Assessing Malcherek’s Outflow Theory to Deduce the Theoretical Stage-Discharge Formula for Overflow Structures

Abstract

New theoretical stage-discharge relationships of different sharp-crested weirs were developed in this study using the new Malcherek’s outflow theory. Although Torricelli’s outflow theory is basically used to estimate the stage-discharge formula for overflow structures, it is indicated in this work that the stage-discharge curve obtained by Malcherek’s outflow theory improves the theoretical estimation significantly. The new theoretical stage-discharge formula requires estimating the momentum correction factor (β) using velocity profiles instead of using an unknown discharge coefficient. Accordingly, for the rectangular weir, it was indicated that the available velocity profiles over the weir crest could be used to estimate the momentum correction factor and associated stage-discharge curve accurately. Moreover, the optimum β-values for rectangular, triangular, and circular overflow structures were suggested to be calculated using indirect prediction of the momentum correction factors by introducing the stage-discharge data points available in the literature. The performances of different stage-discharge approaches were evaluated and practical advice was suggested. It was found that the proposed stage-discharge curves were in an excellent agreement with the observed values.