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Classical Approach to Dimensional Analysis

The pi theorem is a generalized method of dimensional analysis and detailed discussions can be found in [1-7]. Below is a brief review of the pi theorem. [Pg.353]

Consider the magnitude/j of some physical quantity depending on other, independent magnitudes g, g2, , gm then [Pg.353]

Equation 8.1 is required to be dimensionally homogeneous. The pi theorem says that if the number of distinct reference quantities required to express the dimensional formula of all n magnitudes is r, then the n magnitudes may be grouped into n — r independent dimensionless IT terms, resulting in the relation [Pg.353]

An immediate advantage is demonstrated if Equation 8.1 is compared with Equation 8.2. That is, the number of independent variables to be studied is reduced to n — r. [Pg.354]

The next step is to define the dimensional matrix whose elements are the exponents of the fundamental dimensions M, L, and t appearing in Table 8.3. [Pg.354]


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