Potential Flow Solution for Open-Channel Flows and Weir-Crest Overflow

Abstract

Weirs used for water discharge measurement in open-channel systems normally operate under free-flow conditions, for which the specific energy reaches a minimum at the weir crest. This type of transitional open-channel flow can be simulated using the ideal fluid flow theory. The traditional application of that theory requires the computation of the flow net over the weir. In this work, a potential flow model using a semi-inverse mapping is proposed in order to simulate potential flow over weirs. The model reduces the computation of the entire flow net to the determination of the streamline flow pattern only. The computations are conducted numerically using a simple finite-difference technique, in which conservation of energy, momentum, and the critical flow condition with curvilinear streamlines is considered. The model is used to display parameters of engineering interest at the point of minimum specific energy.