A generalized stage-discharge relationship for sharp-crested power-law weirs by dimensional analysis and self-similarity

Weirs are characterized by a stage-discharge relationship which mainly depends on the shape and dimensions of the hydraulic structure. A weir with symmetrical power-law sides is a versatile weir that can produce some known weir types (rectangular, triangular, parabolic) as special cases. In this paper, the outflow process of sharp-crested power-law weirs is investigated using the dimensional analysis and the incomplete self-similarity theory. A new generalized theoretical stage-discharge relationship is proposed, and its applicability is tested using measurements available in the literature for different weir types.