Being able to control the level of water in a river is beneficial in quite a few ways. Historically, mills relied on water power to drive saws, grinding wheels, and other equipment. Raising the water level in a river can also allow boats and ships to navigate areas that would otherwise be inaccessible. Finally, having control of a river can help mitigate the damaging impacts of flooding. But, how we do get this type of control over the level in a body of water? Hey I’m Grady and this is Practical Engineering. On today’s episode, we’re talking about wiers.

A weir is a small dam built across a river to control the upstream water level. Weirs have been used for ages to control the flow of water in streams, rivers, and other water bodies. Unlike large dams which create reservoirs, the goal of building a weir across a river isn’t to create storage, but only to gain some control over the water level. Over time, the term weir has taken on a more general definition in engineering to apply to any hydraulic control structure that allows water to flow over its top, often called its crest. In fact, the spillways of many large dams use weirs as control structures. So how do they work?

If you watched my previous video on the basics of open channel hydraulics, you’ll remember that for subcritical flow, that is slow, tranquil flow seen in most rivers, the depth is controlled by downstream conditions. That means adding a weir across a river will increase the water level upstream. But by how much depends on the flow. This is the equation for flow over a weir. We’re not going to do any calculations here, but it’s important to know the factors that govern the performance of our hydraulic structure. This equation says that the amount of flow that passes over the weir depends on three factors: the length of the weir, the height of the water level above the crest of the weir, and this coefficient which changes depending on the geometry of the weir. The graph of a hydraulic structure’s flow versus water level is called its rating curve, and this is the rating curve for a typical weir.

In many cases, a weir is a passive structure, meaning once it’s installed there’s no way to change this rating curve. And that’s not always ideal. Streams and river are subject to tremendous variability in flow rate. A hydraulic structure may normally flow a small amount, but in flooding conditions be asked to pass incredible volumes of water. With a passive structure and fixed rating curve, that variability in flow means tremendous variability in the water level upstream. During a flood, a weir may back up the water badly enough to cause damage upstream. If you’re using a weir for the spillway on a dam, you might have to build your dam much higher just to handle the water level that occurs during very rare but extreme cases, increasing the overall costs of the structure. Ideally, hydraulic structures used to control water level would have a flat rating curve, meaning over a wide range of flows, you only get small changes in level. So how could we flatten this curve?

Going back to the weir equation, there are only two other parameters available to increase the flow for a given water surface. We could improve the geometry of the weir to increase its efficiency. Different shapes of weirs can pass flow more efficiently and thus have a higher discharge coefficient, but this has a practical limit. The most efficient shape for a weir is to match the curve that the water would take off of a sharp crest. This part of the flow is called the weir’s nappe, and the shape that matches it is called an ogee. With ogee-crested weirs, we can get discharge coefficients as high as around 4, but that’s pretty much the limit. The other parameter we can change is the length of the weir, but in many locations, the available footprint for the weir is a fixed size that can’t be increased. Even if the footprint isn’t fixed, increasing the length of the weir can add significant costs.

Of course, this challenge is easy to address if we allow for structures with moving parts. Many dams and spillways have large gates or valves to control flow. There are a wide variety of types of controlled outlets used on hydraulic structures, including crest gates that act like weirs that can be raised or lowered. The benefit is that the structure’s capacity can be increased while flows are high by opening gates, and then decreased when flows return to normal. Controlled structures provide more flexibility in how water gets released or held back, essentially turning a static rating curve into a family of curves which can be selected from to meet the operational goals.

Of course, controlled outlets come with a major disadvantage of increased complexity, and in many cases, requiring an actual person be available 24/7 to operate the gates and make releases based on inflows. So what if we could get the benefit of a controlled outlet without the disadvantages of increased complexity and operational obligation? Well, there’s one other trick that hydraulic engineers have up their sleeves.

Remember when before I said that you could only fit a certain length of weir within a fixed footprint. That’s not completely true. We can actually fold a weir to get more length within a given space. This is called a non-linear weir and it’s used in situations where you want greater discharge within a given footprint but without the need for actively controlled outlets. To show how this works, I’ve built this flume and some model weirs. This first weir just goes directly across the flume with no bends. I’ll mark the water level in the flume first using this straight weir. Now, with the same flow rate, I’ll replace the linear weir with the folded version. This has just about twice as much weir length in the same footprint. You can see that, even though the weir is passing the same amount of flow, the water level is lower, almost half the distance to the crest from the original level. We’ve flattened the rating curve, allowing for greater discharge at a lower water level. Non-linear weirs with folded cycles like this are call labyrinth weirs and they’re becoming more common as hydraulic control structures. There are also rectangular versions called piano key weirs.

It’s easy to see how beneficial weirs can be, from generating power to improving navigation, controlling floods, and even acting as the spillways for dams. With all those benefits, there are definitely some downsides as well. Impoundments across rivers affect the aquatic environment. Low head dams can also pose a serious danger to swimmers and boaters, a topic I’d like to discuss in the future. In fact, many old weirs that are no longer needed are being replaced or completely removed to restore the river to its natural state. But as long as we need to control the flow of water in our constructed environment, weirs will continue to be an important tool for a hydraulic engineer. Thank you for watching, and let me know what you think!