I'd like to know if there is a simple way to approximate the minimum length a funnel should be in order to have smooth airflow within. More specifically, my problem is that I want to place a 70cm diameter fan a distance away from a 4x4m panel of filters, with the fan above the center of the filters, blowing air as equally as possible through the filters (and not just through the innermost filters.
Here's a rough drawing of what I'm trying to make:
I'm interested in knowing what H should be to allow the air from the fan to pass through the filters at the bottom evenly. I wondered if perhaps there was an equation that gives an approximate answer under certain assumptions (e.g. assuming increase in cross-sectional area of funnel is constant per unit height, instead of curved as I have drawn it, assuming walls are rigid, etc.) without resorting to solving PDEs or CFD, etc. Or am I approaching this problem wrongly?