Rapid calculation method for minimum navigable flow discharge in backwater zones of small to medium rivers based on slope correction

The minimum navigation flow discharge (MNFD) required to maintain waterway dimensions in basins affected by water transfer projects is often subject to strategic interactions over ecological compensation among stakeholders, making its rapid determination highly important. However, in backwater zones of small to medium rivers, water level is jointly controlled by topographic variations and downstream backwater effects, complicating its estimation. This study develops a rapid calculation procedure for MNFD in such zones through theoretical analysis and numerical simulation, introducing a water surface slope correction into the Manning equation. Taking the Shiguan River, affected by the Huai River, as a case study, a two-dimensional hydrodynamic model was constructed to compare the simulated MNFD with the proposed method's result. Results indicate that, for a Class IV waterway depth of 3.10 m, direct application of the Manning equation yields an MNFD of approximately 1,529 m³/s, while the proposed rapid procedure gives 616 m³/s, and the numerical simulation indicates 600 m³/s. Compared with the direct Manning estimate, the proposed method substantially improves agreement with the numerical result, reducing the relative deviation from 155% to 3%.