Greek Water Clock
The ancient world is well known to have used the flow of water to tell time. This is much less technical than geared machines. There are various issues with using water to tell time.
Use of Flowing Water
Water draining out of a small hole in a vessel runs at essentially a constant rate. This is because water pressure is a function of the depth of the water alone. The pressure does not depend on the volume of water in the vessel. The rate of flow is thus a function of the depth of the water and the size of the hole.
As the water level in the vessel changes so does the rate of flow. So a simple vessel, like a clay jar, does not itself have a constant flow out of a hole in the bottom.
By keeping the source vessel full of water at all times the rate of flow of a hole becomes constant. Keeping the vessel full is done with a second stream of water flowing over the top of the vessel.
Here is a short documentary that cites the known ancient development of this idea.
Key Points
Any clock built around the flow of water will require a constant source of water. This usually means they must be located near a spring. With this constraint on where water clocks can be located, that constant flow of water can then be harnessed to tell accurate time.
The flow of water coming out of the vessel must then be used to drive an indicator of some sort to show the passage of time.
The biggest issue is having ready access to some regular flow of water. This is not usually possible unless living near a steam.
For towns and cities this would not be a problem. Towns themselves require a regular source of drinking water, otherwise they cannot exist.
Use of well water, though, is not very good for water clocks since water clocks would then require constant manual tending.
Elaborate dials can be added to the basic design of a water clock. But, secondary vessels and simple floats were also commonly used with ancient water clocks.