Which depth is critical?

yc is the depth at Fr = 1 for that Q and width. In a jump, y1 < yc < y2. The jump does not stop at yc; it overshoots to y2.

Can a jump travel upstream?

A weak jump on a steep slope can wash out. Tailwater must be high enough to hold the sequent depth, which is the stilling-basin design problem.

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Open channelIntermediate

Hydraulic Jump, Froude Number, and Critical Depth in Rectangular Channels

Q: Can a jump travel upstream?

A weak jump on a steep slope can wash out. Tailwater must be high enough to hold the sequent depth, which is the stilling-basin design problem.

Fr > 1 can jump to a sequent depth. Bélanger relation, energy dissipation in stilling basins, and how critical depth sits between the two.

6 August 2026Updated 16 August 2026Solver360 Hydraulics10 min read

Key takeaways

Fr = V/√(gy). Fr < 1 subcritical, Fr = 1 critical, Fr > 1 supercritical.
Bélanger: y2/y1 = ½(−1 + √(1+8 Fr1²)).
Energy loss ΔE = (y2−y1)³ / (4 y1 y2) is why stilling basins work.
Undular jumps (Fr 1–1.7) dissipate little energy.

A hydraulic jump is a rapid conversion from supercritical to subcritical flow. Depth rises, velocity falls, and a roller dissipates energy. It is classified by the upstream Froude number.

Froude and critical depth

Fr = V / √(g y) yc = (Q² / (g b²))^{1/3} (rectangular)

Fr1	Jump type	Notes
1.0–1.7	Undular	Little dissipation, wavy surface
1.7–2.5	Weak	Oscillating; poor stilling
2.5–4.5	Oscillating	Common design range
4.5–9	Steady / strong	Good energy kill
> 9	Strong	Spray, air, rough basin

Open solver: Jump, Fr, and yc

Sequent depth and energy

y2/y1 = ½ (−1 + √(1 + 8 Fr1²)) ΔE = (y2 − y1)³ / (4 y1 y2)

Example: b = 2 m, y1 = 0.35 m, Q = 1.8 m³/s. V1 = 2.57 m/s, Fr1 = 1.39 (undular). yc = 0.43 m. y2 ≈ 0.54 m and ΔE is small. Raise Q or drop y1 until Fr1 > 4.5 if you need a stilling basin that actually dissipates energy.

Open solver: Uniform flow into the jump Open solver: Weir (often upstream of a jump)

Frequently asked questions

Not as written. The sequent-depth relation changes with the section shape. Use a momentum balance on the actual area, or a tabulated jump chart.

Keywords

hydraulic jump calculatorfroude number open channelcritical depth rectangular channelbelanger sequent depthstilling basin energy dissipationsupercritical flow