New stage-discharge relationship for inclined non-rectangular weirs

Abstract

In this paper, the outflow process of inclined non-rectangular weirs is studied applying the dimensional analysis and the incomplete self-similarity theory. At first, a new stage-discharge equation, applicable for the non-rectangular weirs having a different geometrical shape (parabolic, semicircular, inverted semicircular), is theoretically deduced using a characteristic width. Then, this power stage-discharge relationship (Eq. (17)) is calibrated and tested using measurements carried out by Raiknar for parabolic, semicircular and inverted semicircular weirs having different inclination respect to the vertical (10° 20° 30° 40° and 45°). For each geometrical shape, the analysis showed that the exponent of the power stage-discharge relationship is quasi constant while its coefficient is related to the weir inclination. Finally, the accuracy of the stage-discharge relationship was improved taking into account the effect of the weir inclination angle. The proposed stage-discharge equations (Eqs. (20)–(22)) allow to calculate discharge values which are characterized by an estimate accuracy always greater than that of the corresponding values calculated by relationships proposed by Raiknar.