Please read Sec 14.8 (!) of your text.
The Shallow Water equations are really part of a GFD course, but they are a less abstract way of thinking about fluid flow than some of what follows, and thus is an interesting application of the basic physics we have covered so far.
Q Make sure you can derive equation 14.42 from the hydrostatic pressure relationship.
Q Why is w=D\eta/Dt (pg 627)