I'm trying to figure out how to calculate leak rate for various materials used for elastic vacuum seals (such as Viton) from permeation coefficient K. I'm basing this on values from a paper referenced below. The units provided in the paper are m2 s-1 hPa-1. A similar combination of unit I have seen is cm3 cm/cm2 s-1 atm-1.
Leak rate is then F = K A (p1 - p0) / d, where A is exposed area of the seal, d is the thickness of the seal, and (p1 - p0) is the pressure differential. Since I'm dealing with vacuum systems, this can be assumed to be 1 atm (~1000 hPa). The A / d term is the reason for the cm / cm2 portion of the units combination, or if you combine all the distance units, you get something like m2.
Where I get confused is if you work through this equation, you end up with m3 / sec. However, leak rates are usually stated with units such as Torr liter / sec. Which makes sense, because the pressure-volume product defines a molecular quantity of gas (it's the left-hand side of the Ideal Gas Law, PV = nRT). Specifying just the volume is meaningless. So there is a quantity of pressure missing somewhere?
Sometimes, I see the units include "std" - what is this unit in reference to?
Thanks for the all help!
Paper: Journal of Geophysical Research (2004) vol 109, D04309, "Permeation of atmospheric gases ..." by P. Sturm et al.
Hey,
I didnt understand your problem clearly, but your equation reminds me Darsi formula for liquids:
K=S*v*d/(P1-P0)=[m3*(Pa*s)*m]/[m2*s*Pa]=m2, where S is speed of filtration=m3/[m2*s]=m/s, v - viscosity of liquid=Pa*s, d - distance of filtration (m), P - pressure (Pa), K- coefficient of permiability (m2).
If we exclude from this formula viscosity, we end up with K=S*d/(P1-P0)=(m3*m)/(s*m2*Pa)=m2*s-1*Pa-1 as you found in paper.
S=F/A=[m3/s]*m2, where F - volume of liquid filtrtion for 1 sec., A-area of tube cutting.
F/A=[K*(P1-P0)]/d; F=KA(P1-P0)/d - that is exact your equation!!!
F=(m2*m2*Pa)/m=m3*Pa or if we return viscosity into equation F=(m2*m2*Pa)/(Pa*s*m)=m3/s as you found through working with your equation.
I hope that this can help you,
Regards,
Rail.
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