BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: System liquid volume
- What it is
- The total volume of liquid in the closed system: pipes, radiators or emitters, boiler or chiller, tanks and heat exchangers.
- Units and format
- Enter a number in L: litres. The form accepts 0.000001 L to 100000000 L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The expansion volume, and so the vessel needed, rises in direct proportion.
- Get it right
- Add every component’s water content from maker data; pipework is often underestimated.
What this means: Fill (cold) temperature
- What it is
- The liquid temperature when the system is filled and the vessel is at its pre-charge pressure.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 400 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the coldest fill or standby temperature, as expansion is counted from there.
What this means: Highest working temperature
- What it is
- The highest temperature the liquid reaches anywhere in operation.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -50 °C to 400 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger rise above the fill temperature gives proportionally more expansion.
- Get it right
- Use the highest possible temperature, such as the high limit setting, not the normal flow temperature.
What this means: Mean volumetric expansion coefficient
- What it is
- The average fractional increase in liquid volume per kelvin of temperature rise between the fill and working temperatures.
- Units and format
- Enter a number in 1/K: 1/K. The form accepts 0 1/K to 0.01 1/K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.00041 1/K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Expansion volume rises in direct proportion to the coefficient.
- Get it right
- Take it for your liquid and temperature range from property tables or the glycol supplier.
Pressures
What this means: Pre-charge (and fill) pressure
- What it is
- The gas pressure in the vessel before liquid enters, set equal to the system fill pressure at the vessel, above atmospheric.
- Units and format
- Enter a number in bar g: bar g. The form accepts -0.9 bar g to 100 bar g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 bar g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher pre-charge, for the same final pressure, leaves less room for expansion and needs a larger vessel.
- Get it right
- Enter gauge pressure; check the vessel’s pre-charge with a tyre gauge before it is connected.
What this means: Highest working pressure
- What it is
- The highest gauge pressure allowed at the vessel when the system is hot, kept below the relief valve setting.
- Units and format
- Enter a number in bar g: bar g. The form accepts 0.000001 bar g to 200 bar g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.5 bar g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher final pressure gives the vessel more acceptance and reduces the size needed.
- Get it right
- Allow for the height between the vessel and the relief valve, and keep a margin below the valve setting.
What this means: Atmospheric pressure
- What it is
- The local atmospheric pressure, added to the gauge pressures to give the absolute pressures the gas law needs.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.5 bar to 1.1 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.013 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the standard value unless the site is at high altitude.
What this means: Vessel volume fitted
- What it is
- The total (nominal) volume of the expansion vessel you plan to fit, compared with the volume needed.
- Units and format
- Enter a number in L: litres. The form accepts 0.000001 L to 10000000 L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the nominal vessel volume from the maker, not the acceptance volume.
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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