 So, I want to talk about the Reynolds number and I thought I'd use the tablet so you could see it because we're going to put down numbers and make sure you see it all. So, if you have a specific type of fluid, it usually has about a fixed density and a fixed viscosity while the flow speed and the flow depth change through time. What I want to talk about now is the effect of density and viscosity of the fluid on the flow. So, we have three main types of fluids that we're going to talk about and we have the density and the viscosity. And we have liquid water and I'm just going to say water for that. And we have ice and we have air. There are other types of flows too but these are the ones we're going to talk about. So, the density of both water and ice are about, we're going to use kilograms and meters. So, 10 to the 3 kilograms per meters cubed, that's about 1 gram per centimeter cubed. And the same is true for ice, it's slightly less which is why it flows but it's pretty similar. And of course, air is much less dense. It's about, it's a little more than 1 kilogram per meter cubed but it depends a lot on the density of the air and how much water is in it. So, we have air being much less dense. In terms of viscosity, the viscosity of water is about 10 to the minus 3 and that's kilograms per meter second so that's how fast it flows relative to the mass. For ice it's very, very dependent on the temperature. For ice it ranges from 10 to the plus 3 to greater than 10 to the 20th kilograms meter second. So this, it's less viscous at warm temperatures and it's more viscous when it's cold. So ice and glaciers that are warm flow much faster than glaciers that are cold. And then the viscosity of air is very low. It's 1.8 times 10 to the minus 5 kilograms meter second. So what we see here, I'm going to change to another color, is that the density of water and ice are about the same but water having a much lower viscosity than even the fastest flowing ice means that it flows much faster. The air has an even lower viscosity and that's one of the reasons that the wind has so much turbulence because we have the viscosity in the denominator of the Reynolds number. So the smaller this number is, the bigger the Reynolds number and the more turbulence that's present. Okay, so I'm going to write the Reynolds number again over here so we can refer to it. So we have the flow speed times the flow depth times the density over the viscosity. Okay, so you'll notice that we have the density over the viscosity as the two properties of the flow. So what we can do is we can actually take the ratio of these two to understand how the difference in density and viscosity affect the Reynolds number. So if we look at the ratio, we have 10 to the third divided by 10 to the minus third so that's 10 to the sixth and the units from the bottom the second and we have one meter that counts as that one of the three before so we have meters squared. We'll take the warmest ice and you can see here that if we take the warmest ice, 10 to the third divided by 10 to the third is one centimeters or seconds per meter squared. And then if we take air and divide those two, we get, let's see, I have to divide one over 1.8 and I actually calculated that with the others but it's about 6.8 times 10 to the fifth, seconds per meter squared. So if we look at, if we compare these numbers, go back to the yellow here, what we see is this for ice, it's very low and because that multiplier is low, the Reynolds number is usually less than 500. So for example, if you wanted it to be 500, you'd have to have either a really fast flow speed or really, really thick ice. However, it's very hard to get a fast flow speed if you have a very small viscosity. So if we look at water, 10 to the sixth is 100,000 and so almost always this is high enough that usually the Reynolds number is greater than 2,000. However, the Reynolds number does depend on the flow speed, let's go back right here. And if the flow speed of the water is zero, that will make the Reynolds number zero. So it's usually a turbulent flow but not all the time. We can also look at it for the air. And so the air here, this number is also large. So we can say this is high and that also means that the air is usually turbulent. So even when air is still though, we do have this interesting case for the air and I'll make the air, the comment on the air light blue here. Usually because we're dealing with a very thick atmosphere, the depth of the flow is also large. And what that means is that for air, the Reynolds number is usually much greater than 2,000 and wind has a lot of turbulence. If you've been in a strong windstorm, especially when the flow speed is high, you know that there's a lot of force to that wind. So the next set of videos are going to be showing some examples of some of these flows. Thanks for watching.