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Hydraulic Jump Conjugate Depth (Bélanger Equation) & Energy Dissipation Calculator

Easily calculate and compute hydraulic jump conjugate depth (bélanger equation) & energy dissipation calculator with accurate equations, live formulas, and expert guidance.

Shallow high-speed depth before jump.

Must be supercritical (Fr₁ > 1.0).

Calculated Result
2.65 m

Sequent Depth (y₂)

Sequent Depth (y₂)

2.65 m

Downstream Sequent Depth Y2 Meters

2.65

Conjugate Depth Ratio Y2 Over Y1

5.88

Head Loss Energy Dissipation Meters

2.23

Energy Dissipation Percent

44.5

2.65 — m

Calculation Breakdown

  1. Applied FormulaCalculates the subcritical sequent depth (y₂ in meters), conjugate depth ratio, and kinetic energy dissipation head loss (ΔE) across a hydraulic jump in dam stilling basins.\frac{y_2}{y_1} = \frac{1}{2}\left(\sqrt{1 + 8 \text{Fr}_1^2} - 1\right), \quad \Delta E = \frac{(y_2 - y_1)^3}{4 y_1 y_2}

Hydraulic Jump Dissipation Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.71.32.02.6Sequent Depth (y₂)

What Is the Hydraulic Jump Conjugate Depth (Bélanger Equation) & Energy Dissipation Calculator?

This tool computes hydraulic jump conjugate depth (bélanger equation) & energy dissipation calculator with high precision arithmetic.

How Does the Hydraulic Jump Conjugate Depth (Bélanger Equation) & Energy Dissipation Calculator Work?

Calculates the subcritical sequent depth (y₂ in meters), conjugate depth ratio, and kinetic energy dissipation head loss (ΔE) across a hydraulic jump in dam stilling basins.

Hydraulic Jump Conjugate Depth (Bélanger Equation) & Energy Dissipation Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

y2y1=12(1+8Fr12−1),ΔE=(y2−y1)34y1y2\frac{y_2}{y_1} = \frac{1}{2}\left(\sqrt{1 + 8 \text{Fr}_1^2} - 1\right), \quad \Delta E = \frac{(y_2 - y_1)^3}{4 y_1 y_2}

Calculates the subcritical sequent depth (y₂ in meters), conjugate depth ratio, and kinetic energy dissipation head loss (ΔE) across a hydraulic jump in dam stilling basins.

How to Use the Hydraulic Jump Conjugate Depth (Bélanger Equation) & Energy Dissipation Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Hydraulic Jump Conjugate Depth (Bélanger Equation) & Energy Dissipation Calculator Example

Input Values:

upstreamInitialDepthY1Meters:0.45
upstreamFroudeNumberFr1:4.5
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required m.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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