Modelling of the tributary momentum contribution to predict confluence head losses

Abstract

ABSTRACTThis paper proposes a new model to determine the head losses at confluences in one-dimensional models of open channel networks, making use of a momentum conservation approach. Momentum conservation has been applied in several theoretical models for confluence head losses, giving satisfactory results in general. However, for larger confluence angles between the main channel and the incoming tributary, the model accuracy diminished. Many authors identified that a correct estimation of the tributary momentum contribution is a prerequisite for accurate results. This work reports on the development and application of a theoretical model for the tributary momentum contribution, based on similarities with the flow upstream of a circular bend in a straight open channel. It describes the two-dimensional depth-averaged flow features in the tributary under the assumption of a 90° angle confluence in which all channels have equal widths, in order to obtain the resulting momentum contribution. The proposed model predicts head losses within the same order of accuracy as a numerical model solving the shallow water equations in two dimensions throughout the confluence.