How does a barge stay a float?

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Barges are heavy, but they're also huge, and not just a big, solid chunk of metal. There is plenty of "space" in a boat or ship or barge. This space is filled with air, which we know is lighter than water.
This leads to the discussion of two concepts; displacement and buoyancy.

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Displacement refers to the volume of water the ship displaces (moves out of the way) or the weight of the water displaced - depending on context.

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Buoyancy - as "discovered" by Archimedes is what actually makes the boat/ship float. This is the upward force applied by the water. (The water is trying to fill the void created when the ship displaces the water, so it's pusing against the hull.)

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The boat only displaces water equal to its weight. If you've taken a statics class this is easy to figure out. Forces have to be balanced or else the object moves until equilibrium is achieved. The weight of the vessel is equal to the weight of the water the hull is displacing. However the boat has reserve buoyancy - typically on a small boat that means that the vessel sits high enough in the water that adding extra weight (thereby lowering the boat in the water) does not cause the edges of the hull to sink dangerously close to the water level. In larger vessels there are water tight tanks, called ballast tanks, which can be filled with water or emptied to adjust the weight of the vessel. this maintains the displacement of the vessel even as it changes the weight of cargo it is carrying.

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by the amount of water it displaces

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Dispacement of water = a lot of weight.

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The boat has to weigh less than the water it displaces.

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It's easier to demonstrate using the metric system because one cubic meter equals one tonne of water.

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assume a barge had a volume of 10 cubic meters but weighed only 2 tonnes. When put into the water it would replace, displace or move aside 2 tonnes of water.

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So 80% of the boat's volume would be above the water. It would require more weight or force to push the barge deeper. You can experience this by pushing a floating ball under water.

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When we use a life jacket we are actually decreasing our weight in relation to the increase volume represented by the life jacket, thereby giving our selves more buoyancy.

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Barges have what are called wingtanks down each side of the barge and underneath it. If these tanks were to fill with water, the barge would sink.
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