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Thread: Depth and pressure in a fictional water world

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    Depth and pressure in a fictional water world

    'Allo!

    I have been playing Mass Effect 3 and at one point in this wonderful story, protagonist Commander Shepard is working to discover a mysterious, powerful alien presence on the planet of 2181 Despoina.

    The planet is a water-world; covered by a globe-spanning ocean. The probe her ship sent to find the alien is transmitting from thousands of feet below the water's surface.

    Following the obligatory fight, Shepard takes command of a Trident 'Mech - a deep-diving submersible - and drops into the abyss to confront the alien force the Alliance has dubbed "Leviathan".

    The following confrontation is powerful, terrifying and Class-A storytelling, IMO.

    BUT - I became curious as to the science of the environment and wanted to ask here. How much pressure is on the Trident when Shepard reaches the end of her long drop?

    The 'Mech's HUD shows the depth clearly: 3276m. Orbital scans show that the planet's surface gravity is 0.92g.
    From that, can we calculate the pressure on the 'mech at that depth? This is purely a matter of idle curiosity.

    Trying to remember 30-year-past scuba training and making a guess or two, I would guess that Shepard's vehicle is sitting at about 300 pressures; a horrifyingly huge number. But that's just a non-mathematic idle guess.

    Given the values shown above, what would the pressure on the Trident be at that extreme depth?
    Thanks

    Of course, I would not be me if I didn't offer a video of the encounter so here it is.
    https://www.youtube.com/watch?v=YujyLlV1f50

    Cheers!

    (ETA: And for what it's worth, to my mind this is some of Jennifer Hale's best work in the series. Shepard's voice is tight and tense; she is clearly frightened but adamant in her determination. As the tension builds she gets more clipped and stressed, but never for a moment loses her iron-hard discipline. SUPERB voice acting, in my opinion.)
    Last edited by NorthernDevo; 2017-Dec-16 at 01:04 AM.
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    That is not a non-mathematical idle guess, it is a pretty good estimate. Ten meters of water on Earth means one atmosphere more than at the surface, so 3276 meters at 0.92g is about 300 atmospheres, or about 4,400psi.

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    When James Cameron went to the bottom of the Mariana Trench apparently the pressure was like 1,000 atmospheres. That's pretty freaky.
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    Quote Originally Posted by Hornblower View Post
    That is not a non-mathematical idle guess, it is a pretty good estimate. Ten meters of water on Earth means one atmosphere more than at the surface, so 3276 meters at 0.92g is about 300 atmospheres, or about 4,400psi.
    Oh excellent; I'm pleased I remembered that correctly (33ft.=1 atmosphere), thank you. I was guessing that 0.92G would be 'a little less' so I just rounded down.
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    ro,g. h is the formula in consistent units, ro is density
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    Quote Originally Posted by profloater View Post
    ro,g. h is the formula in consistent units, ro is density
    Luckily, water is fairly incompressible, but to get an exact number -- which isn't needed for a story -- one needs to account for the fact that water density is a function of temperature and pressure; for liquids, in general, is good enough (where z is positive down, and measured from the surface and p0 is atmospheric pressure.

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    Quote Originally Posted by Hornblower View Post
    That is not a non-mathematical idle guess, it is a pretty good estimate. Ten meters of water on Earth means one atmosphere more than at the surface, so 3276 meters at 0.92g is about 300 atmospheres, or about 4,400psi.
    Don't worry your Rolex Deepsea Sea-Dweller will still be OK at that depth.
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    Quote Originally Posted by swampyankee View Post
    Luckily, water is fairly incompressible, but to get an exact number -- which isn't needed for a story -- one needs to account for the fact that water density is a function of temperature and pressure; for liquids, in general, is good enough (where z is positive down, and measured from the surface and p0 is atmospheric pressure.
    True and at great depth we have to remember g is reducing with radius, salinity would change too, so both ro and g are changing if you want accuracy.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
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    Quote Originally Posted by profloater View Post
    True and at great depth we have to remember g is reducing with radius, salinity would change too, so both ro and g are changing if you want accuracy.
    Uhh....what? Gravity reduces the deeper you go? Could you please explain that? That was just a major 'duh?' for me; I would think it is increasing.

    Edit: Oh...wait, would g be decreasing because a whole lot of the planet's mass - the water - is now above you?
    Last edited by NorthernDevo; 2017-Dec-15 at 11:58 PM.
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    Do remember that at 60 miles of depth, in a one g environment, water crushes into a solid. A form of pressure induced warm ice.

    And are we sure about that depth to pressure formula?

    I somehow feel you're off by an order of magnitude. That water pressure should increase 1 atm per meter.
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    Quote Originally Posted by BigDon View Post
    Do remember that at 60 miles of depth, in a one g environment, water crushes into a solid. A form of pressure induced warm ice.

    And are we sure about that depth to pressure formula?

    I somehow feel you're off by an order of magnitude. That water pressure should increase 1 atm per meter.
    Hallo Don; while I of course do not understand the science and my memory of scuba training is WAY out of date, I can say with absolute certainty that atmospheric pressure does NOT increase at a rate of one atm/meter. Were that the case, just diving off the diving board in a backyard pool would put some fairly serious stresses on the body - diving from a 2-meter board, a swimmer can easily touch the bottom of a 4 meter deep pool.
    The numbers I learned were 1 atm. = 33 feet, or 10 meters.
    Last edited by NorthernDevo; 2017-Dec-16 at 12:36 AM.
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    All good Mr. Devo.

    I'm both a little nerfed and chatty due to it being "happy hour" locally.

    I'll step back and probably log out, as I plan to have a few more. (A long week with a happy ending!)
    Time wasted having fun is not time wasted - Lennon
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    Quote Originally Posted by BigDon View Post
    All good Mr. Devo.

    I'm both a little nerfed and chatty due to it being "happy hour" locally.

    I'll step back and probably log out, as I plan to have a few more. (A long week with a happy ending!)
    ROFL! I'm right in the same boat as you, Mr. Don; I hope you're enjoying your Friday as much as I'm enjoying mine!
    "The difference between theory and practice is that in theory, there's no difference."

    "Aikido: the art of hitting people with planets."

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    Quote Originally Posted by NorthernDevo View Post
    The numbers I learned were 1 atm. = 33 feet, or 10 meters.
    Yes. 1 atmo per 10 metres.

    Quote Originally Posted by NorthernDevo View Post
    Uhh....what? Gravity reduces the deeper you go? Could you please explain that? That was just a major 'duh?' for me; I would think it is increasing.

    Edit: Oh...wait, would g be decreasing because a whole lot of the planet's mass - the water - is now above you?
    Not a significant factor. At depth, the sphere underneath you is still almost four thousand miles in radius. Compare to being on the surface, where the sphere beneath you is ... almost four thousand miles in radius.
    Last edited by DaveC426913; 2017-Dec-16 at 06:13 AM.

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    Quote Originally Posted by Hornblower View Post
    about 300 atmospheres
    That is the equivalent of a Ford Taurus balanced on every square inch of surface.

    For a one-man sub (a pressure sphere maybe 6 feet in diameter) that's sixteen thousand Taurus' carefully balanced on your hull.

    Balancing all those Taurus' bumper-to-bumper, equidistant from the sub's hull would make a sphere more than 4/5th of a mile in diameter.

    (I wonder if Randall Munroe would ever consider that as an illustration in his "What If...")
    Last edited by DaveC426913; 2017-Dec-16 at 06:33 AM.

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    If I remember, the bathyscaphe Trieste, which is a USN submersible, had a high-strength steel sphere about 1.8 m in diameter and 16 cm thick to deal with the external pressure of about 1,000 atmospheres when it went to the bottom of Challenger Deep.

    It's kind of funny that they couldn't use an air-filled float at those kinds of pressures, because air has a density of about 1200 kg/m3 at that depth. The float was filled with gasoline.

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    The 33 feet/10 meters = 1 Atm is EARTH only! You need to take the mass of the water above the craft to get the pressure, by the way is the sea salty? The salt in the Earths seas comes from the land!

    Mark

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    Quote Originally Posted by DaveC426913 View Post
    Yes. 1 atmo per 10 metres.


    Not a significant factor. At depth, the sphere underneath you is still almost four thousand miles in radius. Compare to being on the surface, where the sphere beneath you is ... almost four thousand miles in radius.
    Let us also remember that the decreasing g with depth does not necessarily hold if the surface layers are far less dense than the core of the planet. If I am not mistaken, g continues to rise upon deep descent for a considerable distance in the case of Earth. It can be estimated by taking crustal rocks as having a specific gravity of about 2.5, as compared with a mean value of more than 5.

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    Quote Originally Posted by holmes4 View Post
    The 33 feet/10 meters = 1 Atm is EARTH only! You need to take the mass of the water above the craft to get the pressure, by the way is the sea salty? The salt in the Earths seas comes from the land!

    Mark
    On the OP's fictitious planet, with g about 0.92 or ours, the depth would be about 11 meters.
    Last edited by Hornblower; 2017-Dec-19 at 04:27 PM. Reason: Fix an arithmetic error

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