Velocity profiles in turbulent flow of power-law fluids

5 Velocity profiles in turbulent flow of power-law fluids 

No exact mathematical analysis of turbulent flow has yet been developed for power-law fluids, though a number of semi-theoretical modifications of the expressions for the shear stress in Newtonian fluids at the walls of a pipe have been proposed. 

This region separates the so-called viscous or laminar sub-layer and the fully turbulent core prevailing in the middle portion of the pipe, and it extends over 

A fully turbulent region comprising the bulk of the fluid stream where momentum transfer is attributable virtually entirely to random eddies and the effects of viscosity are negligible. 

A brief derivation of the turbulent velocity profile for Newtonian fluids in smooth pipes will first be presented and then extended to power-law fluids. The shear stress at any point in the fluid, at a distance y Irom the wall, is made up of viscous and turbulent contributions, the magnitudes of which vary with distance irom the wall. Expressing shear stress in terms of a dynamic viscosity and an eddy momentum diflnsivity (or eddy kinematic viscosity), E, 

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