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· All hail the mighty ZOM
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Right. It's dead simple. Immerse somethign in a liquid and you get an upthrust equal to the weight of liquid displaced.

So if you have a 10x10x10 cm cube of something and stick it in say water that has a density of 1 kg/litre then you'll get an upthrust of 1kg. Now- if your 10x10x10 cube weighs less than 1kg (say it's polystyrene which weighs sod all) then it will float as the 1kg upthrust is much bigger than its weight. If the 10x10x10 cube is heavier, say lead, then it will sink as 10x10x10 of lead weighs about 11kg. However it will still have the same 1kg of upthrust so it will actually "weigh" on the bottom of your sink 10kg.

For denser liquids the upthrust is greater- see Digger's post on filling the SETT with mercury.
 

· All hail the mighty ZOM
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26,665 Posts
:frown: I think I understand that bit. It's the order of the calculations that throws me. You know, the multiplying by 1.03 for sea water and 1 for fresh water, the volume of the object minus the displacement, the age of Archimedes divided by the gross annual olive crop etc etc.

Surely, in the real world, if you have to lift an object from the seabed, you take down the biggest liftbag you have, fill it completely full of air and let it go? Do people really sit about calculating how much air they need to the nearest bar? Do they buggery!
Teh problem with lifting stuff isn't getting it to the surface but overcoming the "sticktion" of the seabed.

Anyway. The upthrust of an object is it's volume x density of the liquid. Take that away from it's weight in air and you have the required upthrust you need to make it neutrally buoyant.

So- say you have a 10x10x10 cm lump of lead you want to lift. Weight in air = 11 kg. Upthrust in fresh water = 1 kg. Weight in water = 10 kg. Volume of air needed to make it neutral = 10/1 = 10 litres.

Or for seawater:
Weight in air = 11 kg
Upthrust = 1.03 kg
Weight in water = 9.97 kg
Volume of air needed to make it neutral = 9.97 / 1.03 = 9.67 litres.
 

· All hail the mighty ZOM
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26,665 Posts
Now let's be a bit silly and assume we are diving in pure alcohol.

10x10x10 cube of gold.

Weight in air = 19.3 kg
Upthrust in alcohol = 0.78 kg
Weight in alcohol = 18.52 kg
Volume of air needed to make neutral = 18.52/0.78 = 23.74 litres

So you need more air to lift in booze than in water as the upthrust is lower as the alcohol is not as dense.

BTW for you pedants out there I am assuming that the weight of air is negligible. We could be really silly and lift with argon or something which is a bit heavier so you would need more.
 

· All hail the mighty ZOM
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26,665 Posts
[1] = Strictly speaking, Force isn't measured in kg, but in Newtons (N). To convert to Newtons you need to multiply by 10. If you don't know what a Newton is ignore this.
Very stricltly speaking it's 9.81 at STP but this varies with the distance you are away from the Earth's surface.
 
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