Let's talk about barometers. A barometer is a device that's used to measure the pressure. Now the simplest type of barometer which is the type that we're going to talk about just consists of a column of mercury which is trapped in a little tube of glass and inverted in a pool of mercury. So we've got a nice uniform fluid here and so that means that the pressure got to be the same at each height so that's all fine. The atmosphere is pushing down here and there's nothing pushing up there because there's no air inside of this glass tube. So that means that this height of the mercury directly measures the atmospheric pressure, so we'll have p atmosphere equals density of mercury acceleration due to gravity times height. So this is kind of a nice way of visualizing pressure if the height goes higher then that means that the pressure was bigger, if the height went lower then that means that the pressure went lower there're just directly proportional to one another.
A lot of times people will actually measure pressures just directly in terms of how many millimeters of mercury can be supported in this type of a barometer. Alright now another important idea that's associated with this, is the idea of gauge pressure. Gauge pressure is defined as the difference between the pressure that, whatever it is something is exerting and the pressure that the atmosphere is exerting. So difference between the pressure and the atmospheric pressure, but this is very, very important for things like tyres. So when somebody says your tyre pressure needs to be blurred usually what? 32 PSI or 30 PSI pounds per square inch what they really mean is that the pressure inside the tyre needs to be 32 PSI greater than the pressure outside the tyre. What they're saying is that the tyre needs to support that pressure. So the pressure inside is actually 32 plus atmospheric pressure which is about 14.7.
Okay so that's one situation in which gauge pressure is useful but it's not the only one. It's very, very easy to measure gauge pressure all we need to do is have a little black bar on the mercury column that indicates where atmospheric pressure would be and then we seal up the bottom of it which I'm not showing in this diagram and then we just kind of put whatever we want in there that we want to measure the pressure of. If the height of mercury goes up, then the pressure that we're trying to measure is greater than atmospheric pressure. The gauge pressure will just be density of the fluid which is usually mercury although sometimes people use water times acceleration due to gravity times this difference in height which I can measure very, very accurately. And that's one of the reasons why people like to use gauge pressure.
Of course if the pressure that we're trying to measure is less than the atmospheric pressure this height will be on the other side because the mercury column will go down. And that will mean that the gauge pressure will be negative and you often see that in vacuum pumps. Where you'll look at the pressure reading and it'll say negative in kilopascals so negative 80 kilopascals it doesn't mean that the pressure is negative because the pressure can't be negative what it means is that the pressure is less than atmospheric pressure. So a lot of times it's really gauge pressure that you want okay and the gauge pressure that they're asking for. Now sometimes people will ask you for the total pressure. Total is basically shorthand for saying you need to add 1 at the end, okay 1 atmosphere, because they want to know the total pressure compared to vacuum, compared to 0 pressure what is the pressure. So let's go ahead and do a problem along these lines determine the total pressure 50 meters below the surface of the ocean. Okay well this is real simple. I'll say well jeez the pressure will be equal to density of ocean water times acceleration due to gravity times height.
Now I'm going to actually use the density of ocean water here because there it says ocean. Right so we'll say 1,025 kilograms per cubic meter 9.8 meters per second squared and what do we got? 50 meters, so 50 meters and when we work that all out it turns out to be 502,250 and then what's the unit going to be? Everything is SI so it's going to be the SI unit for pressure which is Pascal's alright but we're not done, because this really only tells us the part of the pressure that we feel 50 meters below the surface of the ocean, that's associated with the ocean water we also got to support the atmosphere because it's there too. Right so really I should more correctly write this as delta pressure. It's the change in pressure between the top of the ocean and where I'm trying to measure. If I want the total pressure I got to take this change in pressure and add the atmospheric.
Of course atmospheric pressure is 101,325 Pascal's and so when we add it together, we'll end up with 603,575 Pascal's okay. So that's total pressure, it's very, very simple but you just have to make sure that you're very careful and understanding what they want. Do they want the gauge pressure, do they want the total pressure? Okay because the difference is 1 atmosphere and I've seen people lose a lot of points for that, it's really kind of silly. Alright that's the barometer.