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that has been hired, promoted internally. Mike has been here seven years, about seven years. Just over six. Just over six years. Mike came from our maintenance position in a couple of different areas that they determined, but he's now our properties manager. So he's managing this field along with every single one, but he will be maintained. So with these two managers in place, Dave, Dave and I introduced our last two, which is our field and our operations manager, Stacy and Andrew. So now with Mike and all of us, we have a management team to take over the day so that we can start looking into the future. Great, so those are the introductions. We'll move on now to the agenda. Do I have a motion to approve the contents of the agenda as opposed? I will move that. It's been moved by Ellen. Is there a second? Second by Robin. Any discussion or proposed application to the agenda? Hearing none, I'll listen. There is a speaker who's saying hi. Hi, hi, hi. Extension, we've got two, I have three public form. See any groups of the publics? We've got a proposed public form. We've got an item four consent agenda. If you want to just make a brief note that we have to move the appointments data to the director's report, the rationale for that is wherever it's, where I was talking about that versus a consent agenda item, we don't talk about a consent agenda. So that's why it has been moved down to the director's report. So it makes just the minutes as the only item in today's consent agenda. So I'll entertain a motion to approve the contents of the consent agenda. So move. It has been moved by Ellen. Is there a second? Second by Chip. Any discussion? Hearing none, I'll listen. I'll be able to see the publics saying hi. Hi. Eight votes. Extensions, we move on to item five. Action items. The first is the budget neutral end of it. I would be willing to entertain a motion to work together for clients in the city council, the approval of the budget neutral end of it and it's outlined in our meeting. Back. So move. It has been moved by Ellen. Is there a second? Sorry, a second by Jeff. Discussion? Nick? Marie extends her apology. She's not able to make today's meeting, but she worked very diligently on this budget amendment and then I'll brief on the financial report later on as well. We're halfway, just about halfway through the year, well, more than halfway through the year. And typically we'll bring a rather large budget amendment, budget neutral amendment to both this board as well as the board finance city council, which are the steps after this. This is a $331,500 ultra amendment again, neutral. So we are truly just shifting some of our expenses that we no longer have been meeting into out at once. We did highlight some of the big ones in there, including everything listed in this particular memo. I do want to just call out one in particular, which is efficiency. I just want to make sure that it's well known that we are reducing the energy efficiency number by $180,000, which is the... The energy efficiency line of them is a capital account. So we weren't able to use that account, start a capital account when we purchased these vehicles. So merely make that energy efficiency line so that we did purchase those particular items. We didn't need it. Other than that, there really is just multiple accounts being moved around, as you can see, with all those fine items, some being increased, some being... So putting the money where we need it as we project the rest of the year and it's taken away some of the new funding I think that's what we're going to suggest. I'm sure there's any discussion on that. Thank you. I was just going to add, one last thing we're probably going to bring back another budget limit also to the end of the years. Can you explain again, is it why you did not use the energy efficiency for the purchase of the three cars? And I heard you say that it came out of capital. Was that a counting requirement that it do that? It is because we capitalized those things so that they'd appreciate which is not able to go this particular kind of different with our operating, O&M operation and maintenance counter. I'm sure there's nothing else for the income side of it. I think my only question on this is, I feel like we see this every few years that when we do a budget and then funds seem to come out of repairs and maintenance and that's $150,000 we're taking out. Can you explain what makes that possible? Are there things we're not doing or are there things we're getting deferred? Always a new question. This really has to do with our parking garage, lighting and our arm system repairs. We over budgeted this in, so we're actually in 25th of Antion in 24 because we weren't 100% sure the basic of that project was going to be. Essentially that project increased that repair and maintenance line item at close to $2 over multiple fiscal years because of the timing, because of working with our contractor, shutting down the project during the winter time and really tying this to what the projected expenses are going to be for the rest of this fiscal year. We were able to reduce this by $150,000. That doesn't mean any of our other deferred maintenance are other areas of our trip. That's just where this particular project did not mean any bad amount of work this fiscal year. You're going to see it in fiscal year 2020, God. Let's just have a discussion. Here we go. I'll just start with a question about the utilities. Was that an additional charge because the space has increased or is that related to the cost of electricity or is it certain that are paying bills? Yeah, there's a couple of utility line items and they're both gassing in case water, waste water, the line items in particular. I don't know the particular reason for that. I can get to you, Melanie. I don't know, just not. But it was a 14,000, it looks like a 14,000, God. I can increase to that. That is for, that is slightly for this story. I'm going to turn a building in some work other than this game part as well, which are some of these charge account codes on this side. I was just going to say, if you want to increase the heat in the summertime in this space here, then I'm all fired. I'm not that doesn't need to be as cold as it has been. Thank you. All right, questions, any other discussions? All right, seeing none of those in favor, just keep on saying aye. Aye. Aye. I think we do have a motion to comment. Okay. Wish I can just add that we do have a motion for a motion for a motion of aye. And the motion in favor of motion, that is our motion. We have a motion for a motion for a motion that said aye. Yes, sir. That is not going to say aye. Yes, sir. Aye. Aye. Aye. Aye. Aye. Aye. Aye. Aye. Aye. Aye. Aye. Aye. Aye. So that we are working on this program with Hudson News or more formally, the Hudson Group, Darlington Joint Venture, which is the HG for going to JT. So they actually partner with a woman-owned business, somewhat local. So not all employees at Hudson News are actually employed by us. We have some employed by the joint venture. Anyways, as part of our North Terminal renovations, what we've just opened up, the exit lanes, expansion of the space, we are working on really utilizing that space for not only steaming pancake and working with them on update, the restaurant space around their system location. Hudson News was also impacted as well. And we asked them to temporarily relocate in that space. They're in a temporary store right now, which is literally up on the stands almost. They cover them with the security closet and that's about it. It's not the most aesthetically pleasing, certainly not the best customer experience right now. However, while we're negotiating that, Hudson wants to reinvest in this airport at close to $700,000, but in exchange, they need to enter 970 piece extension. There at least currently does go until 2028, so they have four more years. So they're looking at 14 remaining piece out there on their ability to put in that $700,000. The new location is essentially where the old security jet one used to be. So it's a much larger space. It's more central to the majority. Sears in the North Concourse. And once again, they're putting in a significant fund to make it more pleasing to the customers and offer additional products, including offering over 50% of products. There really isn't anything else that's being adjusted in the lease except the amendment to extend it by two, excuse me, extend by 10 years with the annual store. And that just went up 1%, right? The two to three? Did that rate? 2%. So the minimum annual guarantees go up 2% annually. They'll go up to 2% annually. They'll continue to remit payment at 13% of their gross sales back sales. But they're guaranteeing us whatever that matter. I don't know the last time, since I've worked here, when they were at the end of the day, they were always much higher. They closed places in airports, make out pretty well. I'm sorry, I was just supposed to do that. I'm sorry, I'm sorry. I didn't mean to. Well, I'm going to make that. I'm going to make that. Right, commissioners, any further comments or questions for the next item? All right, hearing all of those in favor, we say aye. Aye. Any opposed? Stenctions. We're about to add 5.3 snow removal equipment. I'd be willing to entertain a motion for recommended board and client city council to purchase the word we plow. That's how I'm going to keep that in. All of them. All of your roll, Allie. Well, you know, it's kind of, you know. Yeah, I know. I know. I'm just checking it out. So discussion over the day. Sure. Great. This is a primary piece of equipment for us. This place is 1999, older, much older piece of equipment that we do, Decommissioned Actual Souls. This is a 7,500 tons per hour piece of equipment. So it's a massive stuff over that we desperately need to maintain our apparently more services. We did have three betters for this RMP and MV was the winning better, which is a 26, 579 lead time is about between four or 500 days. So we want to bring approval now. This is a different federally funded program through a passenger facility that chargers, so we are going through the final approval process with the FAA. Essentially, if you purchase a ticket price on that ticket, it's a $4.50 in charge per leg of your route. For this particular leg outward to Burlington, that money is going to go back to Burlington at $4.39. So we get a piece of that. We're talking about $2.8 million a year in revenue. However, we need a approval to give me that funding, as well as to spend it. So that's what this piece of the book is being funded. Are there any snow clouds at the military side of the airport now? There are, there's a couple. OK, so is that part of the combination of which is required for snowmobiles? No, they're separate. They take care of this area of people, it's very important. They don't do the runway, but they don't do the runway. OK, so this is really good for the runway. Yes. And why is that? Don't they take off on a runway? Because you might want one entity on the other side of the airport to be controlling the ability to clear the runway for the air. That's right. We have a very different course than the military does. And most of the time, it's going to be pretty important. But we have responsibilities under our certificate to clear what they just call the priority services. We actually have three priorities out on the airfield. The flight is passively, it's to and from essentially air, carrier, usage, spaces is essentially our priority services. Did they contribute at all? Monetarily to purchase it? They do. Yeah, so every expense on the airfield, we take all of our expenses, whether it's normal, painting, anything out there. We put that in one cost center, other real cost center. And then we allocate that based on ratio of operations. So when we go through that calculation for the lease, for example, and then they go through the calculation for fire department use, we see which one is more expensive. The fire department is always more expensive because their ratio is to about 6% to 10% of total operations out of the state. So do they pay directly for it? And what will we get from that? To make sure that we're not being underfunded for what we're getting out of the state. And it makes you really, really happy to know. We can clear our runway faster than the stair forts of our size. For what? For the real good. Our resources, I think, has accrued for our airfare and our conditions and our winter conditions. Perfect. I concur. Yeah. That's great. Yeah, that's good information. Dave and I, and I know that everyone has a trip. But we do visit other airports, especially in the North. I lean on them a little bit. Other directors of New England area, I quote, but this particular airport we went to did not have these, I think so. But they had separate pieces of equipment. This is a blower that we're talking about. Most of our way at five other units called multi-tasking equipment or super shoes, as the group calls them, which does really three things at once with one operator. Other airports are doing three things. Right, three at once. Yeah, so these things are very, very fast. Actually, Jeff just put out a completely awesome video about it yesterday at a cross-sectional company. Yeah, that's great. Great, Sparta. Yeah. This question, actually, does the old one just go like, does the money line just be like a depreciation piece, or does it offset the cost of the agent, though? And no, not really. It's a revenue because we sold it. Surprisingly, we sold it for $16,000, which is way higher than what we thought we were going to get. Yeah, it's 24 years old. It's 24 years old. It's not operational. It was a part. It was a little bit. It was in pieces, but it's somebody I think was smart. And I don't know if this company is still making some orders of that. I don't know if that's true. I still work in the streets. I think the crew called it the company's rider, the circus rider. If you sit on top of the plan, it would be like, whoa. It was a box, a sculpture. Yeah, and then you have to put that inside. Yeah, the audio cut out a little bit. Nick, can I just ask you to clarify what I think you said? I heard you talking about this expense goes into the bucket, you know, the cost, the control center. And then I heard you say they're allocated based on, and then you cut out. So could you maybe clarify? You know, the cost, the control center, and then I heard you say they're allocated based on, and then you cut out. So could you maybe clarify? You know, what is the guard covering from a perspective?  And if the fire expense is greater than their allocable share of other costs, in essence, it's a wash. It would only be if those cost control costs exceeded what they're contributing toward fire and rescue, that a payment would actually be made. Beautifully said. I think you got it all correct there. And that's in the beginning part, that's exactly what I was saying. We take all of the expenses for the airfield cost center and allocate it based on the ratio of operations. That's what I didn't hear, ratio of operations. Okay, thank you. Around that 6% to 10%. When we were going through the lease conversation, there was some public comments about how other airports were receiving payment on the lease close to $200 to $300,000 a year. That is that calculation that's being done. Those other airports never had fire and rescue services. So that's why there is a payment. And the same thing would happen with us, but in this case, if our costs are lower than their costs, then there is no, there is no exchange of funds. Thank you. Thank you, Oscar, Dave or Dave on this. Right here, now I'll close the paper. This is my best hangout. Hi. Those extensions, we move on to item six, which is the construction update. Thank you. That's in there, everybody. So we have a busy on working on our own closeouts and grant applications for this year. The DMA is willing to adopt our dollars to get back so we can fill those closeouts and grant up so we can receive those funds. So we're expecting the projects we're working on, the concourse, the North Concourse Replacement Project. We had a pre-application permitting meeting with the joint department, planning and joining with the city of South Brooklyn yesterday. We had a 60% page turn of plans on every page today. The airport staff, so everybody got a feel for what we're doing is, you know, what's there, what's not there. Anybody could ask any questions. That went very well. My third grade, J. We had to simply apply for our permits. Next month, we hope to be on the DRB in March. We hope to be pricing by early March so we can apply for grant and closeouts. So that's moving along for progressing for large projects. The XRE building design project is, all the field work is basically done, that's tabulated and the site grading and utilities plans are coming together and that's progressing for long. Also, willing to tech center, that's progressing along. We also had a pre-application meeting with the city of South Brooklyn yesterday for performing in that. We're probably even a little bit ahead on that with respect to the beginning for everything that there's not, there's at the extent of, you know, it's an existing building. So it won't be an extensive pumping process for that. The runway 1533 improvements are rehabilitation projects. We're at 60, now we're seeing 60% design and we're about to schedule meetings with the air guard, the tower, the airlines and all that. So we can start planning for that construction which is still, you know, a year and a half, a year and a half the way down.  So there's a lot of planning that goes into that. There's also a new safety management system plan that has to be done for that project to hold separate new process to new. So we've got to work on that as we come up with it. The airfield management update, it's just about, we were just waiting on the report for that. And I guess we were talking about the new president's office, he's programing the quality of the project. So, other than that, we can't really think of any reports. Do you know where the hotel is? Is that somewhere away from here? They are making a lot of progress they have to redesign it with some other bank not information again. This is DW corporation, so it has not received the RV approval, but we're hopeful that that's going to continue this winter into spring. And still we don't try to have troubles either mid or summer. 2020, okay. Any questions? I have a new product to me, it says that they're available in Korea. They're actually really disappointed for me. For the volunteer test center. They enter another different grant process, et cetera, that he worked on. There's a whole $10 million set aside for that school grant for that project. Not a new one. This is the same congressional director spending that they were appropriated a few years ago grant. My understanding is they do have a grant and it's not for us. They're just implying for the permit through this ASF-Brenton active 50s, so we're going to get them all fire-punched. Right, right, right. And so that's the way I understood it. The way it's worded is the Burlington School District has been given award of $10 million in which they are in the process of applying for. Which is true. Which... They already have it based on what I understand. So they know it's... We'll double-check it. I think they have the grant and we'll double-check it. It's been appropriated to participate in this. Similar to us, similar, quite right next, where we don't have to go in for that particular project, but we have the appropriation and the federal bills to award us the third. They still have to go through the application process. That's the same thing. These are two different pools. They're not getting theirs from FAA. Right. I'm actually saying the 10-9 doesn't 10-9 doesn't even change the last three years. That's right. I don't know what they're going to do. What do you mean just to them? I mean, right, if there was another 10 million land, we might need it, you know, for that to happen. I'm just saying. That I would be. We are not part of the sex conversation side. We're just working on the project now. We've committed to permitting in the initial design but we've said we're going to do that in the future. And so, we're helping the government. Mr. Sandy Oscar-Lehrer. Quick question out of the DIC. Number 13, the purpose of this project is to improve the glyphos system. Can you just expand on that a little bit? Is there a problem with the current system or what do you mean by improve it? What's happening on number 13? The DIC? That's what I was saying. I think it's. That's right. OK, so for years now, it's been to improve that system, minimize the glypho that's going into the ground for three of it. OK, so the next step is to design a smart system that takes more heavy, heavily concentrated stuff we collect and send it to a frat tank site, right? Then take that frat tank and send it to the former main and have it recycled so we can reuse that material and then send it back to us and we can use it again. So this is, I mean, since I started working here, we never thought that that was the ultimate system that we should have and we should. So I know this grant that we can't do a couple of months ago about the respect of the state, federal government for stormwater. Part of that money will be used to an evaluation of the facility to determine some options you might have to improve that system. And then from that standpoint, we work with the FAA to get them to say, yes, this is the fundable. We'll apply for a grant for full design and construction of that system. So that's been on this list for a long time. It's time to go back and forth with the FAA, but it wasn't fundable and we always thought it was the back to it is. So we want to, we need to do better, we have. Right now, we're doing everything that's a viable under the climate. But like Larry said, there's there's systems and technology out there. Yeah, Larry, Dave, myself, Kurt went out to Portland, Maine and that airport, although they had much more significant issues with climate all discharge, we don't. But they, they literally do that. They deice the aircraft on a particular apron that deice explode goes into the catch basins, pumped into a pretty much a distiller oil down essentially. And that heavily concentrated stuff gets pumped into glycol tanks where they have the oil to start spraying out there. They get shipments from Newark, New York City, all over the Northeast. And they do that, because they're one of the, that does that. It would be a wonderful to have a full system like that here. Of course, it's cheaper, but we would have to try. That have a concentrated material out to a facility. And it's going to take us a long time. Yeah, it's good. It's really right now, I'm not actually able to put it plan that size just to distill this material. So it will stay with do truck it out there. We don't do that right now. It just goes into a tank and it just sticks to the ground. Yeah, it's it's like all that's into it. It's it's it's it's it's probably it's probably it's probably it is. I'll get you two plates of ingredients. This is Madison now. Hey, I'm not sure. It's something that's being approved. Okay. It's a different set. It's a different set. Okay. Anything else from there? Just a quick follow-up. Is there anything else on guard today? Do we de-ice their plants? No. And just to clarify, we don't de-ice any. All the de-ices will come from heritage. Really, FedEx does their own de-icing. And then heritage has all of the air character operations. And there's small operations. Like from tanks every now and then. Most of it. Dude, the jets, the fighter jets get de-iced or don't de-muted. They're basically kept inside. So you don't have to de-ice when you're inside. And then when they go outside to go over, they go really fast. And then the other practice, they're not going to find those. And again, they're all kept inside. So the reason we have to de-ice the airliners is because they sit overnight in the snow and the frost and then, and so they put off the first layer, but you can't have anything adhered into the wings to save the takeoff. Whenever you're sitting in the airline, you usually see two of the colors being sprayed to the aircraft. So there's various reasons why the aircraft, so there's various reasons why those two different types of de-ice are needed to go over. So it's to get rid of it so that it doesn't continue to stand. Thank you. It's all about the time after they spray, they get to the runway at takeoff. And because we're in Rovington, we always get held for whatever big airport we're going to from here. So that's why you get held longer.  I think you're safe. One of the places to use toys. Yeah. Yeah. Yeah. No. No. No. We've got to proceed. So I'm not going to play with this. That's all I can do. Okay. Anything else for Larry? Larry off the door to item seven, which is the most comparative ability for them. Okay. Thank you all for your time. Thank you. Thank you. The big news is. Sign-in isolation program. Projects. One of the days two are necessary. We will be completed this week. Next week or the week after they will do the testing to make sure we meet those requirements for some reduction with the homes. So I guess everybody is. Positive that we will because the world knows the moving forward. With respect to next year, the phase three, the grant we just received are out which is a little bit slow to start, but we're in the number the 40s now with regard to to do people signing up to have their house insulated or sound and go with Spain. And we're working towards that 50 so we get it out to bid and grant it by mid-April first of the day. So home workers are alive. We need to try out different avenues of getting to these people, some people hasn't said, you know, and keep going down that list, you know, so it was a little hard getting to that, but we are now even going to the door to make sure people are signing up. So we want to make sure we keep moving forward out. And as far as noise exposure, Matt, we were probably going to have our folks phone this month, speaking with the board to the technical advisory committee, and we're waiting for this and now we just brought that one. Bren, we did get your email too, so thank you very much. That should actually be outdated either right now or tonight. Great. I appreciate that. So what's the new date? We don't have it yet. Okay. The audio was just cutting out, so I didn't catch that it was to be determined date. Question about the finding, you know, the remaining 10 homes. Is there, do you have insights on, is there language barriers? You know, what additional kind of support can we offer to help get those selected? You know what, that's a really great question I think between South Burlington and what you see, I'm not sure what the ratio is. It might be helpful to start coordinating with either your clerk chargers office or even just website scenarios so that way people can, if they go to your website, they know there's an option available to sign up for the program. I don't think the last 10 are anything specific that's not letting them sign up. I think it is just a matter of they either don't know or they're saying no, so we have to continue to move on to the next one. So people are waiting also to see how it goes for other people. Are you, for the folks that are saying no is that, are you getting like some type of document signed to acknowledge that or are you kind of using that as initial no and then coming back around to them? What's the process there? The latter. If you say no, that doesn't mean you're out of the program. That means today it might be, no, you might not be in this particular grant round, but we're going to come back to you for to ask again. Are these single family owner occupied homes or are these rental, multi-family properties? What are, what's the demographic? I think this year is the first, or this round anyways, is the first round that a lot of homes were in a new scheme that were multi-family or apartment, more than two units per building. Okay. We do have landlord registry. We might be able to distribute some information through to landlords through that registry. Obviously that goes to kind of the broader list and not necessarily the specific eligible properties, but that could be a resource. I don't know if you're connected with our housing director or our public outreach director to kind of brainstorm around mechanisms for successfully contacting the homes, kind of addressing any concerns or hesitations or anything like that, but let me know, let me know how I can help. That, that'll, it's time to do that with Minozki. So yes, thank you. Yeah. Absolutely. Just to build on Bryn's question, when, when people say no, what are, what are the most common reasons? Well, initially, the first one I tend to see, because there were people in the system, second is you want to see how people go before the house to do that. So I think those are the two main reasons. So we've met a couple here and there, I think that just don't want to participate. They just upgraded their own windows or, or just upgraded or renovated, etc. And so I'm just, they'll reset all that. It's a huge disruption. I replaced one window and I thought I was going to lose it. It's very fast. But they bet that's probably the thing that don't believe because nothing actually happens. I think I have a lot more to say. It will, because I mean, you know, once we're out, I think these people did a nice job getting in and getting out and keep people aware even though we had some delays because of storm windows and storm doors. They were well informed. Breanna, who supports the jungle fans, that's out there. Don't want people to do it at door, it's keeping everybody warm. Yeah, but they don't start anything to let all the stuff, right? Take your job.  Yeah, I can't get that window there. Yeah, that's not happening. So they got it. Even if there's still in there, it's waiting for them. Correct. People then, and talking to people. Are the people who have had it done, and you noted that many of you are very favorably impressed? Are you using their comments or experience as a sales pitch? Didn't it be well to get in and send a page or something? Yeah. There's a good article, a good testimony of people that were in the middle of the renovation. I think that, of course, is from the people who just waited it. That's why we really wanted a Michael House setup as well, because it's really hard to show this with a private house, of course. So we do want a house in this neighborhood. It's a life estate property, and that property will become the model house working with a house, of course. So if you walk in and say, oh, this is what you need, you can meet with our consultant, you can see what type of windows you can choose from or doors or just different styles. This is also going to be a random amount connected to the landscaping program eventually, so that there's also a station at the same station as water, things like that. So it's a multi-use standard office for our folks to be here all the time. I was just wondering if there was a one or two-page flyer or FAQ or something like that that might help. Again, just kind of demystify what to expect, what does this mean, what's the timing, how disruptive would it be to people's homes if they work from home? Just not knowing what people's day-to-day living situation is, how many people are home, how many kids under age are home. Just thinking about some of those demographic factors that may play into some of their perceived barriers. Breonna does hand out flyers with a lot of that information. We should probably actually put that online as well. We don't have the day, we have to book us now, too. They would be great if they have them online. We should have that later in this session. Seeing none, we will move to the financial update. All right, just a couple of brief highlights. I'll start with the big one, which is our audit. We are just finalizing our audit probably in the next couple of weeks. My hope is, suddenly, February, about March, you'll see our final audit report. Everything so far throughout this entire audit season, which has been challenging, especially because our audit or company was acquired, so things have changed and procedures have changed. It's taken a little bit longer than we expected, for many different reasons. So far, there are multiple findings, but I do not see that changing, but it's not. You see Marie's very great right up here. As usual, there's a lot of good highlights, increasing revenues year over year, slightly increasing the expenses as well. Again, a lot of that has to do with parking garage projects. We continue to have a very, very strong cash up hand account. Still, the highest we've had ever at this airport, at least within our records, now continue to climb to as we close out some of these inadequate projects, which right now is close to $2.2 million in projects that are going to be closed down. It hasn't paid any purchase for that amount yet, so that $2.2 million will in our account. Our rolling in time period looks really strong. Landing fees have and has been really leveled off for some months now. Car concessions and CFC account still, the concessions still are climbing, believe it or not, which is great. The CFC needs to definitely level in off, and you see that down tick again. That's because we increased our CFC rate for a period of time. That's now back to our $4 per transaction rate, so that's why you see the big, I'm sorry, back now. Parking garage revenue, normal parking garage continues to climb. As I mentioned, I think it was last year, I think about that one before. This year, this season, not a lot of employees, all employees of the terminal essentially parking our garage this season because it's full and it's fluctuating. Very, very fast. Much faster than we used to. Some days, it can be around 65, 70%. Both days, it's over 85%, and it can peak, especially during the holidays and during school vacations. It'll hit close to 95%, if not, people won't argue with the same percent. I hit on everything. Again, yeah, again, I will wrap up in the next couple of weeks, and we'll be sure to email that audit report to you prior to the meeting, and we'll have that as a point if you wish. Okay, future news. Is it a Vermont company, or is it a company just on the airport? No, this is a company that does the entire city of Wellington. Oh, okay, same company, sorry. I can't remember exactly where it is. It doesn't matter, I will remember. Marie will know it in a second. Great, if there's any questions on the fanciest, okay. We will move on to item nine, which is the director's report, I think. Great, like Tim said, and I agree with moving the operational statistics over to this report because I always have something to say about it, and it's still good news. I thought the month of November was going to have a little bit of a downturn every year on passengers, but it didn't. We're almost 4% up over last year, November of last year to November of this year, which is fantastic. October again was our highest month in probably 15, over 15 years for that particular month. We continue to see strong numbers for this year. Obviously the calendar year is wrapping up. We don't have those numbers in this particular report, but we will on February 7th, which is our next day of work mission meeting. So you'll see the full calendar year, which right now we will exceed last year. You can see right now year to date we're at 612,000. We ended the calendar year last year with 617, so if our projection for December, which will be around 45,000 passengers, will be close to 650,000 passengers again for the calendar year, which is close to our 2017 number, not quite as high as our 2018. This will start to shift again to January. It's the month that JetBlue ended service. Their numbers were decreasing, but this is the month that we also don't have new airline service with that 30 people, or nobody's service specifically. I shouldn't say nobody. The JetBlue market is out of pre-sales. I started so we can't say that. Fortunately, again, I can't compare it on a one-for-one basis, because a lot of those past years have been utilized by other carriers for their traveling needs. Pre-sales is still doing really, really strong. So in the month of February, their pre-sales are still the highest in the route system in Burlington, and we'll just see that continue with the rest of the city. And where are they flying to again? So the breeze will start January 31st to Tampa, Florida, and then February 14th, they'll fly back to Burlington. Is anyone else decreased their JFK flights? Because I thought that that was also going to be a problem. I doubt that those go to the Delta's the only other one that goes to JFK. They did decrease it for 20-ish days, 30 days, and then they increased it right back up with them. On January 4th? I think right now there's still two a day. And then the only other ones are JFK flights. And then we have both Delta, LaGuardia, and Newark. Yeah, Delta goes JFK, and LaGuardia, and FDIS. And once a day? I think it's once a day on the 7th. And they'll start turning up PCs as well. Every year after September, except for October, October always goes up. November, December, our flights will start much well. Was there any more talk with JetBlue about getting them back eventually? So there's lots of changes with JetBlue. Lots of recent changes with JetBlue. I mean, just in the past week, in the past 48 hours. So Jeff and I did meet with the CEO of JetBlue. Six weeks ago now, so we've decided what it's all about. Great meeting with Rod Hays, the CEO of JetBlue and his leadership team. Very clear that things needed to be fixed in the New York City area, as far as air traffic control, you want these. And the spirit merger needed to go through before JetBlue could turn back to. The couple of things that have changed. Rod and Hays is no longer going to be the CEO of JetBlue. He's second down in the CEO, the first CEO of the large airline company. We'll be starting, I think, with February. Also yesterday, this week, the Department of Justice, the judge ruled that spirit and JetBlue were not allowed to enter the country. So they obviously that's going to continue. Legal action, but right now that is the case. Lots of speculation on both companies, what's going to happen. I have my own opinion, which I'd be happy to share with you later on. But I think really getting reason here, potentially additional other low cost carriers is what our work really needs to serve. Not only the warmer Florida markets, what other markets that we're working. How long does breeze has breeze committed to us there? There's sort of known right now in the industry as a breeze. I haven't heard that they they're relatively new. They're only been on the market really engineering or they're going into markets that are testing markets for sure. They haven't committed to a length of time. No one ever committed a length of time. Since I worked in this industry, I normally I project that they are alive. Breeze wants to make a sustainable long-term now. They see the potential, the demand for a Florida destination for a Florida market out of the Burlington area. For the seasons, right? No, it's not. No, they want to be all year. They're here all year, two times a week to each one of those Vesta Ancients, very similar to what we're made starting with. They now have six routes for a breeze. It's all depends on the supply and the amount of our markets. We would want it to be a crisis. This I think is going to be an extremely positive increase. And the facts as far in just on pre-sale numbers taken about half, more than half of what Jeff moves by. Just on a two-tidal week for a destination. So we heard a number like 65,000 where Jeff lives. So we got 30 back. That's correct. Projected. Even with, yeah, projected even with just the two times a week. The problem is you can get down and hang it back. So unless you're staying within the two days that they come back, you can't. That's right. But 30,000, it's good. What like 30,000? I'm exaggerating that Breeze, they've been an exceptional partner to start working with. Yes, there are two times a week, but two strategic days per week. High days. There's always a way of that, girl. So if you can get to anywhere in the world out of girl attention, then you might not be able to. Jeff and I will be flying on the inaugural flight in, what, 13 days? Are you in next? Yes. We can't come back for five days, but I don't buy that. Well, it would be a inaugural flight. First flight. So you're coming from Atlanta to be here. You can have my handbook. Okay. But you can tell. That's right. Again, there's lots of options. We have American Delta, United, all flying too. That'll be great. Have a good one. Are we doing anything special that day for the flight? We are. Jeff's got a really great plan. I think he has a marching band coming for himself. Burlington. Nice. Oh, Burlington. Nice to meet you. Nice to meet you. Here I have a bit of an instruction. Actually, it could be for the person who's been to Burlington. It's okay to see you. So would you all just show that some of the people who have been to Burlington have made a good choice? That also. So it's not really a marching band. Now it's like a five-piece classical sound show. Yeah. Oh, yeah. And we'll have a Christmallow Prince for a smaller band as we fly in for the first time on their aircraft. Breeze, of course, will have their personnel here to celebrate with us. And then the first flight we'll go out with that. And I'll work with that thing. Of course. Sorry. Right. I'm going to just roll into here. Oh, all right. See, this is fly time. All right. So we put together a quick report, kind of an end of year summary report. It is online and shared. I already introduced Paul Holtz and Mike Waite. I think Mike is still on and Paul. But again, really, really excited to see the completion of this reorganization come together. Again, we do have one vacant position with our deputy director slot. I am not moving forward with that right now, just to get Paul and Mike up to speed and work with them and really test this reorganization. Right now it's working really, really well where Paul and Mike really did the ground running and started working better. I think they are already super, super excited. Which took a lot of effort to get up to speed. That's fine. That's more work. Jeff can probably talk about a little bit on this, but I just wanted to bring up local Maverick. We tested out a different gift store idea in the terminal building. Super successful and super likely. Really, really positive feedback from not just our customers and our passengers, but our employees as well that utilize this work. This was set up, this particular picture was set up in our, in the new building up on the seventh floor. And I believe these are individual owners or at least one of them is an individual owner selling her own product with local Maverick. This still needs to be played out, hashed out, created out. So we're preparing that.  This really was an opportunity to make sure that the demand in our terminal building could sustain something like this, which is what I understand. So super, super excited. Yeah, they're doing another trial right now. What they're doing is trying different times of the day to see what makes sense for them to be open. They've invested in significant funds to try to make they work from furniture to new kiosk systems. They hired another employee to help. So they're very serious, but they had very successful days here. So they're going to be here through the 29th, and it would be like to be another test run for the February vacation, which they have agreed to give us, say, a small commission, by select you for working with them to try one more time. So how is this different than the Vermont products that are getting the other places present? Yeah, is this more of a sneaky kind of stuff? Very much so. Yeah, I think he started this a few years ago. I don't want to say this model. Yeah, so what he's in the business of is these comic makers will pay him a subscription held by marketing services, help build a website, mobile brand. He has a small store downtown, which is off of Main Street, where they're selling some of these products. And really like some meat and ice cream products, so really wide array. And so now we're bringing it here. He's giving them more access. He's actually seeing more people reaching out. And it's a lot of jewelry or cannolis. The woman on the plate, she makes the cotton candy lady, I think it's her name. So she makes like different freighter kind of candy. She does a lot of that as well. So she doesn't have to have you for these local makers to expand upon their business. So sort of small batch stuff. Small and can Hudson uses. It does have mobile Vermont products for many orders. So Hudson News doesn't have any reason to have agreed for a competition. After they do, but I think it's a healthy competition. Okay, but it's not, it's not something we can do. It's not ourselves. So it's our legal step. No, there's no exclusivity either person or state. And then the Maverick is really just the holding place. The person that's running Maverick decides what what items would come to your part. Not the minute. It's not going to be the same. It's what it's recalling. That's right. I think some of the obvious is some of the same, right? But there's new stuff in the background. And it's something to like, we'll use Kessler coffee, for example. He actually buys the product for now and brings it in. So it's not just once a week, he's self-made incubating for a long time. He's not funding, but supporting. So yeah, it is revolving. He's, he also helped in Burlington. And I love Burlington. He sends out their products there as well. So it's really, he does specials in events as well. He's connected to a lot of businesses that you think might be interested in appetizing here too. So it's a good partnership. Super good partnership. And a really unique feature of this too. And I think, so the one on the left, yeah, did a demonstration to teach how to cook with the product or how to use the product. In this case, we use it, maybe serve to make it better. However, yes, I'm sure Dr. Tripp had a scenario, which is really interactive. And so all customers walk past this one. This one goes upstairs. So just the American, I think 60 plus percent of them pass. The parties is molded. Right now we're looking at molded to hold for this next quarter. We talked a lot about Marie's again. Super excited to have them. That should actually say, January 31st, starting to Tampa and February 14th, starting to Portland, Florida. Jeff and I are on the road next week. We're going to be in the Willis Tower in Chicago. We can get airlines to make sure to, we usually see them once or twice a year, just to go check out their sales. They're going to help them and we can partner with them. And there's always a ask, say, to brand bear service or additional work to our network based on all the data that we collect. Similarly, probably in the next two weeks, unfortunately, American right now is not letting people visit headquarters. In fact, I'm pretty shy of them, right? It is letting us down. Most airlines have kind of shut that down since COVID. But we are going to be the Americans soon, their domestic planner manager, which is really fantastic. We'll do the same thing with Delta, trying to get on the schedule to go visit Atlanta. I am planning. We are planning a employee city airport employee celebration for early February. Again, Robin, you said it earlier, the folks that work here are really working, really, really awesome. Both from the ambassadors, the employment policy team, our many-hand standpoint, Mike and Andrew's team, our operations team out there every single day with the conditions. So this is kind of after holiday season, been to a celebration and talk about with some gifts that were there to help us. Really, it's about that particular thing. Similar as being, but this one, this next bullet point is administration truth. So this is going to be able to all four of our managers. This will celebrate them, but this will also assign additional tasks to their ever-growing list to make sure that we're working ahead of each one of our really big projects that we have coming up the pipeline all the way down to the small details. Like how can we hope lunch are being in various in part of that retreat, but really on a daily basis, we're just preparing for the spring, training of the spring, preparing for the weather. It's already mid-January, so that's pretty good. But we have way a lot of the tasks are ahead for spring and of course, over some of the construction, including finishing the south apron, which is the big apron in front of new data technologies manufacturing site, planning for project next, and getting that shovels and grab ready, as well as the big projects like what are you just talking about? In big events too, Jeff is planning a big solar eclipse event here at the airport. We're working with downtown. We're going to be sponsoring all of the classes for all the city events downtown, so we'll have 50,000 solar classes to hand out, hello, we're in the city arts stand. So really exciting. Next couple of months, next quarter, we're really starting to get to the summit. Have to highlight this once again, not only are we going electric, we've gone electric, vehicles, I think you saw those vehicles that are one of our previous meetings, those were the exact ones that we delivered. The day, I think it was three days after it was passed by city council, the dealership was able to deliver that earlier than expected. So we now have all three vehicles that you look for at prior meetings. This Mach-E, of course, is sitting, sorry that's a stock photo of the but the Mach-E is, of course, we're in front of our building. That's actually fully wrapped and now has our logo on the side. And it's there, it is being used quite often. We haven't charged it yet, it's been a week and we've continued to drive it, it's pretty good. I hope that is good. Next one, I just wanted to give a quick highlight and shout out to Hannah and Jillian, Jillian Wadey and so many others, including folks from Burlington City Arts as well as the mayor's office. Their world, we put out a bid in partnership with Burlington City Arts for the wall right behind this wall right here in the hallway for a call for our artists. We received 140, 160, 180, 140 bids from artists all across the country to build something creative for us. So a huge shout out to the team that was involved in narrowing this down. I will say I was not involved in the 140 selection but coming down to narrowing it down and super excited to give you a little sneak peek of what it's going to look like but also I would say that TV low was the selected artist, a local artist and she's going to start presenting this pretty soon. This is under $50,000 so you're not going to see this come to the board but it's under 50 or 15. 50 bids here last year but it's super exciting. It's a massive, massive display. We just hired her to do a spoke to another time. I'm just going to move this mic. Pat Jen wrote it's going to be in J.C. Park. It's really beautiful glass and it's all these things like this. That's very cool. She's working with another person. She incorporated some of that here where there's like glass pieces, back lids. It's very, very, very cool. And then the last segment here is just some of the big highlights of 2023. We had a really successful year as we wrap up the numbers which are very easy to see the final numbers for December. Of course, one of the big highlights was our brand new A. You're going to see more and more important logo changes including this room. Maybe on February 7th, Jeff, this is one. Oh yeah, that's actually in front of tickets next week. Awesome. So this will be changed. New logos on the doors. Lots of little pieces. I did handouts for those physically here. Some new stickers. These are all printed in house now. So we're doing a lot of our printing and logo design in-house with my studio right up for downstairs here. It's unbelievable what they said. And this goes as big as changing all our logos and all of our big vehicles as well. We do that all in-house which is fantastic. Bigger projects figured inside this wall and cars, full-wrap cars. We do Alice first. Again, a highlight of 2023 was finalizing and hiring for and hiring for the re-organization of the airport. So a new director level position that's Jeff. Seems to be working. He's doing it well. As well as our four new managers. Announcement of new air service like Breeze. I won't say that again, but I love Breeze. Increase in implements which also goes into our garage utilization very high. We're going to continue to see that high. We are expecting some records that can to the February school vacation as well as the April school vacation. One of our projects next year needs to expand some of our service slots and make sure we're ready for this as the future continues. A couple of warrants just as a reminder that we want including Vermont Business Magazine one of the fastest growing companies in the state and national recognition that's voted number eight USA Today. I personally got to enjoy some really phenomenal shirts including representing the airport at the airport points of international airport work. Airport is an international summit in London, which was really great. In fact, I've still been in communication with some of these worldwide airports on some of the things that we're doing and some of the things that I see them spring back to this. I don't think we talked too much about this other bullet point, but we did put together a donation truck stuff the truck that we call those trailer stuff the truck so that we could donate flood relief efforts. We had many of our employees as well as just folks that were nearby drop off stuff till we deliver that. We also celebrated women in aviation with Robin and her team. I'm excited to continue to do that. We do annually, if not more, as well as a couple of community engagement. Some of them being landscaping program and some of the forwarders that we have here. Great events here too. You can see a couple of the pictures on the screen. Mamava opening and ten year anniversary celebration as well as their new model which is behind all of us there. We celebrated a couple of occasions with their congressional delegation including Senator Welch and his wife right there. I mean Jeff Jones has said is in the rest of it. Mamava I'm also going to be on a bypass soon called the potatiously optimistic leadership program. So it's Mamava as the owner one of the co-founders of Mamava Sasha who is standing to my right in that picture. She started this podcast and she's in a country that do use Mamava. Some of them do, some of them don't. But it's about Sasha's leadership style as well as what the name implies potatiously optimistic. I'm up within the workplace. And I've already talked about the Washington. That is my summary of some of the great things that I like that we wanted to re-share with you 2023. Question about 2024. Where is the airport at with the open house for the guard September 11th? And then the subsequent sort of uniting with Green Mountain Aviation for this sort of Asian day. So we do meet with Green and Green Aviation day occasionally. We're not interested in meeting the details with planning that particular event. For all sorts of various races but we want the logistics, the security, the safety of the students. I don't want to call it a nature but a static display celebration of Vermont Aviation that many entities are interested. It seems to be going very well on the planning side. My understanding of the meetings we're not flying. Right? Not at this age. So we're not flying this airport. And the guard is still just like they did well. It'll be two years right because they do theirs by email.  They learned a lot. Did they? My goodness, who expected 10,000 people to show up there? And everything else is sort of happening in little silos. Right? Like a heritage site or a vein of silo and sort of a westbounding range sort of silo. Yeah, that's right. Yeah, that's right. From my understanding that's correct. As far as the guard event goes, I mean with the leadership of the guard once a month, we'll continue to help what we need. Mostly our role in that because it's pretty expulsively on their side is to share with the public what we have to offer. Last time we put our snow rollout there, but the kids come up into it and that sort of stuff. So we'll definitely update you as we find out more about both events and health. And I move on to item 10. Just the commissioner on it. So it did not receive any advance, but is there anything that the commissioner would like to discuss at this time? Well, just one thing. And I mentioned that the council went through all the steps we needed to take a precarious circle off the state roadmap. This was an area where the dog park used to be and were much houses. It was just a little cul-de-sac and they were torn down. And I just wanted to share so we need to go through this where we're all in the state. So so it's now it's all grass and we've ridden with snow. And there's a snow marsh. And it's a storm. Yeah, water chambers under it. So it's kind of double moves in double duty. But a couple of them council's really noted how beautiful the trees are there as well as the stuff up front where you know the trees and they're open that they'll be maintained. And the question that I put in the answer was if is that portion of the land you own is that going to be part of the walking paths and where the card circle was? Yeah. Right now it's not. I didn't think it was. But it was because that you know that that road was there. It was even really challenging to get it across that versus using the side of that through the water towards KERDI O2. So right now that's not part of it. Okay, I understand it. But they really were hoping that those trees stay there because they're really quite make them to our team takes a significant amount of Yeah. and their truth. And when what's once happened you still see a lot of the trees really tell for us to get in there. But I'm sure it's no shoes or or why not. So we'll go by I think that was frame of horses. That's most positive. Or what that happens is you can tell it's hard. Okay. So I just wanted to share that comment. I think that that should be the toilet here being arched here. Okay. Well, I'll offer a compliment. Also, I don't know who is responsible for collecting or curating the artwork that's in the hallway. The upper artwork, it was really nice. I mean, it's always been nice. But this month's selections are a nice sort of combination of the format scenery. And just vibrant African arts. We have a really strong partnership with Burlington City Arts Arts. So they have a rotating art display. We ramp that up this year because it is on the the passenger side about the terminal with work and spending the past and of course outside the extended the entire hallway this year to incorporate more. And they're helping us, of course. We are all and but also pieces that like to work have required to store like this by what it's not such a the artist Anything else? I move on to I don't want much to follow up items or no items. Previously, it's less than their names that should be added to this list. So it should be following up on the future meeting. Okay, very good. We move on to item 12 six active sessions. So those are ways to part motion called part one's principle for two three complicated. This is our part one. So I'd be like to entertain a motion on the premature discussion on the airport's legal affairs. We rarely place the airport as substantial as it can be. So moved. That's been final. Is there a second? Better. Everybody ready? Any discussion? I don't even understand what's going on. So it's basically we're saying that they're not there are legal affairs that are affecting the airport that we let discuss but because premature disclosure to the public would affect could affect how those initiatives are going. It's we want to do a second session. Back with you. Okay, thank you. Yes, Chairman. I just have a point of inquiry. Are we expecting to come back in the regular session to vote or is this merely informative? I'm only I'm just being mindful of the time and not sure. But that'll be covered in part two of the motion but essentially the plan is to adjourn this session. Move into executive session and knock that because there's no action is expected to be. Thank you. That's what I needed. So all those in favor of this motion please signify by saying aye. Aye. Aye. Take those. I think who would you like to be involved in the executive session? Everybody in the table, Jeff and then Paul and Michael sitting in that too. But yeah, everybody's at Paul. Sorry, not so good. It's very important you take a second. All right. So just make sure. Yes, so tell me TV. Is there a separate link for this executive session? No, we're going to actually stay in this session. Okay. So it's going to need to come back to the regular session any more. You're going to stay in this like and just make sure that those people should not be here. Okay. Thank you very much, everybody. Thank you. So now


Hey guys it's Jess and welcome back to my channel. So today's video is one that is short to melt all your stress away. It's my de-stress pamper routine. So I know you guys love my routine videos so I really wanted to make another one and I thought I would put a little bit of a twist on it and show you guys how I relax and just look after myself throughout a really busy year. So I really think it's important that you always take time out just to care for yourself, to do something nice for yourself every day whether it's to have a bath, make a tea and watch your favorite show, whatever it is just so that you don't experience burning out as the year goes on. So don't forget to thumbs up if you enjoy it and of course if you're new, subscribe so you can join in and get notified whenever I post up my study tip videos and let's get into my de-stress pamper routine. You can actually smell the essential oils I've been burning today. So nice. All right let's get started. Okay first thing I like to do for my de-stress pamper routine is you guessed it go and take a yoga class and I usually like to do a yin restorative class which is more meditation and stretching than an active class just if I'm feeling a little bit tired. So I walk down to my yoga studio and take a class and then when I come back sometimes I'll also grab a green smoothie. This one's also got some berries and banana so it's quite sweet. I really love it and I think it's so important when thinking about de-stressing to focus on your mind and your body as well. So you want to get lots of good vitamins into your body and make sure you're looking after yourself and taking good care of yourself. And then something else I really love to do after a yoga class, after using my body and stretching it out is to take a nice relaxing and hot bath and sometimes I will have a bubble bath other times I won't. Comment below if you guys prefer bubble bath or no bubbles or if you guys even use a bath bomb because I haven't actually tried one of those. And sometimes I'll also light some candles just to set the mood and sometimes I'll listen to music other times I'll just lie there in silence and ponder the world. And then something else I'll do is make a cup of tea and this one's a really relaxing one. It's by Puca Tea and it's the love tea so it's got rose and lavender and chamomile and I also really like to light a candle and some incense or burn some essential oils. So I love burning lavender oil or lemongrass oil those two are my absolute favorites and I'll just put it in my little oil burner next to the TV and then I usually like to curl up on the couch and just read one of my favorite books or I don't know just watch some TV as well and just bask in the aroma of my beautiful essential oils. So at the moment I am reading a couple of different books I kind of swap between the two one of them is called work smarter live better and the other one is the life plan so I'm just gonna pop on my new reading glasses. I love these buns they're so fun I thought I really wanted to go for something different so sipping my tea and then yeah just picking up where I left off in one of my books and I actually also have a pencil there because I really like to make notes as I read if I find something really interesting or I want to share something with you guys too so yeah I could honestly just sit on the couch for a good couple of hours and then finally I guess I'll just have to peel myself off the couch to do something else. So yeah I just really like to sit and I like that spot in particular because it's where the sunshine comes in in my apartment and even if it's raining outside then I can just look out the window as well so yeah I just really like to have a really easygoing and slow pace day when I'm trying to just relax and pamper myself. So I don't know about you guys but I'm feeling pretty relaxed right now so I hope you guys did enjoy it and thumbs up if you did if you want to check out some previous videos you can click the cards up above and also check out my study skills book the High School Survival Guide I'll link that in the description box as well. Have a very happy and productive and also relaxing and calming week. Bye!


Welcome to this lecture number 23 on the NPTEL course on fluid mechanics for chemical engineering undergraduate students. The topic of our discussion in the last lecture was differential momentum balance and we were proceeding towards the derivation of the complete differential momentum balance and in that context we introduce the notion of the stress tensor. The differential momentum balance is essentially derived the way we did it is to take an infinitesimal control volume of a simple geometry let us say cube and of sides delta x delta y delta z in the three quarter directions that is the volume of the cube delta x times delta y times delta z and essentially we wrote down the integral momentum balance as applied to a control volume in the limit as the size of the control volume shrinks to a point. Then we obtained the following simplified relation we obtained the fact that sum of all forces acting on this control volume is equal to rho times the substantial derivative of velocity volume times del v where del v is the volume of the control infinitesimal control volume. Now there are two contributions to forces acting on the control volume one are called body forces the other types of forces are called surface forces body forces a common example is gravity. So, if you have a fluid with density rho in present in the control volume and the acceleration due to gravity vector is g then the force acting on this control volume is mass times g m g m mass is rho times the volume. So, g is acceleration due to gravity these this is the body force if the body forces gravity is due to gravity there could be other body forces such as electrical body forces present in ionic liquids or magnetic body forces those will not be of concern to us in this introductory course, but the most common body force that is encountered in many applications is of course gravity. So, that will be the force that we will include in this discussion in our course. Now surface forces are little more tricky now the surface forces are due to the fact that suppose you have a surface of that cube which we just drew and let us draw it the full cube there are six phases to the cube x y and z. So, each phase is denoted by a unit outward normal. So, this phase has a unit outward normal n is in the plus i direction whereas, this phase as a unit of normal n is in the minus i direction likewise this phase as unit outward normal n is in the plus j direction and this phase has unit off normal in the minus J direction likewise, you can do it with the plus k minus k direction I will refrained from doing that because it will reduce the clarity of the picture because one cannot draw three dimensional pictures very well in a paper. So, I will just leave it like this. Now, on each phase in general the force exerted by the fluid that is present outside on this phase can in general be in some direction. That force is since we are all we are considering only infinitesimal forces I will denote it with the delta f. The force can act in general on a given surface in an arbitrary direction. This force acting on a surface whose unit normal is in the direction n can have two components in general. Suppose I take an arbitrary surface of area delta a and unit normal n. There can be two contributions to the forces. One is the direction along the normal those are called the normal forces and then there are two tangential directions to this surface. So, there will be two components along the direction of the tangent. So, in general you will have delta f t 1 delta f t 2 along the two tangential directions on the surface. So, the normal forces are predominantly due to pressure because pressure acts purely normally plus also due to the fact that there could be normal viscous stresses. The tangential forces are purely due to or also called as shearing forces or shear stresses. If you define it in terms of per unit area these are only due to viscous stresses in a fluid. So, it is normally convenient to write the force per unit area as the normal force per unit area sigma n as limit delta a tending to 0 delta f n by delta a. Likewise the shear stress is denoted as tau n 1 is limit delta a tending to 0 delta f t 1. So, tau t 1 let me explain the notation. This denotes the fact that you are considering a surface whose unit normal is in the n direction and this is the tangent vector in the one direction and that is similarly there is also a tangential force in the other direction. All we are saying is that for any given plane any surface with an arbitrary orientation n the force that acts on that surface due to the fact that fluid is the neighboring fluid the force exerted by the neighboring fluid on this surface could have three components one along the normal and two in the two tangential directions along the surface. That is all we are saying, but now we have considered a cube with six faces in our control volume x y and z. So, each face will have three components this face will have the unit normal is in the plus i direction and in general the force exerted will be the force exerted will have three components. So, the three components of the force are we can write this as one along the normal direction which is actually the x direction here. Because that is the direction of the unit normal then the two tangential directions are y and z. So, delta f y and delta f z. So, we can write three components of the stresses the force per unit area as follows sigma x x. So, let me write the two x's in two colors sigma x and I will explain you the reason write it slightly bigger sigma x x is equal to limit delta a tending to 0 delta a tending to 0 where a x is the let us say this is the area of this face with unit outward normal in the plus x direction delta f x by delta a x. This is the normal component of the stress acting on that surface that shear stresses are usually denoted by tau the greeks symbol tau. So, now I am going to use two colors to the two subscripts tau x y is equal to limit delta a x tending to 0 because that is the face we are considering. But the force is now in the y direction the area on which the force is acting is in the x direction similarly can have tau x z is equal to limit delta a x tending to 0 delta f z by delta a x. Now, let me explain the colors for the two subscripts that explain the reason for the two subscripts in the orange color refers to the direction of the unit normal to the surface the unit outward normal to the surface on which we are considering the forces. So, this tells you the orientation of the surface orientation. Now, that is the purpose of the first subscript the second subscript the green subscript tell you the direction of the forces the forces can act in either x y or z direction on a surface whose unit normal is in the plus x direction which is i. So, this on this surface you could have forces with three components. So, therefore you need two subscripts to denote the two issues that is one is the direction of the force the direction other is the direction of the unit outward normal to the surface on which we are considering the force likewise you could also write tau y x sigma y y tau y z this is you consider a phase whose unit normal is in the y direction j direction and you are considering the forces in the x y and z. So, the first subscript denotes the direction of the unit outward normal and the second subscript tells you the direction of the force. So, you need two subscripts and likewise you can have in the on a plane whose unit normal is in the z direction that is plus k tau z x tau z y sigma z z. So, as the control volume shrinks to a small point this the forces on this tiny cubic volume element can be summarized as an array of numbers sigma x x tau x y tau x z sigma sorry tau y x sigma y y tau y z tau z x tau z y sigma z z. So, this is an array of numbers that describe the state of stress on a cubic volume element with nicely defined surfaces along the three coordinate directions x y and z namely. Now, what is the this is this collection of the state of stress present in a less in a fluid is called the stress tensor y is it called a tensor it is because of the following reason if you have a vector like velocity you can write it as v x times i plus v y times j plus v z times k. You need only one subscript to denote the direction of the components in which the velocity is pointing velocity has is a vector has only one direction associated with it one physical direction associated with it namely the direction of the velocity itself. But if you consider something like a stress which is denoted with two underlines two underlines to denote that it is something more higher than a vector it is actually a tensor because it has two physical directions associated with it associated with it. So, velocity is a vector stress is a tensor. Now, what are those two physical directions the two physical directions are the direction of the unit normal on which the force is acting and the direction of the force itself. Stress is force divided by unit area force as a vector has a direction and the area itself has a direction because of its orientation. Now, so at each and every point in the fluid if one has a knowledge of this matrix or the tensor sigma x x tau x y tau x z tau y x sigma y y tau y z tau z x tau z y. If one has the collection of this one has an information about this nine elements then there is a result due to Cauchy which states that if I have at a given point and a surface with arbitrary orientation that is you have put a coordinate system x y z. But this orientation of the surface is not along any of the three directions x y and z, but it is an arbitrary orientation n x times i plus n y times j plus n z times k. It is it is oriented in an arbitrary fashion not necessarily along one of the three coordinate directions then and the area of the surface is delta a let us see. Then what is the force the force on this surface will in general have three components in the x y and z direction. So question one can ask is what is the force acting on such a surface what is the force per unit area what is the stress acting on such a surface. The answer due to Cauchy which I will not derive is that simply take the local value of the stress on this surface take the stress tensor acting at that point. So, remember this is an infinitesimal it is a point and you have an infinitesimal area surrounding that point. So, at that point you should know what is the stress tensor sigma x x tau x y tau x z tau y x sigma y y tau y z tau z x tau z y sigma z z and according to Cauchy's result you simply have to do a matrix multiplication of the three components of the unit vectors with the stress tensor. This is like a matrix multiplication of a matrix three by three matrix with a three by one vector. So, the answer will be a three by one vector which is this. So, by having the knowledge of the stress tensor at a given point which the stress tensor is a given point in the Cartesian coordinate system tells you what are the forces per unit area acting on directions which are perpendicular to the three unit vectors in the Cartesian frame of reference. But if you have an arbitrary phase arbitrary area then you can get the force per unit area acting on that surface with an arbitrary orientation in this fashion. But by merely multiplying the elements of the stress tensor or the stress matrix with the column vector containing the components of the unit vector. So, that is the power of doing the Cauchy construction. Now, having understood what are the stresses acting on the surface also the sign convention for the stress which we mentioned last lecture. Suppose you have a surface that is pointing in the plus j direction and suppose we say that tau y x is 10 Newton per meter square this is the x direction this is the y direction. What this means is that you have a force. So, y represents in our convention the direction of the unit normal. So, that is in the plus j direction x tells you the direction of the force. So, if it is positive tau y x is positive then the force of 10 Newton per meter square force per unit area that is it acts on the plus x direction on a surface use unit normal is in the plus y direction. So, if you have both the direction of the unit normal and so if you have the answer of the stress tensor to be positive. That means that both the direction of the unit normal and the direction of the force are positive or it could also be the following that on the same surface at the same point you could consider a unit vector in the minus j direction. You could consider and each plane has two unit normal one is the normal pointing in outward direction other is normal pointing in the inward direction. So, if you consider the unit vector to be pointing in the minus j direction then the force acting on this surface is in the minus x direction this is plus x the magnitude of the force is 10 meters 10 Newton per meter square. So, if somebody says that you have a force or stress tau y axis plus 10 Newton per meter square it could either mean that in this could either mean that a force of plus 10 is a Newton per meter square is acting in the plus x direction in a surface on a surface whose unit normal is in the plus y direction or a force of 10 Newton per meter square is acting in the minus x direction on a surface whose unit normal is in the minus y direction. So, that is the meaning of positive terms positive stress values. Suppose you have negative stress values if somebody says the element of a stress tensor is negative that means the following if you have a unit normal in the plus j direction the force is acting in the minus x direction and the magnitude of the force is plus 10 magnitude of the force is 10 or vice versa if you consider the unit normal in the minus j direction then the magnitude of the force is in the plus x direction the force acts in the direction of the force is in the plus x direction while the magnitude remains 10. So, if the stress value is negative then it means that the direction of the force and the direction of the unit normal or opposite to each other. If the stress value is positive then the direction of force in the direction of unit normal or along the same direction. They both could be positive here or both could be negative. Here, if one is negative, the other is positive and vice versa, one is positive, the other is negative. So, that is the sign convention for the stress tensor. Having done all this, we went back to the differential momentum balance, which simply said that is rho g times delta v plus the surface forces acting on the cube. Now, the way we did was to consider each phase of the cube, take each direction x, y, z. So, we first wrote down the x momentum balance. How do we do that? We did that by saying that take the x component of this equation delta v is rho g x delta v plus all the surface forces acting along the x direction on this control volume. What are the various surface force acting on the x direction? On this phase, there is a force sigma x x. On this phase, there is a force tau y x. On the front phase, there is a force tau z x. All these are pointing, the direction of the force is remember the second subscript. So, all these are pointing in the x direction, but there are not just three phases. There are also these opposite three phases, which for which the unit normal is in the opposite direction. We have to consider those forces as well and then use the Taylor series expansion for tau at x plus delta x in terms of tau at x to arrive at this simplified relation.  So, the volume of the control volume drops out of the equation, because both terms are multiplied by the same quantity. Now, we also said that in a static fluid, the only force that is acting are the normal pressures. So, the stress tensor becomes and this pressure acts inward. So, you will have a minus p. In a static fluid, the stress tensor is this. In a flowing fluid under flow, we want to write the stress tensor as this, which would be the case if the fluid were to be static plus stresses that come up because of the viscous resistance of the flow of the fluid. So, this is written as x y.  Under flow therefore, these are the terms that will happen only these are non-zero only under flow non-zero only if flow exists. This is these are the viscous stresses. The stresses that come about because a fluid resist motion continuous deformation. So, these are the viscous stresses that are generated by the fluid to resist the deformation.  This is the first term the x component the y component of the momentum balance this is x y and the z component. So, these are the three momentum equations the differential form the momentum equations these are also sometimes referred to as the Cauchy momentum equations. These are the differential form of the momentum balance these are also called the Cauchy momentum equations. And we also have the mass balance if you remember for an incompressible fluid the continuity equation which in Cartesian coordinate means. So, we have four equations three components of the momentum equation and one continuity equation. So, we have number of equations is equal to four. So, far and the number of unknown variables that we have we can count as follows three velocities the three components of the velocities one pressure and the nine components of the stress. So, the problem is highly under specified because the number of equations. So, far is less than the number of unknowns. So, we cannot solve this problem. So, we cannot solve this problem as such right now. So, that is the idea that we cannot solve the problem because you have far two equations than unknowns. Now, we have to look at the problem why we have this situation that we are not able to solve the problem completely. And that is because we have not said anything about whether the material is fluid or a solid even now. Because all that we have done is to apply Newton second law to a control volume and then took the limit as the control volume shrunk to 0 size 0. But nothing has been told. So, far whether the material that resist deformation is a fluid or a solid that is the constitutive nature of the material has not yet figured in our framework. So, we need to specify something about the nature of the fluid that will relate the stresses to the velocities and thereby we will be able to achieve some closure. But before that we can also write down equation for angular momentum that will tell us that tau y x is tau x y tau z x is tau x z tau y z is tau z y. That is the stress tensor is a symmetric tensor that is the matrix of elements is a symmetric matrix. That is you have whether you write it like this tau x x tau x y tau y x whenever you write it like this these two terms are the same and these two terms are the same the green terms and likewise these two pink terms are the same. They are the same because it turns out that when you do the angular momentum balance and if there are no internal couples that generate angular momentum within the fluid which is true for almost all fluids. Then one can show that the stress tensor is identically symmetric always. So, we are left with only a symmetric matrix has only six elements because there are three equalities that relate three that give you three additional equations. Therefore, a symmetric matrix has only six independent components as opposed to the nine independent components for a second order tensor six independent components. But nonetheless we are still left with more unknowns than the number of equations that we have to solve them. So, we have to specify what is called the constitutive relation. In this context one way is to do one way to approach the problem of constitutive relations is to do experiments on known fluids and try to correlate the stresses with velocities and so on. That is one way and that is often done in labs to characterize fluids. The other way is to guess the form of constitutive relation based on some general principles. Now, let us try to guess the form of constitutive relation from an intuitive or physical point of view. Now, firstly let us take a very simple system that is flow is happening between two plates x and y bottom plate is stationary static top plate moves with the velocity v. So, you will have a velocity that looks like this in between the two plates. Now, the question that one can ask is the relevant component of the stress is you have a plate whose unit normal I mean I am just drawing across section actually it is a plate it is extends whose unit normal is in the plus j direction and the direction of the stress would be in the plus x direction. So, the component of stress will that will be of interest is tau y x. Now, what should tau y x be a function of what can tau y x depend on? We can say the tau y x will depend on the velocity velocity of the flow, but that is not all because that does not tell you the whole story. Because if it just depends only on the velocity then you can say that well what about the distance between the two plates will it be the same if I have the same velocity, but a very large distance will it be the same if I have very small distance. So clearly the velocity tau y x cannot be a function only of the velocity somehow the distance between the two plates have to come in. Also from a physical point of view the stress cannot be in a fluid if the entire fluid moves with the constant velocity then there cannot be any internals viscous stresses generated because that is merely rigid body motion. Stresses are generated in a fluid only if there is relative deformation between two points. Two points move past each other relative to each other. Now that so only then stresses will be viscous stresses will be generated. Now that part is accurately captured by what is called the gradient of velocity. So stresses in a fluid cannot be generated purely by a rigid body motion of the entire fluid. There has to be relative deformation between two points in a fluid and that is captured by what is called the gradient of velocity. That is if you have flow in the x direction the velocity component of interest is v x the x component of the velocity. If the x component of the velocity is different at two different points then we say that there is a gradient. So this is denoted by d v x y d y. So in this particular case there is indeed a variation in velocity in the y direction. So there will be stresses that are generated because there is a difference in velocity at between two different points in the fluid. If you say both the plates are moving with the constant velocity v then of course there would not be velocity gradients and there would not be any viscous stresses because this amounts to merely moving the entire fluid as a rigid body. So only gradients of velocity can generate stresses not absolute velocities. So in this simple context which we just discussed let me just show the picture here itself. You have two plates one at y equal to 0 other at y equals h and the top plate is moving with the velocity v then the relevant component of the stresses tau y x because you are considering the force acting on this part of the fluid that is the top surface on in the x direction because that is the relevant component of the stress. So tau y x must be proportional to p y. The constant of proportionality is called viscosity of the fluid this is called the viscosity. Now the dimensions of viscosity area can be estimated as follows. Stress is force per unit area this is force divided by area. The dimensions of velocity gradients are simply one over time. So the dimension of viscosity stress can be written as m is times t to the minus 1. If we take to the other side then the dimensions of viscosity is m l to the minus 1 t to the minus 1 k g per the units in s i units are k g per meter second. So this is a material property of the fluid it is a material property of the fluid of the fluid. So this is the simplest expression because we consider a relatively simple flow between two parallel plates the flow is only in one direction and but the in general the flow can be much more complex. But before I go to the complex situation this is often called the Newton's law of viscosity. This is merely an expectation from our side intuitive expectation from our side. It is not guaranteed that all fluids should obey this expression this relation. In fact many fluids do not. For example if you consider fluids like toothpaste or shampoo or ketchup they do not obey this relation they are much more complex. But many simple fluids like air, water, glycerin and so on they do obey this simple relation. Such fluids are called Newtonian fluids the fluids which obey the Newton's law of viscosity which says that the stress the shear stress is directly proportional to the velocity gradient and the constant of proportionality which is a true constant it is independent of the flow parameters like velocity or velocity gradient is called the viscosity of the fluid. Now this is for the simplest case but Newton's law must also be written for the most general case. So the Newton's law of viscosity for the most general case where the stress the flow can be in all the three directions tau x y tau. Remember the stress tensor is symmetric from angular momentum balance. So let us hope that I have used mu use mu is the symbol used for viscosity normally tau x z tau z x is mu tau x sorry tau y z is mu and then you have the normal stresses tau x normal viscous stresses is 2 mu is 2 mu tau z z is 2 mu partial w y partial z. And this is the constitutive relation these are called constitutive relations because they tell they have some information about the constitutive and material that make up the fluid these are called constitutive relations. And the ones we have written are for a simple Newtonian fluid such as air and water. Now we have written all the stresses in terms of the velocities or the gradients of velocity. So now we have exactly the same number of equations as you have unknowns because you have three momentum equations and one continuity equation and we have three components of velocity and one pressure as the unknown. So that completely specifies the problem. So now let us substitute all this in the momentum equation.  Now let us substitute all the three components.   Now I can write the first term as since it is 2 I can write it as sum of two terms partial partial x mu partial u partial x plus again the same thing. Now in all these equations I am going to take out I am going to write the first term separately all the other two sorry all the other two terms. I am going to write separate of the first term plus partial partial y of mu partial v partial x plus partial partial z of mu partial w partial x.  Now I am the order of these derivatives partial derivatives are interchangeable. So let me write this as partial partial x and we will assume that mu is constant independent of special portions. So we can pull out mu of partial u partial x that is from this term.    So I am going to write the x component of the momentum equation after using the constitutive relation for the Newtonian fluid as rho the substantial derivative of the x component of the velocity is partial p partial x partial gradient term rho g x the gravity term plus mu partial squared u by partial x squared plus partial squared u by partial y squared plus partial squared u by partial z squared. This is nothing but the Laplacian del squared of u where del squared is the operator partial squared by partial x squared plus partial squared by partial y squared plus partial squared by partial z squared. So the x component of the momentum equation can be simply written as rho partial substantial derivative of the velocity is minus partial p partial x pressure gradient term plus the gravity term plus the viscous stress term which becomes like this. So I can write similar equations for the y component of the momentum equation just by analogy one can of course go through the algebra in the same manner and you will end up the same thing this is x component y component this is the z component mu del squared w and of course one has continuity equation mass conservation equation the mass balance differential form of mass balance which is partial u partial x plus partial v partial y plus partial w partial z is 0. Now I can write this in a coordinate free form just as the mass conservation equation in a coordinate free form became del dot v 0. I can multiply these three components by the unit vectors and add them up and I will get the following equation d v d t is minus gradient of pressure plus rho g vector now plus mu del squared velocity vector. These two equations are called the Navier Stokes equation for an incompressible for an incompressible Newtonian. So this is the mass balance this is the differential momentum balance. So the next task for us is to understand these equations by providing some solutions of these equations in simple physical context. We will continue this in the next lecture.