 So another concept that's usable to discuss in the relationship between volume and flow is a concept called residence time. So if we're considering sort of a large, maybe a conceptual volume, for in this case, the water that's in the atmosphere, the water that's in the entire atmosphere, we have ways of estimating what that's going to be. And I'm going to go ahead and give that. There's a volume associated with that. And I'll use one value here of 1.3 times 10 to the 13th cubic meters. That's an estimate about all the water that's in the atmosphere, on average, at any one time, around the entire Earth. So if we think about that, the water that's there is always changing, because at any one time, you have some water that's being evaporated and added to the water in the atmosphere, and you have a flow out of precipitation. So here's our flow due to precipitation, and here's our flow in due to evaporation and other similar sources. So that's changing the water in the atmosphere on a regular basis. So the amount of time that it takes a system that is an equilibrium to exchange all of the water that's inside. It's kind of like our filling up the pool. All right, when we filled up the kiddie pool, we assumed it went from 0 to the full volume. Well, the amount of time that it takes to exchange all the water in the atmosphere is something known as residence time. And in this case, we can reverse our definition. Remember our definition here, that flow is equal to the change in volume over the change in time. Well, if we do a little algebra, the residence time is equal to that change in volume, basically the entire volume, divided by the flow. But in this case, it's not the net flow. It's either the flow in or the flow out. You can think about it as emptying the entire thing and then refilling it. So this is the flow of either in or out, because they're equilibrium. We'll go ahead and say q out, since that's the one we happened to have measured in this case. So if we have a value here for the amount of precipitation, we can make estimates here that the amount of precipitation over the entire planet has a rate of, let's see here, 5.18. 5.18 times 10 to the 14th meters cubed per year. Notice this seems a little strange. This number here is bigger than the overall volume of the atmosphere, which means the amount that it rains in a year is more than the atmosphere can store. Well, it might seem a little strange at first, but then you can sort of think about this, that it doesn't all happen at the same time. It happens over the course of the year. So this number would be smaller if we divide it by 12 and talk about the rate per month. It would be even smaller if we talk about the rate per day. So the relative values of these volumes is actually not particularly important, because a lot of it depends on the time frame and the unit that we're using there. So let's go ahead and calculate the residence time. How long does water, on average, stay in the atmosphere? Well, if I plug in the two values here, take the volume of 1.3 times 10 to the 13th meters cubed. That's the change in volume if I want to change all the water in the atmosphere out. And I divide that by my flow out, in this case, the precipitation of 5.18 times 10 to the 14th meters cubed per year. Notice the meters cubed is going to cancel out, and the unit in years being in the denominator of the denominator will move up to the numerator. And we'll get an answer in years. OK? Well, that answer ends up being the time, the residence time here ends up being 0.025 years. If I decide I would like to convert that, we notice there are 365 days, roughly in one year. And we get an answer of about 9.2 days. So what this means is that all the water in the atmosphere, if you're a little droplet of water, you get evaporated, you come in here through evaporation, you spend an average of about 9.2 days in the atmosphere before flowing out to precipitation. Now, that's not true of everything. There are some water molecules or water droplets that could stay up there for extended periods of time. And there are some that could evaporate and almost immediately condense and precipitate again. OK? But in general, your average time spent, the average amount of time you spent in the atmosphere is about 9.2 days. That's another example of the relationship between volume and flow.