Welcome back, everyone. In this video, we'll cover a type of pressure gauge, which remember is just an instrument used to measure pressure called a manometer. Let's go ahead and check this out. Remember that all pressure gauges use height differences to calculate pressure, and we do it by using this equation here, the p bottom equation. There's nothing new here. We've seen this equation a lot before. Alright? So here's what a manometer looks like. It kinda looks like this sort of U-shaped tube like this that ends with a bulb on one side. This bulb has a type of gas. It could be a vacuum or it could be a type of gas here. And on the other side, you could have the manometer be closed or it could be open to the outside air. So, generally, what happens is there's another type of gas over here. I'm gonna call this gas 1. I'm gonna call this one gas 2, actually. And, basically, depending on these gases and their pressures, it causes this liquid to sort of go up and down and change heights. Alright? So I want to show you how this manometer works through a couple of different scenarios that you might see.

Now, the first one here is where you have the manometer that's closed on the left side and normally what that means is that the pressure is going to be 0. You're going to have a basically a vacuum on the left side. So, you have zero pressure over here and if the right side is also at the same pressure, so in other words, if you also have a vacuum over on the right side, then basically you're going to have 0 pressures on both the right and left sides of the column. Now remember, if you have zero pressure and they're equal, then basically neither one of them is going to be pushing down more on the column than the other one. And so they're going to remain level at the same height. This makes sense because you have the same liquid. Right? You have the same liquid here. And remember, the same liquid at the same height should give you the same pressure. So the other way around of saying that is that the same liquid at the same pressure should remain at the same height. Now, you also could have a manometer that's open on one side, in which case you have it basically exposed to air. Almost always, it's going to be air. So that air is pushing down on the left column, presumably with 1 atmosphere of pressure. Now if the bulb is also filled with a gas at 1 atmosphere, then the gas is also pushing on the right side with 1 atmosphere as well. So again, because these two things here, because the tops of these liquids are both going to be exposed to the same pressure on the left and right sides, and they're going to be at the same height. So these two sorts of cases here are trivial, right? There's nothing really interesting going on here. All this is doing is reinforcing the idea that equal pressures on both right and left sides are going to give you the same height. Where things get a little bit interesting is where you have these gases that are at different pressures. Pressures.

Now before I get into that, I just want to remind you that the pressure of the gas does not change a whole lot with the height difference. What I mean by this is that when we had columns of liquid like this depending on where you were, how deep you were throughout the column, and if it was long enough, the pressure could be significantly different. But that doesn't happen with gases. And so basically, what this means here is that if you're pushing down with 1 atmosphere over here, then it's going to be 1 atmosphere throughout the entire column all the way up to the bulb. You're never going to have weird situations where it's 1 atmosphere here and 0.9 up here or something like that. Alright. So you can always assume that it's basically just uniform throughout.

Okay. So here's what happens when you have different pressures. Right? So in one case, if the manometer is closed on the right side, remember, this just means that you have p equals 0 over here, so you have no pressure. But on the right side, if you have the bulb that's filled with, let's say, with 1 atmosphere of pressure, then basically what happens is that 1 atmosphere on the right side is going to push down more than on the left side. And what happens is you're going to end up with a height difference. This height difference is always where the liquid hits the leftmost gas and where the liquid hits this interface over here. So basically, these two points are your most important points. You're going to draw this across and this is going to be where you measure your height difference for. So your height difference is always going to be this thing over here. This is the h that you're going to plug into your equations for, ρ g h or your p b o t t o m = p t o p + ρ g h . Now remember, you're usually going to use this equation when you have columns of liquid, that you have and you have a density, and you're going to have different pressures at the top and the bottom. So in this equation, what corresponds to the p bottom and the p top? Well, basically, this thing here is always going to be your p top and this thing over here is always going to be your p bottom. And what I want to mention here is remember that this gas here, this liquid is going to be the same height as this liquid over here. So, basically, p bottom is basically these two these points over here, or this point over here or also this point over here. P bottom is always basically just whatever is on the right side of the column. Okay? It's because of these rules that we have that the same liquid at the same height is goin...