Day: 22 January 2021

How to understand the nature of buoyancy

Sand is the most extracted resource on the planet. It makes sense, too, when you realize that it is a crucial ingredient in concrete, glass, and, of course, electronics – it shows up almost everywhere. But in recent years, the extraction of sand has increased dramatically. Growth in urban cities, and of course, smartphone use, has been a massive driver for this.

It’s a good thing we have huge deserts like the Sahara ready to go to help out with extra sand, right? Wrong! Unfortunately, the sand found in deserts is far too smooth to be adequately processed. The right kind of rough sand needed is most often found in certain rivers. In total, the correct type of sand is found only in a tiny fraction of the area of the planet. In terms of scale, the sand we need is a resource that is quite misunderstood.

These kinds of misunderstandings can lead to severe problems down the road. Sometimes, you can pinpoint them from a critical assumption. In hydrodynamics, the buoyancy force shows up in applications from marine vehicles to mooring design: it shows up almost everywhere. But it is a concept that is often misunderstood, too. In this article, we’re going to talk about the fundamental nature of buoyancy forces.

To make concrete, glass, electronic circuits, you need sand – but not the kind you can find in the desert

Buoyancy is one of the most essential forces

It is a key effect when designing almost any kind of equipment in a marine environment. The nature and behaviour of buoyancy is critical for understanding how marine vehicles and ships will move and float. For mooring systems, the buoyancy from floats keeps the mooring upright up in the water column and resists the effects of other forces like drag from ocean currents and wind.

You might know that buoyancy is the weight of displaced water

While this isn’t wrong, there’s more to it than that. Fixating on the volume and weight of the displaced water can sometimes cause confusion about what buoyancy is. But before we talk about buoyancy specifically and where it comes from, we first need to talk more about pressure in the ocean. Specifically, hydrostatic pressure. It’s this hydrostatic pressure that is the root of the effect of the buoyancy force.

Hydrostatic pressure is everywhere in the ocean

The ocean is a fluid: it doesn’t have any structure to support its own weight. This means that anything that goes into the ocean will feel the effect of the hydrostatic pressure field. You feel this when you jump into a lake or the ocean and feel the pressure on your ears once you’re in the water. There’s no escaping this pressure field – no matter where you go under the water – if you’re at the same depth, you’ll feel the same pressure.

But knowing there’s a pressure field is only the start of the story

The next key is understanding that the hydrostatic pressure field grows with depth. Why does it grow? Ultimately, you feel the pressure caused by the weight of all the water above you. The weight of all the water above you – and the corresponding hydrostatic pressure field – grows linearly with increasing depth. Again, this will be something you feel in your ears the deeper you swim down into the water – you can feel the squeeze increase as you go further down.

You will feel pressure in your ears the deeper you swim down into the water

This increase in hydrostatic pressure with depth causes buoyancy

When we are considering dynamics, we want to resolve forces acting on structures and this includes floats on moorings and vehicle hulls. Pressure is almost the same as a force, but not entirely: pressure is a force distributed over an area. Now that we know there is a linearly increasing hydrostatic pressure field, what happens when we put something in the water?

Consider a square float in the water. This is easier to draw pressure lines on than a circular float!

To understand this, you have to add up the cumulative effect of that pressure field around the entire shape in the water. The pressure field’s horizontal effects will cancel each other out. There’s no net horizontal motion from this force, but the hull will still feel a squeezing effect.

Now it’s the vertical effect where things get interesting. Since the hydrostatic pressure field grows with depth, the pressure on the top will be less than the pressure field pushing up on the bottom of the float. This difference is where the buoyancy force arises. It’s the difference between the vertical hydrostatic pressure pushing on these surfaces. This means there will be a net resulting force, but only vertically up toward the water surface: this is buoyancy.

A) Hydrodstatic pressure on all faces of the square float – but pressure increases with depth B) Horizontal pressure cancels out, and there is a net vertical pressure on the float: buoyancy!

So, where does the weight of the volume of water come into play?

It’s a mathematical shortcut that relates the effect of hydrostatic pressure on the surface of a shape to its displaced volume. This is also why a lot of the discussion about buoyancy focuses on the displaced water volume. It’s easy to work with volume formulas of simple shapes, after all. But at the end of the day, it’s essential to understand that buoyancy comes from the hydrostatic pressure field acting on a hull.

Beware of confusing buoyancy with net buoyancy

All things have weight, regardless if they are in the water or not. This weight is the force from the gravitational pull of the Earth. Sometimes this weight is referred to as the dry weight of oceanographic equipment – it’s the weight measured when the equipment is not in the water. A lot of dense equipment only has a small amount of buoyancy force. But this small amount of buoyancy force opposes the gravitational weight. This is often referred to as the wet weight of the equipment, which is less than the dry weight.

Oceanographic moorings have a series of floats and equipment, each with their own net buoyancy or, equivalently, wet weight.

Likewise, the net buoyancy is the buoyancy force less the gravitational weight. The net buoyancy is what a real float will do when it’s in the water because, in actuality, those two simultaneous forces are present at the same time: the hydrostatic pressure field from the ocean, as well as the Earth’s gravitational pull. There are two kinds of mistakes that may happen when working with buoyancy in mooring design.

The floats have much more buoyancy than weight, B1 and B2 and help lift the mooring up in the water column. The instruments and other components typically have only a little buoyancy that reduces their weight in the water. This is the wet weight W1 through W4.

One mistake is forgetting to account for weight

This mistake uses buoyancy alone and forgetting to include the weight of the component itself. If a designer makes this mistake with an oceanographic mooring, there may not be enough flotation. After deployment, the resulting mooring tensions would be lower than expected, and knockdown in a current would be larger than expected.

Another mistake is confusing net buoyancy with buoyancy

Remember, in net buoyancy, the weight is already deducted from the net buoyancy value. If buoyancy is confused with net buoyancy, the weight is deducted twice. If a designer makes this mistake with an oceanographic mooring, there may be too much flotation. After deployment, the resulting mooring tensions would be higher than expected in reality, and the knockdown would be less than expected. Higher mooring tension than expected can reduce the anchor holding capacity and cause the mooring to drift.

Often, supplier spec sheets will report the net buoyancy for flotation

Net buoyancy is useful for direct mooring design as it is the resulting lifting force float and buoys will provide. But the terminology is inconsistent in spec sheets, and you may see terms like net uplift, uplift, net buoyancy, buoyancy, flotation, etc. When in doubt, it’s essential to confirm the terms mean with the supplier.

Our civilization fundamentally needs sand for buildings and electronics. But assuming the deserts are an almost endless supply for us to use is a big misunderstanding. Similarly, buoyancy is the foundation for nearly everything we do and design for in the marine environment. Hopefully, this article helps clarify a few misconceptions about where it comes from and how it works, and where you may go wrong.

Next step

While buoyancy is one of the essential forces to understand, so is drag force. Read more on the nature of drag forces here.