Calculate the nominal volume of a hydraulic accumulator from usable volume, precharge pressure and pressure range with a polytropic gas model.
Set the inputs and run the calculation.
Determine nominal volume and gas states from usable volume, precharge and pressure range.
Usable volume ΔV, precharge p₀, minimum/maximum operating pressure p₁/p₂, polytropic exponent n and optional nominal volume.
Precharge enters the gas law as absolute pressure and is below minimum operating pressure. Too much precharge prevents usable volume; too little raises risk of bladder damage or liquid hammer.
For absolute pressure p·Vⁿ is constant. Gas volumes at p₁ and p₂ give ΔV = V₁−V₂; precharge is below minimum operating pressure so oil can enter the accumulator.
With p₀ = 90 bar, p₁ = 100 bar and p₂ = 200 bar, usable swing is small relative to p₂ and a larger vessel is needed.
Sources and limits: Polytropic gas law in the ISO 4413 context; check manufacturer limits, gas, temperature and pressure cycles.
Determine nominal volume and gas states from usable volume, precharge and pressure range.
Hydraulic calculations link pressure difference, effective area and flow. Pressure determines force, flow determines speed, while line losses and efficiency reduce ideal values.
For absolute pressure p·Vⁿ is constant. Gas volumes at p₁ and p₂ give ΔV = V₁−V₂; precharge is below minimum operating pressure so oil can enter the accumulator.
Usable volume ΔV, precharge p₀, minimum/maximum operating pressure p₁/p₂, polytropic exponent n and optional nominal volume. Precharge enters the gas law as absolute pressure and is below minimum operating pressure. Too much precharge prevents usable volume; too little raises risk of bladder damage or liquid hammer.
Enter the required usable volume, precharge pressure, minimum and maximum operating pressure and the polytropic exponent. The calculator determines the accumulator's required nominal volume.
With p₀ = 90 bar, p₁ = 100 bar and p₂ = 200 bar, usable swing is small relative to p₂ and a larger vessel is needed.
Precharge enters the gas law as absolute pressure and is below minimum operating pressure. Too much precharge prevents usable volume; too little raises risk of bladder damage or liquid hammer. The result is a pre-sizing point. Higher pressure raises cylinder force; more flow raises speed but usually also increases losses and heat.
Volume in litres, pressures in bar (absolute), polytropic exponent dimensionless.
Sizing a hydraulic accumulator for a required usable-volume swing, or checking how much a changed pressure range affects the required nominal volume.
Polytropic gas law in the ISO 4413 context; check manufacturer limits, gas, temperature and pressure cycles.
Common mistake: Don't use gauge pressure instead of absolute pressure – the polytropic gas law p·Vⁿ = constant only holds with absolute pressures. Don't set precharge too close to minimum operating pressure, or the last usable oil quantity becomes too small as minimum pressure is reached and the accumulator responds too abruptly.
Only once system pressure exceeds precharge does it further compress the gas and admit additional oil; too high a precharge would block the accumulator before minimum operating pressure is even reached.
For fast charge/discharge cycles with negligible heat exchange, nitrogen is commonly modeled at n ≈ 1.4 (adiabatic); very slow processes are closer to n ≈ 1 (isothermal).
The closer p₁ and p₂ are, the smaller the gas-side volume change per bar of pressure difference, so a larger nominal volume is needed for the same usable volume.
Pre-size a bladder or piston accumulator for a required fluid working volume.
Results are preliminary engineering estimates. Component approval, safety functions, material, fatigue, installation checks and the complete system assessment remain separate.