 So now I'd like to talk a little bit about which grains move. So it's actually a little bit complicated discussion, but we can start looking at the balance of forces on the different grains. So let's say grain one has mass one and for mass and G for gravity. And grain two has mass two times G for gravity for its downward force. So in terms of the lift force that's needed, if these two grains have the same density, this one's smaller and so the mass would be smaller. So we can basically say if M1 is less than M2, grain one needs less lift to get off the bed. So we have this relationship here that the lift force is smaller, but it's also sitting and it's experiencing a lower force on the top of the grain. If we look at our flow speed with depth here, I'll draw an exaggerated boundary layer here, something like that. This grain experiences a faster flow speed at the top than this one does. So this grain gets a little bit of a larger lift effect. So it really depends on the characteristics of the boundary layer, which grain moves in different ways. It could be that grain one is actually maybe a denser mineral than grain two. So maybe it's a pyroxene and grain two is quartz, the density of pyroxene is greater. So we can say that if M1 is about equal to M2, the lift force would be the same to move them. But in this particular case, the lift force will be greater on the larger grain because the flow speed is faster at the top of the grain, which will create a lower pressure at the top than this particular grain. So one of the reasons that you often can get concentrations of dense grains is because they don't stick up as high into the boundary layer. So the lift force for the same mass or gravitational force, so the lift force is lower. And I promised earlier that we'd talk a little bit about gold in California. We'll come back to it again. But gold is very dense as a metal, and it gets concentrated in these layers where the boundary conditions are such that larger quartz grains, less dense grains, can be lifted into the flow and moved away, but the gold grains get left behind. And when you actually pan for gold, you're doing that effect as well. Okay, so we have our grain here, and the area with our flow moving to the side here, the area of low pressure is from the top of the grain to the side over here. So we have low pressure here. And in particular, the lift component of pressure comes from the component of the grain that's at the top right here. So I've been drawing round grains, but some rocks and minerals, whether into more platey shapes. So if we have a platey grain like this, we'll call it grain three here. So we have mass three times gravity. It has a much larger area with the low pressure zone. So the low pressure can go like all the way from here to here. And because there's so much, such a larger surface area of the fast flow going over the top, basically if you have more area, you get more lift. So the way I drew this, we don't know the density of this grain. The way I drew it is much larger, because I wanted a lot of surface area here. But the point is that even if it's much larger, it might get lifted sooner because you get this really large area for that low pressure to work on to develop a greater lift force. So the shape of the grain also matters a great deal. And there's one more thing that I want to talk about, and that's the geometry of the grains on the bed itself. Let's start over here. So we have our surface. And in natural environments, we have a lot of grains, maybe some different sizes, different shapes, some of them sitting on top of each other. And the grains that move, it varies a lot depending on the pressure. So let me redraw this one so that it sticks way up here. So we have our flow speed moving downstream here. This grain is sticking up a little bit higher, so maybe it gets a little bit of a lift force and gets pulled up into the flow. This one doesn't have very much pressure on the surface area in the top to lift it, but it might have a lot of force going to the side. So maybe this one might tend to roll, except that it's jammed in with this grain here. And so if it rolls, it might push this grain up and shift the others around. So if we have, I'm going to add another grain right here. So if we have a little grain here, this may be a quartz, so it's not super dense. This one has a less force pulling down, but it might still have a pretty effective lift force from the Bernoulli effect. Maybe it would lift up as well. In contrast, this grain here might be the same size and the same composition, but it's down nestled in among the other grains, and so it can't move at all. So we have the complexity of the distribution of grains on the bed that matters as well. So I'm going to list out some of the things that influence which grains move. So the first one is how high it sticks up into the flow. That determines how much shear is associated with the grain. The second thing is the mass, which is what controls the force pulling it down in terms of gravity, and that depends on the size of the grain and the density. The third thing is the shape of the grain, because the shape influences how much surface area the low pressure has to act on. And then the fourth thing is the grain's position relative to other grains. If it's jammed in between grains or it's in the flow shadow of a larger grain, it's less likely to move, if it's balanced right on top of something sticking high up into the flow, it's more likely to be lifted up into the flow. So, thanks for watching.