velocity pressures on bridge piers

Then you go to the "LOADS" section of your Bible.

The drag is proportional to the square of the velocity--a standard fluid mechanics text will have the same relationship. However, the appropriate drag coefficient is a matter of code.

A real slow drag.

Back in the old days, BC (Before Computers) there was a very simple method of determining the effect of flow of water on piers:
P = KV^2
P = Pressure on pier in psf
V = stream velocity in fps
K = pier shape factor==>2/3 for circular piers
1/2 for angle ends L<30deg
1 3/8 for square ends.

This was too simple, effective, and useful so AASHTO had to change it.
Best Tincan