Hydraulic Jump Calculator Formula
Understand the math behind the hydraulic jump calculator. Each variable explained with a worked example.
Formulas Used
Upstream Froude Number
froude1 = upstream_velocity / sqrt(9.80665 * upstream_depth)Downstream Depth (y2)
downstream_depth = (upstream_depth / 2) * (sqrt(1 + 8 * pow(upstream_velocity, 2) / (9.80665 * upstream_depth)) - 1)Energy Head Loss
energy_loss = pow(((upstream_depth / 2) * (sqrt(1 + 8 * pow(upstream_velocity, 2) / (9.80665 * upstream_depth)) - 1)) - upstream_depth, 3) / (4 * upstream_depth * ((upstream_depth / 2) * (sqrt(1 + 8 * pow(upstream_velocity, 2) / (9.80665 * upstream_depth)) - 1)))Variables
| Variable | Description | Default |
|---|---|---|
upstream_depth | Upstream Depth (y1)(m) | 0.5 |
upstream_velocity | Upstream Velocity(m/s) | 5 |
How It Works
Hydraulic Jump
A hydraulic jump occurs when supercritical flow (fast, shallow) abruptly transitions to subcritical flow (slow, deep).
Downstream Depth
y2 = (y1/2) * [sqrt(1 + 8 Fr1^2) - 1]
where Fr1 = v1 / sqrt(g y1) is the upstream Froude number (must be > 1 for a jump to occur).
Energy is dissipated in the turbulent roller, making hydraulic jumps useful for energy dissipation in spillways.
Worked Example
y1 = 0.5 m, v1 = 5 m/s.
upstream_depth = 0.5upstream_velocity = 5
- 01Fr1 = 5 / sqrt(9.807 * 0.5) = 5 / 2.214 = 2.259
- 02y2 = (0.5/2) * (sqrt(1 + 8*5.103) - 1)
- 03y2 = 0.25 * (sqrt(41.82) - 1)
- 04y2 = 0.25 * (6.467 - 1) = 1.367 m
Ready to run the numbers?
Open Hydraulic Jump Calculator