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