 So let's consider an example of gauge discharge, okay? In a case here, we have a raceway, basically some sort of area that's a rectangular area that's meant to transport water from one place to another. And we're interested in knowing how much flow is going through the raceway. In order to know that, we're going to need some information about the geometry of the way Here we have a width of the raceway. We're going to, we're given a value of 45 feet for the width of the raceway. We're interested in the value for a depth of three feet, knowing that that depth might change, that might change with different amounts of water that are coming through. And again, one of the things we do for gauge discharges, we're assuming steady flow, that there isn't changes, that the depth isn't changing over time, that it's pretty consistent depth, at least for a long enough period of time for us to calculate the flow, okay? So we have this width, we have a depth. We're also going to need a slope of the raceway. So we go and we look at the raceway and we measure and we realize that for a section near where we're measuring, it rises a value of three feet over a length of a thousand feet, a horizontal length of a thousand feet, okay? So if we use that, we can calculate S, which is our slope, which is that three feet, divided by that thousand feet, which gives us a value of 0.003. And again, unitless, the feet will cancel out. The other thing we're going to need to be able to calculate here, to determine this, is a Manning's N. And in this, we would have to look and see what the raceway was made out of, okay? In this case, it says it's a channel with a gravel bottom, okay? And without any weeds. Well, if we look up something like that in a chart, we might see a value similar to 0.0275. Or if you're given a problem example in class, it might give you the example there, okay? So this appears to be all the pieces we need. Let's see here. If we look over here at our Manning's equation, we have N. We've just calculated S, but we also need to figure out our area and our wetted perimeter. Well, the area here is fairly straightforward. Area equals width times depth. So our area is going to be the 45 feet times our 3 feet, since we have a rectangular raceway. And that's going to give us a value of 135 square feet. Our wetted perimeter is the place where the water is touching the sides of my raceway. And it looks to me like we have W plus D plus D, or W plus 2D. All right, so our wetted perimeter in this case, Pw, our wetted perimeter is going to be a length of 45 plus 3 plus 351 linear feet. Well, now we have all the values that we need. Let's go ahead and plug all these values in to our Manning's equation, or the flow version of Manning's equation, okay? We plug in each of these pieces. Our flow, which depends upon D, is going to be equal to 1.49. And notice all these things were measured in feet, so the 1.49 is the appropriate unit, feet, one-third per second, over our Manning's coefficient of 0.0275 unitless. We have our area here of 135 square feet to the five-thirds power. That means to the fifth power, and then we take the cube root of that. We divide that by 51 feet to the two-thirds power. And finally, we have our slope 0.003 to the one-half power, which is the square root. And we can't quite see that, the one-half power. Okay, if I put those values in, plugging in a few more values here, I get, let's see if I can, I believe this is 54.18 feet to the one-third per second, keeping my units here. I have 3,653 feet to the 10-thirds. Notice feet squared to the five-third powers to the 10-thirds over 13.75 feet to the two-thirds. And then the value here is a unitless value of 0.05477. Trying to keep about four significant digits here. Finally, when I put all those into place, I end up with a value of 788, keeping only three significant digits, because I believe that's the number that we have for our Manning's N, and also for our, well, for almost all our values. Okay, 788, what? What are the units? Well, if I look carefully here, I have per second, there's the per second. Okay, but what are our other units? Well, we have foot to the one-third plus feet to the 10-thirds, which is going to be feet to the 11-thirds. We're adding exponents. And then we divide by feet to the two-thirds, which gives me feet to the nine-thirds. Well, feet to the nine-thirds is cubic feet, which is exactly the type of units we want for volume per time. So our flow rate for this particular raceway in this situation is 788 cubic feet per second. Notice, if I wanted to calculate it for a different depth, I would have to go through and recalculate the area and the wetted perimeter, although the slope and the Manning's coefficient would remain the same.