Morphology of branching trees related to entropy

Analyses of river systems by geomorphologists have suggested that for minimal entropy production in the movement of water down the river the fall in altitude should be equal in each order of branching of the tributaries. In this paper the same concepts have been applied to the bronchial tree and pulmonary arterial tree, assuming that the energy associated with pressure difference is analogous to that associated with altitude difference in rivers. The morphology of the bronchial tree is such that, given laminar flow or air, the calculated pressure difference across each order is equal. This may indicate that the bronchial tree is designed for minimal entropy production. In the arterial tree, however, this result is not obtained, probably because we do not know how to calculate the pressure drop in blood flowing through a branching system. It is therefore not currently possible, on the basis of this approach, to say whether the pulmonary arterial tree is designed for minimal entropy production or not.