I have designed a flow resistance element and I would like to be able to keep the total pressure drop across the element to < 5.0 inches of water (from 5cc/min to 5,000 cc/min). I have run some bench tests on the current design and the pressure drops are a bit too high. I would like to avoid changing the diameter of the bore and would prefer to shorten the length of the flow path. What would be the best way to calculate the ideal flow path length to achieve the pressure drops I am looking for?
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Use the Darcy-Weisbach equation and the Swanee-Jain correlation in order to calculate the pressure drop and the friction factor:
$pressure drop = rho*f*(L/D)*v^2/2 $
And this formula (the first one): https://es.m.wikipedia.org/wiki/Ecuación_de_Swamee-Jain
Where rho is the density, f the friction factor, L the ideal length, D the diameter and v the speed.
Finally, K is the absolute roughness and are the Reynolds number.
If your element isn't exactly a pipe, you can model it as a pipe by using the equivalent length:
https://www.cedengineering.com/userfiles/Pneumatic%20Conveying%20Systems.pdf
Go to page 57.