New Nondimensional Parameters in Fluid Mechanics and Their Application to Turbine Flowmeter Data Analysis

Abstract

Dimensional analysis has been used in experimental fluid mechanics for over a hundred years. Controllable and uncontrollable variables in an experiment can be efficiently organized into nondimensional groups or parameters. Such nondimensional parameters are used for geometric scaling, and for developing dynamic similitude in experimental processes. Commonly used nondimensional parameters in fluid mechanics include Reynolds number, Mach number, Froude number, Weber number, Strouhal number, etc. Most modern text books and technical papers discuss the use of Buckingham Pi theorem for developing the nondimensionalization process. An often ignored and somewhat older technique is the Rayleigh method. Both the Pi theorem and the Rayleigh method are founded on the principle of dimensional homogeneity, and require some experience in the grouping of physical variables. The present paper uses the Rayleigh method to develop two new nondimensional parameters. A discussion is presented about the use of the parameters in the application of turbine flowmeter calibration and test data analysis. It is shown that data analysis for turbine flowmeters is considerably simplified by the use of the new parameters.