A dimensionless set can exist
Fluid Mechanics pp 51-61 | Cite as
In the course of the dimensional analysis, dimensionless combinations of quantities arise that influence a problem under consideration. As will be shown below, the number is such dimensionless key figures of a problem is always smaller than the number of dimensional influencing variables from which they arose. This helps with a compact, “generally valid” presentation of results or makes it possible at all with a reasonable amount of effort.
A result (also in a dimensionless, related form) then applies not only to a certain case, but to all physically similar problems, which are however determined by the numerical values of the respective characteristic sizes, with the same values of the dimensionless key figures.
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- Buckingham, E. (1914): On physically similar systems; Illustrations of the use of dimensional equations. Phys. Rev., 2nd Ser., Vol. 4, 345-376CrossRefGoogle Scholar
- further details e.g. in: Zierep, J. (1978): Similarity laws and model rules of fluid mechanics, Braun-Verlag, Karlsruhe, and: Szirtes T. (1998): Applied Dimensional Analysis and Modeling, McGraw-Hill, New YorkGoogle Scholar
- see also Herwig, H .; Gloss, D .; Wenterodt, T. (2008): Flow in Channels with Rough-Walls - Old and New Concepts, Proc. of ASME-ICNMM2008, Darmstadt, GermanyGoogle Scholar
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