Turbulent Non-Newtonian Velocity Profiles in Pipes

Abstract

A semi-empirical method is described that permits the prediction of velocity profiles of turbulent flow of purely viscous, Newtonian, pseudoplastic, or dilatant fluids and suspensions in smooth circular pipes. The suggested model is based on the physical concept of turbulent motion and boundary layer theory and, therefore, has physical meaning. The effect of turbulence on viscous stresses is also considered. Using the suggested method, the validity of the method is tested by comparing all experimentally determined velocity profiles reported in literature with the predicted profiles. The flow rate, diameter of the pipe, and rheological parameters of the fluids or suspension are the only values used in the prediction. It is found that the method is quite accurate for Newtonian and pseudo-plastic fluids and suspensions. It is also found that the method is sufficiently accurate to predict the velocity profiles of elastico-viscous fluids with relatively small viscosity. Because data are not available for dilatant fluids, the verification of the method for dilatant systems is not possible at present.