Empirical Estimation of Strong Hydraulic Jump Length in a Rectangular Channel for Sustainable Stilling Basin Design

Abstract

Hydraulic jump length is a critical parameter for determining the required length of stilling basins and downstream energy dissipation structures. However, existing empirical equations may not adequately represent strong hydraulic jumps generated under high pre jump Froude number conditions. This study investigates strong hydraulic jump behavior in a rectangular laboratory channel and develops empirical relationships for predicting hydraulic jump length. Experiments were conducted using a physical spillway model with two chute slopes, 1V:1H and 1V:0.8H. Seventeen discharge conditions ranging from 5 to 27 liters per second were tested. The observed pre jump Froude number ranged from 10.05 to 22.09, indicating strong hydraulic jump conditions. The main measured parameters were pre-jump depth, post-jump depth, post-jump Froude number, jump height, and hydraulic jump length. Calibration results showed good agreement between analytical and observed values, with mean absolute percentage errors of 4.86% for pre-jump depth and 7.96% for pre jump Froude number. The observed hydraulic jump length ranged from 85 to 315 centimeters. Regression analysis showed strong relationships between hydraulic jump length and pre jump depth, post jump depth, jump height, and upstream Froude number. The dimensionless formulation based on hydraulic jump length to pre jump depth ratio and pre jump Froude number produced the best predictive performance, with a mean absolute percentage error of 3.93%. Comparison with previous equations showed that most existing formulas underestimated the observed jump length. The proposed relationship provides an improved basis for estimating stilling basin length under strong hydraulic jump conditions.