Hydraulic Jump Calculator – Sequent Depth, Energy Loss & Froude Analysis

Hydraulic Jump Calculator – Sequent Depth & Energy Loss

Rectangular channel · Froude number analysis · 2D profile · PDF report · Batch CSV · Trend chart

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📐 1. What is a Hydraulic Jump?

A hydraulic jump is a sudden transition from supercritical (high velocity, shallow depth) to subcritical (low velocity, deep depth) flow, dissipating large amounts of energy. It is commonly used in stilling basins downstream of dams, spillways, and sluice gates. The key parameters are the sequent depth (y₂), energy loss (ΔE), and jump length (L).

Froude number (Fr₁) = V₁ / √(g·y₁)
Sequent depth: y₂ = (y₁/2) × (√(1 + 8·Fr₁²) – 1)
Energy loss: ΔE = (y₂ – y₁)³ / (4·y₁·y₂)
Jump length (approximate): L = 6 × y₂ (for 4.5 < Fr₁ < 9)

🚀 2. Live Hydraulic Jump Calculator

Upstream Depth (y₁) m

Upstream Velocity (V₁) m/s

Channel Width (B) m (optional for unit discharge)

Sluice Gate opening (optional, m)

Output Unit

Batch CSV Upload

✅ CSV: y1, V1, width (optional)

Get PDF Report via Email

CSV Template

📊 2D Hydraulic Jump Profile

📉 Energy Loss vs Froude Number

📈 Calculation History & Trend

📂 3. How to Use the Calculator

Enter upstream depth (y₁) and velocity (V₁). Optionally, enter channel width to compute unit discharge.
If a sluice gate opening is given, the tool estimates the upstream velocity using orifice flow (optional).
Compute: Click "Compute Jump" – the tool calculates Froude number, sequent depth (y₂), energy loss, and jump length.
2D Profile: Shows water surface from supercritical to subcritical flow.
Froude badge: Indicates jump type (weak, oscillating, steady, strong).
Energy chart: Shows how energy loss varies with Froude number for the given y₁.
Batch CSV: Upload multiple designs for bulk analysis.
PDF Report: Download a detailed report with the profile image.
History: All calculations saved locally; export or clear anytime.

📈 4. Real‑World Example

Stilling basin downstream of a spillway, Bangladesh
Upstream depth y₁ = 0.5 m, velocity V₁ = 5.0 m/s.
Fr₁ = 5.0 / √(9.81×0.5) = 5.0 / 2.21 = 2.26 → weak jump (Fr 1.7–2.5).
Sequent depth y₂ = (0.5/2)×(√(1+8×2.26²) – 1) = 0.25×(√(1+40.86)-1) = 0.25×(6.47-1) = 1.37 m.
Energy loss ΔE = (1.37-0.5)³/(4×0.5×1.37) = 0.87³/2.74 = 0.658/2.74 = 0.24 m.
The calculator will draw the jump and show the results.

❓ Frequently Asked Questions

❓ What is a hydraulic jump used for?

It dissipates excess kinetic energy, prevents erosion, and helps in mixing chemicals or re‑aerating water.

❓ What is the range of Froude numbers for a stable jump?

A steady jump occurs for Fr₁ between 4.5 and 9. For lower Fr₁, the jump is weak; for higher, it is strong and may require a stilling basin.

❓ Is the tool free?

Yes, completely free. Batch processing supports up to 100 rows per CSV.

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