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 :
Δ P = R p Q where R p is the resistance, Q the flow, and Δ P the pressure potential:
R p = 8 η L π R 4
with η = 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 ; Δ P = 2 bars
Thanks !
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Answers (1)

graffus1hb30
Answered 2022-05-09 Author has 16 answers
The Hagen Poiseuille (HP) equation you found can also be used in approximation for gases, as long as the pressure drop Δ P isn't too large.
Here we have:
Δ 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 ( m 3 s 1 ) Q 1 can be found.
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