Modified theoretical stage-discharge relation for circular sharp-crested weirs

A circular sharp-crested weir is a circular control section used for measuring flow in open channels, reservoirs, and tanks. As flow measuring devices in open channels, these weirs are placed perpendicular to the sides and bottoms of straight-approach channels. Considering the complex patterns of flow passing over circular sharp-crested weirs, an equation having experimental correlation coefficients was used to extract a stage-discharge relation for weirs. Assuming the occurrence of critical flow over the weir crest, a theoretical stage-discharge relation was obtained in this study by solving two extracted non-linear equations. To study the precision of the theoretical stage-discharge relation, 58 experiments were performed on six circular weirs with different diameters and crest heights in a 30 cm-wide flume. The results show that, for each stage above the weirs, the theoretically calculated discharge is less than the measured discharge, and this difference increases with the stage. Finally, the theoretical stage-discharge relation was modified by exerting a correction coefficient which is a function of the ratio of the upstream flow depth to the weir crest height. The results show that the modified stage-discharge relation is in good agreement with the measured results.