Air Entrainment and Sequent Depths in Horizontal Closed Conduits

In order 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, resulting in the aptly-named "incomplete" jump. This requires the sequent depth equation to account for both open-channel and closed-conduit flow. When using momentum theory to calculate sequent depths in conduits, it is commonly assumed that the conduits are prismatic, fairly horizontal, and relatively 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 viscosity and air entrainment are negligible. However, research recommends that air entrainment be included in closed-conduit sequent depth calculations. This paper therefore reviews momentum theory as applicable to hydraulic jumps in closed conduits, provides a general sequent depth solution that accounts for air entrainment and which is applicable to complete and incomplete jumps within all conduit shapes, and then compares these solutions to those that do not account for air entrainment. In practice, these solutions may be used to more accurately predict the size and location of potential hydraulic jumps within conduits and culvert barrels in order to facilitate cost-effective designs for energy dissipation.