Reservoir Emptying Time
Calculate the time to empty a constant-surface-area reservoir through a bottom orifice, t = 2·A_s·√H ÷ (C_d·A_o·√(2g)), from the water-surface area A_s (m²), the outlet orifice area A_o (m²), the initial head H (m, water height above the orifice) and the discharge coefficient C_d (≈ 0.6 for orifices). The formula integrates Torricelli's equation over the drawdown: as orifice flow drops while the level (and head) falls, emptying decelerates, and total time results from integrating dH/dt. It is useful for designing dam bottom outlets (used to lower the reservoir in emergencies or for maintenance), emptying industrial tanks and basins. Time grows with reservoir area and the square root of head, and falls with orifice area — emptying large reservoirs takes a long time, a real limitation in dam emergency management. It assumes constant A_s; real reservoirs vary with elevation. Enter the surface area, orifice area, initial head and discharge coefficient.
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Tempo de esvaziamento de reservatório
O tempo para esvaziar um reservatório (ou tanque) de área de espelho constante através de um orifício de fundo é t = 2·A_s·√H ÷ (C_d·A_o·√(2g)), a partir da área do espelho d'água A_s, da área do orifício de descarga A_o, da carga inicial H (altura da água acima do orifício) e do coeficiente de descarga C_d (≈ 0,6 para orifícios). A fórmula é a integral da equação de Torricelli ao longo do esvaziamento: a vazão pelo orifício é proporcional a √(carga), mas a carga diminui à medida que o nível cai, então o esvaziamento desacelera progressivamente — o último metro demora muito mais que o primeiro. Integrando dH/dt obtém-se o tempo total. É útil no projeto das descargas de fundo de barragens (usadas para rebaixar o reservatório em emergências, para inspeção ou para manutenção a jusante), no esvaziamento de tanques industriais, piscinas e bacias de detenção. O tempo cresce com a área do reservatório e com a raiz da carga, e cai com a área do orifício — o que revela uma limitação prática importante: esvaziar reservatórios grandes leva muito tempo (dias ou semanas), uma restrição real na gestão de emergências, quando às vezes é preciso baixar o nível rapidamente para aliviar a barragem. A fórmula assume área de espelho constante; reservatórios reais têm área que varia com a cota (curva cota-área-volume), exigindo integração numérica. Informe a área do espelho, a área do orifício, a carga inicial e o coeficiente de descarga.
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Silo Emptying Time
Calculate the time to empty a silo by gravity discharge, t = M ÷ W, from the stored product mass M (kg) and the mass discharge rate W (kg/s). Since the discharge rate of a granular material through an orifice is practically CONSTANT (independent of the product height above, by the Janssen effect and per the Beverloo equation), the emptying time is simply total mass divided by rate — a direct relation, unlike a liquid's emptying, which slows as the level falls. This time is an important operational parameter in silo, hopper and storage-unit design and operation: it sets the dispatch capacity (how fast a truck, rail car or ship is loaded), sizes the downstream conveying systems (belts, bucket elevators, screws) that must match the discharge rate, and frames shift logistics and vehicle queues at grain terminals. The discharge rate W can be estimated by the Beverloo equation from the outlet diameter, closing the calculation: larger outlets discharge faster (W ∝ D₀^2.5), reducing emptying time. Enter the stored mass and the discharge rate.
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Reservoir Life (Sedimentation)
Estimate a reservoir's useful life from sedimentation, Vu = V ÷ V_s, from the reservoir's useful (or total) volume V (m³) and the sediment volume deposited per year V_s (m³/year). Every reservoir, by impounding a river, slows the flow and makes water lose its sediment-carrying capacity — sand, silt and clay from the watershed settle on the bottom, gradually reducing storage. The useful life is the number of years until sedimentation impairs the reservoir's function (power, supply, regulation). It is a crucial design parameter in hydrology and watershed management: reservoirs in basins with erodible soils, deforestation or intensive agriculture silt up fast (decades), while well-conserved basins last centuries. The sediment inflow V_s comes from the basin's sediment yield and the reservoir's trap efficiency (Brune curve). The simple constant-rate model gives the order of magnitude. Conserving the basin and flushing through bottom outlets extend the life. Enter the reservoir volume and the annual sediment inflow.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.