This question already has an answer here:
Though the mathematical concepts underlying quadratic air drag are quite straightforward (a single variable differential, just like the linear drag equation), my text book (and online text books) completely ignore the reasoning behind why the "drag" at high speeds on a trajectory through a fluid is proportional to the velocity squared. I know that this could not just be an empirical result.
Is there an intuitive reason for this (perhaps like momentum transfer or kinetic energy?). If possible, I would also like to ask for an intuitive reason behind the units $m^2/s^2.$