Pressure development in a non-Newtonian flow through a tapered tube 1

Abstract

The flow of viscous fluids through a tapered tube is very interesting from the standpoint of blood flow in blood vessels. The taper of the tube is an important factor in the pressure development. In the first place, we have given a brief summary of our theory of the steady convergent flow of non-Newtonian fluids characterized by an arbitrary time-independent flow curve through a slightly tapered tube. Based on our general formula for the flow per unit time, explicit formulae of the pressure gradient are obtained in several cases of non-Newtonian fluids specified by particular flow curves: power law fluid, Bingham body, and the fluid obeying Casson’s equation. In all these cases it is shown that the pressure gradient is not constant along the axis but increases with decrease in the radius of the tapered tube. If we neglect quantities of order α ² (α: angle of taper), then the pressure gradient increases linearly with the distance along the axis of the tube.