Hydraulic Jump Calculator

Calculate the sequent (conjugate) depth and energy loss in a hydraulic jump occurring in an open channel when supercritical flow transitions to subcritical flow.

SEQUENT DEPTH (y₂)
--
Froude Number (Fr₁)
--
Energy Loss
--
Jump Height Ratio
--
Downstream Vel
--

What Is a Hydraulic Jump?

A hydraulic jump is a phenomenon in open channel flow where water transitions rapidly from a supercritical (fast, shallow) state to a subcritical (slow, deep) state. This transition is accompanied by significant turbulence and energy dissipation. It is analogous to a shock wave in compressible gas dynamics.

Hydraulic jumps occur naturally downstream of spillways, weirs, and sluice gates. They are also intentionally created in stilling basins to dissipate the kinetic energy of fast-moving water and prevent erosion of the downstream channel bed. The Froude number upstream must exceed 1 for a jump to occur.

Sequent Depth Formula

y₂ = (y₁ / 2) × (√(1 + 8Fr₁²) - 1)
Fr₁ = V₁ / √(g × y₁)
ΔE = (y₂ - y₁)³ / (4 × y₁ × y₂)

Types of Hydraulic Jumps

Froude NumberJump TypeEnergy Loss
1.0 - 1.7Undular jump< 5%
1.7 - 2.5Weak jump5 - 15%
2.5 - 4.5Oscillating jump15 - 45%
4.5 - 9.0Steady jump45 - 70%
> 9.0Strong jump> 70%

Engineering Applications

  • Stilling basins: Designed at the base of dam spillways to dissipate energy safely.
  • Wastewater treatment: Used in mixing and aeration of water in treatment plants.
  • Irrigation: Controls flow transitions in canals and distribution systems.
  • Flood control: Energy dissipation structures in flood channels use hydraulic jumps.

Frequently Asked Questions

What happens if the Froude number is less than 1?

If the upstream Froude number is less than 1, the flow is already subcritical and a hydraulic jump cannot form. The flow is tranquil and energy dissipation occurs gradually through friction rather than through a sudden jump.

How is energy lost in a hydraulic jump?

Energy is dissipated primarily through intense turbulence in the jump roller. The turbulent eddies convert kinetic energy into heat through viscous dissipation. The energy loss increases dramatically with the upstream Froude number.

Can a hydraulic jump move upstream?

A hydraulic jump position is determined by the downstream water level (tailwater depth). If tailwater rises, the jump moves upstream; if it drops, the jump moves downstream. Engineers design stilling basins to keep the jump within the protected area under all flow conditions.