A discharge-based velocity profile model for unsteady open-channel flow

Unsteady open-channel flows exhibit pronounced differences in velocity distribution between the rising and falling limbs of a hydrograph due to flow acceleration and deceleration, which cannot be accurately captured by conventional steady-flow formulations. In this study, a discharge-based velocity profile model is proposed in which flow unsteadiness is incorporated through a correction factor (C), expressed as a function of the discharge rate (Qr). Separate formulations were developed for the rising and falling limbs of the hydrograph, allowing acceleration and deceleration effects to be represented explicitly. The model is calibrated and validated using present laboratory experiments and independent unsteady flow datasets reported in the literature. Predictions obtained using steady-flow equations result in substantial errors, with mean absolute percentage error (MAPE) values exceeding 300% in several cases. In contrast, the proposed model significantly improves prediction accuracy, yielding MAPE values mostly below 15% and low root mean square error across a wide range of flow conditions. The modified formulation shows good agreement with observed point velocities over the entire flow depth, with particularly strong agreement in the mid-depth and near-surface regions for both hydrograph limbs. This discharge-based correction approach provides a novel and robust framework for predicting velocity distributions under unsteady flow, with strong potential for applications in hydraulic design, flood routing, and environmental flow modeling.