Blood Flow through Narrow Tubes

Abstract

IN the course of an extensive investigation (with Prof. A. C. Burton at the University of Western Ontario) of the hæmodynamics of perfused vascular beds, it was found necessary to examine the somewhat simpler case of blood flow in narrow glass tubes. Accordingly, the pressure-flow curves in tubes of radii 50–750µ for human erythrocytes suspended in standard acid–citrate–dextrose were measured at 25.5° C. over a wide range of hæmatocrits^1–4. A typical set of such pressure-flow curves is shown in Fig. 1. The curves were found to approach linearity at moderate flow rates; if the linear segments are extrapolated back, they intersect the positive pressure axis at finite values and then converge to a common ‘nodal point’ on the negative flow axis. However, in the non-linear region at very low flow rates, the curves appear to converge toward the origin. There is no evidence of any yield stress or intercept on the positive pressure axis. All the curves can be represented by an equation of the form: where Q̇ is the volume rate of flow and P the pressure gradient; the parameters M and k depend on both tube radius and hæmatocrit, whereas the nodal point B depends only on the tube radius³. Pressure-flow curves of similar shape have been obtained by other workers and can be inferred from the apparent viscosity data of Kümin⁵.