Laminar entry length problem for power law fluids

Abstract

The main purpose of this paper is to present a new approximative method for predicting the changes in pressure drop in laminar entrance region flow of purely viscous power law fluids in circular tubes. The “transformation method for describing the tube flow of non-Newtonian purely viscous fluids”, first introduced by the present authors [1, 2, see also Appendix] has been extended and adopted to construct a pseudo-Newtonian model of the flow under consideration. To derive the dimensionless equations for calculating the changes in pressure drop in the entrance region flow and the velocity distribution in both the developing boundary layer and inside the inviscid core the momentum integral method has been applied. The analysis leads to only one single curve correlation — independent of any value of flow behaviour index — between the pressure drop and the axial distance from the tube entrance which is presented in a form suitable for engineering designs. A comparison of the dimensionless pressure drop curve as predicted in this paper with the experimental data obtained by other authors points out an excellent agreement. The results of the present work hold for high Reynolds number (Re>500) flow only.