The wiki features a perpetual motion machine. You have a circle of channels, with a water wheel on one side and a screw pump on the other. Directly under the pump is a solid wall blocking the channel. You build the pump, then the axle, then the water wheel. Fill the channel, then start the pump manually.
The pump will move water from one end of the C-shape channel to the other. Then the water runs all around the C, back to where the pump is pulling water from. This means the water is moving, and the water wheel is generating power.
Once the water wheel generates power, it powers the pump. Your pump dwarf then runs off to do something else. The system now runs constantly.
The trick is that the pump uses far less energy than the wheel produces. So you have surplus energy, which you can redirect elsewhere by building more axles off the wheel or the pump (as far as I know, powered machines transmit power).
Another, simpler way is to make an aqueduct between your river and your chasm. This acts as both a well and a diverted flowing water source, which you can fish from, and since it's moving constantly you can slap down some water wheels along it.
Plus, since you're disposing of the water, you can easily put in a waterfall in your dining room or whatever to make mist.