Hydraulic Jump

Rapidly varied flow from supercritical to subcritical; momentum analysis and sequent depth ratio for rectangular channels; energy loss, height, length and efficiency of a jump; classification by Froude number (undular, weak, oscillating, steady, strong); location of jump — free, repelled and submerged jumps and tailwater; uses of the hydraulic jump and stilling basins; positive and negative surges — with solved numericals.

Hydraulic Jump

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📑 Contents (9 sections)

Last reviewed 16 Sept 2026 · 5 min read

What a hydraulic jump is

A hydraulic jump is the abrupt rise of the water surface when flow changes from supercritical to subcritical. It is a form of rapidly varied flow marked by a turbulent roller, air entrainment and a large loss of energy.

Jumps form, for example, at the foot of spillways, below sluice gates, and where a steep slope changes to a mild slope.

The depth before the jump $y_{1}$ (supercritical) and after it $y_{2}$ (subcritical) are sequent (conjugate) depths.
Because the energy loss is unknown, the analysis uses the momentum equation, not Bernoulli: specific force is the same on both sides (bed friction over the short length neglected).

Sequent depth ratio (horizontal rectangular channel)

FormulaHydraulic jump equations

Sequent depths:

\frac{y _{2}}{y _{1}} = \frac{1}{2} (1 + 8 F r_{1}^{2} - 1), \frac{y _{1}}{y _{2}} = \frac{1}{2} (1 + 8 F r_{2}^{2} - 1)

with $F r_{1} = \frac{V _{1}}{g y _{1}}$ .

Equivalent form: $\frac{2 q ^{2}}{g} = y_{1} y_{2} (y_{1} + y_{2})$

Energy loss:

E_{L} = E_{1} - E_{2} = \frac{( y _{2} - y _{1} ) ^{3}}{4 y _{1} y _{2}}

Height of jump: $h_{j} = y_{2} - y_{1}$

Length of jump (horizontal apron, practical): $L_{j} \approx 5$ to $7 (y_{2} - y_{1})$ — commonly 6(y₂ − y₁)

Efficiency: $η = E_{2} / E_{1}$ ; relative loss $E_{L} / E_{1}$

Power lost: $P = ρ g Q E_{L}$

For a general (non-rectangular) section, sequent depths satisfy equal specific force: $\frac{Q ^{2}}{g A _{1}} + A_{1} \overset{z}{ˉ}_{1} = \frac{Q ^{2}}{g A _{2}} + A_{2} \overset{z}{ˉ}_{2}$ .

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