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Calculating of Water Expansion Tanks

Water expansion volume in open, closed and diaphragm expansion tanks

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Expansion tanks are required in heating, cooling or air condition system to avoid unacceptable increases of system pressures when water expands during heat-up.

Explosive Power of Super-heated Water

  • 1 lb (0.45 kg) of nitroglycerin > 2 000 000 ft lbf (2 700 000 J)
  • 1 lb (0.45 kg) of water flashed into steam > 750 000 ft lbf (100 000 J)

Expansion tanks are in general designed as

  • open tanks
  • closed compression tanks
  • diaphragm tanks

Net expansion volume of water when heated can be expressed as

Vnet = (v1 / v0) - 1                                      (1)

Vnet = expansion volume of water (ft3, m3)

v0 = specific volume of water at initial (cold) temperature (ft3/lb, m3/kg)

v1specific 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)

v1specific volume of water at operating (hot) temperature (ft3/lb, m3/kg)

Note that in an open expansion tank fresh air is constantly absorbed in the water and tends to corrode the system. Open expansion tanks must also be located above the highest heating element, in general on the top of buildings, where they may be exposed to freezing.

Closed Compression Expansion Tanks

Closed compression tanks can be designed as

  • adjustable expansion tanks - air is evacuated or injected by automatic valves to the tanks to control system pressures when temperature and expansion of water rises or falls
  • pump-pressured cushion tanks - water is evacuated or injected to the systems to compensate for temperature rise or fall
  • compression tanks with closed gas volumes - the tanks contains specific volumes of gas which is compressed when temperatures and system volumes increase

Required volume in a closed expansion tank

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

Required volume in a diaphragm expansion tank

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 in Open Expansion Tank

A system with 1000 gallons of water is heated from 68 oF to 176 oF.

Minimum expansion volume in an open expansion tank with a safety factor 2 can be calculated as

Vet = 2 (1000 gallons) [((0.01651 ft3/lb) / (0.01605 ft3/lb)) - 1]

    = 57 (gallons)

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