As a critical parameter of the steady uniform friction model, the roughness coefficient changes with flow unsteadiness in flood events; i.e., the flow conditions of the stream segment significantly affect the flow resistance. In this study, a modified formula was established to improve the unsteady friction simulation; ten terms relating to the first- and second-order time and space partial derivatives of hydraulic parameters were selected as additional terms. The results of a hydraulic experiment show that the hysteresis between flow depth and mean cross-sectional velocity cannot be neglected in unsteady flows that disturb the performance of a steady uniform friction model. Six terms have a strong correlation with objective friction. Further, three of them have a small variance in correlation coefficient. Then, the composition of the proposed formula was determined. The results show that adding too many additional terms provides better performance in the calibration phase, yet reduces the accuracy of the validation phase because of an overfitting phenomenon. The optimal number of additional terms is three, and the established formula can improve the unsteady friction simulation.

To enhance the passing capacity of the Bailongtan Ship Lock on the Hongshui River, this study focused on the design scheme of its water conveyance system reconstruction and expansion project. A three-dimensional mathematical model meeting the experimental accuracy requirements was established based on the RNG k-ε turbulence model and the Volume of Fluid (VOF) free-surface tracking method. A 1:30 scale ship lock water conveyance system physical model was built and used the independently developed system for hydraulic test monitoring, acquisition, and control. Experimental research on the hydraulic characteristics and shape optimization of the water conveyance system was carried out. The experimental results show that, under the condition of a maximum head difference of 16.0 m between the upstream and downstream of the ship lock, in the design scheme, the flow in the corridor after the filling valve fails to diffuse adequately, forming a high-velocity zone and a significant pressure difference between the inner and outer sides, which poses an operational risk. By optimizing the shape of the corridor after the valve (deepening the bottom end by 2.0 m and adjusting the turning angle from 75° to 70°), the range of the high-velocity zone can be shortened from 3.0 m to 1.5 m. The pressure difference between the inner and outer sides of the corridor at the horizontal turning section is reduced by 19.2% from 5.35 m to 4.32 m of the pressure head at the moment of maximum flow rate, and the velocity in the horizontal section is less than 15 m/s. Physical model tests confirmed these improvements, with mooring forces within safety limits (longitudinal ≤ 32 kN, transverse ≤ 16 kN). The research findings indicate that integrating numerical simulation with physical model testing can effectively mitigate risks in the original design of the ship lock water conveyance system. This approach notably enhances the reliability and safety of the design scheme, as demonstrated by the significant reduction in high-velocity zones and pressure differentials. Moreover, it offers a robust scientific basis and practical technical reference for in-depth hydraulic research and targeted optimization of ship lock water conveyance systems.

Although steady uniform friction formulas have been introduced to the framework of a one-dimensional (1D) hydrodynamic model for centuries, the error of friction calculation inevitably undermines the performance of flood routing. Based on successful results of unsteady channel friction research studies, a newly proposed unsteady friction model is introduced to establish a modified 1D hydrodynamic model (namely, the modified SVN model). With the help of a carefully designed parameter calibration method, the performance of the modified SVN model was compared with that of the original SVN model in a simulation test for a hydraulic experiment. This study’s results revealed that compared with the original SVN model, the modified SVN model could achieve a better simulation in both the flow depth and the sectional averaged velocity simulations. Furthermore, it could reduce the peak value error and the time-at-peak error as well, indicating that the use of an unsteady friction model can efficiently improve the performance of a 1D hydrodynamic model.

A weighting function model was developed to account for the relationship between flow unsteadiness and frictional resistance. The Manning equation cannot fully describe such processes, leading to deficiency in predictive capability under some conditions. Two fundamentally new contributions to our approach are the development of (1) an additional unsteady component using time derivatives of flow-state, and (2) an additional component that utilizes instantaneous and historical information to update the current system. Compared to the results from the Manning equation, the proposed model reduces the overall simulation error and also improves the accuracy in peak simulation. Furthermore, parameter values can be conveniently constrained for model prediction and show strong dependence with the friction coefficient n. However, the proposed model incorporates more parameters and is more complicated than the Manning equation. Further research is needed to explore specific physical meaning of the parameters, for its simplification, practical application, and parameter identification.