# Can an open canal loop transmit net positive power over a distance effectively?

I’m designing a society in a hostile climate which transports its energy from remote stations to a city with an absolute minimum of maintenance and infrastructure requirements. The concept is to use a constantly circulating lazy river to transmit power to the city. A canal flows continuously between two points in a loop; at the sources, paddles or screws force the fluid to flow, and at the destination, the flowing fluid pushes paddles connected to generators. It’s an open hydraulic transmission transmitting rotational torque over a distance.

Ultimately, the power enters and is retrieved from the system by gravity, so paddles inserting energy must be lifting the fluid a certain vertical distance, and forcing it to “fall” again in the desired downstream direction (toward the city). Retrieving the energy requires the fluid’s horizontal momentum to be converted into a lifting force (it hits a dam of sorts), which then must fall again to power a wheel in the city.

This is all in my head right now and i’m wondering if a net positive torque could actually be transmitted in this way as it seems?

My assumptions are to use a large volume of an extremely dense fluid such as mercury to transmit lots of power using relatively slow flow and low vertical level changes. The amount of work the system can do should be simply the product of the downward force of the elevated volume of fluid times the vertical distance through which it falls. For argument’s sake assume my paddles lift 10 cubic meters of mercury a height of 0.5 meters. Could I recover a significant amount of that work on the other end and also return the mercury to the generator? The canal loop is 10km long.

• The paragraph "Ultimately, the power enters..." confuses me. What powers the lifting paddles? There must be some external force (not gravity!!); otherwise, you just have a perpetual motion machine. Jan 22, 2021 at 2:11
• Also, mercury has very high surface tension (which slows it down), and a "scum" forms on top. Very poor choice of fluid. Jan 22, 2021 at 2:14
• pumping water uphill is a good way to store energy, but you need to put in a lot more energy than you get out. using water flowing downhill to push water uphill was used fairly often, the catch is you pump a LOT less uphill than is going downhill.
– John
Jan 22, 2021 at 17:03
• Are you asking about a level canal loop, where energy is carried in the form of kinetic energy rather than potential energy? Where, in other words, the power source sends water flowing down your canal at such a great speed that it travels 5 km and still has a significant amount of kinetic energy left over when it reaches the end? Jan 22, 2021 at 19:32
• Why a canal loop when you have rain? It's not uncommon to use water to transmit power oer a comparatively short distance. You divert water from a river somewhere upstream, have it flow in a canal or pipe that slopes less than the river, then let it fall to run your hydroelectric generator or old-fashioned millwheel. Jan 23, 2021 at 2:52

## Both the walls of aqueducts and powerlines exert resistance

...so, the real question should be if this is more efficient than using a high-voltage powerline.

Your primary competing product to your canal system would be high-voltage, direct current (HVDC) powerlines which are normally used for transferring power over very long distances. The longest and possibly most efficient HVDC system in the world is a 1.1MV, 12GW line system in China that is ~3300km long. I can't find any specs on the composition of the wire itself, but if can assume it's really freaking big, but made out of something economical enough to make very long. So it is probably a number of parallel copper wires with a total cross section of something like a 10,000kcmil(50.67cm^2) giving us a total 22.5% drop in power from friction. (https://www.calculator.net/voltage-drop-calculator.html)

Now let's try to cover that distance, efficiency, and throughput with an aqueduct. Hoover Dam produces 1.1GW of power, so an equivalent system needs to support a flow of water 10.8 times that of Hover Dam. This means an equivalent hydroelectric system needs a flow of about 36,087m^3/sec of water dropping an average distance of 160m to turn the generators.

To get about the same resistance out of an aqueduct, you would need a pipe with a radius of ~77m. According to Manning's Equation (https://www.lmnoeng.com/manning.php), this will result in a total drop of about ~18.7m over 3300km in either direction. This means your aqueduct would need a total height at its highest point of about 197.4m, it would drop to 178.7m when it gets to your city, drop to 18.7m where it powers your turbines, then returns to the source to be lifted back up again giving you ~23% power loose.

## It is not as efficient as using powerlines

For starters, pipes are WAY bigger construction projects. The required cross sections about 37,000 times that of the wire, it also has to be built up to massive heights to cover really long distances when compared to HVDC lines. If your world truly is hostile, buried lines would be much safer than an above ground megastructure. Secondly, it requires a massive powerstation inside your city to convert that water into electricity which kind of defeats the point of producing power elsewhere. In contrast, HVDC wires just need a simple transformer station to convert its high voltage DC current into usable AC low voltage currents.

All this said, you may very well not need 12GW of power, and 3300km may be much farther than you actually need to go, but you will want to keep in mind that the smaller you make your pipe, the steeper it needs to be; so, going smaller actually makes this kind of system progressively less efficient.

## As for using Mercury

This would be less efficient than water. For a system like this, you want to minimize sources of resistance; so, viscous fluids are going to be far less efficient. If you want to make it more efficient you may want to use some kind of alcohol or maybe even liquid propane: https://www.engineeringtoolbox.com/absolute-viscosity-liquids-d_1259.html

• Thank you for the calculations with water, the fluid would be mercury in this case and the canal would be quite large, so it does not require a high flow velocity. This means lower friction losses, maybe even negligible. I’m curious about what maintenance requirements a canal would have? A buried cable would seem to be harder to maintain? Jan 21, 2021 at 21:13
• @VogonPoet buried cables are protected from wind damage, temperature variation, lightning strikes, etc. so they can in theory last for hundreds of years without maintenance, as long as you insulate it in something non-biodegradable. Generally speaking: the only time you lose a buried cable is if someone digs into it, or if you are in a major earthquake zone. Jan 21, 2021 at 21:18
• It’s post-apocalyptic. The conditions are toxic and corrosive. Few materials could last long even underground. Jan 21, 2021 at 21:50
• @VogonPoet It's easier to insulate a wire than a giant aqueduct. So, if the world is really acidic, insulating your wires in teflon will protect them. If its an alkaline corrosion, then use nickel plating. If you are concerned about salt corrosion, titanium is a good option. All of these materials are also resistant to rusting from moisture which is normally the biggest concern with buried wires. Also, wires won't risk becoming contaminating and piping that outside poison into your safe zone. Jan 22, 2021 at 0:52
• "First, neither water nor any fluid which can dissociate are an option" - Interesting, why's that? Is the temperature so great that water spontaneously decomposes? I'm wondering why whatever material you're building the canals out of is capable of keeping a fluid in, but isn't capable of keeping the surrounding matter out (away from a cable). I also wonder why you want to use an open canal instead of a closed pipe. Jan 24, 2021 at 4:43

Aqueducts!

Ancient times can has many surprising feats of engineering. Aqueducts are one of these feats of engineering. Look at this one:

https://en.wikipedia.org/wiki/Zaghouan_Aqueduct

It drops an average of 0,3% it's total length over 90KM (56 miles). This small incline is enough for a continuous water flow. All by careful measurements in an age where lasers, GPS and other location/level tools were not in the mind for centuries. It moved between 200 and 370 liters of water a second. Although not comparable to modern electric generation, it's still impressive.

Let's say you make such an aqueduct. You can already see from the example that you can use natural resources to simply move into the aqueduct and arrive at the city! In addition to fresh water, you'll have water flow, which equates to power when you put dynamos with water wheels into the water.

To make this work you need two aqueducts. The water drops a bit, generate your power and then have the second aqueduct move it back, without raising the water. As an example, the water travels a kilometer and drops 1m. It gets to the city, the flow and a 1m drop is used to make power and then it us sent back a kilometer to the power stations with another meter drop. The water is now 3m lower and requires this height to be pumped up by the power stations to flow back to the city.

To get enough energy you can widen the aqueduct and sharpen the decline, as well as increasing the amount of aqueducts. Making the fluid heavier with lower friction will help as you suggest. How much is out of my scope however.

Problems

The problems are that a power grid is likely more efficient and less maintenance heavy. Even a passive aqueduct requires regular maintenance. More that a few power poles.

Is that a real problem? Not to me. I really like the energy transport you've described. Sometimes cool us enough. You can always imagine some explanations for this. A copper shortage and concrete is better able to survive the hostile environment by not attracting active forces for example.

• Aqueduct, not aquaduct. The system must have given you the underline-red spelling hint. Jan 21, 2021 at 18:46
• @puppetsock your edit seems a bit malicious for no reason. That and your assumption is wrong. Jan 21, 2021 at 19:15
• If made wide and deep enough these can also be used to transport cargo. Indeed, a remote power generation system could be an add on to a canal network with flow being artificially produced by the power stations. Jan 21, 2021 at 19:18
• @Trioxidane technically, it was "aquæ ductum" (aquæ being the genitive form of aqua, water, and ductum from dūcĕre, bring or lead, meaning "duct, pipe"). Aquaeductus was both the aqueduct and the water-right. In composite words the æ became "e", hence early proto-Italian "aqueduttus" and modern Italian "acquedotto". But you have something there: the Latin "aquaductum" would have meant "carried by water". Therefore, the power transported might, indeed, be called "aquaduct" in the adjective form. Jan 21, 2021 at 21:51
• @Lserni: Ah, aquaduct power is transmitted aquaductum using an aqueduct. Jan 22, 2021 at 12:30

I was all set to call this idea ridiculous. Then I investigated.

Modern water turbines operate at up to 90% mechanical efficiency. Electrical generators can be 90% efficient or more. So, more than 80% of the energy delivered to the generator location could get turned into electrical power. After that, it's the local grid's problem.

To make the flow of water along the canal not lose much energy, you need the flow velocity to be relatively low. That means you want a cross-sectional area of the canal that is much larger than the flow area through your turbines. So width-times-depth of the water in the canal has to be much larger than the area of the flow through the turbines.

You would need two canals. One located at higher elevation will bring the water to the generators. A second at lower elevation takes it back. Unless you have extra power along the way, you need the level of the bottom of the canals not to change much over it's length, or fall just a little. Then at your energy source you lift the water from the lower canal to the upper canal. Very large gerbils or whatever. And you would need a source of makeup water to account for evaporation, leaking, people taking water for various purposes, etc.

The amount of energy you get per kg of water through the circuit depends on how much elevation change you can accept. And that determines how much deeper the return canal needs to be. Note that this may well be a huge engineering work.

Consider a flow area of 1 meter squared in the turbine. And suppose you need 100 m^2 in your canal. Say 20 meters wide by 5 meters deep. If it's a drop of 10 meters to produce your energy, that means you need to dig a canal 10 meters lower than your supply canal, and 20 meters wide. For the entire return half of the circuit. And it can't gain any altitude on the return. It has to be 10 meters below the supply canal the whole way. That's a lot of ditch.

Though not impossible. This construction in Winnipeg, Canada, shows that it is possible. And it is possible to sustain quite large flow rates.

So it is possible.

• Can the flow itself carry energy in a system with both canals at an equal level? For example, the fluid in this case is mercury. It will have a lot of energy in its momentum as it flows. A carrousel wheel at the city end would rotate due to this momentum, and the velocity would obviously decrease. Instead of storing energy in gravity, it could be stored in the mass of the fluid as momentum. What’s confusing is that fluid will be leaving the city slower than it arrives, and leaving the source faster than it leaves. Can such a system be a closed loop? Jan 21, 2021 at 21:27
• The force exerted on the carrousel in this case would be mass of mercury times the change in velocity per unit time. Jan 21, 2021 at 21:31
• @VogonPoet the lateral momentum of a stream of any sort comes from gravity pulling it downward along a elevation gradentant. There are more than one way of creating an elevation gradentant, (either 2 shallow slopes and 1 big drop or 2 steeper slopes and no intermediate drop), but you ultimately need that drop to happen somewhere for your medium to have any force with which to turn the turbine. Jan 22, 2021 at 14:26
• @VogonPoet, the higher the flow speed, the larger the losses, so keep the water high and flowing slow until the turbine to get highest efficiency. Jan 22, 2021 at 17:13
• @JanHudec, I assume losses accumulate through friction with the walls, so if I increase the cross-sectional area while reducing velocity, isn't the net loss the same? I have increased wall surface area but decreased velocity. I don't know if either relation is non-linear. Feb 14, 2022 at 7:25

NO. AT LEAST NOT AS YOU THINK

Flowing fluids can surely power a city. But you cannot use the same fluids in a closed loop. You have to pump the fluid to the top again by spending at least the same amount of energy the flow has created. Surely you can use multiple paddles turbines downstream depending on the flow but if you want the fluid to go where it started (a loop) you will end up with a net zero power in an "ideal" scenario.

Only sensible "net positive power" way to carry water back to where it started is weather events like snow and rain. Even that is not actually net positive and made possible by the star light reaching the planet. But the scale is too large for humans to feel the effects.

• This is the key. Any fluid that's sent down the canal which is ultimately used to power a machine to lift that fluid back into the reservoir would have been better not being sent at all. Due to the inevitable energy losses, the descending fluid will only carry enough energy to lift less fluid into the reservoir. It would be better to just keep the fluid you already have in the reservoir, rather than wasting energy draining the reservoir, which you can do for free in the first place. Jan 22, 2021 at 16:01
• @NuclearHoagie exactly! Jan 25, 2021 at 5:02
• Certainly all transmission systems have net zero power, I’m missing the criticism? Power is generated at A, stored in the canal as kinetic and/or potential energy and carried to the city B. A generator extracts a portion of the kinetic/potential energy for consumption, and remaining kinetic energy returns the fluid to the source. There is no precipitation because the fluid will be a liquid metal. A closed pipe requires room for expansion, has greater friction losses (more surface area) and higher maintenance. Yes, power is being put into the system at A. Jan 27, 2021 at 17:36

I think the idea is bonkers, but if implemented it would make a nice scenery. Here's why:

Water flows downward. I think with actually existing rivers, anything from a few % down to 0.1% (a drop of a few tens of meters down to one meer per km of flow.). So your loop is essentially a spiral, with a lifting station at one point.

Let's say a low gradient of 0.5%, distance of 40 km, and we want to extract 5m of useful work from water (or rather 5m x density x g x volume flow (m³/s) = power of the station). So we have 200m height difference in one canal, then 5m in the power station, the another 200 m on the way back - the lifting station will need to lift the water 405 m. The water arriving at the power station will have some kinetic energy, so you could probably extract more then just the energy equivalent of 5 m, but I'd need to put some thought into how to do that.

I think at the power station, you will not use a paddle wheel, you will use an auger pump or axial pump (both are good, efficient systems for high flow low head situations). At the reception station, I would build a dam and a small turbine. The steeper the gradient, the faster the flow.

If you want to go low tech - say middle ages or early modern, stick with the auger pumps or bucket elevators for the lifting station, paddle wheel for the lowerstation.

One advantage of an open loop system is the you can store energy in one part of the loop. But this would probably be more efficient with a system of closed pipes and one large reservoir.

Another advantage of an open loop system is that slow barges can cycle along the loop (they have to be lifted, via cranes or something, at both endpoints.)