Partial Density

  • Thread starter womfalcs3
  • Start date
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.
 
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.
 
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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