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Jun 1, 2021 · Fourier established the principle of dimensional homogeneity which states that units in either side of the equation should be the same. The principle of dimensional homogeneity was reported in his book Théorie analytique de la chaleur from 1822.
- Alberto N. Conejo
- 2021
The conventional view of dimensional homogeneity is generally credited to Fourier (1822). Objectives: The objectives of this article are to describe the alternate view of dimensional homogeneity and to demonstrate its application to practical engineering problems.
- Eugene F. Adiutori
- 2018
One important physical contribution in the book was the concept of dimensional homogeneity in equations; i.e. an equation can be formally correct only if the dimensions match on either side of the equality; Fourier made important contributions to dimensional analysis. [12]
Feb 4, 2022 · A fundamental element of the analysis is the principle of dimensional homogeneity, allowing immediate verification of the correctness of the equations describing a physical process, which has important applicative consequences.
- sandro.longo@unipr.it
Dimensional analysis, or the principle of similitude, to use Lord Rayleigh’s term, usually gets short shrift in textbooks. What one finds is mostly an admonition about checking the dimensional homogeneity of equations as a way of finding errors. This is good advice, but perhaps lacking in profundity. The remarkable power of
Much of the practical import of dimensional analysis arises from the powerful and simple logical (or, perhaps, grammatical) principle regarding the requirement of dimensional homogeneity, which is applied to dimensional equations. The principle is known as the principle of dimensional homogeneity.
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Can dimensional homogeneity be a dimensional equation?
By using dimensional homogeneity, obtain a set of simultaneous equations involving the exponents a, b, c, ..., m. Solve these equations to obtain the values of the exponents a , b , c , ..., m . Substitute the values of exponents in the main equation, and form the non-dimensional parameters by grouping the variables with like exponents.
