Hydraulic Jump Calculator
Flow 0.3 m deep at 6 m/s (Froude number 3.5) jumps to a sequent depth of 1.34167 m, dissipating about a third of its energy.
1.34167255791354 m
Full answer, then cut to fewer decimals (not rounded):
- 1.34167255791354 m
- 1.3416725579135 m
- 1.341672557913 m
- 1.34167255791 m
- 1.3416725579 m
- 1.341672557 m
- 1.34167255 m
- 1.3416725 m
- 1.341672 m
- 1.34167 m
- 1.3416 m
- 1.341 m
- 1.34 m
- 1.3 m
- Upstream Froude number F₁
- 3.498084412
- Downstream velocity V₂
- 1.341609016 m/s
- Head loss (y₂ − y₁)³/(4y₁y₂)
- 0.7020465127 m
- Energy loss fraction
- 32.87520809 %
- Power dissipated ρgQh_L
- 37.17751194 kW
- Jump length ≈ 6 y₂
- 8.050035347 m
- Jump type (USBR)
- oscillating
Step-by-step solution
- F₁ = V₁ ÷ √(g y₁) = 3.498084412
- y₂ = (y₁/2)(√(1 + 8F₁²) − 1) = 1.341672558 m
- h_L = (y₂ − y₁)³ ÷ (4y₁y₂) = 0.7020465127 m
Hydraulic Jump Formula
y₂/y₁ = ½(√(1 + 8F₁²) − 1)
F₁ = V₁/√(gy₁); head loss h_L = (y₂ − y₁)³/(4y₁y₂)
Worked Example
Flow 0.3 m deep at 6 m/s entering a 3 m wide stilling basin:
- F₁ = V₁ ÷ √(g y₁) = 3.498084412
- y₂ = (y₁/2)(√(1 + 8F₁²) − 1) = 1.341672558 m
- h_L = (y₂ − y₁)³ ÷ (4y₁y₂) = 0.7020465127 m
Downstream velocity V₂: 1.341609016 m/s · Head loss (y₂ − y₁)³/(4y₁y₂): 0.7020465127 m · Energy loss fraction: 32.87520809 % · Power dissipated ρgQh_L: 37.17751194 kW · Jump length ≈ 6 y₂: 8.050035347 m · Jump type (USBR): oscillating
GATE tip
Momentum, not energy, is conserved across a jump. That is why the sequent depth comes from the momentum equation and the head loss follows from the energy difference.
More Hydraulics and Groundwater Calculators
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Manning's Equation Calculator
V = (1/n) R^(2/3) S^(1/2), Q = VA
R = A/P hydraulic radius; SI units (multiply by 1.49 in US units)
Example: A 2 m wide concrete rectangular channel flowing 0.5 m deep at a slope of 0.001: Discharge Q = 1.01351 m³/s.
-
Critical Depth Calculator
y_c = (q²/g)^(1/3), E_c = 1.5 y_c
specific energy E = y + q²/(2gy²); V_c = √(g y_c)
Example: A rectangular channel carrying 2 m²/s per metre width: Critical depth y_c = 0.741617 m.
-
Darcy's Law Calculator
Q = K i A, i = Δh/L
Darcy velocity q = Ki; seepage (linear) velocity = q/nₑ
Example: An aquifer with K = 10 m/day, 2 m head drop over 100 m and 50 m² cross-section: Discharge Q = 10 m³/day.
-
Well Yield Calculator
Confined: Q = 2πKb(h₂ − h₁)/ln(r₂/r₁)
unconfined: Q = πK(h₂² − h₁²)/ln(r₂/r₁)
Example: A confined aquifer, K = 20 m/day, 30 m thick, with heads 40 m at the 0.15 m well and 45 m at 300 m: Well discharge Q = 2479.91 m³/day.
Frequently asked questions
Why build stilling basins?
Water leaving a spillway is fast and supercritical; forcing a jump dissipates energy safely on concrete instead of scouring the river bed.
Which Froude numbers make a good jump?
A steady jump forms for F₁ between 4.5 and 9; oscillating jumps (2.5–4.5) send waves downstream and need special basins.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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Scientific Converters. (2026, October 15). Hydraulic Jump Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/hydraulic-jump-calculator/
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