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Dimensional analysis and dimensional reasoning.

Bissell, J.J. (2012) 'Dimensional analysis and dimensional reasoning.', in Ways of thinking, ways of seeing : mathematical and other modelling in engineering and technology. Berlin: Springer, pp. 29-47.

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.

Item Type:Book chapter
Full text:PDF - Accepted Version (382Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/978-3-642-25209-9_2
Publisher statement:The original publication is available at www.springerlink.com
Record Created:10 May 2012 11:05
Last Modified:18 May 2012 12:22

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