Pressure and Pascal's principle (part 1) | Fluids | Physics | Khan Academy
Summary
TLDRThis 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
💧 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.
🔧 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.
Mindmap
Keywords
💡Fluid
💡Compressibility
💡Incompressibility
💡Liquid
💡Gas
💡Volume
💡Pressure
💡Work
💡Conservation of Energy
💡Force
💡Piston
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.
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