Power Law Non Newtonian Fluid Friction Loss & Pipe Roughness

The friction factor equation for this fluid is based on the Darby relationships (Chemical Engineering Fluid Mechanics). Note, Darby states that there is insufficient data in literature to provide a reliable estimate of the effect of roughness on friction loss for non-Newtonian fluids. However, evidence that does exist suggests that toughness is not as significant for non-Newtonian fluids as it is for Newtonian fluids. This is partly due to the fact that the majority of non-Newtonian flows lie in the low Reynolds number range and partly due to the fact that the laminar boundary layer tends to be thicker for non-Newtonian fluids than for Newtonian fluids, i.e. generally in the hydraulically smooth range for common pipe materials.