Hydraulic Jump Calculator
A hydraulic jump is a sudden transition from fast (supercritical) to slow (subcritical) flow in an open channel — it dissipates kinetic energy as turbulence. Enter the upstream depth and velocity to find the sequent (conjugate) depth, downstream Froude number, energy loss, and estimated jump length.
m
m/s
m
Conjugate depth after the hydraulic jump
- 1
Upstream Froude number
Fr₁ = 4.5 ÷ √(9.81 × 0.3) = 2.623Fr₁ > 1 confirms supercritical upstream flow — a hydraulic jump can form. - 2
Radical term (1 + 8Fr₁²)
1 + 8 × 2.623² = 56.046 - 3
Sequent depth
y₂ = (0.3 ÷ 2) × (√56.046 − 1) = 0.973
How does this calculator work?
For supercritical upstream flow (Fr₁ > 1), a hydraulic jump forms and the sequent depth is y₂ = y₁/2 × (√(1+8Fr₁²)−1). Energy is dissipated as ΔE = (y₂−y₁)³/(4y₁y₂). Enter upstream depth and velocity to get downstream depth, energy loss, and jump length (≈ 6y₂).
Formula
How this is calculated
A hydraulic jump occurs when fast (supercritical, Fr > 1) flow is forced to decelerate — at the base of a spillway or downstream of a sluice gate, for example. Momentum conservation across the jump, for a horizontal rectangular channel, gives the conjugate-depth ratio y₂/y₁ = ½(√(1 + 8Fr₁²) − 1), where Fr₁ = V₁/√(gy₁) is the upstream Froude number. The downstream depth y₂ is always greater than y₁.
The energy head loss ΔE = E₁ − E₂ = (y₂ − y₁)³/(4y₁y₂) is always positive, confirming that energy is dissipated (as turbulence and heat) rather than generated. The stronger the jump (higher Fr₁), the larger the proportion of energy lost — this is why hydraulic jumps are used as energy dissipators below dams and barrages.
The jump length is estimated empirically as about 6y₂ (Peterka, USBR). The formulas assume a wide rectangular channel with negligible friction at the bottom and horizontal floor — for sloped or non-rectangular channels, more complex momentum equations are required.
Frequently asked questions
A jump forms when supercritical flow (Fr > 1, typically fast and shallow) is forced to transition to subcritical flow (Fr < 1, slower and deeper) — for example at the toe of a dam spillway, downstream of a sluice gate, or where a steep channel enters a milder grade.
It comes from applying the momentum equation (not energy) across the jump, since energy is dissipated but momentum is conserved. The result gives the only positive, physically realistic downstream depth.
The rule jump length ≈ 6y₂ is an empirical approximation from US Bureau of Reclamation data; real jumps vary with channel roughness, tailwater depth and Fr. Values of 4–8 times y₂ are reported in literature. Use this as an order-of-magnitude guide for stilling-basin design.
Also known as
TG we-Calculate Editorial Team. (2026). Hydraulic Jump Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hydraulic-jump-calculator
TG we-Calculate Editorial Team. "Hydraulic Jump Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/hydraulic-jump-calculator.
TG we-Calculate Editorial Team, "Hydraulic Jump Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hydraulic-jump-calculator
@misc{wecalculate_hydraulic_jump_calculator, title = {Hydraulic Jump Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hydraulic-jump-calculator}}, year = {2026}, note = {TG we-Calculate} }
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