Fluid Mechanics

Hydraulic Jump Simulator

Analyze open-channel water flow transitions from high-velocity supercritical flow to low-velocity subcritical flow. Observe sequent depth formation, energy dissipation, and flow profile sweeps.

Upstream Regime

Supercritical

Jump occurs

Energy Loss

0.24 m

86.6% Eff. remaining

Output Mode

Live profile

Bélanger equation

Parameters

Regime Presets

Upstream Depth (y₁)0.50 m

0.13

Upstream Velocity (v₁)5.00 m/s

0.515

Velocity flow sweep

Hydraulics Equations

Upstream Froude Number

Fr₁ = v₁ / sqrt(g * y₁)

Bélanger Equation (y₂)

y₂ = y₁/2 * (sqrt(1 + 8*Fr₁²) - 1)

Head Loss (Energy Dissipation)

ΔE = (y₂ - y₁)³ / (4 * y₁ * y₂)

The jump forms only if upstream flow is supercritical (Fr₁ > 1).

A steady jump is highly turbulent and typically occurs for Fr₁ between 4.5 and 9.0.

Hydraulic Jump Flow Diagram

Froude Number (Fr₁)

2.26

Sequent Depth (y₂)

1.37m

Downstream Velocity (v₂)

1.83m/s

Head Loss (ΔE)

0.24m

Water Depth & Specific Energy Profile

Jump Profile Nodes

Position x (m)	Depth y (m)	Velocity v (m/s)	Energy E (m)
0.0	0.50	5.00	1.77
1.0	0.50	5.00	1.77
2.0	0.50	5.00	1.77
3.0	0.50	5.00	1.77
4.0	0.64	4.50	1.67
5.0	0.93	3.42	1.53
6.0	1.23	2.33	1.51
7.0	1.37	1.83	1.54
8.0	1.37	1.83	1.54
9.0	1.37	1.83	1.54
10.0	1.37	1.83	1.54