Pressure and pressure differences in fluids

Most people know that liquids are fluids; we often hear the phrase "drink your fluids".
But most people don't know that gases are also fluids !

Why are they both "fluids"?
Its because of their particle structure; they are both made up of particles that are able to move around fluidly (meaning: over and around each other, unlike the particles of a solid which are fixed in positions, free only to vibrate). Hence the term "fluid".

OK. So, now we know that both liquids and gases are fluids, what causes them both to exert pressure on objects?

Well, again, it is due to their particle nature.
Their particles are constantly moving and quite literally bashing into whatever gets in their way. So, if an object, such as a person, is "in a fluid", like water, it is bombarded by the fluid's particles causing it to "feel a pressure".

Why don't we notice the pressure of the air when we are "in it"?
It's because in a gas, the particles as so free to move that they bombard us equally on all sides and in every direction, including top and bottom, so although the pressure is there we don't notice any single direction of pressure.
So, the first thing to learn is - in a fluid Pressure acts in every direction. See diagram 1.

Because the pressure acts in every direction over our body, we tend not to notice it.

The situation when we get into a liquid, however, is different!

Pressure DIFFERENCES in liquids cause objects to float.

In any volume of a liquid there are vastly more particles, compared to in air, so there is a greater pressure (due to more bombardment).
But, there is also a greater pressure DIFFERENCE over an object, such as a person, that is partly in and partly out of the liquid.

In diagram 2 you can see that the pressure due to the Water, even just below the surface is greater than the pressure due to the Air.

And as you look deeper in the Water you see that the pressure arrows get bigger indicating a larger pressure.

It is this Pressure DIFFERENCE that is the cause of floating.

Pressure, Force and Area

If you look again at diagram 2, you should be able to agree that all of the left pointing pressure arrows cancel with all of the right pointing pressure arrows, leaving just a single black downward Air pressure arrow and a single blue upward Water pressure arrow.
In diagram 3 we have deleted the left and right arrows leaving just the single up and down arrows since these are the ones that are causing the overall pressure DIFFERENCE.

Now, can you see that the DIFFERENCE of these pressures will cause a single resultant force and it will be upward, won't it?

This upward force is called Upthrust and if the Upthrust is big enough to balance the person's weight then he or she will float.

OK, so far so good, but what has Area to do with this?

Well, the water particles have to bombard the object (the person) to produce the Upthrust. If they only have a small area over which to act (just the feet), then it makes sense that the final upward force, or Upthrust, will be relatively small compared to if, for example, the person was lying down!!

In diagram 4 the person is lying flat in the water and so many more upward pressure arrows are able to act.

Since this pressure is acting over a larger area, it produces a larger resultant upward force or Upthrust. This is why it is easier to float lying down.

Note: It is not the Pressure or Pressure DIFFERNECE that is greater due to the increased area; it is simply that a given Pressure DIFFERENCE acting over a larger Area must inevitably produce a larger Upthrust force.

So objects with a large Area will be more likely to float.

Floating and Sinking

Any object will float if its Weight is less than the Upthrust due to the pressure DIFFERENCE between the fluids, water and air, acting on the object.

And we have seen that the way to make the Upthrust large is to make the surface area of the object as large as possible.

With this knowledge, we are masters of floating and sinking !
We can control what floats and what sinks!

Let's consider 2 examples, humans and ships.

Humans

It is probably true that all humans, wearing a swimming costume, can float so long as they lie on their back as in diagram 4 above and repeated below.

If, however, the person puts on some clothes such as a shirt, trousers, socks and shoes, then their Weight will increase, but the Upthrust due to the water will not, so it will become likely that the Upthrust will NOT balance their weight and they will start to sink.
This is why rescuers make every effort to take off clothes before they jump into water to rescue another person.

Ships

How is it that a ship, made from iron and steel, with a mass of half a million tons can float?
If you took such a lump of steel (or even just a 1 Kg lump of steel) and simply dropped it in the water it would sink, no doubt.

The reason that the gigantic steel ship like an oil tanker floats, is that the steel is spread out into a hull that covers a huge surface area which, with a lot of water pressure acting on it, generates an enormous Upthrust, large enough to balance the massive Weight of the ship!

Obviously, if the ship's captain took too many passengers or too much cargo then the Weight of the ship could begin to get close to the size of the Upthrust putting the ship in danger of sinking, and this has happened in the past, but not so often on modern large ships today.

The ship shown in profile above has plenty of hull surface area to spare; it could be loaded up and drop lower quite a bit before there was any risk of sinking.

Pressure of Water And Its Depth

In the Ship diagram above we state that the ship has plenty of hull surface area to spare, so it could be loaded up, drop lower in the water and still float.

Why is this?

It is for two reasons.

One, if the water acts on a larger hull area, which is what will happen when the hull drops lower in the water, then there will be a larger Upthrust force

Two, the water pressure increases as depth increases (we stated this nearer the start of this page).

So, for these 2 reasons, as the ship drops in the water, the upthrust gets greater.

Why does pressure increase with depth? Well, the liquid (or fluid) is made from particles; there will be more particles in a larger/deeper column of fluid above a point and so there will be a greater weight of fluid and so a greater pressure.

Imagine 3 fish at 3 different depths of water, as shown below.

The first fish has less water particles above it, so less weight of water above it and so less Pressure; hence shorter pressure arrows compared to the third fish in the deepest water.

Don't make the mistake of thinking that the pressure due to the column of fluid above a point always acts downwards and so causes a downwards force; it doesn't!
Remember what we said at the start of this section - in a fluid, pressure acts in every direction.

So, if we put an object 1m below the water it doesn't get forced downwards by the water, instead we might feel it being buoyed up by the water and it might even want to float!
This is because the pressure lower down will always be greater than the pressure higher up, making an object float or making it feel less heavy.

A heavy bag is lowered into water on a rope.
It is "buoyed" up due to a greater pressure at the bottom compared to the top.
But take note that the pressure acts all over the bag.

A good example of how water pressure increases with depth is a dam built across a lake to make a reservoir. Engineers know that the base of the dam has to be built stronger than the top to cope with the higher pressure.

Water Pressure At Extreme Depth

Did you know that submarines are limited in how deep they can dive in water?
If they go below a certain depth the increasing water pressure would eventually crush the steel hull of their vessel.
Whilst a World War Two submarine could operate at a depth of about 200m, a modern nuclear sub can operate at close to 500m, but not any deeper.

However, a special submarine designed purely with one purpose, to take one man down to the deepest part of any ocean on Earth, reached its destination, a depth of 10,900m in Feb 2012 and the pilot of the vessel was the film director James Cameron (director of Aliens, Avatar, Titanic, Terminator etc.)

The link between Pressure, Force and Area

Let's take our ship example. If the ship floats, then we know that its Weight (the downward Force), equals the Upthrust (the upward Force) due to the water Pressure acting on the surface Area of the ship's hull.

These 3 quantities are linked by the following formula:

So, let's say our ship weighs 100,000 N and the surface area of the hull is 100 m²; what is the water pressure acting on the hull?

Solid Objects and Pressure

Now, we have said a lot about liquids or fluids and how their Weight causes them to produce a Pressure and an upthrust Force, and we know an equation that allows us to calculate the size of this Pressure.
Well, we can use the same ideas and exactly the same equation to consider the Pressure produced when a solid object acts on any surface or Area.

For example, see Diagram 1, to the right or below.

What will happen to this Pressure if the person is wearing very thin heels and tilts back onto these thin heels?

The Weight will be unchanged, but the Area will reduce significantly to about 0.0002 m² (that is an area of 1cm² for each heel). See Diagram 2.

This second example serves to illustrate the effect that Area has on the size of the Pressure exerted by a solid object

Once you understand the effect that contact Area has on pressure you can choose the contact Area to suit your need, eg. if you had to walk across a field of soft snow you could choose to wear snow shoes which would be like fitting two tennis rackets to the bottom of your shoes; the large contact Area would enable you to produce a small Pressure on the ground (the snow) and reduce your chance of sinking. Alternatively you could wear a pair of skis, which would have the same effect.

A good example of choosing a small contact Area to produce a high Pressure is a drawing pin! Just think how easy it is to push a drawing pin into a board with the force of your thumb. It is due to the tiny, tiny contact area of the pin, producing an enormous pressure at the point.

Solid Objects, Pressure and Stress

When an object such as the drawing pin mentioned above is pushed towards a surface we can say that it "stresses" the surface in a certain way.
It might sink into some surfaces,
but it might just scratch other surfaces.

A person standing on a polished floor with normal shoes is not likely to damage the surface, but
a person standing on the same floor in sharp heels is likely to damage the floor due to the high pressure causing the heels to sink into the surface.

So, you need to be aware that it is the size of the pressure and the nature of the surface which will determine the effect produced on the surface; whether it will be essentially unaffected or whether it will be damaged due to the object sinking into it or scratching it or breaking it.

Since the size of the Stress produced on a surface must be the same as the size of the Pressure exerted by the object, the same formula is used to calculate "size of Stress":

Atmospheric Pressure

Air is a Gas and we have already stated that a gas is a Fluid, just like a liquid.

Reminder: gases and liquids are called fluids due to the nature of their particles - they are able to move around or to "flow", fluidly.
A solid, on the other hand is not a fluid because its particles are not able to flow; (they do move, but only in the sense of a vibration).

Since the air particles are particles of matter (again, like liquid particles) they are held by the force of gravity, forming a "blanket" or "belt" of particles around the Earth which we call the "atmosphere".

Here is a definition for Atmosphere:
The atmosphere of Earth is the layer of gases, commonly known as air, that surrounds the planet and is retained by Earth's gravity.

Living at the bottom of this layer of gases, as we humans and most animals do, we feel the maximum atmospheric pressure on a daily basis. So, what is the value of this Standard Atmospheric Pressure?

It is a huge value, approximately 100,000 N/m².

Two questions immediately arise the first time you see this number;
1) Why is it so large? and
2) Why aren't we crushed by such a huge pressure? (it is equivalent to a force of 1000N acting on every cm² of our body.

1. Why is atmospheric pressure so large?
The answer is pretty obvious when you think about it; we have said that the atmosphere is a layer of gases and we are at the bottom of it! So, as we walk about the Earth, there is always something like a 20Km thickness of gas above our heads weighing down on us. The atmospheric pressure is due to the weight of the long column of particles above us. So, its not surprising that the pressure is large.

2. Why aren't we crushed by such a huge pressure?
At the beginning of this section on Pressure, on the first outline diagram of a person, we showed AIR pressure arrows pointing inwards, but the diagram must be incomplete. (Let's repeat diagram 1 here.)

Now that you know the size of the indicated inward atmospheric pressure you should realise that the person would get crushed IF diagram 1 told the whole story.
So, what is missing from the diagram?
Answer- there MUST be arrows inside the body pointing outwards!
There must be air inside the body producing an outward pressure to balance the inward pressure due to the atmosphere.
This turns out to be true.
There is air inside our bodies, in particular inside our lungs, ears, throat, stomach etc. This air produce a pressure which balances the inward pressure due to the atmosphere.
Additionally, there is a lot of liquid in our bodies, and liquids, unlike gases are incompressible so they resist the atmospheric pressure and push back on it with the same pressure.

Now we know why we are not crushed by the atmosphere, let's move on.

Atmospheric Pressure Varies With Height

At sea level a person has about 20 Km of atmosphere (air) above him or her producing a maximum pressure of about 100,000 N/m². If the person goes higher and higher up, say by climbing a mountain (a very big one, like in the Himalayas) then it is obvious that there will be less atmosphere above him or her and hence less weight acting downwards and so, less pressure.

So, we can initially conclude:
Pressure is due to the action of particles bombarding or colliding with an object. The higher up one goes, the lower is the atmospheric pressure because there are less particles above the person or less weight of air above the person.

See diagram 2.

But there is a second reason why Air pressure gets lower with height (a reason not shared by liquids, our other "fluid").

Unlike water and other liquids, the density of air is not constant.
As height increases, the density of the air in our atmosphere decreases. We say, it "gets thinner". At the very highest points we say that the air is "too thin to breathe" and at that point people need to bring their own air with them in cylinders. We see RAF jet pilots and mountaineers on Everest doing this, wearing full face breathing apparatus.
A decrease in density means a decrease in number of particles in the column of air above the person and hence in the weight of the column and thus in the pressure.

See diagram 3

So, we can finally conclude:

Atmospheric pressure varies with height due to two reasons:
1. As one moves higher up into the atmosphere, there is a shorter column of air above a person, so the weight of the air above a person decreases and the pressure decreases.
2. As one moves higher up into the atmosphere, the density of the air decreases and so the number of particles decreases, causing a decrease in the weight of the air above a person and a decrease in the pressure.