Someone is trapped in a small room (say, 20ft by 20ft), 100 feet underground. If there is water nearby the room, how could it be used to get a human out? There is not concrete around the room, to clarify, just dirt.
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I would like more information, but I'm going to try and take your question exactly as asked. My assumptions are:
- Room is enclosed
- Room is big enough to stand and move in
- There is no exit (natural or otherwise) - 6 closed walls
- There are no heavy/power tools
- The surroundings contain flowing groundwater (since you mention geysers and underground streams)
This person is going to have to break down a wall to escape no matter what. With any kind of scraping/bashing tool they should be able to do this. How will they know which way is up? Backcountry skiers are often told that if buried in an avalanche they should spit and see which direction it falls. If you spit and it falls into your own nose you are upside down. But really if the room is big enough "up" will be apparent when moving. After orienting themselves and breaking down a wall, what will our unfortunate person encounter?
surrounding dirt/rock: This means you have to dig your way out. Let's say for a human you need a hole about 1.5 ft in diameter - you would have to excavate ~180 cubic feet (maybe 1-1.5 large dump truck loads) of material. Remember you would mostly be working wedged inside a small hole, and you would have to push all the excavated material below you (although maybe you could end up standing on it?). Also, let's assume you are lucky enough to hit/tap the surrounding groundwater and thus your needs for hydration are taken care of. Humans can live almost two weeks with no food and fresh water. We should assume one week, because in this scenario you will be expending a LOT of energy. For hard rock or clay this is probably a death sentence. There's just not enough time to chip away at these materials, especially without having any food to sustain yourself. For more "crumbly" rock or softer dirt, I get the feeling that this would be pretty doable despite being a terrifying endeavor.
underwater stream: This one is the most uncertain. Underground streams are often water traveling through a more porous section of dirt rather than a stream as we would think of on the surface. Let's assume however that you found an underwater stream that was open enough to fit into and flowing quickly enough to carry you. This would probably be a last resort. You have to climb onboard and hope that you make it to the surface without:
-running out of air
-reaching a blockage
-the passage narrowing too much
-hitting an area of reduced flow and becoming disoriented
geyser exit hole: this actually may be the best outcome. I think it would be somewhere between dangerous and impossible to "ride" the geyser. However, between eruptions of the geyser they should have a nice hole to climb out of. If the hole is wide enough or they are able to widen it at blockages, 100 feet up a rocky chute is actually probably the easiest escape.
Assuming the room is at the bottom of the vertical shaft, in wet climates it will naturally turn into a well. It might take some time to fill, and he needs to stay buoyant and not freezing for the duration. He might need to damage walls to help water do its job, and then the last few feet before the surface is left as an exercise.
I assume the person can get out of the room itself, like there is a door, or walls are breakable. And I also assume guy has access to water; otherwise he will not be able to do any physical work after a few hours.
After getting out of the room, it depends on what is around and above the room.
If the room was built by conventional means, there must be an access hallway or shaft or cave next to it. You mention water, and waters carve caves out of the rock quite often.
If the room is buried in dirt, sand, or gravel, you guy should be able to dig out, especially if he can use some digging tool - furniture from the room, door handle, pieces of drywall. Otherwise, he will wear his fingers down to the bone, but it is better than dying.
If the room is teleported into solid rock, covered by concrete, will never make it out, at least not without some serious tools.
Riding a geyeser is impossible: hot water will cook him. Climbing up a geyeser tube is unlikely: even if time between eruptions is enough to climb 30ft, the walls will likely be hot.