IS IT HESS-MURRAY LAW ALWAYS VALID?

Abstract

Complex flow systems such as the vascular and respiratory trees are made of large and small ducts in series. While the literature has reported extensively cases that are in agreement with Hess-Murray law, there are also branching patterns of natural systems that deviate from this law. Is it this deviation to Hess-Murray law possible to predict? In this study, a numerical analysis was carried out to investigate laminar fluid flow of Newtonian and non-Newtonian fluids in T-shaped flow structures with different ratios between the sizes of parent and daughter ducts. The performance of the branching systems was evaluated in terms of total hydraulic resistance and distribution of shear stresses. We showed that the optimal design of a bifurcating ducts not always match a constant reduction factor of 2^(-1/3) for the duct sizes. The results were compared with nalytical results obtained based on constructal law.