New nondimensional parameters in fluid mechanics and their application to turbine flowmeter data analysis

Dimensional analysis has been used in experimental fluid mechanics for over a hundred years. Controllable and uncontrollable variables in an experimen t can be efficiently organized into nondimensional groups or parameters. Su ch nondimensional parameters are used for geometric scaling, and for develo ping dynamic similitude in experimental processes. Commonly used nondimensi onal parameters in fluid mechanics include Reynolds number Mach number Frou de number, Weber number Strouhal number etc. Most modern text books and tec hnical papers discuss the use of Buckingham Pi theorem for developing the n ondimensionalization process. An often ignored and somewhat older technique is the Rayleigh method. Both the Pi theorem and the Rayleigh method are fo unded on the principle of dimensional homogeneity, and require some experie nce in the grouping of physical variables. The present paper uses the Rayle igh method to develop two new nondimensional parameters. A discussion is pr esented about the use of the parameters in the application of turbine flowm eter calibration and test data analysis. Ir is shown that data analysis for turbine flowmeters is considerably simplified by the use of the new parame ters.