**Concept:** How Barometers Work

Hey guys. So in this video we're going to talk about barometers which are classic pressure gauges in physics, let's check it out. Alright, so pressure gauges are devices or instruments that use height differences to calculate pressure and most of the time we're going to use this equation right here. Alright, 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 the liquid is going to 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 ride 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 to 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 Rho, 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 the pressure at 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 0, whenever you're touching vacuum the pressure at that point is 0 so this is just 0 because it's vacuum. So you're left with Rho, g, h and that is the equation it becomes simpler. Now, if you are trying to calculate pressure you would use a known liquid, let's write this here, you would use known liquid so that you know its density, you can plug it in, you're on earth so you know gravity or if you're somewhere else you would presumably know 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, this is a device that's used to calculate the pressure of air, you might be thinking is it the pressure of air just one atm, well, not really, if you go up really high in a mountain you have lower air pressure so you can carry your little your little barometer with you and 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 here, if this was water the column would have to be 13.6 times taller, okay? And usually when you, usually when you build a barometer these are about a meter high which is about this much, right? With mercury. Now imagine something, that's 13 times bigger than this and I got to carry this friggin thing around, right? So that wouldn't be very good. So they figured hey, let's just put the heaviest thing, we can think of, they could 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, a barometer question. So it says, your classic barometer as shown above is built with a 1 meter 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 known liquid but here we're going to use an unknown liquid but it's gonna be okay. So let's just draw a thing here, very simple and this thing here is it's 1 meter. So when I talk about height it's the height of the column over here, I'm actually going to draw this over here, this is one meter and you fill it up with a liquid,it says the liquid goes 76 centimeters up the glass tube when the barometer is exposed to standard atmospheric pressure. So I'm going to draw a little liquid here,I'm gonna make it blue and we're going to say that this liquid goes 76, 76 centimeters high, okay? So, this is going to be 76, 0.76 meters which means there's a little bit left here you don't need to calculate it but it's 24 meters, okay? And the height is always from the base of the of the tube to the 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 Rho, g, h. I just told you earlier that the Rho is known. So that you can find p air, in this problem we're flipping that, I am telling you what the pressure at the bottom is, I'm telling you what P airis because I told you that it is standard atmospheric pressure, in other words, this is just 1 atm, the pressure at the bottom is 0 and now I'm giving you this and asking for this or just flipping the equation around, that's fine too, okay? So let's move some stuff around here, the density will be the pressure of air divided by, the 0 is gone, divided by g times h, pressure of air is standard atmospheric pressure, well, remember you can't plug in 1 atm, you have to play them in Pascal and 1 atm is 1.01 times 10 to the fifth Pascal, gravity is, I'm going to be precise here, 9.8 meters per second squared and the height is this height difference right here. 0.76 meters, okay? Now, when you divide this when you divide this you're going to get, you're going to get thirteen thousand 560 kilograms per cubic meter and if you were to look this up on Wikipedia or Google or whatever, you would figured 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 an known liquid and figure out what the pressure around you is you can also have a 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, 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 84 centimeters up the glass, I'm just going to draw this real quick and the idea is that this is now 0.84 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 Rho g,h. p bottom in a barometer is always going to be the pressure of the air around you, p top is always going to be 0 and then we have Rho g, h. Here we're looking for the pressure there and known 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 9.8 and then the height is 0.84 and when you multiply this you're going to get 112,000 pascals, okay? So instead of it being, which by the way is 1.12 times 10 to the fifth Pascal and if you convert this to, if you want to convert this to ATM you can just do 1 ATM is the same as 1.01 one times to the fifth and this will tell you that this is 1.1 atm, okay? So, the liquid went higher, the liquid went up higher which means that the pressure of the event outside of you is stronger which pushes the liquid farther up and this is verified here, because here we had one atm, here you have 1.1 atm 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 keep going.

**Problem:** A classic barometer (shown below) is built with a 1.0-m tall glass tube and filled with mercury (13,600 kg/m^{3} ). Calculate the atmospheric pressure, in ATM, surrounding the barometer if the column of liquid is 76 cm high.

If a liquid only half as dense as mercury were used in a barometer, how high would its level be on a day of normal atmospheric pressure (when the mercury barometer reads 76 cm)?

A. 152 cm

B. 76 cm

C. 19 cm

D. 304 cm

E. 38 cm

Watch Solution

The height of water in a water barometer is 883 cm at 20°C. The density of water at 20°C is 0.998 g/cm^{−3}. What is the pressure?

1. 8.64 × 10^{3} Pa

2. 86.4 kPa

3. 88.3 kPa

4. 8.81 × 10^{3} Pa

5. 101 kPa

Watch Solution