Emperical relationships between variables are not reliable in evaluating any area. What do you think? For example, between porosity and permeability?

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Hubert Quinn

You are absolutely correct. The published literature on permeability in packed and empty conduits is filled with rubbish. A new model, the QFFM, was published in 2019. It is called Quinn's Law of Fluid dynamics and you can google it for free. It is the new gold standard and has been validated over 11 orders of magnitude, i.e. from creeping flow to fully developed turbulence.