What this calculator does
A closed water loop expands as it is heated. If nothing takes up that expansion the pressure climbs until something relieves it. This calculator sizes the vessel that absorbs it, and shows the pressure spread it depends on.
How to use it
- Enter the total water content of the loop — this comes from the design, not from an estimate.
- Enter the coldest and hottest the water will be, and the fluid’s expansion coefficient (water defaults to 2.07e-4 per K).
- Enter the vessel pre-charge and the relief / maximum permitted system pressure, both as gauge.
- Note the usable fraction: if it is small, the vessel has to be very large, and the pressure spread should be widened first.
Governing formula
V_t = (β × ΔT × V_s) / (1 − P₁/P₂) Where:
-
V_t= Vessel working volume, litres -
β= Volumetric expansion coefficient, 1/K -
ΔT= Temperature rise, K -
V_s= System water content, litres -
P₁, P₂= Pre-charge and relief pressure, bar ABSOLUTE
Derived Equations:
V_exp = β × ΔT × V_s Worked example — 5,000 L loop heated 10 → 80 °C
The figures below were produced by running this page's own engine with the example inputs (System water content (L), Minimum water temperature (°C), Maximum water temperature (°C), Vessel pre-charge pressure (bar g), Relief / max system pressure (bar g), Static head at the vessel (bar g), Atmospheric pressure (bar a), Expansion coefficient (1/K)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Loop expansion volume | 72.45 L |
|---|---|
| Required vessel working volume | 193.83 L |
| Usable fraction of the vessel | 0.37 |
| Recommended pre-charge | 1.5 bar g |
| Temperature rise | 70 K |
| What this means | The loop gives up 72 L on heating. At a usable fraction of 37 % that needs a vessel of about 194 L working volume. |
- A 70 K rise expands the water by 2.07e-4 × 70 = 1.45 % of the loop.
- On 5,000 L that is about 72 L the vessel has to absorb.
- The usable fraction is 1 − 2.513/4.013 (absolute) ≈ 0.374.
- 72 / 0.374 ≈ 194 L of vessel working volume.
Assumptions & limitations
Engineering calculation. Vessel working volume from loop expansion and the usable pressure fraction, with the pre-charge and relief pressures converted to absolute before the ratio is taken.
- The expansion coefficient defaults to 2.07e-4 /K for water. For a glycol mix or a different duty temperature, enter your own value — nothing is looked up.
- Static sizing only. It gives the vessel working volume; it does not size the relief valve, the air separator or the fill/expansion pipework.
- The pre-charge is expressed as a gauge value and converted to absolute internally. Entering gauge values directly for the ratio understates the vessel substantially.
- A loop volume must come from the design. It is not estimated from pipe runs or drawings.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- Closed water-system pressurisation practice — BS EN 12828 and ASHRAE Handbook, Systems and Equipment.