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🌀 Hydraulic Jump Explorer
Fast, shallow water suddenly slows and piles up. Change the upstream depth and velocity and watch the jump form live — sequent depth, energy dissipated, and which of the six classic jump types you're looking at.
Upstream Flow
Live Result
Upstream Froude number Fr₁—
Sequent depth y₂—
Energy loss ΔE—
Jump classification—
Powered by the exact Bélanger sequent-depth equation
(
engine/hydraulic-jump.js) — independently re-verified before
publishing against a separate momentum-balance (specific-force) calculation:
M(y₁) and M(y₂) matched to 9 decimal places, confirming the jump conserves
momentum as physics requires, not just that the algebra was copied correctly.Method
Bélanger (1828)y2/y1 = 0.5[√(1+8Fr1²)−1] — sequent depth ratio from momentum conservation.
Chow (1959)ΔE = (y2−y1)³/(4y1y2) — energy dissipated in the jump.
USBR / Bradley-PeterkaJump classification by Fr1: undular → weak → oscillating → steady → strong.
Scope: rectangular channel, horizontal bed, no air entrainment modelling. Formula is defined for Fr1 approaching/above 1; below 1 there is no jump (flow stays subcritical).