Dimensional Analysis Revisited
Dimensional Analysis Revisited
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-Ria-bouchinsky 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.
dimensional analysis, indicial matrix, thermomechanics, computer code
1365-1375
Butterfield, R.
630c6573-427b-41c3-9dc6-0b614a69db27
23 November 2001
Butterfield, R.
630c6573-427b-41c3-9dc6-0b614a69db27
Butterfield, R.
(2001)
Dimensional Analysis Revisited.
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 215 (11), .
(doi:10.1243/0954406011524748).
Abstract
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-Ria-bouchinsky 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.
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Published date: 23 November 2001
Keywords:
dimensional analysis, indicial matrix, thermomechanics, computer code
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Local EPrints ID: 53966
URI: http://eprints.soton.ac.uk/id/eprint/53966
ISSN: 0954-4062
PURE UUID: f9dd6577-d8ee-46a1-8692-ce0fdf270b19
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Date deposited: 23 Jul 2008
Last modified: 15 Mar 2024 10:42
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Author:
R. Butterfield
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