Fluid Dynamics Questions

1. Sep 25, 2008

Michael K

I am trying to solve for the temperature/pressure profiles of a small closed-end (one side) tube inside a pressurized container kept at constant temp./pressure. For now, I am assuming that vacuum conditions exist within the tube. I am not sure, however, which equations I should be using.

Initially I reasoned as follows: For molecules just entering the tube opening (at t=0) I would have to use effusion rates to calculate P(t) existing at the opening; and then, afterwards, plug this into Poiseuille's equation to get a picture of overall pressure buildup over time. Is this correct? Do I need to work with effusion rates, or, is there some other, more correct, (or, better) way to solve this?

Also, I am aware that the effusion equation only applies to conditions where the area of the hole is smaller in scale to the mean free paths of gaseous molecules. The scenario I am working with calls for a tube diameter within mm range (length is ~ meter range) at pressures above atm (2-3) and temperatures above 100 C. I believe that the equation no longer apllies. Is this correct? Are there any alternatives?

Finally, I have solved the differential eqn. for effusion into a vacuum, but I believe that my answer is incorrect because I assumed temperature remains constant. Can I make this assumption? If not, how do I rectify my diff. eqn? ( dP/dt = kT/V dN/dt, where dN/dt =
(Po -P(t))A / sqrt(2piMRT) Po = pressure of container, k = Boltzman's constant M = molecular mass, A = area)

Any help would be appreciated.