# Pressure

by Jared Rovny

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00:01 Let’s now move on to pressure. We’re going to discuss pressure which is of course very important in medicine and will play a role both in the blood system when we’re talking about human beings as well as the air tract when we’re talking about the lungs and the pressure you need to apply to the air in your lungs. Pressure, we’re going to discuss in terms of this beach ball as you see here.

00:21 If it’s full of air, there’s something that’s keeping it inflated. That is if we zoomed in very closely, that each molecule in there is moving very quickly and bouncing off the walls of the beach ball.

00:31 This is actually what keeps it inflated. So, all of these little collisions, all these little blue particles as we’ve drawn them here bouncing against the walls apply a force. Pressure in this beach ball is defined by the amount of force being applied per unit area of the walls of the container.

00:50 The units of pressure, since pressure is defined as the force per unit area, will be the units of force divided by the units of area. Those units we call pascals. So, this is kilograms over meter second square.

01:05 So, we have pascals as the units of pressure in our normal SI units that we’ve been using.

01:12 These pascals can also be rewritten. So, this is just something to be aware of. We can also rewrite the units just by collecting them in a different way in using the units of energy, joules, that we’ve already discussed and think about pressure as being an energy per unit in volume, how much energy is stored in a given amount of volume. The important thing also about this equation, you might notice that when I wrote pressure, I wrote pressure is force per unit area but in the subscript to the F, I also put this little perpendicular symbol because in fact, when we’re being very careful to analyze what pressure means, we only care about pressure perpendicular to the walls of the container. So, when these little particles are bouncing off the walls of this container, we don’t really care about the motion sideways or along the wall.

01:55 We only care about the motion of the particles directly against the wall, applying a force directly outwards to the walls of our container. So now, we’ve discussed some basic properties of fluids are ways to describe fluids and talk about fluids which we will be using over and over.

02:09 So now, we’re ready to talk about hydrostatic pressure. If you’re a person standing on the earth, you have what we call 1 atmosphere of pressure already on top of you right now.

02:21 This pressure from the air is pushing down on you with in fact a huge amount of force that turns out to be about 100 kilopascals of pressure. The pascal is being the unit we just discussed.

02:31 Kilo, meaning that it’s 1000 pascals. So, 100 kilopascals of pressure is just a force over the pressure from the force of the air and its weight on top of you. Fortunately, we don’t feel this pressure because we also have air pressure inside of us and liquid pressure inside of us also pushing outwards.

02:48 So, it’s a balance of these forces that keeps us from feeling any negative effects from this huge amount of pressure that we already have on us at the surface of the earth. If we go underwater for example, we have more pressure on us than just the pressure from the atmosphere. We can measure this amount of pressure first by analyzing how much water is on top of us. If we have a certain mass of water and we know maybe an area of a container and we know the height of that container, we can tell how much volume this water has on top of us. We know the force of the water from gravity is its mass times this gravitational acceleration downwards. We can rewrite this expression by dividing by the area, collecting our terms, and then seeing that the pressure from this water that is on top of us right now is in fact equal to the density of the water times the gravitational acceleration times the height of the column of water that is ahead of us. These equations that I wrote on the right here, it’s not important that you understand exactly what they are in terms of being able to derive it yourself.

03:49 But this is simply a way of showing you that we can start with a simple expression for the force of gravity from water just being mass times the gravitational acceleration and do a few simple logical steps to rearrange the equation and find the pressure by analyzing force per unit area of the water on top of you.

04:05 So, this pressure as the density times g times h is simply a rewriting of the force of gravity pulling down on the water on top of you. So, this pressure which is equal to ρgh, an expression you’ll hear quite often, pressure equals ρgh is in fact only what we call the gauge pressure.

04:24 By that, we just mean it’s the pressure amount by which the pressure measured in a fluid exceeds the atmospheric pressure. In other words, what I’ve just mentioned here, all this analysis of the weight of the water on top of you bearing down on top of you is just the pressure from the water.

04:40 We haven’t also included the atmospheric pressure yet. If we want to talk about the total pressure, we would take this gauge pressure, ρgh and then we would add to it the atmospheric pressure that’s also pushing down on you. So, we would take the total pressure by finding ρgh which would come from a particular fluid and then adding any external pressures, in this particular case, the pressure from the atmosphere.

### About the Lecture

The lecture Pressure by Jared Rovny is from the course Fluids.

### Included Quiz Questions

1. N/m²
2. N/m³
3. J/m²
4. Kg/s²
5. Kg/(m²s²)
1. Both tubes have the same pressure
2. The wider tube has a larger pressure
3. The thin tube has a larger pressure
4. Cannot be determined without knowing the thickness of the tube walls
5. Cannot be determined without the volume
1. 10 m
2. 1 m
3. 100 m
4. 1,000 m
5. 10,000 m
1. 1,000,000 Pa
2. 1,000 Pa
3. 1 Pa
4. 0.001 Pa
5. 10,000 Pa

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