Deducing the stage-discharge relationship for contracted weirs by the outflow theory of Malcherek

The aim of this paper was the deduction of a new stage-discharge relationship for a contracted weir, having a crest length less than the channel width, by using the Malcherek’s outflow theory. The average outflow velocity over the rectangular contracted weir was expressed in terms of the head over weir, the momentum correction coefficient and the ratio between the crest length and the channel width. This theoretically deduced stage-discharge formula was calibrated by measurements carried out for values of the ratio between the crest length and the channel width ranging from 0.3125 to 0.9375. In particular, a relationship to estimate the momentum correction coefficient for contracted weirs was deduced. The analysis showed that the proposed stage-discharge relationship is characterised by an excellent performance and allows to measure discharge values characterised by errors which are, for 96.0% of the measured values, less than or equal to ±5%.