I am familiar with isothermal and adiabatic ideal gas compression problems where a force is exerted on a piston of area A to move it some displacement in order to calculate work done. However I am looking for how to calculate the time needed needed to move the piston head and compress the gas.

In my actual problem I have water entering one side of a piston at pressure Pw and flow rate Qw. The other side of the piston is filled with air at Pa.

I know the friction resistance of the piston seals, I know the piston mass, I know the force applied to piston by water pressure, and I know the gas properties. I would like to know how to find how long it takes for the force to compress the gas down and equalize the gas pressure with the force exerted. I believe this would be a power equation where P=W/t?

  • $\begingroup$ Flow rate and volume should define the time… $\endgroup$
    – Solar Mike
    Commented Sep 30, 2022 at 13:59
  • $\begingroup$ I figured that would be a part of it, however the fill rate should exponentially slow down to zero as the air pressure approaches the force applied by the water. Until the system comes to rest at equilibrium, I want to know how long it takes to reach that equilibrium. $\endgroup$
    – Austin Fox
    Commented Sep 30, 2022 at 14:24
  • $\begingroup$ You may need some conditions upstream, like what happens to the flow rate when the pressure at the piston is increased. $\endgroup$ Commented Sep 30, 2022 at 20:39
  • 1
    $\begingroup$ I think this question is answered here: physics.stackexchange.com/questions/37634/… $\endgroup$
    – J. Ari
    Commented Oct 1, 2022 at 18:18


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