For the benefit of anyone who finds the technical aspects of this rather confusing (which includes me), I offer this simplified explanation of how I think an accumulator might work. Corrections will be gratefully received - I'm on a learning curve too.
The function of an accumulator depends on the physical properties of the air sealed in it, particularly in relation to pressure and volume. These are determined by Boyle's Law, which states that for a gas such as air any increase in pressure results in a decrease in volume, and vice versa, so that pressure x volume is always the same (a constant), providing temperature remains the same. In this case pressure means absolute pressure which is gauge pressure (what we normally use) + atmospheric pressure.
For example if we start of with a bag of air at atmospheric pressure (1 bar absolute) with a volume of 10 litres, then we immerse it in water 10 metres deep (atmospheric pressure + 10 metres head of water (1 bar) = 2 bar) the volume will then be 5 litres. Doubling the pressure causes the volume to halve.
To take a more practical example with an accumulator of 200 litres volume and a precharge pressure of 0.5 bar gauge pressure (1.5 bar absolute pressure - gauge pressure + atmospheric pressure), a static mains pressure of 2 bar gauge (3 bar absolute) and a dynamic pressure at the outlet tap of only 0.5 bar gauge (1.5 bar absolute) with a flow of 10 litres/minute. (The low dynamic pressure and flow rate at the tap is of course the problem that the accumulator tries to solve.)
With no flow (tap turned off) the mains pressure (3 bar absolute) will apply throughout the system, so the air in the accumulator which occupied 200 litres at 1.5 bar (absolute) will now be compressed to 100 litres at 3 bar (absolute). Consequently the 200 litre vessel will now contain 100 litres of water at mains pressure.
When the tap is opened and assuming an initial flow of say 20 litres/minute, the dynamic pressure will start off at 3 bar (absolute) but gradually decrease (quickly at first) as the accumulator discharges its water store. As the pressure drops the flow rate from the tap will decrease, the proportion of flow from the accumulator will decrease and the proportion directly from the mains will increase until eventually the accumulator has fully discharged, the dynamic pressure is back to 1.5 bar (absolute) and the flow rate down to 10 litres/minute, all from the mains.
In the above example with 100 litres of stored water at 2 bar (gauge), the duration of the benefit of the accumulator might last (I would guess) about 10 to 20 minutes in total, although the benefit might only be substantial for about 5 to 10 minutes. I think the actual calculation would be quite complicated since the overall flow rate and the proportion of flow from accumulator and mains are constantly changing - I suspect calculus would be involved!
In practice a pressure boost from 0.5 bar (gauge) and 10 litres/minute to (again just guessing here) over 1 bar (gauge) and at least 15 litres/minute for up to 10 minutes might be very welcome indeed. Obviously higher or lower mains (static) pressures and larger or smaller accumulators would affect the results.
The function of an accumulator depends on the physical properties of the air sealed in it, particularly in relation to pressure and volume. These are determined by Boyle's Law, which states that for a gas such as air any increase in pressure results in a decrease in volume, and vice versa, so that pressure x volume is always the same (a constant), providing temperature remains the same. In this case pressure means absolute pressure which is gauge pressure (what we normally use) + atmospheric pressure.
For example if we start of with a bag of air at atmospheric pressure (1 bar absolute) with a volume of 10 litres, then we immerse it in water 10 metres deep (atmospheric pressure + 10 metres head of water (1 bar) = 2 bar) the volume will then be 5 litres. Doubling the pressure causes the volume to halve.
To take a more practical example with an accumulator of 200 litres volume and a precharge pressure of 0.5 bar gauge pressure (1.5 bar absolute pressure - gauge pressure + atmospheric pressure), a static mains pressure of 2 bar gauge (3 bar absolute) and a dynamic pressure at the outlet tap of only 0.5 bar gauge (1.5 bar absolute) with a flow of 10 litres/minute. (The low dynamic pressure and flow rate at the tap is of course the problem that the accumulator tries to solve.)
With no flow (tap turned off) the mains pressure (3 bar absolute) will apply throughout the system, so the air in the accumulator which occupied 200 litres at 1.5 bar (absolute) will now be compressed to 100 litres at 3 bar (absolute). Consequently the 200 litre vessel will now contain 100 litres of water at mains pressure.
When the tap is opened and assuming an initial flow of say 20 litres/minute, the dynamic pressure will start off at 3 bar (absolute) but gradually decrease (quickly at first) as the accumulator discharges its water store. As the pressure drops the flow rate from the tap will decrease, the proportion of flow from the accumulator will decrease and the proportion directly from the mains will increase until eventually the accumulator has fully discharged, the dynamic pressure is back to 1.5 bar (absolute) and the flow rate down to 10 litres/minute, all from the mains.
In the above example with 100 litres of stored water at 2 bar (gauge), the duration of the benefit of the accumulator might last (I would guess) about 10 to 20 minutes in total, although the benefit might only be substantial for about 5 to 10 minutes. I think the actual calculation would be quite complicated since the overall flow rate and the proportion of flow from accumulator and mains are constantly changing - I suspect calculus would be involved!
In practice a pressure boost from 0.5 bar (gauge) and 10 litres/minute to (again just guessing here) over 1 bar (gauge) and at least 15 litres/minute for up to 10 minutes might be very welcome indeed. Obviously higher or lower mains (static) pressures and larger or smaller accumulators would affect the results.
