A new theorem concerning the Buckingham Rayleigh methods and general dimensional analysis

This chapter tries to demonstrate the compatibility of the Rayleigh, Buckingham, and general dimensional methods. It presents the fundamental theorem of dimensional analysis. Applied in 1899 for studying one problem of heat transfer, Rayleigh’s method settled functional dependence between a dependent quantity and independent variables which influenced them. The chapter presents the Buckingham method (p theorem). C. I. Staicu started from the findings of the Rayleigh and Buckingham methods, which need laborious experiments for identification of the numerical values of the exponents and of the proportionality constant value. Staicu proposed to determine values for all exponents through calculation and to determine the proportionality constant, based on experimental data.