Pool Volume, Turnover and Dosing

Everything downstream is proportional to a number nobody measures

A pool has no meter on it. Its volume is reconstructed from a length, a width and a depth that is itself an average, and that reconstruction then propagates into three different answers: how much chlorine to add, what flow the pump must deliver, and how large the heater has to be. The first two are directly proportional to it and the third very nearly so, for a reason the section on heating sets out. An estimate that is a fifth high produces a fifth too much chemical, a fifth too much pump and most of a fifth too much heater — consistently, in the same direction, every time it is used.

The length and width are honest measurements. The depth is where the error enters, because a pool with a shallow end and a deep end has no single depth, and averaging the two extremes is exact in only two cases: a floor that falls at one uniform rate end to end, or a shallow and a deep section of equal plan area. Built pools are usually neither. One that is 1.0 m at one end and 2.5 m at the other, reached as a flat shallow section, a slope and a flat deep section, does not hold 1.75 m of water unless that arrangement happens to divide the plan in half. Where the shallow section is the larger — which is the usual arrangement, because that is where people stand — the plain average overstates the volume, and it overstates every answer built on it.

The correct treatment is to take the pool floor in pieces and weight each depth by the area it covers. The pool volume page on this site, rectangle, circle, oval or kidney, asks for one average depth or for the two end depths it averages, and says plainly that it is doing a simple average; that honesty is the point, because it tells you which input to spend effort on.

A dose is a concentration, so it follows the volume and ignores the shape

Pool chemistry is quoted in parts per million, and in fresh water a part per million is a milligram per litre. A litre of water weighs a kilogram closely enough for this purpose, so one part per million is also one gram per cubic metre — and that single identity is what makes the dosing arithmetic trivial. Raising 50 m³ by 1.5 ppm needs 75 grams of the active substance. The pool could be a rectangle, a kidney or a circle; nothing about its geometry appears anywhere in that sentence.

What does appear is the strength of the product in the bottle, because you are not buying the active substance on its own. Those 75 grams delivered as a 12% liquid mean 625 grams of product; as 68% calcium hypochlorite granules, 110 grams. The dose is the concentration rise times the volume divided by the active fraction, and that is the whole calculation.

One caution on the product term. The percentage printed on a container of liquid chlorine may be a mass fraction or it may be available chlorine per litre, and at hypochlorite densities the two are not the same figure. Granular products are unambiguous: a mass of active in a mass of product. If a liquid dose is close enough to matter, read which convention the label is using before you pour. And a mass of product is not a volume of it: a 12% hypochlorite solution weighs around 1.2 kg a litre, so those 625 grams are about 0.52 litres in the jug rather than the 0.63 that treating it as water would give.

Turnover fixes the flow, but not the way the word suggests

Circulation is specified as turnovers: how many times a day the whole body of water passes through the filter. Choose a number of turnovers and a number of hours you are willing to run the pump, and the required flow falls out with no further physics. Fifty cubic metres turned over once in an eight-hour run needs 6.25 m³/h — about 104 litres a minute, or 27.5 US gallons a minute.

The two inputs trade against each other, and they do not trade evenly. Running the same turnover over sixteen hours instead of eight halves the flow, and by the pump affinity laws shaft power varies with the cube of speed. Half the flow for twice as long is roughly a quarter of the energy for exactly the same volume circulated. This is the entire argument for a variable-speed pump, and it is a physics argument rather than a marketing one — slower water also filters better, because a cartridge or sand bed separates more at low face velocity than at high.

The word turnover then invites a false picture: a queue of water filing through the filter, everything treated once, job done. Water does not queue. A pool behaves closer to a stirred vessel, where filtered water returns and mixes straight back in, so some of what the pump draws next is water it has already cleaned. Under complete mixing the fraction of the original water still untreated after one turnover period is not zero but about 37%, decaying exponentially: two turnovers leaves 14%, three leaves 5%. One turnover is a bookkeeping quantity meaning the pump has moved a volume equal to the pool — not a claim about any particular litre of it.

Real pools mix worse than that model, not better, and no increase in flow rate fixes a dead zone behind a bench or in a corner. Nor is the computed figure what a given pump will deliver: it produces that flow only against the head the system imposes through filter, heater, pipe runs and fittings, which is a separate hydraulic problem the page defers to rather than answers.

Heating is the one place the volume proportionality half breaks

Warming the pool is a volume problem: the energy to lift 50 m³ by eight degrees is fixed by mass and specific heat capacity, and works out at about 465 kWh, or 19.4 kW spread over a day. Holding it there is a surface problem. Heat leaves through the water surface — mostly as evaporation, which carries away roughly 2.4 megajoules for every kilogram that leaves, about 0.67 kWh a litre — and the surface does not grow when the pool gets deeper.

The consequence is worth stating plainly, because it inverts an intuition. Doubling the depth doubles the energy and the time needed to warm the pool up and changes the standing loss by nothing at all. A wide shallow pool is the expensive one to keep warm. It is also why a cover outperforms a larger heater: suppressing evaporation attacks the term that runs all season, while heater capacity only shortens the days at the start of it.

This site's heater page infers the water surface area from the volume at an assumed 1.5 m mean depth, because it does not ask for the plan dimensions. For a pool near that depth the result is fair; for a shallow lap pool it understates the surface term and therefore the standing loss. That is stated on the page as a limitation rather than buried, and it is the reason the heater page carries a low confidence rating where the flow page carries a high one. The dose page sits between them at medium, for a different reason: its arithmetic is exact and the volume it consumes is not.

Three doses only go one way

Salt, stabiliser and calcium hardness share a property chlorine does not: the pool does not use them up. Chlorine is spent by sunlight and by whatever it oxidises, so it is dosed again every week. Salt, cyanuric acid and calcium stay dissolved until water leaves the pool, and ordinary pool care removes them no other way — Hayward's salt cell manual says of salt that the only way to lower it is to partially drain and refill. Each is dosed with the same arithmetic as chlorine, the rise times the volume over the product's strength, but an overshoot is corrected by draining rather than by the next dose, which is why their pages say to add them in stages and test between.

Draining is itself a mass balance. Let a share of the pool out and refill it with water at the fill level, and the level becomes the old one times what stayed plus the fill level times what was replaced. Solved for the target, the share depends on the fill water as much as on the pool: stabiliser-free mains water makes lowering cyanuric acid from 120 to 80 ppm a third of the pool, calcium from 450 to 300 with fill water at 150 is half, and with fill water at 300 no amount of draining gets there.

How the water is replaced changes how much is used. Running the hose while the pool overflows mixes the new water with the old as it arrives, and the water needed becomes the volume times the natural log of the ratio — for a third off, 0.405 of the pool instead of 0.333, about 22% more. Where a pool cannot be lowered far, two equal stages reach the same level: two drains of about 18% each match one drain of a third.

Stabiliser also has a second source that nobody adds on purpose. Trichlor and dichlor are stabilised chlorine: a mole of trichlor releases three moles of chlorine and one of cyanuric acid, so each ppm of chlorine from it leaves 129.07 / 212.72 = 0.61 ppm of stabiliser, and from dichlor 0.91. A pool run on tablets all season climbs whether or not stabiliser is ever bought, and is eventually drained because of it.

pH moves against a buffer, so no ratio doses it

Every other dose here is a concentration rise times the volume. pH is not a concentration anyone adds; it is the balance point of the water's buffers, and how far a litre of acid moves it depends on how much buffer there is at the pH the water is at. The measure of that is the buffer intensity — the alkalinity it takes to shift pH by one unit — and it changes as pH changes, which is why a fixed ounces-per-tenth rule is right for one pool and wrong for the next.

The page works it the way Wojtowicz set it out for pool water. Carbonic acid's two ionisation constants follow the water temperature, from Plummer and Busenberg's equations; dissolved solids set the ionic strength, and the Davies approximation turns that into activity coefficients; the measured alkalinity, less the share the stabiliser contributes, fixes the total carbonate. Acid then lowers alkalinity at that fixed carbonate — the carbon dioxide it forms has not left yet — and soda ash raises it while adding carbonate of its own. The model is held to the papers' own tables: 0.002 M bicarbonate and cyanurate buffer 12.9 and 30.4 ppm as calcium carbonate per pH unit at pH 7.5, and the page's arithmetic lands on both.

Two consequences follow that most dosing charts leave out. Stabiliser buffers too, more strongly than bicarbonate at pool pH for the same molar amount, so a stabilised pool takes more acid than its carbonate alone suggests. And the carbon dioxide an acid dose makes leaves the water over the following days, which lifts the pH back up — Wojtowicz's worked examples of pool water losing carbon dioxide level off near pH 8.3 — so a pool whose pH keeps rising is usually telling you its alkalinity is high, not that the last dose was short.

What the volume cannot tell you

Covers and liners are not on this page. Both are surface quantities: a cover is cut to the water plane and a liner wraps the floor and walls, and neither scales with the volume at all. A deeper pool of the same footprint needs the same cover and more liner, while needing more of everything else here. Mixing the two families up is the quickest way to buy the wrong quantity of something.

Nor does the dose calculation know whether the chlorine it computed will work. Free chlorine exists as hypochlorous acid and as the far weaker hypochlorite ion, and the split is set by pH: the pKa sits near 7.5, so at pH 7.5 roughly half the free chlorine is in the active form and at pH 8.0 roughly a quarter. Same dose, same test reading, half the disinfecting power. Cyanuric acid adds a second, slower reservoir that binds chlorine and releases it gradually, so a rising stabiliser level quietly reduces what a given free-chlorine reading is doing. The arithmetic here sees none of that.

Which gives the one operating rule that follows from the whole method: dose once, run the pump for a full turnover, then test. Never dose twice from the same calculation. If the volume estimate is wrong — and it usually is, somewhat — the error is present in both doses, in the same direction, and the second dose is what takes a pool past target rather than to it.