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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Vazão de vertedouro (Creager/ogee)
O vertedouro (extravasor) é o órgão de segurança mais importante de uma barragem: é por onde as cheias escoam de forma controlada, evitando o galgamento (overtopping) do barramento — a causa nº 1 de ruptura de barragens no mundo. A vazão sobre um vertedouro de perfil Creager/ogee é Q = C·L·H^1,5, onde C é o coeficiente de descarga (2,0 a 2,2 no SI), L o comprimento da soleira e H a carga sobre a crista. O perfil ogee tem a forma da face inferior de uma lâmina vertente livre: assim a água adere à soleira sem se descolar, maximizando a descarga e mantendo a pressão próxima da atmosférica (o que evita a cavitação, que destruiria o concreto). O coeficiente C já embute a gravidade e os efeitos de aproximação, sendo por isso maior que o de um vertedor retangular de soleira delgada. O dimensionamento do vertedouro parte da cheia de projeto — frequentemente a cheia decamilenar (TR 10.000 anos) ou a PMF (cheia máxima provável, para grandes barragens) — e calcula o comprimento de soleira necessário para liberar essa vazão sem que o nível do reservatório suba a ponto de galgar a crista da barragem. Errar para menos é catastrófico; por isso o vertedouro costuma ser superdimensionado. Informe o coeficiente de descarga, o comprimento da soleira e a carga hidráulica.
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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.
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 Retention Time (HRT)
Calculate the hydraulic retention time (HRT) of a reactor or tank, HRT = volume ÷ flow, dividing the working volume (m³) by the influent flow (m³/h). The result, in hours, is the average time the liquid stays in the unit and is decisive in designing clarifiers, anaerobic reactors, lagoons and aeration tanks: short times prevent reactions or settling from completing, while long times raise cost and footprint. Enter the working volume and the inlet flow.
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