Variable denisty in the contiuity and momentum equaiton

In summary, variable density in fluid dynamics refers to the fact that the density of a fluid can change at different points in space or time, and is often affected by factors such as temperature, pressure, and composition. This affects both the continuity and momentum equations, as it must be accounted for in order for the equations to be accurate. Variable density is important in real-world scenarios such as weather patterns, ocean currents, and airflow around aircraft. Scientists use various methods, such as empirical data or numerical methods, to account for variable density in fluid dynamics calculations.
  • #1
hoomanya
90
0
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
 
Engineering news on Phys.org
  • #2
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.
 

FAQ: Variable denisty in the contiuity and momentum equaiton

What is meant by variable density in the continuity and momentum equations?

Variable density refers to the fact that the density of a fluid can change at different points in space or time. This is often the case in fluid dynamics, as density can be affected by factors such as temperature, pressure, and composition.

How does variable density affect the continuity equation?

In the continuity equation, variable density is accounted for by including a term for the change in density over time. This is necessary because if density is changing, the amount of fluid flowing through a particular point in space will also change, and this must be taken into consideration for the equation to be accurate.

What impact does variable density have on the momentum equation?

Variable density affects the momentum equation in a similar way to the continuity equation. It is included in the equation through a term that accounts for the change in density over time. This is important because as density changes, so does the momentum of the fluid, and this must be accounted for in the equation.

What are some examples of situations where variable density is important in fluid dynamics?

Variable density is important in many real-world scenarios, such as weather patterns, ocean currents, and airflow around aircraft. In these situations, factors such as temperature, pressure, and composition can cause the density of the fluid to vary, and this must be taken into account for accurate predictions and calculations.

How do scientists account for variable density in fluid dynamics calculations?

There are various methods for accounting for variable density in fluid dynamics calculations, such as using empirical data to determine the relationship between density and other factors, or using numerical methods to solve the equations for variable density. It ultimately depends on the specific situation and the accuracy needed for the calculations.

Similar threads

A How to show spin ##= \pm 2/\omega## for a circ-polarized gravity wave
Replies
0
Views
616
FAVRE-average: Compressible or just varying density
Replies
6
Views
2K
Does viscosity vary with temperature for liquids and gases?
Replies
1
Views
4K
Time to empty gas cylinder (problem worked, but would like feedback)
Replies
7
Views
2K
B The physics of flywheel launchers (like tennis ball shooters)
2
Replies
60
Views
1K
Height to time equation: water cylinder with pinhole
3
Replies
70
Views
5K
I Momentum-Position vs. Energy-Time Uncertainty Relations
Replies
10
Views
2K
I Conservation of Mass for Compressible Flow
Replies
33
Views
3K
A How to Solve Isothermal Incompressible Navier-Stokes for Compressible Fluid?
Replies
20
Views
6K
Automotive Finding the Peak Pressure of a Diesel Injection Pump
Replies
9
Views
3K

Hot Threads

Recent Insights

Back
Top