A Fluidity Approach to Non-Newtonian Laminar and Turbulent Flow

Abstract

The rheological properties of some non-Newtonian fluids can be equally well represented on the basis of fluidity. The analysis reveals that there can be some advantage in this in that an explicit form for the friction factor in laminar flow is found. The analysis is extended to the turbulent region and a logarithmic form for the time-average axial velocity in flow is found using a functional analysis method which obviates the need to involve a mixing length hypothesis. The expression for the velocity leads to a friction factor - Reynolds number relation which also has a fluidity number as a parameter. Methods are considered for the solution of problems which obviate the need for iteration. The corresponding treatment for the usual viscous representation is given in the Appendix.