Designing a river which does not overflow

... And if it absolutely has to, then such river should overflow in predictable matter.

I have a city idea in mind, where such the city has a river contained in an artificial tunnel beneath such city. I instantly know one huge design flaw of such a city, which is the floods.

So, I have to take one step back and come up with a design of a river which does not overflow.

Setup

• Earth-based planet, but not necessarily Earth
• This river may be on an island or on a continent, I do not really care
• The land mass around a city sitting on such river should be big enough to support city of at least 100 000 citizens
• The weather should support civilization, best would be northern Europe -like weather (seasons, temperatures between -30 to +35 degrees Celsius, long term average 18 C)
• The river itself should be at least 50 km long and at least 4m wide on widest point

So, is it possible to come up with setup which supports a predictable river?

• "All" you need to do, is to control the rate at which water can enter the tunnel. And to make the tunnel wide enough to handle that max flow rate. So, your flood defense will actually be situated outside of the city, at the place where the river enters the tunnel. – cmaster - reinstate monica Nov 12 '18 at 8:08
• Singapore has very similar problems with a majority of all canals/river beds in the city (due to rain mostly), you can look into the solutions they use – Nicolai Nov 12 '18 at 8:55
• 4 metres wide is more a large stream than a river, we'd casually put such a thing through a sewer if it was in the way. There are bigger rivers running under London. – Separatrix Nov 12 '18 at 9:40
• Bypass tunnel set at a slightly higher elevation than the normal run of the river, of 3-4 times the capacity of the main tunnel. If the water overflows, it will enter the bypass first and exit the city. – nzaman Nov 12 '18 at 11:58
• The Grand Canyon (Arizona, USA) will never overflow. Unless something is extreme, there will be the occasional flood. Because you build for 99 years out of 100. That unusual circumstance is too hard to build for and is the one that will get you in the end. – Cyn says make Monica whole Nov 12 '18 at 16:22

Rivers with stable flow (with data source)

River downstream of a large lake

• The larger the lake, the most stable the flow out of it. Also, it helps that the lake be in a temperate environment, oo water input into the lake doesn't vary too much. The lake can freeze over, as can the outlet river, without really affecting flow much; this happens in the case of the example.

• Example - Saint Mary's River (between Lake Superior and Lake Huron in US/Canada) at Sault Ste. Marie. Other good examples are the Rhone downstream of Lake Geneva, and the Neva downstream of Lake Ladoga.

• Pro - Very stable flow rate, year round (assuming the lakes don't freeze). Low ratio and magnitude of seasonal fluctuations. When improved with canals and locks, this makes for a great trading city.

• Con - In many cases, these outlet rivers are steep and un-navigable.

Extreme high flow       3590
Expected annual high    2385
Average flow            2142
Excess over expect high 1205
Excess over average     1448
Ratio over expect high  0.51
Ratio over average      0.68


(Note, all units are in cubic meters per second, except ratio)

Large tropical river

• A large tropical river where half of the river basin is in each hemisphere. As the monsoon rains are pushed by the Intertropical Convergence Zone back and forth between the hemispheres, you will end up with relatively stable rainfall throughout the year.

• Example - Congo River measured at Kinshasa.

• Pros - Very low seasonal flow variance. Also, an enormous basin for river-borne trade with the city.

• Cons - Very high magnitude of flow variance. When the river is this big, even a little bit of flooding is a big deal.

Extreme high flow       80832
Expected annual high    56081
Average flow            39536
Excess over expect high 24751
Excess over average     41296
Ratio over expect high  0.44
Ratio over average      1.04


A temperate river with little snowmelt

• The next best scenario is a river with a small basin with constant, low level rainfall, and little snow accumulation.

• Example - Seine River at Paris.

• Pro - Despite being a big enough river for a truly large city, the magnitude of highest recorded flood to average winter high water is not large.

• Con - Large seasonal fluctuations, can be difficult to navigate in summer time due to low water levels.

Extreme high flow       1284
Expected annual high    560
Average flow            268
Excess over expect high 724
Excess over average     1016
Ratio over expect high  1.29
Ratio over average      3.79


Continental river with large, dry basin

Example Arkansas River in the US, measured at Little Rock. In the interior US, random thunderstorms lasting for a few days can cause serious flooding, usually in spring or early summer.

Extreme high flow       8220
Expected annual high    2044
Average flow            1066
Excess over expect high 6176
Excess over average     7145
Ratio over expect high  3.02
Ratio over average      6.71


Continental river with enormous spring snowmelt

Example - Tom River measured at Tomsk, in Siberia. While the high river levels with snowmelt is relatively predictable, it is still very large compared to regular river levels.

Extreme high flow       7500
Expected annual high    4622
Average flow            1047
Excess over expect high 2878
Excess over average     6453
Ratio over expect high  0.62
Ratio over average      6.16


River in Monsoon area

Example - Vijayawada river in southern India measured at its mouth. While the timing of the monsoon is predictable, its magnitude is not. An erratic monsoon can produce spectacular flooding.

Extreme high flow       16555
Expected annual high    6266
Average flow            1642
Excess over expect high 10289
Excess over average     14913
Ratio over expect high  1.64
Ratio over average      9.08

• Also rivers and lakes that freeze damming water behind them to be released in flood. – KalleMP Nov 12 '18 at 18:10
• The Seine river in France is probably not a good example: it is known to have rare but somewhat regular large floods: en.wikipedia.org/wiki/Seine#Flooding "A 2002 report by the French government stated the worst-case Seine flood scenario would cost 10 billion euros and cut telephone service for a million Parisians, leaving 200,000 without electricity and 100,000 without gas" – Autar Nov 13 '18 at 10:37
• @Autar I linked a data source. Please compare the Seine with rivers of comparable size. Its flooding is less severe than seen on the Moselle, Oder or Neckar, for example. – kingledion Nov 13 '18 at 12:12
• @kingledion Depends on how you measure it. In terms of water flow or frequency sure, but the 1910 Paris flooding had water nearly 9 meters above normal levels. In 2016 and 2018 it was above 6m. I would think this makes it unsuitable for the question. Anyway that was more of a side comment, I think your answer is great and your information source very appropriate. – Autar Nov 13 '18 at 13:18
• Awesome answer! Very, very minor nitpick: The river that borders Northern Michigan and Ontario is the Saint Mary's (or Marys) River, sometimes also shortened to St. Mary's River. – zmerch Nov 14 '18 at 15:18

You can realize a large basin upstream, where you can divert the excess water during overflow time.

You can then opt for:

• leaking that excess water on a path avoiding the city, going through expendable areas
• let that water drain through the terrain

First one is preferred, as in case of exceptionally extreme cases, you might prefer flooding low value areas instead of the city. Of course you need to take care that no abusive buildings are built in the area designated for being flooded.

• Reservoirs and canals, basically. One question though: what’s an abusive building?? – Joe Bloggs Nov 12 '18 at 8:48
• @JoeBloggs, it is a building built without the needed permissions or in violation of the local building regulation – L.Dutch - Reinstate Monica Nov 12 '18 at 8:50
• Aaah! I was just picturing a building with nasty graffiti.. – Joe Bloggs Nov 12 '18 at 8:56
• @JoeBloggs which may be the result after the occupants are evicted and no-one is willing to pony up the cost of the demolition. – ratchet freak Nov 12 '18 at 10:23
• A Dutch answering a question on handling water; seems legit ;) – Matthieu M. Nov 12 '18 at 11:55
1. Build it massively over capacity

This is the expensive option, and would be really hard to get through your funding committee. Though of course it would have to be built above "normal" capacity to handle day to day fluctuations in flow. "Flooding" is basically the point at which your system is over capacity, if the capacity of your system is high enough it will never flood.

1. Beavers

This is one of the flooding prevention options. We've mostly killed off the beavers, but they provide an important service where they still exist. Their dams slow the river flow and hold back floods to smaller areas upstream. This slowed flow means that it never builds up to the point of flooding in downstream areas.

1. More vegetation in your river catchment

Another flood prevention option. The more permanent vegetation, the slower the rainwater reaches the river. Again meaning that even with heavy rains the water filters down to the river at a more measured rate and never builds up to the point of flooding further downriver.

1. Don't build on the floodplain

Leave the river space to flood. This sounds like a very simple and obvious option but you'd be amazed how many cities are built on the main floodplain of their river. Even new build is still going up on the floodplains.

1. Accept that it's going to flood sometimes

I spent a portion of my early childhood living in a house on legs. Under the centre of the building was a staircase leading up to the house, with legs around the outside.

• You can make the residents be the beavers by building those catchment dams upstream (and even use them for power gen depending on terrain) – ratchet freak Nov 12 '18 at 10:24
• "you'd be amazed how many cities are built on the main floodplain of their river." - not really, seeing as flood plains are the flattest and most fertile areas availiable to set down roots and start building communities. – Baldrickk Nov 12 '18 at 14:59
• 2. Beavers, except when the beaver dam breaks... – Draco18s Nov 12 '18 at 17:00
• Japan follows the first example, en.wikipedia.org/wiki/… – John Nov 13 '18 at 16:41
• I like option 1. If great fatness is possible, make sure your pants are very very large. – Willk Nov 13 '18 at 17:02

Use an artificial system of locks, weirs and dams to control the flow of the river. When the water level is too low, close the downstream gates so the river backs up. When the water level is too high, close the upstream gates so it empties.

In order to be able to deal with droughts or downpour, you will of course need some room to store excess water upstream (a natural lake, artificial reservoir, floodplain or a section of river flowing through a deep valley) and to drain water downstream (like a larger river or ocean).

You see systems like this in many cities which have rivers flowing through them. Let's take the river Alster which flows through the city of Hamburg in northern Germany, for example. The river flows through two artificial lakes in the center of the city. Those lakes have a nearly constant water level all year around. How do they do this? With a system of variable weirs along the 50km upstream which meticulously control the inflow and a set of locks which control the outflow into the larger Elbe river (as well as prevent inflow from the Elbe when it has high tide). The system was built over 400 years ago, so you don't need 20th century technology to achieve that level of water flow control (although modern meteorology and electronic communication do of course help to improve the reliability). There is a German wikipedia article about the Alster lock system with lots of pictures.

This actually pretty hard to do. Here's why: Water flows downstream. You need a difference in water level between upstream and downstream of your city. Flow through a pipe is essentially a rather complicated function - typically you use the Darcy Weissbach equation in combination with a Moody chart - of this level difference. Approximately, the head loss, or required level difference between upstream and downstream, quadruples when you double the flowrate.

In open flows like rivers the relationship is far more complicated because with higher flow rate the river bed or channel is usually filled more, which means less then quadruple head loss for double flow rate. Open channel flow is not trivial but please read around a bit

What does this mean for your city?

Let's take one of the rivers from Kingledions answer, the Seine with low flow around 100 m³/s, average flow of 280 m³/s and extreme flow of 1280 m³/s

It's often a good idea to look at flow systems starting downstream. Let's say at average flow conditions you have a downstream water level of 50m above sea level. You city is 5 km across, really small. This calculator tells me, with an 8m diameter, 5km long pipe, my pressure loss is 72.445 Pa wich is equivalent to a head loss of 7.2 m. So my upstream reservoir level will be 57.2 m at average conditions.

Now, let's take the extreme flow, now I have 1513.962 Pa - 15m! We need a dike between our upstream reservoir that's 65m above sea level, and 7 m above the normal level of the lake or what have you. Actually more, because at extreme flows the downstream level will be higher too, by a few m!

I suggest a second channel or even third that's only opened at high flow events, also play around with the sizing of the pipes.

On the other hand, what happens at low flow? At normal flow, we have a flow velocity of 3.6 m/s . At low flow - 100 m³/s - the flow velocity is 1.3 m/s. The DWA-M 275 (An industrial code, Germany, for designing piping systems in wastewater treatemtn plants that I happebn to have open at the moment) advises a flow velocity of at least 2m/s for raw sewage. Why? Sedimentation! at lower flow velocities, sand etc. will sediment and remain in the pipe. In actuality I don't see this problem, because in all likelyhood your pipe will be the fastest streaming part of the river system.

Environmental impact assessment

The pipe will stop migrating fish, at least most of the time, from swimming upstream. This could seriously impact aquatic ecosystems along your river.

• Also the intake works would probably need bar screens or similar to protect the pipes from large debris that might block them (trees etc), also to maybe safe people before they get sucked in, this would add to the head loss and introduce many additional engineering headaches. – mart Nov 12 '18 at 19:51

So, very much like London then?

Whilst the Thames is an iconic feature of London, virtually all London rivers which feed into it are now culverted and carried in pipes underground. This Wikipedia page lists many of them, but of course there are more. This website and book may also be of interest.

The simple answer is that the culverts start outside the city. If the river overflows, the area around the culvert floods, but the city itself is not affected.

What if it's more about the city's design that the river's ?

Any body of water can overflow.

A city that could float, though, wouldn't necessarily suffer from this - it could just rise with the waters.

• This answer has been automatically flagged as low-quality due to it's length. Try expanding on it; there's definitely something to this. – Philip Rowlands Nov 12 '18 at 12:07
• What would a city that could float look like, especially considering that it's probably going to be on solid ground most of the time? Would this have a reasonable cost, considering you need to specifically design an entire city for this? – NotThatGuy Nov 12 '18 at 12:15
• @NotThatGuy: Why would it be on solid ground most of the time? You're basically looking at a flotilla of house boats. – MSalters Nov 13 '18 at 12:36
• @MSalters Because it doesn't seem like a river, especially like one OP has in mind, would be nearly wide enough to support an entire city (probably). – NotThatGuy Nov 13 '18 at 19:32

This is not as complicated as it seems and a wholee lot more work then it seems

First off you need to design the tunnel to meet your requirements whatever they may be, Rivers want to find the easiest and shortest route to lower ground every turn in the river slows it down fractionally. so make your tunnel nice and straight. but as few blockages like grates and covers in the tunnel as possible this will allow the water to flow freely without impediment and also stop anything that gets washed down the tunnel from creating a blockage.

Overflow Pipes

Have these staggered along the the length of the tunnel, should water reach high enough then it will fall into these overflow pipes and out of the tunnel. have these every so often so that if 1 somehow gets overwehlemed for some reason the water will then drop into the next one and the next one etc etc.

These pipes should lead to either a second much large tunnel that would spend a lot of time mostly empty, or out of the city and into another river somewhere else.

Flow Control

This is one of the most important parts have something like a Dam or series of Dams upriver from your city, this will ensure enough water can enter your tunnel but stop or at least limit flash flooding. obviously build your Dam how they try to build them in real life, with overflow piping and the ability to divert water elsewhere if required.

So long as you build it along these lines then your city should be fine. although there is always the old proverb about "best laid Plans"

Have a restricted entry for the river - for example, it passes through a hole in the bottom of a wall.

If the river starts to flood, then the hole limits the amount of water that can come through into the city portion of the river, while the wall redirects the flood waters to tributaries or around the city (into a moat?)

The river then exits through a matching hole at the other end of the city, and (optionally) rejoins the overflow.

(The flow rate of water through the hole when it is submerged should be slightly under 14 * Size_of_Hole * Height_of_Water_above_Hole m3s-1. Build your wall and the flood-plains alongside it accordingly.)

Similarly - if you have a deep /wide ditch or gorge around your city, you have bring the water in via an aqueduct, which will overflow into the gorge in case of a flood, instead of into your city.

• Works fine if one city does it. If every city does it, and then embankments are used to protect the roads, and then farmers decide to protect their fields, you get the modern Mississippi. The reduction of available channel area means that floods are much deeper than they were before everyone started building walls. – Mark Nov 12 '18 at 21:11

The easiest solution is to build your city where existing geography supports your goals. The most obvious (and extreme) example of an overflow-proof river on Earth would be the Grand Canyon in the Southwestern United States. With the walls of the canyon rising an average of 670 meters above the river bed, there’s no chance of it overflowing a hypothetical city built above it.

You’d want something similar, though probably not as extreme - a river cutting through (and eroding) hard rocks to create high, nearly vertical canyon walls that prevent overflow. The specific rocks and age of the river would determine how high the canyon walls are, so adjust as desired. It took the Grand Canyon anywhere between 6 and 70 million years (depending on who you ask) to develop into its current state, so adjust your time scale as necessary and you’ll get what you want.

Build a top water limit for the river, like a roof.
When the initial river overflows, at the river will contain always the same amount of water, while the overflow water will go somewhere else.
You can even make the roof out of glas, so you have a modern view of the river

Hope this helps:)

Nothing easier.

Make the river Very Slow, but able to flow fast

The flow of a river can be measured in cubic meters per second. How fast does it flow? The math is rather straightforward: take a cross section of the river, note its area in square meters, and divide its m3/s flow rate by the area in m2. The result is a speed, in m/s.

Normally, rivers flow at a relatively consistent rate, and have just the cross-sectional area they need. When flow increases, the river rises. Since its banks are sloped, raising the river causes a quadratic or increase in its cross sectional area, but it also causes flooding.

We're going to change that all up. We'll make a river with a very large cross-sectional area. As such, the water moves very, very slowly, e.g. 0.05 metres/sec. When the storm comes, and the river's flow rate increases by a factor of 50, we increase flow to a factor of 50. Now, water is tearing by at 2.5 metres/sec, and canal boaters accustomed to the near stagnant river are like "nope!" We wildly overdesign this thing so even a 1000 year storm won't flood out our town every 5 years (assuming Al Gore exists on your planet).

Level control

The problem is gradient. Every river is on a grade, that's why it's not a lake. At normal / low-in-the-design-range flow rates, the water will want to be on the bottom of the deep channel,like that sad little garden hose trickle known as the Los Angeles River.

We fix that with some sort of weir that can quickly be moved/removed. Something like lock gates, notched to let pleasure traffic by. Or my favorite, inflatable rubber weirs that arch up from the river bottom. This will be a deep channel allowing the passage of deep ships, and if you can't make passable weirs any other way, you just treat the entire river like a flight of locks, opening and closing each weir serially to let the ship through, lowering the weir ahead of the ship and letting water level dip temporarily.

In wartime, all those weirs get blown to hell, and their failure mode is to let the river run free, so it ends up at the bottom, LA style. Wrecks it for navigation, which would be the enemy's aim, but failure mode is "not flood the city".

If you have a waterfall downstream and a relatively straight river bed, limiting the amount of water guarantees your to never have any flooding - all the water that is able to enter the tunnel is able to flow away just as fast.
If managing the amount of water entering the tunnel is not possible, you need to manage the flow speed inside: low friction materials on the tunnel walls and, if necessary, turbines that can use electricity to increase the flow velocity could increase the amount of water you can get rid of indefinitely (the water has to come in through the tunnel entrance, so if you can make it keep its velocity all the way through and the tunnel has a constant size, the amount of water exiting the tunnel always equals the amount entering it).

It's "trivial" (read: rather difficult) to calculate the maximum possible flow of the river:

Take the size of the catchment area. Multiply it by the maximum rainflow rate over that area that you expect to get.

You will have to figure out what level of that rain, for how long, you wish to handle.

You can put in as many systems of catchment areas and lakes and so on as you like, but once they become waterlogged and saturated, they are no use. So your two options are: either build upstream flood-management systems that can handle every raindrop that can land on the ground, for as long as it might rain; or make a way for the water to flow through the city faster than it can fall on the ground.

Combining both obviously gives you a good backup ability if one fails, and focusing on management and mitigation obviously also saves those upstream from the city.

Management and mitigation is covered well through other answers.

Throughput is best handled through smooth, wide, deep channels through the city, and for some distance beyond.

Another option is to put turbines in there that can be driven by stored power, to drive water through at an accelerated pace, and provide power in non-flood times.

Another possible cause of flooding is by tidal flow and storm surge from the ocean. In this case, a raisable barrier in front of the city would seem to do the job.

But what if both floods happen at once? A day of storm surge, AND a day of maximum flow from upstream? At this point it definitely needs the turbines, since the upstream water under the city will not of its own accord flow into the deeper water of the ocean: it needs to be pushed by the turbines.