KEVOS® MAKEOS · Engineering
Expansion Vessel Sizing (Liquid Expansion, Pre-Charge and Final Pressure, Vessel Volume)
For a closed heating or cooling water system, how much does the water expand when it heats up, and how big must the diaphragm expansion vessel be to take it within the pressure limits?
Sizing of a gas-cushioned (diaphragm or bladder) expansion vessel for a closed liquid system: the expansion volume from the system volume, a mean volumetric expansion coefficient and the temperature rise, the acceptance factor from the pre-charge and final pressures by Boyle’s law at constant temperature (as the gas law tool), the vessel volume needed, and the gas volume left at the final pressure, against the vessel you have.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| System liquid volume | L | Total volume of liquid in the system (pipes, emitters, boiler or chiller). |
| Fill (cold) temperature | °C | Temperature at which the system is filled. |
| Highest working temperature | °C | Highest temperature the liquid reaches. |
| Mean volumetric expansion coefficient | 1/K | Mean volumetric expansion coefficient over the temperature range (water is about 0.0003 to 0.0007 per kelvin, rising with temperature; glycol mixtures are higher). |
| Pressures | ||
| Pre-charge (and fill) pressure | bar g | Gas pre-charge of the vessel, normally equal to the static fill pressure at the vessel. |
| Highest working pressure | bar g | Highest pressure allowed at the vessel (below the relief valve setting). |
| Atmospheric pressure | bar | Atmospheric pressure. |
| Vessel volume fitted | L | Nominal volume of the vessel you have. |
Method and formulas
- Expansion volume V_e = V_s β (T₂ − T₁).
- Gas compressed from P₀ to P_f at constant temperature: V₂ = V₁ P₀ ÷ P_f (as the gas law tool, absolute pressures); acceptance factor = (P_f − P₀) ÷ P_f.
- Vessel volume = V_e ÷ acceptance factor.
- Example: the water expands 14.35 L; with an acceptance factor of 0.42699 the vessel needs 33.608 L.
Limitations
- Isothermal gas compression; a hot vessel gas cushion takes slightly less.
- No allowance for a water reserve or system leaks; add one for systems that lose water.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the expansion vessel for a heating or chilled water loop
- Check an existing vessel after adding volume
- Set the pre-charge pressure
Who it is for
- Building services engineers
- Process engineers
- Maintenance engineers
What you get
- Expansion volume
- Acceptance factor
- Vessel volume needed against the vessel fitted
Interpreting the result
- Raising the final pressure or lowering the pre-charge makes the vessel smaller; a high fill pressure makes it much larger.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3032–3041. Topic reference; no source tables or recommended settings are reproduced.
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