Hydraulic Jump Length
Estimate a hydraulic jump's length, L ≈ 6.9·(y₂ − y₁), by the classic empirical formula, from the upstream y₁ and downstream y₂ sequent depths. Unlike the sequent depths (from momentum), jump length is empirical, from lab tests, since the jump has no mathematically sharp end — its length is the distance from the upstream face to where the surface stabilizes. Several formulas exist (Smetana ≈ 6(y₂−y₁), USBR vs Fr, Elevatorski ≈ 6.9(y₂−y₁)); all give the order of magnitude. Jump length sets the stilling basin size downstream of a spillway: the basin must be long enough to contain the whole jump so dissipation completes within the concrete-lined structure before water returns to the natural bed. Undersizing throws the still-erosive jump tail onto the unprotected bed. Enter the upstream and downstream sequent depths.
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Comprimento do ressalto hidráulico
Quanto comprido é um ressalto hidráulico? Uma estimativa clássica é L ≈ 6,9·(y₂ − y₁), a partir das profundidades conjugadas de montante y₁ e de jusante y₂. Diferente das alturas conjugadas (que saem da física da quantidade de movimento), o comprimento do ressalto é empírico, obtido de ensaios de laboratório — porque o ressalto não tem um fim matematicamente nítido: define-se seu comprimento como a distância da face de montante até onde a superfície da água se estabiliza. Existem várias fórmulas (Smetana ≈ 6(y₂−y₁), USBR em função do Froude, Elevatorski ≈ 6,9(y₂−y₁)), todas dando a mesma ordem de grandeza. Esse comprimento é o que dimensiona o tamanho da bacia de dissipação a jusante de um vertedouro: a bacia precisa ser longa o bastante para conter todo o ressalto, garantindo que a dissipação de energia se complete dentro da estrutura revestida de concreto resistente à erosão, antes de a água voltar ao leito natural. Subdimensionar a bacia é um erro perigoso e caro: joga o fim do ressalto — ainda turbulento e erosivo — sobre o leito desprotegido a jusante, escavando uma fossa que pode progredir até descalçar a estrutura. Blocos de impacto e soleiras terminais ajudam a encurtar e fixar o ressalto, permitindo bacias menores. Informe as profundidades conjugadas de montante e de jusante.
Related Tools
Hydraulic Jump Energy Loss
Calculate the specific energy dissipated in a hydraulic jump, ΔE = (y₂ − y₁)³ ÷ (4·y₁·y₂), from the upstream y₁ (supercritical) and downstream y₂ (subcritical) sequent depths. The hydraulic jump is one of the most efficient energy dissipators in hydraulics: intense turbulence in the transition converts kinetic energy to heat and sound, removing excess flow energy. This head loss ΔE is exactly what is sought downstream of spillways, gates and bottom outlets — water arrives with very high energy (able to scour the riverbed and undermine the structure), and the stilling basin induces the jump to 'burn' that energy in a controlled way. The higher the incoming Froude number, the greater the dissipated fraction — jumps with Fr > 9 dissipate up to 85%. Enter the upstream and downstream sequent depths.
Hydraulic Jump Sequent Depth
Calculate the sequent (conjugate) depth downstream of a hydraulic jump, y₂ = (y₁/2)·(√(1 + 8·Fr₁²) − 1), from the upstream depth y₁ (supercritical) and the incoming Froude number Fr₁. The hydraulic jump is the abrupt transition from fast, shallow (supercritical) to slow, deep (subcritical) flow, with strong turbulence and energy dissipation. This Bélanger equation, from momentum conservation, is the basis for designing stilling basins downstream of spillways and gates: water descending a spillway arrives at very high (supercritical) velocity and must be decelerated before returning to the river, otherwise it erodes the bed catastrophically. The sequent depth y₂ sets the required basin depth for a stable jump. Enter the upstream depth and the Froude number.
Spillway Discharge (Creager/Ogee)
Calculate the discharge over a Creager/ogee dam spillway, Q = C·L·H^1.5, from the discharge coefficient C (typically 2.0-2.2 in SI for well-designed ogee profiles), the crest length L (m) and the head over the crest H (m). The spillway is a dam's most critical safety structure: it releases floods safely, preventing overtopping — the leading cause of dam failure. The ogee profile follows the shape of the underside of a free nappe, maximizing discharge while keeping crest pressure near atmospheric (avoiding cavitation). The coefficient C absorbs gravity and approach effects, exceeding that of a sharp-crested weir. Spillway design starts from the design flood (often the 10,000-year flood or the PMF) and sets the required crest length. Enter the discharge coefficient, crest length and head.
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