Calculating Expansion Tanks

Calculating expansion volume in open, closed and diaphragm expansion tanks

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

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 an open expansion tank can be expressed as

V_et = k V_w [(v₁ / v₀) - 1]     (2)

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)

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

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

where

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 ) ]         (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

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

    = 57 (gallons)

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