Size hydraulic accumulators using Boyle's Law (isothermal) or adiabatic processes for energy storage.
Hydraulic accumulators store pressurized fluid in a gas-charged chamber so the system can deliver short bursts of high flow, absorb shock, or maintain pressure during pump-off intervals. This calculator sizes accumulator volume from the duty cycle's working pressure, gas pre-charge, and required discharge volume, using Boyle's law for isothermal sizing and a polytropic correction for fast cycles.
Boyle's law P₁V₁ = P₂V₂ defines the isothermal relationship between charged gas volume and pressure. Required accumulator volume V₀ = ΔV / (P_pc/P₂ − P_pc/P₁) where P_pc is the pre-charge pressure, P₁ is minimum working pressure, P₂ is maximum working pressure, and ΔV is the delivered fluid volume. For fast cycles (< 1 minute), use the polytropic form (P₁V₁^n = P₂V₂^n) with n = 1.4 for nitrogen, which gives a smaller effective volume per discharge. Rule of thumb: set pre-charge to 90% of minimum working pressure for bladder accumulators, 95% for piston accumulators. Sizing also depends on temperature swing — gas pre-charge shifts ~1% per 3 °C so cold-climate systems need recheck.
A press designer needing 5 liters delivered between 200 bar and 150 bar charges a 10-liter bladder accumulator with 135 bar nitrogen pre-charge and verifies the discharged volume meets the dwell-stroke requirement.
A hydraulic technician suppressing piston-pump pulsations adds a 1-liter accumulator with 80% pre-charge of system mean pressure, smoothing the pressure waveform from ±15 bar to ±2 bar at the gauge.
A vehicle systems engineer sizes a backup steering accumulator for 3 full-lock turns after pump failure, computing required gas volume so residual fluid flow at end-of-discharge still exceeds steering-valve crack pressure.
Charge to 90% of your minimum working pressure for bladder accumulators (so the bladder doesn't slap the poppet) and 95% for piston accumulators. Always recheck pre-charge after temperature changes or annually for safety.
Bladder accumulators (most common) handle fast cycles and contaminated fluid well. Piston accumulators offer larger volumes (≥10 L) and longer life. Diaphragm accumulators are compact and suit lower-volume duty (≤1 L).
Nitrogen pre-charge expands with heat — pressure rises ~1% per 3 °C. A unit charged at 25 °C and operating at 50 °C reads ~8% higher pre-charge, which reduces effective discharge volume.