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[Kanddak]

Wow. Some people really need to test whether they actually know what the hell they're talking about before they go running their mouths to players with questions. I stack waterwheels next to each other in practically every fort I make and they always work.
Usually they are indeed connected to another component, because they need support to be built over water. But I just tried supporting a row with a waterwheel built on solid ground, and those worked too.

There is some kind of strange black magic involved in the calculations for waterwheels and I only have a very vague idea of what works and what doesn't. You can have flowing water that the wheels don't seem to recognize, and you can trick wheels into turning in water that isn't moving. Usually I just try to build them in rivers, because this seems to be foolproof. It doesn't really have to do with whether it's 7/7 or not. I suspect it may relate to the "static" flag for a water tile which Toady has mentioned in the context of pressure calculations.

[Quietust]

If you look at your water and the tiles aren't regularly toggling between ≈ and ~ (turn off SHOW_FLOW_AMOUNTS in init.txt), then it isn't flowing and your water wheels will never generate any power from it.

Any body of water that has a direct connection to a river automatically gets permanent flow, even if the connection is subsequently cut off. Oddly, though, when it's first filled, the flow doesn't show up immediately, but after a minute or two it'll all instantly start flowing at once.

[Shakma]

Just to clarify what I said before since everone is ignoring it, if you designate like so:

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wwwwww
*wwwwww
 wwwwww

 but the dwarves build this wheel first:

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wWwwww
*wWwwww
 wWwwww

Then I think only the first wheel next to the gear below will have power once they are all built.  Probably what happens is the first wheel built (2nd from left) isn't next to a gear so the game tags it unpowered when it is built.  All the others to the right will also then be unpowered.  Even when you finally build the one next to the gear, the game will not switch the others to powered, only the left most wheel.  I don't know that this happens 100% of the time, but it's happened like that to me and rebuilding the wheels fixed it. 

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WWWWWW
*WWWWWW
 WWWWWW


[Shakma]

I could also depend on if the gear is actually built as you can designate a gear for building and all the waterwheels and the hanging wheels can actually be built even if they normally couldn't without a gear already built. 

[worldspawn]

I built them in order starting from the gear assembly. I had to. If I built one somewhere down the middle then as soon as it was finished it would collapse back into logs since it wasn't supported by anything.

Let me go into more detail about the setup. There's a 31 tile wide river in my map that I've decided to route through my entire fort for waterfall use and then pumped back out again. I want to use waterwheels to power all of the needed pumps to do so. I built a hydrodam in this river and dug a 31 tile wide chasm in the center of it. This chasm drops about 10 Z levels and then the huge tunnel to the rest of my fort follows from it. When my dam is opened the whole river flows into this chasm and throughout my fort from there.

I initially put 2 rows of waterwheels in my dam itself, but this didn't work since they're RIGHT next to the drop, so the water level is never higher than a 2/7 so the wheels don't turn. I shut it off so I could then build 2 more rows of wheels inside the tunnel itself (well one Z level above it). The tunnel itself builds up to 7/7 but even then those wheels don't turn either. All in all I have about 112 wheels set up and maybe 2 of them ever turn.

If further examples are needed I can upload the save.

[Shakma]

I built them in order starting from the gear assembly. I had to. If I built one somewhere down the middle then as soon as it was finished it would collapse back into logs since it wasn't supported by anything.

Actually, no, it will let you build them. 

In any case, maybe screenshots would be best or a map so people can see what's going on.

[Kanddak]

Any body of water that has a direct connection to a river automatically gets permanent flow, even if the connection is subsequently cut off. Oddly, though, when it's first filled, the flow doesn't show up immediately, but after a minute or two it'll all instantly start flowing at once.

Hot damn. Do you have any lovely illustrative experiments at hand for that one?

[Saber Cherry]

Any body of water that has a direct connection to a river automatically gets permanent flow, even if the connection is subsequently cut off. Oddly, though, when it's first filled, the flow doesn't show up immediately, but after a minute or two it'll all instantly start flowing at once.

Hot damn. Do you have any lovely illustrative experiments at hand for that one?

I can't prove this is universally correct, but I have noticed it to be true every time I've tried it - even if the river has to go through bars and underground to get to some remote pond.