Calculating Flow of Helium in a Verticle Pipe

[Q_Goest]

I have a long, 24" diameter vertical pipe. There is a flow of gas through this pipe in which pure helium enters at the top and exits at the bottom where it exits to atmosphere. In this case, there must be a gradient of gasses with helium at the top and air at the bottom and a mixture between the two due to diffusion.

My question is, what flow of helium is needed to keep this gradient constant? In other words, I want to maintain pure helium at some upper point in the pipe - so how can I determine the flow of helium needed to keep the air out?

I know it has to do with Fick's law but I've never had to do a calculation like this one. Any thoughts?

 

[Chestermiller]

I have a long, 24" diameter vertical pipe. There is a flow of gas through this pipe in which pure helium enters at the top and exits at the bottom where it exits to atmosphere. In this case, there must be a gradient of gasses with helium at the top and air at the bottom and a mixture between the two due to diffusion.

My question is, what flow of helium is needed to keep this gradient constant? In other words, I want to maintain pure helium at some upper point in the pipe - so how can I determine the flow of helium needed to keep the air out?

I know it has to do with Fick's law but I've never had to do a calculation like this one. Any thoughts?

The equation you are dealing with is $$V\frac{dC}{dx}=D\frac{d^2C}{dx^2}$$ where C is the concentration of the air, and v is the flow velocity of the helium.