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Dimensional analysis and dimensional reasoning

Bissell, J.J.

Authors

J.J. Bissell



Contributors

C.C. Bissell rzrz55@durham.ac.uk
Editor

C. Dillon
Editor

Abstract

This chapter explores some of the ways physical dimensions, such as length, mass and time, impact on the work of scientists and engineers. Two main themes are considered: dimensional analysis, which involves deriving algebraic expressions to relate quantities based on their dimensions; and dimensional rea-soning, a more general and often more subtle approach to problem solving. The method of dimensional analysis is discussed both in terms of its practical applica-tion (including the derivation of physical formulae, the planning of experiments, and the investigation of self-similar systems and scale models) and its conceptual contribution. The connection between dimensions and the fundamental concept of orthogonality is also described. In addition to these important uses of dimensions, it is argued that dimensional reasoning (using dimensionless comparisons to sim-plify models, the application of dimensional homogeneity to check for algebraic consistency, and the ‘mapping-out’ of solutions in terms of parameter space) forms the implicit foundation of nearly all theoretical work and plays a central role in the way scientists and engineers think about problems and communicate ideas.

Citation

Bissell, J. (2012). Dimensional analysis and dimensional reasoning. In C. Bissell, & C. Dillon (Eds.), Ways of thinking, ways of seeing : mathematical and other modelling in engineering and technology (29-47). Springer Verlag. https://doi.org/10.1007/978-3-642-25209-9_2

Publication Date 2012
Deposit Date Feb 7, 2012
Publicly Available Date Mar 29, 2024
Publisher Springer Verlag
Pages 29-47
Series Title Automation, Collaboration, & E-Services
Series Number 1
Book Title Ways of thinking, ways of seeing : mathematical and other modelling in engineering and technology.
ISBN 9783642252082
DOI https://doi.org/10.1007/978-3-642-25209-9_2