# What volume of air will lift 1kg underwater?

Caladon | 20:41 Tue 07th Jun 2011 | Science
I am trying to find a website that can show me the differences between depth, volume and mass when using air bags to lift weight from the sea bed. 1 litre of air lifting x mass differs if the depth differs, but does anyone know of some basic info?
Thanks, Cal

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as you say depends on lots of variablles = company that are supplying air bags should be able to supply lift data
It depends on the depth.

Air has a density at sea level of about one kilogram per cubic metre. Water has a density of 1000 kg per cubic metre. So at sea level a one cubic metre bag will lift 999 kg.

However as the bag descends, the pressure increases. At a bit over ten meters the water exerts the same pressure as the atmosphere so the absolute pressure in the bag has doubled, halving the volume of the bag. The air still weighs a kilo but the mass of water displaced is only 500 kg. The bag will now only lift 499 kg.

Each 10.3 metres depth increase the pressure by one atmosphere. This is added to the pressure of the atmosphere itself so at about 93 meters the bag is one tenth the volume and lifts 99 kg.
Beso - surely you mean grams, not kg, from 999kg onwards ?
No it is kilograms. Note I was using the cubic metre as the volume. If I used litres that would be the case but as a science kind of person I tend to work in SI units (metres, kilograms and seconds)
Sorry, I'm still having difficulty imagining a 1 cu m bag lifting almost 1 tonne. I don't believe it !
To lift a mass of 1kg underwater the airbag needs to displace 1kg of water. Assuming water to be incompressible(reasonable) this will be a volume of 1 litre. Obviously as depth increases so does the water pressure thus the mass of air required will increase.
The question is about air and water becuase it is about the buoyancy of air in water.

Buoyancy is determined by the difference between the mass of water displaced and the mass of the float itself. Water weights one kilogram per litre or 1000 kilograms per cubic metre since there are 1000 lites in a cubic metre.

If you doubt this then take a beach ball, lets say a diameter of two feet (600 millimetres) and try to submerse it. It is impossible for most people because with a volume of 0.113 cubic metres it will have a buoyancy of about 113 kilograms.
Beso is correct. In theory you might want to make adjustments for temperature and density of water ( seawater being denser you will require a proportionately smaller volume of air than would be needed in freshwater). In practice these considerations are insignificant.
The crushability of the container (and the weight) would make a difference too.

surely 1KG could be lifted by a 1.001 litre bottle of air to any depth assuming you could find a infinite strength container with 0 mass?
Also, in the real world the 1kg load would have its own volume and be subject to buoyancy force. This would reduce the volume of air required to achieve lift.
Scotman ..I had assumed that Caladon meant that the weight was the weight in water! Since we are discussing lifting rather than achieving neutral buoyancy too much lift should be good enough.
Scotman: That is an important point when considering what is to be lifted.

Chuck: I would like one of those infinitely strong massless one litre containers. Bound to be useful sometime

With one of those I would go one step better than air with a bottle of vacuum. That would lift 0.1 percent more than the bottle filled with air.
As soon as I invent the infinite strength massless container I'll let you have one :)

Although I'm now thinking about a bottle of vacuum being 0.1 percent more buoyant than a bottle of air, would that not make a 1litre container of hydrogen about 7.1 percent more buoyant than a bottle of nothing.... My brain hurts thinking about it, but that doesn't seem possible.
Nothing is better than nothing. Hydrogen would be the next best thing to nothing, followed by Helium.

Nothing weighs nothing while Hydrogen weighs two grams per mole. (One mole is about 24 litres at room temperature and standard pressure.)
Lift bags are generally filled with air at their working depth. So, in practice, the problem of the air in the bag being reduced in volume with increasing depth doesn't normally arise. Instead, the problem is one of expanding air with reducing depth. This is overcome by venting off air from the bag as it rises so as to maintain a steady air volume.
As said already, for a 1 litre bag at 10 metres depth, the water pressure is rwice atmospheric pressure. It will therefore require 2 litres of air pumped from the surface to fill the 1 litre bag. With every 10 metre increase in depth, and the additional 1 atmosphere of water pressure, an additional 1 litre of surface air will be needed to maintain the bag's 1 litre volume.
There's a pretty comprhensive article on the subject, (unfortunately dealing with cubic feet and long tons), but an evening's work converting the units should provide any answers...

Comment. This is an age old problem for divers to whom it is known as 'the Bends'. Nitrogen is compressed and absorbed into the blood stream (Air is approx. 80% Nitrogen) at depth. During resurfacing the relaxing pressure allows the nitrogen to reform as bubbles in the divers blood with potentially disastrous results.
Addendum to Comment. Fish have an air bladder which they compress to achieve neutral buoyancy at varying depths.

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