1.1 Introduction to Pressure

Pressure can mean a lot of different things. We can be under pressure to perform, we can be peer pressured, we can pump tyres to a certain pressure, we can measure our blood pressure.

Today we aren’t looking at metaphoric pressure that we might feel when we’re nearing a deadline. We will be looking at pressure as it relates to our environment (air and water) and how it is relevant to submarines.

Pressure in a scientific context is fairly unique and can sometimes be described as a force but is actually a measure force acting on a given area. Pressure measures forces acting on an object and is more uniform than our typical understanding of forces. When we think of a force we might think of gravity, or something behind kicked or hit. Pressure is a bit different, it can be related to gravity but isn’t a force the same way gravity is.

When we stand outside we can’t really feel the pressure of the air around us. Or when we jump into a pool. But! We can definitely feel when pressure changes - you would have felt a change in pressure if you have ever been on a plane or gone up a tall hill (higher altitude). The same strange thing that happens with your ears when you go very high up, also happens when you go very far down, either lower in altitude or under water.

When our ears feel pressure they aren’t measuring pressure in the same way we would measure the temperature using a thermometer. What our ears are doing is telling us that there has been a change in pressure.

This change in pressure is what we will be looking at and what matters to us with our submarine.

When there’s a difference in pressure we call this a pressure differential.

How pressure changes from where we start to where we end up is what is most worth looking at when it comes to subs.

Pressure is a measure of perpendicular force acting on a specific area. We can visualise this simply by thinking of something being squashed, we’re applying downward pressure on something that is on a flat surface.

In cases where we’re looking at something getting squashed pressure is quite simple. It’s the amount of force divided by the area.

In the example below we will see how a balloon handles being placed on a bed of nails. We can guess that a single nail will definitely pop a balloon.

But what happens when we have a lot of nails and spread the pressure being applied by the balloon over many nails?

Earlier we said that Pressure is a measure of force in a given area. We can write that mathematically using this formula, P = F/A.

Where P is pressure,

F is force, and

A is area.

Why does Area Matter?

Let’s think about this equation for a second. If we are trying to determine pressure a major contributing factor is area. Let’s assume that the value for Force is constant.

If we substitute a value for Force, let’s say… “1”. Let’s consider what happens when we change area.

So, if P = 1/A, what do we get if A, or Area, is a very large number?

What do we get if A is a very small number?

Use your calculator to find out what happens to our result for pressure when our area is large, and when our area is small.

With our nail experiment we know what happens when we have 1 nail. But, when we increase the area to include many nails, the effects of pressure aren’t as great.

Why is all this about “uniform”?

Uniform is a word that comes up a lot when talking about pressure. What uniform means is that everything is the same, just like a school uniform.
In the nail example, uniform means that each nail is actually carrying an equal load when it comes to the pressure exerted by the balloon. All the nails are pushing just as hard as each other, spreading out the force being applied and thus greatly reducing the pressure caused by each nail.

Why is perpendicular force relevant with the nails and how might this translate when working with gases?

In this example all the nails are pointing vertically upwards, they are all pointing in the same direction. The force being applied from the balloon isn’t a flat surface but when it hits the nails, they all act on it at a right angle.
If one of the nails in the bed of nails was at an angle, it wouldn’t actually be applying the same amount of force as all the others.
Perpendicularity isn’t so much related to pressure, as it is related to how we measure pressure. When working with gases, which move about completely at random, the gases which will leave the biggest mark on our measuring devices will be those moving at a right angle, they’ll be the only ones counted because they will be applying a stronger force than those that aren’t at a right angle.

As we mentioned above, pressure is a measure of force and not in fact a force itself. If you look up forces you will find there are two different types, contact forces and non-contact forces. A non-contact force is something like gravity or magnetic attraction, these can be useful in some cases but aren’t directly related to pressure - we will use gravity in a pressure calculation later on but this is to determine acceleration and the force itself isn’t considered.

Contact forces are what we are measuring when we look at a pressure gauge or measure pressure. Whenever we consider pressure we are considering only the normal (or perpendicular) force being applied uniformly to a given surface area.

Perpendicular means “at a right angle.” Earlier we saw that a bed of nails distributes pressure across a large number of nails and really reduces the amount of force being applied on whatever is pressing against the bed of nails.

With gases in a fixed container particles are moving about randomly at all different angles in all different directions. While everything is moving randomly we would consider normal gases to eventually reach a uniform state, where they take up space in the container they’re in and distribute themselves evenly. When talking about gases the even distribution in a container is referred to as being “uniform”.

Uniform is a word that will come up quite a bit. When something is uniform, it’s the same throughout - you can remember this by thinking about a school uniform, when everyone is wearing a uniform, they’re all dressed the same and look the same.

We have considered two cases of uniformity so far. First, all the nails are uniform in their interaction with the balloon. Second, gases will fill a space uniformly.

There are three states of matter which are worth considering and understanding before going any further with our submarine. The three states of matter are solid, liquid and gas. The main ones we want to focus on are liquid and gas, understanding how these two states of matter behave is critical to achieving a successful submarine.

• Our submarine is made of solid parts which are fixed and take up physical space.
• Within and around our submarine parts there will be air (the gas state of matter), taking up space and effecting how our submarine interacts with the matter both inside and outside our submarine.
• Lastly, there will be water (liquid state of matter) all around our submarine. Water will try to fit into any open space and fill up any space that’s empty.

Pressure and measuring pressure is really useful in everyday life. Some obvious ways we see pressure are in the tyres of vehicles we use every day.

Pressure is also critical in making sure our organs and bodily processes work properly, for example, our kidneys use pressure to be able to filter & clean our blood.

In our everyday interactions with the world around us the physical universe is always trying to reach its most comfortable state. In science, this is called equilibrium. In biology, it’s called homeostasis. Wikipedia describes this as “The Balance of Nature” or Ecological Balance.

When we’re working with pressures underwater, the objects we’re working with are always working to reach a stable pressure. This can be a major problem with a submarine.

In the balloon experiment above, we saw that blowing a balloon up and taking it underwater will shrink the balloon and cause it to be harder to pop, the same amount of air that was on the surface is now taking up less space. The balloon instead of being stretched out, is less stretched out but still contains the same air that was put in at the beginning.

As the balloon is taken to a deeper depth, the air and water and fighting with each other to try and reach an equilibrium. Naturally, the balloon wants to float, and reach the surface, where the air is, so that the air pressure inside the balloon matches the air outside the balloon. Because the balloon is underwater, the water is actually trying to fight its way into the balloon, collapsing the walls of the balloon, making it smaller.

The same thing will happen with your submarine. Once sealed on the surface and taken underwater, the water will be fighting to get into the submarine. This is called a pressure differential which we will discuss later on.

Atmospheric pressure is the pressure created by the atmosphere. When we measure atmospheric pressure we are trying to “weigh” the amount of air pushing down on a certain area. It’s not something we can physically feel and we would need to use a sensitive tool to measure atmospheric pressure.

To help you remember it, you can think of something at sea level and compare the atmospheric pressure bearing down on that thing to something that might be on Mount Everest. On Mt. Everest there is much less air above being pulled down by gravity so there will be far less atmospheric pressure than at sea level. In the same way, pressure increases as you go below sea level and greater still underwater.

We don’t really consider air as something that’s heavy but on a large scale we can use this “weight” of air to create weather maps. Looking at how air is behaving in certain locations can help us predict weather. In the image on the left each line represents a different amount of air pressure.

Wind is caused when air moves from areas of high pressure to areas of low pressure. In nature and in the case of pressure systems the different pressures are trying to equalise or reach an equilibrium. While nature is always working towards a balanced state it’s almost never reached - in the case of weather there are many other factors that will influence air pressure - altitude and temperature are the main contributors.

In the two videos below we will see two versions of the same experiment. The question we are asking is…

How long is the longest possible straw we can use to drink from an open container?

Use the videos below to watch the experiments take place. You can also try this experiment yourself.

Before you start have a think about the question. Is there an actual limit to the length of a straw that we can use to draw water from?

What role do our lungs play?

What forces are acting at each stage of the experiment. Before any water is drawn, when water is beginning to be drawn and when it’s at the end either, all the way up the straw or reached a point as far as it can go.

When we’re “sucking” on a straw, what are we actually doing? What’s the atmospheric pressure doing?

Would altitude or straw diameter effect this experiment?

Why is sea level relevant?

In the experiment above we saw very real, and defined physical testing. In theory, we can work out the actual maximum height that the water will be able to go, there is a theoretical limit. When undertaking experiments, there will always be a slight variation between the expected theoretical results and the experimental results.

It’s important to keep in mind the distinction between theory and experimentation. As we develop our submarine, it’s important to draw on theoretical knowledge to base our views, opinions and design decisions upon. It’s also important to test our ideas through experimentation.

By definition, pressure is the amount of force applied to a certain area. We can write this down mathematically using the formula below.

In the formula,

P - represents pressure and is measured in Pascals.

F, represents force and is measured in Newtons, and

A represents area and is measured in metres squared.

Using this formula we can derive another formula for pressure. We will use the new formula to see if we can determine the maximum height water can reach in a straw.

Re-arranging the formula - Microsoft Word - Converting P=F:A.docx

In this derived equation:

h - represents the height of the water in metres, we don’t know that yet and want to find it.

P - represents pressure in pascals, in this case, we’re going to substitute the value for 1 atmosphere of pressure, we are assuming the experiment is taking place at sea level.

g - represents the acceleration caused by gravity in meters per second squared. On Earth we know this is 9.8m/s/s

In this experiment, we can see that someone is trying to draw water up through a straw.

When we suck on a straw, we remove air form our mouths. Decreasing the pressure inside our mouth. Atmospheric pressure is still pushing down on everything around us, including the water in the glass. Our sucking doesn’t actually do much at all, it’s the atmospheric pressure, pushing down on the water in the glass, that does all the work.

The actual maximum limit that the water can be drawn up is equal to the pressure the atmosphere is exerting.

For this reason, because it’s not actually our ability to reduce the pressure in our mouths that limits the height of the straw, but actually the weight of the air in our atmosphere itself.

Using this logic, we will not be able to pull the water higher than a specific limit. At some point, the weight of the water in the straw, will be as heavy as the atmospheric pressure.

Using the logic that it’s actually the atmosphere pushing down on our glass causing the water to rise in a straw, not our ability to reduce pressure in our mouths.

We can determine the actual maximum height. Use the internet to find out the value of 1 atmosphere of pressure in Pascals (the required units for the formula). Also find values for the density of water and the acceleration of gravity. We will plug these values into our equation.

Rearrange the formula so we can determine “h”, the height is what we want to find a value for.

Determining h and units for h - Microsoft Word - Longest straw possible.docx

A visual representation of the experiment we’re working out.

When underwater our submarine will be subject to the pressures of its environment, in this case it is the water around the submarine.

What we have found by re-arranging our equation is critical to understanding how water acts on our submarine.

In our derived equation we can see the most important factor when it comes to measuring how much pressure our Submarine is under, it’s actually the only factor we can change when manoeuvring. It’s the value we found for “h”, but when talking in sub-sea terms, it’s actually the depth of our submarine that will influence how much pressure it’s under.

The counterintuitive thing here is that the depth is the only thing influencing the pressure being applied to our submarine.

It’s important to keep this in mind for further calculations, testing and predicting what might happen with your submarine.

Looking at the equation we can see that two things are unlikely to change - the density of the fluid we’re in (it’ll either be salt water, chlorinated water or fresh water), the density of the water we’re working with will generally be constant. And gravity, g, is also constant.

As we increase the value of “h”, our value for pressure will also increase. There is a direct relationship between height (or depth with a submarine) and the pressure it is under.