LHG there are a number of things which mean that it can be any order.
Im fairly sure it should perform according to q^2 only. A constatn term could happen best guess is that its so small in this case that it may not exist, but a constant pressure drop can happen. There maybe be a cubic term coming in there due to mixing effects.
As it so happens the big book has a chapter on this but i dont have time to look at it this weekend
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