Pressure and Pascal's principle (part 1)

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.