From http://ask.slashdot.org/comments.pl?sid=993269&cid=25350317
Since most of these things don't change while we're driving, the proportionality can be expressed more simply:
F = kv^2
In other words, fluid drag is equal to some constant multiplied by speed squared.
The cube comes into it if you multiply both sides by v again:
Fv = kv^3
Because Fv is force times speed, which is just another way to write power. (Fv = Fd/t = E/t = P where d is distance, t is time, E is energy, and P is power.) Therefore the power dissipated by fluid drag (and thus the power required to maintain speed) is proportional to the cube of the speed.
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