Critical Depth in Rectangular Channel
Calculate the critical depth of a rectangular channel, y_c = (q² ÷ g)^(1/3), from the unit discharge q (flow per unit width, m³/s/m) and gravity g. Critical depth is the depth at which specific energy is minimum, marking the boundary between the two open-flow regimes: above it the flow is subcritical (slow, deep, Fr < 1, downstream-controlled); below, supercritical (fast, shallow, Fr > 1, upstream-controlled); exactly at it, Fr = 1. Critical depth is central to channel and structure hydraulics: it defines the control section at spillways, weirs and flumes (Parshall), where flow passes through the critical regime stably and the stage-discharge relation is unique — allowing flow measurement from head. It also determines whether a hydraulic jump can form and guides water-surface profiles. Enter the channel's unit discharge.
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Profundidade crítica em canal retangular
A profundidade crítica de um canal retangular é y_c = (q² ÷ g)^(1/3), função apenas da vazão específica q (vazão por unidade de largura) e da gravidade g. Ela é o tirante para o qual a energia específica do escoamento é mínima, e marca a fronteira entre os dois regimes do escoamento livre: acima dela o escoamento é subcrítico (lento, profundo, Froude < 1, controlado por jusante — como um rio calmo); abaixo, supercrítico (rápido, raso, Froude > 1, controlado por montante — como uma corredeira); exatamente nela, Froude = 1. O conceito de profundidade crítica é um dos pilares da hidráulica de canais. Ele define a seção de controle em vertedouros, soleiras e medidores de vazão (calha Parshall, vertedores de medição): nesses pontos o escoamento passa pelo regime crítico de forma estável, e a relação entre vazão e nível torna-se unívoca — o que permite medir a vazão simplesmente lendo a altura da lâmina d'água. A profundidade crítica também determina se um ressalto hidráulico pode se formar (só há ressalto na transição de supercrítico para subcrítico) e orienta o traçado das linhas d'água em remansos, quedas e mudanças de declividade. É a referência em torno da qual toda a hidráulica de canais se organiza. Informe a vazão específica do canal.
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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.
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Calculate the energy density of an ocean wave, E = (1 ÷ 8)·ρ·g·H², from the water density ρ (kg/m³, ~1025 for seawater), gravity g and the wave height H (m). The result, in J/m² (energy per surface area), is the sum of the wave's kinetic and potential energy — proportional to the square of the height, so large waves carry far more energy. It is the basis for calculating wave energy generation potential and the impact on coastal structures and beach erosion. Enter the water density and the wave height.
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