Hello, my name is Jim Schall, and I'm an instructor for Federal Highway
Administration training delivered under the
National Highway Institute. The National Highway Institute, or NHI, is the training branch of the
Federal Highway Administration. The videos you're about to watch are based on some of the training courses developed by the National Highway Institute, in particular the Introduction
to Highway Hydraulics course, NHI Course 135065, and the Culvert Design course, NHI course 135056. I've been an instructor for
National Highway Institute training courses for 25 years. I completed my undergraduate
engineering degree at Purdue University, and did my Masters and
PhD at Colorado State. The videos are based on
demonstrations and experiments that we do primarily in
these two training courses built around a portable flume. The flume is six inches wide and approximately five feet long and recirculates water
from a 30 gallon sump. The videos, there are
six of them to watch. The recommended order in
which to watch those videos, first, open channel flow concepts, then grate inlets, culvert hydraulic concepts, hydraulic effects of culvert liners, aquatic organism passage design concepts, and energy dissipators for culverts. Thank you for your interest in Federal Highway
Administration training. I hope you find this video series helpful in completing highway
drainage design projects. This video will demonstrate
culvert hydraulic conditions. The purpose of the video is to see how different factors of a culvert influence the headwater, which is the amount of ponding at the upstream side
of a culvert entrance, as well as how they might impact the velocity coming out
of the end of the barrel. Those are the two primary design variables when we start talking
about culvert hydraulics. Before we get into the
actual model demonstrations, we need to define the basic concepts of inlet and outlet control. Inlet and outlet control
are central to understanding the Federal Highway Administration culvert analysis methodology. When we say inlet control,
it's as it sounds. The control is at the inlet of a culvert. Everything that matters
is happening right here. If the inlet were not
constricting the flow, the barrel could carry more water, but it's the conditions at the inlet that are restricting how much
water gets into the barrel and how much headwater we have. Inlet control culverts are
typically on a steeper slope, and we have part-full, supercritical
flow inside the barrel. In contrast, in outlet control we're typically on a flatter slope. If we have part-full flow,
it's going to be subcritical, or it could be full pipe. In fact, the only time we'll
ever have full pipe flow in a culvert barrel is in outlet control. And as with inlet control the word outlet control means specifically that the control point is at the outlet, or sometimes further downstream
in the tailwater condition so that everything about
this culvert installation is important. The entrance condition, the pipe, the length of the pipe,
the roughness all matter. If we think about that for a minute, in the inlet control, going
back to the steeper slope barrel when everything that matters
is at the entrance to the pipe, then it really doesn't matter
what's going on down here. That will not change
the headwater condition if that's really true. Another concept to remember in hydraulics is when we say control,
that has specific meaning. It usually means where the flow is passing through critical depth. So in this case, in inlet control, we're saying that the flow
passes through critical and accelerates down the barrel to a supercritical flow condition. In outlet control, typically
again my flatter slope barrel, I would be at critical at the outlet or under tailwater control if the tailwater is
submerging critical depth. There are a number of factors that enter into how a culvert operates hydraulically, and if we just look at the model, we can walk through those. Certainly the headwater, which is the ponding that occurs that helps overcome the
energy losses in this barrel. The area, the size, in
other words, of the barrel, the shape of the barrel,
whether it's round, pipe arch, arch, elliptical. The barrel slope and inlet configuration. The barrel roughness, whether it's smooth, say an RCP pipe with an n value of .012, or a CMP with an n value of around .024. The barrel length as it
affects the friction loss, and the tailwater condition as well. So there are eight factors. In outlet control, all
eight are important. The control is at the
outlet, or the tailwater. The amount of flow getting
through this barrel, the amount of headwater
we have will be influenced by all eight factors. In inlet control on a steeper slope, only the conditions at
the entrance matter, so the headwater, the area, the shape, and the inlet configuration
are most important. The barrel slope has
a little bit of effect in inlet control on the
headwater condition. It has a larger effect
actually on the exit velocity coming out of the end of the barrel, steeper slope, we have
a higher exit velocity. So those are the basic concepts
of inlet and outlet control. We're going to do the demonstration initially using a double barrel model. One side is rough pipe, simulating a CMP. The other side is smooth. I'm going to start with the
plug in the smooth barrel side, and we'll start observing
the changes in these factors. I can't show you everything
of the eight factors that I listed. For example, my model is a two inch pipe. I can only show you a two inch pipe. It's circular, I don't have
pipe arch or elliptical shapes, but otherwise, I can show
you pretty much everything. Certainly by changing which
barrel I send water down we can look at roughness. I can raise the slope. We can look at barrel length by using one of my inlet models that we'll be referring to later, but this inlet model, we call
it a groove end projecting, matches the headwall
configuration on my barrels. I have a groove end, a
socket end if you will, so that I can insert my inlets. So by using the groove end inlet, I can extend the length of this barrel without changing the K sub e, so we can look at length. Certainly I can vary tailwater by putting stop logs at
the end of the flume. So, we can look at most all the factors, and of course in the inlet configuration, I'll be changing and looking
at a wide range of inlets and how that affects culvert
hydraulic performance all the way from models with headwalls to very specialized inlets,
the tapered design inlets that provide great hydraulic improvement. So we'll start with the rough barrel pipe, and we'll be monitoring
the changes in headwater primarily on the stilling well. So the first question
we always need to ask is whether we are in
inlet or outlet control. A hint is that I'm on a pretty flat slope, and outlet control is usually
on your flatter slope barrels. The other indicator in my flume is that my pipe is running full, and again, you can only
have full barrel flow when you're in outlet control. So we are in outlet control
with water going down the CMP pipe. I'll mark the headwater here. And the first question that we'll look at is how does length affect the headwater? And I'll do that again by
using my groove end inlet to allow me to extend the
culvert basically 25%. This is a 2 foot culvert
model, this is a 6 inch inlet. So I'll be extending the length about 25%. So once I'm sure I've got
a stable reading here, it looks pretty good, I'll put this on the
front end of the barrel and we'll see the headwater
starting to increase. The reason the headwater
increases in outlet control is because of friction loss. In outlet control, we
have the entrance loss, the friction loss, and the exit loss. All three contribute to
the headwater condition. In outlet control,
we're basically applying the energy equation. We're applying it from
the exit of the pipe at a known HGL. We calculate the energy
losses that are occurring, and project upstream to
get the upstream HGL. So anything that increases the energy loss will change the headwater
condition in outlet control. So the question is in terms
of a real world scenario, you've got a roadway widening project, and you go talk to the maintenance people, and they say, "You know, that 24 inch pipe "that's been working really
fine for the last 30 years, "we think you can just
go ahead and extend it "as part of the roadway widening project. "You don't have to worry
about the rest of the barrel." If you're in outlet control,
you have to be careful, because by extending it, you have increased the friction loss, and where you might not have had an overtopping situation previously, in the roadway widening, you would end with potential
for a higher headwater and possible overtopping condition. So that's the effect of barrel length. We can also look at the
effect at this point of inlet configuration. I have a K sub e of 0.2
in the flume right now with my groove end projecting. I'll switch that to what we
call a thin edge projecting, which has a K sub e of 0.9, and I'll go ahead and move this up to mark this starting point. And we should see a
little bit of a change, but we don't see a huge change, because in this outlet control scenario, the inlet loss is just one of three, and in fact, the friction loss, what's happening in the barrel, tends to be more dramatic and controls the hydraulic performance as much as the inlet or the exit loss. So we did see a slight increase here by changing the K sub e from .2 to .9 So we've looked at the change in length, we've looked at the effect
of inlet configuration, let's go ahead and look at
the tailwater condition, and I can do that by adding my stop logs, and the question is, I'll
mark this headwater now, will the headwater change
as I start changing the tailwater condition? So these stop logs are one inch. The first one inch change has no influence on the headwater condition. So it appears that maybe
tailwater isn't a factor. Well, it isn't a factor yet,
because what's happening is as my flow exits out of the barrel, remember, we're in outlet control, and in hydraulics the
control typically means we're passing through critical depth, so I am passing through critical depth as I exit this barrel and plunge into this low tailwater condition. This would be like a barrel, say, in a overbank area or a relief culvert that is plunging into a
pasture or forested area. There's no tailwater to speak of. Well, let's increase the
tailwater a little bit more so I can start to see
if I have any influence, and of course I won't have any influence until my tailwater drowns
out critical depth, and that just happened, as you can see, we're starting to climb a little bit now. I'm going to let this stabilize. And what's actually going to happen now, and it's very interesting, a change in tailwater now is immediately reflected to the headwater, so if I have a 1 foot
change in tailwater I would see a 1 foot
change in headwater. And the reason that is, we'll talk about that while
this is still stabilizing, gets right back to the
fundamental equation in outlet control, which
is the energy equation. Remember, we're applying
the energy equation from a downstream HGL, a known point, we calculate the energy loss, and we get the upstream HGL. So now if there's no
change in the energy loss, which my pipe is flowing full so the velocity doesn't change, I have the same friction loss, I have the same entrance loss, I have the same exit loss, so if I raise the downstream tailwater, the hydraulic grade line, the HGL, and I add the same energy loss, I'm going to get this
translated to the upstream side by the amount of the tailwater. So we can do that. We should see this headwater rise basically by the amount of this
stop log, which is 1 inch. You can see it's going up. While it stabilizes, let's talk about another
real world scenario. You've got a culvert that has
been fine for quite awhile, and all the sudden,
the upstream land owner is calling the DOT and saying, "You know, I think there's
some sediment in that culvert. "The last couple rains, I've
had flooding in my pasture, "and I've never had that problem "since the last time you were
here to clean the barrel. "So could you send the
maintenance crews out "and have them clean out this culvert?" So sure enough, you send
the maintenance crew out, and they do an inspection, and they find, well, there's really
nothing in that barrel. There's no sediment,
there's no debris blockage, and you just conclude, well,
this fellow just has forgotten how bad it can flood when it really starts to rain around here. But sure enough, the next time it rains, he's on the phone again, wanting you to come out
and fix the culvert. Well, it's quite possible that it was not anything at all related to the culvert. In fact, it could have been
something off the right of way, perhaps quite a ways downstream
if you’re in flat country, where the tailwater has changed. You're in outlet control,
the tailwater's changed, and that effect is reflected
all the way upstream to the headwater. It could be as simple as a
tree falling into the channel, it could be perhaps a
beaver pond got built, maybe there was some bank caving, any one of a number of scenarios, but it had absolutely nothing
to do with the culvert. So be aware of that, the importance of tailwater
in outlet control, particularly when the tailwater takes over control of the culvert operation, and that happens again when the tailwater submerges critical depth. So I'll take these back out, and what we'll do now is we'll switch over to the smooth barrel, so I'm going to go from my n value of .024 approximately,
to an n value of .012. And with that change, we
should see a reduced headwater, because we'll have less friction loss. I'll use the same inlet,
the thin edge projecting, and we'll start from that point. And as expected, the headwater's dropped due to this change n in value, because again, in outlet control, we're applying the energy equation, and by reducing the friction loss, we've cut down the energy loss, the headwater will be lower. So we've looked at culvert length, we looked at the roughness, we've looked at inlet configuration, we've looked at tailwater. Let's go ahead and look
at the effects of slope. Before I do that, while I can't demonstrate
the effect of area and shape, a larger diameter barrel
would have a lower headwater because of the larger flow area, and interestingly enough,
some of the low profile pipes, like an elliptical or a pipe arch, would also have a lower
headwater in outlet control because the center of gravity is lower on a low profile pipe. So, for the same headwater elevation I'm getting more pressure, more headwater, to move the water through the culvert. So let's go ahead and
start increasing the slope, and we're going to do that and monitor a couple different things. I'll start by marking the headwater here, the headwater depth, but I also want to pay attention
to the headwater elevation, which I'm going to monitor with this yellow scale. It's sitting on the tabletop,
so it's on my datum, so I'm using the words carefully here. I'm looking at elevation
on the yellow scale versus headwater depth
on my spilling well. And right now it's about 12 inches is where my headwater elevation is. So the question is, what will
happen to the headwater depth, and what will happen to
the headwater elevation as I start to raise the flume slope? So let's raise it up a little bit. And what we see is the headwater depth has dropped, but the headwater elevation
is still sitting at about 12. Now at first that might
seem a little confusing. How could the headwater depth change, but not the headwater elevation? Well, it gets back to
the basic equation again, the energy equation. Remember, we're applying
the energy equation from the outlet of the
pipe to the upstream side. My control at the moment is critical depth as it plunges out of
the end of the barrel. I haven't changed the energy loss, so when I project through
the energy equation from the downstream HGL
to the upstream HGL, that elevation doesn't change, but the headwater depth does because I've raised the flume up. In essence, what I've
done is redistributed the potential head terms. I've increased the elevation head, but I've reduced the pressure head. So what this tells you in outlet control is if you have a culvert with a clearance issue
at the upstream side, perhaps it's a fiber optic line and you can't put it as
deep as you would like to, you could raise it up
to clear that utility, whatever it might be, without changing the headwater elevation, meaning the overtopping condition. You might change the depth, but you wouldn't change the elevation. Now of course as we continue
to increase the slope, remember, when we introduced the ideas of inlet and outlet control, I said a steeper barrel is
typically on inlet control. So as I continue to raise the slope now, we're going to see this culvert transition from outlet control to inlet control. And we'll be able to see that, because when that happens, there'll be a big air pocket that forms in the inlet of this culvert, and I can accelerate that a little bit. You'll start to see a vortex forming here, that pulls air into the barrel and we end up with what we're seeing now. We have a part-full,
supercritical flow condition. We are in inlet control. Everything that matters now is happening right here at the entrance, so it really doesn't
matter what's downstream. And I can prove that by switching back to the rough barrel pipe. Now you might initially think, "Well, you know, this n
value on this smooth pipe, "this RCP, is like .012, "and if he switches that back over, "and runs water down the rough barrel, "well, that's an n value of .024, "so the headwater's got to go up." Well, let's find out. So I'm going to mark this,
now that we're pretty stable. Okay, so we have a good stable condition in this smooth barrel pipe, and what I want to do is
switch over to the rough barrel to prove to you that in inlet control the only thing that matters is
what's happening right here. It doesn't care what's
downstream, and if that's true, when I make the switch, there should be no difference between the headwater elevation. So we'll do this, It'll take it a minute to stabilize because I momentarily have a
double barrel culvert going, but we should come right
back up to that same O-ring. And as you see, we're
getting there pretty quickly. So, in inlet control when we're in this
steeper slope condition, rule of thumb for box
culverts is anything over 1% tends to be an inlet control, what's happening downstream whether it's the roughness of the pipe, the length of the pipe, even
the tailwater condition, let me show you that, will not change this
upstream headwater condition. So to do this, I'm going to add tailwater, and what you'll end up seeing is a small hydraulic jump
forming inside the barrel. So the hydraulic jump is
sitting right about in here at the moment. And an important factor of hydraulic jump that a lot of designers don't understand is that it's commonly thought that the hydraulic jump creates
the downstream tailwater, when in fact it's the downstream tailwater that creates the hydraulic jump, meaning if I change this tailwater I can move that jump back and forth. And the concern here is some states use a design called a broken back culvert, which is quite often a steep slope barrel coming to a flat slope near the outlet, and the designer says, "Oh yeah, "I remember my fluids. "This is supercritical
because it's a steep slope. "This barrel down here," if
I were to try to model that, something like that, "is on a flat slope, "so I'm going to have a
hydraulic jump right here, "and I'm going to have a nice
tranquil flow exiting the barrel, "and I don't have to worry
about energy dissipation." That is true only if there's
enough tailwater here to make that jump happen
inside the barrel, and if not, that jump will sweep out and start creating serious
erosion problems downstream. Okay, so that's the effect of
tailwater in inlet control. It didn't really change
the upstream headwater. It wouldn't change the
headwater until we put so much tailwater on it
that we push that jump all the way upstream and out
of the end of the barrel, and then we've transitioned
from inlet control to outlet control. Okay, so if I've proven to you
that there is no difference in inlet control with what the
pipe material is downstream, I'm going to take the
double barrel model out and put in the single barrel,
which is a smooth pipe only, because it allows me to demonstrate my headwall models, which I can't do in the
double barrel model. So let's make that change. And just so you don't think there's some magic going on here, I'm going to start with
a block on my barrel and demonstrate all the models until I get to what's called
a slope tapered inlet, at which point I'm going
to take this block off, because with a slope tapered inlet, it's called that because we elevate this part of the inlet, it slopes down to this point, so if I rotate the barrel back down, I'm going to be putting this entrance, I'll be daylighting, at the same position as all the other models
that I'm demonstrating so that there's no change
in the upstream condition. So we'll start with the block on, and when I get to that last inlet, which is the slope tapered model, I'll have to lift this out
and pull the block off, and that's why I'm doing that. We're going to go through the inlets in order of K sub e, starting with the thin edge projecting. This would be like a CMP
projecting from the fill. The K sub e, which is the
entrance loss coefficient, we multiply that K sub e
times the velocity head to get the energy loss with that inlet, the K sub e for the thin
edge projecting is .9. This has the highest energy
loss of any inlet type we have. That's not to say it's a bad practice. There are many CMP pipes
projecting from the fill in the highway business. We just need to know that it creates the highest energy loss. So let me put this in the flume, and we'll make a mark at the headwater. This'll be our reference point, and then as we work through
the other K sub e values and reduce the energy loss, we'll see a corresponding change
in the headwater elevation. While that's adjusting, if we look at the flow
conditions in the barrel, we see that we are now in part-full flow, in fact, it's part-full supercritical. We're in inlet control,
and this big air pocket, particularly on that thin
edge projecting, like a CMP, is a real risky factor for design, because there's such a
buoyant force created, it's a little bit like trying
to hold a 55 gallon barrel under the water. As a result, a common
failure in inlet control, with this air pocket on
a thin edge projecting from that buoyant force, is
the barrel actually rotating about the fill and bending upwards. Because of that, the Federal
Highway Administration recommends barrel sizes,
particularly over 48 inches, should be anchored because
the larger the barrel, the greater that buoyant force. We have seen similar
failures on smaller pipes, so be aware of that on
a thin edge projecting in inlet control. This is a concern for failure. Our headwater's fairly stable. I'll adjust the O-ring. We're very near the top
of the stilling well, so this is our starting point. We'll start working now
through our K sub e values. The first one is what we
call mitered to the slope. This has a K sub e of .7. At times, I'll be using my pitot tube to help get the air into the barrel, eventually, if we wait long enough it will make this transition, and that air is a result
of typically the vortex that you see at the entrance
during inlet control. That's a pretty good
indicator out in the field. If you're out during a flood and you're looking at the
upstream side of a barrel and you see a big vortex, more likely than not that
culvert is in inlet control. So we have the same supercritical
part-full pipe condition. Give it a minute to make sure it's stable. I'll go ahead and start marking it here. So with a K sub e of .7, we see a small decrease in
the headwater as a result of the changed energy loss,
the reduced energy loss, with this mitered to
the slope configuration. The next entrance we'll look at, we call it a thick edge projecting, the K sub e is .5. This would be like an RCP
pipe that's been cut off. The groove end projecting,
or the socket end, has been cut off exposing that
thick edge of the concrete. Let's see where the headwaters will go with a K sub e of .5. So again, supercritical flow,
part-full in the barrel, running the full length of the barrel on this thick edge projecting, and as expected, we see a slight decrease from our K sub e value of .7. Another inlet with the
same K sub e value would be a headwall with a square edge. I'll be comparing that shortly to a headwall with a bevel. So the headwall with the square edge also has a K sub e of .5. If we had our thin edge projecting pipe with its K sub e of .9 and wanted to improve the
entrance configuration, the entrance loss condition, one option would be to put this CMP pipe in a headwall with a square edge and that would reduce the
K sub e from .9 to .5. So we should see this
come back to the same spot as the O-ring that marked
the K sub e of .5 for the thick edge projecting,
and as you can see we're right at about that spot. So I'll go ahead and switch
over to the K sub e now of .2, which is the same headwall,
but now we have a bevel. The bevel on this headwall
is a 45 degree bevel. It follows the Federal
Highway Administration design standard described
in Hydraulic Design Series Number 5 on culvert design. It amounts to about a half inch
per foot of barrel diameter, so it's not a very large bevel. Even if you take, say, a
6 foot diameter pipe, we're only talking about
a 3 inch bevel. So it's a combination of that
reduced K sub e at .2 now, and the bevel reducing the contraction
effect as we get into the pipe causing the improved
hydraulic performance. So once this is stable,
I'll mark this spot for our headwall with a bevel. The benefit of a bevel is
primarily in inlet control, but because there's also a
little bit less energy loss associated with it it's a recommended
practice in outlet control, meaning if you're going to
have a headwall standard you might as well have
a headwall with a bevel, and whether it's in
inlet or outlet control you'll see some improvement. Certainly more improvement
in inlet control, because again, everything
that matters is right here, and anything we can do to help the water get into the barrel will make better use of this pipe that we have downstream. So there's our K sub e
of .2 with the bevel. We have one more K sub e value of .2, which would be our RCP pipe with the socket end projecting upstream, or the groove end, as
it's called at times. While that is not a bevel, it does create what I call a step bevel, so you get a similar
hydraulic performance. We should see this one as well come back to this very same location of a K sub e of .2, or very
nearly the same location. And it's creeping up fairly close to that, so while that's stabilizing at that, I'll introduce the next two
inlets we're going to look at. These are called tapered inlets. These are by far the most
hydraulically efficient inlet designs that we can come up with. There are two standards in the Federal Highway
Administration practice as described in HDS 5. One is a side taper and the
other is called a slope taper. Let's look at the side taper first. It's pretty much exactly
what it sounds like. It's a flare side to side with no change in the vertical dimension. A little complicated geometry
on a circular pipe. There are some concrete pipe manufacturers that have the forms to do this. There are some metal pipe manufacturers that can create this. Certainly on a box, on a
cast in place in particular, it would be a fairly easy
construction to flare the ends, keeping the vertical dimension the same. So this is called the side taper. You can see where we're at. We're right back to our K sub e of .2. This is also a K sub e of .2, but it has the added
benefit of greatly reducing the contraction effect. So, we're going to see a
pretty dramatic improvement in hydraulic performance now. So we've lowered the headwater yet again, and remember, we started all of this with our thin edge projecting, like a CMP projecting from the fill, at the very uppermost O-ring here, and we've dropped the
headwater by this amount simply by changing the
inlet configuration, by changing the inlet loss coefficient, and now in these designs,
along with the bevel, but certainly in the tapers, improving the contraction, minimizing that contraction effect, allowing the area of the barrel to be more effectively utilized. The last inlet I have to show you is called a slope tapered inlet. This is tapered side to side
very similar to a side taper, but it also has a slope taper, a rapidly changing slope
at the upstream end. The way we build these
is we actually rotate the barrel down, and then we kick the inlet back up, so this point daylights
at the same location. What this does is it lowers
the throat of the culvert so that for a given headwater elevation we get more head acting on the culvert. So again, improved hydraulic performance, we're going to see this drop even further by the amount of the rotation, and I'll mark this side taper location with a marker. And we'll see now I have
to take the step off to allow this slope tapered inlet, the inlet edge, to be at the same location in elevation, and what we'll see is
the headwater will drop basically by the amount of the rotation, because we're allowing that much more head to act on the throat, and as you can see, it's already pretty close. The block was one inch, so we've dropped about one inch here from our side tapered location. And in fact, the barrel is very close to going full pipe, meaning it's nearly going
back to outlet control. We've improved the entrance configuration and the inlet conditions so dramatically, where this is no longer the
constriction that it once was. The barrel is at times,
we call this slug flow, it'll go full pipe for a little bit, and then it'll oscillate back
to part-full supercritical. This is one reason, for example, in the Federal Highway
Administration design standard, we look at both inlet and
outlet control conditions on any culvert we analyze
and we take the worst case, because it's sometimes
unpredictable as to where you'll be and you can have an oscillating headwater. So, dramatic improvements
with our tapered inlets. It's important to realize
though that these improvements really only occur when
you're in inlet control, because everything that
matters is at the entrance. In outlet control,
there would be no value. You wouldn't recover the cost you've spent to build these tapered inlets,
which are more expensive, because it's just one of
many energy loss factors. You have the entrance
loss, the friction loss, the exit loss, friction loss typically being
the greater of those three. So the benefits of a
tapered inlet, in particular in outlet control, it doesn't bring the value
that it does in inlet control. So by review, in culvert design, the Federal Highway
Administration design standard, based on Hydraulic Design
Series Number 5, is built on this idea of
inlet and outlet control. In outlet control, all
eight factors matter. Everything about the culvert
installation is important in terms of the headwater
that we're going to get. In inlet control, only those factors at the entrance to the
barrel are important, and the biggest one is
probably inlet configuration. When we can, for a given
pipe size and shape, adjust the inlet configuration
to reduce the energy loss, we're going to see improved
hydraulic conditions. All of this information is reviewed in the Hydraulic Design Series Number 5 on culvert design. These equations and these relationships are also implemented in the Federal Highway
Administration software program, HY 8, for doing culvert design. So refer to those if you
have additional questions or the training course, the
accompanying NHI training course on culvert design, 135056. Thank you for your interest in Federal Highway
Administration training. I hope you found this video
on culvert hydraulics helpful.
