Hydraulic Jump Energy Loss Calculator
Enter upstream and downstream depths of a hydraulic jump to compute the specific-energy loss.
Input Data
Results
At a glance:A hydraulic jump occurs when supercritical flow (Froude number >1) abruptly transitions to subcritical flow (Froude <1), with a roller and much turbulence. The specific-energy loss across the jump is ΔE = (y₂−y₁)³/(4·y₁·y₂), derived by equating momentum flux before and after and subtracting the specific energies E₁ = y₁ + v₁²/(2g) and E₂ = y₂ + v₂²/(2g). y₂ is the conjugate (sequent) depth of y₁, found from the momentum function. The energy loss grows with the difference between depths and is the basis for stilling basins that protect downstream channels from erosion. This tool computes ΔE directly from y₁ and y₂.
Formula
Energy loss: ΔE = (y₂−y₁)³/(4·y₁·y₂)
Conjugate depth: y₂/y₁ = ½(√(1+8Fr₁²)−1)
$$\Delta E = \dfrac{(y_2 - y_1)^3}{4\,y_1\,y_2}$$How to Use
- Enter the upstream depth y₁ (m).
- Enter the downstream depth y₂ (m).
- The calculator returns the energy loss ΔE.
Case Studies
Stilling basin design
y₁ = 0.3 m, y₂ = 1.5 m.
ΔE = (1.2)³/(4×0.3×1.5) = 1.728/1.8 ≈ 0.96 m.
About 0.96 m of head dissipated across the jump.
FAQ
Why does a hydraulic jump dissipate energy?
The transition from high-kinetic-energy supercritical flow to high-potential subcritical flow converts kinetic energy into turbulent eddies and heat, losing mechanical energy irreversibly.
What are conjugate depths?
The depth y₂ that can carry the same momentum flux as y₁ at a hydraulic jump; they are paired by the sequent-depth relation above.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.