A Semi-Analytical Equation to Estimate Hydraulic Jump Length

Abstract

Empirical methods for determining the length of hydraulic jump, including USBR graphical method are not accurate. In addition to reduced errors, providing an analytical equation will result in the possibility of programming and development of hydraulic software application. In this research, based on the principles of dimensional analysis, an analytical equation was achieved for estimating the length of hydraulic jump of E and classical type. Dimensionless coefficient of this equation was determined as a function of slope and Froude number using Table Curve software. For this purpose, 387 data series (258 calibration data and 129 validation data) of experiments conducted in this research, USBR studies, results of a research in the laboratory of Ohio University and in an appropriate range of the flume width, discharge, Froude number, the velocity before jump as well as the slope were used. At calibration stage, a simple equation was provided that indicates the hydraulic jump length in values Lj /y1 depends on the slope of the flume and Fr2 with determination coefficient of 94% and standard error less than 8%. Also at validation stage, the observed data and computed values was close to identity line with a determination coefficient of 0.97. Presenting the hydraulic jump length in values Lj /y1 versus Fr1 (which is very similar to USBR graphical method) was not satisfactory even with zoning Fr1 .