Hydraulic Jump Calculator

A hydraulic jump is a rapid transition from shallow, fast, supercritical open-channel flow to deeper, slower, subcritical flow. The water surface rises abruptly, intense turbulence develops, and part of the flow's mechanical energy becomes heat, sound, and small-scale motion. Jumps are familiar downstream of spillways, sluice gates, and steep channels. Engineers often create them deliberately in stilling basins because controlled energy dissipation protects downstream beds and structures from erosion. The Froude number identifies the flow regime by comparing inertial effects with gravity-wave effects. It equals mean velocity divided by the square root of gravitational acceleration times hydraulic depth. For a wide rectangular channel, hydraulic depth is the water depth. A Froude number above one is supercritical, a value below one is subcritical, and one is critical. A classical hydraulic jump requires an upstream Froude number greater than one. If the entered value is at or below one, the conjugate-depth equation still produces a numerical result, but it does not describe a normal energy-dissipating jump. This calculator applies the momentum relationship for a horizontal, rectangular channel. The downstream conjugate depth equals one half of the upstream depth multiplied by the square root of one plus eight times the upstream Froude number squared, minus one. Continuity then gives downstream velocity from the ratio of upstream to downstream depth. The downstream Froude number is evaluated from that new depth and velocity. The specific energy dissipated across the ideal jump equals the cube of the depth difference divided by four times the product of the two depths. The equations assume steady flow, hydrostatic pressure away from the roller, uniform velocity across each section, negligible bed slope over the jump, and no important lateral contraction. Real jumps are three-dimensional and their length is several times the downstream depth. Tailwater conditions determine whether a jump forms at the expected location, becomes submerged, or sweeps downstream. Use these results as preliminary hydraulic values and pair them with stilling-basin guidance, freeboard checks, sediment considerations, and physical or numerical modeling for consequential designs. Units must be consistent; the provided defaults and labels use metres and seconds.