Let’s Talk About Buoyancy

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Physics: Archimedes’ Principle

Diving is all about buoyancy. It is one of if not the most important skill to master in scuba diving.

At first glance, buoyancy control looks like a simple matter of balancing the downward force of your weights against the upward force of the gas in your BCD. When the two are equal, you’re neutrally buoyant and can hover in midwater.

Since the weight on your weight system doesn’t change with depth, it seems as though you have only one variable to deal with and that is the amount of gas in your BCD, in other words the upward force of your BCD. It sounds easy, right, so why isn’t it?

To better understand buoyancy while diving we first have to talk about Archimedes’ principle and then add a little bit of explanation with simple physics.

Read more about buoyancy tips on scubadiving.com.

Archimedes’ Principle

In diving we should be familiar with Archimedes’ principle (the famous mathematician’s name is not so important, but the principle is), which states that:

A body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.

In other words, an object submerged in fluid is seemingly lighter for the weight of the fluid displaced.

To explain this principle and apply it to diving situations we have to talk about density. Density is a measurement that compares the amount of matter an object has to its volume or in other words how much mass do we have per volume.

An object with much matter in a certain volume has high density, i.e. lead (12.000 kg/m3). An object with little matter in the same amount of volume has a low density, i.e. air (1,3 kg/m3). Since cubic meter has 1.000 litres we could also write that the density of lead is 12 kg/l and the density of air is 0,0013 kg/l. Let’s have a look at density of some other things we usually talk about in diving theory: wood (average 0,4 to 0,7 kg/l), water (1 kg/l), stone (average 2 to 3 kg/l), aluminium (2,7 kg/l), iron and steel (8 kg/l).

Buoyancy

Everybody knows that wood floats on water, regardless whether it is fresh or sea water (1 kg/l is more than 0,4 to 0,7 kg/l). Wood weights less then the water it displaces. Stone and metals don’t float on water (1kg/l is less than 2 to 3 kg/l for stone or 3 to 12 kg/l for metals). Stone and metals weight more then the water they displace. In terms of buoyancy, wood is positively buoyant in water (floats) and stone and metals are negatively buoyant in water (they sink).

With density in mind we can easily say objects float in fluids that are more dense than the object immersed.

Let’s have a look at another not so common example. If we melt lead (melting at 330 degrees Celsius), iron or steel will float solid on the surface of melted lead, because the iron or steel floating on the surface weights less than the displaced lead. This means iron or steel are positively buoyant in liquid lead.

We express how much positive or negative buoyancy an object has with a number that tells us what the difference between the weight of the displaced fluid and the object is. If this difference is positive the object will have that much positive buoyancy. If the difference is negative, the object will have that much negative buoyancy. If the difference is zero the object will be neutrally buoyant. Adding or removing weight will make the object sink or float.

Fresh and Salt Water

Fresh and salt water have different densities because of the salt dissolved in salt water that makes it more dense. 1 litre of fresh water weights 1 kg. 1 litre of salt water weights 1,03 kg.

A rubber balloon filled with fresh water would float in salt water (positively buoyant), whereas a rubber balloon filled with salt water would sink in fresh water (negatively buoyant). A rubber balloon filled with fresh water would hover (be neutrally buoyant) in fresh water and a rubber balloon filled with salt water would hover (be neutrally buoyant) in salt water (density of rubber is very close to water +/- less than 10%).

If an object is either neutrally or positively buoyant in fresh water it will be positively buoyant in sea water.

If an object is neutrally buoyant in sea water it will be negatively buoyant in fresh water.

If an object is positively buoyancy in sea water you cannot tell what will happen to its buoyancy when it will be placed in fresh water without additional information.

Buoyancy and the Human Body

The average density of the human body is 0,985 kg/l and the density of seawater is about 1,03 kg/l. The average density of the human body after taking a deep breath of breathing gas changes to 0,945 kg/l. So you can see where this is going. Wearing only a swim suit most people if they inhale will be positively buoyant and if they exhale will be negatively buoyant.

Adding scuba gear will complicate things a bit. Most of the scuba gear except the exposure suit is more or less neutral or a little negative. Exposure suit is positively buoyant and changes buoyancy with depth. The scuba cylinder is negatively buoyant, but as the amount of gas in the cylinder changes so does it’s buoyancy. A 12 litre cylinder filled to 200 bar contains 2,4 m3 of gas which weights around 3kg. An aluminium cylinder could be positively buoyant towards the end of the dive. Divers can compensate the buoyancy of themselves with all gear in place by adding weights and later air in the BCD and their lungs. The amount of air in the lungs effects buoyancy only if we dive open circuit scuba.

Simple Buoyancy Calculations

When you do simple calculations in order to determine the buoyancy of an object suspended in fluid you need to know the weight of the object, the volume or weight of  water it displaces and the density of the fluid displaced.

Exercise 1: How much gas must you add to a lifting device to make a 300 kg object that displaces 100 l or fresh water neutrally buoyant?

The weight of the objects is 300 kg. The weight of the displaced water is 100 l x 1 kg/l = 100 kg. The object is 200 kg negatively buoyant. To make it neutral we have to displace 200 kg of water with the lifting device. The volume of  the gas to add is 200 kg / 1 kg/l = 200 l. So the answer to the question above is: we have to add 200 l of gas to the lifting device to make it neutrally buoyant.

Exercise 2: A diver weighting 90 kg dives in fresh water and displaces 100 litres.  How much lead weight must he wear to have 2 kg of negative buoyancy on the bottom?

The weight of the water the diver displaces is 100 l x 1 kg/l = 100 kg. The diver is 10 kg positively buoyant. To make him neutral, he needs 10 kg of weight. To make him 2 kg negatively buoyant, he has to wear a total 12 kg weights.

Exercise 3: An anchor weighting 450 kg is lying at the depth of 20 m in salt water. The anchor displaces 130 litres.  How much gas do we have to take from a scuba tank and transfer it to a lifting device to bring it to the surface?

The weight of the water the anchor displaces is 130 l x 1,03 kg/l = 134 kg which makes the anchor 316 kg negatively buoyant. To make it neutral we need to displace 316 kg of salt water. The volume of 316 kg of salt water is 316 kg / 1,03 kg/l = 307 l. The pressure at 20 m is 3 bar. We have to take 3 x 307 l from the tank and transfer it to the lifting device where the air will be compressed back to 307 l. So the answer to the question above is 921 l.

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