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Partial Density

  1. Feb 21, 2009 #1
    1. The problem statement, all variables and given/known data

    I am trying to integrate the momentum equation in the Navier-Stokes equations, and I need to make sure I have the density formulation correct. I'm unsure of my work because a lot of the terms in the end are canceling out.

    It's a two-phase mixture, so the sum of the partial pressures is:

    P = P_a+P_v

    Where a and v denote air and vapor, respectively.

    2. Relevant equations

    Ideal gas law

    density=P/(R_gas*T)

    3. The attempt at a solution

    Using the sum of partial pressures, I'm getting this for total density:

    [tex]\rho[/tex]=[tex]\rho_{a}*R_{a}/R[/tex]+[tex]\rho_{v}*R_{v}/R[/tex]

    Where R is the total gas constant.


    I am trying to find an equation for the total density in terms of the partial densities.
     
  2. jcsd
  3. Feb 21, 2009 #2
    Does the total density relation to the partial densities look correct?

    Intuitively, I was thinking total rho = rho_a + rho_v, but the equation, obviously doesn't support that.
     
  4. Feb 22, 2009 #3
    EDIT:I realize the images are big. I'm the process of scaling them down and re-uploading them.

    EDIT 2: Re-hosted and included updated images.

    I apologize for the bump, but can somebody please just go through this formulation and verify my work?

    It seems I am in fact eventually getting total density being the sum of partial densities.

    That kind of makes sense given Dalton's Law, but the specific gas constants throw my intuitive thinking off.

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