# Compressible flow or incompressible flow equation?

• ulfaazmi

#### ulfaazmi

Hello everyone..
I am using 2-dimension Navier Stokes equation, but I confused that my problem is compressible or incompressible flow form, because if I have initial pressure and temperature and velocity for x-axis only in one grid that they are so very high but the others grid are zero. Can I consider the equation is compressible flow??

Thank you

Is it a liquid or a gas?

• ulfaazmi
Is it a liquid or a gas?
It is Nitrogen gas.

It is Nitrogen gas.
Then the flow is compressible. Can you provide more details on your difficulty?

• ulfaazmi
Then the flow is compressible.
But the effects of compressibility might be negligible. You should compute the highest local Mach number $$Ma=U/c$$ in your flow. If it is smaller than say 0.1, the effects of compressibility can be ignored and you can use the incompressible Navier Stokes equations. If it is higher than 0.3, then you should definitely use the compressible form.

• ulfaazmi
Then the flow is compressible. Can you provide more details on your difficulty?

Not necessarily. Gas flows can be simplified as incompressible depending on the details - you should look at pressure variation thoughout your flowfield, as well as local mach numbers. If your pressure variations are small relative to the overall static pressure and the local mach number never exceeds 0.3 or so, you can reasonably treat the problem as incompressible.

• ulfaazmi
But the effects of compressibility might be negligible. You should compute the highest local Mach number $$Ma=U/c$$ in your flow. If it is smaller than say 0.1, the effects of compressibility can be ignored and you can use the incompressible Navier Stokes equations. If it is higher than 0.3, then you should definitely use the compressible form.

Thank you for your help, actually the driving force of flow is caused by pressure. So, initially the flow is in a steady state in a closed horizontal pipe until pressure is introduced into that flow caused by a high speed projectile hits the wall of pipe. It also affecting temperature becomes higher at the area exactly in the center of the left side of pipe. Can I guess the velocity can be obtained from the equation :
P = ρ/U ?

Not necessarily. Gas flows can be simplified as incompressible depending on the details - you should look at pressure variation thoughout your flowfield, as well as local mach numbers. If your pressure variations are small relative to the overall static pressure and the local mach number never exceeds 0.3 or so, you can reasonably treat the problem as incompressible.
Then the flow is compressible. Can you provide more details on your difficulty?
Thank you for your help, actually I have problem to get the correct equation of my study. I am difficult to converting the equation into the non dimensional system because the condition is not clear yet. If it doesn't bother you, would you like to check my equation, I will send it in a picture because it is difficult to write here, also include with the illustration of my problem??

Thank you for your help, actually I have problem to get the correct equation of my study. I am difficult to converting the equation into the non dimensional system because the condition is not clear yet. If it doesn't bother you, would you like to check my equation, I will send it in a picture because it is difficult to write here, also include with the illustration of my problem??
Sure. Let's see what you got. Just upload it.

• ulfaazmi
An illustration of your problem would be very helpful for us to determine the best approach to take.

• ulfaazmi I attached my picture file in this link (https://drive.google.com/drive/u/0/folders/1CTWibwiW33ngNlEEWQLOIKGgMj5I9-sv), I am really pleasure if you would like to help me.

Thank you very much.