Intro to Density

by Patrick Ford
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Hey, guys. So now we're going to start talking about fluids, which is also sometimes referred to as fluid mechanics, fluid dynamics or just liquids. Now, the first topic you need to know really well is density, so let's jump right into it. Alright, so liquids and gasses are types of fluids, types of fluids. So liquid is a fluid and a gas is a fluid. So we're going to use the term fluids, um, to refer generally to both liquids and gasses. And the reason we do this is because liquids and gasses behave very similarly in a lot of different situations. So instead of saying liquids and gasses, liquids and gasses all the time, we're just gonna say fluids, which refers to both both things cool. So density is the first big concept you have to understand, and you may remember density from chemistry class. The density of material has to do with how tightly packed the molecules are. So, for example, here you got the same sort of volume, this sort of blue um, cup, and it's got these little green balls here. They're not very packed together, so we're going to say that this is low density and here they're very tight together. So this is going to be high density. Okay, so the more compressed things aren't the high density you have Density in physics is given by the letter by the Greek letter Row row, which is a little p a car VP. And if you remember, it's simply mass divided by volume mass divided by volume. So mass and physics is always kilograms and volume is a three dimensional length, so it's going to be cubic meter, so it's kilograms per cubic meter. Remember, if you have the three dimensions of an object, like a rectangle or something, then the volume of a rectangle would be the width of the rectangle times the height, times the depth right. And sometimes you see length instead of one of these three measurements. And because each one of these guys is a meter, you got me to meet a meter. You have cubic meter cool. Now, sometimes you are given the density and you're given these dimensions, right, so you're given density rho and you're given the three dimensions. Whenever you're given to three dimensions, you're able to find volume. And if you have row and volume. If you have row in volume, then you're going to be able to find the Mass. And that's because of the equation. Row equals mass divided by volume. Therefore, if I move the V appear, I hope you see that right away you get em equals row volume. So let's put this this over here mass equals row volume, all right? And they try to trick you with this, but it's very straightforward. Um, it's just a play on this original definition here, off density. Sometimes you see something that says that objects have the same material. Um, intensity problems is usually means that they have the same density. Okay, so if you have a if you have two pieces of wood and we say it's the same kind of would you can also infer that they have the same, you can conclude that they have the same density. Cool. And then the last quick point I wanna make and we'll do an example is if you have liquids in a container to liquids or more liquids two or more liquid in a container, the liquid with the higher density will be at the What do you think? Top or bottom higher density liquid will be at the bottom. Okay, the high density liquid to be at the bottom. And you can think of this as higher density being heavier. Now I'm putting this in quotes because it's not necessarily heavier. It's gonna be heavier depending on whether you have mawr or less volume of it. Um, but on a per molecule basis, it is heavier or per small area or per small volume. Um, it is heavier. Therefore, it's gonna go to the bottom because liquids can sort of move around. So you might have seen something like this where they put all kinds of different things and you can see them becoming very different. Sort of a heterogeneous mixture. Here, Andi, honey is all the way at the bottom. Which means, honey is the, uh, the highest density out of all these things that are here. Cool. So we'll see some stuff like that later. Let's do a quick example here. What is the total weight of off air molecules inside a large warehouse? And I give you the dimensions here, so I want the total weight of air, right? So where does have a weight and So first, let's start with Wait, wait. Remember is just mg mass times gravity and I know gravity I'm gonna use here just for the sake of keeping this simple gonna say gravity's approximately 10 meters per second squared, So I'm gonna use 10. So if it's asking me for weight and I know gravity, all I really need is mass. So this question is really about finding the mass of air in this space. Now I'm giving this right so you can sort of draw this. It's 100 wide. Ah, 100 deep. So it looks something like this not to scale. Okay, so this is 100 m here, 100 m here in 10 m high. Whenever you come in, three measurements taken right away Find the volume volume with just those three measurements together, multiplied 100 times, 100 times 10. And here you could just count the zeros or five zeroes. So this is 10 to the fifth, and I got meter times, meter, times, meter. So cubic meter. Right? Or you can write it out if you want. 12345 So it's 100, cubic meters. Okay, Now I have the volume. I have the density right here. So I confined the mass because remember, density is mass over volume. I have the volume. I have the density it was given right here. So we can just find the mass. Which is the equation I showed you just a few moments ago. So Roe v and then you're gonna multiply. The two row is going to be one points, 2 to 5 kg per cubic meter. I highly recommend you put the cubic meter down here, right? They don't put it over here. If you put it in the bottom, it's gonna be easier to play with it times the volume, which is 100,000 cubic meter and then notice what happens here right away. This Kansas with this. And you just got this big multiplication. The mass, therefore, is going to be. If you put this in the calculator, you're going to get 00 You're left with kilograms. A little bit of dimension analysis here. Cool. Are we done know? Because we're getting mass so that we can plug it in here and get the weight. But that's the last step. I'm gonna do here. Weight is mass times gravity and I just have to multiply those two we're gonna use gravity is 10. So we just have a extra zero here and the unit for weight since it's a force is Newton's. So this is a million Newtons of weights. Cool. So the air in this entire thing is actually pretty heavy. If you would put that entire air on top of you, it would crush you in a very small amount of time. Alright, cool. Let's do this example here. If you want, you can pause the video and give this a shot yourself. I'm gonna keep rolling here. It says the density of whole blood so whole blood means it's all the different parts you have, you of your blood plasma. Everything else is nearly this nine Physics, whenever they see a value is nearly or approximately, we're just gonna use that value. So density is Rome of whole blood is 1.6 kg per leader. I'm gonna write it like this. Notice that it didn't say kilograms per cubic meter instead of said per leader. Um, in these two are not equivalent, but they are related. We'll talk about this in the future video. So we're just gonna leave it like that for now. And then it says, How many kilograms are in a pipe? Pints of whole blood. So asking how many kilograms kilograms is the units for mass? If I say how many kilograms I'm asking for the mass. So what is the Mass? And then I'm given the volume here. The volume is 4 73 mL. Now you can't really use milliliters. You're supposed to use leaders. But let's leave it alone. For now, let's not sort of prematurely convert units here. All right, so this is very straightforward. I have three variables that are related by this equation by the definition of density, which is mass over volume. I wanna know mass. I have the other two. I just have to move things around. This question is a little bit more straightforward than the other one, PV or Roe V. And this is 1.6 kilograms per leader. Times of volume, which is 4 73. Milly leaders can't really do this without changing either leaders in 2 mL or milliliters into leaders. Hope you remember. This is very straightforward one leader is 1000 mL. So I'm actually just gonna scratch this and put 1000 milliliters right here. Middle leaders will cancel, and then you're left with kilograms, which is what you want. So all we gotta do here is multiply this big mess. And if you do that, you get 1.6 times 4 73 divided by 1000. This is gonna be in kilograms. And if you do this in the calculator, you got 05 or 1 kg. That's how many kilograms or how much the mass of the mass of blood of whole blood. If you have one pint of it with this density Cool. That's it for this one. Let's go to the next one.