Pressure losses in non-Newtonian flow through rigid wall tapered tubes

Abstract

Pressure drop and pressure gradient were measured in steady Newtonian and non-Newtonian flow through tapered tubes having angles of taper, α, between 0.5° and 1.25°. Aqueous solutions of polyacrylamide, characterized as power law fluids, were used for the non-Newtonian flow measurements. These solutions had power law parameters similar in magnitude to those of blood. The pressure drop-flow rate data compared well with the predictions of a semi-empirical flow model over a large range of flow rate (Re _α up to 10 for Newtonian flow and 5.7 for non-Newtonian flow). The pressure gradient increased with distance, z, into the taper as the radius decreased. The linear relationship between pressure gradient and z, derived by Oka (Biorheology, 10, 207-212, 1973) was found to be valid only when ${\mathit{\alpha }}_{\mathrm{z}}$ was small. For the tapered tubes examined here, agreement was confined to the region near the inlet. If higher order terms in ${\mathit{\alpha }}_{\mathrm{z}}$ were taken into account the agreement was extended further into the taper. However, under higher flow conditions, when the inertial losses are not negligible, the semi-empirical model provides much better estimates of pressure gradient.