I will make container from steel or aluminium ( 0.5 mm thickness ) and fill it with air (2 bar) and I want to know how much pressure would the container loose overtime (20 years) ? I have asked this question before but I got 2 answer the first one " gas flow rate"$$ Q = {kA\over d} (p_1-p_2) $$ but someone said me that is the wrong equation because its used for porous wall or very thin wall of metal (like 0.001 mm) but steel and aluminium are not.

The second answer is volumetric flow rate $$ Q = {K*A*dp \over na*d} $$

I have searched in internet for the value of K but there are no such information ! All information is about polymer

the container 15*15*15 cm 0.5 mm thickness

Who is right and how do I approach this problem ?


  • $\begingroup$ I once worked in a lab where we had to worry about hydrogen seepage out of a controlled atmosphere container through out steel equipment. We used a chart on hydrogen diffusion rates through different materials. For air, look up the diffusion rates of each gas separately for your container material. You could just approximate it as nitrogen. If you don't want to do that then use the different component fugacities (I.e. Partial pressures of each gas species). $\endgroup$ – R. Rankin Jul 16 '16 at 10:46
  • $\begingroup$ thank you for the answer .. there is no single website in internet about " nitrogen diffusion rates through metal " $\endgroup$ – user118676 Jul 16 '16 at 14:08
  • $\begingroup$ The diffusivity of nitrogen in steel is given in the following articleCalculation of nitrogen depth profiles in nitrided multi-component ferritic steel J.-D. Kamminga a,⁎, G.C.A.M. Janssen b,1, Surface & Coatings Technology 200 (2006) 5896–5901 $\endgroup$ – Chet Miller Jul 16 '16 at 16:06
  • $\begingroup$ This problem in the realm of statistical mechanics rather than Bernoulli. The governing equation should contain temperature as well as pressure. So I doubt either of the equations you show are valid models. $\endgroup$ – docscience Jul 16 '16 at 16:19

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