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Extending some of my earlier questions

How to stop a massive canal system from silting up?

Roughly how much water would my desert civilization need every year?

My preindustrial* society needs to control water flows on a massive scale. They need vast amounts of water to feed into the head waters of their draught stricken rivers south of the mountains. The only way of accessing it is to tunnel through into a vast lake to the north of a mountain pass.

Once south of the mountain pass, this water then needs to be split into 3 separate channels each 50%, 30% and 20%. They will have previously built canals east and west to distribute this water into the other river systems. They also need to arrange an annual flood of the rivers once a year.

Using this calculator https://www.copely.com/tools/flow-rate-calculator/ It would appear that a 10m wide tunnel dug 400m through the rock 30 metres below the lake surface might release as much as 2100 cubic metres/sec. This scale of tunnel should be possible for them to build.

For comparison (discharge rates in cubic metres per second) Nile 2,830 Mississippi 7,957 Amazon 209,000

Can this order of water flow be managed and controlled by my society? Or are they going to end up with an uncontrolled flooding on a biblical scale down one of their river valleys if they build the tunnel?

Things to consider: can the society carry out the necessary calculations? Can they build sufficient infrastructure that is sufficiently robust for all of that water? What happens when the tunnel through to the lake is first opened? Anything else you think is relevant.

Bonus: roughly how long do they need for construction?

Assumptions *no steam power, no internal combustion engines, no gunpowder. Cement is only available in limited quantities so cement mortar, but no Hover dams. This world is similar to Earth except it has much less water.

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    $\begingroup$ A subterranean aqueduct carrying three times as much water as the Nile, built in the Antiquity. Without using concrete. Right. (And your numbers are profoundly wrong. Fun calculation: assuming a circular tunnel, the cross section area would be about 7 m²; to get 7,000 m³/sec you need the water to flow at 1,000 m/sec, or 3,600 km/h. For comparison, the speed of sound in air is about 1,235 km/h, and the maximum speed of an F-14 Tomcat is 2,485 km/h.) (In a real pre-modern aqueduct you want the water to flow slowly, not more than a few meters per second, so that it doesn't destroy the walls.) $\endgroup$ – AlexP Nov 13 '20 at 21:47
  • $\begingroup$ Please double check the calculator. It appears to me that it gives the results per minute, not per second. $\endgroup$ – Alexander Nov 13 '20 at 21:53
  • $\begingroup$ @AlexP thanks for that let me have a look and see if that is correct. $\endgroup$ – Slarty Nov 13 '20 at 22:48
  • $\begingroup$ PS not sure it counts as an aqueduct? $\endgroup$ – Slarty Nov 13 '20 at 23:07
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    $\begingroup$ The new numbers resolve to a flow speed of about 100 km/h (60 mph). You may want to chose very carefully the material out of which the lining of the aqueduct / tunnel / penstock (whatever you call it) is made... $\endgroup$ – AlexP Nov 14 '20 at 0:12
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Leonardo da Vinci designed a diversion of river Arno in Florence, to manage the river flow.

He had devised a project to regulate the course of the Arno and create a canal to connect Florence to the sea, and had theorized the canalization of a marshy French region located south of Paris, the Sologne.

To build the canal, Leonardo studied excavating machines, designing an innovative and powerful one. He also studied systems to cut or drill the Serravalle hill and to build locks that would allow boats to overcome the unevenness of the stream. He also designed the way in which, on different levels, the canal could intersect other existing rivers in the plain of Prato and Pistoia.

The realization of this project began in August 1504 but then the company was abandoned: "The river laughed at those who wanted to give it the law"

But the Arno river, with 110 $m^3/s$ and a basin of 8228 $km^2$, is a joke when compared to the Mississippi, with 17000 $m^3/s$ and a basin of 3238000 $km^2$.

I highly doubt that a pre-industrial civilization could be able to conclude such a feat.

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    $\begingroup$ I think you are probably right, but having said that the situation I describe is a bit different. There is no war going on so they have lots of time and civilization depends on it. The primary danger in my world (unlike Leonardo's) is the prospect of initial success in digging the tunnel, to be turned into disaster when the shear force of the water enlarges the new tunnel causing run away erosion and a cataclysmic dam busters style flood. I might need to give them a very modest tunnel to start with and let the infrastructure build up over centuries of building with more small tunnels added. $\endgroup$ – Slarty Nov 14 '20 at 10:19

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