Isometric growth: flow profiles
The relationship between flow and
driving pressure depends on the flow profile: is gas flow
laminar (all gas molecules move orderly at the same time in
the same direction) or turbulent (there is no orderly flow
as above, and there are many eddies)? We assume that you are
not interested in any details. So please accept that, taking
into account these extremes and by applying Poiseuille's and
Darcy's equations, as appropriate, it can be shown that in
the case of isometric growth flow should increase as a power
function of volume, where the power may vary between 0,67
and 1,0.
PS: If we take into acount that lung elastic recoil may play a role - it takes too much time to explain quickly - then the power k may be as large as 1.37. It also matters whether the pressure loss in airways should only be attributed to acceleration of gas molecules or also to frictional pressure losses, but this is similarly specialist matter.