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Today we're going to change topics.

I'm going to talk to you about fluids, hydrostatic pressure and barometric pressure.

If, for now, we forget gravity and I would have a compartment closed off and filled with a fluid —

could be either a gas or it could be a liquid —

this has area A, here —

and I apply a force on it in this direction, then I apply a pressure.

Pressure is defined as the force divided by area —

has units newtons per square meter which is also called pascal.

One newton per square meter is one pascal.

Now, in the absence of gravity, the pressure is, everywhere in this vessel, the same.

And that is what's called Pascal's principle.

Pascal's principle says that the pressure applied to an enclosed fluid is transmitted undiminished to every point in the fluid and to the walls of the container.

Keep in mind, pressure is a scalar, it has no direction.

Force has a direction and the force exerted by the fluid on anything —

therefore also on the wall —

must be everywhere perpendicular to the wall, because if there were any tangential component, then the fluid would start to move.

Action equals minus reaction, so it starts to move and we are talking here about a static fluid.

So if I take any element —

I take one here at the surface, little element delta A and the force must be perpendicular to that surface, delta F, and so delta F divided by delta A —

in the limiting case for delta A goes to zero —

is, then, that pressure P.

This has some truly amazing consequences which are by no means so intuitive.

This is the idea of an hydraulic jack.

I have here a vessel which has a very peculiar shape.

Ooh, ooh, an opening here.

And let there be here a piston on it with area A1 and here one with area A2.

It's filled with liquid everywhere and I apply here a force F1 and here a force F2.

So the pressure that I apply here is F1 divided by A1.

So according to Pascal, everywhere in the fluid, that pressure must be the same.

For now, I just assume that the effect of gravity, which I will discuss shortly, doesn't change the situation very significantly.

But I will address the gravity very shortly.

So the pressure, then, will be the same everywhere, but the pressure due to this side is F2 divided by A2...

and so the two must be the same, if the liquid is not moving.

So what that means is that if A2 over A1 were 100, it means that this force could be a hundred times less than that one.

In other words, I could put on here a weight, a mass of ten kilograms, and here I could put 1,000 kilograms and it would be completely in equilibrium.

That's not so intuitive.

This is used in all garages.

What they do is, they put on top of this —

if I blow that up here, so this is this platform, there's a rod here and on top of it is a car.

And someone pushes here and then this goes up.

The car goes up.

If I push here with a force a little bit more than ten kilograms —

so that would be 100 newtons —

this level would go up.

And so your first thought may be, "Gee, isn't that a violation of the conservation of energy? Am I not getting something for nothing?" Well, not really.

Suppose I push this down over a distance d1, then the amount of fluid that I displace —

that is, the volume, is A1 times d1.

That fluid ends up here.

So this one will go up over a distance d2.

But the same amount of fluid that leaves here adds there.

I'm going to talk to you about fluids, hydrostatic pressure and barometric pressure.

If, for now, we forget gravity and I would have a compartment closed off and filled with a fluid —

could be either a gas or it could be a liquid —

this has area A, here —

and I apply a force on it in this direction, then I apply a pressure.

Pressure is defined as the force divided by area —

has units newtons per square meter which is also called pascal.

One newton per square meter is one pascal.

Now, in the absence of gravity, the pressure is, everywhere in this vessel, the same.

And that is what's called Pascal's principle.

Pascal's principle says that the pressure applied to an enclosed fluid is transmitted undiminished to every point in the fluid and to the walls of the container.

Keep in mind, pressure is a scalar, it has no direction.

Force has a direction and the force exerted by the fluid on anything —

therefore also on the wall —

must be everywhere perpendicular to the wall, because if there were any tangential component, then the fluid would start to move.

Action equals minus reaction, so it starts to move and we are talking here about a static fluid.

So if I take any element —

I take one here at the surface, little element delta A and the force must be perpendicular to that surface, delta F, and so delta F divided by delta A —

in the limiting case for delta A goes to zero —

is, then, that pressure P.

This has some truly amazing consequences which are by no means so intuitive.

This is the idea of an hydraulic jack.

I have here a vessel which has a very peculiar shape.

Ooh, ooh, an opening here.

And let there be here a piston on it with area A1 and here one with area A2.

It's filled with liquid everywhere and I apply here a force F1 and here a force F2.

So the pressure that I apply here is F1 divided by A1.

So according to Pascal, everywhere in the fluid, that pressure must be the same.

For now, I just assume that the effect of gravity, which I will discuss shortly, doesn't change the situation very significantly.

But I will address the gravity very shortly.

So the pressure, then, will be the same everywhere, but the pressure due to this side is F2 divided by A2...

and so the two must be the same, if the liquid is not moving.

So what that means is that if A2 over A1 were 100, it means that this force could be a hundred times less than that one.

In other words, I could put on here a weight, a mass of ten kilograms, and here I could put 1,000 kilograms and it would be completely in equilibrium.

That's not so intuitive.

This is used in all garages.

What they do is, they put on top of this —

if I blow that up here, so this is this platform, there's a rod here and on top of it is a car.

And someone pushes here and then this goes up.

The car goes up.

If I push here with a force a little bit more than ten kilograms —

so that would be 100 newtons —

this level would go up.

And so your first thought may be, "Gee, isn't that a violation of the conservation of energy? Am I not getting something for nothing?" Well, not really.

Suppose I push this down over a distance d1, then the amount of fluid that I displace —

that is, the volume, is A1 times d1.

That fluid ends up here.

So this one will go up over a distance d2.

But the same amount of fluid that leaves here adds there.

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