A surprising amount of engineering is just avoiding conflicts. I’m not talking about arguments in the office, I mean conflicts when two or more things need to be in the same place. There are a lot of challenges in getting facilities over, under, around, or between each other, and there’s a specific structure, ubiquitous in the constructed environment, that’s sole purpose is to deal with the conflict between roadways and streams, canals, and ditches. Hey I’m Grady and this is Practical Engineering. Today, we’re talking about culverts.
Culverts are one of those things that seem so obvious that you never take the time to even consider them. They’re also so common that they practically blend into the background. But, without them, life in this world would be quite a bit more complicated. Let me explain what I mean. Imagine you’re designing a brand new roadway to connect point A to point B. It would be nice if the landscape between these points was perfectly flat, with no obstructions or topographic relief. But, that’s rarely true. More likely, on the way, you’ll encounter hills and valleys, structures and streams, and you’ll have to decide how to deal with each one. Your road can go around some obstacles, but for the most part you’ll have to work with what you’ve got. A roadway has to have gentle curves both horizontally and vertically, so you might have to take soil or rock from the high spots and build up the low spots along the way, also called cut and fill. But you’ve got to be careful about filling in low spots, because that’s where water flows.
Sometimes it’s obvious like rivers or perennial streams, but lots of watercourses are ephemeral, meaning they only flow when it rains. If you fill across any low area in the natural landscape, you run the risk of creating an impoundment. If water can’t get through your embankment, it’s going to flow over the top. Not only can this lead to damage of the roadway, it can be extremely dangerous to motorists and other vehicles. One obvious solution to this obvious problem is a bridge: the classic way to drive a vehicle over a body of water. But, bridges are expensive. You have to hire a structural engineer, install supports, girders, and road decks. It’s just not feasible for most small creeks and ditches. So instead we do fill the low spots in, but we include a pipe so the water can get through. That pipe is called a culvert, and there’s actually quite a bit of engineering behind this innocuous bit of infrastructure.
I know what you’re thinking: “Just a pipe under a road? How complicated could it be?” Well, allow me to introduce you to the U.S. Federal Highway Administration’s Hydraulic Design of Highway Culverts, third edition. Yes you’re seeing that right - 323 pages of wonderful guidelines on how to get water to flow under a road. But worry not, because I have taken my favorite parts of this manual and built a demonstration in the video so you can appreciate the modern marvel that is the highway culvert as much as any red-blooded civil engineer.
A culvert really only has two jobs: it has to be able to hold up the weight of the traffic passing over without collapsing, and it has to be able to let enough water pass through without overtopping the roadway. Both jobs are pretty complicated, but it’s the second one I want to talk about. And it turns out that figuring out how much water can pass through a culvert before the roadway overtops is a pretty complicated question. In fact, there are eight factors that can influence the hydraulics of a culvert: (1) Headwater, or the depth of flow upstream of the culvert, (2) The cross-sectional area of the culvert barrel, (3) the cross-sectional shape of the culvert barrel, (4) the configuration of the culvert inlet, (5) the roughness of the culvert barrel, (6) the length of the culvert, (7) the slope of the culvert, and (8) the tailwater, or depth of flow downstream. We don’t have time to demonstrate how all these parameters affect the culvert flow, but the Federal Highway Administration actually has a pretty comprehensive video on YouTube (with a much nicer flume than mine) if you want to see more [https://www.youtube.com/watch?v=vnXmGyb_hKQ].
One thing I do want to show is the two primary flow regimes for culverts which are outlet control and inlet control. And these are pretty much exactly what they sound like. Outlet control happens when water can flow into the culvert faster than it can flow out. That means flow is limited by either the roughness and friction in the culvert barrel or the tailwater depth at the outlet. The entire area of the barrel is being taken advantage of for flow. In outlet control flow, conditions downstream of the culvert can affect the flow rate. For example, if a tree falls across a ditch downstream, that can back up water reducing flow through the culvert and causing the roadway to overtop.
Inlet control happens when the culvert inlet is constricting the flow more than any of those other factors. Everything that affects the amount of water passing below the road is happening at the inlet. That means changing the roughness of the inside of the barrel or anything downstream won’t change how much flow makes it through. It’s easy to show this in my model because you can see inside the culvert barrel. You can tell that the flow depth in the culvert is shallow and the full flow area of the barrel is not being taken advantage of. There are a wide variety of configurations that the inlet to a culvert can have. If you pay attention, you’ll see all kinds of culvert inlets. Some common types include projecting, where the pipe protrudes from the embankment, mitered where the pipe is cut flush to the embankment, and headwall where the culvert begins at a vertical concrete wall, sometimes accompanied by concrete wing walls to further direct flow into the barrel. Unsurprisingly, each of the multitude of different inlet configurations has a different effect on the culvert hydraulics.
In my demo, I can do a test of two of these inlet configurations to show the difference. First I’m testing the projecting inlet. This is one of the least efficient configurations because there’s nothing to help train the flow into the culvert. You can see that the headwater elevation is quite high, even close to overtopping the headwall in my flume. And, even with all that pressure upstream, there’s not that much water coming through the culvert. It’s only flowing about half full.
Next I reconfigured the demo to make the culvert flush with the headwall. And I also rounded over the inside edge of the pipe, giving the flow a smoother entrance. I didn’t change how much flow the pump is creating, but you can see that the headwater is much, much lower. That means the inlet is more efficient, because it takes less driving headwater to get the same amount of flow through the barrel. In fact, as I cranked up the flowrate higher and higher, I realized that - even with as much headwater as I could create - this configuration was still acting as an outlet-controlled culvert. The smooth and flush inlet was allowing as much flow as possible through.
Of course, there are really elaborate culvert inlets that can be extremely efficient, but like all infrastructure, culvert design is an exercise in balancing cost with other factors. You can spend a lot of money on a fancy culvert inlet that has perfectly smooth edges to guide the water gently into the barrel, or you could just bump up to the next pipe size. Calculating flow through a culvert can be quite complicated, because culverts can transition between inlet and outlet control depending on flow rate. And, even within these two major flow regimes of inlet and outlet control, there are a whole host of subregimes - each of which has its own hydraulic equations. Of course we have software now, but back in the 1960s and 70s the Federal Highway Administration came up with a whole group of cool nomographs to simplify the hydraulic design of culverts. The way this works is you first find the right chart for your situation [7A]. The one in the video is a culvert with a submerged outlet flowing full. Each one is a little different, but in this one you draw a line connecting the culvert length to its diameter. Then draw a line connecting the headwater depth to the intersection of your other line with the turning line. Extend this line to the discharge scale to find out the flow rate passing through the culvert. I love little tricks like this that boil down all that hydraulic complexity into a quick calculation you can do with a straightedge in less than a minute.
Next time you’re driving or walking along a street keep an eye out for culverts. And, if it’s raining, take a look at the flow. See if you can identify whether the culvert is outlet or inlet controlled, and be thankful that we have this ordinary, but remarkable, bit of infrastructure to let you safely walk or drive right over.
