Flow of gas into a vacuum system through an orifice

[Bcreative]

Hello, I'm sorry if this is in the wrong section but I recently took real interest in physics, particularly fluid mechanics, so this is my first post. Consider the following:

A glass system has a pump pulling gas out of the system, which has an orifice to the atmosphere at the opposite end of the system. How do you calculate the flow rate of gas into the system through the orifice?

 

[Q_Goest]

Hi Bcreative. Welcome to the board. The pressure ratio across an orifice with ambient pressure on one side and something close to a hard vacuum on the other results in what's known as "choked flow".

Here's a good site that describes it in easy to understand terms:
http://www.okcc.com/PDF/Choked Flow of Gases pg.48.pdf

These two sites provide equations and a bit more detail:
http://www.efunda.com/forum/show_message.cfm?start=1&thread=16827&id=16827
http://en.wikipedia.org/wiki/Choked_flow

The hard part about calculating the flow rate is determining the discharge coefficient for your orifice (C_d). The discharge coefficient is a function of the geometry and less so a function of velocity.