Abstract
The use of dimensional analysis to derive analytical results where these do not exist is extensively illustrated by three case studies. These phenomena are turbulent flow, particle abrasion in flow channels and electrostatic charging in fluid flow. These derive some results that were previously unknown. A fourth study of the elementary theory of the kinetics of gases corrects a standard, but analytically quite unjustified, assumption and demonstrates the care necessary in allocating dimensions to physical concepts.
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Notes
- 1.
The results in [8.4] that show a Reynolds number dependency are for low values of the Reynolds number which accord with the flow at the end of transition where the turbulence has not fully developed.
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Gibbings, J. (2011). Analytical Results. In: Dimensional Analysis. Springer, London. https://doi.org/10.1007/978-1-84996-317-6_8
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