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Basic pressure change over time

  1. Feb 25, 2015 #1
    Im tryng to solve an equation for how pressure changes over time in a container. It goes something like this

    There is a 10 liter sealed container(V1) with x amount of initial pressure (P1), and a 1 liter container attached to it (V2) with one valve that opens between them, and then another valve that opens to atmosphere. The initial pressure in the 1 liter attachment is atmospheric (P2).

    For each cycle the valve opens between the pressureised 10 liter container and the one liter at 1 atm, the pressure then equalizes in both containers. Then the inner valve is closed and the outer valve is opened on the 1 liter container and pressure is vented to atmosphere (so the 1 liter container returns to 1atm) then the outside valve is closed and the cycle continues.

    I need to find out after how many cycles does the large 10 liter container reach a certain pressure above 1 atm...

    I can figure out what the pressure is in the container after they equalize each time which is
    P= (P1*V1 +P2*V2)/(V1+V2)

    So lets say the initial pressure is of P1 is 2atm after the first cycle the pressure would be P = (2*10l +1l*1atm)/(1l+10l) = 1.91 atm

    then the second cycle would be P = (1.91*10l +1l*1atm)/(1l+10l) = 1.83 atm

    etc etc

    so what would be the equation t describe this pressure drop over a certain number of cycles? i.e. P(c) = ?
     
    Last edited: Feb 25, 2015
  2. jcsd
  3. Feb 25, 2015 #2

    Bystander

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    Okay.
    Now try it.
     
  4. Feb 26, 2015 #3

    Merlin3189

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    I'll have to accept your physics, because I don't know how to do that, but juggling your equation round and using V1, V2, and P2 as constants, I get a formula for Pn after n cycles, as

    ( (Pn ) -1 ) = ## (\frac {10}{11})^n ## ((P0) -1 )

    Edit - added excess brackets just to make clear
     
    Last edited: Feb 26, 2015
  5. Feb 26, 2015 #4

    Merlin3189

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    Or in a more general form

    ( Pn - Px ) = ( P0 - Px ) ##( \frac{V1}{V1 + V2})^n##

    Where Px is the sink pressure, P0 is the container starting pressure and Pn is the container pressure after n cycles.

    Edit - BTW this looks so nice to me, that I think your physics must be correct!
    Edit2 - and it looks as if you could start with container pressure below atmospheric as well.
     
    Last edited: Feb 26, 2015
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