What Tube Length Is Needed for Helium-4 Flow at 4.2K?

[coolnessitself]

I've got a very small tube (about .01" outer diameter, I can't recall the inner diameter $D$ at the moment) of length $L$. It's going to run from a helium bath to a near vacuum ($\Delta P$ ). I'm trying to calculate the length of this tube required to get a flow of $\dot{N}$ (in mols or liters for example) of Helium-4 (viscosity $\eta$) through the tube at temp $T=4.2K$. Several equations I've looked at have given drastically different results, and I'm guessing they just fail in this regime of something very small. Anyone know a good model or approx for this type of thing?

 

[cliff]

I can't offer much help on a correct formula. But I'll throw this in as a general comment. When the diameter of a tube becomes less than a millimeter, the laws of nano physics start coming into play with the ever decreasing diameter of the tube. And then there is the flow characteristics of Helium 4. That in itself goes against the norm in flow characteristics in the normal world. Still... there is quite a bit on the web on nano flows.