Method for calculating the average cross-section pressure distribution in tube flows within the vorticity-streamfunction formulation
This article describes an integral method for obtaining the average cross-section pressure distribution in tube flows by using the vorticity-streamfunction formulation. The method derives from the fact that the average cross-section pressure is related in a fundamental way to the power required to move the fluid through the tube. This relationship holds for flows in which the pressure distribution itself is nonuniform across the cross section. The analytical basis for these statements and a discussion of the circumstances in which they are true is given. Numerical calculations of a recirculating venturi flow and a flow in an irregular model coronary artery geometry reveal that in these flows the average cross-section pressure distributions calculated using the integral method are similar to the centerline and wall pressure distributions obtained from a full primitive-variable calculation based on the finite-element method and to wall pressure data obtained experimentally. This can be attributed to the nearly uniform pressure distributions that occur in tube flows with a low rate of change of cross-sectional area with distance.