Hydraulic Jump Calculator

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Metric uses metres and m³/s; imperial uses feet and ft³/s.
The rectangular channel width measured at the water surface.
m
Volumetric flow rate through the channel cross-section.
m³/s
Flow depth immediately upstream of the hydraulic jump.
m
Standard gravity is 9.81 m/s² (32.174 ft/s² in imperial). Change only for non-Earth applications.
m/s²
Conjugate (sequent) depth (y₂)Steady jump
1.9164

Downstream depth after the hydraulic jump - the Belanger equation solution

Jump typeSteady jump
Upstream Froude number (Fr₁)4.858
Upstream velocity (V₁)8.333
Downstream velocity (V₂)1.305
Downstream Froude number (Fr₂)0.301
Depth ratio (y₂ / y₁)6.388
Jump height (h)1.6164
Head loss (ΔE)1.8364
Jump length (L)11.456
Jump efficiency (η)0.5%
4.858
Subcritical (no jump)<1Undular jump1-1.7Weak jump1.7-2.5Oscillating jump2.5-4.5Steady jump4.5-9Strong jump9+

Steady jump with Fr₁ = 4.858 and 52.2% energy retained

  • The upstream Froude number is 4.858, confirming supercritical flow. A steady jump forms.
  • The jump dissipates 1.8364 m (or ft) of specific energy, reducing it to 52.2% of the upstream value.
  • Steady jumps (Fr₁ 4.5-9) are the most efficient for energy dissipation basins and are preferred in hydraulic engineering design.
  • The conjugate depth ratio is 6.39:1, so the water is about 6.4 times deeper downstream.

Next stepPair these results with a stilling basin design (USBR Type I-IV) or check tailwater conditions to confirm the jump remains on the apron.

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