Calculating Expansion Tanks
Calculating expansion volume in open, closed and diaphragm expansion tanks
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Expansion tanks are required in heating, cooling or air condition systems to avoid unacceptable increase of system pressures during heat-up.
Expansion tanks are in general designed as
- open tanks
- closed compression tanks
- diaphragm tanks
Net expansion of water can be expressed as
Vnet = (v1 / v0) - 1 (1)
Vnet = necessary expansion volume of water
v0 = specific volume of water at initial (cold) temperature (ft3/lb, m3/kg)
v1 = specific volume of water at operating (hot) temperature (ft3/lb, m3/kg)
Open Expansion Tanks
Required volume of an open expansion tank can be expressed as
Vet = k Vw [(v1 / v0) - 1] (2)
Vet = required expansion tank volume (gallon, liter)
k = safety factor (approximately 2 is common)
Vw = water volume in the system (gallon, liter)
v0 = specific volume of water at initial (cold) temperature (ft3/lb, m3/kg)
v1 = specific volume of water at operating (hot) temperature (ft3/lb, m3/kg)
With an open expansion tank fresh air absorbed to the water tend to corrode the system. Open expansion tanks must be located above the highest heating element, in general on the top of buildings, where it may be exposed to freezing.
Closed Compression Expansion Tanks
Closed compression tanks can be designed as
- adjustable expansion tank - air is evacuated or injected by an automatic valve to the tank to control the system pressure when the temperature and expansion of the water rise or falls
- pump-pressured cushion tank - water is evacuated or injected to compensate temperature rice or fall
- compression tank with a closed gas volume - the tank contains a specific volume of gas which is compressed when the temperature and system volume increase.
The required volume of closed expansion tanks can be expressed as
Vet = k Vw [ ( v1 / v0 ) - 1 ] / [ ( pa / p0 ) - ( pa / p1 ) ] (3)
where
pa = atmospheric pressure - 14.7 (psia)
p0 = system initial pressure - cold pressure (psia)
p1 = system operating pressure - hot pressure (psia)
- initial temperature 50oF
- initial pressure 10 psig
- maximum operating pressure 30 psig
Diaphragm Expansion Tanks
The required tank volume of diaphragm expansion tank can be calculated as
Vet = k Vw [ ( v1 / v0 ) - 1 ] / [ 1 - ( p0 / p1 ) ] (4)
- initial temperature 50 oF
- initial pressure 10 psig
- maximum operating pressure 30 psig
- safety factor aprox. 2
- acceptance factor aprox. 0.5
Example - Volume Open Expansion Tank
The minimum volume of an open expansion tank for a system with 1000 gallons of water heated from 68 oF to 176 oF can be calculated as
Vet = 2 (safety factor) (1000 Gallons) [( (0.01651 ft3/lb) / (0.01605 ft3/lb) ) - 1]
= 57 (gallons)
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