Dimensional Analysis and Stage-Discharge Relationships for Vegetated Weirs

Abstract The deduction of the weir flow stage-discharge relationship is a hydraulic problem generally solved by energy considerations and using the discharge coefficient to correct the gap between theoretical results and experimental measurements. In this context, the dimensional analysis represents an alternative to find simple and reliable equations to obtain the rating curve. In this study, the outflow process of vegetated weirs is investigated applying the Π-Theorem of dimensional analysis and the incomplete self-similarity theory. The aim of this paper is to propose a new theoretically-based stage-discharge relationship, and test its applicability by measurements recently published in the literature. The results showed that the errors in discharge estimate obtained by the proposed stage-discharge relationship are always less than or equal to ± 10% and less than or equal to ± 5% for 97–100% of cases. The main advantage of the proposed relationships is providing a single stage-discharge relationship, which has better performances than the equations reported in the literature and excludes the use of discharge coefficient.