Culverts: The Ponded Condition Assumption

When analyzing culverts, a pooled condition, or zero approach velocity, is typically assumed at the inlet, which results in an appreciable amount of headwater. This is reasonable since a culvert’s opening is usually very small compared to the upstream cross-section (e.g. a natural watershed or wide channel) and water has to “slow down” or “wait in line” before it can flow into the culvert.

The Hallway Analogy
To visualize the ponded condition, picture this scenario: You’ve just finished watching a concert, and now it’s time to head home. You and a crowd of people are walking down a hallway, and there’s only one door at the end. Of course, it’s going to take a while to get out since only one person can go through at time. You have to slow down and wait for the other guys to go through. This is how water behaves in the ponded condition, more or less; not only is there a backup of people at the door, but you had to stop walking altogether due to that backup. In other words, your approach velocity is zero, and the backup of people represents the headwater depth.

Now, imagine the same scenario, except the hallway has wide, sliding doors, and perhaps a tapered entrance. Here’s how that might look:

Although both analogies makes us look like a bunch of sheep, this hallway obviously lets more people through, resulting in less of a backup and allowing you to maintain your pace, or approach velocity. When it comes to culverts, they pretty much behave the same way.

Ponded Condition in Real Life
Ponded conditions may or may not exist for a culvert, but it’s normally assumed since it’s a worst-case scenario and makes calculations much simpler. However there are actually many cases where there is an appreciable amount of approach velocity. For example, if there is a channel that facilitates flow into the culvert, the approaching water will preserve much of its kinetic energy as it passes through. As a result, there’s less energy lost and this results in a lower headwater depth (or “backup”) than that calculated if pooled conditions were assumed.

Here’s an example of a culvert that would have a good amount of approach velocity that probably shouldn’t be neglected, especially at lower flow conditions (if anybody is willing to send or refer me a better picture than this, I would greatly appreciate it! I only have pics from wikicommons at the moment):


Photo © Michael Trolove (cc-by-sa/2.0)

Now compare the above culvert to the one below, where the upstream end isn’t as channelized and the approaching water appears tranquil:


Photo © Bonnachoven (cc-by-sa/1.0)

And here’s an extreme example of a culvert where there would definitely be ponded conditions in most cases:


Photo © Peter Ellis (cc-by-sa/3.0)

When NOT to Neglect Approach Velocity
The above pictures give you a nice visual of when the approach velocity is and isn’t significant, but it’s not always clear when you should neglect it. It’s your judgment call, but the approach velocity should generally be included in calculations if:

  • There is a channel that directs the flow smoothly into the culvert at design flow (similar to the first picture above)
  • The area of the approach channel to the culvert is less than five times the area of the culvert barrel (per a USGS report1)
  • The culvert is large enough to have free surface flow all throughout the barrel (no backed up water at all), or if the culvert can be considered a bridge.
  • The culvert is part of a larger storm drain system, or if you’re required to model the water surface profile throughout the culvert or entire system
  • There are significant effects from upstream or downstream drainage structures
  • The culvert is used as an irrigation structure
  • The culvert must incorporate aquatic organism passage (AOP)

This isn’t an exhaustive list, but if your culvert falls into any of these categories, you would be better served using software that performs gradually varied flow (GVF) calculations to carry the water surface profile through the culvert. HEC-RAS and WSPG are a couple of popular programs that can do this.

Conclusion
It’s generally safe to assume zero approach velocity since you’ll always calculate a more conservative (higher) headwater depth. The nomograph solutions for culverts and the FHWA’s HY8 culvert program make this assumption, and it’s perfectly reasonable.

The “ponded condition” assumption is a simple one, but hopefully my explanation made sense. As always, there are disclaimers and exceptions when modeling the flow of water, so I may not have covered everything here.

*I highly recommend reading the FHWA’ culvert design manual (HDS-5) or taking a look at this Youtube video they published if you want to learn more about culvert hydraulics.

1 Computation of peak discharge at culverts. Ronald William Carter. US Geological Survey, 1957.