Steady flow in a model of human central airways

Abstract

We studied the pressure-flow relationships and flow distribution under steady conditions in a model of human central airways, over a range of tracheal Reynolds' numbers (350-30,000) by using air or helium. We found that the Moody diagram [log coefficient of friction CF = delta P/[1/2 rho (V2/A2)] vs. log Reynolds' number (Re)] had a slope of -1 for Re less than 500, a slope 0 for Re greater than 10,000, and slopes between -1 and 0 for 500 less than or equal to Re less than or equal to 10,000. The distribution of flow among branches was dependent on tracheal Reynolds' number so that, as tracheal Reynolds' number increased, the upper lobes received proportionally less of the total flow than the lower lobes. Because the airways in the upper lobes generally had greater branching angles than those in the lower lobes, this result was consistent with the hypothesis that the effective resistances introduced by branching angles was flow dependent, increasing proportionally more the greater the angle.