# Calculating of Water Expansion Tanks

## Water expansion volume in open, closed and diaphragm expansion tanks

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 lb*_{f}(2 700 000 J)*1 lb (0.45 kg)*of water flashed into steam >*750 000 ft lb*_{f}(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

V_{net}= (v_{1}/ v_{0}) - 1 (1)

V_{net}= expansion volume of water (ft)^{3}, m^{3}

v_{0}= specific volume of water at initial (cold) temperature (ft^{3}/lb, m^{3}/kg)

v_{1}=specific volume of waterat operating (hot) temperature (ft^{3}/lb, m^{3}/kg)

### Open Expansion Tanks

Required volume of an open expansion tank can be expressed as

V_{et}= k V_{w}[(v_{1}/ v_{0}) - 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)

v_{0}= specific volume of water at initial (cold) temperature (ft^{3}/lb, m^{3}/kg)

v_{1}=specific volume of waterat operating (hot) temperature (ft^{3}/lb, m^{3}/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

V_{et}= k V_{w}[( v_{1}/ v_{0}) - 1] / [( p_{a}/ p_{0}) - ( p_{a}/ p_{1})] (3)

where

p_{a}= atmospheric pressure - 14.7 (psia)

p_{0}= system initial pressure - cold pressure (psia)

p_{1}= system operating pressure - hot pressure (psia)

- initial temperature
*50*^{o}F - initial pressure
*10 psig* - maximum operating pressure
*30 psig*

### Diaphragm Expansion Tanks

Required volume in a diaphragm expansion tank

V_{et}= k V_{w}[( v_{1}/ v_{0}) - 1] / [1 - ( p_{0}/ p_{1})] (4)

- initial temperature
*50*^{ o}F - 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 ^{ o}F to 176^{ o}F*.

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

V_{et}= 2 (1000 gallons) [((0.01651 ft^{3}/lb) / (0.01605 ft^{3}/lb)) - 1]

= 57 (gallons)

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