How to get the velocity field from the pressure field
Hi,
I calculated the pressure field (in 2D) of air flowing through a graphite (porous material) using the finite difference method. Because I want to visualise the streamlines of the flow in the graphite I need to calculate first the velocity field. My question is: How can I calculate the velocity field (in 2D) if the pressure field is known ? 
For quasistationary flows in porous medium one uses Darcy law, where velocity is proportional to the pressure gradient. If it is your case, just take gradient of the pressure.

you should get plugged flow..
you should use BrinkmanForchheimerextended Darcy equation to get the flow field. A lot of research has been done on this, and you can find numerous journal papers written about it.. good luck 
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