My water system spans 5 Z-levels and 8 screens, but just for you, I am making an image Sparks.
Here is Z 7, the Cave River.
Here is Z 6, the Entry Flood Path/Initial Spillway.
Here is Z 5, the Falls.
Here is Z 4, the Falls 2
Not pictured is an Identical image to Z 5.
Here is Z 3, The Farms.
Here is Z 2, Downstream Flow/Spillway.
Here is Z 1/3 E, Emergency Water Release System
Not pictured is the Emergency Pressure Release one Z level lower of the Spillway, which consists of a large room bordering the chasm for 14 tiles, all with fortifications carved in, or the Overflow room, which is the same, one Z Level Up.
And that is the Water System. It's a fairly advanced one, but it has the core elements:
1) Flow Control system to ensure that the water can be stopped at the source
2) Large Rooms inside of the system so as to prevent a quick gush from overflowing the containment area
3) An exit system to get rid of the water when no longer needed so that dwarves can enter the system to make important changes.
As long as you keep those concepts in mind when designing your own, you'll have a successful water system.