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On Dimensional Analysis

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The dimensions of physical quantities q are interpreted as vectors qii1, γi2, …,γin)≡γi1b1i2b2+…+γinbn, where the basic elements bj generating the vector space represent the basic quantities of the dimensional system and the coefficients γj are defined by an equation. This interpretation permits the application of the theorems on vector spaces to dimensional analysis. Some results of this approach are simplified rules for the transformation of dimension and unit systems and a physically more transparent derivation of a complete set of dimensionless products by a transformation of bases. The new notation yields a sequential order of physical equations which may lead to a dimensional analysis based on appropriately selected equation groups.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:4 ,  Issue: 3 )

Date of Publication:

July 1960

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