Pressure drop over time

[htsmech]

I have a system that uses a bellows to pressurize air in a fluid reservoir with a small exit tube. I am trying to model the flow rate of the fluid over time. I am assuming PV=C, and that dV/dt=(P-Pa)*K, where C and K are constants.

The air volume (including bellows) is large compared to the fluid volume, so the change in fluid volume will not track the change in air volume very quickly. I need to find out how quickly.

I am assuming PV=C, and that dV/dt=(P-Pa)*K, where C and K are constants that I can estimate.

Is this a valid model? If so, how do I solve the ODE? I get to dV/dt=CK/V-Pa*K, but the V in the denominator throws me.

Thanks,

Steve

 

[Cockroach]

No, I think this is wrong. Your statement "PV=C" is valid only given isothermal applications; clearly this is not the case for compressable flows, squeezing gas liberates heat for example. Therefore your "large air volume" working with a bellows as a pumping mechanism would certainly promote exothermic contraction, endothermic expansion.

Without additional information on your setup, you may need to revisit the various laws of thermodynamics. I'm thinking "unsteady state, unsteady flow" or USUF models associated with the subject.

Maybe for the benefit of others who will review this post, you could be more specific and give numbers?

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada