Calculating Expansion Tanks

Calculating expansion volume in open, closed and diaphragm expansion tanks

An expansion tank is required in a heating, cooling or air condition system to avoid an unacceptable increase of the system pressure during heat-up.

Expansion tanks are in general designed as

• open tanks
• closed compression tanks
• diaphragm tanks

The net expansion of water can be expressed as

V_net = (v₁ / v₀) - 1 (1)

V_net = necessary expansion volume of water (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)

Open Expansion Tanks

Required volume of open expansion tanks can be expressed as

V_et = k V_w [(v₁ / v₀) - 1] (1)

V_et = required expansion tank volume (gallon, liter)

k = safety factor (approximately 2 is common)

V_w = 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)

An open expansion tank has the disadvantage of allowing air to enter the system via absorption in the water. In general it must be located in the top of the building where it also 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

V_et = k V_w [ ( v₁ / v₀ ) - 1 ] / [ ( p_a / p₀ ) - ( p_a / p₁ ) ] (2)

p_a = atmospheric pressure - 14.7 (psia)

p₀ = system initial pressure - cold pressure (psia)

p₁ = system operating pressure - hot pressure (psia)

• initial temperature 50^oF
• initial pressure 10 psig
• maximum operating pressure 30 psig

Diaphragm Expansion Tanks

The required tank volume of diaphragm expansion tank can be calculated as

V_et = k V_w [ ( v₁ / v₀ ) - 1 ] / [ 1 - ( p₀ / p₁ ) ] (3)

• 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

V_et = 2 (safety factor) 1000 (Gallons) [(0.01651 (ft³/lb) / 0.01605 (ft³/lb) ) - 1]

= 57 (gallons)

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