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.
- 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
Frequently Asked Questions
Where do hydraulic jumps occur in nature?
At the base of dams and spillways, in tidal bores (like the Severn Bore), and when a fast stream enters a deeper, slower pool.
Can a hydraulic jump be used to mix fluids?
Yes. The intense turbulence in the jump is excellent for mixing, aeration, and chemical treatment in wastewater facilities.
What happens to the energy?
Kinetic energy is converted to turbulent mixing and heat. The energy loss increases with the Froude number.
Ready to run the numbers?
Open Hydraulic Jump Calculator