# Partial Density

#### womfalcs3

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:

$$\rho$$=$$\rho_{a}*R_{a}/R$$+$$\rho_{v}*R_{v}/R$$

Where R is the total gas constant.

I am trying to find an equation for the total density in terms of the partial densities.

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#### womfalcs3

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.

#### womfalcs3

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.

"Partial Density"

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