 So, if we consider flow into or out of our control volume, it can be partitioned into a number of different groupings that are called sources. Sources generally representing flow that is coming into our volume and sinks. Sources which are flowing out of our volume. And there may be multiple sources or sinks of these flows that are going in and out. Okay, so typically, when we use our letter Q to represent flow, we assume that Q is some sort of magnitude and we usually assume that it's positive, that it's a positive magnitude and we let the direction of the flow either into or out of our volume here. We let the direction of the flow sort of be indicated by the arrows or by signs within our system. Okay, so Q is usually positive. And what we can do is say that our change in our volume over our change in time is now not equal to just to one flow measurement but is equal to the sum of all these sources of all the flows that are in minus the sum of all the sinks, the flows that are out. So here we have Q in and a variety of Q flows coming out. So for our Eulerian flow, when we're thinking about Eulerian flow here, something coming in and something going out and we're staying with the volume but not worrying about the things that are flowing and flowing out after they leave our area, okay? And Eulerian flow is in equilibrium, we're in equilibrium when this change in volume over the change in time is equal to zero. In other words, that the amount of flow in and the amount of flow out, sum to zero. One of the other ways of saying it is that the sum of our flows in is equal to the sum of our flows out. So for example, let's consider our lake that we've sketched up here. Perhaps we have measured some inputs. Let's say for example that the lake receives 47 million meters cubed per year, 47 million meters cubed per year in runoff, I'll put that as QR. In other words, there's water running off the sides of the mountain, okay, or running off into the stream and it's measured in 47 million meters cubed per year, okay? Similarly, we might measure direct precipitation, maybe the rain is falling directly into the lake, okay? And we'll say Q, our flow due precipitation, might have a value, let's use a value of 30 million meters cubed per year. So those are examples of flows that are coming into our lake. And let's say we measure, we discover that there's a stream or we have one stream that we're able to measure of water that's flowing out. However, usually with something like a stream, we don't measure that stream sort of over an entire year. We might be measuring that sort of more regularly, but if we find that there's an average flow of that stream, maybe the average flow of that stream, the Q of the stream is equal to two meters cubed per second, okay? So we have flows in and flows out, okay? But let's talk about is this stream an equilibrium or what is the status of this stream? In this case, we're doing what's called a water budget. We're actually looking at the stream and seeing how much water's coming in and how much water's coming out, very similar to the kind of thing you might do with your finances, okay? So let's take the total of all the flow that's coming in, which is simply adding those two values, equals the 47 million meters cubed per year and adding the 30 million meters cubed per year and we end up with a total of 77 million meters cubed per year. If I want to compare the flows that are in and the flows that are out, what I want to do in this particular case is convert this to the same units. So let's take my flow out, which as far as we know is only this stream of two meters cubed per second and let's go ahead and convert that into how many seconds there are in a year. Let's see here, I need seconds on the top here and year on the bottom and in this case we would have to multiply 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day and then finally our 365 days in a year. If you do that, some of you might remember the song Rent, I mean the song from the movie Rent, 525,600 minutes, that's one number that you can remember. Actually another quick and easy number to remember the number of seconds in a year, at least to three decimal places, is it's roughly equal to 10 pi million seconds in a year. Notice 10 pi million would be the equivalent of 31.4 million, okay it's actually closer to 31.6 million but that's a good estimate or something that you can kind of remember it here. I didn't use the number 31.6 million here, actually 31.5 million, so 31.5 million here seconds in one year, if I multiply that out I get an outflow of about 63 million meters cubed per year. Notice these two things are not equal, okay, which means one of two things. It either means that we are going to get a change in our volume, that the volume is going to change over time, in fact that what's going to happen is each year we're going to add the difference between these two things. So if I take my Q in and subtract my Q out I get a difference of 14 million meters cubed per year, well that's going to be my change in volume over change in time. So if things remain the same like this I'm either adding 14 million meters cubed to my lake per year, which eventually means the lake is going to continue to grow and grow and grow, however nature tends to balance these things. Nature tends to actually balance out the values that if it continued to flow more would flow out the stream. So most of the time nature, at least over time, tends to be an equilibrium that lakes tend to maintain more or less a constant volume unless there's severe drought or unless there's severe flooding. So if that's the case and we assume equilibrium instead, what we're saying is perhaps we're missing some of the outward flow and in this case you might be able to think of things that we might not be taking into account. For example there's a couple things that we might consider that maybe some of the water we're unable to measure because there's a flow due to groundwater and outward flow due to flowing out through pores in the bottom of the lake. So groundwater flow. In addition another big contributor might be evaporation and or transpiration. Transpiration being basically the exchange of water into the air by the activity of plants and or animals. Okay so in this case it's actually not likely that we're going to have the lake continue to grow. What's more likely is that we're missing some of the flows and that if we do have equilibrium we know that these two pieces here, these two outflows or any ones that we're not considering are probably equal to that 14 million meters cubed per year. Generally for most larger systems we can assume that they're going to be an equilibrium over time and it's a matter of finding the appropriate flows that are flowing in and balancing them with the flows that are going out.