How this calculator works
Momentum conservation across a short rectangular jump gives the conjugate-depth relation. Continuity then gives downstream velocity and the energy equation quantifies dissipation. The ideal result assumes hydrostatic pressure away from the roller, negligible bed friction and a nearly horizontal channel. Jump location also depends on tailwater. Length is empirical, so an editable length factor is shown separately; the default six downstream depths is only a rough scale, unsuitable as a stilling-basin design rule.
Formula
Fr1 = v1/sqrt(g y1); y2/y1 = [sqrt(1 + 8Fr1^2) - 1]/2. Q = b y1 v1 = b y2 v2. Delta E = (y2-y1)^3/(4y1y2). Approximate length = entered factor times y2.
Worked example
With y1 = 1 m, y2 = 3 m and g = 10 m/s2, conjugate flow has v1 = sqrt(60) m/s and Fr1 = sqrt(6). Head loss is 2/3 m and remaining specific-energy fraction is 5/6.
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Frequently asked questions
Why require upstream Froude number above one?
A hydraulic jump transitions from supercritical to subcritical flow. Subcritical upstream conditions do not form this jump.
Does the calculated depth guarantee a jump at my location?
No. Available tailwater and channel controls determine where the jump can stand.
Is jump length exact?
No. It depends on Froude number and basin details. Consult empirical design charts for engineering use.