors
Bangalee, M. Z. I.; Shohrab, Muntasir
- Abstract
Dimensional Analysis is a simple and qualitative technique used to predict physical parameters. It is important to find out dimensionless terms from a set of variables that are used in an equation describing a natural phenomenon. Two methods are used to determine the dimensionless terms, also called the Pi terms. They are known as the method of repeating variables and the Rayleigh method (also known as the row reduced echelon form method). The method of repeating variables, which is commonly used to determine the Pi terms, uses the Buckingham Pi Theorem. The Rayleigh method was introduced by Lord Rayleigh to develop a theory of sound. The computational algorithms for both methods are developed and comparative analysis between the two methods is also discussed. The complexity analysis of both algorithms shows which algorithm performs faster for a particular number of variables and reference dimensions. These methods have also been tested on several problems. The analysis of these problems describes the stability of these algorithms along with their limitations. It is found that the method of repeating variables can lead to an error if the number of reference dimensions differs from the number of basic dimensions, unlike the Rayleigh method. However, the method of repeating variables can be faster than the Rayleigh method in some cases.
- Subjects
COMPARATIVE method; DIMENSIONAL analysis; COMPARATIVE studies; ALGORITHMS
- Publication
IAENG International Journal of Applied Mathematics, 2022, Vol 52, Issue 1, p177
- ISSN
1992-9978
- Publication type
Article