How to power a 200 z level pump stack

A screw pump only needs 10 power, putting a pump stack of 200 stories high at 2000 power. You could use a dwarven water reactor for this. A water wheel outputs 100 power, but consumes 10 power itself, giving a net gain of 90 power. So with a good design, you COULD do it with only 23 waterwheels at the bottom.
I really like Nick's idea of making an automated minecart track. I think this would probably be a lot less time-consuming.

Dwarven power multiplier:

This design is similar to a large scale dwarven nuclear reactor, but with an advantage and disadvantage compared to a reactor. The disadvantage is it requires one dwarf pump operator to power it, and he will occasionally need a break so it is not ideal for assured continuous power. The advantage is that it requires fewer mechanisms since you don't need to build or connect a lever to shut down power.

The design uses three Z levels. The top level is the waterwheel/powertrain level, where the waterwheels, gear assemblies and axle for power transmission are built. The middle level has the pump and a raceway where the water flows under half the waterwheels, makes a U turn, flows under the rest of the waterwheels, and then drops through a channeled hole to the bottom (water reservoir) level. The bottom reservoir level is just a sealed chamber that stores water.

The reservoir level is designed to be a little bigger than the size of the raceway so as to provide sufficient water for the water wheels and to improve pumping efficiency. If you don't overfill with water, when your dwarf stops pumping all water should return to the reservoir level, leaving the raceway level dry.

---Top View---

XXXXXXXXXXXXXXXXXXXXXX  Z+1: waterwheel/powertrain level
X....WWWWWWWWWWWWWWW.X  You only need access to build it.
X.....GAAGAAGAAGAAG..X   It can be sealed off afterward.
X....WWWWWWWWWWWWWWWFX
XX.XXXXXXXXXXXXXXXXXXX
  S

XXXXXXXXXXXXXXXXXXXXXX  Z+0: pump/raceway level
X....^^^^^^^^^^^^^^^.X  Dwarf access to the pump via
XXXXXXXXXXXXXXXXXXXX.X  the stairs required to run.
XPPPP^^^^^^^^^^^^^^^.X
XX.XXXXXXXXXXXXXXXXXXX
  S

XXXXXXXXXXXXXXXXXXXXXX  Z-1: water reservoir level
X^^^.................X  Access required to build,
X....................X  seal off afterward since it will be flooded
X^...................X
XXXXXXXXXXXXXXXXXXXXXX
  S

---Side view---

X....WGWWGWWGWWGWWGW.X  Z+1: waterwheel/powertrain level
XPPPP................X  Z+0: pump/raceway level
X....................X  Z-1: water reservoir level

Key:
  X=Wall or ummined tile
  W=waterwheel
  G=gear assembly
  P=pump
  A=axle
  .=mined out tile
  ^=floor on Z level above channeled out
  S=access stairwell

In the example above, with one dwarf manually cranking the pump, and with 10 water wheels (5 on outgoing raceway, 5 on returning raceway), we see a power output of 837. From one dwarf!

1000 (10 water wheels X 100 power per)
-100 (10 water wheel  x  10 friction per)
- 25 ( 5 gear assemblies x 5 power per)
-  8 ( 8 axle tiles x 1 power per)
-----
 867 net power

If you lengthen the design by a pair of waterwheels, you add the additional two waterwheels, a gear assembly, and a two tile axle, resulting in a net 173 additional power per pair of waterwheels (180-5-2). So a 24 waterwheel design will provide 2087 net power, enough for a 200 high pumpstack with 87 extra power for axles and gears to connect it to your pumpstack.

If you build this device at the bottom of your fortress where you found the very deep water you could connect it to a pump stack and use it to pump water up to the surface (or wherever).

If you expanded the design long enough, you might consider making the raceway snake back and forth in a S path, which would shorten but widen its footprint. No matter how long the raceway becomes, the water from one dwarf pumping is enough to power all the waterwheels.

My motto: one dwarf to power your entire fort.