Experimental study of discharge formulas for rectangular sharp-crested weirs under free flow condition

Abstract

Laboratory experiments were carried out to investigate the discharge characteristics of rectangular sharp-crested weirs under free flow condition. The performances of available discharge formulas have been evaluated by using the experimental data sets of present and previous studies. Error statistics of our experimental data indicate that the recent stage-discharge relationships show satisfactory performances. Discharge formula in terms of weir Reynolds number proposed by Vatankhah gives the highest accuracy among the existing slit weir equations, with E±4=100.00% (i.e. percent error less than or equal to ±4) and a mean absolute error |E|m=0.88%. The full-range discharge equation presented by Bijankhan and Mahdavi Mazdeh shows the highest accuracy among the relationships in terms of weir contraction ratio, with E±4=100.00%, |E|m=0.91% for slit weirs and, E±4=94.64%, |E|m=1.60% for partially contracted weirs, respectively. The weir velocity formulae suggested by Gharahjeh et al. exhibit the relatively better performance, with E±4=98.41%, |E|m=1.34% for slit weirs and, E±4=91.07%, |E|m=1.91% for contracted weirs, respectively. Statistical results of this study confirm the weir velocity approach presented by Aydin et al. and show that, the weir velocity is a predominant quantity for rectangular sharp-crested weirs, unique characteristics of the weir velocity curves make it more suitable for expressing the discharges. Moreover, it is important to point out that the performance of weir velocity formulae can be further improved.