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Rate of air flow between containers of different pressures

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data
    I am given a container of volume V of pressure p filled with hydrogen gas. Outside the container, the volume can be taken as infinity and pressure can be taken as 0 (eg: in space). The temperature T is fixed throughout (there is a heat generator in the container that will maintain the temperature at T throughout the experiment).

    There is a small hole of area S at the side of the container. The shape of the hole and the location of the hole (with respect to the container) is not stated. My task is to find the time taken for the pressure inside the container to drop from p to p2.

    2. Relevant equations
    a) pV = nRT
    b) Dynamic pressure q = 0.5ρv2
    c) Mass flow rate dm/dt = CYS√(2ρΔp)

    where V = volume of container,
    n = number of moles of hydrogen,
    R = molar gas constant (8.31 J mol-1 K-1),
    T = temperature of gas in container,
    ρ = density of hydrogen in the container,
    v = rate of air flow through hole,
    C = coefficient of discharge,
    Y = expansion factor,
    Δp = difference in pressure, also = pressure in the container, since pressure outside is 0.

    3. The attempt at a solution
    The question I have is regarding the rate of flow of gas, given the pressure difference. I tried equation (b) but it seems to give me a contradiction, in that:
    p = p-0 = Δp = q = 0.5ρv2, and
    ρ = m/V = (2/1000)n/V = (2/1000)(p/RT)
    So p = 0.5(2/1000)(p/RT)v2, and
    v = √(1000RTp/p)
    v = √(1000RT) which is independent of p --- (does not seem to make sense)

    But if I try equation (c), I seem to be missing the values for C and Y, which is not stated in the question - or am I missing something?

    Once I am able to get the velocity of air flow (given pressure differences), or rate of air flow (whether in mass per unit time or volume per unit time), I should be able to evaluate the rest of the solution myself. Please help me with this, thanks!

    PS: My level of Physics is pre-University. This question is not in my homework but is for enrichment.
  2. jcsd
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