Hydraulic Accumulator Calculator: Usable Oil and Stored Energy

The oil an accumulator delivers and the energy it stores between a minimum and a maximum pressure.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

A gas-charged (bladder or piston) accumulator stores energy in compressed nitrogen. Enter the precharge pressure, the accumulator size, and the minimum and maximum working pressures. The calculator gives the gas volume at each pressure, the oil delivered as the pressure falls from the maximum to the minimum, and the energy stored.

Choose the gas exponent: 1.4 for a fast discharge that takes a few seconds, 1.0 for a slow one. The isothermal (slow) value is always higher, and the calculator shows both. It also shows how far out the naive pressure times volume is, which overstates the energy by several times.

Pressures are absolute in the formulas. You can enter gauge pressures and the calculator adds atmospheric pressure. A common rule is a precharge of 0.6 to 0.9 times the minimum working pressure. Always check the rated pressure of the accumulator before you use the result.

Formulas used

  • V_1 = V_0\left(\frac{P_0}{P_1}\right)^{1/n}
  • \Delta V = V_1 - V_2
  • E = \frac{P_2V_2 - P_1V_1}{n - 1}

Worked example

With the default numbers in the calculator above:

  1. Gas volume at the minimum working pressure: 14.97 L
  2. Gas volume at the maximum working pressure: 10.39 L
  3. Oil delivered between the two pressures: 4.58 L (22.88 % of the size)
  4. Usable energy stored (fast discharge, exponent n): 88.22 kJ
  5. Isothermal limit (slow discharge, n = 1): 102.17 kJ
  6. Naive pressure times volume (overstates the energy): 500.00 kJ, about 5.6677 times too high

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What precharge should I use?

Usually 0.6 to 0.9 times the minimum working pressure. A lower precharge gives more oil for the same size, but leaves the bladder worked harder.

Why is the energy not pressure times volume?

The pressure rises as the gas is compressed, so the average is much less than the maximum, and the gas volume is much smaller than the size of the accumulator at high pressure.

Which exponent should I use?

1.4 for nitrogen when the discharge is fast, 1.0 when it is slow enough for heat to flow back into the gas. If in doubt use 1.4, which gives less.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Accumulator manufacturers' sizing guides (Parker, Bosch Rexroth); Hydraulic fluid power texts (gas-charged accumulators).

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