Absolute pressure, or the answer is wrong
Gas law works on absolute pressure and a hydraulic gauge reads gauge pressure. A 1,500 psig precharge is 1,514.7 psi absolute, and 2,000 psig is 2,014.7. Fourteen point seven psi sounds like it should not matter next to two thousand, and at these pressures it barely does — but the habit of adding it is what saves you at 50 psig, where forgetting it makes the answer wrong by a factor of four.
With the gas at the precharge, it fills the shell. Squeeze it to 2,014.7 absolute and it occupies 1,514.7 over 2,014.7 of the shell, which is 75.2 percent. Squeeze it to 3,014.7 and it occupies 50.2 percent. The difference — 24.9 percent — is the oil the accumulator actually holds.
A five gallon accumulator holds about a quart
Five gallons is 1,155 cubic inches, and 24.9 percent of that is 288 cubic inches, or 1.25 gallons. That is the whole return between 2,000 and 3,000 psi, out of a vessel labelled five gallons, and it is the single most common surprise in accumulator work. The label is the gas volume, not the oil volume, and nothing is wrong with the accumulator.
Push a 3 in bore cylinder with it and 288 cubic inches is 40.7 inches of stroke — a real amount of work, but nothing like five gallons of it.
Precharge is the lever
The usable fraction rises the whole way as the precharge rises toward the bottom of the band. Take the same shell and band and set the precharge at 1,000 psig instead of 1,500 and it returns 16.7 percent of the shell, or 193 cubic inches. Set it at 1,800 and it returns 29.9 percent, or 345 cubic inches. Set it right at 2,000 and the arithmetic gives 33.2 percent, or 383 cubic inches — the theoretical maximum for this band.
Nobody runs it there, and the reason is mechanical rather than arithmetic: at that setting the bladder or piston reaches its stop every single cycle. How far below the bottom of the band a precharge belongs is set by the accumulator maker for the type and the duty, and this page does not have an opinion about it. What it can tell you is the price of any particular setting, in cubic inches.
Fast and slow are different accumulators
Gas that expands slowly stays at oil temperature and follows the exponent 1. Gas that expands in a fraction of a second has no time to take heat back from the shell, so it cools as it expands and takes up less room than the isothermal arithmetic says. At the far end, nitrogen behaves near 1.4.
The same five gallon shell across the same band returns 288 cubic inches at exponent 1 and 236 at 1.4 — eighteen percent less oil, from an accumulator that has not changed in any respect. Which exponent describes a given cycle is a judgement about the discharge time against how fast heat crosses the gas, and it is why the exponent is a field on this form rather than a number baked in.
That direction is not a law, though it is written down as one often enough. It holds while the precharge sits up near the bottom of the band, which is where accumulators are normally set. Drop the precharge far below it and the ranking turns over: the same shell precharged to 50 psig across a 2,000 to 4,000 psi band returns 1.60 percent of its volume at exponent 1 and 3.33 percent at 1.4, which is more than twice as much. The page prints the whole column rather than a rule, and names which row is smallest for the numbers you entered.
The gauge reading moves with the weather
Precharge pressure follows absolute temperature. Set 1,500 psig at 70 F and let the machine warm the accumulator to 140 F, and the same gas now reads 1,700 psig with nothing added and nothing lost. That is 530 degrees absolute going to 600, a ratio of 1.132 applied to 1,514.7 absolute.
So a precharge check is only meaningful with the temperature attached to it. A charge that looks 200 psi high on a hot machine may be exactly right cold, and one that looks right on a hot machine is low cold. The maker states how and when to check it.
Questions people ask
How much oil does a hydraulic accumulator actually hold?
Far less than its rated volume. A five gallon shell precharged to 1,500 psig and working between 2,000 and 3,000 psig gives back 288 cubic inches, which is 1.25 gallons or a quarter of the label. The rating is the gas volume with the bladder or piston fully out; the oil is only the difference in gas volume between the two ends of your pressure band.
Do I use gauge or absolute pressure for accumulator calculations?
Absolute, always. Add 14.7 to every gauge reading before the ratios. At three thousand psi the correction barely shows, but the same arithmetic done in gauge pressure on a low pressure accumulator is wrong by a large factor, and it is the standard way these calculations fail. A gauge reading 1,500 is 1,514.7 absolute.
What does a higher precharge do to usable volume?
It increases it, right up to the point where the precharge equals the bottom of the pressure band. On a five gallon shell across 2,000 to 3,000 psi, 1,000 psig of precharge returns 193 cubic inches, 1,500 returns 288, and 2,000 returns 383. Real settings sit below the bottom of the band because a bladder driven onto its stop every cycle is a mechanical problem, and how far below is the maker figure.
Should I use the isothermal or adiabatic exponent?
It depends on how fast the accumulator discharges, not on the accumulator. A slow cycle where the gas stays at oil temperature is exponent 1; a discharge over a fraction of a second gives the gas no time to take heat back, and nitrogen approaches 1.4. On the default settings the shell returns 288 cubic inches at 1 and 236 at 1.4, so the choice is worth about eighteen percent. That ordering is not universal, though: with a precharge far below the bottom of the band the higher exponent gives more rather than less, so the page prints the whole column and names the smallest row instead of stating a rule.
Why does my accumulator precharge read differently when hot?
Because gas pressure follows absolute temperature. A 1,500 psig charge set at 70 F reads 1,700 psig at 140 F with nothing added — 530 degrees absolute going to 600 is a ratio of 1.132. A precharge figure is meaningless without the temperature it was read at, which is why the maker states the check conditions along with the pressure.
How long will an accumulator supply a given flow?
Usable volume divided by the flow. At 288 cubic inches, or 1.247 gallons, a 5 GPM demand runs for 15 seconds with the pump contributing nothing. On a live circuit the pump is usually still delivering, so the accumulator only covers the shortfall and lasts proportionally longer. The figure on the page is the pump-does-nothing case.