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I'm looking for a pneumatic formula in order to have the flow. I found many formula, but only for hydraulic :

$\Delta P = R_p Q$ where $R_p$ is the resistance, $Q$ the flow, and $\Delta P$ the pressure potential:

$$R_p = \frac{8\eta L}{\pi R^4}$$ with $\eta =$ dynamic viscosity of the liquid ; $L =$ Length of the pipe ; $R =$ radius of the pipe

I don't know if I can use them, since I'm in pneumatic ! After doing research on the internet, I found some other variables like : sonic conductance, critical pressure coefficient, but no formula...

I think that I have all the information in order the calculate the flow : Pipe length = 1m ; Pipe diameter = 10mm ; $\Delta P =$ 2 bars

Thanks !

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  • $\begingroup$ If $\Delta P$ isn't too high, then you can use your 'hydraulic' formula as a good approximation. $\endgroup$
    – Gert
    Commented Apr 8, 2020 at 9:26
  • $\begingroup$ The formula you gave is valid only for laminar flow. For the situation you described the flow is going to be turbulent, and the formula will give the incorrect results. See Transport Phenomena by Bird, Stewart, and Lightfoot to learn how to determine the pressure drop-flow rate relationship for turbulent flow. $\endgroup$
    – Chet Miller
    Commented Apr 8, 2020 at 10:49
  • $\begingroup$ Thanks for the answer. But, I don't want to buy a 40$ book only for this question and I don't have the knowledge to understand this book. $\endgroup$
    – user676767
    Commented Apr 8, 2020 at 13:28

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The Hagen Poiseuille (HP) equation you found can also be used in approximation for gases, as long as the pressure drop $\Delta P$ isn't too large.

Here we have:

$$\Delta P=P_1-P_0$$

where $P_1$ is the pressure at the entrance of the pipe and $P_0$ at the outlet.

Once $Q$ has been estimated with HP, we can still apply a correction using the Ideal Gas Law. Assume the flow to be isothermal, then:

$$Q_0 P_0=Q_1 P_1$$

from which the corrected volume throughput $(\mathrm{m^3 s^{-1}})$ $Q_1$ can be found.

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  • $\begingroup$ Thank you for this answer. I'm still curious about the "real" way to calculate the flow. I have the impression (may be I'm wrong) that you're using some "tricks" here. Can't we have a "classic way" like the HP law for pneumatic application ? And how to calculate it, if you have large pression ? What's a large pressure drop for you ? $\endgroup$
    – user676767
    Commented Apr 8, 2020 at 10:02

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