# A dimensionless set can exist

Fluid Mechanics pp 51-61 | Cite as

### abstract

*characteristic sizes*related to the problem. This has two key advantages:

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.

*physical / mathematical model*according to the definition given in section 4.1. This is either already explicitly formulated or it can be formulated in principle (because it is known which physical situation exists).

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### literature

- 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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