Required accumulator size V0
-Precharge / P1
-Compression ratio P2/P0
-Usable oil from your size
-All results
| Gas volume at P1 (oil nearly all stored) | - |
| Gas volume at P2 (maximum charge) | - |
| Oil delivered V1 - V2 | - |
| Absolute pressures P0 / P1 / P2 | - |
| Same size with the other gas exponent (n = 1.0 / 1.4) | - |
Method and formulas
Ideal gas law for the nitrogen side, with absolute pressures. The gas volume V1 is at minimum pressure (most gas, least oil) and V2 at maximum pressure.
| Quantity | Formula |
|---|---|
| Gas law | P0 V0n = P1 V1n = P2 V2n |
| Gas volumes | V1 = V0 (P0/P1)1/n, V2 = V0 (P0/P2)1/n |
| Oil delivered | ΔV = V1 − V2 |
| Required size | V0 = ΔV / [(P0/P1)1/n − (P0/P2)1/n] |
| Absolute pressure | P = gauge + 14.696 psi (1.01325 bar) |
Worked example: 5 L between 120 and 200 bar, 100 bar precharge, fast discharge
Absolute pressures: P0 = 101.0, P1 = 121.0, P2 = 201.0 bar. With n = 1.4 the denominator is (101.0/121.0)0.714 − (101.0/201.0)0.714, so V0 = 5 / that = 18.71 L. Gas volumes: V1 = 16.44 L and V2 = 11.44 L, a difference of 5.00 L. With slow, isothermal behavior (n = 1.0) the same duty needs only 15.05 L, which is why the exponent matters.
Questions
How do you size a hydraulic accumulator?
Use the gas law for the nitrogen charge: P0 V0^n = P1 V1^n = P2 V2^n with absolute pressures. The oil delivered is dV = V1 - V2, so V0 = dV / [(P0/P1)^(1/n) - (P0/P2)^(1/n)]. P0 is the precharge, P1 the minimum and P2 the maximum working pressure.
What is the right precharge pressure?
A common rule for bladder and piston accumulators is about 90 % of the minimum working pressure (P0 = 0.9 P1) at operating temperature, which keeps the bladder off the valve and gives close to the largest usable volume. Always follow the manufacturer's limits.
Isothermal or adiabatic: which exponent do I use (n)?
Slow charge and discharge, over about 3 minutes or more, lets the gas exchange heat, so n is close to 1.0 (isothermal). Fast discharge such as a shock-absorbing or emergency stroke is close to adiabatic, n = 1.4 for nitrogen. Use 1.4 for the discharge when unsure; it gives the larger accumulator.
Why must pressures be absolute?
The gas law needs absolute pressure. Gauge pressure plus atmospheric pressure (14.7 psi or 1.013 bar) is absolute. The calculator takes gauge pressures and adds atmosphere for you.
Does temperature matter?
Yes. Precharge pressure rises about 1 % per 3 degrees C (about 1 % per 5 degrees F) of gas temperature; set the charge at the working temperature or correct it. This calculator assumes the gas starts at the precharge temperature.
What does this calculator not cover?
It models an ideal gas and does not include gas leakage, bladder or piston limits (compression ratio P2/P0, usually about 4:1 maximum for bladders), pressure drop in the lines, pump flow, or code requirements for pressure vessels. Verify critical designs.
Engineering aid for guidance. Ideal-gas model only. Pressure vessels are regulated: follow the manufacturer's data, the applicable pressure equipment code and safe-discharge procedures, and verify critical designs.