1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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?

  4. Jun 20, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook