19. Fluid Mechanics

Density

# Density Values & Specific Gravity

Patrick Ford

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everyone. So now that we've seen density, we're gonna talk about a slightly less familiar term, which is called specific gravity. Now, if you've never heard that or seen that in your classes, you can probably go ahead and skip this video, but some professors might want you to know it. So it's a good thing to know. It's actually very straightforward. So let's just jump in. Right? So we have the specific gravity which doesn't really have a variable, so we just we just abbreviated as S. G. Is a term that's sort of related to the density of a material, but it's not exactly density. The specific gravity of any material is defined as the density of that material divided by the density of freshwater. Now, freshwater is always going to be on the bottom and we know that there is a fixed value. So really quickly here, what happens here is that if you're dividing two densities, you're gonna divide the units right, kilograms over meters, cubed, kilogram over meters cubed. And whenever you divide two variables that are the same, they cancel out. So this is just a number that has no units. It's just like two or five or 0.5 or something like that. Alright, so just to put into an equation, you know, just make a little bit simpler, the specific gravity of any material, which I'm just gonna call X is equal to the density of that X. That material divided by the density of fresh water. Now again, like we said, the density of fresh water is always a fixed value. It's 1000. So one really simple way we can sort of phrase this or write this equation is the density over 1000. Alright, so pretty straightforward. So let me just go ahead and run it through some quick examples if you know that the density of some material is equal to 2000 kilograms per meters cubed and that means that the specific gravity of that material is 2000 over 1000. So in other words it's just too, it's twice as dense as water. It also works the other way around. If you know what the specific gravity for material is, I'm going to say that the specific gravity of some material y is equal to 0.7, right? Less than one or more than one, then that that means that the density of that material is equal to 0.7 times 1000 which is equal to 700. Right? So it works both ways. If you know the density, you can figure out the specific gravity and then vice versa. Alright, so really what we can see here is that the specific gravity doesn't really have anything to do with gravity. It's kind of one of those unfortunate terms That later on we figured out it's not really it doesn't really have to do with gravity. Um but it's sort of that's what we stuck with. So, you know, we're kind of stuck with it. Right? But it's just a relative number. Right, so two or 0.7 or something like that for how many times denser a material is relative to freshwater. Alright, so that's all it is. It's just a number that says how much times denser it is than water. So, that's all there is to it. Let's let's go ahead and just work out this example. All right, so, we're gonna calculate the volume of some wooden cubes. In other words, we're gonna calculate V. That's the volume for a specific gravity of 0.8. So, we have S. G. That equals 0.8 and it weighs 16,000 newtons. Now. Be careful here because we have newton's. So you might think it's mass, but it's actually wait some of the words, the W which is equal to M. G. Is equal to 16,000 newtons. Alright, so then how do we calculate the volume? We're gonna have to relate this back to the density equation. We have row that equals M over V. If you re arrange for this, you see that V is equal to M over row. Right? These two things swap places. So, in order to calculate the volume, I'm gonna need the mass, which I don't know that's the mass and I'm gonna need the density. So, the way I'm gonna do this is that this s G here is gonna give me density, Right? Because remember that's the relationship between specific gravity and density and then this equation here for weight is gonna give me the mass. Alright, so let me go ahead and just do this one first. Um So I'm just gonna bring this down here. So we have that M equals W. Over G. Which is 16,000. And we're just gonna use 10 Fergie. Just make it really simple here. So you can knock off one of the zeroes. And just this just becomes uh this is actually 100 kg. Alright, so that's your mass. And then on the other side we have the specific gravity. So we have S. G. Is equal to 0.8. So what that means here is that the density Is going to be 0.8 times 1000 right? It's 0.8 times the density of freshwater. So in other words, you're gonna get 800 kg Per meter. Cute, this makes sense. We've got a number that was less than one, which means that it's less dense than water. And we got 800. So that makes sense. Alright, actually I did this wrong, so this is yellow and this should be blue. Alright, so now we're just gonna plug both of these into our equation here and we're gonna get that V is equal to 1600 divided by the density which is you just get to and the units for that are going to be in meters cubed. Right? So we have kilograms and then kilograms grams per meter cube. So you have S. I. Units so you should end up with are also S. I. Units, so that is your final answer. So pretty straightforward, let me know if you guys have any questions.

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