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

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SUMMARY

The discussion focuses on determining the required tube length for Helium-4 flow at a temperature of 4.2K, specifically through a tube with an outer diameter of approximately 0.01 inches. The user seeks a reliable model to calculate the flow rate in moles or liters, noting discrepancies in existing equations for small diameters. It is established that when tube diameters fall below one millimeter, nano physics significantly influences flow characteristics, particularly for Helium-4, which behaves differently than conventional fluids.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly at low temperatures.
  • Familiarity with Helium-4 properties, including viscosity and flow characteristics.
  • Knowledge of nano-scale physics and its impact on fluid behavior.
  • Experience with pressure differentials and their effects on gas flow.
NEXT STEPS
  • Research nano fluid dynamics and its implications for small diameter tubes.
  • Study Helium-4 flow characteristics in low-temperature environments.
  • Explore mathematical models for calculating flow rates in micro and nano tubes.
  • Investigate existing literature on pressure drop calculations in small diameter gas flows.
USEFUL FOR

Researchers, engineers, and physicists working with cryogenics, particularly those involved in fluid dynamics at low temperatures and in nano-scale applications.

coolnessitself
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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?
 
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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.
 

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