Hey guys. So in this video, we're going to 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. Alright. So imagine that you are next to the ocean. Okay. So you're 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 going to be 1ATM, 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 heights, the pressure will change. The easiest way I think to remember what happens to the air pressure, whether it 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 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 weight. So the air pressure decreases. Okay, because there's less weight pushing down on you. Now, the air density is going to decrease as well. And number 2 follows from number 1. 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 are more squished together because there's all this weight on top of them. Okay? So you can think that the air density here is lower and here it is higher of molecules. The molecules are more spread out up there because they're not being squished by the weight of the molecules on top of them. If you remember that, you don't even have to memorize that as you go up in height, your pressure goes down and then your density goes down as you go up in height. Okay? Now, here's what's even more important for you to remember: the density of air is very low as it is. So both of these changes are 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, Pair at 100 meters above sea level? So remember, changes are only significant over large distances. And I should say for very, very large distances, such as how high an airplane is flying. So 100 meters is not a very large distance, even though it'd be pretty tall, but it's not significant. Therefore, the answer is that the atmospheric pressure here is basically going to be the same as it is at sea level, okay. So it's the same because there's very little difference. It's approximately the same. Cool. So if you're not sure which pressure to use, you should be using 1ATM, which of course is this number right here. It's 1.01. I made 1.00 just because I was rounding. And if they don't tell you, you can use that number. Cool. 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, the pressure differences will be much more pronounced. They're going to be much bigger 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 and 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, but the idea is that the pressure will increase as you go down here. And everyone knows that if you start swimming, if you start going underwater, the deeper you go, your ears start to feel a lot of pressure. And that's because the water pressure increases as you go down in height or depth, okay? It increases. And it increases because there's more 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 more 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 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 pretend that water density is always the same always. Cool. And then the last point here is that the pressure in the liquid, such as water but really in any liquid, depends on this equation or can be calculated according to this equation. This is a very important equation and it tells us that the pressure at the bottom of 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, at the bottom, is going to be equal to the pressure at the top, which is this, plus ρ, this is the density of the liquid, g, gravity, and h, which is the height difference 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 going to 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 at the bottom depends on the pressure at the top. That's why this one's called relative. So sometimes you see questions that will throw these terms at 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 says, suppose you are 1.8 meters tall and your heart is located 1.4 meters from your feet. So I'm going to draw, I'm going to draw a person here, pretty big. So that we can do this and your heart, let's say is over here and your total height is 1.8 meters and your heart is 1.4 meters away from your feet. So it follows that your, so if this is 1.4 and this is 1.8, This gap here, heart to top of your head, must be the difference between those 2 which is 0.4 meters. So that's you. It says the blood pressure near your heart is 1.3×104 Pascal. And we want to know the, we 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 want to know the pressure at the bottom of your feet. Pressure feet. And guess what? We're going to 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 Alright. So Alright. So check this out. We know this here, this is our known and these are our unknowns. So for both of these questions, we're going to do the same thing. We're going to set up an equation be with a known pressure and an unknown pressure. Between these two guys. Which means we can set up an equation between these two guys. So if you set up an equation between these two guys, it's always going to be that pbottom=ptop+ρgh. And the h is the gap between them which is 0.4. So I know pbottom, I'm looking for ptop 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 ptop. I know the density, 1060. I know gravity. We're going to use 10. Actually for gravity, we're gonna use 9.8 because I wanna be more accurate since we're dealing with the human body here. 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 add sub. I can write that pbottom=1.3×104=ptop+ρ×1060×9.8×h×0.4. For the sake of time, I'm not including units here, but all the units are standard, which means my pressure will have standard units at the end Pascal. So if I move this around, you end up with ptop=1.3×104-right,thisgoestotheotherside,-andIhaveithere,1060,9.8×0.4.Andthisisgoingto,I'mroundinghere8800pa. So, let me write this here. This went from 1.3×104. If I want to rewrite this with a 104, I'm going to do this kind of quickly, but it would look like this. 0.088×104. Okay. You can validate that if you would like. Let me get out of the way. Alright. And I want to do that so that we can write all of these answers with a power of 4. Let's do part b. So for part b, we want to know what is the pressure of blood or blood pressure on your feet. So again, we're going to set up an equation pbottom=ptop+ρgh. But now we are talking about this interval here. Okay? So this green height was this height right here, but now the blue height has to do with this height right here. And perhaps obviously, this is and now for this equation, bottom is the feet and top is the heart. Okay? Just to be very careful here, when I did this, the bottom was the heart and 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 pbottom whereas before we were looking for ptop, okay? Be careful. If you're careful, it's going to be easy. So let me write this over here. pbottom=ptop+ρ×1060×g×9.8×h×1.4, 1.4 meters. All the units are standard so I'm going to get the answer in Pascal. And if you do all of this, you get 275100, 275100. Or if you want to write it in terms of a power of 104, right, you can write this as 2.75×104<