Dimensional analysis and stage-discharge relationship for weirs: a review

Deducing the weir flow stage-discharge relationship is a classical hydraulic problem. In this regard Buckingham’s theorem of dimensional analysis can be used to find simple and accurate formulas to obtain the rating curves of different weir types. At first, in this review paper the rectangular weir that is a very common hydraulic structure is studied. It is indicated that the crest shape, approach channel width, obliquity (angle between the weir crest and the direction normal to the flow motion) and vertical inclination (pivot weir) are the key-parameters affecting the flow over the rectangular weirs. The flow over the triangular, labyrinth, parabolic, circular, elliptical, and W-weirs are also studied using dimensional analysis and incomplete self-similarity concept. For all mentioned weirs the stage-discharge relationships are presented and the application limits are discussed. The results of this paper can be used and implemented by the irrigation and drainage network designers to simplify the procedure of weir design.