🌊 Hydraulic Jump Calculator
Find the downstream (sequent) depth and energy loss produced by a hydraulic jump in an open channel, from the upstream flow depth and velocity.
What a hydraulic jump is
A hydraulic jump is the abrupt rise in water surface that occurs when a fast, shallow (supercritical) flow transitions to a slow, deep (subcritical) flow, such as below a spillway or sluice gate. It dissipates kinetic energy as turbulence and is a key feature in open-channel and spillway design.
The formula
The upstream Froude number is Fr₁ = v₁ / √(g·y₁). The downstream sequent depth follows the Belanger conjugate-depth equation: y₂ = (y₁/2)·(√(1 + 8·Fr₁²) − 1). The energy dissipated in the jump is ΔE = (y₂ − y₁)³ / (4·y₁·y₂).
These relations assume a horizontal, rectangular, frictionless channel and are standard results from open-channel hydraulics; they are provided for general engineering and educational reference.