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Does the Hagen-Poiseuille equation work for controlling vacuum induced flow via a tube? Decreasing the flow rate induced by vacuum via control of the radius of the tube and the length is the issue.

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  • $\begingroup$ Ignoring viscosity, what is the formula, including Darcy-Weisbach considerations, for relating vacuum pressure in mmhg (P1) to the length a tube of 4mm I.D. to achieve P2 flow rate at 2l/minute? Thanks for first answer $\endgroup$
    – N2bate
    Dec 9, 2016 at 20:11

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"Vacuum" may mean several things. If it is just lower pressure and laminar flow, the answer is yes. But for me vacuum means that one is in the Knudsen regime, with the tube limiting the mean free path. So this does not work for ultra-high vacuum equipment.

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Yes, the Hagen-Poiseuille equation just tells you the pressure gradient for a given flow rate, viscosity and tube dimensions. It doesn't matter how the pressure gradient is created. As long as the flow is laminar the Hagen-Poiseuille equation will apply.

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  • $\begingroup$ Small comment: at sufficiently high flow rates, the input pressure of the tube is no longer atmospheric pressure and this will affect the result. It might be argued that by the time this is a significant factor, you no longer have laminar flow, and there are bigger issues... $\endgroup$
    – Floris
    Dec 8, 2016 at 18:55

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