Hydraulic Jump Calculator
Find the sequent depth, downstream velocity, and energy loss of a hydraulic jump in a rectangular channel from the upstream depth and velocity.
🌀 What is the Hydraulic Jump Calculator?
A hydraulic jump is the sudden, turbulent transition an open channel flow makes from fast, shallow supercritical flow to slower, deeper subcritical flow. This calculator finds the sequent (downstream) depth, downstream velocity, and energy dissipated across the jump, given only the upstream flow depth and velocity in a rectangular channel.
Hydraulic jumps appear at the base of dam spillways, immediately downstream of sluice gates and control structures, at culvert outlets where flow exits under high velocity, and in laboratory flumes used to study open-channel hydraulics. Engineers deliberately design stilling basins to force a hydraulic jump to occur in a controlled location, because the jump dissipates a large fraction of the flow's kinetic energy as turbulence, protecting the unlined channel or riverbed downstream from erosion that would otherwise occur if the high-velocity flow continued unchecked.
A common misconception is that any change in flow depth is a hydraulic jump. In reality, a jump requires the upstream flow to be supercritical, meaning the upstream Froude number Fr1 must exceed 1. If Fr1 is 1 or less, the flow is already subcritical or exactly critical, and no jump can physically occur, this calculator checks that condition and explains the result instead of returning a meaningless negative energy value.
This calculator is useful for hydraulic engineers checking spillway and stilling-basin designs, students verifying momentum-equation derivations by hand, and anyone studying why jump type (undular through strong) matters for erosion protection and structure sizing.
📐 Formula
📊 Hydraulic Jump Classification by Froude Number
The character of a hydraulic jump changes considerably with the upstream Froude number Fr1, from a barely visible ripple to a violently turbulent roller.
| Upstream Fr1 | Jump type | Character |
|---|---|---|
| 1.0 - 1.7 | Undular jump | Smooth standing waves, little turbulence, minimal energy loss |
| 1.7 - 2.5 | Weak jump | Small rollers and surface eddies begin to appear |
| 2.5 - 4.5 | Oscillating jump | Unstable jet oscillates top to bottom, produces waves |
| 4.5 - 9.0 | Steady jump | Stable, well-defined, most efficient energy dissipation, ideal for stilling basins |
| > 9.0 | Strong / choppy jump | Rough, intermittent surface, high energy dissipation |
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Spillway stilling basin (steady jump)
Example 2 - Culvert outlet (oscillating jump)
Example 3 - Mild channel transition (undular jump)
❓ Frequently Asked Questions
🔗 Related Calculators
What is a hydraulic jump?
A hydraulic jump is a sudden, turbulent transition from fast, shallow supercritical flow to slower, deeper subcritical flow in an open channel. It occurs at spillway toes, downstream of sluice gates, and in stilling basins, and it dissipates a large amount of the flow's kinetic energy as turbulence and heat.
What is the formula for sequent depth in a hydraulic jump?
y2/y1 = 0.5 x (sqrt(1 + 8 x Fr1^2) - 1), where y1 is the upstream depth, y2 is the downstream (sequent or conjugate) depth, and Fr1 is the upstream Froude number. This comes from applying momentum conservation across the jump.
When does a hydraulic jump form?
A hydraulic jump forms only when the upstream flow is supercritical, meaning the upstream Froude number Fr1 = V1 / sqrt(g x y1) is greater than 1. If Fr1 is 1 or less, the flow is already critical or subcritical and no jump can occur.
How much energy does a hydraulic jump dissipate?
Energy loss across the jump is deltaE = (y2 - y1)^3 / (4 x y1 x y2). Energy dissipation increases sharply with upstream Froude number, an undular jump near Fr1 = 1 dissipates almost no energy, while a strong jump at Fr1 above 9 can dissipate 70 percent or more of the upstream specific energy.
What are the different types of hydraulic jumps?
Jumps are classified by upstream Froude number Fr1: undular (1.0 to 1.7, smooth standing waves, little turbulence), weak (1.7 to 2.5, small rollers and eddies), oscillating (2.5 to 4.5, an unstable jet that oscillates and produces waves), steady (4.5 to 9.0, a stable, well-defined jump with good energy dissipation, the most desirable for stilling basins), and strong or choppy (above 9.0, rough and intermittent with a very turbulent surface).
Why do spillway stilling basins aim for a steady jump?
The steady jump range (Fr1 = 4.5 to 9.0) gives efficient, stable energy dissipation with a predictable jump length and minimal downstream wave action, protecting the channel bed and banks from erosion. Oscillating jumps below this range produce unpredictable waves that can travel far downstream and erode unprotected banks.
What is the downstream Froude number after a hydraulic jump?
The downstream Froude number Fr2 = V2 / sqrt(g x y2) is always less than 1 after a genuine hydraulic jump, confirming the flow has transitioned to subcritical. If a calculation produces Fr2 greater than or equal to 1, the input Froude number was not actually supercritical to begin with.
How do I find the downstream velocity after a hydraulic jump?
By continuity, the discharge per unit width is conserved across the jump: V1 x y1 = V2 x y2. So downstream velocity V2 = V1 x y1 / y2, using the sequent depth y2 calculated from the Froude number relation.
What is the difference between sequent depth and conjugate depth?
Sequent depth and conjugate depth are the same quantity, two names for the downstream depth y2 that satisfies momentum conservation with a given upstream depth y1 and Froude number. Both terms appear interchangeably in hydraulics textbooks and papers.
Why is the energy loss so small for an undular jump?
As Fr1 approaches 1 from above, the sequent depth ratio y2/y1 approaches 1 as well, meaning upstream and downstream depths become nearly equal. Since energy loss scales with the cube of the depth difference (y2 - y1)^3, a small depth difference produces an even smaller, often negligible, energy loss.