Hydraulischer Sprung

A hydraulic jump is a sudden rise in fluid depth occurring when high-velocity supercritical flow transitions to slower subcritical flow. It requires an upstream Froude number exceeding 1. In subcritical flow where the Froude number is less than 1, hydraulic jumps cannot form because the flow lacks sufficient excess energy for the transition.

Hydraulic jump types depend directly on the upstream Froude number. Classifications range from Jump Impossible (Fr<1) to Strong Jumps (Fr>9.0), including Standing Wave, Weak, Oscillating, and Stable jumps. As the Froude number increases, the depth ratio and energy dissipation also rise, signifying more significant depth changes and greater head loss across the jump.

Hydraulic jumps dissipate energy in structures like dam spillways, protecting downstream channels from erosion. High-speed water exiting spillways can damage downstream areas, but hydraulic jumps convert supercritical flow to subcritical flow, reducing velocity and energy while providing energy considerations in open channel flow management.

A standing wave or undulant jump occurs with barely supercritical flow (Fr=1 to 1.7), causing minimal depth changes with low energy dissipation. An oscillating jump forms at higher Froude numbers (Fr=2.5 to 4.5) and is unstable with regular oscillations, moderately dissipating energy compared to the standing wave's localized effect.

Submerged jumps occur in sloped or obstructed channels when downstream depth is artificially raised by structures like weirs or gates. They dissipate energy over a longer distance than surface jumps, adapting to channel conditions. These tailored solutions differ from standing waves in behavior, efficiency, and spatial requirements for specific engineering needs.

Head loss, or energy dissipation, increases significantly with higher upstream Froude numbers. Stable jumps (Fr=4.5 to 9.0) cause substantial energy loss, while strong jumps (Fr>9.0) exhibit highly turbulent conditions with considerable energy dissipation. Weak jumps at lower Froude numbers produce minimal head loss compared to these higher-energy transitions.

Hydraulic jumps cannot occur in subcritical flow because they would require negative head loss, which violates thermodynamic principles. Energy cannot be created; it can only be dissipated or conserved. Subcritical flow with Froude numbers less than 1 lacks the excess energy needed to transition to a higher depth state.