The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids

It is well known 1** that if a Newtonian fluid such as water flows through a tube of circular cross-section under conditions for which the critical Reynolds number is exceeded, the relation between pressure gradient and volume rate of flow is non-linear. Further 2, the radial distribution of velocity (averaged over regions large compared with the eddy dimensions) departs markedly from the parabolic distribution which would be expected for a Newtonian fluid. These results suggest that some analogy may exist between the turbulent Newtonian fluid and the laminar flow of a non-Newtonian fluid. It is the object of this note to pursue this line of thought and to indicate some of the phenomena which might, in accordance with it, be observed in turbulent fluids.