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Hydraulic Jump — Reference

The rapid transition from supercritical to subcritical flow used to dissipate energy below spillways, chutes, and outlets. Subscript 1 = upstream (supercritical) section, 2 = downstream (subcritical) section.

Core Equations (Rectangular Channel)

Froude:   Fr&sub1; = V&sub1; / √(g·y&sub1;)
Sequent depth:   y&sub2;/y&sub1; = ½( √(1 + 8·Fr&sub1;²) − 1 )
Energy loss:   ΔE = (y&sub2; − y&sub1;)³ / (4·y&sub1;·y&sub2;)
Jump length:   Lj ≈ 6·y&sub2;   (range 4.5–7·y&sub2;)

The relation is reversible: y&sub1;/y&sub2; = ½(√(1 + 8·Fr&sub2;²) − 1). The two depths are conjugate (equal specific force), not equal specific energy — the difference is the dissipated ΔE.

Jump Classification by Upstream Froude Number

Fr&sub1;TypeCharacter & energy dissipation
1.0–1.7UndularStanding waves, minimal loss (< 5%)
1.7–2.5WeakSmooth surface, low loss (5–15%)
2.5–4.5OscillatingAvoid — jet oscillates, sends damaging waves downstream (15–45%)
4.5–9.0SteadyStable, well-balanced, best performance (45–70%)
> 9.0StrongRough, intense turbulence, very effective (up to ~85%)
Design targets. Aim the design point into the steady jump range (Fr&sub1; 4.5–9). The oscillating range (2.5–4.5) is functional but its surface waves erode unlined channels and riprap downstream — USBR Type I–IV stilling basins add chute blocks, baffle piers, and end sills to stabilize the jump and shorten the basin in this range.

Sources: Chow, V.T. (1959), Open-Channel Hydraulics. USBR, Hydraulic Design of Stilling Basins and Energy Dissipators (Engineering Monograph 25). FHWA HEC-14.

Designing a dissipator? Open the stilling basin calculator → · Need the approach flow? Manning's & channel geometry.

Related cheat sheets and tools

Get the approach depth and velocity from Manning's with the channel geometry card, design the basin in the stilling basin tool, and protect the downstream channel with riprap sizing. For routing the spillway flow that feeds the dissipator, see HydroComplete.

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