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Scrooge McDuck swimming pool

If I wanted to build a gold coins swimming pool [as in DuckTales], what engineering (not security) concerns would I need to address to make such a pool feasible? For example, since gold is much heavier than water, would I need to be concerned more about the overall weight that is supported by the base or the lateral pressures applied to the sides of the pools?

Some more details:

  • He had metal walls. Would steel walls be sufficient, would I need something stronger like Titanium?
  • Humans are, in nearly all cases, under $3$ meters tall. Even though Scrooge's depth gauge is at $90 ft$, for engineering reasons let's keep the pool to $3$ meters of depth. Note: the question originally proposed a $30m$ x $30m$ x $30m$ pool, which I am now changing to a $30m$ x $30m$ x $3m$ pool.
  • The density of the gold coins is near enough the density of pure gold, i.e. $19.3\frac{g}{cm^3}$
  • The gold coins would be as tightly packed as they would be if you expect them to get jostled around often (e.g. swimming!). They would not be in neat stacks.
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    $\begingroup$ I would like to be the individual for whom this is a real, practical concern. (In point of fact, this video shows a "pool" of coins in a bank vault, though the coin material and depth/volume are not specified.) $\endgroup$ – Air Mar 3 '15 at 16:16
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    $\begingroup$ @Air I think those are a copper, aluminum, nickel alloy. $\endgroup$ – durron597 Mar 3 '15 at 16:23
  • $\begingroup$ I think the real question is: could you even fill that vault with gold? $\endgroup$ – user608 Mar 3 '15 at 16:40
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    $\begingroup$ Can you say whether you would want to actually swim in the coins? This would require the pool to vibrate in order to 'liquify' the solid coins, and would therefore require significantly more engineering. $\endgroup$ – jhabbott Mar 3 '15 at 21:33
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    $\begingroup$ Relevant "What if?" (shamelessly stolen from chat) $\endgroup$ – Air Mar 3 '15 at 21:56
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The weight of the gold would be about 52,110,000kg, over 900 meters square of floor area. This is about 82.4psi of floor pressure, or, under standard gravity, 57.9kN/m^2 live load. This is only an order of magnitude greater than typical industrial (storage, assembly) buildings that accept 7.5kN/m^2 across the floor surface.

The total weight of the gold is about 1/5 the weight of the empty empire state building, but it's about 8 times smaller in area (900 square meters for the gold vs 7,400 square meters for the empire state building).

So, back of the napkin, it would be reasonable to assume that you'd be able to find a piece of land that could support the structure.

Typical steel building techniques will be perfectly fine with sub 100 PSI support structures, though I'd suggest a concrete floor anyway. No need for exotic materials, though I daresay you can afford them. Single wall pressure vessels can handle the pressure for the walls, if you can make your building circular rather than square, but if you insist it must be square then you'll probably need to have double walls with some diagonal bracing to keep the structure square and the walls straight in the center of the walls. While 80PSI isn't extraordinary, over 30 meters of wall it will exert exceptional force.

Note that this is a quick back-of-the-napkin analysis, and I'm freely mixing pressure and weight to make determining whether it's feasible or impossible easier. A more rigorous design and analysis would be required to actually build such a structure.

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"Swimming" would be about impossible.
IF the gold conveyed buoyancy as water does, which it wouldn't, - at full density you'd "float" with about 5% immersed.
If mean density due to packing was about 50% then you'd "float at about 10% immersed.

However, if you dug/burrowed/dived (ouch) a hole and coins then piled in on top of you the mechanisms that cause buoyancy - by transferring force uniformly to all adjacent surfaces and balancing pressure across the body - would not apply, and it would be like trying to surface from a trench cave in, but worse.

If your body projected frontal area was about 0.5 m^2 then a 100mm / 4 inch layer of coins above you at full density would weigh about one ton/tonne.
Even at half average gold density that's 500 kg.

Swimming in bricks may be less painful.

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    $\begingroup$ Maybe if it would be alloyed with some mercury, tallium and such? $\endgroup$ – peterh - Reinstate Monica Mar 6 '15 at 5:16
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Gold Properties

From here:

$\gamma=19.3\ g/cm^3 \\ yield\ strength=205MPa$

How Tall?

Gold is relatively soft. It is also relatively dense. At some point a stack of gold coins will stop being separate coins on the bottom. The stack will be so tall that the bottom coins are smashed together.

It turns out that this height is about 1,000 meters.

Good news! Your gold coins will remain coins; you won't have to swim through a solid blob of gold.

Horizontal Pressure

We are going to assume that a pile of gold coins behaves somewhat like a pile of rocks. This angle of friction is 10 degrees per XKCD and this random post.

$\phi=10^\circ$

Using Rankine active earth pressure:

$K_a = tan^2(45-\frac{\phi}{2})=0.70$

This means that 70% of the vertical force of the gold is exerted laterally on the walls of the vault. This is a lot. A typical soil is less dense and exerts only about 30% of the lateral force.

Depending on the height of the gold, the following forces would have to be resisted by the bottom of the wall:

  • 3m of gold = 0.4 MPa (8,300 lb/sf)
  • 30m of gold = 4.0 MPa (83,000 lb/sf)

This would be a very sturdy wall!

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    $\begingroup$ For reference, the water pressure on the bottom portion of the Hoover Dam is in the region of 2.1 MPa. $\endgroup$ – anaximander Mar 6 '15 at 16:49

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