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pi theorem

one of the principal methods of dimensional analysis, introduced by the American physicist Edgar Buckingham in 1914. The theorem states that if a variable A1 depends upon the independent variables A2, A3, . . . , An, then the functional relationship can be set equal to zero in the form f(A1, A2, A3, . . . , An) = 0. If these n variables can be described in terms of m dimensional units, then the pi (pi) theorem states that they can be grouped in n - m dimensionless terms that are called pi-terms-that is, phi(pi1, pi2, pi3, . . . , pin - m) = 0. Further, each pi-term will contain m + 1 variables, only one of which need be changed from term to term

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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