Theoretical Determination of Sequent Depths in Closed Conduits

Abstract

To predict hydraulic jump characteristics for channel design, jump height may be determined by calculating the subcritical sequent depth from momentum theory. In closed conduits, however, a hydraulic jump may fill the conduit entirely before the expected sequent depth is reached. This paper reviews momentum theory as applicable to closed-conduit hydraulic jumps and presents general solutions to the sequent depth problem for four commonly shaped conduits: rectangular, circular, elliptical, and pipe arch. It also provides a numerical solution for conduits of any shape, as defined by the user. The solutions assume (1) the conduits are prismatic, fairly horizontal, and relatively frictionless within the jump length; (2) the pressure is hydrostatic and the velocity is uniform at each end of the jump; (3) the effects of air entrainment and viscosity are negligible; and (4) atmospheric conditions exist at the entrance. The implications of these assumptions are discussed briefly. In practice, the derived solutions may be used to predict the size and location of potential hydraulic jumps within culvert barrels or storm water sewers to facilitate a cost-effective design for energy dissipation.