Intro to MoDOT Hydrology and Hydraulics - Lesson 7 Culverts

So now we're moving on to lesson seven, and we're  going to go until about nine o'clock and then   we can have a ten minute coffee break. So  I'll try to keep my eye on the clock up there. And this is a caveat, so there's actually a  three-day culvert design course that we teach at   the National Highway Institute. So what  you're getting is kind of like the, the   very basic nuts and bolts that we probably  cover in half a day to two-thirds of the day of  the culvert design course. I'm not going to say this  is sufficient for everything you'll ever need for   culvert design, but it will introduce you to some  of the basic concepts, so that if you go into   the resource document which is HDS5, Hydraulic  Design of Highway Culverts, when you start   reading it it won't seem like it's written in  Greek. It hopefully will make a lot more sense,   because it talks about some concepts that take  a little while to get used to. Inlet control and   outlet control there's a lot of vocabulary and  stuff. But hopefully after this session, which   may actually take us till about lunchtime,  I think you'll have more of an appreciation   and understanding of the very basics.  And again that's what I keep saying,   continuing the message from yesterday, we're  looking at the big picture concepts and once you   understand the big picture concepts then you  can start getting into the weeds a little bit more,   and that stuff is a little bit more actually  cookbook. But the big picture concepts you can   apply those using your design or an engineering  intuition to make sense of a lot of the issues   and problems that you're going to run into in  your design. Do we know when the culvert design   class is going to come back around in our area?  It's all, Chase who does the training coordination? Yeah   we haven't really talked about doing another one  yet, but yeah if you guys want one we can do one.   We've got a couple people that would be interested.  Okay. And if you want that I would be interested.   I, I taught it here with Jim Shaw the last time  it was offered, and I would be interested in   coming back again. Okay. It's an awesome course.  again you'll get the flavor of it from this,   and if you go watch Jim, Jim's YouTube video  on the culvert design terminology and stuff with   the flume. But if the course is actually offered  here he brings the flume with them and then we   have a split class between workshop exercises  and fluid exercises it's really interesting. All right learning objectives, so these  are the things that we want to accomplish.   Describe inlet and outlet control. List  the factors that influence culvert design.   We'll summarize the hydraulic design process, so  this is just the hydraulic design process. There's   also a structural design component that's equally important. We'll describe the procedure for calculating   culvert outlet velocity. So that's something that  you get introduced to and that you'll probably   have to meditate on for it to completely make  sense. So we'll talk about it today and if you   think about it overnight and then if you have more  questions we can come back to it tomorrow morning.   We'll size of culvert using nomographs, and  then we'll actually, I would actually like   to take the time to run the same problem  using HY-8. So we'll see how our time is   working out, we do that in the culvert design  course and I think it would be kind of neat.   So again, going back to what are the important  resources for culvert, the hydraulic design   of culverts the Federal Highway has. Again  there's Jim doing his YouTube, or his YouTube   flume demos, it's the 056 culvert  design course through NHI that's really good. We actually have again free web-based training  on how to use HY-8. So HY-8 is the Federal Highway   program for culvert analysis. So I, if you haven't  taken that and I'm guessing probably most of you   have not, it probably is about a three to four  hour effort you do it at your own pace. If you're,   if you register with NHI, so you have an account  you just go in there and sign up and take it and   it's free. And it's pretty valuable and it gives  you the very basics of using the HY-8 software program,  so I, I would recommend that. And then the  document is Hydraulic Design Series 5   that you download from, I'm not sure if it's  posted on your R drive, that you downloaded   directly from the Federal Highway website. All  right, so terminology and we'll be talking a lot   about headwater. And so typically what happens  when we do a conventional culvert design   we have a barrel area that more often than not  has a, has an area, a flow area that's less   than the flow area of the channel. So the water has  to contract to go into the culvert of our barrel,   and to get the energy to do that it builds up it  ponds water at the inlet of the culvert and that's   what we call the headwater. On the downstream  side if we have headwater up there then this   is the tailwater elevation down here. This is  something that we actually need to calculate   and if we have steady, uniform flow conditions  we can calculate the tailwater depth using? Energy equation. Another one, steady uniform flow conditions? Manning's. Manning's equation yeah. We do use the energy equation to analyze culverts   in outlet control and we'll be talking about  that. All right so tailwater with steady, uniform   flow so in your ditch lines that's usually just  fine, Manning's equation you calculate the tailwater.   We have a barrel slope on our culvert, a lot of  times that is equivalent to the channel slope   and there may be reasons why at some point we  have a different slope, maybe it has a lesser slope. And if that's the case then there will be an  elevation difference and we'll talk about why   that might be important. Then we have our invert  and our crown of our pipe, the crown the pipe is the   top the invert the bottom so here's the invert at  the outlet and here's the invert at the inlet side.   And then up here's our roadway, so flows  going this direction through the culvert   and here's our roadway and  traffic is this direction. All right, so now here's, here's the  thing whenever we do culvert analysis   we're going to look to see if the  culvert is what we call inlet controlled   or outlet controlled, so we'll start with the inlet  controlled one first. An inlet control culvert is   on what we call steep slopes, well then you ask  well what's a steep slope. Well a rule of thumb   that we've kind of put out there is that you know  a steep slope is kind of like one percent or more.   So you could have an inlet control culvert on a  slope that's less than one percent, and you have   to analyze for that, but another definition of  steep slope is when you have supercritical flow.   So that's sometimes used to describe steep slopes.  So an inlet control culvert steep slope, the barrel,   the barrel of the culvert flows part full in  supercritical flow. So it's that faster moving flow   and if we have our headwater here, the water  comes in and this is inlet control, so this   is super critical flow. The flow depth is less  than critical depth, and it dives down through   what depth? It's going from sub to supercritical so  it has to transition through what specific depth?   Critical depth. Critical depth, so we also say that inlet  controlled culverts, critical depth occurs   at the inlet and we also said that critical  depth in culvert design can also be called   the control section. Okay? So critical depth  of the control section occurs at the inlet. In this case then, we're actually  going to analyze the culvert   as a weir at lower flows, when it's not submerged, or as an orifice at higher flows when it's fully   submerged and knowing that it transit, there's a  transition zone from weir flow to orifice flow. We also say that the barrel is not flowing at  capacity, and the inlet is actually regulating   the amount of flow, or controlling the amount  of flow and so it's a flow limiter. If we did   something to improve the inlet, so that flow could  transition into the barrel, we would actually get   more flow into the barrel and we'd be able to then  lower our headwater because it would take less   energy to force flow through here. So the control  section critical depth is near the inlet. The inlet   actually restricts the amount of flow we can  get into our culvert and it's on steeper slopes. All right so we're going to go through this a few  times, because it takes a few times discussing this   in different ways for it to maybe sink in. But that's  the general gist of an inlet controlled culvert. So   if I asked you, what flow type do you have in the  barrel in inlet control conditions you would say?   Super. Super critical flow. If I said where is the  control section in an inlet controlled   culvert you would say? At the inlet. If I  said to you what's restricting the flow   in an inlet control culvert you would say? The  inlet, okay? If I did something to improve the inlet   then I would get more flow into my culvert  because it's not using a lot of its area.   It's inefficient because the inlet  is restricting the amount of flow.   What would be an example of this? If I'm really  thirsty and I've been working outside cutting   the grass or whatever and I have a nice big cool  drink. If I take that and if I drink it like this, that's kind of defeating the purpose. Right?  Because this, my mouth, is limiting the flow. If   I open up my mouth wider, then I can get more flow  or more of that cool refreshing liquid beverage   into my throat, or the barrel of the culvert.  So if I do something to improve the entrance   by making it wider, making it a more favorable  inlet configuration, maybe changing the shape   a little bit, I can get more flow in the barrel.  So this is an inlet control condition, right here. Here's some different cases of inlet control.  So how do we know this is inlet control? Again you see here is the case we kind of just looked  at. You have water it's coming in through the   barrel, that's cascading down through critical  depth and it's flowing in super critical flow.   Same thing here, water it cascades through  critical depth goes to super critical flow.  And I know this is super critical  specifically here because why? Hydraulic jump. You see a hydraulic jump, and we  always know that with a hydraulic jump   that's a rapid transition from  super to subcritical flow and   you see it's occurring right here under  this higher tailwater condition. You see   the barrels full here but you still have critical  depth you still have the control section here you   still have super critical flow so you know  that this is still inlet control condition. Same thing over here, you have a lower  headwater you have high tailwater,   but you still see this hydraulic jump so you  know this super critical flow, supercritical   flow in the barrel equates to inlet control. So on  C there it's sub critical flow before it enters?   Yeah this is, yeah that's a good point. This is most  yeah, because it's gonna you know. It's gonna still pass through.  Actually, actually we don't know. Okay. If we had  critical depth, and if critical depth is like here   then that would be super critical. You can  have different depths of super critical flow   but once it exceeds critical  depth and it goes back into sub. So   I don't know, this could be sub-critical or it  could be super critical entering the barrel. Up here we have a low, and this might be another  case too, it looks like this is probably diving   down through critical depth. So this is probably  sub-critical, but we have low headwater, low tail   water, super critical flow in the barrel so  we know that's inlet control. And you said super   critical flow in the barrel indicates inlet  control, that's just true all the time? Yeah, yep. All right. So in inlet control I said what's limiting the flow or what's limiting   the ability to, to pass more flow through the  barrel is the stuff that happens at the inlet. Okay?   The throat doesn't affect it at all  because I have a lot of extra capacity here.   I just need to get the flow through the inlet  into the barrel, so whatever I can do to change   the things at the inlet side will help me  improve my hydraulic capacity in the culvert.   And the things that happen at the inlet side are  listed here. Headwater of course is at the inlet. There's   the area of the inlet, there's a shape of the  inlet, and there's something that we call the inlet   configuration. Does anyone know what that might  be? The inlet configuration, what does that mean? The skew angle. Yeah it could be kind of related to the  alignment, I could see that. The edges of   the barrel. Yeah so the edges so if you have  kind of like a square edge, and we'll take a look   at a couple pictures, if you have a square edged  entrance which would be, thinking like a box culvert   just with square edges, like in a headwall. And you  don't, you don't put a bevel on it. Right? But if you   actually go in and put that kind of like taper or  that bevel around the headwall, that would be an   improvement to the entrance and that would help  you get more flow into the barrel. So those are   things and we'll take a look at some pictures,  but those things relate to inlet configuration.   The barrel slope itself is not important for  determining the headwater and then the capacity   of the culvert itself, however we know that  barrel slope is important for the outlet velocity.   A barrel slope like this will have less velocity  coming out the outlet than a barrel slope like   this. Right? It's kind of like the water slide,  if you go on a water slide like this you're   gonna like say that's no fun. If you're on a water  slide like this then you're gonna go zipping down   through there because you have a lot of velocity.  So like, so like at the inlet, so like if you had   wings, say on a concrete box you had wings that  would be part of that in the configuration? It   depends on the flare angle. So there are favorable  flare angles and there are ones that really don't   help you out at all, and the you know the most  dramatic case of that is when they're actually   perpendicular to the flow it's not really helping  that flow transition into the barrel. If they're, if   they're flared and flow's coming this way, and this  is in HDS5, if they're flared at a certain range   of angles that helps that will pick up that  water and then transition it into the barrel.   And we're taking advantage of what principle, which  of the three big equations? Continuity. Not continuity. Momentum.   Momentum, it's momentum, because we talked about  yesterday water is not going to take right   right turns, right? 90 degree turns. It wants  to transition gradually, unless it's forced   to do something else, and when you force  it to take abrupt turns it's going to   pay you back with scour and erosion and all  kinds of issues but you want it to gradually   turn. So if you have your wing walls flared at  you know a certain range of favorable angles   that could help that water gradually turn  into the barrel. And this is where it helps   seeing the stuff in the flume because you  really get a good idea of some of this. So again, I introduced the topic but we're  going to come back and talk about it   at least a couple more times. So this is just  planting the seed. So we talked about inlet   control, the other way that a culvert could  be operating is what we call outlet control.   Outlet control occurs on mild slopes, and the  flow could be one of two conditions in the barrel.   In this condition you see full barrel  flow, so it uses the entire barrel area.   It can also be subcritical flow. Mild slope  subcritical flow, steep slope super critical   flow. So there's another way that you can  describe those, those two different flow types, sub and super critical. So if we have mild slopes subcritical or  full barrel flow, that culvert is operating   in outlet control. And outlet control it  becomes a little bit more complicated, because   we also have to consider what's going on inside  the barrel. In inlet control the barrel doesn't   matter with the headwater, it doesn't impact the  headwater. It's just whatever happens here at the   inlet that you can have some control over. In  outlet control, the barrel now comes into play.   So you have to be concerned with the barrel length  and the barrel roughness, and then also what your   tailwater condition is. So all aspects of the  culvert including tailwater affect the flow.   We're not using the weir and orifice equations  in this condition, we're going back to using one   of our good friends the energy equation. So what  we'll actually do is, just like we kind of did   yesterday in one of our exercises, we're going to  look at what is the total energy here and that's   going to equal total energy at the outside of the  culvert at the downstream end plus head losses.   And that's why the barrel comes into play,  because we have additional head losses. We have,   we have a head loss as the flow contracts at the  entrance and that's a local loss that's a very   common local energy head loss. We have a head  loss as the water proceeds through the barrel   due to friction, energy lost through the friction  with the boundary so we have, that's the biggest   one you know in outlet control, the friction loss through  the barrel. And then we have another head, local   head loss as flow re-expands into the tailwater  at the downstream side. So those are the three   basic head losses, and so if we can calculate those  and if we can calculate the energy level here,   and we add on those head losses, and we bring that  back up and we now have our, our total energy up   here. And we've done our analysis and that can give  us our headwater elevation or our headwater depth,   and we just calculate outlet velocity as something  else that we need to do. So in inlet control   it's a combination of using the weir  and orifice equations for the analysis.   In outlet control it's strictly an application  of the energy equation that we looked at yesterday. And actually that's that's probably about 75  percent of the hydraulic design of culverts. Seems   kind of almost underwhelming doesn't it? You're  looking for something shocking, revolutionary   and it gets you really excited we pulled the  curtain back and that's pretty much what it is. So here's some different outlet control  cases, similar to what we did for inlet control.   High headwater, high tailwater this barrel is flowing?   Full, right? We have high headwater lower  tailwater and so the barrel is flowing? Full. Well it's full up here, right  this and then it transitions into   subcritical and then what do  you think is happening here? Critical depth. Critical depth, exactly. So if we talk about control  sections once again, we say critical depth is   a control section. So right here our control  section would be wherever it hits critical depth.   Here we don't have critical depth anymore right? Because this is all full flow and sub   and subcritical, so in this case the control would  be the tailwater, this, we'll talk about this again   but just to introduce the concepts. Here the  control is the tailwater, here the control   is it the critical depth at the outlet. All right  here we have subcritical flow, subcritical flow   through the barrel and it looks like this is also  a tailwater control because I'm not seeing where   it would transition through critical depth. Here  we have subcritical, subcritical it looks like   it's probably diving down through critical  depth, so here the control would be critical   depth at the outlet. Critical depth, tailwater, critical depth, tailwater control. I have a question. Yes? It seems to me, A is the same as the one in the inlet control. It kind of looks the same, doesn't it? Yeah ,and it's just a matter of the flow types. And  we can't tell here, but it's inlet controlled so   this has to be super critical. And maybe we  could have illustrated that better but this   is super critical flow this has to be critical  depth, so this is probably diving down through   critical depth right in here somewhere. But  it does look very much the same I agree. Here we're just saying it's subcritical, so  critical depth must be down in here somewhere,   it's probably like right here. And maybe that  would help, if we actually had were, drew in   the line for critical depth just so  you can see that this is subcritical   and then this is super critical and maybe we'll  do that next time we revise this. I don't know if   it matters, but it looks more like the water's  like humped up, on the other one it kind of looks   like it's diving down. Yeah. Yeah I think, I think  you know there's opportunity to touch these   up over here. And it probably would help just  drawing a line were critical depth is,   and then you can, and then that's what you're  actually looking for is. Is it subcritical? Is   it super critical? Where's critical depth located?  And that tells you if it's inlet or outlet control. So factors that influence our culvert design,  so that's our headwater calculations primarily.   We're looking for, of course the headwater. We have  the area of the barrel, the shape of the barrel,   the inlet configuration is still important because  we said we have an energy, a local loss at the   inlet. So as the water contracts into the barrel  in outlet control there's that local loss at the   inlet. So if we can improve the inlet a little bit  that might help push that local loss down a little   and so we'd have a little bit less energy loss.  However, most of the energy loss in outlet control   condition comes through that frictional resistance  as the water is being pushed through the barrel. Barrel slope is important. Barrel length and roughness are the  combined frictional resistance. So   if you have a rough barrel that's short,  you have so much frictional resistance.   If you have a rough barrel that's really long  then you have a lot more frictional resistance.   So there's two components, the barrel roughness  and the barrel length, and these two combine to let   you know what your frictional resistance and your  friction loss is. And then the tailwater condition   So if I go to the amusement park and  I get up at the top of the water slide   and, I actually haven't been  on a water slide in like maybe 20 years. So I don't know, like do they still use mats or something or do you just go down? Sometimes. Okay. So say there's a mat and I jump on the mat. And I'm looking really, I'm looking down really far here   and I take the plunge and I zip down that water  slide, the flow type would be? Super critical. Super critical all   right. So if I'm standing right there at the edge  and there's someone down who's already gone down   and they're splashing around, do I notice any of  that? If they're splashing around in the water   as they're going down the slide, does that  impact me whatsoever standing up here at the top? No. But because-- It won't propagate upstream. That's absolutely, 100 percent correct. Nothing, no none of that disturbance or   those energy losses or whatever propagated  upstream, I don't even know I don't care.   It might as well be like nothing below me  even exists, because it does not impact me.   Okay? Once I get onto the slide and I'm part  of the flow then I have a certain velocity   which translates into eventually my outlet flow  velocity, but standing up here I wouldn't even   know that someone down there is splashing  around. That's an inlet control condition.   In inlet control the flow that's entering the  barrel, it doesn't even care what's going on in the   barrel because the water the barrel is zipping  by so fast that none of those disturbances or   energy losses or whatever else is going on there  translate, translates to the headwater where I'm at   at the top of the water slide. I might as well just  be looking at an opening and anything beyond that   is irrelevant. Okay? And so once again that's  why we can use the weir and orifice equations   because we're only considered with that one  little section, that that entrance. What happens   downstream of that is is completely  irrelevant, it just doesn't matter.   That's inlet control, and that's why we use the  weir and orifice equations to analyze that one section.   Conversely, I actually did this was actually, this was  pretty scary. I never thought I would be scared of   this. So during Halloween I went to one of  these haunted farm kind of things. So they had   the haunted barn. Anyone ever do, that kind of like?  Does anyone like to do that? I love scary stuff. I   love scary movies, I like haunted attractions.  So I went to this this big haunted farm they had   the haunted barn, and so one thing and this, this  totally freaked me out you go in and then   they have like this tunnel, that the entrance is  illuminated with like the black lights. Okay so you   go into the tunnel and then it gets dark, and then  the tunnel contracts in area. And so you're going   like this, and there's there's like people coming  in behind you and you can't see anything, you're   down like this and all of a sudden it contracts  so much that I'm on my hands and knees, and I'm   crawling and I'm starting to get claustrophobic,  and starting to freak out and you can't see and   then you're almost having to push your way through  the last part of the tunnel until you come out in   the room on the other side. So the last like  10 or 15 feet you're having to squeeze and   push and then there's people coming in behind you  trying to push and it's just really, really scary.   That is outlet control condition, all right. Because  you get in, you get in through the entrance, and the   entrance wasn't a big deal, it wasn't contracted  enough where you know I maybe had to turn a   little bit there's a little bit of energy loss.  But then that barrel I tell you what, I'm pushing   and trying to get past all that frictional  resistance and I'm losing a lot of energy.   Right? And there's, you know I'm squeezing through  there and then all of a sudden I try to squeeze   out through the other side and I have that  expansion loss as I get back out into the room,   that's outlet control. So the entrance matters  a little bit. The big thing that matters is the   barrel and what's going on in the barrel. And  then I have a little bit more energy loss as   I re-expand into the room of the barn at the exit.  That's outlet control condition, I'm moving slowly   subcritical or full flow. Right? When I get down  to real, where it's really contracted even I   filled up the barrel and it was full flow that's  sub, that's outlet control subcritical or full   flow. So the way you make sense of these things  and the way you make sense of anything in life,   is put it in a metaphor that you can relate to and  it kind of makes sense. And that's the way you can   also explain it to other people. So if there's a  difficult concept, pull back out of the weeds think   of what is the big picture? The big picture is  always, usually pretty straightforward and simple.   Think of the big picture put it in terms of a  personal metaphor that other people can relate to. Going back to our friend the og spillway then. Can I borrow that water bottle? This is your culvert.  If I turn this is it going to spill or anything? No, you're good. Pretend I have my culvert, and it's right here. The control section, say its critical depth  in this case is right here at the outlet,   and therefore you know it's outlet control.  The control section is outlet control is   either at the outlet or it's the tailwater. Okay?  If it's, if there's critical depth occurring if   this is shallow tailwater and it's spilling out  through critical depth the control section is here.   If it's high tailwater then the tail  water actually is the control section. Mild slope it's either flowing in subcritical flow,  right? This is all subcritical flow we discussed   this yesterday, this is subcritical flow here, so  this water in the barrel is either subcritical   or full-flow. The water is trying to push through  the entrance and it's pushing through the barrel.   The barrel is actually regulating how much flow is  passing. If you could do something to improve the   barrel condition, you'll probably get more capacity  and more flow going through there. Okay? So the barrel is actually, the   barrel or the tailwater is actually constricting  the flow and regulating the flow condition. Conversely if I put my culvert here,  this is the water slide. So this was  this was the scary tunnel in the  haunted barn, and this is the water slide.   The water of the flow type in this  barrel is? Super critical. The control section that is?   At the entrance, and that's critical depth.  The factors that are important here are?   The factors that are kind of regulating  and controlling the flow or the inlets,   and those would be the area, the shape, the inlet  configuration, and the headwater level, right?   The barrel really doesn't  matter at all with the headwater   calculations, it's irrelevant. Because this  just appears to the water like an orifice   once it gets in here it's just it's fun time,  it's just zipping away. The barrel is irrelevant. The only thing is with the slope, the slope is  important to calculate our outlet velocity in the   inlet control condition, as it is with the outlet  control condition. Inlet controlled, outlet control.   Supercritical flow, full flow or subcritical flow.  Analyze using the wear and orifice equations,   analyze because we have to consider the frictional  resistance of the barrel, the inlet energy local   loss, the outlet local loss, analyze this with  the energy equation. Questions? Thanks Andrew. Ponder these things, oh I'm sorry, okay. I'm sorry what's your question  again? On the previous slide,   on outlet control we said how  inlet configuration affects I'm sorry which one? That one. This one? It says inlet configuration in factors influencing-- Yeah. The inlet configuration is important in outlet control because we're doing an energy balance or an energy analysis. Okay? So   typically for your simple public designs, you're  going to have three components to your energy loss.   There's going to be a local loss at the inlet,  as the flow contracts to go into the opening   and we'll describe how to calculate that. Then  there's the frictional resistance of the barrel.   And then there's the local loss at the outlet as  the flow re-expands into the flow of the outlet   side, and we'll talk about how to calculate all  these pieces. So in, the inlet configuration is   important in outlet control because if you  can make it more favorable ,so the flow has   a more gradual turn in the culvert, you can drop  or diminish that local energy loss at the inlet.   And it matters a little bit, in the outlet control  it matters a little bit. So we say if there's   something easy that you can do, bevels that's all  you need to do for outlet control, and you're good   to go. And that will drop that local energy loss  at the inlet by a little bit. But the big thing   is the barrel itself, because you're going to lose  a lot of energy through the frictional resistance in the barrel. So ponder this stuff, let it stew a little bit  this is what happens in the culvert course. I   actually had culvert design in college and I  came out still not knowing what was going on.   And then I attended this NHI course, and then  I attended it again and then it's started to come   into place. So it takes a little while partially, but again focus on the big picture concepts,   inlet control and outlet control. What matters in  inlet control what matters in outlet control? What   are the flow types in inlet control and the flow  types and outlet control? What equations are used   in inlet control what equations are used in outlet control? That's the key stuff right now. Outlet. Outlet. Outlet. Outlet. Inlet. Both. Inlet. Outlet. Inlet. Outlet. Outlet. That was a test to see if I could do some  instruction without actually saying anything,   and I think it worked out really well, nice job.  That's more credit to you than for me actually.   Yeah, so you got them all  right. So is it making sense? Because we'll hit it all again too, as  we go through the next few slides but   again the basic thing is when you start  thinking about inlet or outlet control.   What flow type do you have? Super critical flow,  nothing downstream matters if you're standing   at the inlet, so you're just worried about the  actual inlet condition itself. Once you get past   the inlet, you're off to the races, you're zipping  through supercritical flow through the barrel   frictional resistance doesn't matter or  tailwater doesn't matter, you're just gone.   Outlet control you're kind of slogging through  because it's on a mild slope, subcritical flow or   full flow. So you get through the entrance and  then you're slogging through the barrel and   encountering frictional resistance and then  you have to push yourself out into tailwater.   So that's where all the losses are considered and  it's more of an energy problem at that point. Right?   Because you're losing energy as you're trying to  push through all that stuff. Excellent. All right, so   we once again we'll hit the factors on the inlet  control it's the stuff at the inlet that matters.   And so again that's the headwater, the inlet  area, shape, and configuration. The barrel slope   doesn't really impact the headwater, it does a tiny  little bit and it's so tiny that we just neglect it.   What it does impact is the outlet  velocity. This is inlet controlled   it's greater than one percent slope and  has an outlet velocity that's less than   this inlet control condition on the water slide. So  the slope will impact the outlet velocity, which   is also an important design consideration.  Outlet controlled everything matters. You   push through the inlet and you have a little  bit of energy loss, so you have the headwater.   The inlet configuration, you're into the barrel  so the barrel has a certain area and shape and   slope. You're losing frictional resistance and that  comes into play with the roughness and the length.   And then you have to push out into the tailwater, and you encounter another local loss   as you re-expand into the flow, and so the energy  analysis takes into consideration all these things. All right, so let's look at some  of these factors and how they impact   situations. what flow condition is this? Inlet or outlet controlled? Inlet. Why? It's supercritical. Your control section, your critical depth is  here at the inlet. You can see the flow diving   down through into a very shallow depth so critical  depth is right near the entrance. Same thing with   this, it's not flowing full for sure and if it's  going through critical depth, then this is super   critical flow, so this is inlet control. And it kind  of makes sense that if we have a situation where   we increase the area of the inlet, we can get more  flow past the inlet and that's what we see here.   If we were to keep the headwaters the same, then  in this case with a two foot diameter pipe we   have 32 cubic feet per second and with a 48 inch  diameter pipe we have 115 cubic feet per second. Probably what actually happens in  reality is, as you increase the size   of this you do get more flow through  here but you also drop the headwater. So effect of the shape on the culvert performance,  and again this is inlet control. So we look at   a circular pipe, this one, and an arch pipe  pipe arch that's this one here. They have   about the, actually the exact same barrel area.  And we see that with this circular pipe culvert   and we just pick a headwater here let's say it's  eight feet for a circular pipe we're passing about 263.28 cfs. That's pretty accurate. Right? Exactly right. That's what I'm saying  don't do that. Yeah, 260 cfs give or take   20 percent, that's more like it. Right? And then we see with the pipe arch we go over here and it's passing   maybe something like you know 280 290. So for the  same headwater level, and that's again a pond of   water at the entrance, the pipe arch with the same  barrel area actually passes more flow. Why is that?   Because it's, the flatter base, the gravity doesn't  impact the the water going through the pipe as   much as it does on a circular pipe, because it  requires more headwater to keep that water   at a higher elevation in a circular pipe than an  arch pipe. I think, I think you covered it pretty   well. The center of area of this is here, the  center of area of this is probably down in here   somewhere. So you have more pressure head pushing  on the center of area here pushing water through,   and you have a lesser pressure head pushing water  through the center of area of this shape here.   So it's kind of like, if you go dive into the deep  end of the pool. And you dive down for that quarter,   as you get closer and closer to the bottom you  can feel all that pressure pushing on you that's   kind of like that pressure head. That  pressure head is pushing on the center of area,   there's more pressure head, so you're diving  actually down further there's more pressure   head pushing on the center here than pressure  head pushing on the center here. So you have more energy pushing through the meat of this area than you do in this one. So you would expect this one actually to be  more efficient. But why, apart from that, why else   might you use a pipe as opposed to this one. Cover. Yeah cover. Yeah you know a lot of stuff that we do   in design is dictated by the site conditions, and  the geometry, and the terrain. And if you have an   issue with getting enough cover over your pipe  for the structural integrity of the system and   you can actually get more cover over a pipe arch  and pass even more flow than for circular shape. Alright. Can we go back for just a second? Can we go back for just a second? I have a question, on your round and your arch pipe. The circumference on your arch  pipe is a little bigger which makes sense,   because the circle would have the smallest circumference of the-- Correct. for the given  area. Kind of like the, the perimeter the   perimeter. Not the, if it's flowing full  it would be the wetted perimeter. Right, the hydraulic radius is higher. So for this example, and I don't know if it's  every case then, I would imagine that depends   on what the pipes are made out of. But in this  example then the difference in the pressure head   is bigger than, it's more of an impact  than the roughness of the edge of   the surface of the pipe? Correct, yeah and  Steve the point you're making here is if these   are actually flowing full, then the water in  here is contacting more of the boundaries. So   you'd think you have more frictional resistance  than this, but what condition are we looking at? Inlet control. Inlet control. So frictional resistance, it  doesn't matter. But in outlet control yeah it   would play, there's a balance of more frictional  resistance but more pressure head pushing on   the center of area. So it's a trade-off and I'm  thinking that the pressure head probably is more of an impact  than that additional frictional loss. We're going  to see that later or am I just way out on a tangent? No that's a good point. I don't know, I can't remember if we look at this in outlet control, and   I may have clipped it out due to time constraints.  But you do if you do your analysis in HY-8 you can   check the two different shapes in outlet  control and see. I believe the pressure   head is probably the bigger, you know what  I'm postulating that, I don't know for certain. Well if they had the same roughness  coefficient, the circular one and the pipe arch.   So you'd have to look at the corrugation patterns,   and honestly I don't know how they're fabricated,  if they have the same corrugation pattern or not. All right so degree of contraction. So we're going  to consider real briefly inlet configurations   and again we're looking at inline control  conditions. We have these different types   and I think I have pictures of most of these. We've  covered, we cover this in a lot more detail in the   culvert course. You have thin edge projecting, so you  have like a corrugated metal pipe and sticking out   of your embankment that's a thin edge projecting  condition. If you then take that corrugated   metal pipe that's sticking out protruding  from your embankment, and you slice it off   so that it's flush with your embankment, that would  be mitered to the fill slope. And so that's actually   a little bit more favorable for water to bend in  than the thin edge projecting. And even more favorable   is a culvert in a headwall with a square edge.  And even more favorable for water to gradually   turn into the barrel, is if you have your concrete  pipe delivered to your site you know there's   there's one end of it that's going to have  that bell end on it, that grooved end, if you   actually have that as your inlet condition  that's pretty hydraulically efficient.   It almost functions it's called like a step  bevel, so it almost functions very similar to a   bevel condition. Then you have your beveled edge  and again that's just taking that sharp corner   and just making a nice little taper, and it doesn't  take much to improve your hydraulic efficiency.   Tapered inlets, we're not going to talk about.  That's if, if you're interested during a   break I mean I can pull those up and show you some  pictures. If you have your barrel and then it,   and then at the entrance of the barrel you widen  the face out. So you're changing the area and the   shape a little bit, so you widen that face out so  that it slopes that side tapers into your barrel,   that's a side tapered entrance. And then you  can also taper it this way, and drop it down   and rotate your barrel down a little  bit, and that's a slope tapered entrance.   And again I can show you some pictures  during break, during lunch if you're   interested in seeing what that looks like.  Those are very, very hydraulically efficient in inlet control conditions. All right. So here we have, that's that socket or grooved end entrance, so  you're just kind of like leaving this on your   concrete pipe when it's delivered, you're  not cutting it off. Okay? Here you have yeah here, you see this top bevel right  here and again it's it's not a lot   it's a half inch per foot of rise or span,  whichever one gives you the greater bevel.   But it's not a lot, half inch per foot. You  could also go up to an inch for foot and that   increases your efficiency just a little bit  over the half inch. You also see a bevel here   on this piece of headwall in this one, and these  wing walls these may be at that favorable angle   where, you can kind of get the idea. And a lot of  this is visualization, but the flow is coming in and it kind of catches this, it's kind  of hard to do and bend into the barrel   flow's coming in this way and flow's coming  in this way catches this and kind of bends   into the barrel here. These are almost, these are  probably thin edge projecting because they're   sticking out a little bit. You can see they maybe  at some point they were tapered to the fill slope,   but it looks like there's been some erosion around  here so it probably transitioned back into thin edge   projecting. I wouldn't take credit for these  being tapered to the fill slope, but that's the   general idea. You take that pipe and you cut it  and you and you you make it flush with the fill. Here's a thin edge projecting over here. This does  not have a bevel so this is just a square edge   condition. This, I would probably consider a little bit  better than a thin edge projecting condition.   But if we're not sure, we always err on the side  of conservatism, so I might just consider this   a thin edge projecting condition. And we'll  show you how that impacts the, the analysis. Actually this one is a cool one to  focus on for a minute. When we talk about   if this is outlet controlled, we talked  about energy losses. Right? So in this case   you might add a little bit additional  entrance head loss because water has to   get through this grate. And then that  grate's going to eventually do what?   Clog. It's going to start picking up trash, and drinks,  and things like that, so you also may want to   if you were to design something like this  for safety reasons, maybe you don't want kids   crawling inside your culvert, you probably would  maybe experiment with diminishing the opening   area a little bit and see how that impacts your  hydraulic performance. But you want to do something   knowing that this probably is not going to be  maintained on a regular basis, and you want to be   very conservative with your design then. So maybe  diminish the open area a little bit, maybe add in,   if it's outlet controlled, add in some additional  energy losses, whatever you think appropriate. And   then again like Veronica said the other  day, put that in your design documentation. All right, so here's an inlet bevel here. Here's a  better picture of an inlet bevel, this is just on the head wall.  If these, if these wing walls are the square edge  ones, then you might want to try to experiment   with the bevel on these. If they're flared at a  good angle, then you're not going to put a bevel   on those, because the flare will take care of  the increased performance of the water coming   in from the sides. And then as the water comes in  from the top and bends down, this is going to   improve that efficiency. You know what that  vena contracta is? It's kind of like when   water comes down into a culvert, or an opening,  same thing occurs with bridges. And here's,   here's the, the bridge opening here, this water  bends down through here. It's not automatically   going to come here and hit the top of your  culvert or the inside of your bridge. Right?   It's going to bend down, it's going to bend down  like this and then turn in. And so you have kind of   like this air pocket up here of no flow occurring,  and that's diminished capacity. So it's going to   bend down like this. If you put a nice little  bevel here, then as it bends down it's going to   contract, it's going to decrease that vertical  contraction to maybe something more like that. So that's why we put the bevels on the top.   We put, would a rounded be more efficient  but it's just easier to do a bevel--   Yeah, you know what-- for the minor difference you  get? I think and I'm not sure, actually it was   Wisconsin, when we were teaching the culvert course in Wisconsin, in Green Bay a few weeks   ago. They actually do some rounded bevels on some  of theirs. I would think it is a little bit more   tricky to form, as opposed to just having like a  linear bevel, but yeah they're, they're actually   one state that does it in some cases. But I  don't know many states that actually do rounded bevels. All right. So here's just a good picture.  We're standing at what end of the  culver the inlet or the outlet? Outlet. Inlet. Inlet. So I heard inlet and outlet, no one said the middle which is good.  So at least that's something right there.   We're actually standing at the outlet because,  you know a big part of being successful in   drainage design and hydraulic engineering  is being able to visualize the flow and   think about what's going on and why. So you  see water up here is kind of ponded, right?   This is the headwater, and as water enters this  barrel, it cascades down through critical depth   it flows in very shallow turbulent fashion  through the barrel, and then it splashes out   at the outlet. And you can see here the tail  water pull, right? So we're actually standing at   the outlet looking back up through the barrel.  And this is what type of control condition?   Inlet control. It's inlet control, so you get a good  idea of what inlet control looks like.   Look how much capacity we have in  that barrel that's not being used,   and this isn't a real high flow condition, but  even if this water were up here we probably   wouldn't have a very high water level in the  barrel. So if we could do something to change this   entrance configuration, to make it more favorable  for the momentum of the water to carry into the   barrel and we could use more of this capacity  and also at the same time drop the headwater level. I feel like if it's going to be flowing full,  I feel like that dirt is going to be moving.   Like-- Well yeah. I feel like the pipe is--  That's, that's one of the crappiest culverts, the way it is.    I wouldn't recommend that, from that aspect it's horrible. But yeah, that's probably, you know what   that's probably, and I don't know for sure  that's maybe a forced road somewhere,   maybe it's even a temporary  crossing or something. You, you would never do something like this here in Missouri. All right, so effect of barrel  slope on culvert performance.   I already know that inlet control culverts  have steep slopes. Slope in inlet control   impacts the headwater to such a negligible degree  that we don't really account for it, or worry about   it. But again it has a lot to do with outlet  velocity. So we're going to talk a little bit   about outlook velocity at the end of this lesson.  If you're seeing that your outlet velocities are   really high, there's a couple of main things  that you can do with your culvert design,   apart from using energy dissipaters,  which we're not talking about this week.   But there's something, two things that  you need to try with your culverts design.   And those would be, if your  outlet velocity is high, you can try? The slope? Decrease your slope. You can do something with? I heard slope, and it was a tentative almost whisper, answer. But I'll  take credit for someone saying it. So slope, so the most   powerful thing you could ever do is decrease  the slope of your culvert. That will have a   dramatic impact on the outlet velocity, but that  said we don't always do that a lot because you   can introduce some issues of, then you have to make  a transition from the stream bed into the culvert   barrel. Because what you've really done is rotated  the inlet of the culvert below the stream bed.   This is the, this is the outlet and you're  rotating the inlet below the stream bed   to get a more shallow slope to drop velocity,  and then you have to worry about well how do   you get the water in there. Are you going to  create some channels instabil, instabilities   and head cuts, and things like that. So it can be  an issue. What else could you try? Increase the roughness of the base of the culvert. Yeah that's exactly it. So it's maybe a material  selection issue. So if you're using a concrete   culvert or a smooth high density polyethylene  culvert, maybe you try a corrugated profile.   And I know some states are getting away from  using corrugated metal pipe, because they have   you know corrosion and abrasion issues. But if you  went from a smooth profile to a corrugated profile,   increase the roughness that can have a significant  effect on your velocities, your flow velocities.   Outlet control, culvert barrel slope is important  for both your headwater and your outlet velocity   calculations. All right so here we are, talking  about effective roughness on the culvert. And so   this is exactly the situation we're talking  about, but this is more from a headwater   angle and not a velocity angle. If I have  initially a, what type of pipe do you think   I'm using here if the roughness is 0.012? You  said you use about .013 it's? Concrete. Probably concrete,   or a smooth plastic. Smooth plastic would probably  even be a little bit, it might be like 0.01. So if you have a concrete pipe with 0.012, under a  headwater of whatever this is then you're passing   about 109 cfs. That said then, if you go to a  corrugated metal pipe, and again a 0.024 is   pretty common for corrugated metal, then you're  dropping your capacity from 90, or 109 to 94 cfs.   But the flip side that is, you're dropping  the flow through here but you're also   decreasing velocities. And so we also  know that, what type of control is this?   Outlet. Outlet control, and we know that for two reasons.   First because it's full pipe flow, so that's an  outlet control condition, mild slope full pipe flow   you're dealing with a lot of frictional  resistance. The other reason we know that is? There's no critical depth. Yeah so there's, oh well actually so there's  three reasons another one is there's no critical   depth represented anywhere here. Right? No  critical depth, it has to be in outlet control,   because the tail water is not the control section.  The other reason we know that is we have this  effect. And we said that for capacity reasons,   for capacity calculations the barrel roughness has  no impact in inlet control, it just doesn't matter.   Because the water just sees that orifice, and that's  the scary part, and once it gets past that opening   then it's smooth sailing it doesn't care  what's going on in the barrel because it's   just zipping through there. So the frictional  resistance does not matter inlet control   and where, here we see there's an impact so  this has to be outlet control condition. So we said frictional resistance is a combination  of roughness and length. Okay, so up here you have   your initial roadway that was built maybe  back in the 50s, and you used a four foot diameter   culvert with a length of 50 feet, and you see  that your q is now 94 cubic feet per second. Well here in 2019, maybe you're doing roadway  widening or you're adding some lanes. And you know   you've talked with, you've gone out in the field  and talked with the maintenance folks and you know   the landowners around there, and said yeah we've  never had any problem with roadway over topping   or flooding or whatnot. You say you know what that four foot pipe is doing a good job, and so when   we extend this we're just going to continue  on with that four foot and we're good to go.   Right or wrong? Well if you don't analyze  it maybe you run into an issue. Because now   you have a length of maybe 200 feet of  pipe. And if it's outlet control condition,   what have you done, you've introduced a lot more?  Frictional resistance. So what does that water do?   Slows down. It comes and looks at that and says you know  what I'm not sure I'm up for this, deep breath,   get bulked up build up more headwater  more energy and squeeze through that 250,   200 feet of you know frictional resistance. So in this case it's showing, and maybe we change this, but   in this case it's showing you you're dropping your  capacity. In reality what's going to happen is   for the same flow rate it's going to have to  build up more and more headwater to push that same   flow rate through there. So guess, what and this is  kind of cool because we can show this in the flume, is it going to go over the roadway or is it not?  You need to know, and you need to do the hydraulic   analysis. All right? So this is another reason  why you have to look at is it inlet control is   it outlet control. If I do a modification on the  pipe, if I lengthen the pipe, if I tried other pipe   material what's going to happen with my headwater?  What's going to happen with my outlet velocities?   Don't guess, gotta do some calculations. That's  why we're spending time talking about all this,   and why we're going to do a nomograph solution  and look at HY-8. All right, effect of tailwater. Inlet control, effect of tailwater on headwater.  So here's my headwater up here, I can move this   up and down, here's the control section, I can move  this up and down. Tailwater in outlet, tailwater   in inlet control's not going to affect the the  headwater. Until, maybe I push his tail water up and   up and up, and what this does is it causes more of  a reaction force and pushes water back up this way.   And here's that hydraulic jump, and if you can  picture this, as you increase this tail water it's   going to push back on this and back on this and  at some point you could possibly flood out this   hydraulic jump it'll flood out critical depth  and turn this into a? Outlet control, and then   every time you increase the tailwater you're  going to see that, see that reflected in the   headwater. But that doesn't happen very often, it  could potentially happen but not very often. So   in most cases we say in inlet control  changing the tailwater is just not going   to do anything to you. It's like on that water  slide down in that plunge pool at the bottom,   you know they maybe put more water in the  plunge pool because of safety concerns or   whatever, standing up here at the top of the  water slide I just don't see it. I don't even know what's happening. Outlet control, with low tailwater, the  control is actually critical depth. Right? So   if I have this low tailwater and if I raise  it a little bit, as long as I maintain critical   depth here there's no impact whatsoever on the  headwater, doesn't matter. Now when I raise it high   enough where I flood out critical depth, and as I  raise the tailwater I also raise the headwater.   So it's just a matter of is the tailwater  the initial control or critical depth. And   if it's critical depth, as long as I maintain  critical depth here, this is super critical   flow, whatever I do with that supercritical flow  doesn't matter until I flood out critical depth   and this is now subcritical flow. And then  as I increase this, I increase my headwater. I think that's shown in the  culvert video on YouTube. All right, so this brings us to the process. I  know you're saying finally, right? So here we go.   You go out in the field, and maybe you're doing a  paving project. And you're checking, you're doing due   diligence so you're walking your project, and  you see a series, or a row of culverts here.   Maybe they're ditch relief culverts, maybe a  couple of them are stream cross, crossing culverts.   You start taking a look at them and you see one  that's kind of shaky looking it has that abrasion   I think that Dorothy had, had implied. And so  you say, you know what I think we can do better,   we might need to replace this. So let's figure out,  let's do a hydraulic analysis and figure out what   the replacement culvert will look like. So first  you're going to select a culvert, and you say well   the maintenance folks say this existing one has  been fine, we haven't really had any you know   maintenance issues here, no roadway overtopping,  maybe I'll start with that as my initial guess at   a replacement culvert. So you select it and you use  some educated guesses from your site visit, from   talking with folks. Right? So you take a guess at  one, and then you're running through the analysis.   there are two parts to analysis you check it under  inlet control condition, you check in under outlet   control conditions. Because you don't design a  culvert, 99 times out of 100, you don't design a   culvert to be inlet controlled or outlet controlled. I  get that question all the time. How do I design   a culvert to be outlet controlled? Because I want to  make sure I use as much of the barrel as possible.   You don't do that. It's more dictated by what? Your,  your site conditions and your slopes. So depending   on what that is, that will probably play a large  part into determining if that is an outlet control   culvert or an inlet control, that's not something  that you put into your design necessarily.   But you need to consider both, because you don't  know how it's flowing, you're not going to guess.   You're going to check it for inlet control  and you're going to check for outlet control, and see which one gives you the highest headwater  elevation. Okay? So you're going to check it   under both these conditions, you're going to  calculate that upstream headwater elevation   and you're going to take the larger of those  two. Here's the crazy thing about culverts,   they sometimes go back and forth between inlet and  outlet control sometimes they have flood flow, they   may get plugged with debris, they can switch things  around some crazy things happen out there on your   projects. And one time it may be inlet control, at  one time it may be outlet controlled, you're not   necessarily always sure so we're going to use the  worst case for our design. And the worst case one   is the one that gives us the highest headwater at  the inlet. So we're going to check both, compare the   headwaters, and take the worst case scenario that's  what we call the minimum performance criteria.   Okay? And that's going to be our controlling  headwater. Now we have to compare that to   something to make sure that's okay, and we compare  that to what's called the allowable headwater. The allowable headwaters not necessarily something  that you calculate, it's actually something that   you set as a do not exceed threshold for your  design event, and that's based on your site visits   and some of the background homework that  you do for your project. If there's a sag   point in my roadway, and I don't want roadway over  topping, right, for my design event. Then maybe your   allowable is set below that with some freeboard  built in, so maybe my allowable headwater is here.   If you have some private property that  could potentially be impacted and you   don't want to flood them out, and if you're into  working in the flood insurance study area you   realize that you have to be very careful about  raising the water surface for your design flows.  If you don't want to flood this person  out, maybe your allowable headwater is below   the level of their basement, or it's maybe  set by some commercial properties or   other situations. What are some other situations  that will help you set allowable headwater?   Can you think of any? It's basically to  mitigate any damage that could result from   your design flood occurring. So it's not, again it's  not necessarily something you calculate, but it's   something that you set as a threshold. Because  if your design flood exceeds that threshold   and the damage that's caused it's not something  that you can live with. Utilities? Utilities perfect,   perfect. There's another criterion and this  is a little bit, you know, this goes back in the   day when they were setting you know allowable  headwaters. Headwater to the rise of your barrel,   and if this is a pipe culvert it's head  water to diameter, if this is a box culvert   it's headwater water to the vertical rise  of the opening. And I think limits in the day   were set around this ratio of maybe, 1.5, 1.2 and  you know it varies. Why do you think this could   be a criterion for allowable headwater? Headwater  to rise ratio, say 1.5, why would that be important? Probably because of the capacity. It's not necessarily a capacity thing. Think  about back in the swimming pool. You dive down into   the water to get that shiny silver dollar that  someone threw in there, maybe your favorite uncle says hey, trying to coax you into being a better swimmer throws that silver dollar in there. The further down you go? Pressure. The more pressure. Think of a headwater to diameter  ratio of two, or three, or five you're building up   more and more and more of that hydrostatic  pressure. And guess what, roadway embankments   aren't designed to be dams right? Most of the  time, and we, we always say in Federal Highway   don't design your roadway embankments to  be dams, you don't consider them to be dams.   As that hydrostatic pressure, those water  forces increase with increasing head,   that can destabilize your embankment. In fact the  buoyant forces, if you're not careful can float   the entrance of your culvert, they can do  all kinds of crazy things. It could be a safety   issue if a vehicle departures off the roadway, so  there are some good reasons why this was limited   and why we still limit this. So this could  also set your allowable headwater elevation. So once you have your allowable headwater  elevation, you've calculated you're controlling   headwater based on minimum performance, so you  take the headwater that's the greatest between   inlet and outlet control you compare these two  and see if you're controlling headwater is less   than you're allowable. And if it is you feel pretty  good about that, so you passed one design criteria.  The next thing you're going to  check. Is my outlet velocity okay?   If you're designing a culvert and  you're contra, you're contracting   the flow area, we know from continuity  Q equals AV as the flow area goes down   the velocity goes up. And sometimes you can have  some crazy scour issues if you're, if you're   making that flow area too small. This is what  we see with undersized culverts all the time.   These outlet velocities are way too high, they  didn't design them appropriately, they didn't   use energy dissipation techniques, and you get  these ginormous scour holes. All right? That water   comes flying out of there, and again water is like  me, it wants to be chill, maybe a little bit lazy.   It wants to calm down and it's going to want to  reduce its energy, and it does that by picking up   soil, your stream channel, your stream  banks, and it just picks them up and   eats them and moves them and drops them  and then it's back at its natural velocity.   All right, so we need to make sure that our  outlet velocity is okay you should have   criteria for that in your EPG.  Am I saying that still correctly, is it EPG? Okay. If you've satisfied your headwater is okay, you're  not doing any flooding or over topping your road,   etc, etc. Your outlet velocity is okay. Then you  also need to make sure, we talked about this   with cover situations and other things. Will  my culvert system actually fit in my site,  or will I hit utilities? Or do, or do I have  a limited cover situation where my culvert is   actually going to stick up above my road  surface? Which isn't going to work. You know   those other types of things will actually  fit within the site condition. If that's okay, and if you   don't have any special requirements for  aquatic organism passage. Do you have those here? Special requirements for fish passage, aquatic  organism passage? Because if you have to meet those   then that also has to go into the design  process, and that's that's kind of like a   another lesson in our culvert design course. But  let's assume for this, say you're doing like a   ditch relief culvert, so you don't have that and if  this is all okay then you're probably good to go.   You also have to do your material selection, so  you probably have material selection policies here.   So another thing that you have to do is if  you have really corrosive soil and water, then   if you choose a metal pipe then you probably  also have to select some special coatings, and   maybe you have to select a thicker gauge of metal  so it lasts longer and doesn't corrode so quickly.   Maybe you use concrete, or maybe you use high  density polyethylene or some other materials,   so there's also a material  selection component to that as well. So that's the general idea and you may have  questions, and then my response to that would be   we're going to practice. So we'll actually  do this, to make sure that it makes sense. So again, just some review. The inlet  control analysis to calculate the   internet control headwater, again we use  weir flow when our culvert is not submerged.   It eventually transitions into orifice  flow when our culvert becomes submerged,   and so we use charts that build in the weir  and orifice equations. And those were determined   from laboratory experiments back in the day by  the Bureau of Public Roads and other entities.  Outlet control analysis, we actually do the  energy analysis. So we're balancing energy   from the upstream and downstream sides.  The cool thing about the outlet control analysis, is that for the conventional culvert  design where you actually have some ponded   headwater upstream. We assume the velocity head is?  Zero. Zero, because it's probably pretty close to zero,   right? The ponded water upstream of culvert is  really subcritical, it's not moving very quickly   has a low velocity, a very low velocity component,  so V squared over 2g is going to be pretty low.   So we'll say that at the upstream side  the total energy is your elevation head   plus your pressure head, which is the water surface. On the downstream side, if we have this, if we  assume the same cold conditions like high tail   water. Then we'll say that on the downstream side  the velocity head is pretty close to zero, and   again this isn't the case in a lot of situations.  But if we were to assume that, then we would start   off with the elevation head, which would bring  us to the bottom of the channel. Maybe the water   surface, which would be our pressure head. We add  in the energy losses, which are the entrance loss,   in most cases the entrance loss, the frictional  loss, and the exit loss. So those are all the   energy losses, we add all that stuff up, we bring  it back up to the top of the culvert and that   becomes our headwater elevation at the entrance.  So we'll start simple in assuming those things.   So here's the case here,  elevation that gets you to here. This gets a little bit tricky, so let's pretend  we're looking at the tailwater for a second.   The pressure head gets you here, so this is your  hydraulic grade line. If you add in all of the head   losses, entrance, barrel friction loss, exit loss,  add all those in. You come back up, and this total   energy plus the head losses equals this total  energy, which is your headwater up here neglecting   V squared over 2g. We have to go back here and  look at this tailwater for just a quick second.   Back in the day before they had computers,  like we mentioned earlier, they developed   charts and figures to do all these  calculations. They didn't do them,   they didn't do all these tedious  calculations by hand every single time.   When they developed the charts for outlet control  condition, they assumed full barrel flow, all the   way through. And therefore friction, full barrel  friction loss, all the way through the barrel.   If we have low tailwater, we know that we  don't have full barrel flow all the way through.   Because it's going to cascade down through? Critical depth. So they had to make an adjustment  so they could still use their charts, that were   developed for full barrel flow all the way  through and make that compensation, so they   didn't count this part of the friction loss. So  what they had to do was, they had they determined   this from a little bit of experimentation,  they said if my tailwater is really low   to actually use those charts that that were  developed for frictional resistance of the   entire barrel flowing full, I have to make a little  bit of an adjustment. So if my tailwater is low, I   also need to calculate critical depth plus  the rise of my culvert and divide it by two,   and I'm going to calculate that value, and  again this is determined through experiment.   I'm going to compare this value to the tailwater,  and I'm going to use the one that gives me the   largest answer. And that's going to become my h sub 0 value, or kind of like the pseudo starting point   of your hydraulic grade line, that you then add  the friction loss or the all the energy losses   onto that you then translate up here to get your  headwater. All right? So again this is an adjustment   for very low tailwater situations,  where I violated my full barrel flow,   and my full barrel friction loss all the way  through. So you make this adjustment, so what   we're going to do in our in our hand calculations,  we're actually going to compare the low tailwater   with d sub c plus D over 2, and we're going to use  the larger of that, the larger of those two values as   our hydraulic grade line value here. Add on  energy losses, and then come up here through   balancing the energy equation and say this is our  total energy up here, neglecting V squared over 2g. What what was the capital D in that equation, what  did that stand for again? I say it's it's the pipe,   I say it's the culvert rise because we're not  always dealing with pipe culverts. If you're   using exclusively pipe culverts, it's the pipe  diameter. Okay. But since we use box culverts, and   arch pipes, and other types of shapes it's really  the rise, which is the distance from the invert to crown. It's one of those things, again what is this?  It's a minutiae. It's one of those little details,   you can spend a lot of time wrapping  yourself around the axle on it.   It's an adjustment if we don't have full barrel  flow, so that we can use the nomographs that   were developed for full barrel flow. It's  not, it's important to remember to do it,   but it's not one of those cool big  picture things that we need to keep our eye on. Is S 0 normal depth or? Oh I'm sorry, so this is  slope. Anytime you see S it's slope.   No h 0. Oh this? Yeah is that normal depth? Is it  normal depth? It's not. It's not always. If, actually this is a good question.   So the question is, is h sub o normal depth?  If tailwater is the greatest of these two. And if you calculated tailwater using? Instead of uniform flow conditions, using? Manning's.  Manning's equation, then h sub 0 is normal depth. If you use tailwater, but you don't have steady  uniform flow conditions and you calculated tail   water in another way then h sub o is not normal  depth. Or if you calculated tailwater using Manning's   equation, but it's less than d sub c plus D over  2, so you use this value then it's not normal depth. Does that make sense? But again, that's another  mi, it's a great question it's more of the   the in the weeds kind of thing so. All right, so how do we calculate  energy losses, inlet energy   loss. Okay so how do we calculate our inlet  energy loss for what type of flow control? Where are we calculating, calculating energy  losses? Where are we calculating energy losses ,  it's outlet control. We're not calculating energy  losses for inlet control we're using the weir and   orifice equations. So how do we calculate,  so when you see inlet energy loss don't   equate that with inlet control. Okay? Inlet  energy loss for our outlet control condition.   This is the same thing with pipe flow, if you're  doing water distribution and other types of things.   The energy losses are typically some sort of a  coefficient, times your full barrel velocity head.   Okay? And that's what we're going to  use, is the velocity head in the barrel,   and that that coefficient comes from tables.  You're going to look these up in your EPG,   we also have them in HDS5 which is the manual  on culvert design and they're in Appendix C.   For a thin edge projecting, the k sub e is  0.9. For mitered to fill slope 0.7. End section,   that one's a weird one that's actually conforming  to fill slope. Square edge at 90 degrees is 0.5. Socket   end or a beveled entrance is 0.2, you put  that bevel on your head wall that's a 0.2.   So which is more efficient, thin edge projecting  or a, maybe that bell end on your concrete pipe? Which one's more efficient, this one? Socket. The socket, and why? If k sub e is 0.2, if I take   0.2 times my velocity head, I end up with a head  loss that's less than almost a full velocity head.   So this one has less energy loss than this one.  This one is more hydraulically efficient than   this one. So as the k sub e value goes down, your  hydraulic efficiency goes up, because your energy   losses at the entrance are less. So you said we, so  if V squared over 2g is negligible, is that only at   the inlet side? So that's what, yeah so that's when  we're looking at the total energy level before   it comes into the culvert. But we still need to  calculate that all of the sum of those head losses   then the head loss coming in through the entrance,  as that flow actually contracts and picks up   velocity head as it goes into the entrance.  So there is there is a measurable velocity   head as it goes into the entrance, and we're  going to assume the full barrel velocity head,   and therefore use that to calculate that  energy loss at the entrance. Yeah but up there,   up here in the pool level the, the, the  average velocity coming in is pretty low. Culvert barrel friction loss, actually is a  rearrangement of Manning's equation. There's   friction loss as it goes through the barrel, so  we're going to actually be able to calculate that.   And that's, you could calculate that through  looking at Manning's equation, however the   nomographs have that built in, so it's not  something additional that you need to calculate.   HY-8 it does it automatically as well,  so it's not something that we do by hand.   Culvert exit loss, we in the past have typically  assumed that we're losing one full velocity head   as the water comes back out into the barrel, or  into the tailwater. So it would be 1 times V   squared over 2g, and that V squared over 2g uses  the velocity, that full barrel flow velocity. That's historically what we've done, and if you have and I  don't have a good picture here. If your tailwater   is high, and it's above the outlet of your culvert  it's a good assumption, because that water pushes   into that high tail water it's going to lose one  full barrel velocity head. If you have low tailwater,   then that assumption is overly conservative, and  what you can do is you can take the velocity head   in the barrel minus the velocity head in the  tailwater, because your tailwater will have   some velocity at that point. You subtract those two  and the coefficient you'll use most likely is one,   and that will give you something that's a  little bit less conservative, but more realistic. Tailwater depth, for your ditches  you're using Manning's equation. The question came up I think, and we'll partially  address it here. This is probably where I need   to show off my horrible artistic  skills, looking at pipes in series. If I do it over here can you see this okay? Maybe we could use that thing? Yeah, you could use that   too. Eric, there's also this digital  projector you could do it on. Oh yeah. It doesn't matter. We're going to set that  up for our work problem, but maybe for   this if I just sketch it real quick on this  it'll be fine. So again this is going to be horrible. You have your channel slope here, and then you have culvert here, and then you have-- It is what it is. I actually, you know I like the  smell of markers and I'm not going to apologize for it. So you have another culvert here, and again this, I, I feel bad this is just  absolutely ridiculous. Two cars going uphill. It looks like,   that's exactly what it looks like. I'm sorry.  I was just thinking that this looks like   two cars when, right before you said that.  Do I have steady uniform flow conditions?   No, because during my flood event what's  going to happen is, if this were normal depth here, what I actually have happen is that the  water backs up here and I have this headwater,   and then it comes back down like this. Right? So  if I use normal depth, I hope this is okay, if I   use normal depth as my tailwater here I'm going  to be underestimating the actual tailwater depth,   potentially significantly if these culvert  crossings are fairly close together.   Something that you could do that would be on the  conservative side is, you could actually go to the   downstream culvert, run the hydraulic analysis on  this, calculate this headwater and then use that   headwater as the tailwater for this one. That  would be a little bit conservative, or maybe a   lot conservative, but it would be better than using  normal depth which would be way under conservative   and could cause you some, some design issues. the  other thing you could do is say, well I'm not, I   don't want to use normal depth, and I don't want to  use this headwater. I'm going to try to maybe you   sketch out this profile, and maybe you sketch in  what you think the water surface looks like and it   comes down a bit and maybe you just use that value  for your headwater, or your tailwater for this one.   It's going to be less than the headwater for  the culvert, but it's going to be greater than   the normal depth you would have calculated using  Manning's equation. So you've got to make some   engineering judgment there, and again you put  this in your documentation. Does that make sense? What if between that, between those two culverts  there was a cross pipe also adding to the flow what would you do? Yeah. Same, same exact process you think? I would, you know I would go, I would start at my culvert outlet and I   would look downstream and think, is there anything  that causes me to question the validity of normal   depth? And if it is I would go directly to that  point, and figure out how that's influencing things   and if I could do a hydraulic calculation on it to  determine the depth, and then back that up into my   tailwater. It's whatever is the the first thing  downstream that I encounter. It could get more   complicated than that, but again for most of your  projects as roadway designers, you probably don't   need to do a lot of extra sort of things like  that. It might be a ditch check, or a little check   damn in your ditch line, maybe that bumps up your,  your normal depth and plus a little bit extra.   So just use your engineering judgment and put it in  your documentation. Your ditches, your ditch, your   your ditch relief culverts are usually lower  risk than your stream and river crossings. So   the level of effort should reflect the level  of risk. If you have, if you're working on a   bridge project and you're worried about this, then  you're not even using the HY-8, you're using HEC-RAS   or a 2D model, and it will take that into  consideration. Right? It does a standard   step, you know energy balance going from the  downstream to the upstream. One more for the road. So that's what this says here, when you're working   in streams and rivers you're typically  not using the HY-8 as much, because HY-8   it doesn't look at a series of cross sections  along your channel. It's really just what's   happening at the crossings with one tailwater  section, and we'll see that when we pull HY-8 up. All right, minimum performance design concept.  So we check inlet control and outlet control   headwaters, we take the larger of the  two, we compare that to our allowable.   If it's less than allowable, then the headwater  is okay, and then we check outlet velocity. Outlet velocity Q equals VA. If you need to  figure out the outlet velocity of a culvert,   the big picture concept, which is  always simple. I'm maintaining this,   I'm not going to back away from this, big  picture ideas are usually pretty straightforward.   I know my flow, I know my design Q. If I know  my flow area, I can calculate the outlet velocity.   The devil is always in the details,  I need calculate the flow area.   Once you calculate the flow area, it's easy  sailing from there. In inlet control, again remember the picture here, as the  water dives down through critical depth   it eventually goes to supercritical. It's not going  to be uniform flow in this piece, because it's   kind of doing this and that's not uniform. But  for one of these longer culverts, it eventually reaches   its normal depth again. So here's a key, normal  depth does not equate to subcritical flow.   Subcritical flow has a normal depth, you can  also reach normal depth and supercritical flow.   Okay? It's just the flow that normally occurs  under that condition, so as this kind of strives   back towards normal depth, then the flow area  that I use to calculate my my outlet velocity   is the flow area associated with  normal depth and inlet control.   So once this reaches steady, uniform flow  conditions, I use Manning's equation. I can   calculate the normal depth, we actually did that, we  looked at that iterative process. We did it by hand,   it's kind of a pain but you could technically do  it, for box culverts it would be easy. For circular   shapes it gets kind of crazy. Okay? But you  can calculate normal depth, and then you can   calculate the flow area. Q equals AV, I know my Q, I  know my flow area, I get my outlet velocity. So in   inlet control conditions I can use steady, uniform  flow approximation calculate my outlet velocity. In outlet control, again I'm looking for   what is my flow area, and then once I have  my flow area, I take Q over A and I get V.   So my flow area if my tailwater is up here,  what is my flow area coming out of my culvert?   It's just the flow area, it's just the  area of culvert. My tailwater is up here   my flow area is the area of this culvert, as the  water comes out I use that area. And if it's,   if it's a circle the area of the circle is what?  Pi r squared. Pi r squared or pi d squared over four.   Or pi, what is it? Pi d squared over four. Pi d squared  over four, or pi, people like to use r, I usually use d so I don't need that. Pi r? Pi r squared. Pi r squared. So you can calculate the flow area very easily,  if you have a pipe culvert with high tailwater,   straightforward. If I have very low tailwater and  this plunges through critical depth at the outlet,   the depth of flow I'm going to  use to calculate the flow area is? Critical depth. If I can calculate critical depth  for that shape, and I use that to calculate the   flow area, and Q divided by A equals V, I get  my outlet velocity. If my tailwater is above critical   depth but below the crown of my pipe, I can't use  the full barrel area, I can't use critical depth,   I use the area associated with? My tailwater, and  you've already calculated your tailwater depth.  Right? Using probably Manning's equation,  so you have your tailwater depth,   you actually just use that to calculate the  flow area, Q divided by A equals velocity. So my, I have low tail water I  calculate flow area using what depth? Critical Depth. I have high tail water, I calculate flow area based on what depth? The rise of my pipe or my culvert. If I have tail  water that's less, that's under the crown of   the pipe but above critical depth, just use  the tailwater depth to calculate the flow area. If   you have a rectangle, straightforward. But if  you're not using a box culvert, do it by hand   you go insane, even for a circle. That's why we  have charts to figure those things out for us. And in HY-8 you don't worry about it  at all it just calculates it for you. Once you have your velocity  then, how do you know it's okay? What criteria do you check it against? If you have an outlet velocity of  10 feet per second, is that all right? We could look at our EPGs. Yeah and I don't know what's in  your EPG as far as outlet velocities.   Chase, do you happen to know? It's like they try to keep it between 3 and 20 feet per second, so.   Did you say between 3 and 20? 3 and  20 feet per second yeah. That's a huge range.   Yeah, well they keep it between 3, or it has to  be at least 3, because anything less than 3   you know deposition might happen, and then  anything more than 20 would be erosion, so  yeah. Well you can get, depending, it depends on your  channel material. But if you have a sandy channel   you can get erosion at you  know 7, 8 feet per second.   I think that's considered through pipes though so  I don't know what it would be through channels. Yeah,  so you would want to look at what the permiss,   and we talked, we talked about this kind of like   with channel design except more from a shear  stress perspective, but for outlet velocities   you would kind of see what the criterion  are in a channel for permissible velocities.   The general idea is you want to try to match the  natural channel velocities to the degree that you can.   It's going to be hard if you're putting in a small  culvert, because you know you've already violated that.   But you want to do your best to try to match,  in an ideal situation, match the natural channel   velocities, which means putting in a larger culvert,  most likely. Which means probably more expensive, so you do a balance and you just the general  idea is you need to check it against something.   Okay, and if you suspect that you're going to  have outlet scour because the velocity is high,   can you change the material selection? Do you  need an energy dissipater? Do you need maybe   just something as simple as an apron at  the outlet which is usually pretty standard   for culverts and even in ditch lines. You  just need to do a comparison against something.   The slide before this, in the blank at  the bottom, is that Manning?   Exactly. Yeah, anytime you see normal  depth you know that's calculated using Manning's equation. Yup steady, uniform flow. Outlet velocity, so here's the  thing and so maybe I just misspoke. Here's a calculation that we've done. This is an  inlet control, so think of your water slide example   again. We have this large culvert, and maybe say  this is, maybe say that's a four foot diameter pipe. We see that we have this outlet velocity at  14 feet per second, which is actually really high,   and probably in most cases, unless you're  discharging onto bedrock it's going to be   erosive to a degree. So we're not quite  liking that. Actually I did that backwards, we have this two foot one, sorry delete  that out of the video, so we have   this two foot one and we see that the  other velocity is 15 feet per second. This is velocity sub n which means what? We  calculated this, this is the normal velocity,   we calculated this using? Manning's equation.  So we say well this two foot pipe is not going   to cut it, if we just put in a four foot pipe  our velocity should be fine. Well we put in the   four foot one and we see that the outlet velocity  went from 15 feet per second 14 feet per second. Why is that? Well we've just redistributed the  flow area a little bit, right? We've redistributed   from this to that, but we still have pretty  much the same flow area at the outlet and   therefore if our flow area is about the same  our velocity is going to be about the same. What we could have done with that two foot pipe   is saying, maybe instead of concrete, maybe we use  a corrugated metal or corrugated plastic. And even   if we have the same size, we see that going from  15 feet per second, we change the material type   cover and everything else remains the same or  backfill and we've dropped it from 15 to 1,1 which   is pretty good. It may still be too high, but  that had certainly more of an impact than making our pipe bigger. So that's just something to keep in mind.  For the situation where you could actually   make some hay on increasing the size of your  culvert to reduce outlet velocity, would be a   situation where you have at least, well definitely  high tailwater. Right? Because you figure if you   go from this size to this size you are increasing  your flow area, and you're dropping your velocity.   If you have, in outlet control, if you have very low  tailwater increasing the size isn't going to do   anything for you. But if you have high tailwater  then yeah, you have a lot more flow area you know.   So you are decreasing outlet velocity there,  that doesn't happen a lot. Could, could happen, but   not a lot. I would think probably,  unless you're on really mild slopes   that your tailwater is going to  be fairly low in a lot of cases. All right, with that I am chewing

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Length: 106min 8sec (6368 seconds)

Published: Thu Mar 10 2022