Here is a crash course that isn't going to cover everything, but it may answer a few questions you might have.

Depending on the need, water is then pumped to the city or up into the tower. The water in the tower is just there in case it is needed. It holds a lot, about 50 swimming pools full, but still wouldn't last a city very long. It is probably enough for about a day. It can be used if power goes out, which would shut down the pumps. It can also be used for emergencies, such as fighting a fire. It is also used as a supplement if what is being pumped from the water treatment plant isn't enough.

There are plenty of good math applications involved here. Obviously, finding the capacity of the tower can be important. As can be seen, they might be conical, spherical, or cylindrical, or even combinations of shapes.
Finding the amount of pressure of the water flowing from the tower would be important. Every foot in height supplies 0.43 pounds per square inch. Thus, the higher it is, the more pressure. We'll look at these issues a little more next time.
Until now, I obviously never took the time to look into this topic. I got a lot of my information from several sources, but http://people.howstuffworks.com/water.htm was probably the best. That is where the diagram below is from.
A = From Treatment Plant
B = Pump
C = Water Tower
D = To Customers