Dimensional Analysis of Hydrological Response of Sluice Gate Operations in Water Diversion Canals

The hydrodynamics characteristics of artificial water diversion canals with long-distance and inter-basin multi-stage sluice gate regulations are prone to sudden increases and decreases, and sluice gate discharge differs from that of natural rivers. Research on the change characteristics of hydrological elements in artificial canals under the control of sluice gates is lacking, as are scientifically accurate calculations of sluice gate discharge. Therefore, addressing these gaps in long-distance artificial water transfer is of great importance. In this study, real-time operation data of 61 sluice gates, pertaining to the period from May 2019 to July 2021, including data on water levels, flow discharge, velocity, and sluice gate openings in the main canal of the Middle Route of the South-to-North Water Diversion Project of China, were analyzed. The discharge coefficient of each sluice gate was calculated by the dimensional analysis method, and the unit-width discharge was modeled as a function of gate opening (e), gravity acceleration (g), and energy difference (H). Through logarithmic transformation of the Buckingham Pi theorem-derived equation, a linear regression model was used. Data within the relative opening orifice flow regime were selected for fitting, yielding the discharge coefficients and stage–discharge relationships. The results demonstrate that during the study period, the water level, discharge, and velocity of the main canal showed an increasing trend year by year. The dimensional analysis results indicate that the stage–discharge response relationship followed a power function (Q∝(He)constant) and that there was a good linear relationship between lg(He) and lg(Ke) (R2 > 0.95, K=(q2/g)1/3). By integrating geometric, operational, and hydraulic parameters, the proposed method provides a practical tool and a scientific reference for analyzing sluice gates’ regulation and hydrological response characteristics, optimizing water allocation, enhancing ecological management, and improving operational safety in long-distance inter-basin water diversion projects.