Pressure In Air and In Liquids

by Patrick Ford
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Hey, guys. So in this video, we're gonna look into how pressure works. If you have an object that is surrounded by air as opposed to if you have an object surrounded by a liquid such as water, let's check it out. All right, So imagine that you are next to the ocean. Okay, So your next next to the ocean. And if you're next to the ocean, remember that the pressure of the air molecules around you let's make air molecules green. The pressure that the air is going to exert on you at this level next to the ocean is gonna be one A T m, which is the standard atmospheric pressure at sea level. Okay, so if you're out in the open, you have air molecules around you, and that's what happens now as you go up in height. As you go up in heights, the pressure will change, and the easiest way, I think, to to to, um to remember what happens to the oppression whether increases or decreases is just to think that if you go up in air, there's going to be less air above you. So if you are here, you can imagine there's a column of air molecules on top of you. But if you're here, there's a smaller column of air molecules on top of you. So because there's less air on top of you, the air pressure will be lower. It will decrease. Okay, remember, air pressure. Um, air pressure decreases. Air pressure comes from the weight of air molecules on top of you. So if there's less air on top of you, there's less of a wait so the air pressure decreases, Okay, because there's less weight pushing down on you. Now, the air density the air density is going to is going to decrease as well, and number two follows from number one. So here you have a ton of air molecules on top of you and the air molecules up here push down against the air molecules down here so the air molecules down here arm or switch together because there's all this weight on top of them. Okay, so you can think that this is this is low density, and this is higher density off molecules. Okay, the molecules arm or spread out up there because they're not being squished by the weight of the molecules. on top of them. So if you just remember that e think if you think about it in terms of what's on top of you, you don't even have to memorize that. As you go up in height, your P air goes down and then your row goes down as well as you go up in heights. Okay, now here's what's even more important for you to remember is that the density of air is very low as it is. So both of these changes air very insignificant. In fact, most of the time we're going to ignore changes in pressure and density of air. Okay, so this first example deals with that Which of the following is the best approximation for the atmospheric pressure? Pierre at 100 m above sea level, So remember changes are Onley significant over large distances, and I should say, for very, very large distances, such as how high and airplanes flying. So 100 m is not a very large distance, even though it be pretty tall. Um, but it's not significant. Therefore, the answer is that the atmospheric pressure here is basically gonna be the same as it is at sea level. Okay, so it's the same because there's very little different. It's approximately the same cool. So if you're not sure which which pressure to use, you should be using 1. 80 m which, of course, is this number right here. It's 1.1 I made 1.0 just because I was rounding on def. They don't tell you you can use that number. So it's a little bit different if you have liquids, however, So if you were an object or under a liquid submerged in a liquid, um, the pressure differences will be much more pronounced. They're gonna be much bigger, different differences in pressure, even for a little bit of a distance, because liquids have much higher density than air. Okay, so but now, in air, we moved up in our pressure changed. But if you are in water, you're going to move down. Okay, so here the pressure depends on your height, and here it depends on your depth. Okay, Now, we just used H for both of those, Um, but the idea is that the pressure will increase as you go down here. And everyone knows that if you start swimming, uh, If you start going underwater, the deeper you go, your year start to feel a lot of pressure. And that's because the water pressure increases as you go down in heights or depth. Okay, it increases and it increases because there's mawr liquid above you. So before, if you went up, it would go down because there's less air Now. If you go down, the pressure will go up because there's mawr stuff on top of you. There's more liquid on top of you, so there's more weight pushing down. It's the same logic as before. The difference here is that changes are significant even for small distances, right? And if you're swimming and you just go a little bit lower underwater, you can tell those differences are pretty significant. Water density does not change much, so we're always going to assume that water this density is constant because the changes are very insignificant, even for very large distances. So you can pretty much assume you could even assume that I never even mentioned this and just pretended. Water density is always the same, always cool. And in the last point here, is that the pressure in the liquid, um such as water. But it really many liquid depends on this equation, or it can be calculated according to this equation is this is a very important equation and it tells us that the pressure at the bottom off a column. So let's draw a little beaker here and let's say we have Let's say we have some liquid and there are two lines that are important here. The highest point here, Okay. And the lowest point of the liquid here. So the pressure at the bottom right here pressure at the bottom is going to be equal to the pressure at the top, which is this plus row. This is density of the liquid G gravity and H h, which is the height difference between these two or the depth of the liquid. Okay, so I can calculate the pressure at the bottom if I know the pressure at the top. And if I know the h Okay, we're gonna use this equation quite a bit. Now you should know that the pressure at the bottom is called the absolute pressure. The pressure at the top is called the relative pressure, and the pressure difference between these two is called the gauge pressure. Okay, gauge pressure is the difference between the two pressures. How much greater one is than the other. And the idea is that this pressure here is relative to the top. Pressure, the pressure, the bottom depends on the pressure, the top. That's why this one's called relative. So sometimes you see questions that will throw these terms that you so you should know what they are. Let's do an example real quick, and then we'll be done with this. So it's as suppose you are 1.8 m tall and your hearts located 1.4 m from your feet. So I'm gonna draw. I'm gonna draw a person here pretty big s so that we can do this. And your heart, Let's say, is over here. And your total height is 1.8 m and your heart is 1.4 m away from your feet. So it follows that your if this is 1.4, this is 1.8. This gap here, heart to top of your head must be the difference between those two, which is 0.4 m. So that's you. Um, it says the blood pressure near heart is 1.3. So right here the pressure at your hearts is going to be, um, is going to be 1.3 times 10 to the fourth, but scow and we wanna know that way. Want to calculate the blood pressure at the top of your head? So we want to know the blood pressure here. Pressure of head. And we wanna know the pressure at the bottom of your feet. Pressure feet. And guess what? We're gonna use this equation highlighted in green right here to figure this out one at a time. So the first one we wanna know what is the pressure of your head? Okay. Blood pressure of your head. This here, by the way, is the density of blood. So I'm gonna right here that row blood is 10. 60 on. We're gonna use that number. All right, so check this out. We know this here. This is our known, and these are our unknowns. So for both of these questions were the same thing we're gonna set up in equation with a known pressure in an unknown pressure. And if you look at this known pressure and this unknown pressure. We know we know this distance right here, which means we can set up in equation between these two guys. So if you set up in equation between these two guys, it's always gonna be that P bottom equals P top plus row G. H. And the H is the gap between them, which is 0.4. So I know P bottom. I'm looking for P Top, and this is just because this is at the bottom, This is at the top. It's that simple, right? This is the guy at the bottom that's at the top. So I know I want P top. I know the density 10. 60. I know gravity. We're gonna use 10 actually, for gravity. We're gonna use 98 because I wanna be more accurate. Since we're dealing with the human body here, um, and H h is going to be the distance between top and bottom, so this is very important. H is the distance between top and bottom, which in this case is 0.4. So let's set this up. I can write that P bottom is 1.3 times 10 to the fourth equals P top, which is what we want. Plus row 10 60 gravity 9. h, 0.4 for the sake of time. I'm not including units here, but all the units Air Standard. Which means my pressure will have standard units at the end by scout. So if I move this around, you end up with P Top equals 1.3 times 10 to the fourth minus right. This goes to the other side minus, and I have it here. Um 10 9804 And this is gonna I'm rounding here 00 p a. So let me write this here. This went from 1.3 times. 10 to the fourth. If I want to rewrite this with a 10 to the fourth, I'm gonna do this kind of quickly, but it would look like this 0.88 times 10 to the fourth. Okay, you can validate that if you would like. Let me get out of the way. All right. And I want to do that so that we can write all of these answers with a power of four. Let's do part beat. So, for part B, we want to know what is the pressure? Um, of blood or blood pressure on your feet. So again, we're gonna set up in equation P bottom equals P top plus row G h. But now we're talking about this interval here. Okay, So this green Heights was this height right here. But now the blue height has to do with this height right here. And perhaps obviously, this is now for this equation. Bottom is the feet and top is the hearts. Okay? Just to be very careful here. When I did this, the bottom was the hearts in the top was the head. But this is all sort of relative, right? So now that I'm writing another equation for a different interval for this height here bottom and top change. Okay, so be careful there. And we are looking for P bottom, whereas before we were looking for P top. Okay, be careful. If you're careful, it's gonna be easy. So let me write this over here. P bottom p top is the heart. So 1.3 times 10 to the fourth plus road 60. Gravity 9.8 and H is 1. 1.4 m all the units, air standards. So I'm gonna get the answer in Moscow. And if you do all of this, you get 27 500 27 500. Or if you want to write it in terms off a power of 10 to the fourth, right, you can write. This is 2.75 times 10 to the fourth, Pascal 275 10 to the fourth. But scout, let me get out of the way. And last thing I do is put it over here that this is 2.75 times 10 to the fourth Moscow. So I want to quickly show you these answers. This is 100.8. This is 1.3 and this is 2.75 And the important point to make here is that as you go down, you have mawr and more pressure. And that's what you should have, because at the bottom of your feet you have all the weight of the blood and your entire body pushing down on you. So the lowest blood pressure should be all about the top. The Onda, the highest blood pressure should be all the way at the bottom um, Now, this is a little bit simplistic. The human body is a little more complicated than that, but this is good enough for physics. Approximations theory. Last last point I'm gonna make here is that this equation actually technically works for air pressure. But we're not going to use it most of the time because most of the time we're just going to ignore changes in air pressure. Okay, so if I tell you that you are on top of a building that's 100 m tall, you're not going to calculate the pressure up there because it's not gonna be very different from atmospheric pressure. You can try it and you'll see that it's a very small difference. So we tend to think of this equation as an equation for pressure in liquids, even though it would work for air. It's just that air pressure changes are very, very subtle over small distances. Cool. That's it for this one. Let's keep rolling.