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Dimensional Analysis Revisited

R. Butterfield
Journal / Anthology

Proceedings of the I MECH E Part C--Journal of Mechanical Engineering Science
Year: 2001
Volume: 215
Issue: 11
Page range: 1365-1375

Dimensionless groups, the output of a successful dimensional analysis, are usually developed via Buckingham's pi theorem. Because this theorem provides a necessary but not sufficient condition for a solution, such a dimensional analysis may, on occasion, appear to fail. The paper presents the necessary and sufficient conditions in a simple form and builds on them to demonstrate how new physical knowledge can augment a 'primitive' set of dimensions to arrive at an optimal number of dimensionless groups. The formulation is used to elucidate the historical Rayleigh-Riabouchinsky controversy and a related thermomechanical problem is analysed to demonstrate the complete 'new knowledge' algorithm. Mathematica code is appended which incorporates these ideas and generates the complete set of admissible dimensionless groups for any specific problem.

*Science > Physics > Mechanics
*Science > Physics > Thermodynamics and Statistical Mechanics

dimensional analysis, indicial matrix, thermomechanics, computer code

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