Volume to fill pneumatic spring at a pressure

[rulmismo]

Hi, I am reviewing a pneumatic calculation. One step is to calculate how many liters of air (at normal conditions) are needed to fill up some pneumatic springs.

The calculation does the following for getting the volume to add needed (Vn) to get a predefined pressure, (liters at normal conditions):

Vn = Vnew * (pmax + p0) + Vinitial * (pmax - pmin)
OR ALSO SAYS THAT CAN BE DONE:
Vn = Vinitial * (pmax - pmin) / p0

where:
Pmax: final pressure to get (manometric in bar)
Pmin: initial pressure of the spring (manometric in bar)
P0: atmospheric pressure (absolute, 1 bar)
Vinitial: initial volume
Vnew: Increase in volume of the spring due to the pressure increment.
Vn:volume of air in normal conditions to add to the spring in order to get the final pressure.

I don´t really trust this formulae, applying Boyle I have got:

considering no volume change and manometric pressures Pmin Pmax:
Vn = Vinitial * (pmax - pmin)/(pmin + p0)

considering volume change Vnew and manometric pressures Pmin Pmax:
Vn = Vnew*(pmax+p0)/p0 + (pmax - pmin) * Vinitial / (pmin + p0)

What do you think? am I correct? or you see some logic to the original formulae that I can´t understand?

Regards

 

[Navin A S]

,Your formulae appear to be correct. The logic behind the original formula is that the volume of air (Vn) needed to fill up the pneumatic springs is equal to the initial volume (Vinitial) multiplied by the difference in pressure (pmax - pmin), plus the increase in volume due to the pressure increment (Vnew) multiplied by the sum of the maximum pressure (pmax) and atmospheric pressure (p0).