Pressure and Pascal's principle (part 1) | Fluids | Physics | Khan Academy

Summary

This educational video script delves into the concept of fluids, distinguishing between liquids and gases by their compressibility. It uses the example of water in a rubber sphere to illustrate a fluid's ability to take the shape of its container. The script further explains the incompressibility of liquids versus the compressibility of gases, using balloons as a visual aid. It sets the stage for exploring the principles of liquid motion and the relationship between force, pressure, and volume in fluid dynamics, promising to continue the discussion in a follow-up video.

Takeaways

• 💧 A fluid, in physics and chemistry, is any substance that takes the shape of its container, including liquids and gases.
• 🌐 The defining characteristic of a fluid is its ability to conform to the shape of its container, as opposed to solids which maintain their shape.
• 🔵 The difference between liquids and gases is that gases are compressible, meaning their volume can be decreased by applying pressure, while liquids are incompressible and maintain a constant volume regardless of pressure.
• 🎈 An example of compressibility is a balloon filled with air, which can be squeezed to reduce its volume, whereas a water-filled balloon cannot be compressed to change its volume.
• 🔄 The script introduces the concept of work in the context of fluid dynamics, relating work to the force applied over a distance, which is a measure of energy transferred into or out of a system.
• ⚙️ The principle of conservation of energy is applied to explain that the work input into a system is equal to the work output, assuming no energy is created or destroyed.
• 📏 The script uses the formula for work (force times distance) to illustrate the relationship between the force applied to a liquid and the displacement that occurs.
• 🌀 It is explained that when a force is applied to a liquid in a container, the liquid's volume remains constant, leading to a displacement that maintains the initial volume.
• 📉 The concept of areas in fluid dynamics is introduced, where the area of the container's opening affects the volume of liquid displaced when a force is applied.
• 🔄 The script demonstrates that the volume of liquid displaced at one end of a container (area 1 times distance 1) must be equal to the volume displaced at the other end (area 2 times distance 2), due to the incompressibility of liquids.
• 🔑 The takeaway is that understanding the properties of fluids, especially their incompressibility and how they respond to forces, is fundamental to studying fluid motion and dynamics.

Q & A

What is the definition of a fluid in the context of physics or chemistry?

A fluid is any substance that takes the shape of its container, which includes both liquids and gases.

How does the behavior of a fluid in a container differ from that of a solid?

A fluid, unlike a solid, does not maintain a fixed shape and conforms to the shape of its container.

What are the two main types of fluids mentioned in the script?

The two main types of fluids mentioned are liquids and gases.

What property of a gas allows it to be compressed?

A gas is compressible because it can become denser when the volume of its container is decreased.

How is a liquid different from a gas in terms of compressibility?

A liquid is incompressible, meaning its volume cannot be changed by applying pressure.

Can you give an example of how the compressibility of a gas is demonstrated?

The compressibility of a gas can be demonstrated by blowing air into a balloon and then squeezing it, which shows the gas can be compressed.

What principle from physics is used to explain the relationship between the work done on a fluid and the work done by a fluid?

The principle of conservation of energy, specifically the law that work in is equal to work out, is used to explain this relationship.

How is the volume of liquid displaced related to the force applied and the distance moved?

The volume of liquid displaced is equal to the area of the container at the point of application times the distance the force is applied.

What happens to the volume of liquid when it is pushed down in a container with varying cross-sectional areas?

The volume of liquid remains constant and is displaced to a new level in the container, following the principle of incompressibility.

What is the relationship between the areas and distances in the two parts of the container when a liquid is pushed?

The product of the area and distance in the first part of the container (A1 * D1) is equal to the product of the area and distance in the second part (A2 * D2), due to the incompressibility of liquids.

Why is it important to understand the incompressibility of liquids when analyzing fluid motion?

Understanding the incompressibility of liquids is crucial for analyzing fluid motion because it ensures that the volume of liquid displaced is conserved, which is key to understanding pressure and force relationships in fluid dynamics.

Outlines

00:00

💧 Understanding Fluids and Their Properties

This paragraph introduces the concept of fluids from a physics and chemistry perspective. It explains that a fluid is any substance that conforms to the shape of its container, such as water in a rubber sphere that changes shape with the container. The paragraph distinguishes between two types of fluids: liquids and gases, highlighting that liquids are incompressible, meaning their volume cannot be changed by pressure, unlike gases which are compressible. The script uses the example of a balloon filled with water versus one filled with air to illustrate the difference. It also sets the stage for further exploration of fluid dynamics and phase changes in future content.

05:03

🔧 The Physics of Liquid Motion and Work

The second paragraph delves into the principles of work and energy in the context of liquids. It begins by discussing the conservation of energy and the relationship between work input and work output, emphasizing that work is equal to force times distance. The script introduces a scenario involving a piston compressing a liquid, calculating the work done as the force applied times the distance the piston moves. It then explores the implications of liquid incompressibility, explaining that the volume displaced by the piston must be equal to the volume that rises elsewhere due to the incompressible nature of liquids. The paragraph concludes with the setup for an equation relating the areas and distances of two different sections of a container, which will be continued in the next video, indicating a deeper exploration of fluid dynamics and pressure relationships.

Keywords

💡Fluid

A fluid, as described in the script, is any substance that takes the shape of its container. This includes both liquids and gases, and is fundamental to the theme of the video, which is to understand the properties and behaviors of fluids in physics and chemistry. The script uses the example of water in a glass sphere to illustrate how a fluid conforms to the shape of its container.

💡Compressibility

Compressibility refers to the ability of a substance to be compressed, or to have its volume reduced under pressure. In the context of the video, gases are said to be compressible because they can be squeezed into a smaller volume, unlike liquids. The script demonstrates this concept by comparing the behavior of a balloon filled with air versus one filled with water.

💡Incompressibility

Incompressibility is the property of a substance to resist changes in volume when pressure is applied. The script emphasizes that liquids, unlike gases, are incompressible. This is exemplified by the inability to change the volume of a water-filled balloon no matter how much pressure is applied from the sides.

💡Liquid

A liquid is a state of matter that is fluid, takes the shape of its container, and is incompressible. The script distinguishes liquids from gases by their lack of compressibility and uses the example of water to explain the concept of a liquid in the context of fluid dynamics.

💡Gas

A gas is a state of matter that is fluid and compressible. The script explains that gases fill their container and can be compressed, becoming denser, which is in contrast to liquids. The behavior of air in a balloon is used to illustrate the compressibility of gases.

💡Volume

Volume, in the context of the script, refers to the amount of space a substance occupies. It is a key concept when discussing the properties of fluids, as the script explains that the volume of a liquid remains constant regardless of the shape of its container, highlighting the incompressibility of liquids.

💡Pressure

Pressure is the force applied per unit area. The script discusses how pressure can affect the volume of a gas but not a liquid, as gases are compressible under increased pressure, which can lead to a change in volume, whereas liquids remain incompressible.

💡Work

Work, in physics, is defined as force times distance and is a measure of energy transfer. The script introduces the concept of work to explain the relationship between the force applied to a fluid and the resulting displacement, using the example of pushing a piston into a container of liquid.

💡Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, only transformed. The script mentions this principle in the context of work, explaining that the work put into a system (energy input) is equal to the work that comes out of the system (energy output), which is fundamental to understanding fluid dynamics.

💡Force

Force is any interaction that, when unopposed, will change the motion of an object. In the script, force is used to describe the action of pushing a piston into a container filled with a liquid, which results in work being done and the liquid being displaced.

💡Piston

A piston is a component that moves within a cylinder, often used to transfer force into linear motion. In the script, a piston is used as an example to demonstrate how force is applied to a liquid, causing it to be displaced and move within the container.

Highlights

A fluid is defined as anything that takes the shape of its container, including liquids and gases.

In a zero gravity environment, fluids conform to the shape of their container regardless of gravity.

The concept of fluidity is demonstrated using a rubber sphere filled with water, showing how the water changes shape with the container.

Gases, unlike liquids, are compressible and can be squeezed into a smaller volume.

Liquids are incompressible, as shown by the inability to change the volume of a water-filled balloon by squeezing.

The difference between liquids and gases is highlighted by their compressibility.

Phase transitions between liquid, gas, and solid states will be discussed in later lessons.

The focus shifts to liquid motion and fluid dynamics, introducing a unique container shape for demonstration.

Work is defined as force times distance, and its conservation is linked to the energy put into and out of a system.

The relationship between work input and output is explained using the concept of mechanical advantage.

A piston is used to illustrate the work done on a liquid, emphasizing the incompressible nature of liquids.

The volume displaced by pushing a piston into a liquid is calculated using the area and distance moved.

The principle of incompressibility ensures that the volume of liquid displaced is conserved throughout the system.

The relationship between the areas of two different openings in a container and the distances the liquid moves is established.

The video concludes with an introduction to the relationship between force, distance, and pressure in fluid dynamics, to be continued in the next video.

Transcripts

Let's learn a little bit about fluids.

You probably have some notion of what a fluid is, but let's

talk about it in the physics sense, or maybe even the

chemistry sense, depending on in what context you're

watching this video.

So a fluid is anything that takes the

shape of its container.

For example, if I had a glass sphere, and let's say that I

completely filled this glass sphere with water.

I was going to say that we're in a zero gravity environment,

but you really don't even need that.

Let's say that every cubic centimeter or cubic meter of

this glass sphere is filled with water.

Let's say that it's not a glass, but a rubber sphere.

If I were to change the shape of the sphere, but not really

change the volume-- if I were to change the shape of the

sphere where it looks like this now-- the water would

just change its shape with the container.

The water would just change in the shape of the container,

and in this case, I have green water.

The same is also true if that was oxygen, or if that was

just some gas.

It would fill the container, and in this situation, it

would also fill the newly shaped container.

A fluid, in general, takes the shape of its container.

And I just gave you two examples of fluids-- you have

liquids, and you have gases.

Those are two types of fluid: both of those things take the

shape of the container.

What's the difference between a liquid and a gas, then?

A gas is compressible, which means that I could actually

decrease the volume of this container and the gas will

just become denser within the container.

You can think of it as if I blew air into a balloon-- you

could squeeze that balloon a little bit.

There's air in there, and at some point the pressure might

get high enough to pop the balloon, but

you can squeeze it.

A liquid is incompressible.

How do I know that a liquid is incompressible?

Imagine the same balloon filled with water-- completely

filled with water.

If you squeezed on that balloon from every side-- let

me pick a different color-- I have this balloon, and it was

filled with water.

If you squeezed on this balloon from every side, you

would not be able to change the volume of this balloon.

No matter what you do, you would not be able to change

the volume of this balloon, no matter how much force or

pressure you put from any side on it, while if this was

filled with gas-- and magenta, blue in for gas-- you actually

could decrease the volume by just increasing the pressure

on all sides of the balloon.

You can actually squeeze it, and make the

entire volume smaller.

That's the difference between a liquid and a gas-- gas is

compressible, liquid isn't, and we'll learn later that you

can turn a liquid into a gas, gas into a liquid, and turn

liquids into solids, but we'll learn all about that later.

This is a pretty good working definition of that.

Let's use that, and now we're going to actually just focus

on the liquids to see if we could learn a little bit about

liquid motion, or maybe even fluid motion in general.

Let me draw something else-- let's say I had a situation

where I have this weird shaped object which tends to show up

in a lot of physics books, which I'll draw in yellow.

This weird shaped container where it's relatively narrow

there, and then it goes and U-turns into

a much larger opening.

Let's say that the area of this opening is A1, and the

area of this opening is A2-- this one is bigger.

Now let's fill this thing with some liquid, which will be

blue-- so that's my liquid.

Let me see if they have this tool-- there

you go, look at that.

I filled it with liquid so quickly.

This was liquid-- it's not just a fluid, and so what's

the important thing about liquid?

It's incompressible.

Let's take what we know about force-- actually about work--

and see if we can come up with any rules about force and

pressure with liquids.

So what do we know about work?

Work is force times distance, or you can also view it as the

energy put into the system-- I'll write it down here.

Work is equal to force times distance.

We learned in mechanical advantage that the work in--

I'll do it with that I-- is equal to work out.

The force times the distance that you've put into a system

is equal to the force times the distance

you put out of it.

And you might want to review the work chapters on that.

That's just the little law of conservation of energy,

because work in is just the energy that you're putting

into a system-- it's measured in joules-- and the work out

is the energy that comes out of the system.

And that's just saying that no energy is destroyed or

created, it just turns into different forms. Let's just

use this definition: the force times distance in is equal to

force times distance out.

Let's say that I pressed with some force

on this entire surface.

Let's say I had a piston-- let me see if I can draw a piston,

and what's a good color for a piston-- so let's add a

magenta piston right here.

I push down on this magenta piston, and so I pushed down

on this with a force of F1.

Let's say I push it a distance of D1--

that's its initial position.

Its final position-- let's see what color, and the hardest

part of these videos is picking the color-- after I

pushed, the piston goes this far.

This is the distance that I pushed it-- this is D1.

The water is here and I push the water down D1 meters.

In this situation, my work in is F1 times D1.

Let me ask you a question: how much water did I displace?

How much total water did I displace?

Well, it's this volume?

I took this entire volume and pushed it down, so what's the

volume right there that I displaced?

The volume there is going to be-- the initial volume that

I'm displacing, or the volume displaced, has

to equal this distance.

This is a cylinder of liquid, so this distance times the

area of the container at that point.

I'm assuming that it's constant at that point, and

then it changes after that, so it equals area 1 times

distance 1.

We also know that that liquid has to go someplace, because

what do we know about a liquid?

We can't compress it, you can't change its total volume,

so all of that volume is going to have to go someplace else.

This is where the liquid was, and the liquid is going to

rise some level-- let's say that it gets to this level,

and this is its new level.

It's going to change some distance here, it's going to

change some distance there, and how do we know what

distance that's going to be?

The volume that it changes here has to go someplace.

You can say, that's going to push on that, that's all going

to push, and that liquid has to go someplace.

Essentially it's going to end up-- it might not be the exact

same molecules, but that might displace some liquid here,

that's going to displace some liquid here and here and here

and here and all the way until the liquid up here gets

displaced and gets pushed upward.

The volume that you're pushing down here is the same volume

that goes up right here.

So what's the volume-- what's the change in volume, or how

much volume did you push up here?

This volume here is going to be the distance 2 times this

larger area, so we could say volume 2 is going to be equal

to the distance 2 times this larger area.

We know that this liquid is incompressible, so this volume

has to be the same as this volume.

We know that these two quantities are equal to each

other, so area 1 times distance 1 is going to be

equal to this area times this distance.

Let's see what we can do.

We know this, that the force in times the distance in is

equal to the force out times the distance out.

Let's take this equation-- I'm going to switch back to green

just so we don't lose track of things--

and divide both sides.

Let's rewrite it-- so let's say I

rewrote each input force.

Actually, I'm about to run out of time, so I'll continue this

into the next video.

See you soon.