Pressure

Usually when someone achieves something we say that the person has reached great heights. There is something lofty about achievement. It implies being above the norm. But in James Cameron‘s case, he’s achieved great depths. And that was no mean feat to be nearly 36 000 feet below sea level. He achieved what no other person has done so far, on their own. He is the first person to achieve the deepest solo dive. To be able to accomplish this requires a whole team of designers, engineers and scientists, amongst other professionals, including the support of National Geographic. There are some interesting Physics going on here as well. So let’s dive straight into it.

I think the most challenging part of diving is overcoming pressure. It is not obvious that the deeper you go in water the more pressure you should feel on you. Why should the pressure be different when you are just beneath the surface as compared to being right at the bottom of the sea? You’re in the same fluid, in this case water, and you’re completely submerged by it so you should, presumably, feel the same effect of that fluid on you wherever you are in that fluid. That is not the case, however. Experience tells us that the deeper we dive, the more pressure builds up. Which is quite the opposite of what happens when we fly or go higher in the atmosphere. As we rise higher and higher, the atmospheric pressure gets smaller and smaller. The way we deal with atmospheric pressure and aquatic pressure is the same in that they are both fluids. The atmosphere is just a compilation of different gases (nitrogen, oxygen, carbon dioxide and so on) and gases are part of this class of matter called fluids. To put it simply, fluids can be either liquids or gases. So, the way we analyse pressure under water is the same way we analyse atmospheric pressure.

Atmospheric pressure at ground level is bigger than that at a given altitude. This is because, at ground level, we have much more atmosphere weighing down on us than when we are high up in the air. The atmosphere gets thinner and thinner the higher up we go so at the top of the atmosphere there’s less of it than at ground level. If we consider a patch of land 1 square metre in area then we can imagine a column of atmosphere with the following dimensions: 1 m by 1 m by 100 km (if we assume that the atmosphere is about 100 km thick and is fairly uniform in density – these are very loose approximations but it won’t change the concept or idea I’m trying to get across). So this column of atmosphere or air is acting down on that patch of land. If we know the density of air and we know the volume of air in that column then we can work out the mass of air acting down on the patch of land. This mass of air has a weight. And weight is nothing but a force acting downwards due to Earth’s gravitational pull. So, the weight of the column of air acting down this patch of land is what causes this thing we call pressure or, more specifically, atmospheric pressure.

Pressure is nothing but a quantity that measures how much force is acting on a given surface area. If you press down with your thumb on the table, then the pressure you’re applying is the force with which you’re pressing down divided by the surface area of your thumb. The more force you press down with, the bigger the pressure. If, you were to press down with your index finger instead and apply the same force, then there will be a bigger pressure because the surface area of your index finger is less than that of your thumb. With an even small surface area pressing down, the pressure increases. This is why when you press down a fork, for example, on the table, you are able to leave a dent (or four small dents to be exact) while all you leave behind when pressing down with your thumb is your thumbprint even though the force applied is the same. So pressure has to do with both force and area over which the force is acting.

Under Pressure

The reason you can pop a balloon with a pin but not your finger is again because of the pressure acting on the balloon. Pin, tiny surface area, huge pressure, balloon pops. Finger, larger surface area, less pressure, small dent on balloon’s surface, no pop. A sharp knife slices smoothly through a chunk of steak while using a blunt one to cut through anything is such hard work. Again, this is because of pressure. Sharp knife, very thin cutting edge, extremely small surface area, immense pressure, glides through almost like using a lightsaber, blunt knife, thicker edge, less pressure, you might as well try cutting using a hammer.

So, back to our atmosphere: the pressure acting down underneath this 100 km column of air is given by the weight of this column of air acting on 1 square metre. How do we determine the weight of air? Well, we have to know the mass because, as Newton told us, mass time acceleration due to gravity is weight, right? So how can we find the mass of this column of air? We look at air’s density. Density is related to mass and volume as such: density is  mass divided by volume. We know the density of air (roughly) and we assume it’s constant throughout this column 100 km high. We know the volume of air: that’s the length of the column (100 km) times the area of the column (1 square metre). So we can calculate its mass as the product of density and volume. Multiplied this my acceleration due to gravity (call it g), we get weight, divide the whole thing by area, we end up with the atmospheric pressure. You’ll notice that in calculating the volume of air, we multiply height by area but then in working out the pressure, we divide by area. What happens is that this ‘area’ quantity actually cancels each other out. So we do not need to worry about area in calculating atmospheric pressure. All we need to know are the following: the height of the column of air, the density of air and g. That’s it. Because g is deemed to be constant and because we can assume that air density doesn’t quite change, then all that matters, really, is the length of column of air acting down. The smaller the length, the smaller the pressure. This is why, as we rise in altitude, the length of the column of air gets smaller and therefore pressure gets smaller.

Now, let’s look at aquatic pressure. What happens to pressure as you sink into water? Imagine you’re in a big pool of water and you want to work out the pressure of water acting on a patch of floor at the bottom of the pool. Again, we consider the force exerted by this column of water acting down on the area of the floor. Because water, like air, is a fluid, we use the concept of working out the mass (and therefore the weight) of the column of water using its density. It turns out (and you can easily verify that logic) that all the pressure depends on, really, is the length of the column of water. (The density of water and g also come into play but because we can assume that they are constant then all that counts is length of water column.) Another way of thinking about this ‘length of water column’ is to consider it as the depth below the surface of water. Thus, the deeper we go, the more the pressure becomes.

The Deepsea Challenger went to a maximum depth of about 11 km. The pressure it had to sustain was about 110 MPa (mega Pascal) or 110 million Pascal. Atmospheric pressure at ground level is about 101 kPa. Which means, the Deepsea Challenger had to be able to sustain slightly more than a 1 000 times atmospheric pressure! A truly amazing achievement for engineering as well! At these depths, pressure is so high that it has the ability to compress steel. In fact, the deep-diving submersible shrunk by about 7 cm in length under the immense pressure!

6 thoughts on “Pressure”

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