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[Shinziril]

Here's a nicely compact and easily-expandable perpetual motion machine.  This one works without a river and/or if it's underground, too. 

z0:
#####
#+++#
#+#+#
#+#+#
##+##
#####
  ^

z1:
#####
#=.=#
#=%=#
#=%=#
#+.+#
##^##
  v

z2:
+++++
+...+
++*++
+++++
+++++
++v++

# is wall
+ is floor
^ and v are up/down ramps
= is waterwheel
% is pump (pumping from south)
. is open space
* is gear for power output

Fill using pond designations on z2.  It should start up automatically once it's about half full.

If you want it completely full, so there's no visible movement of water, you have several options.  I find the simplest is to construct a wall and ramp for access to z3 directly above the open space on z2, and use a single pond designation on z3 to drop the last few tiles in.  Once all tiles on z0 (except for the pump intake tile, which will stay dry due to pump-magic) and the three tiles on z1 north of the pump are 7/7, you can remove the pond designation, clear the wall and ramp, and pave over the open space on z2. 

[Mechanoid]

Definitely sounds like a bug to me.  What logical reason would there be for it to work outside but not inside, and only in constructed walls?

Probably caused by the game forgetting that there are constructed walls in the way of the flow and never removing the "did not flow" thing. Could be tested by digging a channel in natural rock, and then replacing one of the walls in the water pit with a construction.
I imagine it shaking like jello.

[epdtry]

Here's a nicely compact and easily-expandable perpetual motion machine.  This one works without a river and/or if it's underground, too. 

Spoiler: Diagrams (click to show/hide)

z0:
#####
#+++#
#+#+#
#+#+#
##+##
#####
  ^

z1:
#####
#=.=#
#=%=#
#=%=#
#+.+#
##^##
  v

z2:
+++++
+...+
++*++
+++++
+++++
++v++

# is wall
+ is floor
^ and v are up/down ramps
= is waterwheel
% is pump (pumping from south)
. is open space
* is gear for power output

Fill using pond designations on z2.  It should start up automatically once it's about half full.

If you want it completely full, so there's no visible movement of water, you have several options.  I find the simplest is to construct a wall and ramp for access to z3 directly above the open space on z2, and use a single pond designation on z3 to drop the last few tiles in.  Once all tiles on z0 (except for the pump intake tile, which will stay dry due to pump-magic) and the three tiles on z1 north of the pump are 7/7, you can remove the pond designation, clear the wall and ramp, and pave over the open space on z2. 

Cool.  Here's a 2-level version that should work just as well:

z0:

#####
#+++#
#+#+#
#+#+#
##+##
 ###
  ^

z1:
#####
#=.=#
#=%=#
+=%=+
++*++
 +++
  v

Make sure you construct floors under the non-blocking waterwheel tiles.  Mark the gear assembly (which has open space beneath it) as a pond, then run the pump manually while filling it with water.  Stop when the tile beneath the gear reaches 2/7.  At this point, all other tiles on z0 and the three tiles behind the pump on z1 will be at 7/7.

If you add a 3rd level to this design so the gear can be placed above the pump, you can put a waterwheel with a nonblocking part over the pump's input tile to get a bit of extra power (though it may be tricky to connect up).  In this case, you need to fill the input tile to 4/7 rather than 2/7.

[Shinziril]

Very nice.  I suppose I was a bit leery of pumps intaking through gear assemblies, but what the hey, we've already murdered all the laws of thermodynamics, what's a few more broken laws of physics. . .

And that design does look easier to dig out if you're already underground (versus my designs, which were often constructed aboveground for comprehensibility).  If you need more power, the design is easily scalable to any level by simply putting extra waterwheel-pump-waterwheel units next to each other without walls in the middle like so:

z0:
########
#++++++#
#+#++#+#
#+#++#+#
##+##+##
 ######

z1:
########
#=.==.=#
#=%==%=#
#=%==%=#
++.++.++
 ++++++


Put the power-take-off gear on whichever pump intake you like. 

This design also works quite well with aquifers- dig out the layer above the aquifer for z1, channel the appropriate squares for z0, put in the machinery and use a dwarf to jump-start it and you're good.

[epdtry]

Spoiler: Design #1 (click to show/hide)

z0:

#####
#+++#
#+#+#
#+#+#
##+##
 ###
  ^

z1:
#####
#=.=#
#=%=#
+=%=+
++*++
 +++
  v

Spoiler: Design #2 (click to show/hide)

z0:
########
#++++++#
#+#++#+#
#+#++#+#
##+##+##
 ######

z1:
########
#=.==.=#
#=%==%=#
#=%==%=#
++.++.++
 ++++++

This design also works quite well with aquifers- dig out the layer above the aquifer for z1, channel the appropriate squares for z0, put in the machinery and use a dwarf to jump-start it and you're good.

Have either of these designs been tested?  (Not in an aquifer; I have a different concern with the aquifer version of #2.)  I've just thought of a flaw that should cause them to fail: there will be no flow in the tiles below the center of the waterwheels, since they are not diagonally connected to the pump's input tile.  To provide flow, there must be open space below the south tile of each waterwheel, and I worry that the system may leak through that tile rather than maintaining non-zero water levels in the pump's input tile (as is required to provide consistent 4/7 water below the waterwheel).

Regarding the idea of building #2 with the lower level in an aquifer, I suspect it will not work.  This is what I think may happen:

• Aquifer fills all tiles on z0 with 7/7 water.
• Pump is started manually.  Pump fills the 3 tiles behind the pump on z1 to 7/7, while aquifer maintains consistent 7/7 water in the input tile.
• Each tick, the pump draws water from the input tile and pushes it back into the aquifer stone (since there is nowhere else for it to go).
• The aquifer refills the input tile (may or may not produce flow in the input tile).
• There is no flow under the waterwheels because the diagonally-connected tiles have no opportunity to spread water into the input tile.

If you test the aquifer version, please report the amount of water visible in the input tile as well as the power output of the waterwheels.  This information should reveal when aquifer filling occurs relative to water spreading, checking of plates and waterwheels, and pump operation.

[Shinziril]

I can verify that I have used those designs both on an aquifer and with artificially-filled reservoirs and it worked in both cases. 

Water doesn't have to be "spreading out" in order to power the waterwheels.  In those designs, the waterwheel ends up with constant 7/7 water under all three of its tiles and still provides power (the pump "teleportation" effect causes it to count as flowing, as far as I can tell).  The pump intake tile on z0 stays muddy but perpetually empty of water. 

It's kind of nice, since the water is never even seen to move, and thus presumably takes up less processor power. 

[Grimlocke]

Thats a desing pretty similar to the one I usualy go with for smaller amouths of power required, though mine is slightly smaller. Like this:

1st  2nd

####  ####
#77#  # w#
##7#  #PW#
#7##  +pw+
#R##  +h++
####  ++++
Where # are walls, + is floors, R is water covered ramp, 7 is 7/7water, H is a floor hatch, P is a pump, W is waterwheel and where the capital letters indicate an impassable building tile. The pump pumps to the north.

It lags minimally, can have another waterwheel without losing power or stability, and is easy to set up and connect to power.

Great - this is the kind of thing I was hoping for when I requested "clever perpetual motion designs!"

It looks like your generator and mine work pretty much the same way, though I had never really considered using the impassable square of the waterwheel as part of the containment for the pump's output.

Have you checked frame-by-frame to see if the power output is consistent?  I would be a little surprised if it was, since this similar design I tested loses power for about one tick in 20:

(pumps from north to south)
Losing power occasionally isn't much of a problem for running pumps, but for millstones, losing power for even 1 tick will cancel all the jobs.

Late reply time!

The desing you put there might falter because of the diagonal pass before the waterwheel, and because the waterwheel only has 1 tile of flowing water beneath it. I havnt tested mine for consistenty, but I dont realy use millstones anyway, I just use those to presurise early magma and water cisterns.

Also, the ramp I put there to easily get rid of stone, and left it there because I didnt have a reason to remove it. The hatch is for an emergency brake. I like my emergency brakes.

The desing mentioned above is pretty much the same, safe for one tile that doesnt matter so much. The waterwheel seems to draw enough power from just 2 tiles of water below, I left mine at 2 to need less water when I duplicate the desing (like the 2nd desing quoted by epdtry 2 posts above).

Also interesting to mention is the possibilty to have the generators transfer power below them by placing a pump at the water level. As such:
1st  2nd

####  ####
#77#  # w#
#P7#  #PW#
#p##  +pw+
#R##  +h++
####  ++++
Where # are walls, + is floors, R is water covered ramp, 7 is 7/7water, H is a floor hatch, P is a pump, W is waterwheel and where the capital letters indicate an impassable building tile. The pump pumps to the north.