What is it about?
In conventional engineering, it is assumed that parameter symbols represent numerical value and dimension, and that experiments reveal how the numerical values and dimensions of parameters are related, and consequently the resulting correlations describe how the numerical values and dimensions of parameters are related. But dimensions cannot be related. Meters cannot be related to kilometers, seconds cannot be related to temperature. In the new view of dimensional homogeneity, parameter symbols represent only numerical value, and experiments describe how the numerical values of parameters are related. If an equation is quantitative, the dimensions that underlie parameter symbols must be specified in an accompanying nomenclature.
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Why is it important?
It is important because, if parameter symbols represent only numerical value, all equations are inherently dimensionally homogeneous, and parameters such as h and E can be abandoned because their sole purpose is to transform inhomogeneous equations to homogeneous equations.
Perspectives
The abandonment of parameters such as h and E greatly simplifies the solution of problems that concern nonlinear behavior because parameters such as h and E are extraneous variables that greatly complicate solutions.
EUGENE ADIUTORI
Read the Original
This page is a summary of: An Alternate View of Dimensional Homogeneity, and Its Impact on Engineering Science, The Open Mechanical Engineering Journal, August 2018, Bentham Science Publishers,
DOI: 10.2174/1874155x01812010164.
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