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enter image description here

Source: http://www.cbc.ca/news/canada/new-brunswick/friday-flood-new-brunswick-2018-1.4647979

Is there a way to calculate how much weight a vessel can carry (in fresh water) before it submerges?

Assumptions:

  • The water is not disturbed (no waves or wind) and the cargo does not move
  • The vessel weighs 200 lbs when empty
  • The vessel's volume is 60 cubic ft
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  • $\begingroup$ Feel free to add hypothetical variables. I don't have a background in engineering; I've just guessed at the variables that apply. $\endgroup$
    – Wilson
    May 4 '18 at 14:10
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    $\begingroup$ Basically the total weight has to be less than the volume of water displaced, see Archimedes principle. $\endgroup$
    – Solar Mike
    May 4 '18 at 14:30
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    $\begingroup$ Based on that picture I it will take more sand bags than you can pile in the boat as water is not as deep as the boat. $\endgroup$
    – paparazzo
    May 4 '18 at 18:43
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    $\begingroup$ The vessel will sink as soon as the waterline exceeds the lowest point of the sheerline. i.e. the lowest point of the sides of the boat. The maximum load available is exactly equal to the weight of the fluid displaced up to that point. Even the smallest wave will unbalance the system, as will any asymmetry in the loading which will cause the boat to heel or pitch. $\endgroup$ May 4 '18 at 21:12
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    $\begingroup$ Best thing at the moment is thst none of the answers agree... $\endgroup$
    – Solar Mike
    May 5 '18 at 9:55
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A problem is that volume is not exactly displacement. Typically a boat will be a little lower in the middle and / or more weighted in the rear.

Pretend this is a perfect boat and volume = displacement.

Buoyancy is exactly displaced water * water density.

Density of water is nominally 62 lbs per cubic foot.

60 ft^3 * 62 lb / ft^3 = 200 lbs + x lbs
3720 lb - 200 lbs = x lbs
x = 3520 lb

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To show you how simple this in metric units:

  • Your boat is 91 kg.
  • Your boat is 1700 litres.
  • Water weighs 1 kg/L.

As Archimedes pointed out a couple of thousand years ago, the buoyancy will be equal to the mass of the water displaced.

  • Your boat can displace up to 1700 L. The buoyancy at that load will be 1700 kg.
  • The boat weighs 91 kg. The maximum load will be 1700 - 91 = 1609 kg.

Go metric, man. Go metric. It's so much simpler.

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    $\begingroup$ SAE is not harder if you just use SAE. Exact same math. $\endgroup$
    – paparazzo
    May 4 '18 at 18:41
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Damn customary units, its equal to the weight of the displaced water minus own weight. So

60*0.3048m^3 * 1000 kg/m^3 -0.45kg*200=1600kg = 3500 lbs

I would load it with max 0.8, so it is 1280 kg= 2800 lbs.

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