Hydraulic Jump Calculator

A hydraulic jump is an abrupt transition in open channel flow from supercritical (fast, shallow) flow to subcritical (slow, deep) flow. It is accompanied by significant turbulence and energy dissipation. Hydraulic jumps commonly occur downstream of sluice gates, spillways, and steep chutes, and are deliberately engineered to dissipate excess kinetic energy.

The Froude number (Fr) compares inertial forces to gravitational forces in the flow. Fr > 1 indicates supercritical flow (required upstream of a jump), Fr = 1 is critical flow, and Fr < 1 is subcritical flow (always occurs downstream). The upstream Froude number determines the jump intensity and classification — higher Fr₁ means a more energetic jump.

The sequent depth downstream of the jump is calculated using the conjugate depth equation: y₂/y₁ = 0.5 × [√(1 + 8·Fr₁²) − 1]. This formula is derived from the momentum equation applied across the hydraulic jump in a horizontal rectangular channel, assuming no friction on the channel bed.

Hydraulic jumps are classified by the upstream Froude number: Fr₁ 1–1.7 is an undular jump (gentle surface waves), Fr₁ 1.7–2.5 is a weak jump, Fr₁ 2.5–4.5 is an oscillating jump (unstable, should be avoided in design), Fr₁ 4.5–9 is a steady jump (best for energy dissipation), and Fr₁ > 9 is a strong jump (very rough and choppy). Steady jumps are typically preferred for stilling basin design.

The head loss (ΔE) across the jump is computed as ΔE = (y₂ − y₁)³ / (4 × y₁ × y₂). This represents the difference in specific energy between the upstream and downstream sections. Larger Froude numbers produce proportionally greater energy losses, which is why hydraulic jumps are used as energy dissipators.

Jump length is estimated empirically as L = 220 × y₁ × tanh[(Fr₁ − 1) / 22], a formula by Chaudhry (1993). It represents the distance from the toe of the jump to where the surface becomes relatively smooth. Jump length is important for sizing stilling basins and aprons downstream of hydraulic structures.

A hydraulic jump can only occur when upstream flow is supercritical (Fr₁ > 1). Subcritical flow cannot transition abruptly to a higher-energy state without an external energy source. If Fr₁ ≤ 1, no jump is possible and the calculator will indicate invalid conditions. In practice, you need high velocity and shallow depth upstream to produce supercritical flow.

Hydraulic jumps are intentionally created in stilling basins below dam spillways, weirs, sluice gates, and drop structures to safely dissipate high kinetic energy before water reaches downstream channels. They are also used in water treatment to mix chemicals, in irrigation canals to reduce erosive velocities, and studied in flumes for fluid mechanics research.