Free‐Overfall Flow Measurement in Sloping Inclined‐Wall U‐Shaped Channels

ABSTRACT

Accurate discharge estimation in open‐channel systems is essential for irrigation water management, particularly in geometrically complex channels. This study investigates free‐overfall flow in inclined‐wall U‐shaped channels using combined laboratory experiments and CFD simulations, aiming to develop a practical discharge estimation method based on the end‐depth ratio (EDR). Experiments covered two plexiglass U‐shaped channels, five bed slopes (s = 0,1/800,1/600,1/400 and 1/200), discharges of 0.0063–0.0576 m ³ /s and a constant Manning roughness coefficient of n  = 0.011. CFD simulations were used to analyse free‐surface profiles, velocity distributions and Froude number variations near the brink. The results show that channel geometry and bed slope jointly affect free‐surface development, flow transition and the end‐depth–critical‐depth relationship. The U‐shaped geometry introduces curvature effects and non‐uniform velocity distributions that differ from simplified channel sections. Empirical discharge relationships were established using measurable hydraulic variables. The slope‐dependent formulation performed best, with R ²  = 0.99, MAE = 1.13 × 10 ⁻³ and RMSE = 1.44 × 10 ⁻³  m ³ /s. Residual diagnostics further yielded a residual–prediction coefficient of determination of R ² _res  = 1.62 × 10 ⁻⁴ and a Durbin–Watson statistic of 1.98, indicating a weak residual trend and little first‐order autocorrelation. These results support the use of the slope‐dependent formulation as the preferred discharge‐estimation relationship within the investigated experimental range.