Analysis of stage-discharge theoretical and laboratory relationships in morning glory sharp crested weir

In this study, a special type of sharp-crested weir is called sharp- crested morning glory weir (SCMGW) is introduced. Due to the special shape of this weir, high measurement accuracy in low discharge, and in flood and sudden discharges, less back water profile is expected upstream. On the other hand, there is no discontinuity in their stage-discharge relationship. Assuming the occurrence of a critical flow in the weir crest, the general stage-discharge relationship was extracted for this type of weir. The next step was to correct this assumption, considering that the assumption of the occurrence of a critical flow in the weir crest is accompanied by an error, and consequently the stage-discharge relationship obtained based on this assumption is not accurate. For this purpose, by measuring 57 experiments on 5 types of this weir, the stage-discharge relationship was extracted and it was shown that for a specific stage, the measured flow is greater than the calculated analytical flow. A correction coefficient was applied to the analytical relation with the aim of matching the stage-discharge analytic relationship with the measurement. This correction factor was optimized and extracted using the gene expression programming method as a function of the weir height-to-head ratio (p / H) and the a / n ratio (a and n parameters of the weir geometric shape). The results showed that the modified discharge-stage relationship estimated the measured discharge values as R2 = 0.98, mean absolute error MAE = 0.442 liters and root mean square error of RMSE = 0.08 liters.