Mathematical expression for the B-Jump sequent depth ratio on sloping bed

Abstract

A common and practical type of hydraulic jump at sloping bed (e.g., concrete, gabion or rock cover bed chutes) is B-jump which its toe located on the sloping bed and ended at the downstream horizontal channel. Determination of hydraulic jump characteristics such as the sequent depth ratio can help to design a safe and economic stilling basin. Many studies have been carried out for B-jump on smooth sloping bed; however on the effect of roughness on jump characteristics no relation is available. In this paper first a general non-dimensional relation was developed using Buckingham theorem. Then by applying the incomplete self similarity theory and using a new dimensionless parameter, N, a new non dimensional relation was developed. The significant of such relation is that it is independent of bed slope. To verified such relation two series of tests were conducted at the hydraulic lab using three different slope angles, five different roughness heights and five different flow conditions both on smooth and roughened bed. The collected data were analyzed by SPSS15.0 software and the required coefficients were obtained. The proposed expression was tested using wide range of data and the average absolute error was found to be 6.4%.