# 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.

### Explosive Power of Superheated Water

*1 lb (0.45 kg)*of nitroglycerine >*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 of water can be expressed as

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

V_{net}= necessary expansion volume of water

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

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

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

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 Open Expansion Tank

The minimum volume of an open expansion tank for a system with *1000 gallons* of water heated from *68 ^{ o}F to 176^{ o}F* can with a safety factor

*2*calculated as

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

= 57 (gallons)

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