Dear Kaleem,

Maybe it is obvious to others, but I do not understand the term "static chamber", do you mean it stationary in space or maybe just constant volume?

I am happy to think along, but you will have to provide more information. Is it adiabatic or isothermal, for instance. And is the flow rate small or large or in other words: what is the overall pressure compared to the expected pressure gradient (due to the flow)?

If the flow rate is fast, information on the entry and exit of the vessel may also be required although there is not much theoretical development there.

Ger

Kaleem,

Is the vessel initially evacuated?

If so, this is a trivial matter of integrating the flow rate (which will be pressure dependent - presumably).

If the vessel is not initially evacuated, and is open in some manner to ambient air, then this is a more complex problem, and you will need to know the size of the 'leak' and its geometry.

Which is it?

"@ james The initially pressure of the chamber is 10-6 torr @ koper flow rate is same.. 

Does the "static chamber" also have an exit valve or port, such that the pressure remains constant, or is the static chamber "air tight" except for the inflow port? Also, is the static chamber thermally insulated? If so, you are dealing with an adiabatic change. If the chamber is under temperature control, the situation is isothermal, as Ger Koper has implied.

You will have described a non-equilibrium situation if there is no escape port. As a gas expands into a vacuum, the pressure will not be constant, both on the average, and because the pressure of expanding gases will depend on the distance from the inflow port. Pressure is an intensive variable only at equilibrium. Equations of state apply to systems at equilibrium. The total pressure at any instance may be lower than that in an equilibrium situation, all else being equal, because of the higher concentration of clusters in the expansion situation.

Assuming your flow rate is low and constant, you should be able to estimate the number of moles of gas flowing into the chamber per unit time. If the chamber is large and evacuated, the pressure will be low and maybe you could use one of the more simplified equations of state. As pressure and temperature increase in the limit of high pressure, the gas will become less and less ideal, especially because an expanding gas is not at equilibrium. 

I'm not sure if any of this helps, but good luck with your project.

Dr. M.G. Ceruti