Expansion Tank Sizing Calculator
Sizes bladder, diaphragm, or plain-steel expansion tanks for closed hydronic (hot water / chilled water) systems using thermal-expansion and pressure-ratio principles.
Preliminary Design Aid
Input Parameters
Result
| Volume of expanded water, Ve | — |
| Water expansion ratio, Ew = vh/vc − 1 | — |
| Piping expansion credit, Ep | — |
| Initial pressure (absolute), Pi,abs | — |
| Maximum pressure (absolute), Pmax,abs | — |
| Acceptance factor (denominator) | — |
Formula & Method
Governing sizing relation used for the selected tank style (derived from the general expansion-tank equation, S. T. Taylor, PE):
Where the volume of expanded water is:
| Symbol | Definition | Basis |
|---|---|---|
| Vt | Required total/acceptance tank volume | gal or L |
| Vs | Total system water volume | gal or L |
| Ve | Volume of water expanded from Tc to Th | gal or L |
| vh, vc | Specific volume of water at Th and Tc | from density correlation, 0–200°C |
| Ew | Unit thermal expansion ratio of water | dimensionless |
| Ep | Unit thermal expansion ratio credit from piping (optional) | dimensionless |
| Pi, Pmax | Initial/precharge and maximum allowable pressures | absolute, same units |
| Pa | Atmospheric pressure | absolute |
Calculation sequence
1. Convert T_c, T_h to a common absolute basis and evaluate v_c, v_h from the water-density table. 2. E_w = v_h/v_c − 1; apply piping credit E_p = 3α(T_h − T_c) if selected. 3. V_e = V_s · (E_w − E_p). 4. Convert P_i and P_max to absolute pressure using P_a. 5. Apply the denominator for the selected tank style (vented / no-precharge / precharged / standard-factory-precharge). 6. V_t = V_e / denominator.Assumptions & Limits
Included effects
- Water thermal expansion between minimum and maximum average system temperature.
- Optional credit for thermal expansion of the piping (Ep).
- Tank pressure ratio for vented, non-precharged, properly precharged, and standard-factory-precharge cases.
- Standard factory bladder/diaphragm precharge of 12 psig (83 kPag) where applicable.
Excluded effects
- Dissolved-air desorption allowance (~2% of Vs, per the full Eq. 1 form).
- Elevation/NPSHR and boiling-margin sizing for water above ~210°F (99°C).
- Tank located below/above pump suction — check static/pump-head interactions separately.
- Manufacturer-specific bladder/diaphragm acceptance-factor de-rates.
Valid input range: water temperatures 0–200°C (32–392°F) for the density correlation; the optional ASME/UMC/IMC cross-check is valid only for 170–230°F (77–110°C) average operating temperature and assumes a non-precharged tank basis.
Design condition defaults: atmospheric pressure 14.7 psia (101.325 kPa); steel piping α ≈ 12×10⁻⁶/°C.
Engineering Notes
- The "precharged" case governs almost all modern bladder and diaphragm tank selections — confirm the tank is field-precharged to Pi before startup; factory-standard precharge is 12 psig (83 kPag) and is often left unadjusted.
- The vented and non-precharged closed-steel styles are legacy designs, shown for reference and retrofit verification.
- Boiling-margin and NPSHR checks (points 3 and 4 of expansion-tank function) become relevant only above ~210°F (99°C) average water temperature and are not covered by this sizing routine.
- Reference method: Steven T. Taylor, PE, Expansion Tank Sizing Formulas, hvac-eng.com; ASME Boiler and Pressure Vessel Code, Section VI (2015); Uniform/International Mechanical Code expansion-tank provisions.
Revision: v1.0 — initial release.
