The square root is the whole story
Water leaving a submerged hole obeys Q = Cd A √(2 g h), where A is the open area, h is the head from the water surface down to the centre of the opening, g is 32.174 feet per second squared, and Cd is a discharge coefficient covering contraction of the jet and losses on the way through.
The square root is what makes basin behaviour counterintuitive. Drop the head to half and the flow only falls to 71 percent. Drop it to a quarter and the flow is still half what it started at. A basin therefore empties briskly at first and then takes a disproportionate time over the last few inches, because by then there is almost no head left to push the water out.
On the default numbers — a 30 by 20 foot basin with 3:1 sides, two feet of water, a three-inch orifice at Cd 0.6 — the drawdown is around 2.8 hours. Split that into four equal depth intervals and the last half foot takes far more of the clock than the first. It is the same reason the final inch of a draining bathtub feels like it takes forever.
Working out the time
Because the surface area of a sloped-sided basin changes as the water falls, the drawdown is an integral rather than a division. The volume leaving in a moment is the flow times the moment; the depth that corresponds to depends on the surface area at that stage. Written out:
t = ∫ Asurface(h) / (Cd Aorifice √(2gh)) dh, from the finishing depth to the starting depth.
That looks unpleasant because of the 1/√h, which blows up at zero. Substituting u = √h removes the singularity entirely and turns the whole thing into a polynomial that integrates exactly, which is what this calculator does. No numerical stepping, no accumulating error.
For the special case of a basin with vertical sides — a tank, a walled structure — the surface area is constant and the result collapses to the familiar form t = 2 As (√h1 − √h2) / (Cd Ao √(2g)). A 600 square foot tank two feet deep through a three-inch orifice at Cd 0.6 gives 7,183 seconds, just under two hours. Set the side slope to zero in the form and you will get that number back.
Cd is not 0.6
It is a habit to write 0.6 and move on, and it is worth resisting. The discharge coefficient depends on the actual geometry of the opening: a sharp-edged plate is not the same as a short tube, which is not the same as a bevelled entry, which is not the same as a pipe stub projecting into the flow. Published values across those cases span roughly 0.6 to 0.8 and beyond, and the difference between 0.6 and 0.8 is a third more flow and a quarter less drawdown time.
Anything else in the flow path matters too. A trash rack partly blinded with leaves is an upstream loss the equation knows nothing about. Tailwater submerging the outlet on the downstream side reduces the effective head. A long pipe downstream of the orifice may end up controlling the flow instead of the orifice, at which point the orifice equation is describing the wrong thing entirely.
Small orifices and the blockage problem
Low-flow outlets on small basins tend toward small holes, and the arithmetic will happily hand you a diameter of an inch and a half. Physically that is an opening a handful of wet leaves will close permanently.
The standard answer is not a bigger orifice, because the orifice size is what controls the release rate. It is to protect the small opening with something that has far more open area — a trash rack, a perforated riser, a hooded inlet — so that debris is caught on a large screen while the orifice continues to meter the flow. Whether a minimum orifice size is required at all where you are, and what protection has to go with it, is set locally.
Maintenance is the other half of that. An outlet that nobody looks at fills up, the basin then holds water it was designed to release, and the first sign is usually water standing where it should not be, or overtopping in a storm that should have been routine.
Drawdown time is not a design
Two things this calculation deliberately does not do. It assumes no inflow while the basin drains, which is fine for the recession after a storm and quite wrong during it — the actual behaviour of a basin in a storm is routing, where inflow and outflow are tracked together against the stage-storage curve, and that is what determines whether the peak leaving the site meets the requirement. And it treats the head as being to the centre of the orifice throughout, which stops being true as the surface approaches the opening and the outlet starts behaving as a weir instead.
What the number is genuinely good for is the question people actually ask: how long will this thing hold water after the rain stops, and is that within whatever drawdown limit applies. Drawdown limits exist mostly for mosquito breeding, for the basin being empty and available before the next storm, and for vegetation survival. What the limit is where you are is a local answer.
The storage side of the pair is on the detention basin volume calculator. The infiltration equivalent — where the water leaves through the ground rather than through a hole — is on the rain garden and dry well pages, sized on the rate from a percolation test. If the outlet discharges to a swale or a culvert, the flow it delivers there is the input to the culvert and swale flow calculator.
Questions people ask
Why does the last foot of the basin take longer to drain than the first?
Because flow through an orifice goes with the square root of the head. At two feet of head the outlet is passing a certain flow; at one foot it is passing 71 percent of that; at three inches it is passing 35 percent. Meanwhile the water surface is shrinking as the level falls in a basin with sloping sides, which helps a little, but not nearly enough to compensate. The result is a curve that falls fast at first and then flattens out, and the theoretical time to reach absolutely zero head is unbounded — in reality the last inch goes by evaporation and soaking in rather than through the outlet.
What discharge coefficient should I use?
The one that matches the detail you are building, taken from your drainage manual or your engineer. The habitual 0.6 belongs to a sharp-edged orifice in a thin plate. A short tube, a bevelled or rounded entry, or a projecting pipe stub all give different values, generally higher, and published figures range up to around 0.8 or beyond for well-formed entries. The difference is not academic: going from 0.6 to 0.8 increases the flow by a third and cuts the drawdown time by a quarter. If you do not know the detail yet, run it both ways and see whether the answer changes anything you care about.
Can I use this for a tank or a swimming pool instead of a basin?
For a straight-sided vessel, set the side slope to zero and enter the plan dimensions, and the calculation reduces to the standard constant-area drawdown formula. It applies to any container emptying through a submerged opening under gravity with nothing flowing in. What it does not cover is a pump, a valve that throttles, a long discharge pipe that becomes the controlling restriction, or a submerged outlet where downstream water level reduces the effective head. Pool draining in particular has its own hazards and its own local rules about where the water may be discharged.
How small can the outlet orifice be?
Physically you can compute any size you like; practically, small openings block. Below about three inches, leaves, grass clippings, silt and litter will close the hole rather than might close it, and the standard response is to keep the small orifice as the flow control while protecting it with a trash rack or perforated riser that has many times the open area. Some jurisdictions set a minimum orifice diameter for exactly this reason and some require specific protection details. Both are local determinations and this page states neither.
Does a drawdown time within the limit mean the basin is designed correctly?
No. Drawdown answers one question — how long water stands after the rain stops — and detention requirements are usually about something else entirely, namely the peak flow rate leaving the property during the storm, often for several return periods at once. Establishing that requires routing the inflow hydrograph through the stage-storage curve against the outlet, which is engineering work. On top of that, the outlet structure, any embankment, and the emergency spillway that handles storms beyond the design event are all components whose failure has consequences downstream. Use this number to check a drawdown; do not use it as a design.