# Hydraulic Accumulator Sizing Calculator > Source: https://netray.co/tools/hydraulic-accumulator-sizing-calculator-precharge-boyle > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Sizes a gas-charged accumulator from required discharge volume, minimum and maximum system pressure, precharge fraction and the compression process exponent. ## Category engineering-plm ## Industry Hydraulic Equipment Manufacturing ## Audience - Design engineer - Maintenance engineer - Estimator ## Tool **Kind:** calculator **Inputs:** #### Oil volume required **Key:** dv **Type:** number **Default:** 2.5 **Min:** 0.01 **Step:** 0.1 **Unit:** gal **Help:** Volume the accumulator must deliver between maximum and minimum pressure. #### Minimum working pressure (P1) **Key:** p1 **Type:** number **Default:** 1800 **Min:** 10 **Step:** 25 **Unit:** psig **Help:** Lowest pressure at which the load still works. #### Maximum working pressure (P2) **Key:** p2 **Type:** number **Default:** 3000 **Min:** 20 **Step:** 25 **Unit:** psig **Help:** Pressure at which the pump or relief limits the circuit. #### Precharge as % of P1 **Key:** pre **Type:** slider **Default:** 90 **Min:** 50 **Max:** 99 **Step:** 1 **Unit:** % **Help:** Bladder types are commonly precharged at 80 to 90 percent of minimum pressure. #### Gas process **Key:** n **Type:** select **Default:** 1.4 **Options:** ##### Isothermal, slow cycle (n = 1.0) **Value:** 1 ##### Polytropic, medium (n = 1.25) **Value:** 1.25 ##### Adiabatic, fast discharge (n = 1.4) **Value:** 1.4 **Outputs:** #### Nitrogen precharge **Key:** p0 **Expr:** p1 * pre / 100 **Format:** decimal **Description:** psig at the stated precharge temperature. #### Gas fraction at P1 **Key:** r1 **Expr:** pow((p0 + 14.7) / (p1 + 14.7), 1 / n) **Format:** decimal **Description:** V1 / V0 on the discharge side. #### Gas fraction at P2 **Key:** r2 **Expr:** pow((p0 + 14.7) / (p2 + 14.7), 1 / n) **Format:** decimal **Description:** V2 / V0 when fully charged. #### Required accumulator size **Key:** v0 **Expr:** dv / (r1 - r2) **Format:** decimal **Primary:** true **Description:** Gallons of nominal gas volume, V0 = dV / ((P0/P1)^(1/n) - (P0/P2)^(1/n)) with absolute pressures. #### Size in cubic inches **Key:** v0_in **Expr:** v0 * 231 **Format:** integer #### Max pressure to precharge ratio **Key:** ratio **Expr:** (p2 + 14.7) / (p0 + 14.7) **Format:** decimal **Description:** Bladder accumulators are normally limited to about 4:1; check the maker rating. #### Usable fraction of volume **Key:** use **Expr:** dv / v0 * 100 **Format:** percent **Primary:** true **Description:** Share of the shell volume that actually discharges. **Chart:** #### Required size vs precharge percent **Type:** line **X:** pre **From:** 50 **To:** 98 **Steps:** 30 **Series:** - v0 **Disclaimer:** Gas law sizing for a single discharge. Add a safety margin of 10 to 20 percent for temperature change, gas loss and bladder wear. Final selection must follow the manufacturer's rating and local pressure vessel code. ## Content **Intro:** An accumulator stores oil by compressing a nitrogen charge. Sizing it right gives you an emergency reserve, shock absorption or pump downsizing; sizing it wrong gives you a vessel that either delivers too little or rides at the edge of its rated pressure ratio. **Sections:** #### How to use it **Body:** Enter the oil volume the circuit must receive between minimum and maximum pressure, the minimum pressure at which the load still works, and the maximum system pressure. Set the precharge as a percentage of minimum pressure; 90 percent is a common starting point for bladder types. Choose the gas process: use 1.0 when the cycle is slow enough for heat to leave the gas, and 1.4 for sub-minute discharge such as emergency stroking of a cylinder. The chart shows how the shell grows if precharge falls too low. **Bullets:** - Precharge with dry nitrogen only, never oxygen or air - Set precharge with the oil side at zero pressure - Correct precharge for temperature if the unit runs hot - Check that P2 to P0 ratio stays within the maker limit #### The gas law behind it **Body:** The nitrogen follows P x V to the power n equal to a constant, with absolute pressures. The oil volume delivered equals the gas volume change from P1 to P2. That gives V0 = dV divided by ((P0/P1) to the 1/n minus (P0/P2) to the 1/n). Isothermal behavior has n of 1.0, adiabatic uses 1.4 for nitrogen, and real cycles fall in between. Real-gas deviation is small below about 3000 psi but nonzero, so the safety margin matters. The approach matches the method used in accumulator catalogs and in the fluid power textbooks. #### Worked example **Body:** A circuit needs 2.5 gallons between 1800 and 3000 psig with a fast adiabatic discharge. At 90 percent precharge, P0 is 1620 psig. The calculation returns a shell near 14 gallons with only about 18 percent of the volume delivered per cycle. That low usable share is normal for a wide pressure window, so the usual way to shrink the vessel is to narrow the pressure range, not to raise precharge to the point where the bladder touches the poppet valve. #### Common mistakes **Body:** The most frequent error is using gauge instead of absolute pressure in the gas law. Next is ignoring the temperature effect: nitrogen precharge drops about 1 percent for every 6 F of cooling, which can leave a cold accumulator under-charged. Another error is precharging at full system pressure, which prevents oil entry. Last, designers forget safety relief and block valves, which are required by many codes for stored energy on a machine. **Cta:** Netray can pull accumulator inspection dates and precharge checks from your maintenance system so a private assistant tells you which vessels are overdue. **Faq:** #### What precharge should I use? **Answer:** For bladder types, 80 to 90 percent of minimum working pressure is common. For energy storage with a wide window, near 90 percent maximizes usable volume. Shock suppression usually uses about 60 to 70 percent of the operating pressure. Follow the manufacturer's instructions. #### Why do I need absolute pressure? **Answer:** Gas law relationships depend on the true pressure of the gas, which includes atmosphere. Using gauge numbers makes the ratios wrong, especially at low pressure, and gives a vessel that is too small. #### Which exponent should I choose? **Answer:** Use 1.4 if the oil is delivered in less than about one minute, 1.0 if the cycle is slow and the gas is returned to ambient temperature, and about 1.25 when you are not sure. Using 1.4 gives the conservative larger shell. #### Does this cover piston and diaphragm types? **Answer:** The gas law is the same, but bladder, piston and diaphragm accumulators have different usable volume limits and ratio ratings. Use this as the first estimate and verify with the product catalog. ## Search terms hydraulic accumulator sizing calculator, bladder accumulator size formula, accumulator precharge pressure calculator, accumulator boyle law calculation, accumulator polytropic exponent 1.4, accumulator pressure ratio, hydraulic accumulator gallons needed, accumulator nitrogen precharge --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json