Boundary shear stress distributions in smooth rectangular open channel flows

This paper presents an analytical method for the computation of boundary shear stress distributions acting on the flow perimeter of prismatic open channels. The approach is based on the premise that the surplus energy of any arbitrary unit volume of fluid in a three-dimensional flow channel with be transported towards and dissipated at a unit area on the wetted perimeter. This leads to a concept which states that the direction of energy transportation will define a minimum relative distance, Phi, between the source of energy in the flow field and the boundary. Based on this concept, a novel method is developed for the partitioning of the flow cross-sectional area into various parts corresponding to the channel shape and roughness composition on the wetted perimeter. The method enables the distribution of the boundary shear over the wetted perimeter to be assessed within each sub-flow area. This paper illustrates the application of the principle to steady and uniform flow in smooth rectangular open channels. Analytical equations governing the boundary shear stress distributions have been derived and are valid for all channel aspect ratios. The formulae have been verified using experimental shear data from published sources.