Theoretical Development of Hydraulic Jump in Trapezoidal Channel Forced by a Broad-Crested Sill

Abstract

Applying the momentum equation reveals that there are three key factors that control the hydraulic jump in a trapezoidal channel caused by a sill: the inflow Froude number Fr₁, the sequence depth ratio Y, which is the ratio of the downstream depth h₂ to the upstream depth h₁, the relative upstream flow depth M, and the relative height of the broad-crested sill "S" which is the ratio of the step's geometric height "s" to the height h₁ of the jump at its upstream section. The aim of this study is to establish the empirical connections governing the broad-crested sill-induced hydraulic leaps in a trapezoidal channel. The goal is to come up with a concrete representation of the theoretical relationship between Fr₁, Y, M, and "S". Applying the momentum equation between the upstream and downstream parts, which limits the leap, enables this. The resulting connection will be contrasted with the traditional hydraulic leap. After that, a comparison with the outcomes of the experiments serves to confirm the theoretical method.