Energy losses and pressure drop in models of human airways

Abstract

The work done by the pressure drop in forcing fluid through a system of tubes is balanced by changes in kinetic energy and by viscous energy dissipation. From measured inspiratory flow profiles in symmetrical models of typical junctions of the human bronchial tree, the viscous energy dissipation downstream of a junction is computed, and is always greater than in Poiseuille flow. It varies with distance downstream and with Reynolds number (Re). We formulate a theory of the factors governing dissipation which agrees with the experimental results. The ratio of actual energy dissipation to Poiseuille dissipation (Z) is given by Δ P=K(ρμ) 1 2 V ̇ 3 2 (d = tube diameter, L = length) where C is a constant, =1.85 for the branching angle and area ratios of our model. This can be used to predict the overall pressure drop in a branched system provided that kinetic energy changes are included.