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40d:Water flow
Water flow is an informal term used occasionally by players to denote the ability of specific water tiles to power a waterwheel. The direction of the flow doesn't matter for purposes of powering a wheel - if it's there, it's there.
While there obviously is a game feature at work, the mechanics are not completely understood at present. It's a bit of a black box - we know some of what happens, what will work and what won't, but not always why.
The simplest way to see if water is flowing is to watch for it to blink from ~ to ≈ while the game is not paused. Water blinking between ~ and ≈ is flowing. If you see numbers instead you may want to set SHOW_FLOW_AMOUNTS to NO in your init.txt file. Alternatively, you can just build a water wheel and see if it turns, which again is indicated by blinking.
Natural flow
Rivers and brooks always have flow. Brooks require that you channel down through the surface to place a wheel, but the flow is there. With natural flow every single tile of a body of water will be constantly flowing. Natural flowing water behaves very differently from artificially created flow.
Channeling from a Natural Source
Channeling out new area from a flowing river or brook does generate flowing water at the same Z-level. It is worth mentioning that when this channel is first connected it is quite likely that you will see it fill fully to 7/7 and stop flowing for a period of time. After some time passes (a season or so) the channel will suddenly start flowing like a natural source. The shape of this channel does not really matter. Natural sources of water will flow quite happily in a dead end on the far end of the map. Another oddity with natural flow is that a closed floodgate will not stop the flow. Diagonals also have no real effect on water flow although they do have use as a means for controlling water pressure. Moving naturally flowing water to a different z-level has somewhat unpredictable effects. More research is needed.
Artificial flow
Unlike natural flow, Artificial flow works on a tile by tile basis. Any time there is a difference in water levels from one tile to the next water has a chance to move. When water moves from one tile to the next, this causes flow for a short period of time. If all the adjacent tiles are the same depth, water will not flow. When the water levels even out for whatever reason this flow will stop. It is quite common to see flow in some tiles but not others.
Creating permanent artificial flow
Artificial flow can be generated either by draining from one level to another, or with pumps. Because a waterwheel generates 100 power and a screw pump only costs 10, it's quite possible to create a perpetual motion machine.
Accidental flow in Aquifers
Rarely, when channeling into a level with an aquifer with no adjacent pre-existing channels or water-ways, a single tile of flowing water will be created, enough to power a water wheel. This flow continues even when surrounding tiles are channeled out. With current understanding, this is not predictable or controllable - if it happens, it happens.
(It is theorized that the water that initially flows in to fill that channeled tile somehow gets "stuck" in the flowing state. This is only a theory.)