A theoretical analysis for turbulent flow of non-Newtonian fluids through smooth round tubes has been performed for the first time and has yielded a completely new concept of the attending relationship between the pressure loss and mean flow rate. In addition, the analysis has permitted the prediction of non-Newtonian turbulent velocity profiles, a topic on which the published literature is entirely silent.
To confirm the theoretical analysis, experimental data were taken on both polymeric gels and solid-liquid suspensions under turbulent-flow conditions. Fluid systems with flow-behavior indexes between 0.3 and 1.0 were studied at Reynolds numbers as high as 36,000. All the fully turbulent experimental data supported the validity of the theoretical analysis. The final resistance-law correlation represents a generalization of von Karman's equation for Newtonian fluids in turbulent flow and is applicable to all non-Newtonians for which the shear rate depends only on shear stress, irrespective of rheological classification. All the turbulent experimental data for the non-Newtonian systems were correlated by this relationship with a mean deviation of 1.9%.