Non-Newtonian fluids in smooth circular pipes - Velocity profile of laminar flow

From a correlation of recent data in the literature(2), the velocity profile for non-Newtonian fluids in smooth circular pipes under laminar flow has been shown to have a remarkable resemblance to that of Newtonian fluids tender turbulent flow. The correlation is based on a generalized exponential equation for each of four separate regions(1) which results in four intersecting straight lines when z = v/v(c), is plotted against y = 1 -(r/R) on log-log coordinates, where v equals velocity at a distance r from the center, v(c) equals velocity at the center and R equals radius of the pipe. Because the data from Reference 2 were for only one condition of flow, no generalized correlation for the non-Newtonian. fluid in laminar flow could be determined. However, when such data will be available for more conditions of flow (preferably two more), a generalized correlation may be performed. The suggested method of correlation is based on the use of art average Reynolds number in which an average viscosity for the non-Newtonian fluid is given by (mu(0) mu(u))(1/2), where mu(0) equals viscosity at the center and mu(w), equals viscosity at the wall.