Study on the basic flow required to maintain navigable channel scale in small and medium rivers

The determination of the minimum discharge for maintaining waterway dimensions influences navigational safety and the efficient utilization of water resource use. Amid the context of rapid development of inland navigation and high-grade tributary waterway construction, swiftly analyzing its quantitative relationship with topographic and hydrological changes holds notable scientific and engineering value. Minimum discharge is typically defined by waterway class, scale, and navigation standards, yet is affected by multiple variables. This is especially true for small to medium rivers, where terrain-driven water level fluctuations complicate discharge estimation. Traditional methods—hydrological analysis, numerical simulation, and empirical river regime formulas—often fall short when balancing computational efficiency and accuracy. This study introduces a rapid calculation method for minimum discharge in small to medium waterway channels, using Manning’s equation with a corrected water surface slope at the control section.

Taking the improvement of navigational flow conditions in the upstream Huai River at the Xixian section as an example, this study first selected the inlet section as the control section based on theoretical analysis and according to the variation law of water surface slope under backwater effects, and applied a slope correction. Using Manning’s equation, a rapid calculation method for minimum discharge suitable for small to medium river channels was then developed. Next, based on topographic data from the Xixian reach of the Huai River Xixian reach in December 2020, a two-dimensional hydrodynamic model was constructed to simulate and determine the minimum discharge or channel slope required to maintain navigable dimensions under different schemes. Finally, the proposed method was applied to compute the minimum discharge or waterway slope for each scheme, and the results were compared with numerical simulations to demonstrate the method’s practicality and ease of use.

Using both numerical simulation and the proposed rapid calculation method, this study analyzed the maximum allowable waterway slope to meet navigable depth requirements under the design discharge, or the minimum inflow required under the design waterway slope. Simulation and comparison produced the following findings: (1) To meet depth requirements in the Xixian reach under a design discharge of 12.87 m³/s, the bed slope calculated by the proposed method yielded a bed slope of 0.008 4‱, while the numerical simulation gave a maximum permissible bed slope of 0.017 5‱. (2) Under the designed bottom elevation dredging scheme, the proposed method estimated a minimum discharge of 103.90 m³/s, versus 97.00 m³/s from simulation. (3) The slope correction concept and rapid calculation process are straightforward and efficient; results closely matched simulations, significantly reducing the trial-and-error iterations and computational load. Under design discharge conditions, the proposed method yields a more conservative estimate of bed slope, while under dredging conditions, it predicts a higher estimate of minimum discharge—indicating a safety margin over simulation results. Overall, the rapid calculation method offers a practical balance between computational efficiency and acceptable accuracy for preliminary studies of waterway design and minimum discharge estimation.

The results demonstrate that the proposed rapid calculation method, based on Manning's equation with slope correction, is practical and achieves a balance between computational efficiency and accuracy in engineering applications; it can offer initial trial values for more refined subsequent simulations. The findings provide technical support for the planning and design of waterway channels in small to medium rivers, and serve as a reference for the rapid estimation and in-depth analysis of the minimum discharge needed to maintain waterway dimensions across varied riverine settings.