 # Pneumatic flow formula I'm looking for a pneumatic formula in order to have the flow. I found many Yaritza Oneill 2022-05-08 Answered
Pneumatic flow formula
I'm looking for a pneumatic formula in order to have the flow. I found many formula, but only for hydraulic :
$\mathrm{\Delta }P={R}_{p}Q$ where ${R}_{p}$ is the resistance, $Q$ the flow, and $\mathrm{\Delta }P$ 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 ; $\mathrm{\Delta }P=$ 2 bars
Thanks !
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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 $\mathrm{\Delta }P$ isn't too large.
Here we have:
$\mathrm{\Delta }P={P}_{1}-{P}_{0}$
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:
${Q}_{0}{P}_{0}={Q}_{1}{P}_{1}$
${Q}_{0}{P}_{0}={Q}_{1}{P}_{1}$
from which the corrected volume throughput $\left({\mathrm{m}}^{3}{\mathrm{s}}^{-1}\right)$${Q}_{1}$ can be found.