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>> Hello, class. Professor Anderson, here. Welcome to another installation of the Learning Glass Lectures on Physics. Let's talk about pressure when you go under water. Everybody's sort of familiar with this idea. But when you dive to the bottom of say, a swimming pool, you feel pressure. There's external pressure on you. Why is that? Here you are at the bottom of the swimming pool, blowing some bubbles. You feel pressure. Where do you feel pressure when you're swimming? >> Your ears. >> Your ears. Right. Somebody, hand the mic back to Jamie. And Jamie, let you and I have a discussion. Jamie, are you a swimmer or a surfer? >> I've done both. I love swimming. >> Okay. >> But surf, I'm not really that great at. But, yeah. >> Good. It's good to be challenged with things. Surfing is super hard. And you should just keep practicing, because I think one of the greatest sports, out there. Let's say you're swimming in your pool and you go, dive to the bottom of your pool. Right. How deep is the pool? Ten feet, maybe. Do you feel pressure when you do that? >> Yes. >> Okay. >> You feel it in your ears. >> All right. You feel it in your ears. Why do you feel pressure? >> Because the pressure has increased and then, your ear senses the pressure change, and it's not the same. >> Okay. That's exactly right. But why does the pressure increase? What is going on in this picture to increase the pressure when I'm down there versus when I'm up there? >> There's more water on top of you that, you know. >> There's more water on top of you and that water is in fact, being pulled down due to what? >> Gravity. >> Gravity. Take away gravity, there's no pressure anymore. The only reason that pressure increases with depth is because gravity is pulling down on all that water. And it's exactly the same, doesn't have to be a big pool, doesn't have to be an ocean, it's exactly the same as if you just took a big tube of water and put it on your head. That pressure that you feel at the bottom would be exactly the same if this depth is the same. Literally, it's like you took all those water molecules and just stacked them up on your head and gravity is pulling down on all of them. Okay. So, let's see if we can figure out exactly how much the pressure changes as you go down. And we'll say that you're going down to depth H. What we said is that Bernoulli's equation works for a variety of problems and certainly, here, Bernoulli's equation works just as well. And let's take two regions. We're going to start region one. We're going to end up region two. Bernoulli said that if we add up all these terms, p one plus one half Rho, v one squared, plus Rho gy one. That has to equal all of those terms added up in region two. P two plus one half Rho, v two squared plus Rho gy two. And now, we just have to decide on a few things. One, we're not really worried about moving fluids, here. The water is static. So, we can get rid of that and get rid of that. We're also going to say that up here, at p one, that is just equal to P naught atmospheric pressure. Okay. This is the surface of the ocean. One atmosphere is ten to the five Pascals. We also, need to decide on a coordinate system. So, people like to make sea level, y equals zero, whenever you talk about the altitude of a mountain, you always say, ''How high are you above sea level?'' So, we'll do that. We'll make y equals zero sea level. So, what do we get? Zero for that one. Rho gy one goes to zero, as well. Over on the right side, we have pressure two. What we're interested in. The kinetic energy term went away. And then, we have Rho g times y two. But is y equals zero is way up here, this has to be negative. And so, we are down at negative h. So, look what this equation becomes. P naught is equal to P two, minus Rho gh. We want to solve for P two. And so, we move Rho gh over to the other side. And we get P naught plus Rho gh. This is the pressure at depth h. If P naught is one atmosphere, then you increase pressure by Rho gh as you go down beneath the ocean. And it doesn't take you long to feel that pressure. When you dive under the water, you only have to go down six or seven feet to really feel it already, in your ears. Right. You feel it in your ears predominantly because the membranes in your ears are very flexible. And so, when the outside pressure increases, it starts to flex those membranes and you feel that as pain. How do you fix that problem? Jamie, do you know how to fix that problem? >> You would equalize the pressure that's inside of your ears as to what it is, outside. >> Right. It's called the Valsalva maneuver. And what you do, is you pinch your nose, you breathe air out. Since your nose is pinched, it doesn't go anywhere. That extra air that you're breathing out increases the pressure in your sinus cavities, which pushes the eardrums back out. Pushes that membrane back out. And so, as you go down underneath the water, just do that. Hold your nose and breathe slightly. And all of a sudden, your ears won't hurt, anymore. And if you do it smoothly on the way down, then they really won't hurt all the way down. Okay. Very simple way to fix that problem. There is, of course, pressure everywhere else on your body. But you don't notice that as much, because the rest of your body is pretty tough. Right. If you increase the pressure on your arm, not really going to be uncomfortable. By that.

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>> Hello, class. Professor Anderson, here. Welcome to another installation of the Learning Glass Lectures on Physics. Let's talk about pressure when you go under water. Everybody's sort of familiar with this idea. But when you dive to the bottom of say, a swimming pool, you feel pressure. There's external pressure on you. Why is that? Here you are at the bottom of the swimming pool, blowing some bubbles. You feel pressure. Where do you feel pressure when you're swimming? >> Your ears. >> Your ears. Right. Somebody, hand the mic back to Jamie. And Jamie, let you and I have a discussion. Jamie, are you a swimmer or a surfer? >> I've done both. I love swimming. >> Okay. >> But surf, I'm not really that great at. But, yeah. >> Good. It's good to be challenged with things. Surfing is super hard. And you should just keep practicing, because I think one of the greatest sports, out there. Let's say you're swimming in your pool and you go, dive to the bottom of your pool. Right. How deep is the pool? Ten feet, maybe. Do you feel pressure when you do that? >> Yes. >> Okay. >> You feel it in your ears. >> All right. You feel it in your ears. Why do you feel pressure? >> Because the pressure has increased and then, your ear senses the pressure change, and it's not the same. >> Okay. That's exactly right. But why does the pressure increase? What is going on in this picture to increase the pressure when I'm down there versus when I'm up there? >> There's more water on top of you that, you know. >> There's more water on top of you and that water is in fact, being pulled down due to what? >> Gravity. >> Gravity. Take away gravity, there's no pressure anymore. The only reason that pressure increases with depth is because gravity is pulling down on all that water. And it's exactly the same, doesn't have to be a big pool, doesn't have to be an ocean, it's exactly the same as if you just took a big tube of water and put it on your head. That pressure that you feel at the bottom would be exactly the same if this depth is the same. Literally, it's like you took all those water molecules and just stacked them up on your head and gravity is pulling down on all of them. Okay. So, let's see if we can figure out exactly how much the pressure changes as you go down. And we'll say that you're going down to depth H. What we said is that Bernoulli's equation works for a variety of problems and certainly, here, Bernoulli's equation works just as well. And let's take two regions. We're going to start region one. We're going to end up region two. Bernoulli said that if we add up all these terms, p one plus one half Rho, v one squared, plus Rho gy one. That has to equal all of those terms added up in region two. P two plus one half Rho, v two squared plus Rho gy two. And now, we just have to decide on a few things. One, we're not really worried about moving fluids, here. The water is static. So, we can get rid of that and get rid of that. We're also going to say that up here, at p one, that is just equal to P naught atmospheric pressure. Okay. This is the surface of the ocean. One atmosphere is ten to the five Pascals. We also, need to decide on a coordinate system. So, people like to make sea level, y equals zero, whenever you talk about the altitude of a mountain, you always say, ''How high are you above sea level?'' So, we'll do that. We'll make y equals zero sea level. So, what do we get? Zero for that one. Rho gy one goes to zero, as well. Over on the right side, we have pressure two. What we're interested in. The kinetic energy term went away. And then, we have Rho g times y two. But is y equals zero is way up here, this has to be negative. And so, we are down at negative h. So, look what this equation becomes. P naught is equal to P two, minus Rho gh. We want to solve for P two. And so, we move Rho gh over to the other side. And we get P naught plus Rho gh. This is the pressure at depth h. If P naught is one atmosphere, then you increase pressure by Rho gh as you go down beneath the ocean. And it doesn't take you long to feel that pressure. When you dive under the water, you only have to go down six or seven feet to really feel it already, in your ears. Right. You feel it in your ears predominantly because the membranes in your ears are very flexible. And so, when the outside pressure increases, it starts to flex those membranes and you feel that as pain. How do you fix that problem? Jamie, do you know how to fix that problem? >> You would equalize the pressure that's inside of your ears as to what it is, outside. >> Right. It's called the Valsalva maneuver. And what you do, is you pinch your nose, you breathe air out. Since your nose is pinched, it doesn't go anywhere. That extra air that you're breathing out increases the pressure in your sinus cavities, which pushes the eardrums back out. Pushes that membrane back out. And so, as you go down underneath the water, just do that. Hold your nose and breathe slightly. And all of a sudden, your ears won't hurt, anymore. And if you do it smoothly on the way down, then they really won't hurt all the way down. Okay. Very simple way to fix that problem. There is, of course, pressure everywhere else on your body. But you don't notice that as much, because the rest of your body is pretty tough. Right. If you increase the pressure on your arm, not really going to be uncomfortable. By that.