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So, I have a question that focuses on a character from a show, Spongebob. Sandy Cheeks lives in a reverse aquarium under the sea in Bikini Bottom, in a dome that looks like this enter image description here The Treedome is made out of polyurethane, and had grass and an large oak tree. My question is, could you make the treedome in real life? It would need to solve five problems.

  • Where to get food

  • Where to get water

  • Could she survive in that temperature

  • Where to get oxygen

  • Pressure

Bikini bottom is located in Bikini Atoll’s sea floor, where ch is about 180 feet, or 55 m underwater.

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  • $\begingroup$ Welcome to worldbuilding. Please note that we prefer to have 1 question per post, while here I count more. Please split them into more posts. $\endgroup$ – L.Dutch - Reinstate Monica Jun 17 '18 at 18:59
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    $\begingroup$ @L.Dutch I see only one question here: "Can X be built?" The rest of the post is either explanation of what X is, or factors an answer must take into consideration. I fail to see how this is either too broad or off-topic. $\endgroup$ – Frostfyre Jun 17 '18 at 22:27
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    $\begingroup$ Why on earth are people voting to close this question? It isn't too broad just because the OP is asking for a thorough answer and the question absolutely is about worldbuilding according to our help center. We've answered a lot of questions about undersea habitats here. Are you all rep hunting? $\endgroup$ – JBH Jun 17 '18 at 22:32
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    $\begingroup$ I'll also note that questions about pre-existing worlds are on-topic here; see, for example, worldbuilding.meta.stackexchange.com/q/3141/627. $\endgroup$ – HDE 226868 Jun 18 '18 at 3:48
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    $\begingroup$ @Frostfyre, I see your point. VTC retracted $\endgroup$ – L.Dutch - Reinstate Monica Jun 18 '18 at 5:28
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If she has a basement beneath that dome holding a lot of equipment, yes.

She'll need equipment to do electrolysis to split water into hydrogen and oxygen, so she can breathe. She'll also probably need some kind of furnace, in which she can burn kelp or other plant matter. This is because the tree and grass probably need more CO2 than can be provided by one squirrel. I highly doubt she and the tree are in perfect CO2-O2 equilibrium. She'll need desalination equipment to get fresh water. Pressure is no issue. Submarines regularly dive much deeper. It won't be all that cold, so heating is not too much of an issue. Temperature varies a lot as the ocean currents change, but it will generally be about ~60F or ~20C at that depth. She can get food with hydroponics and grow lights. All of this will require electricity, so she'll need some kind of power generation; maybe geothermal or nuclear. Fossil fuels don't work because she needs the oxygen.

At 55m depth, there will still be some light, but I don't know if it is enough to keep grass and an oak tree alive. It will be approximately 25% of the light on the surface. I suppose she could use more grow lights, but we don't see them when we look at the dome.

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    $\begingroup$ Does she really need electrolysis to make breathable oxygen. Isn't that what the tree is for? $\endgroup$ – J. Joscak Jun 18 '18 at 8:08
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    $\begingroup$ some kind of power generation; maybe geothermal or nuclear. Or simply relying on the current. Wind-based power generation also works as water-current based power generation. $\endgroup$ – Flater Jun 18 '18 at 11:25
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    $\begingroup$ @Mast: Don't underestimate the thickness factor. Plastic bottles are exceedingly thin, compared to a submarine hull. If Sandy's PU wall was as thick as a submarine hull, it would hold as well. $\endgroup$ – Flater Jun 18 '18 at 11:27
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    $\begingroup$ What keeps the whole thing from floating? How can a sandy bottom secure it? $\endgroup$ – Keeta - reinstate Monica Jun 18 '18 at 14:18
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    $\begingroup$ @Keeta: Presumably all the heavy equipment in the basement keeps it weighted down... $\endgroup$ – Chris Jun 18 '18 at 14:27
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At 55m the pressure is about 5.5 bar, which is the same as, roughly, 5.5 atmospheres a polyurethane dome can take that, it's only 80 something PSI. At 55m there's still generally enough light for photosynthesis, but it's getting sketchy, coral bottoms out at about 60m so the grass and the oak tree are a stretch but possible, especially if they aren't quite what they appear to be. The water temperature at that depth is difficult to qualify, depending where in the world Bikini Bottom is it could be as high as 30°C or as low as 4°C but whatever it is, due to the high specific heat of water, the atmosphere of the dome will be the same temperature. With sufficient vegetation food and oxygen are taken care of, as it is in the images we get of the dome that isn't the case for a human sized creature but for a squirrel of "normal size" that may actually be enough photosynthesis and enough acorns and grass seed. Otherwise she's going to need a means of electrolysis to "crack" water for Oxygen and she'll need to bring in food.

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The dome won't make it

Hydrostatic pressure is

$$ p = \rho g h ,$$

where $\rho$ is the density of seawater (1025 kg/m$^3$), $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $h$ is depth underwater (55 m). Thus, hydrostatic pressure at the given depth is 552 kPa.

Let us assume a spherical dome that can contain an oak tree comfortably. Lets say the dome has a radius of 50 meters. The total surface area of such a dome is the area of the corresponding circle, $\pi r^2 = 7854 m^2$. Multiply this by the pressure and we get $4.3\times10^{9}$ N of pressure.

Can such a dome make it? Not if it is made out of any known material that is transparent. Lets assume the force of the water pressure is concentrated around the circumference of this 50 m circle (314 meters). This yields am equivalent of 14 MPa of pressure on the entire glass circumference. Glass typically has a tensile strength of 7 MPa and compressive strength of 1 MPa; not enough for this application.

A glass dome would be crushed by hydrostatic force at this depth. Sandy is getting wet.

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    $\begingroup$ Could the sea pressure be compensated by using compressed gas in the dome, perhaps a trimix pressurised to 552 kPa. It seems your calcuations are based on there being a vacuum inside the dome. (I'm thinking of Cameroon's Abyss, where the deep sea research station is kept under pressure.) $\endgroup$ – James K Jun 18 '18 at 6:43
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    $\begingroup$ If the dome is at 55m and the oak tree is 50m high, then the dome is a little out of the water, which is obviously not the case. I think it's more of a bonzai tree or something. If Sandy is a squirrel, and the sphere is approx 5 times the height of her, then the radius must be something about 1 meter. You might want to recalculate. $\endgroup$ – Asoub Jun 18 '18 at 9:30
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    $\begingroup$ It's also apparently not glass according to the OP. $\endgroup$ – Ash Jun 18 '18 at 10:01
  • $\begingroup$ Have a search for Alon, this first ever transparent Aluminium. it would in theory have the strength required for this dome. $\endgroup$ – Blade Wraith Jun 18 '18 at 10:15
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    $\begingroup$ Ah, I think I've worked out what you did... You took the total force applied to the entire dome (4.3GN) and then effectively assumed it was concentrated on a 1m high strip at the bottom of the dome (314m^2) and so divided the two to get the new pressure. This is not how it should work. At any depth the pressure being applied to an area of the dome will be based solely on the depth at that point so the pressure on the bottom of the dome will be the greatest and will be the 552kPa that you have calculated. $\endgroup$ – Chris Jun 18 '18 at 14:38
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"The Treedome is made out of polyurethane"

Are you absolutely sure about that? PUR is usually used as insulation, so it probably helps with the temperature. But it's generally not strong enough as a weight-bearing material. You can make a couple of bushings, sure, but a dome under that much water... I'd guess it would become a very thick layer. Which brings the following:

Making a dome out of see-through PUR is hard. Especially since PUR tends to discolour under light. Yes, there's not a lot of light at 55m, but it's no total darkness either. There's also the problem of some ground-living fungi being able to eat the stuff, depending on what type of PUR you use. Polyamide (nylon) might be a better fit. Added benefit is PA can be poured instead of woven, making it easier to get it in any shape you want.

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