Archimedes Screw Reservoir

Was thinking, a while back, about the way a preindustrial, archaic city, in a cave, built vertically, would be irrigated. This scene was a sort of proof-of-concept for the design I had in mind--not a technical proof, an artistic proof, to get the space out of my head and into a pseudo-solid form, including the bridge. The scene kind of ballooned from there as I started to add lights, until--here it is.

Looking at it now, I see all kinds of things to fix: the water is supposed to go down when it's not in use, and the canal isn't oriented for that; the trough the screw dips into isn't quite deep enough (not that you can see that); literally everything needs reshaping--can you see a sluice being made as an octagon, or even half an octagon?

In reality, this setup should not exist. In a preindustrial society, no situation would likely occur where it would be easiest to build upwards and transport water to the top--with any low down water source, it would be cleaner and simpler to leave and find somewhere else to settle, to spread out around the water source, or to dig a well and let people walk to it. With a high up water source, just build canals and let gravity do its thing.

Nonetheless, it's fun to think about societal implications of this arrangement. Turning the screws would be hard, and to coordinate every level so that each screw got turned in sequence would be harder--so you'd come to see the lower levels as more desirable, less work to get water.

• Farmers would work on the bottom, where direct access to the water is available; rich people would be above them, just as close as it's possible to be without stealing farmers' access. The rich class may make life hard for the people above; whether the screws have water to lift is determined by their whims, whether they're willing to work their screws or not. To secure their water, the people above may become craftsmen and work to earn trust from the noblemen somehow. Literal social strata.~
• Or maybe there is no rich class, and the craftsmen separate the farmers from the beggars?
• Or perhaps the farmers are the rich class?
• If the city is rich in the barbaric way, they could have slaves to run the screws. Whoever controls the slaveowners, controls the slaves, controls the water--boom, city-sized Roman Empire.

That all said, I invented this system in a specific context where it just might be the most practical option. A group of people move into a ruined, ancient city--but for general fear of harming the ancient, historical buildings, statues, and artworks, they build new homes on the side of the city's ancient, massive wall and pump up water from the old rivers using a setup like this. Scrounged from scrap, in location and livelihood, would almost certainly be the only way a system like this would form.

Incidentally, the sluice is designed for these people, who can control small objects telekinetically. An object is telekinetically inserted into each of the boxes (quick and dirty representations of pouches), and then pulled down to open the sluice and pour out the extra, unneeded water; I don't know how you'd then close it again, when you want reservoir water to stay in for using.
(THOUGHT 9/30/2018: Just have pouches on the top edge also, and be careful that they not fall into the water when they flop down after you're done--or make those ones actual metal boxes as shown here, unlike the other ones.)