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I've been mulling over an idea for my preferred RPG setting, and I wanted to check if anyone knows the following:

Is it possible for a river to flow underground for miles, and then suddenly be put under enough pressure to jet a mile or so into the air (as the focal point of a city) and then flow away as a normal river, out the other side of the city? I prefer natural solutions, but mechanical can be included if necessary. No magic or nonsense :D

The setting, if you have a mechanical solution, is Renaissance.

Geysers can get pretty big, but they're often the result of a sudden release of pressure, whereas this would need to be constant.

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    $\begingroup$ A big problem here: erosion. The needed force is incredible, it's going to erode whatever conduit carries the water. $\endgroup$ – Loren Pechtel Oct 6 '14 at 18:28
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    $\begingroup$ Not an answer, but worth noting - world's tallest gravity fountain: stanwayfountain.co.uk/stanway-fountain $\endgroup$ – Neil Slater Oct 6 '14 at 18:40
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    $\begingroup$ James, it needs to shoot that high into the air because I'd like it to. In the same way that a lot of chinese stories always talk about 10,000 of this or that, so I'd like my fountain going up a mile. 300-400 feet doesn't really have the same ring, though I suppose it's the same principle behind it all. $\endgroup$ – Rowanas Oct 6 '14 at 19:19
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    $\begingroup$ @RowanKallioBaker-Whittaker: Make your society use the length unit of a a {insert funnny word here} which is actually based on the height of your fountain. $\endgroup$ – PlasmaHH Oct 6 '14 at 22:03
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    $\begingroup$ Also, note that a mile high is far too high for most people to actually even see the top, and in a Renaissance-based setting, it's unlikely the average citizen knows much about how to accurately use triangulation to measure vertical distances by sight. make it a ninth of a mile high (about double the height of the Stanway Fountain), then just make "one mile" the common-knowledge answer to the question "how high's the fountain?". A few sages will know better, but the better ring "a mile" has to it will be preserved for the general public, including whomever answers when the PCs ask the question $\endgroup$ – Matthew Najmon Oct 7 '14 at 16:54

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I can think of three ways a river could shoot high into the air:

For my first example, the river begins as a huge lake, high in the mountains, in a natural basin, then flows down through a fissure in the rock, deep underground. It flows underground some distance, then gently bends until pointing directly upwards. With the huge pressure of the lake high above, it jets through a natural nozzle, high into the air. However, there are significant problems with this solution. First, unlike most lakes, a mountain lake does not get much water from runoff, but instead is fed directly by rainfall. The water in the lake would have to be replaced at a rate equal to the rate it is leaving, which means the mountains will have to have substantial rainfall - on the order of monsoon season, all day every day, for even a moderate sized river. Second, the rate of erosion would quickly turn this from a jet pointing upwards to a jet pointing sideways, especially if the water is so highly pressurized that it sprays a mile into the air. Third, the path the water follows would have to be solid rock, capable of withstanding the massive force of the river. In reality, most rock would split, and the river would take multiple paths out, lowering the pressure. This system might be possible if the fissure under the lake opened after the lake was filled and drained the lake drained dry over a period of weeks or even months, but a constantly running stream would be almost impossible. On the up side, this very well might reach a mile into the air, given enough pressure.

The other method would actually be similar to a geyser; water flows down from a natural mountain spring, into an underground passage. As the water moves under the city, it crosses a pocket of magma, which heats the water enough to produce substantial amounts of steam. The resulting increase in pressure would cause the water to jet out of the exit at a much higher rate of flow. However, unlike the previous example, this water would not jet a mile into the air; perhaps only a few hundred feet, at best. The steam, of course, would shoot high into the atmosphere, and could give the impression that the jet of water was much higher than reality. Still, as long as the water maintains a constant volumetric flow, and the magma pocket continues to be heated, you could expect the river to shoot into the air for quite some time. Eventually, of course, the cooling magma and the erosive water would redirect the path of the river, but that may take a century or more.

Finally, my third method uses a bit of engineering and a bit of stage magic. A high natural stream in the mountains is diverted into a huge man-made pipe; the pipe travels down the mountain, and is buried under the city. At the location where the pipe emerges from the ground, the water is funneled into an enormous glass pipe, which reaches high into the air. The pressure forces the water up the pipe, where it then emerges in a geyser. The geyser is only a dozen feet tall, but the water running down the sides of the glass pipe would obscure the pipe itself, giving the impression that the column of water was self-supported, and much higher (and more stable) that would be physically possible. Of all the methods, this is the most likely to remain stable; as long as the mountain stream keeps flowing, and the pipe doesn't break, this system would last for hundreds of years... though don't expect the townspeople to stay in the dark about the glass pipe for very long. It's a tourist trap, not a real magical river.

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  • $\begingroup$ What about a lake on the up side of a mile-high fault, and city below? Tunnel going thorough fault would likely need to be artificial, but plains at the upper side of fault could deliver enough water for a full river. $\endgroup$ – Mołot Oct 8 '14 at 12:46
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    $\begingroup$ You could solve the replenishment problem of the first natural solution by having the mountain lake fed by glacial run-off. If the lake is high enough, the glacial snows heavy enough, and the glacier large enough, the flow of the water could be strong enough to only fluctuate slightly in different seasons. This doesn't solve the erosion problem, unless perhaps the nozzle itself was man-made, or if over time, people had replaced/patched the natural fissure in the rock with piping. $\endgroup$ – JBCP Oct 8 '14 at 19:49
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    $\begingroup$ You might be able to combine the three into a reasonably credible natural phenomenon: take a 2 mile-deep lake replenished by a glacier or melting snow, funneling into a relatively narrow underground river, increasing the pressure. Then let the river encounter magma, like a geyser, but let the river push into the magma flow, with plenty of magma above it. As the highly pressurized steam is pushed up, the magma around it rapidly cools, creating volcanic glass. At the surface, the water is pushed up in a narrow jet. The eroding nozzle is continually replaced with fresh magma. $\endgroup$ – Peter Oct 9 '14 at 6:09
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Here is a bit of math showing what you are up against. we are ignoring wind resistance.

If we want to see how fast that water has to be moving to reach 1 mile in height, we pull out the following equation...

$\sqrt{-2ad+V_{\text{final}}} = V_{\text{initial}}$

Plug in the values for acceleration of gravity, final velocity (0, we stop at 1 mile up), and a distance of one mile, converted to meters.

$\sqrt{-2\times-9.81\times1609.34+0} = V_{\text{initial}}$

$177.69m/s = V_{\text{initial}}$

Convert to mph, and we are looking at a jet of water that has to leave the ground at about 397.5mph. Breaking out Bernoulli's equation, simplified down to $P=0.5\times \rho\times v^{2}$ we can estimate that this would require roughly 15,786.86805 kPa of pressure, or 2,289.69163 PSI.

Again, this is ignoring air resistance, which is serious business when throwing something at that speed. Most of the water sprayed upward would be dissipated and scattered by wind resistance, forming a mist around the fountain itself.

As an extra fun fact, one of the highest pressure systems we have used thus far in modern day has only reached a measly 70,000 PSI, and that was a high pressure water jet cutter that could rip through steel like it was paper. So if you did get this thing running, anyone who touched it would promptly die horribly.

So...in short. No, this is not a thing you can do without magic.

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    $\begingroup$ I tried doing this, but my physics weren't fresh enough to pull it all together. $\endgroup$ – Bobson Oct 6 '14 at 21:16
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    $\begingroup$ As a point of comparison, 15 GPa is roughly the pressure used to make synthetic diamonds. $\endgroup$ – Mark Oct 6 '14 at 21:36
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    $\begingroup$ What would actually happened to water at 15 GPa? Would it remain a liquid? or change to some strange phase like Ice VII? $\endgroup$ – Colin Pickard Oct 6 '14 at 22:34
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    $\begingroup$ @ColinPickard 15 Gpa is 150 kbar, which means that at room temperature the water would be cubic Ice VII. You would have to get to around 500C in order to melt it at that pressure. $\endgroup$ – Superbest Oct 6 '14 at 22:45
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    $\begingroup$ By conservation of energy (of which Bernoulli's equation is an example) in order to generate a fountain 1 mile (1600m) high you'd theoretically need a reservoir 1600m high. that's 160 bar (16000kPa, not 160000000kPa). You're out by a factor of 1000 on your pressure. Your velocity is correct, though. .5 * 1000kg/m3 * (177.69m/s)^2 = 15786868.05 Pascal (no need to add the kilo, remember SI unit of mass is the kg.) 160 Bar is a manageable pressure, but is sufficient to throw gas pipe fittings 1/4 mile in case of rupture. Of course for water, wind resistance means that it's nowhere near enough. $\endgroup$ – Level River St Oct 7 '14 at 10:45
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The other answers have covered why it's not possible, I wanted to address a way to give you the narrative effect you wanted without being impossible. The easiest way is to have the city use it's own unit - lets say hands.

Each hand is 4 inches. 1/3rd of a foot.

Now in the description you can say the river launches itself a thousand hands into the air.

That's a 300' gravity fountain. High, but far more plausible than a mile.

It still sounds impressive - which was your main goal - while not being so impossible as the one mile option.

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    $\begingroup$ Hmm, yes, that does help. It still sounds good from a narrative point of view, but, as you say, isn't nearly so difficult to maintain. Cheers. I'll upvote this, but because this technically doesn't answer the question, I must award the "answer" to armanX. $\endgroup$ – Rowanas Oct 7 '14 at 10:09
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    $\begingroup$ Award the answer to the person who helped you the most, I don't mind, got no shortage of rep :) $\endgroup$ – Tim B Oct 7 '14 at 10:17
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Even if you use magic to generate 2 million+ PSI as calculated by guildsbounty you have a further problem:

"then flow away as a normal river, out the other side of the city"

There's no practical way to get that water back down again. Even ignoring how it would spread out on the way up, Water that starts a mile up in the sky becomes a cloud long before it gets down again. At which point it's likely to leave the city in the way a normal cloud leaves i.e. it will get blown away or rain...

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    $\begingroup$ That very much depends on how much water the river carries. If it is in the amount of some rain in the area of a few square miles, then it will come down as this, a rain of a few square miles area. $\endgroup$ – PlasmaHH Oct 6 '14 at 21:42
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    $\begingroup$ @PlasmaHH: if the jet was constant, so would be the rain. In that few square mile area, all day, all night, forever. Sounds like a horror story! $\endgroup$ – Mooing Duck Oct 6 '14 at 21:48
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    $\begingroup$ @MooingDuck: Unless you are a frog. $\endgroup$ – PlasmaHH Oct 6 '14 at 21:53
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Without mechanical intervention, you will only have the pressure from the water behind the geyser to push the water up. Water pressure is based on the height of the water behind it.

So as was pointed out, naturally flowing water would need an even more impressive backdrop than your mile high geyser, more like a two mile high 'vat' filled with water to keep the pressure relatively consistent. Maybe if you had Crater Lake with an inflow at the top matching an outlet at the very base, you'd have a chance to come up with some thing like what you want, it would be a very big mountain for a 1 mile fountain though...

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I'm not sure about a mile, but perhaps if you had a (water)fall (even underground) of a considerable drop into a sealed underground pipe where the only outlet was the geyser exit you might get some volume. But to have it a mile high you might need to have a 2 mile high plateau beside it that the river could flow from to produce pressure.

Maybe you should focus on a 20 Metre geyser in the centre of a city that would still be pretty impressive.

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This doesn't exactly fit your request because it isn't a river, but it is a naturally occurring and sustained mile-high jet of water. It also comes with some requirements that probably make it unsuitable for your story, but it is interesting.

There's a phenomenon called cryovolcanism that can occur on some types of icy planets. Plumes of water vapor have been observed near the South pole of Enceladus, a moon of Saturn, reaching almost 500 km.

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Based on the calculations by @Guildsbounty I believe the following is not possible:

Having water spray up 1 mile from the earth surface without air friction, powered only at the start of the jet.

That being said, you may still find what you are looking for if you relax one of these constraints:

  1. A mile from earths surface: Of course half a mile should be easier (perhaps still not realistic), and a jet of any length should also be easier if you don't mind the jet following a parabola.
  2. Earth: Seems like the easiest compromise, perhaps you can go for a low gravity setting
  3. No air friction: Perhaps thermodynamics could be such that you have a significant airflow to help you lift all the water
  4. Powered only at the start: Obviously it is possible to pump water up a mile, you could probably construct a glass/open building to do this for you.
  5. Water: I am sure the calculations come out a bit better if you use a lighter liquid, wouldn't you just love a vodka fountain?!

I hope this can give you some inspiration.

On a less serious note: If you want to see water spray up a mile now and then the best natural solution I can think off is the eruption of a volcano.

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$$\text{Pressure} = \text{density} \times \text{height} \times g = 998.2 \text{ kg/m}^3 \times 1609\text{ m} \times 9.80665 \text{ m/s}^2 = 15.75 \text{ MPa pressure}$$ This is perfectly achievable artificially, albeit at high energy cost (about twice that of reverse osmosis desalination).

Theoretically, it is possible naturally, but I doubt it would happen in practice, as the water would have found ways to reach the surface at much lower pressures.

However, air resistance would ensure that the water did not stay as a continuous river, but dispersed into a fine mist.

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The Stanway fountain provides a reasonable guide ... a 300 ft jet in powered by a 580 ft reservoir. So a mile high jet (5000 ft) could conceivably be powered by a 2 mile high reservoir : possible in a big enough mountain range. This ignores wind resistance, pipe friction and making the pipes strong enough.

The pressure of a 30 ft column of water is about 1 atm, 100kpa, 15psi so we are looking at about 300 times that, in the region of 5000 psi - possible.

To reduce friction, use large diameter pipe keeping the water velocity low - except at the nozzle, which may need frequent replacement.

These pressures are within the ballpark of guildsbounty's answer once the mathematical error (confusing Pa and kPa?) is corrected. They are about 2x as high - the same factor as the Stanway fountain, which presumably needs this headroom for pipe friction and wind losses which also apply here.

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Your problem here is not so much the amount of energy required, but what that energy will do to the water.

Adding energy to water causes the $H_2O$ molecules to gain energy. More energetic molecules will collide more often, creating heat. As you approach the amount of energy required, the amount of heat generated may cause the water to evaporate long before you reached the desired velocity (400 mph according to @guildbounty 's calculation).

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If you do not care about all the water going up into the sky.

A Ram pump with a cavern to hold the pressurized water will provide the pressure to send some of the water up high.

The waste water will appear to form your outflow river as well.

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  • $\begingroup$ Mind filling this out more? As is it is more of a comment that a full answer. $\endgroup$ – bowlturner Jan 28 '16 at 1:39
  • $\begingroup$ A second option would be a pulser pump - both of these are ways to take high-flow/low-pressure water and convert (some of) it into low-flow/high-pressure water. This would then pump a small - or in this case, tiny - fraction of your water (if your water source starts 16 meters above your hydraulic ram then a pump producing enough pressure for a 1 mile climb would push less than 1% of the water through.) Your source would need to flow from a nearby mountain. 1 mile is too high - try 300m? $\endgroup$ – Chronocidal Mar 26 '18 at 21:53
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You might file this under nonsense but...

Have you considered using the "extinct civilization" approach? Back before recorded history there was an ancient civilization that built many wonders, one of which is this "rain making water jet"...

For example: https://m.youtube.com/watch?v=ogw6BJRL_rQ

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    $\begingroup$ Welcome to Worldbuilding.SE. If you have a moment, please take our tour. This is an adequate first answer, but our preference is to include more justification or explanation as to why your answer will work. As it stands, this doesn't technically answer the question (how would I do it?) It only provides a framework for answering the question. You can improve this by offering what the ancient' civilization's solution was. $\endgroup$ – JBH Mar 26 '18 at 20:55
  • $\begingroup$ If it was "before recorded history", then how do we know about it? $\endgroup$ – F1Krazy Mar 27 '18 at 9:32

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