Theoretical Determination of Subcritical Sequent Depths for Complete and Incomplete Hydraulic Jumps in Closed Conduits of Any Shape

• Main Author: Lowe, Nathan John
• Format: Others
• Published: BYU ScholarsArchive 2008
• Subjects: hydraulic jump; sequent depth; Belanger; closed conduit; culvert; elliptical; pipe arch; Civil and Environmental Engineering
• Online Access: https://scholarsarchive.byu.edu/etd/1619; https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2618&context=etd

In order to predict hydraulic jump characteristics for channel design, the jump height may be determined by calculating the subcritical sequent depth from momentum theory. In closed conduits, however, outlet submergence may fill the conduit entirely before the expected sequent depth is reached. This is called an incomplete or pressure jump (as opposed to a complete or free-surface jump), because pressure flow conditions prevail downstream. Since the momentum equation involves terms for the top width, area, and centroid of flow, the subcritical sequent depth is a function of the conduit shape in addition to the upstream depth and Froude number. 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 conservatively assume that the conduits are prismatic, horizontal, and frictionless within the jump length; that the pressure is hydrostatic and the velocity is uniform at each end of the jump; and that the effects of air entrainment and viscosity are negligible. The implications of these assumptions are briefly discussed. It was found that these solutions may be applied successfully to determine the subcritical sequent depth for hydraulic jumps in closed conduits of any shape or size. In practice, this may be used to quantify jump size, location, and energy dissipation.