Calculation analysis on the discharge capacity of Piano Key weir and relative influencing factors

In recent years, the problem of insufficient discharge capacity of the existing hydraulic projects has become more and more serious due to the frequent occurrence of extreme floods. The Piano Key weir has a high-efficiency discharge capacity when the water head on the weir is properly low. The calculation analysis of its discharge capacity has great practical value. The discharge capacity is related to the main structural parameters of the Piano Key weir and the water head on the weir. In this study, the influencing structural parameters of discharge capacity of the Piano Key weir was summarized, and the optimal values were suggested. Different overflow patterns formed on the Piano Key weir under different hydraulic conditions. Low water head behavior happened when the water head flowing on the Piano Key weir was low. Based on the existing experimental data, the hydraulic condition and structural parameters when low water head behavior happened were statistically analyzed. A comparative analysis on the existing discharge capacity estimation formulas of the Piano Key weir was performed. Then, based on the existing experimental data, a new discharge coefficient formula including L, W, B, P, W_i/W_o and B_o/B_i was proposed using the least squares method and genetic algorithm, and the predicted results were in good agreement with the experimental data of a large number of different Piano Key weirs with the average error less than 6%. Among the estimation formulas, Machiels’ formula is suitable for the detailed analysis of the discharge of the Piano Key weir. The new formula in this study and Guo Xinlei’s formula are both simple in calculation and can be used to estimate the overall discharge capacity of the Piano Key weir, and the suitable formula can be selected according to the practical requirement.