A dimensionless set can exist

Fluid Mechanics pp 51-61 | Cite as

abstract

An essential aspect in the description of the methodical procedure in fluid mechanics is the dimensional analysis of problems. Unfortunately, it is often underestimated how important such considerations are for the understanding of fluid mechanics and for their compact and generally applicable representation. With the dimensional analysis it is achieved to formulate a fluid mechanic problem dimensionless, by putting all sizes on appropriate 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.

For the concrete procedure in the dimensional analysis, it is crucial whether a problem is known in the form of the underlying equations (the result of which is then to be determined through the solution), or whether these equations are not (yet) available. Instead, it must then be known which influencing variables are used to determine the result sought. In both cases, there is a problem related to the problem under consideration 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

  1. Buckingham, E. (1914): On physically similar systems; Illustrations of the use of dimensional equations. Phys. Rev., 2nd Ser., Vol. 4, 345-376CrossRefGoogle Scholar
  2. 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
  3. 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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