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Recently, I found out about /r/InfrastructurePorn, and I found a particularly interesting photo of the Gouwe Aqueduct in Gouda, NE:

enter image description here

It seems like the bridge that is supporting the boat wouldn't be able to do it. Is the weight of the actual boat being supported by the aqueduct?

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The ship is floating and so is supported by the upthrust due to the water and so the weight of water displaced by the ship.
If the ship travels very slowly so that the level of water does not rise but rather flows away then the weight supported by the aqueduct does not change between the ship present and no ship present situation.
In practice I would imagine the water level does rise but probably by only a little.

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Yes -- because if the boat displaces xx tons (however many tons it is) of water, then if the ship weren't there then the water would be (where the boat is now) -- and it's IMO clear that the weight of that water is being supported by the aqueduct.

I guess the boat looks relatively heavy, but it's mostly hollow.

Another way of looking at it is that the aqueduct needs to carry enough water (width and depth) to float a boat of that size.

If the boat is (eyeballing it) 60m long with 3 decks, that displaces (googles for motor yachts of comparable size) about 1000 tons order of magnitude.

I think that is a lot, compared to e.g. a big truck, which weighs only 30 tons -- but an ordinary road bridge obviously carries several trucks, and that bridge is short and stubby -- so its ability to carry the weight is not implausible.

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Another way to look at this is to ask yourself "how is the water at the bottom to know about the ship above it?" It can't; a given water volume "communicates" only with its immediate neighbors. Now it's possible that the water volume at the bottom experiences different pressures from different sides. This will just push it away along the pressure gradient, until all over the bottom all water volumes experience the same pressure again. That may happen while the ship is passing over a spot, because of the waves created by the ship, but is only minor and temporary. Any water displaced by the ship just flows away until the water pressure is the same again at equal depths all over the length of the canal.

Since the water pressure of the bottommost layer is what the bridge must carry, and doesn't change, what the bridge must carry doesn't change either. Q.e.d. ;-).

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