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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Reservoir emptying time
The time to empty a reservoir (or tank) of constant surface area through a bottom orifice is t = 2·A_s·√H ÷ (C_d·A_o·√(2g)), from the water surface area A_s, the discharge orifice area A_o, the initial head H (water height above the orifice) and the discharge coefficient C_d (≈ 0.6 for orifices). The formula is the integral of Torricelli's equation over the whole drawdown: outflow through the orifice is proportional to √(head), but the head drops as the level falls, so emptying slows down progressively — the last meter takes far longer than the first. Integrating dH/dt yields the total time. It is useful in designing the bottom outlets of dams (used to draw the reservoir down in emergencies, for inspection or for downstream maintenance), and in emptying industrial tanks, swimming pools and detention basins. The time grows with the reservoir area and with the square root of the head, and shrinks with the orifice area — which reveals an important practical limitation: emptying large reservoirs takes a very long time (days or weeks), a real constraint in emergency management, when the level sometimes has to be lowered quickly to relieve the dam. The formula assumes a constant surface area; real reservoirs have an area that varies with elevation (the stage-area-volume curve), calling for numerical integration. Enter the surface area, the orifice area, the initial head and the discharge coefficient.
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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.