So I just want to do a brief introduction before we dive right into our panelists so you all know who they are. We have two very esteemed panelists today. So the first on the far side is Lauren Oates. Lauren is TNC's Director of Policy and Government Relations where she develops, supports, and advocates for science-based policy solutions to our changing climate. In 2020, Lauren was appointed alongside Dr. Dupini Jerome to the Vermont Climate Council as a member with expertise in natural hazards resilience implementation. Prior to joining TNC, Lauren served as Vermont State Hazard Mitigation Officer, working with home and business owners, municipal, regional, state, and federal governments to develop plans and fund projects to reduce hazard vulnerability across Vermont. Particularly noteworthy for this conversation, Floodyne actually brought Lauren to the lab. She lived here following topical storm Irene to assist the town of Waterbury with its long-term recovery training efforts. And has continued in the climate adaptation and flood resilience realm ever since. So welcome, Lauren. Dr. Dupini Jerome applied climate scientists by training Dr. Dupini Jerome's research interests intersect a number of interdisciplinary fields including hydroclimatic natural hazards and climate literacy, geospatial climate and land surface processes, all within the context of our changing climate. Dr. Dupini Jerome has served as this Vermont State Climatologist since 1997 and is the immediate past president of the American Association of State Climatologists. In 2020, she was appointed by the Vermont House of Representatives to the Vermont Climate Council as the member with expertise in climate change science. She continues to work with Vermont State agencies and municipalities and they're planning for adapting to climate change. She is an expert in floods, droughts and severe weather and the ways in which these affect Vermont's landscapes and people. She has worked extensively with K-12 teachers and students bringing the use of satellites, climatology and climate change to all levels of the pre-university curriculum. She is the lead editor of historical climate variability in impacts to North America. The first monogram to deal with the use of documentary and other ancillary records for analyzing climate variability and changing the North American context. Nationally, in 2022, Dr. Dupini Jerome was nominated to serve a three-year term on the board of atmospheric sciences and climate in the National Academy of Science Engineering and Mathematics. She was invited by the White House Office of Science and Technology Policy program to be the presenter on the Climate Change Lead in the Way panel and the COP26 meeting in Glasgow, Scotland in 2021. She served as the lead author for the Northeast Chapter of the 2018 4th National Climate Assessment of the U.S. Climate Change Research Program and is an author of the National Water Chapter of the 5th National Climate Assessment. So, I just want to start off with a few questions for our panelists and then we'd really like to open it up to the crowd. We have Simba over here with a microphone so we can start passing that around. So, one of the questions that I have when I watch something like this is there seem to be a lot of focus on flooding disasters when people talk about the effects of climate change on Vermont. What are some of the other effects of climate change that we can anticipate in Vermont and do you see anything having the disruptive or destructive effect to our daily life as the recent catastrophic floods have had? So, do you mind if I start with you? Sure. So, first of all, thank you to everybody for coming out on this cold and rainy Saturday afternoon. In particular, thanks to those of you who live in Montpelio. I know there are a few of you here in the audience and before I answer, Tom's a really long question. I just wanted to say my heart goes out to you. I wasn't able to visit until about a month ago and just driving through Montpelio and going to the State House, it was really surreal. That's the only way I can come up with for that. The humidifiers are still going and I can only imagine what you're still going through as you drive through, as you look at your homes, as you look at your businesses. So for me, on a personal level, I just wanted to say my heart goes out. My heart really does go out. And in thinking about that and thinking as a scientist, what are some of the other things that we are looking at in terms of our change in climate? Yes, floods are one of those pieces and we'll talk maybe a little bit more about what does it mean to have one in a hundred year event, possibly more than one time in a given year? What does that physically mean? But also remembering that just before the floods in July, we were dealing with drug conditions. And our farmers were probably about to ask for a drought disaster declaration because of how severe that drought was. And it's not only this year, it's in previous years we've seen it. So we're seeing how the ways that droughts are creeping upon us are actually changing. And so that's one of the hazards that we're always looking at. And if you think back even a few months before, we were dealing with frost conditions. And we know that our apple crop produce is actually very affected by the frost that were taking place in the spring. And so as we think about what do we do as people in Vermont, and we think about all the various hazards, there are so many effects affecting different parts of the state differently. One that did affect the entire state was wildfire and smoke. And as a climatologist looking at these events sort of unfolding, and trying to make sure that we're looking at this from a system-wide perspective so that every hazard does not catch us by surprise, doesn't catch our economics, doesn't catch sectors by surprise, just making sure that we are trying to capture how these events are changing so that we know how to pre-state and pre-plan for the next particular hazards coming out of the fight. Always hard to follow up after Lesley Ann. I have very little to add, although I've been an asterisk, especially on the way that we do talk about flooding in this state. The images that we just saw, the drone footage, I'm also a Montpelier resident and they are still striking to see these three and a half months later, two and a half months later. We think of flooding like that often as a species. We think of flooding as inundation style flooding where the rivers spill over their banks and they come up in a really vertical type of manner. In Vermont, actually, even though this is what we're talking about today and those are the images that we just saw, that's actually not our number one natural hazard. Our number one natural hazard is fluvial erosion flooding and that's the really violent, quick, extremely dangerous flooding that we see because of our steep topography and our very narrow river valleys and that's what the majority of our flood damages upwards 75-80% of flood damages in Vermont typically come in that style. And then one more thing to consider just the lasting impacts of how strange this year in particular has been is that we're right next to Lake Champlain right now, which is at a pretty high level for this time of year. If you look at the hydrograph, you'll see it typically starts to really decline starting in July and drops before we go into the winter months, which is actually really important because then when the lake levels lower, it's able to receive a lot of the snow melt coming in March, April, May and June of next year and because it is so high now, if we have a really snowy season, which we love to have as Vermonters, that will have huge implications, lasting implications on our lake shore here. So it's not over yet even because of how much water we received after being in a drought, as we said. So the even flooding in Vermont, I want to say, is there are a lot of different types of hazards, hazards of planning and how we consider how we live along our waterways. And just to add one more piece, because I'll already brought up that Lake Champlain, the amount of water that came down to Lusky and made it to Lake Champlain was so much, we actually set two new records on Lake Champlain as a result of the July floods. So again, it's something that we're looking at because it's critically important as a kind of an experience. See, there's a question. Yeah, do we have, were you saying it's just erosion when it's down slow or is there actually a loop back in here too? Yes, we also have quite a bit of landslide hazards in the state. Yeah, we have a hydrological problem in the state that is multi-passive and depending on where you live, rural, urban, upstate, downstate, it looks a little bit different in all of our towns. So I'm really looking forward to this. Just to jump in before we take a good question, I see a lot of familiar faces here, but some of you may be new to the Nature Conservancy and maybe just talking to zero-lives for aerobatics. Tom, do you want to just really quickly speak to, really quickly speak to some of the things? Really good. And the zero is not cool, of course. Who we are is what we do at the Nature Conservancy. Yes, yes. Thank you for that introduction. I was so excited to introduce our panelists. I forgot to introduce ourselves as the Nature Conservancy. Yes. So the Nature Conservancy is a global organization. We're actually the largest global conservation organization in the world. We currently exist in 77 countries and in all 50 states we have chapters. In Vermont here, we have protected 300,000 acres of lands and waters in Vermont. And 90% of that has been turned over actually to public lands. So a lot of the state wildlife management areas, state forests, things like that, that you all know and love, Camelson, Green River Reservoir, Regie Glory, a lot of those areas were protected by the Nature Conservancy. And we are, as we evolve, are in so many different realms now, not just in direct land and water protection, but we also work closely in our policy work in Lawrence. They'll be talking today. Working with our legislators to really propose robust legislation that can really help protect nature here in Vermont. And I also want to introduce just a few people here that are with us today. We have a couple of our board members and advisory council members. So we have Lucy Landon, who is on our advisory council there, and Beverly Whittle and Linda McGinnis, who are both on our board. And I hope I'm not missing anybody else that popped in in the last minute. Oh, yes. And Rhonda Bergman, Dr. Rhonda Bergman, who is our director of science and freshwater, is here. She did pop in the last minute, so I didn't miss anyone. So she works among our staff at the Nature Conservancy. So I just want to, before I turn it over to more audience questions, I just want to ask one more question for you all, which is, you know, the bike shop over there mentioned the 1927 flood. And it's something that I've always kind of wondered about the context of the 1927 flood. I assume no one in the audience was around for that one, but I'm sure many of you were around for the 1992 flood in La Puyo here, that hit Montpelier in particular really hard, and it was, from my understanding, not dissimilar to what we saw on the video today. And then there was, in 2011, a tropical storm like me, Irene, which was less devastating per se, to Montpelier than maybe water barriers to other communities, and now these new floods. Can you talk a little bit, kind of, about some of these patterns that we're seeing in these floods, and in particular, what was different about the 1927 flood and do we have any of those same conditions that are set out today? Well, the 1927 flood is what we call the flood of Reca, and it stayed like that until Irene came in 2011, and Irene was really concentrated in some part of the state, and so that eight plus inches that we saw in Irene actually set up the flood of Reca conditions for the south, but the 1927 flood still remains north. And the 1927 flood was interesting because it occurred in a year that there was a drought here, and then we see like 200% of the November rainfall in two days. And so we went from drought to this massive amount of flooding as a result of how much rain fell in a short period of time. So it starts to sound familiar with what happened this year as well. And I think one of the things that is important to remember, it's not how frequently it occurs only, but how much rain actually fell, and how quickly that got into the lakes, ponds, rivers, and streets. So when you hear that 100-year event and you hear folks say, oh, but we had a 100-year event in my life, and it's not going to happen again, I think the understanding needs to shift a little bit that the one in a 100-year event is an actual amount of rain that falls. And so let's say it's 8.2 inches, right? So if 8.2 inches fell today and that considers a 100-year event, if two weeks from now 10 inches falls, then that also exceeds that 100-year event. So calling it 100-year storm is a little bit of a misnomer because it makes us think as humans that it can't happen again. When it shifted that a certain amount of rain falls and it's large enough and it falls quickly enough and it's concentrated enough that yes, you will get a point. And after you. The only thing that I'll add to that is actually, since we're referencing back to the video, one of the notes in the video said when these business owners are considering whether or not they want to rebuild, rebuild in kind, change the way or place that they are going to rebuild, they said, you know, especially in a place that might flood again and I would just say again as a Montpelier resident, as a Vermont resident, it will flood again. That is something that we all have to really come to terms with. And 100-year flood is a misnomer. It's easier to really understand, especially for statistically challenged people potentially like myself when we say the 1% annual chance flood, that's just, it feels very academic and isn't necessarily accessible to the general public. So we really need to figure out a better way to communicate what the true risk is to flooding in our communities. But, yeah, I would change that little piece that I'd say to in a place that will flood again because Montpelier will flood again. Linda, before I get to you, I'll ask you a question next, but I lied before when I said I'm going to open up the question because I'm so curious about some of these things myself and I'm directing my questions at the end that I have a question that I want to ask Laura which is, so what do we do about this and what are some of the things, especially from a policy perspective, what are some of the changes that we can make? I'm so sorry if that was a question. What are some of the changes that we can make and what are some of the things, I mean, conservative advocating force that we can both kind of use nature to adapt to our new climate reality but hopefully start to steer the course of our new climate reality. What's the end? Are you sure you don't talk about policy? It's a good question and it kind of, coming off of your question for Lesley, I don't just focus on what we have learned from the past from the 1927 flood from the 1992 flood from Tropical Storm Irene, so much of what we experienced during those floods should and must inform how we're going to experience the next floods as a state. I mentioned that different towns have different types of flooding, so how those towns choose to plan for, develop and respond to disasters, especially flooding, will look different. And yet there are things that we know that we could and should be doing differently. We inherited, all of us in this room here today, we've inherited Vermont's historic settlement pattern of close-knit communities largely very close and snug to our rivers, which on drier and drier seasons and drier years is actually really quaint. It's part of the eucolic nature of Vermont that generally feels really great to be so close to our water, it keeps us connected to nature, it keeps us connected to one another. However, because of the way we built and because of how closely we built, we're going to continue to have these disasters. So looking forward, we need to think differently about where and how we develop. So there are places like Montpelier that have any, any, you all know is Montpelier, right next to me, any road you take, within a mile and a half, you're going to start climbing up a steep hill, and we just, all of that water catches in downtown Montpelier. That's different than other towns in the state. We all have a different topography and different relationship to where the nearest hill is, but we do know that there are places where we have an opportunity to allow our rivers to slow down and store their waters both before and after they hit our communities. And so we need to find places where we can reconnect our rivers to our floodplains. 75% of Vermont's Mack rivers are actually disconnected from their floodplains. And what that means is all that water is getting forced into hyper-managed and very fast, quick, dangerous water conditions. We don't have access to their floodplains where they naturally spill out and release their energy. Our villages are often our floodplains. And so in the future, we need to find those areas that we have not yet developed and protect them from development. Not only so, the people who would otherwise inherit those problems that we created for them don't, but so that we have those spaces to store water and protect our existing other advocates. We have great representation within our Vermont legislature. They now have a mandate because of these floods, truly to reconsider our mandate's patterns and policies. And so we'll be working on making sure that those areas of highest value for river and flood vulnerability will be protected in the future. And the only thing about it is that we consider this as being a really local area who works primarily on a watershed scale. And when we think of a watershed scale the things that we do are going to affect folks downstream. And you would like folks upstream to be also thinking of us. So one of our joint colleagues always says do unto the folks downstream as we would have the folks upstream do unto you. Once again. Your question was what I wanted to ask but I can go a little further than that and ask you to give a couple of examples of where those watersheds have been protected and what happened in this flood. Just to give an example of positive action that we'd like to have a lot more of and then to just give a shout out to some of the policies and things that we've been talking about. Thank you Linda. I have two great examples in different parts of the state. First many of you have maybe heard of how well Middlebury fared during Tropical Storm Irene. Middlebury was one of those places that downstream in Addison County which was severely impacted. They did pretty well even though they are close to the Otter Creek because prior to Irene they invested as a town, as a community in doing quite a bit of restoration work and protection work for their Otter Creek swamps and flood plain. As a student whose name is escaping me and maybe you've ever been or less than I can remember at UVM did a study to understand what was the lost value add. What did Middlebury because they did that proactive work to avoid damages and she had found through doing that work that businesses alone in Middlebury actually avoided $1.8 billion in damages or is that right? That's right. That doesn't include public infrastructure damages which are incredibly expensive it didn't include damages to private homes and a couple of business owners talking about prohibitive flood insurances for FEMA. Middlebury is a really positive success story for figuring out places to store and protect natural spaces that act as sponges while protecting their development downtown. As is Browbro who is a more recent example they have invested it's a pretty densely packed which is unlike a lot of places in Vermont area and they still are able to find along the highly erosive Whetstone Brook a couple of places for flood pay restoration and reconnection. They moved out of the Melrose Terrace community which was a community of five or six buildings and over 100 residents who are 55 plus in a really dangerous area that experience repetitive flooding they moved them out to higher and drier land and used the vast area to drop the flood plain and allow more of the waters to store there and they found a spot just downstream to do the same and they found that the engineers who worked on those two projects together found that those two projects are going to reduce flooding in downtown Browbro by 6 to 12 inches during future flood events. So non-trivial there are places that we can do these types of projects elsewhere in the state that would have a lot of conditions on not only reducing flood but also reducing the need to move people out of where they currently live where they created their communities. Why don't I go to the other person? Yes, I'm sorry. Thank you so much. It's wonderful to hear your critique. I do have an eight questions. One is the part of the community I've been meeting with and they're distressed with this exact negative approach to the future and then with the extent of the run-off that came down with Lucy into the flood in Champlain how is that going to affect our water quality in the future? I'm not talking about E. Cola that's what they measured here but I want to go back to the general questions of phosphorus loading and all those other questions. Thank you. Okay. That's a good question. I'll answer them to the best of my knowledge. First by saying one of my colleague on the Vermont Climate Council is a farmer and the three of us have worked very closely on trying to help develop policies and plans and just creating more conversation around the impacts that our agricultural community is going to face. A lot of our flood plans and river corridors are in agriculture and a lot of our prime agricultural soils are also in our flood plans because that's where historically we have deposition and nutrient turnover which is actually long-term very healthy for crop management but in those flood years is really meaningful and detrimental and because of other policies that I do not work on but support that really try to protect and keep businesses that are in agriculture a float in these trying times our farmers are really living on the edge they live day to day to keep their livelihood and this flood and floods that they've experienced in the recent couple of decades have been really devastating to them we need to figure out places where they can continue to graze cows or grow vegetables but they also need to be investing in both durable but also sustainable approaches to how they're managing our land and making sure that they have a diversification of crops as they had mentioned earlier late freeze in May devastated apple crops across the state and just making sure that we're empowering them and supporting them because in a changing climate we need to make sure that we're also getting a lot of our food more locally and that we are bringing all up from Mexico or Florida or California so policies to support that will be really important in changing climate and that's the question I'm forgetting just give me like nutrient load nutrient load and yes well well from a policy perspective you just really served it up thank you so Lake Champlain has a TNDL which is a total maximum daily load plan for phosphorus runoff into the lake and that plan has a whole bunch of actions policy mechanisms that can be taken and the number one policy mechanism to reduce phosphorus loading in Lake Champlain and therefore allow the state to meet its EPA environmental protection agencies required minimum or maximum rather daily loading is to protect our river corridors from development and so there's it does and there is a difference between building our hardened infrastructure undersized culverts, undersized bridge homes, propane tanks etc etc than a feel that isn't well buffered and not managed if you implicate tile drains and I'm starting to lean into a space that I know a lot less about I know other people in the audience might so if anybody wants to jump in on agriculture please feel free to but yes there we need to look at our river corridors and as you said whole watersheds when we're thinking about nutrient runoff and how it eventually makes it to the lake do you know that the water quality do you want to talk about that I was going to come down to Mike Beverly here we've got a lot of experts in this field it sounds this quiet put it very close thanks for the question I will just answer by saying there's quite a lot of research going on at UVM and the water quality today so we know that when we get these big events there's a long term legacy that can last for hundreds of years with sediments and the plundering that will end up well I will also say that maybe a silver lion is in about 2018 the basin program to quantify the depositional benefits of connected floodplains and we have a study that has sites across the entire lake and we've been lucky enough to get flood events and see the quantity of material that's actually deposited in the plains during floods and it's quite substantial and so it's part of what's motivating us and the former director of our rivers program and Mike really pioneered this work of let's give our rivers room to move and let's take advantage of this natural infrastructure for both the flood mitigation impacts but also the water quality benefits and we have real data that shows that we can trap a lot of material on these connected floodplains and mitigate those downstream impacts and what she's talking about I just want to ask Mike if there's anything you want to add as the director of our rivers program for more than a few years to the possibilities thank you I think the good news is some of the same things that we've been talking about in terms of actions their co-benefits that work hand in hand and they can go with each other the key word is storage I think it was mentioned a couple of times here that many things have happened in our watersheds to reduce the amount of storage both water and sediment and it does mean giving up some room for the river both in the urban setting in hopes that by doing so we reduce the energy of the river the place to spread out the plant life on those river quarters and floodplains can absorb sediments and nutrients and then the lands that are outside of these river quarters but yet still in our valleys might be accessible for our other community needs including the department the policy goals that we pursued with our partners in the river's program and I think the water quality work that we've done has been part and parcel with our efforts to reduce flood damage thank you two people waiting for information I'll go with you can we speak to the sailor can I also switch? this is pretty short for any statistically challenge I think this coming year is just as likely to flood as it was to happen this year so the fact that it occurred doesn't mean now you have another 100 years until it happens again every single year is just as likely and that's before you account for any climate change so it's just going to multiply and at least in other states FEMA is notorious for having poor flood maps the first street foundation I believe and risk factor have developed some further information that's more accurate I don't think it has anything to run off but hopefully you guys are also working with them to see your maps and your validation strategies thank you for waiting patiently thank you I very much appreciate what you're saying about the watershed and the flood plains and the significance of doing work in those areas but I'm also curious about the built environment for example in Montpelier they had this history of flooding there and what steps have they taken in advance of this latest flood to make some changes to the built environment in order to make the built environment more resilient to the flooding I understand that the transportation center worked fairly well the new transportation center and down-screen housing did as well I'm just wondering what things you've seen that are really working for the built environment so for Montpelier a couple of things have happened since the 1927 flood which was very devastating for the town first was actually the development of the dam through a very massive dam that was built there there are all sorts of implications to dams and how they change our river systems in the state and they change the water habitat there are a lot of implications to dams but that dam was built primarily as a flood retention mechanism it nearly was breached which I would say there was a miscommunication but it does not mean the dam is going to fail in July it just means it was performing as it should and holding back as much water as it could before a spillway would have been used which would have exacerbated flooding in downtown but would not have been catastrophic as a dam breach would have been so a dam was built and that was one of the reasons why Irene Montpelier did okay but beyond that it's really about what we're doing in the future for flood inundation we have opportunities to you mentioned the transportation center which is right down our river in downtown Montpelier too but they built, they elevated to where their first floor in livable space was so the first floor is really the transportation where buses come in you can build in things like flood proofing like flood vents that allow river that allow flood water to actually flow through and under almost like across states you allow the property to flood essentially there are safe ways to do that that reduce hydro-static pressure too so you don't have to worry about structural integrity in any buildings I think and hope that a lot of businesses downtown really is not to store much of anything in their basements now because basements will continue to flood even at first floor stop so it's while you need space to house that you should not put your utilities down below the flood plain and those are small things small elevation flood proofing that can't be done and those are things that when we consider places like Waterbury which is also largely a town that's impacted by that inundation style flooding that's what they've done they invested in some home elevations so the homes have been built at a higher grade and therefore can withstand future flood damages on that there are places that are kind of regularly damaged the first floor is several feet below the flood plain that could be cost prohibitive to do flood elevations and that's if there's an opportunity for a buyout there or you can purchase the home demolish it and allow that space to just be flood plain in the future we can't do that at mass scale I think you probably have something like a buyout that we would need to do across the state and we already have a housing crisis so where will those 10,000 families move so we really need to look at different opportunities for storing flood plain or storing flood waters so that those areas that are already built were you able to attend the three different sections in Montpil have you been involved in that experience I don't know there were three sections in Montpil to actually, I think the first session was a reading session. The second session was, OK, let's go up to see what we can talk about. And then the third session, let's get some solutions on the table. And it was interesting to hear a lot of ideas before. Like, should we move to high school, for example? It's not in the middle of the function itself. Should it not even be there? And then another interesting suggestion was, let's learn from other places that are either the low C level, that have done creative things to manage more of them, or have been funded in the past. And that's sort of learned from that. So I think that was a sort of critical time to really get all these ideas on the table to make some really, really hard decisions. I don't live in Vermont, but what we see around the country is that a lot of these kind of climate crisis events are impacting marginalized and minoritized communities, more than everybody else. You know, they're impacted most and harm the most when a crisis happened. They're less able to rebuild and then less able to invest in the future and kind of future proof. So I'm just curious, locally here, what are the examples of those disparities have you seen, and what kind of policy solutions are there? So I was able to base the testimony of the Senate's Economist Committee two days ago. And that sort of came up as one of the things that we put in front of the center, because this is October, so it's ready on the October. We're getting into winter. And we have a large population of on-house or housing insecure members of our population. And I think when we think about some of the peoples who are marginalized, but the front end, front line, are vulnerable. I think now's the time to actually really think about what are the strategies that we need. And some are more immediate than others, right? But all of it could be important. I really appreciate the question. Thank you for asking it. Two discrete examples. First, hearing Leslie and I say it's an all-hazards approach I'll back it up for flooding and say that the Vermont Health Department has done a lot of work around the public health impacts of climate change in Vermont. And actually I found that there are other hazards that we're experiencing, and it might be surprising, maybe especially as a non-Premontor, but the Premontor is two to hear that one of our most problematic to vulnerable population hazard is prolonged heat events. So it's actually not that like, whoa, we had a random day, or it was 95 degrees, and it was really hot, it's, we had a week and a half that never got below 78 at night and was topping over 90. And those prolonged heat events have a significant demonstrable impact on ER or emergency department visits, especially for our elderly population. We are the first or second oldest state in the country. So that is a disadvantaged group of vulnerable group to that climate hazard. And the other to bring back to flooding and a discrete example, you're right, especially the financial vulnerable Premontors among us. We have 12% of our mobile homes, mobile homes and mobile home parks are located in our flood plains over the corridors and only 4% of our single family homes are. It's a threefold increase in the vulnerability that demographic experiences of the month, which is really troubling, not only because, well actually, for exactly the reasons you said, they're the least financially and socially able to prepare for or respond to the color from flooded events. So looking at how we work with those mobile home parks especially and the dynamic that's really hard often, which is mobile home parks themselves, the land is owned by a mobile home park owner, but the structures that are owned them are owned by individual property owners. And that creates a huge, really problematic and really unfortunate bureaucratic problem in accessing a lot of federal funds. And that's a problem that Central Premont Office's economic opportunity has been working on quite a bit to figure out how to reduce the vulnerability of those groups and make sure that the policies that we advocate for really consider them first and foremost. Hard stop into this 158. Is there a lot of movies to show in 215? Okay, let's push a little bit that way. Why don't you go to next question or contribute to the policy? Yeah, thank you. Thanks for all these good questions and wonderful responses. I just wanted to contribute a little to the point about putting solutions on the table. And a lot of the dialogue around how are we looking forward to where and how our towns are developing into the future. One of the things that Mr. Klein has contributed to our thinking around is how and where we help our individual municipalities and towns make those decisions. And right now, as you know, it's really in their hands to decide how we develop within what we're called our river corridors of that area where the river likes to move. So one of the things that we've been working on together with the Vermont DEC is to say, let's help municipalities figure out this mapping to say where is it safe and where is it really gonna be hazardous and difficult for our communities to rebuild. And let's put that into some more robust maps that then can be used for zoning and land use planning. And also let's help municipalities who currently have the authority to decide whether or not they're going to adopt regulations to protect those river corridors. To do so, this is another equity issue in that municipalities that don't have the staff or the money or the time or the expertise to work on this, their communities can be disadvantaged because of that. So while we're working at a state level to say how can we support state-wide some of these decisions, let's also reach out and engage with our municipalities. So if anyone's interested in that, feel free to reach out to us as well. And I wanted just to say one more thing about the dams. So thank you for the comment about the dam. I just want to remind us ourselves that we only have a handful of dams in our state that are actually flood water retention dams. Very, very tiny fraction of our nearly 1,000 dams in the state. And so in many of the dams that are in the state are actually at risk of causing more flooding and damage during heavy rains because they have not been updated or they need repairs. Vermont Dam Safety has recently gone and looked at all of that and found many that we need to look at. So it's just important to bear in mind that not all dams are here for helping us to be safe from floods and we need to advocate for the ones that are helping us and also work on removing the ones that are causing risks. Yeah, thank you. That's a really good point.  So with that, it looks like we are ready to turn this room over. So I just want to thank everybody so much, especially our panelists. Oh, Lauren's gonna say one more super quick thing. Very good. Our mom would be so proud of me for doing this. I have a cut out in seven days that I really wanted to read. Just to tie back to the video before we turn over, the very end, the business owner mentioned that we're living at war with our river and that's how we have treated our river historically and the only way we're going to change our flood water building together is that a community of communities is to live with our river and not against it and I'm really kind of pardoned by this poem from a 13-year-old that I'm just gonna be very quickly that shows that we are changing as a species and how we live. The river speaks. There's a web and it holds us. Pieces come apart so we help rebuild it. We are a species that has forgotten our place on the web so the earth reminds us. It shows us that there are some lines that we do not cross and if we do cross them, the water rises, pushing us back. The water comes back and it takes. It's the destruction of what we've built but also the reconstruction of the natural world. The water roars, it cries and it heals even when we feel hurt. That's Ursic Olmrose from Hardwick. She's 13, which is so inspiring. I think we can say that we can talk about that. So I'm getting it right there and thank you all.


QuickBooks Online 2024. Bank reconciliation month number one checks and cash decreases. Get ready and some coffee because we're going to save time with QuickBooks Online 2024. Here we are in our Get Great Guitars 2024 QuickBooks Online sample company file. We set up in a prior presentation opening up the major financial statement reports as we do every time reports on the left in the favorites right click in the balance sheet opening a link in a new tab same with the profit and loss report also the trial balance right click open link in a new tab let's check out those tabs we open tab into the right the hamburger closing it change in the range 010124 tab 022924 tab we want to see it on a month by month side by side poor father running the report tabbing to the right closing the hamburger to the left changing the range in the middle 010124 tab 022924 tab and then changing the months on the left and then running the report on the right and then going to the tab to the right closing the hamburger on the left changing the range in the middle 010124 tab 022924 tab and the drop down. I feel like I'm announcing a soccer game or something here. And the ball is at the side. Now it's in the middle. Okay. We're going to go into the running of the reports. Let's go back to the balance sheet. And we've been doing our bank reconciliations. Remembering that the bank reconciliation is basically, I would say mandatory for any kind of business as an internal control, whether it be large, small, or using bank feeds or not using bank feeds. We're doing the first month reconciliation, which has that beginning balance issue that we will be addressing at the end of the first month of reconciliation. This is what the books currently say at 88-810-27. This is what our mock bank statement says, 61-24185. So we need to do some reconciliation. And that's what we're doing at this point in time. So let's go back to what we started last time. The tab on the left, we're in the transactions. Remembering that the bank transactions over here, bank feeds can help with the bank reconciliations as we'll see in future section or course. But it is not the bank reconciliation to do the bank feeds. The reconciliation is over here. Even if construction, the books directly from the bank, then you still want to do the reconciliation because it'll at least double check that you haven't double entered anything or hadn't pulled some feed in for some reason. We're in the checking account. We're going to resume. If you weren't resuming, but was starting from scratch, you would have the info in here being the beginning balance. We can see as a problem because that doesn't tie out to our beginning balance over here. We will deal with that later. That's the first bank rec problem. The date is the date on the bank statement. We're not entering anything for the service charges or interest. I think these are old kind of things that we don't really need anymore, but are pulled in as a legacy article from prior times all the way back to the start of the desktop versions. So then we have our reconciliation summary up top, the statement ending balance, which we just typed in there directly from the bank statement. We have the cleared balance, which is this formula below, beginning balance, payments, and deposits, which will give us our difference, the difference between the statement balance and the cleared balance. Currently, we've only done the deposit side of things, the deposit side of things now matching out. If I go back on over, we're at the, actually I'm going to uncheck the 25 here for now. We're at the 14370. That matches the 14370, 85 on the deposits. Now we're going to do all of the decreases. Decreases typically being the largest and most complex portion of the bank reconciliation process if your deposits are properly formatted and grouped in your accounting system. So let's first just give a quick recap of the kind of decreases that we're going to have and what information the bank knows about and what they don't know about. So first we have a check type of transaction. If we have a check, then that means that we physically wrote the check or printed it out of QuickBooks, recorded the transaction when we wrote the check and then had to send the check to somebody. They have to receive it. They have to deposit it in their bank and communicate with our bank before the bank knows about it. So if we're still using manual checks, that means that we're going to have a big difference between the date. The date is going to be much less reliable. The date in our books is going to be much sooner than the date on the bank side because the bank does not know about it until the check has been received, deposited and cleared basically on their side. But we do have the check number with the check, which is great, giving us an added level of ability to tie out what is happening, even though the date is not going to be as relevant for us. And of course, we have the dollar amount. That's what the bank knows. Now the bank also has the canceled check, which usually isn't going to populate in the bank like memo area, but is something that you can often go to your online banking and then drill down on. So if you need to see who the vendor is and what not, or who the vendor is, you might be able to go to the bank statement and look at the canceled check and see the actual check from there. Now if it was an electronic transfer, then of course you're not going to have a check. So if you're paying people buy electronic transfer, you're not going to have a check. But the date is going to be much more close. So even if you're doing a full service bookkeeping system where I pay something in an electronic transfer, enter it at the point in time, the transfer happens, it's still going to clear the bank between like one to three days typically. So if we do a full service accounting system, our date in our books will be sooner than the date on the bank's books still, but they will be pretty close and likely for many small businesses, at least if we're doing electronic transfers, we're probably going to be dependent on the bank rather than enter the transaction on our side at all. In other words, we won't even enter the transaction on our side, wait till the thing clears the bank and then record the transaction with the use of the bank feeds. In that case, those are the easiest transactions to reconcile because we're not even doing a full service bookkeeping system. We're just taking the bank's numbers and pulling them into our system. So those types of transactions again will be the easiest things to reconcile. And then we could have some transactions that are facilitated by the institution that we don't know about like the bank charges. So the bank service charges, they charge us a fee. We didn't know about the fee. We couldn't have entered it on our side because they didn't invoice us for it, they just took it out of our account because it's a bank charge. So for that, we would have to enter that in our system if we didn't use the bank feeds. But if we do have bank feeds turned on, then we're probably going to be able to pick that up with the bank feeds. The bank feeds will show that transaction will approve the transaction and that is how that will typically be recorded. We also could have money that we took out physically possibly at an ATM or at an institution or at one of the bank locations, so the money that we take out would be like a withdrawal. And in that case, all we would see if we took out cash is the dollar amount that was taken out and the date. We're not going to see what it was taken out for, which could be a problem. So given that, we're going to do the same kind of process. We're going to basically say if it's on the bank's books, it should be on our books. And if it's not, we're going to have to add it to our books unless the bank is wrong, which is not typically the case. If it's on our books, but not on the bank's books, then that might be okay because that might be outstanding checks that we know about. But the bank doesn't know about therefore their reconciling items. Because of that system, then we typically want to be going from the bank statement to our books, not from our books to the bank statement, because everything on the bank statement should be on our books, right? Otherwise, we'll get confused. So I'm going to say here's the $12,001, hopefully our check numbers match up.


Thank you so much for coming to our session. We really appreciate your time. So today, we'll be talking about our current solution for environment promotion with Flux. So I'm Adelina Simeon, and I'm a technology evangelist at Form 3, and I'm joined here on stage by Sam Tovokoli, who is a technical architect working at Form 3 as well. And what we'll be talking about today is the Cades Promoter Project, which is open source. We've recently open sourced it, so you can see it on GitHub as well. And it has been the work of a lot of folks from the tooling team. So it's a huge honor to share it with you today. Oh, and it's built using Flux, and it's written in Go, so just to set your expectations. So first, I'm going to tell you a bit about the background, because a lot of the background that we have has influenced our decisions. Then we're going to tell you about the release flows of Cades Promoter. We'll do a demo if the demo gods are with us. And then finally, we'll conclude and let you know some of the next steps for the project. So let's look into some of the decision factors that have shaped our solution. So first off, we had familiarity with Flux V1, and we liked the toolkit approach of V2. So our tooling teams immediately wanted to go ahead and build it with Flux. Our platform has a requirement to deploy on multi-cloud, so our teams are building multi-cloud stacks. And we needed something that would work for the multi-cloud project. And furthermore, this was something that we had to deliver to unblock the teams. So we wanted to build a simple solution and then iterate on it. We had some requirements around we wanted to manage cluster stay and get, and also we needed to enforce release order, as well as easily diff the differences between environments. And finally, of course, because it's such an important piece of software, we wanted to have end-to-end testing of our promotion flow as well. All right, so let me just set a few main concepts before we really show your environments and go into it. So first off, we have jurisdictions which are fully separate accounts for data isolation and location. Then we have stacks, which are ring-fenced isolated copies of our entire platform. And they contain all of the same services, but they give isolation between the stacks. A workload is a unit of work represented by all of its resources, by which we mean, for example, a service and all of its related infrastructure. And then we have the tenant repository, which contains manifests for all of the services in all of the environments. So our environment setup is, as you see it here, we have stacks which are deployed on multi-cloud, on AWS, GCP, and Azure. And a promotion goes in order from dev to test to prod. There is a one-to-one relationship between an environment and a stack, so the same stack cannot exist in multiple environments. And we have multiple jurisdictions that can as many as we need. So we are talking about managing many multi-cloud stacks. But this talk is more about what happens after the CI flow. So our CI flow is standard. Our engineers raise PRs. We have the code review. And then at the very end, of course, you have the CI triggering the build and testing it. And at the end, we have a new image that's pushed to the registry. But how do we move all of these changes in all of the environments that we're talking about? The team considered three main solutions, which you see here. So first, we could have used customized overlays. We could maintain separate branches for each cluster. Or we could go for a directory structure. Maintaining separate branches for many environments is painful, as some of you might know. And the problem with customized overlays was that a change to the base would trigger across all of the environments, breaking our requirement for deploying in order. So I mean dev, test, production. So the solution that we decided to go for, based on our experience and our circumstances, was to go with a directory structure and use it together with manifests. Manifests would give us an immutable artifact that we could then promote across environments. And we didn't consider templating because we wanted to keep a low barrier for adoption. As we said, we wanted to unblock the teams and then iterate on this full solution. So this is the hierarchical directory that represents our environments. So the manifests folder is the source of truth. And changes to the manifests folder will trigger the promotion. And changes in here could be either done by PR or using Flux's image update automation. And each cluster has its own directory from which it reconciles from. And then you also have stacks that have their workloads and their states in this directory. And Sam will show you more about the directory structure and how it works. We use YAML to specify our workloads. And another one of our requirements was to be able to do exclusions. And as you can see here, on lines 8 to 10, we could exclude for a particular cloud or whatever we wanted. The cluster specification is also done in YAML. And you can see it's got labels saying to which cloud and to which environment it belongs to. And furthermore, it's got two paths for the manifest folder that I was telling you has the specification for the workloads. And then you have the configuration folder, which contains environment-specific configuration for that particular workload. But managing all of this, moving manifests via PR requires raising a lot of PRs. So we needed a way to automate this. And the tooling team kicked off the Cades promoter project in March 2021 to automate this for us. And I'll now hand over to Sam, who will tell you more about it. OK. Oh, now. Right. So as Adina said, we wanted to unblock the internal multi-cloud efforts very early on and build on top of it. We didn't want to invest in changing the whole CI flow. We didn't want to invest in replacing that with anything new in that way. So we kept the developer experience of our old approach, which was the PR approach and quite familiar to us. We wanted to be able to gatekeep using our existing cap process. And cap is the change advisory board, which is quite specific to our industry. And we already had quite a lot of bots and integrations to do these sort of checks and info security aspects as well. We also wanted to codify our release and conventions, as in the ordering of what environment needs to get targeted. And we wanted to make sure of the changes that we do since the sort of template of the way that we do releases wasn't very specified in the early days. We wanted to be able to move quickly and change how we worked by being able to test our promotion. So as part of this tool, we also wrote a wraparound go git to implement the HTTP backend so we can kind of visualize, not visualize, but assert on git state over the HTTP wire using our own sort of tests. The tool works with single and multi-tenant setup. And we will focus mostly on the single-tenant approach. So I will go through the sort of flow with case promote at the moment that we have. And then we'll show a little bit of overview of how the tool works. So as I mentioned, the starting point is essentially an author raising a pull request to flux manifest as we consider the sort of source of truth of our workloads. We also have flux image automation controller that sits here scanning our OCI registries and bumping the versions of flux manifest. And this, of course, doesn't go to a PR process, but it's merging to master. But then it triggers ACI flow, which the review process here will do as well after it's been merged. So the review process also includes the cab aspect, as I mentioned earlier. And we have many, many tenant repositories. So once the PR has been merged in the tenant repo, it will kick off the CI job. And it will essentially have three tasks, promote the development, promote the tests, and promote the production, which will kick off the case promoter given these parameters. So the parameters being to our target environment you want to promote. When the tool runs, the first thing it does though, it's it clones or actually checks out master on another repo, which is infrastructure cluster config, which is essentially where we have a cluster definition across our fleet. This essentially means that you don't, in the beginning we had the cluster state as part of the tenant repository, which meant that you had duplicate information across the place. So we optimized that from UX experience to put it into one place. So when the binary runs, for promotion to dev, it will group all of the changes for the dev clusters in one go and raise a PR where the author proves it. For the test task, what it will do, it will observe that there hasn't been any promotion to development. Then hence it won't actually do any promotion, so it just stops executing there. The same happens for promotion. And then once that PR, the phrase to development has been raised, it will, and once it's been merged, it will trigger another merge CI job, which will then again raise three tasks for the case promoter. And once, and as it has observed, the change has now been done in development, it won't do anything. However, for the test clusters, as we have requirements on being able to raise, on conducting changes one by one in that environment, it will raise three individual PRs where the author has to then merge them and then wait for the production. And this essentially repeats for production once all of those changes have been rolled out to test. So if, for instance, only one cluster had been merged, it wouldn't raise the production PR until it's observed the changes across the whole state given infrastructure cluster config. So I will go through the brief overview of the tool itself. The two most important aspects is the fact that which target environment is and the commit range. It goes through the clone step, which is essentially getting the state of the tenant repository and then detect what changes has been happening to the workload. And then there's a filter step where it excludes given the workload exclusions and then also checking the previous environments. And then it will promote it. But the actual step of the detection is it's using GoGit and we do diff tree over the commit range. We then get the sort of the git state of what actually has changed. We infer the workload changes upon this to figure out, all right, given certain changes to manifest inside of these workload directories, the following actions need to happen. And we take those sort of workload operation and pass it on to the filter step, which then observes given these changes to the workload and given the workload exclusion rules, should it be allowed to be promoted upwards or not? And we check and validate the previous environment as well. And as part of the promotion, it's essentially grouping a cluster, checking out the new branch and applying the changes, commit and push and raise the PR as the tool does for us. And that's about it. So as part of the demo, let's see if this works. I pray to the demo gods, let's see. I raise the PR here where essentially it's quite simple. Let's see if I can show the, yeah, let's not. Essentially, I'm raising a change to flux management. Can you see this? It's readable, it should enlarge it. Okay, cool. That I'm introducing a change to just a version that's very simple to the flux manifest demo services. And I am going to merge this. This will then click off the jobs that I mentioned earlier. And hopefully GitHub will be responsive. And we can see for instance, promoted development, set up job, come on. Yeah, let's see. Let's give it two more seconds. I think the other ones actually have gone through, yeah. So for the promoted development, we will see that it will, these are the options going into it. It will begin the promotion and we are promoting the four clusters in one PR and it will actually raise it to GitHub, right? For tests, what it will say is it will observe the fact that it will drop the change. It's observed the change, but it will say that the source is not the development as expected because we're promoting two tests and therefore it won't do anything. And the same goes for production. So if we now go to the pull requests, we now see an overview page which essentially links to the actual change that caused the promotion to kick in. We have an overview of what clusters have been affected which workload it is. And if we had more changes in multiple workloads, we would actually enumerate them as new columns here. And we also introduced to ping the author so that he actually sees that something is being raised. If we check the differences, it's essentially the same version change being promoted to all of the clusters that we can see, right? And this is done by the cluster's definition is here. So this is what it actually checks out to observe the state of the clusters. So if I merge the following pnl, it will then kick off the next one and we will then be able to observe the promotions to test. And hopefully this will go a little bit quicker. Maybe not, but we'll see. If it doesn't, then essentially I would just have to show previous, oh, there we go. So here we can see that it is beginning the promotion. It started to promote to test internal AWS. It raises specific protocols for that. And then it goes on and raises the other PRs. And as you can see, it is not the fastest here, but this is something that we introduced to be able to rate limits on the APIs. And I will explain more about that. But yeah, essentially you will see four pull requests in the end and it's the test promotions. And you would then merge them one by one. But I won't do that now since we're kind of limited on time. But you can see here that this is to a specific test GCP cluster. And yeah, that's essentially it that I wanted to show. So as you can see, there's gonna be a lot of PRs if you have a lot of environments and a lot of clusters. And even though the automation kind of solved the problem of getting those changes in, we still have a lot of PRs to review. And one of the things that people came back to us with is like, even though you don't have to do the automation yourself, if this binary is doing it for you, if you leave a release and come back to it, it's not always easy to understand at what particular state it is in. And that's one aspect that we have problems with. And also the GitHub rate limits, as I mentioned, and this is due to the fact of we could have a number of works concurrently running and we wouldn't be able to control that. So therefore, this caused us a bit of pain. We had to artificially induce, like regulate ourselves given the sort of responses from GitHub. And also the fact that we would have to manage the maintenance efforts to bump the actual case promoter version across the many tenants, which isn't too hard, but it still is labor. We don't like doing labor. So what we've started looking at, well, I'm not part of tooling anymore. I'm in a market team. But what they're doing now is experimenting with pipelines and essentially keeping the sort of initial change to be PR by the CAD process and making sure there's properly reviewed. But past that point, it's essentially is governed by the pipeline itself. So you don't need to kind of review the state of the PR as to be able to induce what sort of cluster the change has gone on to. And here in this example is we produced a pipeline using GitHub Actions. And the sort of development clusters have been released and somebody has approved to deploy it to a specific integration environment. And yeah, that's pretty much it. Come chat to us at our stand. We're here. And yeah, check out the tool. If you like it, if you don't, leave it out.  Yeah, it's pretty nice. Ask me any questions. Do you have any kind of policies that you can define? So for example, you can say that when you deploy something to test, run this particular test suite, and if that passes, just automatically move to production or move between environments? Or is this like a manual process? This is not what Kate Promoter would do. But we have had the thought of having essentially the next iteration of it would be the pipelines and then building progressive delivery on top of that. But no, it's not doing that right now for what you're describing. But nothing really stops us from being, like essentially the Kate Promoter has evolved quite a lot and for a single binding of the steps that it does, it's quite cramped. So we're now separating it, letting the pipeline generation understanding the cluster state be one thing and the actual steps of promoting, moving the changes from the workload from manifest to different environments as a separate step that could run as part of engineering, CLI tooling, but yeah, part of the pipeline. But what I was trying to say is nothing stops us from actually plugging in like flag or anything on top of that, which we, well, at least myself, I will be very keen on experimenting with that, but we haven't yet. But hopefully we got investment time, so hopefully I will do that. Any other questions? All right, we are at break now until 1455 CEST. So five till come back. Thank you. We'll be talking again. Thank you all so much.


So, in the previous lectures, having derived the equations of bulk mass conservation, the momentum equations, the mass transport equation and the energy transport equation, we are nearly, we are now ready to take up their application to a special class of flows which are called boundary layer flows. And I will be beginning with boundary layer flows which are in laminar state. So, the today's lecture is to derive appropriate equations for laminar velocity boundary layers and scalar boundary layers. The purpose is to derive two-dimensional flow and scalar transport equations, invoke the boundary layer approximations, write out two-dimensional velocity boundary layer equations, write out two-dimensional temperature and concentration boundary layer equations and then very briefly mention the methods of solution which we shall be developing in the course of lectures. Recall that our 3D Navier-Stokes equations were written in this manner d rho m by d t d rho m u j by dx equal to 0 and then there were three momentum equations, one each in direction x 1, x 2 and x 3 and it comprised of unsteady term, the convection term, the pressure gradient term, the diffusion term, the body force term and this is the second part of the stress term that gives rise to d by dx j mu d u j by dx i. Go further, we are going to make certain assumptions because as I said we want to avoid use of numerical methods and try and achieve as much as possible by analytical means. This requires that we make certain assumptions. The first assumption is the flow is steady d by d t equal to 0, but I am not at all suggesting that analytical solutions to unsteady flow are not possible but then our main interest in this course is to deal with steady flows in equipments and therefore I will take assume that d by d t equal to 0. I would say that the flow is laminar and perhaps the most important assumption here is that all properties, the intrinsic properties density and specific heat and the transport properties mu k and g are uniform. You will recall mu arose out of stokes stress and strain laws, k arose out of the Fourier's law of heat conduction and d arose out of the Fick's law of mass diffusion. We are going to say that they are all uniform that means they do not vary with position in the flow and therefore for all practical purposes they are constants in space. I will also now since we are dealing with two dimensions, I will instead of writing x 1, x 2, I shall write x and y by saying x is equal to x 1 and y is equal to x 2 and the dependent variables I would change to u equal to u 1 and v equal to u 2 and body forces which are essentially problem specific are presently to be ignored. So, with these assumptions then you will notice our mass conservation equation would simply because density is constant would reduce to du by dx plus dv by dy. I can go back a little to see if density is constant then that term is 0 and this term rho m du j by dx is equal to 0 would simply be du 1 by dx 1 plus du 2 by dx 2 is equal to 0 and therefore that would simply read as du by dx plus dv by dy is equal to 0. The x momentum equation or the momentum equation in x direction would read as rho times u du by dx plus v du by dy equal to minus dp dx plus mu d 2 u dx square and d 2 u device. This requires little explanation. For example, if mu is constant then d by dx j mu du j dx i would simply be written as mu times or if I may use the paper you will see that d by dx j of mu times du j dx i would be mu times d 2 u j by dx j mu by dx j mu by dx j mu by dx i that will be equal to mu times d by dx i of du j by dx j and that is 0 by continuity equations for constant density du j by dx j is equal to 0 and therefore this term simply vanishes. Now, let us look at this term. This term says that d by dx j of mu du i dx j for constant viscosity. This will be d by dx j u i by dx j mu by dx j mu by dx j mu by and in two dimensions this will simply be du 1 by dx 1 d 2 u 1 by dx 1 square plus d 2 u by u 1 by dx 1 x 2 square and with our replacements mu this will be d 2 u by dx square plus d 2 u by dy square. So, that explains how that term would modify. We will look at this term now for constant density and steady flow.   You will see now that how these terms have been modified to read like that. So, you will see in x 1 direction for example, there is rho m u 1 du 1 by dx 1 which is rho u du by dx plus u 2 which is v du by dy equal to minus d p by dx and the two diffusion terms that I mentioned. Similarly, in the y direction you would have that term. So, these are the equations of flow of a uniform property laminar two dimensional flow. We shall now invoke the boundary layer concept and this is perhaps the most important slide for you to remember. Now, the concept of boundary layer near a wall was first introduced by Ludwig Prandtl in 1904 to theoretically predict the drag experienced by a body when it was immersed in a flowing fluid, ships experienced drag, motor cars driving and motorway experienced drag, aircrafts experienced drag and these drags are substantial. You have to expend energy to overcome them and therefore, it is very very important that we know how much is the drag offered by a body when the fluid flows past it. Prandtl suggested that you do not need to consider the total flow around a body, but nearly concentrate on a thin region very close to the wall as shown here which he called the boundary region. It is in this region that significant velocity variations take place and it is the region in which viscosity of the fluid is dominates the determinant of flow. In other words, the viscosity viscous terms dominate very very close to the wall. As you move away from the wall, the importance of these terms becomes ever more negligible and it is these terms which mainly dominate in the far away from a solid surface. Prandtl called the thin and long region near a wall as the boundary layer region. By long and thin, we mean that the dimension lateral to the flow delta at any point x in the flow delta is much much smaller than x. That is what we mean by long and thin flows past a surface or an interface. The region outside where lateral velocity gradients are almost negligible is called the free stream region. In the free stream, there is velocity u infinity, t infinity and a conserved property phi infinity. To develop this mathematical interpretations of this concept of long and thin flow close to a wall, we are going to introduce dimensionless variables.  This is the Reynolds number corresponding to reference length l and the assumption of course is delta is much much less than x and u the velocity in x direction is much much greater than v. It is this condition which ensures that the in a boundary layer conditions or the properties of the flow at one cross section are influenced only by the upstream conditions. The conditions downstream have no influence on the conditions at a given cross section l and u infinity are simply the reference length and reference velocity. Each of these quantities star quantities is a dimensionless quantity and therefore, the equations would read like this. So, let us look at the first equation after non dimensionalization. So, you will see that d u by d x plus d v by d y equal to 0.    Likewise, let us look at the momentum equation.    So, what is this group? This is simply mu divided by rho u infinity l and that is nothing but 1 over Reynolds number.  The dependent variable would be v star and again divided by Reynolds number. Now, I am going to do an order of magnitude analysis of this equation. So, we said u is considered of the order 1 and x is considered of the order 1. Then, according to this assumption, y dimension would be of the order of delta and the v velocity will also be of the order of delta and that is what I have done. So, 1 divided by 1 plus delta star by delta star order of delta star and what this shows is that both the terms are of the order unity and therefore, neither could be ignored in this equation.  Remember here both numerator and denominator are of the order 1. Here both are of the order delta, but it is the derivative which is most important and both are of the both derivatives are of the same order. Likewise, let us do this for momentum equation. Then, u star is of order 1, u star d x star is 1 by 1, this is of the order delta star, u star is of the order 1 divided by y star which is delta star and therefore, each term on the left hand side is of order 1. I will now turn my attention straight away to the diffusion terms.   This term is much much bigger than this term and therefore, I will drop that term, I will drop that term. Now, this term as a whole is of the order of delta order 1. So, order 1 divided by order 1, this is although of the order 1 and this term is of the order delta square, but Prandtl did say that you must have effect of viscosity included if you wanted to predict the drag which means one of these two terms must be included. We have already decided to drop this term. So, if this term is included then if and all terms are of order 1, then Reynolds number or 1 over Reynolds number must be of order 1 or I mean order delta square so that Reynolds number is proportional to 1 over delta square which is a large quantity. Is that correct? So, that the delta square would get cancelled with this delta square and the total term would then be of order 1 and likewise I can say therefore, by deduction this term would also be of order 1.  Let us examine likewise the v momentum equation.  So, you will notice that the left hand side is of order delta square. We have agreed that 1 over Reynolds number shall be of order delta square multiplied by 1 plus delta star by delta star square and again you will see that if I take delta star common then I have delta star cubed is a 1 plus 1 over delta star square. So, you will see that the first term is again much smaller than the second term because the first term is of order 1, the second term is of order delta square and therefore, that can be neglected but the total term again is of order delta star. So, each term in this equation is of order delta square and therefore, d p star by d y star will be of order delta star square. So, we conclude then that in the x momentum equation each term is of order 1 whereas, in the v momentum equation or the y momentum equation each term is of order delta star. This equation as a whole can be ignored in preference to that equation which is much bigger. The principle deduction from this is that d p star by d y star is of the order delta star or can be taken as 0. What this says therefore, is that in a boundary layer in a long and thin flow the pressure variation is negligible in y direction.  I can measure the pressure at the wall I can measure the pressure at the wall in a given flow and I would get the quantity d p star by d x star and the partial derivative is now replaced by total derivative simply because the variation in y direction is 0. The conclusion from this slide is each term in this equation is of order 1 therefore, retain each term in this equation is of order 1. The only term which is not is this term the actual second derivative in actual direction and therefore, ignore each term in this equation is of order delta star and therefore, the equation as a whole is neglected. You will then see the boundary layer approximations that emerge. So, what does it say? It says that u star will be much greater than v star which we had already postulated. The gradient of velocity in y direction the u velocity in y direction would be much greater than the gradient of velocity in because this would be 1 over delta star whereas, this is 1 over 1 this is delta star by 1 and this is delta star by delta star and therefore, this would dominate over all these. We have already shown that the second derivative in y direction will be much greater than the second derivative in x direction both for u and v. We have also shown that the pressure gradient in y direction would be almost negligible and therefore, the pressure gradient in x direction which is of the order 1 can be replaced by either the pressure gradient in the infinity state that is the free stream region or it can be evaluated at the wall state d p star wall d x star.  So, now, just see for a moment if you look at this figure you will see outside in the free stream region the velocity variation with respect to y is negligible or 0 because u remains equal to u infinity outside the boundary layer. So, if I were to write this equation in the infinity state that is in the free stream region I will have this will become rho infinity u infinity d u infinity by d x, but this term would be 0 because d u d y is 0 and also d 2 u d y square is also 0 because this term vanishes in the free stream the free stream region is sometimes called inviscid region because viscosity is not allowed to play any part. The momentum equation written for the free stream region would simply be minus d p by infinity by d x equal to rho u infinity d u infinity by d x and in fact I can replace that term by this term these equations must be solved with and boundary conditions. Because there is a second order derivative in y direction and therefore, you need boundary condition at y equal to 0 which is y equal to wall and y tending to infinity which is the free stream condition. So, if u infinity x is specified one could readily replace that by this condition. So, when the equations are solved with appropriate boundary condition you would have u as a function of x and y and v as a function of x and y as a solution because this term is specified you now have two equations and two unknowns u and v and this can be readily obtained and what you are interested in is the shear stress at the wall which is simply mu times d u d y at y equal to 0 which is the local shear stress d x the average shear stress which is given as 1 over l 0 to l mu d u d y by d x divided by 1 over l will give you the total drag over surface l of length l. So, we have finished our discussion on velocity boundary layer equation. Now, we will turn our attention to energy equation and you will recall the energy equation given that we wrote on the last slide of the previous lecture. So, this is the rate of generation of rate of change of enthalpy plus conduction heat transfer first diffusion heat transfer or the heat transfer due to mass diffusion this is the viscous dissipation this is the pressure work terms and these are the chemical energy and this is the radiation. H m as you know is omega k h k h k is the enthalpy specific enthalpy of species k and h k is also given as heat of formation at some temperature t ref plus sensible heat C p k d t. We again invoke uniform property assumption in two dimensions the equation would read something like that let me go back a little.  So, you will see in two dimensions the equation takes this form and now if I first of all make all our assumptions that the flow is steady therefore, that is 0 h m which is h naught f or h k which is h naught f k and c p k equal to c p m and c p m t minus t ref because all species have the same property of the mixture and therefore, c p k is equal to c p m uniform mixture you have k times d 2 t d t square and if I ignore for the time being the diffusion equation or the diffusion heat transfer for a single phase flow non-reacting flow then or absorb that in this then you will see I get terms like this. Now, I am going to non-dimensionalize these terms.  So, essentially you get that term sigma omega k h naught f k and that is equal to heat of combustion plus c p m t minus t ref and therefore, this term essentially is accounted by the chemical reaction and I can replace h m here for non-reacting flow as c p m t minus t ref. What I am done now is I have said define t star equal to t minus t infinity divided by some reference temperature difference.  That is what you see here the terms are written like that.    The third term the pressure work term the viscous dissipation term is somewhat important in the sense that you will see now that if I were to divide through again then you will see that mu u infinity square divided by l square divided by 1 over rho m c p m delta t naught u infinity into l.  So, essentially it is joules per kg joule is Newton meter by kg Newton meter by kg Newton is kg into meters per second square into meter divided by kg.  So, remember c p m delta c p m delta t naught and u infinity square both have same units and therefore this is a dimensionless quantity. Professor Eckert define a quantity u infinity square by 2 which is the kinetic energy divided by c p m delta t naught which is the sensible energy as Eckert number E c it is called the Eckert number E c and therefore you will see that it is at the moment u infinity square by 2 diversity. So, essentially you get here Eckert number divided by Reynolds into all that what about the pressure gradient terms here you will see only a multiplier E c. In other words the dimensionless equation tells us that there are now three parameters associated with heat transfer one is the Prandtl number the other one is the Reynolds number and the third one is Eckert number. We can readily see if the Eckert number were large both these terms would be important if the Reynolds number is high and Eckert number is small then we can ignore these two terms the pressure work term and the viscous dissipation term. So, with this equation now I can do order of magnitude analysis because it is now in dimensionless form. So, what is the order of magnitude analysis that I do?  So, both the terms on the left hand side are important right hand side remember this is 1 over Reynolds number Prandtl number into 1 divided by 1 square plus 1 divided by delta star square and therefore, that term would be d 2 t star by d x star square will be much smaller than d 2 t star by d y star square. So, if you follow through in this manner you can carry out the order of magnitude analysis and the resulting equation would be simply this rho C p u d t by d x plus v d t by d y equal to diffusion only in y direction plus viscous dissipation due to velocity gradient in y direction plus u d infinity by d x plus q dot cam plus q dot rad. This is the boundary layer form of the energy equation a note on Prandtl number. Prandtl number as you know is the ratio of C p mu k which is also if I divide both the numerator and denominator by rho then it is mu by rho divided by k by rho C p on that is equal to nu divided by alpha or kinematic viscosity divided by thermal diffusivity. So, it is in a way the ratio of the rate at which momentum is transferred divided by the rate at which heat is transferred and in boundary layers this diffusion is taking place only across the boundary layer, but then you also notice that Prandtl number is the property of the fluid it has nothing to do with the flow and therefore, we can classify fluids according to their Prandtl numbers close to 1 close to 1 and little below say from about 0.5 to 1 you usually get gases. From about 3 to 10 or little over 10 is water, but if you extend that to about 100 you will get many organic liquids included in this range. If the Prandtl number is much greater than 100 then usually you will encounter very viscous oils because Prandtl number has viscosity in the numerator and usually oils have very large Prandtl numbers. On the other hand liquid metals like mercury, sodium, liquid potassium which are used for high heat flux heat transfers as obtained in for example, breeder reactors liquid metals are preferred and in those cases their conductivities are so high compared to their viscosity that liquid metals have very very low Prandtl number. There are not many fluids in this range but from about let us say 5 or into 10 to minus 3 to below you essentially get liquid metals. So, you have liquid metal range is very low Prandtl number, gases very close to unity Prandtl number, water and organic liquids between 3 and about 100 and oils much much greater than 100. The mass transfer equation can likewise be derived I am not going to the details and it reads in like this. It can be non dimensionalized and instead of Prandtl number you will have a Schmidt number. We will take up all this when we come to mass transfer and therefore, I can summarize now what we did in this lecture. We started with the derived 3 dimensional forms of the equations of bulk mass, mass transfer, momentum and energy and reduced them to the boundary layer form which contains two convection terms, one diffusion term in y direction and a one source term. It is good to get used to this form of generalization of the equations. You will see for phi equal to 1, you will simply have d rho u by dx plus d rho v by dy and that term would be 0 and s phi is 0. It is essentially the mass conservation equation. For u phi equal to u, you will see that this term is simply the viscosity and this term is minus d P infinity by dx. For temperature, this term can be taken for phi equal to temperature. This term can be taken as K m divided by C P m and all the right hand side will be divided by true by C P m and for species K this. Now you will recall from your undergraduate studies that any two dimensional differential equation written in the form a into phi x x plus 2 b into phi x y plus c into phi y y equal to some source term right hand side which may contain gradients of phi and so on and so forth. Then the discriminant b squared minus ac, if it is 0 then the equation is called parabolic. If b squared minus ac is less than 0, the equation is elliptic and b squared minus ac is greater than 0 then the equation is hyperbolic. Of course, we are going to assume that gamma is constant because we are dealing with uniform property. So, we have only d 2 phi by dy square term that means c is finite but in our equation a and b are 0. Therefore, discriminant b squared minus ac is actually 0 and therefore, our boundary layer equations are parabolic and for such parabolic equation there are three methods of solution. The first one is called the similarity method in which the partial differential equations are converted to ODE's ordinary differential equation integral method similarly and then the numerical method finite difference or finite element. We will take up these methods in the next lecture.


Your coca-cola bottler presents Claudia based on the famous play and novels by Rose Franken Brought to you transcribed Monday through Friday by your friendly neighbor who bottles coca-cola Relax and while you're listening refresh yourself have a coke and now Claudia David aren't you gonna have a second cup of coffee? What for?  Oh, but you love me. Oh David isn't it a lovely morning? Oh, it's lovely. Very lovely. It's raining cats and dogs raining who cares It's lovely inside. I hope mama's headaches better. Of course it is Isn't it a beautiful moon last night? Oh, not bad. I love you even more when you try to be off-handish Oh, I feel so good this morning. I don't even mind the rain Well rain and no rain Off to work. That is the only blot on the Scotchian Scotchian, you don't even know what a blot on a Scotchian is. Of course I do. It's a fly in the ointment You're catching that train every morning is the fly on our Scotchian I thought you were going to say I was catching flies every morning I wouldn't make any sense to anybody including me. Well, then you're not as bright as I am. No, I I guess I'm not Say isn't this house cozy in the rain cozy when it isn't raining. That's because it's well insulated Beautifully designed to we had a wonderful architect. We did Pay them enough I Couldn't find one I'd like better neither could I then all the entire world I couldn't I think we sound crazy to listen to it We seem to like everything about us and like everything we have why not would be crazy if we didn't Oh There's Fritz time to go. Is he driving downtown with you? No, he just had the car out this morning Oh, I forgot to tell you I'm leaving it at the station garage for greasy Boy, we'll bring it back. Good. I won't see I got I won't need it this morning Anyway, and if I do need a car which I won't I can use fritz's truck You feel very swell driving around in the truck. Don't you it gives me glamour What did I do with my keys? Have you got the keys? No, they're in the car. Oh, oh Fritz was driving it. I forgot that now. Don't you come out of the car. You'll get all wet I don't care good morning, mr. Not oh good morning fritz. She's all filled up with gasoline I had her downtown already. Oh, you're certainly up and about at the crack of dawn for it Well, I do it with rain. Good morning fritz. Good morning, Mrs. Norton. Hey, David Drive carefully now since when are you telling me since always? Well, I'm I'm not a woman driver. That is just an accident of birth.  It's raining. It's pouring. I told you to skadoodle into the house You'll catch your death of cold. I got off to doodle if you kiss me a decent. Goodbye. Yeah Mornings are so nice until you leave the way they should be Well, let's see if I got everything or I've got to take this back to the store clean handkerchief Clean nose. See you on the 540. Clean ears. It's a date Mrs. Norton. Oh I don't need to interrupt you. You're not interrupting anything. Good morning, but your mother. I bring her a tray up to bed.  I'll go out and see if she's feeling better.  There it is. Goodbye. Now get back in the house you dope Certainly looks handsome in a car doesn't be better. He looks handsome without a car as a matter of fact He even makes the car look handsome. I Suppose is his profile Goodbye. Goodbye. Goodbye Never change. I hope Such a wonderful world for them who see it it is Even in the rain. Well, that's because our house is so well insulated that is because your hearts are not so well insulated. I Prepare the tray now for mrs. Brown. Oh, um, I think you better wait Bertha. She'll think we're trying to keep her in bed I'll go out and see. Well, I I make out the marketing list. Mrs. Norton. Oh, you are going downtown. Yeah, this afternoon Mr. Norton's having the car fix this morning, so we have plenty of time I'll be down in a minute Bertha. Oh, and you might make a little extra coffee. I'll have another cup with mom. All right with Yeah, what are you doing? Are you in the icebox again? Yeah, just for a glass of milk, huh? You'll get fat. No, a man does not get fat on a farm He just gets healthy and strong and he stays young forever You are kidding yourself. You are pretending Bertha, but you feel like I do. Yeah, I feel like you do black wood Well, I'm not superstitious But I pray it will not change just like a woman. They do not want change. It's what you're going to do now Well, it's raining too heavy for me to work outside. I think I go up to the bar Mr. Norton does not know but I am preparing a painting and pre-building For Christmas we we buy them something to go with the barn. Yeah, huh Christmas like in our own home But we talk too much Christmas is not for months Now I must prepare a tray for Mrs. Brown Bertha the telephone The telephone Mrs. Norton she will answer it. She's upstairs in her mother's room. It doesn't ring up there.  Oh, that is what you think. I understand better Well talking is more important. Well, I will not argue good. I answer Mrs. Norton's residence Mrs. Norton Who is calling her please say there's been a wreck in accident about a mile and a half down the road Yeah, Mr. Norton's car and George Mason all terrible smash up both cars wrecked. Yeah, yeah Looks so funny Well, you tell Mrs. Norton I think she ought to get down here fast about a mile and a half down the river road Yeah You better warn her. It's pretty bad It's an accident. Yeah It's bad. I know. Yeah No, I go see about it first alone. Yeah, maybe Then you will tell you. Yeah, I go now Looking so solemn Who calls and Mrs. Norton I read What is it? Better you tell her It's been an accident David McCartney. Yeah, I'm going in the truck. Tell me fit. No That's all we know now. You stay here. Mrs. Norton. The fritz will will telephone After coming to kitchen with me until he come out. I'll go with you No, no, no, no better you stay now. I'm all right Mrs. Norton, are you sure? So almost as if I knew last night This morning was too perfect here. Take my jacket and the truck is out near the kitchen door Well, I I come to our telephone you better and Bertha, don't tell mama Don't tell mama it'll be all right. I know it'll be all right because it must be Everything was too perfect. I guess I'm ready for it What's no, don't forget to telephone Roll up the window Mrs. Norton or it will rain in How far is it fit? Well, it's just a little way down the road It's the rain it makes everything so slippery. I Had a feeling fritz Yeah, it is the rain. I Never minded the rain But Steve do you believe in premonitions most intelligent people do I Tried not to believe last night, but there was a moment when it was Just like saying goodbye But weren't for that moment Couldn't stand I I know please don't even think like that. You're right. I I mustn't I Faster fritz, please drive faster See people just just a little ways down the road. There's a crowd. Yeah. Yeah, that is it Don't look mrs. Norton There's a car upside down in the middle of the road. There's a house Mastodon's the stone wall But you are all right No, yes you are mustn't let go David wouldn't want me to I think he would want you to cry a little no no It is a great and terrible thing that has happened to us mrs. Norton a great and terrible thing Man be quiet don't let me break down fritz David wouldn't like it really. He's he's always so good in emergencies It's I don't understand David always drove so carefully we will see ask that man Yeah, what was happened? Yeah Be the step on the gas down at the doctor's then maybe Brung down there and it was all mason's fault. He smelled liquor on him when they picked him up And it wasn't David's fault where we go now Help me out now control. No, don't stop the car drive quickly Just get there David. Don't let me think David. Please keep me from thinking we be there in five minutes I'm all right. Of course. I'm all right. I I have to be David knew I'd be he knew it last night Of course, I'm all right. Of course. I'm all right. Let yourself alone mrs. Norton. Let it come I don't feel like crying. I just I just don't feel Maybe because I've already said goodbye. That's all right. Don't let yourself think Everything changes in just one minute doesn't it? Well, that is life now. You sound like David. He understands Yes, he understands now. I understand everything can change in just one minute And there's nothing anybody can do about it Except pray he's drive faster Happen to be having dinner the other night at a home where there was a teenage youngster I drove home with the man of the house and he stopped to buy a case of coke As soon as we carried that case into the kitchen his daughter dashed to the phone called up some friends and Before we sat down the dinner. She'd cooked up a party Give young people ice-cold Coca-Cola and their social life is off to a good start Mr. King you haven't heard for mrs. Norton of wits. Have you know not yet? Oh the reading is terrible I hope I hope when we do hear you don't have to say it We're all missus.  Maybe she has learned enough already Well, I see you tomorrow. Mr. King and with good news. I trust.  Brown? I think I will but first I just want to say that every day Monday through Friday Claudia comes to you transcribed with the best wishes of your friendly neighbor who bottles Coca-Cola So listen again tomorrow at the same time And now this is joking saying or a bar and remember whoever you are whatever you do wherever you may be When you think of refreshment think of Coca-Cola or Coca-Cola makes any pause the pause that refreshes and ice-cold Coca-Cola is everywhere This broadcast of Claudia was supervised and directed by William Brown Maloney And now here's a word from your friendly neighbor who bottles Coca-Cola