New Analytical Formulation of De Marchi’s Model for a Zero-Height Side Weir

Abstract

One-dimensional modeling is often used to simulate the hydrodynamics of free-surface flows, including spatially varied flows as encountered along side weirs. This paper deals with the particular case of a side weir with a zero-height crest acting on fixed bed and subcritical flow, for which a new analytical model is formulated starting from De Marchi’s hypothesis. The proposed model provides an original interpretation of the side weir problem, for which the solution, formulated in dimensionless form in terms of average flow and geometrical variables of the side weir and main channel, is the explicit result of the imposed boundary conditions at the upstream and downstream cross sections. The proposed model appears to be able to analyze a wide range of hydraulic problems similar to the side weir flow, such as lateral diversions, and to solve design and verification problems as first approximation. The analytical model is used to predict experimental data coming from literature as well as from a new set of laboratory data in a very direct way without any need of numerical techniques.