A generalization of the Π-theorem and dimensional analysis

This article introduces a generalization of dimensional analysis and its corollary, the Pi-theorem, to the class of problems in which some of the quantities that define the problem have fixed values in all the cases that are of interest. The procedure can reduce the number of dimensionless similarity variables beyond the prediction of Buckingham's theorem. The generalized Pi-theorem tells when and how large a reduction is attainable.