Variable denisty in the contiuity and momentum equaiton

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To address variable density in continuity and momentum equations, incorporating equations of state is essential, such as P = ρRT, where ρ represents density. This relationship ensures that density is linked to pressure and temperature, allowing for a more accurate representation of fluid behavior. When solving these equations, both velocity and density become interdependent variables, complicating the solution process. Utilizing numerical methods or iterative approaches may be necessary to handle the coupled equations effectively. Understanding the physical context of the flow will also guide how density varies in your specific application.
hoomanya
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Hi,

I am writing a code for a flow with a low degree of in-compressibility. So in my continuity and momentum equations, the density varies. I have never worked with variable density before so I was wondering, how does one usually decide on how the density varies and go on about solving these equations where you have velocity and density as unknowns in the continuity equations.

I would appreciate any hints.

Thanks,

H
 
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You have to include equations of state.

Such as P=rho*R*T
rho = density

Then your momentum and energy equations are no longer uncoupled.
 

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