Empirical Modeling of Flow Characteristics in Stepped Spillways

Present comprehensive study integrates experimental analysis of geometrically different stepped spillway with empirical modeling to optimize uncertain flow conditions. Investigation of flow characteristics such as sequent depth, relative energy loss, relative jump length and roller length were carried out for three different spillway models with varying features and slope under nappe and skimming flow regime. Performance evaluation of each spillway models against varying step heights, step lengths and number of steps for the range of Froude number varying between 1 to 7 were presented. Regression models incorporating step geometry and flow parameters yielded high predictive fidelity for sequent depth ratio and relative energy loss, with R² values up to 0.97, while moderate accuracy was achieved for relative jump and roller length estimation due to experimental limitations. The results demonstrate that increased step height and step number enhance energy dissipation and reduce post jump depths, while milder slopes allow longer flow step interactions, improving dissipation efficiency. Comparison with other researches result and testing of empirical models by statistical indicators R2, MAE, MSE, RMSE and MAPE were carried out with satisfactory value of 1 for R2; close to 0 for MAE, MSE, RMSE; and + 25% for almost all characteristics for MAPE respectively. This research provides empirical relationships and performance insights to guide the design and optimization of stepped spillways, highlighting scale effects and practical modeling constraints for field applications