Turbulent Flow of Power-Law Fluids

Velocity profiles for the steady incompressible turbulent flow of power-law fluids through circular conduits were calculated by numerical quadrature considering both the viscous stresses and the Reynolds' stresses operative over the entire cross section of the flow. A non-Newtonian stress coeffiecient, K_n, was introduced along with mixing length, l, so that the Reynolds' stresses could be put in a form similar to that of the viscous stresses. The form of the Reynolds' stresses thus obtained reduced to the Newtonian form when the flow behavior index, n, equaled unity. Both l and K_n were assumed dependent upon the Reynolds number. Similarly, friction factors for the turbulent flow of power-law fluids were calculated by numerical quadrature. The calculated friction factors were compared to 146 measured friction factors over a range of Reynolds numbers from 2,670 to 108,800. The mean absolute difference between calculated and measured friction factors for this sample was 3% with a standard deviation of 1.9%.