A Study of an Empirical Sequent Depths Equation of the Hydraulic Jump in a Horizontal Trapezoidal Channel

Abstract

This study used existing studies and incorporated Pi theory to establish the connection between the sequent depth ratio (y2/y1) and the influencing factors (Fr1 and M1) on the hydraulic jump on a smooth horizontal trapezoidal channel, using a physical model with a side slope of 1:1. The study proposed four equations, from which the empirical equation (Y3) was used to calculate the y2/y1 ratio of the steady jump (4.0 ≤ Fr1 ≤ 9.0). An analysis of statistical indicators for (Y3) showed that the maximum error was 7.4%, R2 was 0.98, and other statistical indicators were close to the ideal point at zero (MSE = 0.027, RMSE = 0.163, MEA = 0.129, and MAPE ≈ 2.2%). Furthermore, statistical analysis for test data also provided good results (R2 = 0.94, MSE = 0.107, RMSE = 0.327, MEA = 0.25, and MAPE ≈ 3.7%), and the maximum error reached 8.8%. Therefore, the proposed equation ensures that the calculated values can be used in practice.