Sequent depth ratio of a B- jump

Abstract

A B-jump is defined as the jump having the toe section located on a positively sloping upstream channel and the roller end on a downstream horizontal channel. This jump often occurs in the stilling basins with a horizontal bottom and located downstream of a steep channel. For a B-jump, a completely theoretical approach is not sufficient to solve the momentum equation and to establish the sequent depth ratio. In this paper, by using the laboratory measurements carried out in this investigation, some available empirical relationships useful for estimating the sequent depth ratio are tested. Then, by using the Π theorem of the dimensional analysis and the incomplete self-similarity theory, a generalized functional relationship for estimating the sequent depth ratio for different types of jumps is deduced. The estimate of the coefficient appearing in this relationship is dependent on the particular type of jump. In conclusion, the analysis established that the sequent depth ratio for a B-jump depends on a parameter E accounting for the toe section position, the upstream Froude number F1, and the channel slope.