I strongly suggest that you get a [Mechanical Engineer or Chemical Engineer] consultant to do this for you. I believe that even if one such calculation were to be sent to you, it just may not lend itself to easy understanding. I think that the solution must use Partial Differential Equations in order to satisfy the boundary conditions that must be met in solving the problem. Only after the solution has satisfied the boundary conditions does one then calculate the average mass flowrate and therefore the flow requirements.
Just my analysis, but there just might be other ways and possibly even easier
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