How this calculation works
Outflow through a small orifice slows as the water level falls. Dividing discharged volume by the initial flow therefore understates the ideal duration. This page integrates the changing square-root head relationship over the chosen level drop.
Drain seconds = 2 × tank area × (sqrt(initial head) − sqrt(final head))/(Cd × opening area × sqrt(2g))A worked example
With a one-square-metre tank, ten-square-centimetre opening and coefficient 0.6, lowering head from two metres to half a metre removes 1500 litres. The integrated time is about 532.2 seconds. Initial discharge is approximately 3.758 L/s and final discharge approximately 1.879 L/s; using only the faster initial rate would miss the slowdown.
Good to know
Vented constant-section small-orifice model only; no inflow, submergence, siphon, pipe friction or changing discharge coefficient. Use appropriate hydraulic analysis for connected systems. The page is an ideal drainage calculation and does not approve a discharge arrangement or tank structure.
Reference: OpenStax — Bernoulli principle and fluid speed (opens in a new tab) ↗
What the model answers
Outflow through a small orifice slows as the water level falls. Dividing discharged volume by the initial flow therefore understates the ideal duration. This page integrates the changing square-root head relationship over the chosen level drop.
The tank plan area stays constant, so a given volume loss produces the same incremental level change at every height. A tapered vessel would require its area-versus-height relation inside the integration.
The Constant head orifice discharge calculator keeps the head fixed for a single rate. This page instead integrates the same ideal outflow principle while head declines.
Measure and enter consistently
Head is free-surface height above the orifice center. Enter opening area in square centimetres, not diameter. The discharge coefficient is supplied for the intended opening and conditions; no shape-dependent coefficient is selected automatically.
Both the tank and outlet are assumed exposed to atmospheric pressure, with no incoming water. The supported small-opening approximation requires opening area no greater than five percent of tank section. That numeric model boundary is not an equipment operating rule.
Interpret the result
The graph’s height declines nonlinearly while discharge falls with its square root. The initial and final discharge metrics help check the range rather than implying a fixed pump-like flow.
A final head of zero is a mathematical endpoint of the ideal relation. Real puddling, outlet geometry, residual liquid and air entrainment can affect actual emptying. A long connected pipe needs friction and other losses beyond a single orifice coefficient.
Work through the numbers
With a one-square-metre tank, ten-square-centimetre opening and coefficient 0.6, lowering head from two metres to half a metre removes 1500 litres.
The integrated time is about 532.2 seconds. Initial discharge is approximately 3.758 L/s and final discharge approximately 1.879 L/s; using only the faster initial rate would miss the slowdown.
Where this model stops
Vented constant-section small-orifice model only; no inflow, submergence, siphon, pipe friction or changing discharge coefficient.
Use appropriate hydraulic analysis for connected systems. The page is an ideal drainage calculation and does not approve a discharge arrangement or tank structure.
A few questions, answered
Why not divide volume by starting flow?
Starting flow is the fastest point in this scenario. Flow decreases as head drops, so integration is needed.
Can I enter a long drain pipe as the opening?
Not without separately modeling its losses. This page treats a localized small orifice, not a full pipe network.