Volume to fill pneumatic spring at a pressure 1

[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

 

[MintJulep]

I get

Vn = [(Vinit + Vnew)/P0] - VinitPmax/P0

 

[MintJulep]

Oops


Vn = [(Vinit + Vnew)Pmax/P0] - VinitPmin/P0

 

[rulmismo]

Thanks for the reply but the units don´t match, and think that you didn´t take account that Pmin Pmax were relative pressure (manometric):

[volume]/[Pressure]-[Volume]*[Pressure]/[Pressure]

Anyway reviewing it I realised that my formula was wrong:

The correct I think it is:

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

(fill new volume) (increase pressure to Pmax
in the initial volume)

 

[MintJulep]

Much easier to convert all your pressures to absolute before you start.