Calculating/Estimating velocity from pressure driven-flow

I'm aware of this simple question, but….

I do have pressure driven flow, where Pinlet = a * Poutlet for a > 0. It is not a channel, but a 3D "cavity" so I use Periodic Boundary Conditions everywhere except in the inlet and outlet. I do have the value of the density, pressure for ideal gas (i.e. P = density R T) but no velocity values are known at all. My question is: How can I calculate/estimate the flow velocity created in the inlet due to the pressure difference?. Please, any other assumption is possible here.

Even if I assume • points 1 and 2 lie on a streamline, • the fluid has constant density, • the flow is steady, and

• there is no friction. i.e. Bernoulli, then, I need a certain value of a velocity. There is no stagnation, and thereby no where to estimate/calculate the total(stagnation) pressure to be used to determine the velocity latter, so. . . What to do?

Thanks Mecobio

Hi Mecobio

I think you are talking about the so called Poiseuille flow. Take a look at any book of Fluid Mechanis and/or one of these pages:

http://scienceworld.wolfram.com/phys...minarFlow.html http://galileo.phys.virginia.edu/cla...ds2/node6.html http://www.timedomaincvd.com/CVD_Fun...ug_n_Pois.html http://lions.math.hr/tok-kroz-cijev/...euille_en.html http://en.wikipedia.org/wiki/Poiseuille_Flow

Also: http://www.outgribe.com/jason/hagenp/hagenp.html http://www.columbia.edu/cu/gsapp/BT/...os/plates.html www.algarcia.org/Pubs/YihaoRGD02.pdf