About Expansion Tank Sizing Calculator
The expansion tank calculator sizes the tank that absorbs the thermal expansion of water in a closed-loop hydronic heating or chilled-water system. As the loop warms from its fill temperature to its operating maximum, the water expands; with nowhere to go in a sealed system that expansion would spike the pressure and lift the relief valve, so an expansion tank with a compressible air cushion takes up the extra volume.
Using the ASHRAE method, the tool computes the net water expansion (the specific-volume growth less the volumetric expansion of the steel piping), converts the fill and maximum gauge pressures to absolute, derives the acceptance factor for a diaphragm or plain-steel tank, and divides the expansion volume by that factor to give the required tank size. It reports the expansion volume, acceptance factor and tank volume so you can select a standard tank and confirm the relief valve will not lift.
How It Works
- Enter the system water volume and the specific volume of water at the fill and maximum temperatures (from a steam/water property table). The dimensionless expansion factor is (vf2/vf1 - 1) - 3*alpha*dT, where the last term removes the volumetric growth of the steel pipe.
- Multiply the expansion factor by the system volume to get the net water expansion volume Ve that the tank must accept.
- Enter the fill and maximum gauge pressures and the local atmospheric pressure; the tool converts them to absolute (Pi and Pf). For a diaphragm tank the acceptance factor is AF = 1 - Pi/Pf; for a plain-steel tank it is AF = Pa/Pi - Pa/Pf.
- The required tank volume is Vt = Ve / AF. A diaphragm tank always comes out smaller than a plain-steel tank for the same pressures because its full volume is available to accept water.
Worked Example
A 1000-gallon heating loop is filled at 40 F (water specific volume 0.01602 ft^3/lb) and runs up to 200 F (0.016637 ft^3/lb), a 160 F rise, with steel piping (alpha = 6.5e-6 /F). The expansion factor is (0.016637/0.01602 - 1) - 3*6.5e-6*160 = 0.03851 - 0.00312 = 0.03539, so the water expands by 1000*0.03539 = 35.4 gallons. With a 12 psig fill and 30 psig maximum (26.7 and 44.7 psia), a diaphragm tank has AF = 1 - 26.7/44.7 = 0.403, giving a required tank of 35.4/0.403 = 87.9 gallons. A plain-steel tank for the same loop would need about 160 gallons.
Formulas
- Net water expansion factor
ef = (vf2/vf1 - 1) - 3*alpha*dT- Water expansion volume
Ve = Vs * ef- Acceptance factor
diaphragm: AF = 1 - Pi/Pf; plain steel: AF = Pa/Pi - Pa/Pf- Required tank volume
Vt = Ve / AF
Standards & References
- ASHRAE Handbook -- HVAC Systems and Equipment (Hydronic Heating and Cooling)
- Manufacturer methods (Amtrol, Bell & Gossett expansion tank sizing)
- ASME Boiler & Pressure Vessel Code (tank construction)
Frequently Asked Questions
Why is a diaphragm tank smaller than a plain-steel tank?
In a diaphragm or bladder tank the air is sealed behind a membrane and pre-charged, so the entire tank shell is available to accept expanded water. A plain-steel (compression) tank shares its volume between trapped air and water, so it needs a larger total volume to absorb the same expansion at the same pressures.
What is the acceptance factor?
The acceptance factor is the fraction of the tank volume that can actually accept expanded water as the system pressure rises from the fill pressure to the maximum. For a diaphragm tank it equals 1 minus the ratio of absolute fill to maximum pressure; a larger pressure spread gives a higher acceptance factor and a smaller tank.
Why subtract the 3*alpha*dT term?
The steel piping and equipment also expand when heated, increasing the volume of the closed loop. Subtracting three times the linear expansion coefficient times the temperature rise (three for volume) leaves only the net water expansion that the tank must absorb, slightly reducing the required tank size.
What fill and maximum pressures should I use?
The fill pressure is typically set so static water reaches the top of the system plus a small margin; the maximum pressure is kept below the relief-valve setting (often 30 psig for residential, higher for tall buildings). Both are gauge values and are converted to absolute by adding atmospheric pressure in the calculation.