When is a hydraulic jump possible?

A classical hydraulic jump needs supercritical approach flow, Fr1 > 1. Subcritical approach flow is already controlled by downstream conditions and does not form the same abrupt depth increase.

Why does the water level rise while energy decreases?

Momentum balance permits a larger sequent depth, but turbulence, rollers, and air entrainment dissipate mechanical energy. Specific energy drops across the jump even though depth increases.

Open-Channel Flow & Hydraulic Jump

Open-channel flow has a free surface, so gravity waves matter. In a rectangular channel the Froude number Fr = V/sqrt(g y) separates subcritical flow (Fr < 1), critical flow, and supercritical flow (Fr > 1). If a supercritical stream is forced to slow down, a hydraulic jump can form: the depth rises from y1 to the conjugate depth y2 while mechanical energy is dissipated in turbulence and air entrainment. This simulator calculates discharge per unit width, critical depth, approach Froude number, conjugate depth, downstream Froude number, and the classical rectangular-channel jump loss. The canvas combines a channel sketch with a specific-energy diagram.

Who it's for: Hydraulics, civil engineering, environmental engineering, irrigation, spillway, and introductory fluid mechanics courses.

Key terms

Froude number
Hydraulic jump
Conjugate depth
Critical depth
Specific energy

The sequent-depth relation is for a hydraulic jump in a horizontal rectangular channel. The sketch ignores wall friction during the short jump, air entrainment details, non-rectangular cross sections, and gradually varied profiles.

Live graphs

How it works

Open-channel rectangular-flow simulator with Froude number, critical depth, conjugate depth, hydraulic jump energy loss, and subcritical/supercritical regimes.

Key equations

Fr = V / √(g y), yc = (q²/g)^(1/3), q = Q/b

y2/y1 = 0.5(√(1 + 8 Fr1²) − 1), ΔE = (y2 − y1)³/(4 y1 y2)

Frequently asked questions

When is a hydraulic jump possible?: A classical hydraulic jump needs supercritical approach flow, Fr1 > 1. Subcritical approach flow is already controlled by downstream conditions and does not form the same abrupt depth increase.
Why does the water level rise while energy decreases?: Momentum balance permits a larger sequent depth, but turbulence, rollers, and air entrainment dissipate mechanical energy. Specific energy drops across the jump even though depth increases.

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Frequently asked questions