Head loss formula in series pipe

[foo9008]

Homework Statement

i know that the formula of head loss is (V^2) / 2g , where v =velocity , but , why did the author want to change it to k[(Q)^1/n ] ?

Homework Equations

The Attempt at a Solution

 

[haruspex]

I don't know what the author's plan is - seeing the entire text might help - but in that equation the author is merely saying suppose in general that the head height is proportional to the mass flow rate raised to some power. The constant of proportionality and the power constant might allow for drag, say.