19. Fluid Mechanics
Pressure Gauge: Barometer
How Barometers Work
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Hey, guys. So in this video, we're gonna talk about barometers, which are classic pressure gauges in physics. Let's check it out. Alright. So pressure gauges are devices their instruments that use height differences to calculate pressure, and most of the time, we're gonna use this equation right here. All right, so this is what a barometer looks like. I'll quickly describe it. It's got a container here, sometimes called a reservoir fancy. Right. That's where most of liquids gonna be. And there's sort of a closed pipe here. This is typically referred to as the column or because it forms a column of liquid here. Right? So the idea is that you have the bottom part here exposed. So this part here and in this part here are open, are exposed to air so that air molecules around here push down against the liquid and cause it to write up this pipe right up this column. Okay. And what you do here is you Then measure the height difference between the very top of the column and the very bottom of the column, which is over here, right? This part here is just have extra liquid, so don't worry about that. So once you have this height difference right here, you are then able to use this equation. P bottom equals P top plus row G. H. I want to remind you that this is the density of the liquid, not the density of the air. Cool. So let's see, uh, the pressure of the bottom is the pressure over here. And because this part of the liquid is touching air, this is the pressure of air, sometimes also referred to as just the atmospheric pressure. And the pressure at the top is this here, and because it's touching vacuum, the pressure is zero. Whenever you're touching vacuum, the pressure of that point is zero. So this is just zero because it's vacuum, so you're left with row G H. And that is the equation has become simpler. Now, if you are trying to calculate pressure, you would use a known liquid that's right. This year you would use a known liquid so that you know it's density. You can plug it in your on earth, say no gravity, or, if you're somewhere else, you would presumably no gravity, and then the h you measure. I don't know. With a ruler or something, right? And you measure H and that allows you to then find that allows you to find P air. So this is a device that's used to calculate the pressure of air. I might be thinking, Isn't the pressure of they're just won a T M? Well, not really. If you go up really high in the mountain, you have lower air pressure so you can carry your little your little barometer with you on. But you're able to figure out the pressure in different places. Cool. So that's how the barometer works. You should know that the classic barometer invented by Torricelli uses mercury instead of any other liquid because mercury is heavier. So why does that matter? Well, you need a column. This column of liquid here has to be tall enough to push against the air pressure until it balances itself out right And mercury is very heavy, so you don't need that much mercury. So that column doesn't have to be that tall. If this was water, let's write this year. If this was water, the column would have to be 13.6 times taller. Okay? And usually when you usually when you build a A barometer, this thing is about a meter high, which is about this much right with with Mercury. Now, imagine something that's 13 times bigger than this, and I gotta carry this freaking thing around, right? So that wouldn't be very good. So they figured, Hey, let's just put the heaviest thing we could think of. They put Mercury in there, and that's why it works like that. So let's do an example real quick, very straightforward. And you see two different ways you can get a question about, uh, Barometer question. So it says your classic barometer, as shown above, is built with a 1 m tall glass tube and filled with an unknown liquid. So this is an unknown liquid. I just told you that you're supposed to use a gnome liquid, but here we're gonna use an unknown liquid. But it's gonna be OK. So let's just draw a thing here very simple. And this thing here is it's 1 m. So whenever you talk about height, it's the height of the column over here. I'm actually gonna draw this over here. This is 1 m, and you fill it up with a liquid. It says the liquid goes, uh, 76 centimeters up the glass tube. When the barometers exposed to standard atmospheric pressure, someone to draw a little liquid here, we're gonna make it blue. And we're gonna say that this liquid goes 76 centimeters high. Okay, so this is gonna be 76.76 m, which means there's a little bit left here. You don't really need to calculate, but it's 24 meters, okay? And the height is always from the base of the of the tube to the on top of the liquid. Okay, cool. So we want to know what is the density of the liquid. So what is the density of the liquid? And again, we're always going to use the p. The pressure equation. P bottom equals p top plus row g each. I just told you earlier that the row is known so that you can find Pierre This problem. We're flipping that I am telling you what the pressure at the bottom is. I'm telling you what Pierre is because I told you that it is standard atmospheric pressure. In other words, this is just one a t m the pressure at the bottom of zero. And now I'm giving you this and asking for this. So we're just flipping the equation around. That's fine. True. Okay, so let's move some stuff around here, the density will be the pressure of air divided by the zero is gone. Divided by G times H pressure. Very standard atmospheric pressure will remember You can't pull again 1 80 m. You have to plug it in Moscow in one a. T. M is 1.1 times 10 to the fifth Moscow gravity is I'm gonna be precise here. 9.8 m per second square and the height is this height difference right here. 76 meters. Okay, Now, when you divide this, when you divide this, you're going to get you're going to get 13, kg per cubic meter. And if you were to look this up on Wikipedia or Google or whatever, you would figure out that this is actually the density of mercury. Okay, this is actually the density of mercury. So this is mercury cool. So, just like how you can put a no liquid and figure out what the pressure around you is you can also having known pressure and then figure out what the liquid is so you can do both things. So let's look at part B here. Part B says, um, when the same barometer with the same liquid is taken to a different location, the liquid goes up 84 centimeters. The liquid goes 84 centimeters up the glass. So you go somewhere else, Okay, you go somewhere else. And now this thing is going centimeters up the glass. I'm gonna draw this real quick. And the idea is that this is now 0. centimeters. And the question is, what is the atmospheric pressure at this location? So the first place had standard atmospheric pressure. But now we want to know what is the pressure of air in this other place. Okay, so again, p bottom equals p top plus row. G H p. Bottom on a barometer is always going to be the pressure of the air around you. P top is always going to be zero, and then we have row G h here. We're looking for the pressure of air. I know density because it's the same barometer with the same liquid. So the density is going to be this right here, 13,560 gravity is 9. and then the height is 0.84. And when you multiply this, you're gonna get 112,000. But Scouse Okay, so instead of it being which, by the way, is 1.12 times 10 to the fifth Moscow. And if you convert this to if you want to convert this to ATM, you could just do one. ATM is the same as 101 times 10 to the fifth. And this will tell you that this is 1.1 a. T. M. Okay, So the liquid went higher, the liquid went up higher, which means that the pressure of the air outside of you is stronger, which pushes the liquid farther up. And this is verified here because here we had won a t. M. Here you have 1.1 80 m. So it's about 10% higher. That's why this thing went up about 10% higher as well. That's it for this one. Let's get going
A classic barometer (shown below) is built with a 1.0-m tall glass tube and filled with mercury (13,600 kg/m3). Calculate the atmospheric pressure, in ATM, surrounding the barometer if the column of liquid is 76 cm high. (Use g=9.8 m/s2.)