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# Pressure and Pascal's principle (part 1)

## Video transcript

let's learn a little bit about fluids so a and you probably have some notion of what a fluid is but let's let's talk about it in in the physic sense or maybe even the chemistry sense depending on in what context you're watching this video so the fluid is anything that takes the shape of its container so for example if I had a I don't know a glass sphere a glass here and let's say that we're in like a well let's say I completely fill this glass sphere with water I was going to say we're in a zero-gravity environment but you really don't even need that let's say that every every cubic centimetre or cubic meter of this glass sphere is filled with water and notice and then let's say that if I were to and let's say it's not a glass let's say it's a rubber sphere if I were to change the shape of that sphere but not really change the shape of that of the volume and 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 right the water would just change the shape with the container and in this case I have green water and the same is also true if I had a if that was oxygen or if that was just some gas right it would fill the container and in this situation it would also fill the the newly shaped container so a fluid in general a fluid takes the shape of container takes shape of container and I just gave you two examples of fluids you have liquids liquids and you have gases those are two types of fluids both of those things take the shape of their container and now what's the difference between a liquid in a gas then well a gas is compressible compressible which means that I could actually decrease the volume of this container and and the gas will just become denser within the container so you can think of it is if I blew air into a balloon you could squeeze that balloon a little bit there's air in there I mean at some point the pressure might get high enough to pop the balloon but you can squeeze it while a liquid is is incompressible in in compressible and how do I know that liquid is incompressible well imagine the same balloon filled with water completely filled with water if you squeezed on that balloon from every side so let's say that let me pick different color let's say I had 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 actually you know 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 any side on it well if this was filled with gas and magenta balloon for gas you actually could decrease the volume by just increasing the pressure on all sides of the balloon and you could actually squeeze it and make the entire volume smaller so that's the distri in the liquid in a gas gas is compressible liquid is intuitive and we'll learn later that you can turn a liquid into a gas and gas into a liquid and turn liquids into solids but we'll learn all about that later but this is a pretty good working definition of that so 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 okay let me draw something else so let's say I had a a situation where let's say 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 kind of u-turns and to a much larger opening let's say that the area of this opening is let's say that this is a1 that the area of this opening is a two all right and this one is bigger and let's fill fill this this this thing with some liquid which will be blue so that's my liquid let's fill it with some liquid let me see if they have this tool this tool actually there you go look at that I filled it with liquid so quickly all right and and and this wasn't and this was liquid this not just a fluid and so what what's the important thing about liquid is that it's incompressible so let's take what we know about about force actually about work and see if we can come up with any rules about you know force and pressure with liquids excetera so what do we know about work work is Force Times distance or you can also kind of view it as the energy put into the system so I'll write it down here so work is equal to Force Times distance and we learned in the mechanical advantage etc that the work in work in I'll do that I is equal to work out write the the force times the distance that you put into a system is equal to the force times the distance you put out of it and you might want to review the the work chapters on that but that's just a little law of conservation of energy because work in is just the energy that you're putting into a system right its measured in joules and the work out is the energy that comes out of a system and that's just saying that no energy is is destroyed or created it just turns into different forms so let's just use this definition so the force times distance in is equal to Force Times distance out force in onto I like that times distance in is equal to force out times distance out all right so let's say that I pressed with some force on this entire surface so let's say I had like a let's say it's like a piston let me see if I can draw up this channel it's a good color for piston so let's add a magenta piston right here and I push down on this magenta piston let's see I so I pushed down on this with a force of f1 right and let's say I push it a distance of D 1 so let me say so it goes that's its initial position and say its final position I'll do in a see what color the hardest part of these videos is picking the color so let's say like after I've pushed it the piston goes this far so this is the distance that I pushed it right so this is d1 the pitch the water is here and I've pushed the water down d1 meters or whatever right so in this situation my work in is f1 times d1 right but let me ask you a question how much water did i displace how much total water did i displace well it's this volume right I took this entire volume and pushed it down so what's the volume right there that I displaced well the volume there is going to be so the initial the volume that I'm displacing so I'll say that the volume displaced has to equal this distance right this is like a cylinder of liquid of of liquid so this distance times the area right times the area of the container at that point I'm assuming it's constant at that point then it changes after that so it equals area 1 times distance 1 right well we also know that it that liquid has to go someplace right because what what do we know about a liquid is that you can't compress it you can't change its its total volume so all of that volume is going to have to go someplace else so this is where the liquid was the liquid is going to rise some level let me say let's say it gets to this level this is its new level right it's going to change some distance here it's going to change some distance there and and how do we know what distance that's going to be well the volume that it changes here has to it's got to go someplace right you could say well that's going to push on that that's all going to push and that that liquid has to go someplace and 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 display some liquid here here and here and here and all the way until the liquid up here gets displaced and gets pushed upward so the volume that you're pushing down here is the same volume that goes up right here and so what's the volume what's the change in volume or well how much what's the new how much volume did you push up here well this volume here is going to be the distance two times this larger area right so we could say volume two is going to be equal to the distance two times this larger area and we know that this liquid is incompressible so this volume has to be the same as this volume right so we know that these these two quantities are equal to each other so area 1 times distance 1 right this area times this distance is going to be equal to this area times this distance area 2 times distance 2 so let's see what we can do so 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 by well let's just rewrite it so let's say I rewrote each input 4 so actually I'm about to run out of time so I'll continue this into the next video see you soon