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Pressure drop w.r.to time through a orifice dia(D) in a container of volume (V)

  1. Jun 19, 2012 #1
    Let initial preasure (P) = 10 bar,volume of container (V)=100000 cubic cm.
    At what time period pressure will become 5 bar.
     
  2. jcsd
  3. Jun 20, 2012 #2

    Andrew Mason

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    What kind of a substance is in the container? A gas or a liquid? If it is a gas, is it an ideal gas? Is it escaping against atmospheric pressure of 1 bar?

    AM
     
  4. Jun 20, 2012 #3

    haruspex

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    I make no guarantees for the correctness of this, but here's what I got.
    Let vol of tank be V, pressure P(t), mass remaining in tank m(t), outlet area A, exit velocity f(t).
    In time dt, a volume A*f.dt, mass (Afm/V).dt, exits.
    Assuming adiabatic expansion:
    P(t+dt)(V+Af.dt)γ = P(t)Vγ, where γ = 1.4
    whence
    P' = -PγAf/V
    m' = -fAm/V
    By conservation of energy
    (P-Pa)Af.dt = Af3m.dt/2V
    where Pa is ambient pressure.
    I forgot about Pa at first, and obtained
    (γ-1)At = ((P0/P)(1-γ)/2γ - 1)√(2Vm0/P0)
    where P0 = P(0), m0 = m(0).
    I might try to correct that tomorrow.
     
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