Page 411 - The City and Guilds Textbook: Plumbing Book 1 for the Level 3 Apprenticeship (9189), Level 2 Technical Certificate (8202) and Level 2 Diploma (6035)

Chapter 6 Hot water systems

The scientific principles of expansion vessels
The principle of an expansion vessel is that a gas is compressible but liquids
are not. That principle is based upon Boyle’s law. In this case, the gas is air or
nitrogen and the liquid is water.

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Boyle’s law states:
The volume of a gas is inversely proportional to its absolute pressure provided that the temperature
remains constant.
In other words, if the volume is halved, the pressure is doubled.
Mathematically, Boyle’s law is expressed as P V = P V
2 2
1 1
Where:
P = Initial pressure = 1 bar
1
V = Initial volume = 20 litres
1
P = Final pressure = to be found
2
V = Final volume = 20 litres − 10 litres of expanded water
2
So, to find the pressure in the vessel, the formula must be transposed:
P × V 1
1
P =
2
V 2
Therefore:
1 bar × 20 litres
P =
2
10 litres
= 2 bar final cold pressure
If, on the initial cold fill of the system, the vessel required, say, 5 litres of water to be taken in, the air pressure to
apply to the vessel can be calculated. We can assume a water pressure of 1 bar.
P = 1 bar
1
V = 20 litres
1
V = 20 litres − 5 litres = 15 litres
2
P = Pressure to be calculated
2
P × V 1 1 bar × 15 litres
1
P = = = 0.75 bar
2
V 2 20 litres
The capacity left in the vessel after the initial fill is 15 litres with a cold fill pressure of 1 bar and, if 10 litres of
water are to expand inside the vessel, the final pressure of the system will be:
P × V 1 1 × 15 15
1
= = = = 3 bar
P 2
V 2 15 – 10 5
The initial pressure of the empty 20-litre vessel was 0.75 bar. On initial cold fill, 5 litres of water entered the
vessel, reducing the capacity to 15 litres. As a result, the air was compressed even more when the expansion of
water takes place and, instead of 2 bar final pressure, the pressure when the water is heated will be 3 bar.

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