Let's solve a couple of questions on effects of acceleration. So the first one says which of these has the highest magnitude of acceleration. And there is a note which says assume a constant direction of motion. Okay. So the direction is not changing. It's, we can say it's moving in the same direction. We have to choose one answer out of these three options. Why don't you pause the video, read the options and first try this one on your own. All right. Hopefully we have given this a shot. So the first one says a plane flying at 400 kilometers per hour for five seconds. Now we need to figure out the highest magnitude of acceleration. And for that we need to know what acceleration is. We know that acceleration, this is, this is the rate of change of velocity. How quickly or how slowly the velocity is changing. We can write this, we can write it in this manner. This is change in velocity, change in velocity divided by, divided by time taken. This is your time interval. So for the first one, we aren't really seeing any change in velocity as such. The plane is moving with one, with one velocity, 400 kilometers per hour. So there is no change in velocity. So there is no acceleration. So this one is wrong. In the second one, it says a ball rolling downhill while its speed changes from 30 kilometers per hour to 40 kilometers per hour in five seconds. Okay. So here there is some change in speed. And if the direction is constant, this can be written as change in speed as well, because velocity is just speed with direction. So if the direction is not changing, velocity is just speed. Now ball rolling downhill speed is changing from 30 to 40. So let's see what the change in speed is. That would be 40 minus 30, 40 kilometers per hour minus 30 kilometers per hour. So 10 kilometers per hour, that is the change in speed. And this is happening in five seconds. This is happening in five seconds. In five seconds, the change is 10 kilometers per hour. So we can say that in one second, the change would be two kilometers per hour. So the acceleration is two kilometers per hour per second, that is the acceleration. For the third one, third one says a mouse moving uphill while its speed changes from 10 to 15 kilometers per hour in two seconds. So here the change in speed, that is five kilometers per hour. And this is happening, this is happening in two seconds. In two seconds, the change is five kilometers per hour. So in one second, we can say that the change would be 2.5 kilometers per hour. So the acceleration here is 2.5 kilometers per hour per second. We can say that in one second, the speed increased by 2.5 kilometers per hour. But over here in one second, the speed increased by two kilometers per hour. So we can see that the acceleration, it's highest for option C. The magnitude of acceleration is more for option C. And this also tells us one interesting thing which is that it's not necessary that high velocity means high acceleration. It's not always true. Because we need to really see what is the change in velocity. For instance, in option B, we can see that the velocity, it's going from 30 to 40, it's going to a higher velocity compared to at least 15. But still the acceleration in option B is less because the change in velocity, how quickly that speed of velocity changed, that was lower compared to option C. All right, now let's move on to the next question. A car is accelerating. Which of these is necessarily changing for the car? We have to choose one option out of these four options. Again pause the video, give this one a try. All right, again hopefully we have given this a shot. Now the case is just saying that a car is accelerating. That's all that it says. And we need to think about whether or not the speed is changing for this car. So let's try to think about this. What does it mean that a car is accelerating? First, what does accelerating even mean? This is change in velocity that is delta v, change in velocity per unit time. And what was velocity to begin with? Velocity, velocity was speed, speed with a direction. There was magnitude and there was direction. So for an object's velocity to change, either the speed can change, either the magnitude with which it is moving, either that can change or the direction can change. For example, think about an object moving with a constant speed in a circle. Object moving in a constant speed in a circle. Here the magnitude of velocity that is not changing. But the direction is constantly changing. So in this case we can say that there is a change in velocity because even though the speed or the magnitude that's not changing. But the direction is. So even this is a case of change in velocity and even in this case there will be some acceleration. So option A is actually not right because it's not necessary that the speed has to change. Even the direction, only the direction can change and even then there will be a change in velocity and an acceleration. And by similar logic we can say that even option B is wrong because again we can have an object moving in the same direction but with increasing speed. With increasing speed. Now the direction is not changing but the speed is changing which means again the velocity is changing because velocity is both speed and direction. So even here there will be some acceleration. Option B is wrong. Option C says either speed or direction which is right because that is those are the cases that we discussed. For an object to have a change in velocity either the speed or the direction can change. Any one of them can change and there will be a change in velocity. Both of them can also change, there will be a change in velocity. So option C is it's right. And option D says both speed and direction. Now again the question is asking necessarily changing, necessarily. So it's not necessary that the object has both of these quantities changing. Anyone can change and there will be a change in velocity. So even option D, this is wrong, this is wrong. It's not necessary that both speed and direction has to change. Only one changes and there is a change in velocity and there is an acceleration.


f the scope of her job would be to manage our public outreach and this is really a public outreach and it seems like it was housed just at one ultimate place versus all these different school sites I think there may be less potential for a breakdown you know that those school sites should be communicating to our PIOs what's going on what their schedules are and then having that and then lastly that it's an equitable situation that it's like we're not just doing these in the schools in the city of Watsonville in the south zone but the schools in our class that are already getting used of fields where schools you know community use in our schools not happening that everybody's having to go through the same process we don't have one process for the north zone and the other process for the south zone but that's I mean our superintendent constantly preaches equity so I think she would agree with that so yes you're correct this is equity this system is for more central south all throughout the whole district and then this is currently housed in our maintenance department because we also have to assign either custodial services and or maintenance workers the gates need to be opened up closed etc and or the cleaning of those it depends on the fee structure but that's also housed in maintenance but we're also looking at code oversight within the district office but right now it's in maintenance so it's not an age school site that would seem like chaos correct it's at the maintenance department and then it's like the world order that's the easiest way to compare it to the permanent okay thank you and thank you again for your work on this presentation what I know that do we know what percentage our students they actually serve good question so that's actually in our last meeting I requested their rosters and then how many out of their students or players on their lead are our students and so that's something I requested in our last meeting so they're actually working on getting that done good and the reason why I ask that question is because if the annual of building this partnerships and bringing the men into freedom of management school is to expand access to a well maintained field for our students I want to make sure they're given priority another concern I have is ensuring that again our students are given priority when it comes to schedule because I know how they manage several leagues and I just want to make sure that they don't have control of dust correct so that's one good point that going back to the win-win is making sure that our joint studies agreements have district as priority the school site and then the district and that's similar to the Aptos level league is that we have priority and Aptos junior and for example say there's another baseball team that we have at another campus that wants to use that then they get the priority so it'll be a similar set for sure that's what I'm hoping for because I know that they're willing to invest a lot of money in that field but really was a cap not what are they asking for we're moving in that direction of formalizing an agreement I just want to make sure that it's clear that we won't be given preference to won't make over the other it's first our students and then everything else after that any more questions from the board okay all those that we have a motion is it discussion oh it's a motion it's a presentation yeah okay unfortunately we have to extend our meeting because there's been a lot of questions and things we've discussed so we have to extend our meeting I think we should maybe extend our meeting until 11 I think we can get it done by then so I make a motion to extend the meeting to okay all those in favor all those opposed okay the last who's 4-2 10.2 our citizen bond oversight committee by Bill Beecher who's the president I've been involved in Measure Out for 2010 and so I've got a lot of history I thought it was important it was such a new word and a very strong prospect that we're going to have to do another measure there are lessons to be learned and I need a process similar to what Trustee Costin uses mine is you know what went well what did you go well what did you do different the next time rather than do it simplistically I located that into this presentation so for contents we're going to take a look at the independent bond you've already seen this in January when Joe presented it we're going to look at the measure all the lessons learned and the breakdown of the demographics training and critical projects and what the COC did not this came out in the grand jury discussion two years ago and then the thing called augmentation which I think is a wonderful thing that the district did something needs to be said about that so the independent auditors report as you know was presented to the board in January big thumbs up this makes several years in a row where it's just really clean it says a lot about the finance department and how well they have done to track it it also says that we've been spending our money correctly on demographics this was an interesting thing that until I ran for the board I didn't realize that we screwed up when we did measure out there was a major effort done in the south zone to get voters out and to be high they have played a terrific job on the home banks there was a minor effort on the map toss we did get a lot of people out to help us with banks now the demographics are that people in the north zone are in the aptos area to vote and so over 8% of the people vote in the loss of voters less than 40% of the people vote so if we want to act for another measure we ought to work like hell in the aptos area because that's where your voters are and we didn't do that so we were lucky that it did pass so at the training area this is something where I think we really fell down we did good training for the administration and the COC however we did very poor training for the school sites, the principals and site councils this slowed down our ability to implement the programs because the concept that was put in place was that the individual site council and principal would come up with their list of the projects in prioritization truthfully they had no concept about what a prioritization was because when I sat with some of them they just wanted it all not realizing that we may run out of money because we were stuck in on the money allocated for each of the schools and when you don't have that money you've got to cut stuff and then you get into those squabbles and so there was a lack of training now I'm going to address some of this at the end but Joe also has some things he will do in his presentation to look at what are we going to do going forward where are we going to do different so as I said this kind of lays in getting projects started and there was a lot of writing so what should it have what could it have been by learning from this the one you train principals and site councils on the process setting priorities I was shocked that most people didn't understand about setting priorities you can't just have everything and then real making we ran into Victor and I ran into this over and over again changing priorities when we change principal when we change site councils they all had their own idea of what the priorities should be and so they could change them and that meant we had to put a stop on programs that might have already been started to push something ahead of something else and they didn't understand that impact in making change so we need to train principals and site councils as they change over time and I know at Marvisto and a lot of time in the last eight years we've had four principals each with their own idea of what should be done and they create a lot of confusion a lot of frustration for Victor and the solos guys so great good projects this came up after the fact this was not built in an original process this is something that we brought to the board a year ago that Victor and I changed and added into the process that great projects such as replacing roofs or mandated changes were initially left to the site councils that had to be built and so we replaced it with a new procedure they don't get to vote it has to be done and has to be done so what the COC is not there were suggestions in the grand jury report that the COC should have been a proactive committee second guessing plan well if you look at the state law on defining what our role was that's not even it's really the passive role that we look and we're just a judge to make sure that the monies are being spent properly now augmentation is something that the district has done we ran out of money labor return by 5% so in some cases we didn't have enough money to finish some of these projects so they augmented the funds measure L funds with other funds what it was made of 39 or other areas in order to make sure it got done and I think that's a big time thing that the district did and kudos for having done that so questions on my part and then we'll let Joe talk to you about stuff in the future along with we've got projects coming up for the summer yes you have questions this is the one time I get to ask you a question what do you see next well Joe's going to address because I brought up some concerns and things that I have seen and we discussed that and so I think we have some good approaches for doing that Joe are you thinking yes so I have to disagree with you a little bit about the whole Aptos piece because there was a tremendous effort to get out the vote in Aptos on measure L and in fact it won overwhelmingly so I multiple nights we was talking to citizen groups including Aptos soccer club who sent out an email to all 6,000 email addresses you know I was at Aptos Little League I was at Rotary I was everywhere talking about measure L with staff my comments were really more about just the site of the fence on the west side of the highway we had three teachers and one principal myself my wife ordered against measure L because she said teachers don't care why should I go for it so you really helped a lot with the PB high kids getting out the vote in terms of doing the canvassing and so to them we are indebted really but there's something to be learned on how they did that and what they did is wife couldn't be done that better than like great MR don't turn out that's where the money is how many members are on the COC right now and do you need more membership the group was big correct? and how do we appoint people does the board do that or the district has to do that the chief business officer in the past the one that's gone out but it's winding down so it's hard to find people to come in and I'm sad as the chief and I'm not supposed to sit for one or two years nobody wants it yeah so I get unfortunately because I feel like I've got invested part of this thing I don't mind and just for the public's sake do we have any more thoughts to sell or are they all exhausted so they're all exhausted and we took down the third issue we took down the district did that approximately two years ago yeah for the public's sake since we're on the topic and so I heard you say that the money is gone is that true? it's not all spent because we still have the bucket for power for high school etc and all the other projects moving forward we drew down the third issuance the third issuance is allocated so so there is no fourth issuance etc so the money is all drawn down and now we're looking probably about four to five years to phase that money out and the various projects okay and in terms of the endowment trust funds we have like a maintenance trust fund and a technical yeah tech trust fund and I know those trust funds need to be expended within I think a ten year period from 2012 is that correct? correct and how are we doing on those? we're doing really well 700,000, 500,000 annually over that period of time and so I know both our maintenance department and our IT department are maximizing those funds okay great and then are you keeping your finger Joe on the pulse of making sure that if we can refinance any of those bonds that we will I know the interest rates are super favorable compared to what they have been the last three years but I hope somebody's paying attention to that so yes so districts are allowed to refinance as long as you do not drop them down the issuance so the district already drew down the third issuance so we don't have the ability to refinance oh I didn't know that piece but moving forward and I'm aware of that in the oversight committee so as we move forward in the new bond when that time does come we just as fiscal stewards and as board of trustees is making sure that we're maximizing when we do refinance and we maximize those tax dollars okay thank you thank you Bill and everybody on COC for service Mr. Beecher I actually have a couple of questions for you hello good evening sorry it's cold in here for you I have sat on this citizens oversight committee in our community and I know it can be a very daunting and thankless job and the recruitment is an extreme struggle so with that thank you you know one of the things that really caught my attention in what you were discussing there's that old saying you know right two things in life are for certain death and taxes I think a third should have been added to that change good bad and different changes right I mean since this bond our district has seen significant administrative change we have a different superintendent who some could even call a change agent she's very different from her predecessor so in addressing the issue it's important to identify what you're trying to hear what you were saying about the change changes in principles changes in those look the school site level right because kids leave schools we get those parents leave new kids new so what are your thoughts or recommendations to this governing body for addressing that when change is inevitable it's such a thing that it's a long process it's kind of like raising your children you can be very rigid and you just have lots of problems you just have to be flexible you have to look at the situations in the last year was an example where we solved problems with the process so we may change being open and recognizing when things are working and making the necessary changes if you go into thinking you've got a nail augmentation for example where the district breaking out is that we were not alone and then going out to the sites and working for the sites and helping train some of the new principles we went out and we've worked with Bradley and Marvisto recently last month because they wanted to change we wanted to change the priorities so we could get some part of our discussion in the framework and like you recall when Trustee Herrera was on the board and particularly actually with this school we as board members would get complaints that nothing was happening here but he had almost a constant frustration that the local site for the school was almost nothing at times but less a handful of people if you will well that's important with that trouble you know to create like okay so what is the plan for us here at the school so addressing that issue well partly that because this happened at other schools well I mean Bradley just recently at our CMC meeting came in and we heard we haven't done anything Marvisto involved but we haven't done anything well out of like $6 million a month ago what do you mean we haven't done anything transparency was issued four years ago that the way we were reporting the project was very confusing that we had 10 pages of projects but they were in general and so you'd find apps on all 10 pages and you'd hit the hunting pep and made a part for the board for us on the CMC to follow what was being done so to the credit of the major group they organized so that you had the north zone by school so you could look at Marvisto or Anacost High and you saw all the projects for that school right there so it makes it easy for us or for the principal or the site council to say what will be done and that's not going to show how to make sure that things are easily read four years ago it was a jump and we had a lot of discussions with the CEO two back that we needed better transparency and he didn't want to make those changes and under melody we can make some changes and then we got competing up by the branch jury we weren't being transparent we had already made changes for which I voted a very angry rebuttal to the settlement over the castigation that we'd gotten because I thought it was unfair it didn't show what progress we made they reported on something that was true two years before and it was fair to say we were ugly at that time but they didn't show what we'd done it was unfair to the district and to the COC especially the facilities we've been working the parts out so you gotta be aware of what's working what's not working back to your process or my process and you make the justice because if you stay with a rigid plan you'll always be disappointed and you'll be bitter is that... yeah I think you have to trust that maybe you maybe more reports more frequent from the committee to the board's you know just the circumstances yes and no but you know most of the... we need to control and micromanage and just saying to make sure well we have that discussion about how often do we how often we go most of the work is done in the summer so in fact the COC and the youth board need to have an idea going in the summer of what's going on because you're not going to be asked by your constituents we get asked by your same constituents because we haven't done anything and then you need to know in September or October well what did you get done you said here's what we're going to do now tell us that you got it done yeah I agree there should always be the vision to plan the execution the execution is fine to change as long as it's reviewed the what worked and the what didn't work in the last thank you yeah I think we're going to be different the next time thank you alright so quick update on our summer projects and how we're moving forward so for the North Summit plus high school we're preparing a long overdue structural drywall and roof repair and building D&E and then really excited about the Student Quad's safety and accessibility improvements the Student Quad's going to have a shade structure and really a place for students to modernity hang out and really be a Student Quad so we're really excited about that and then Marvista phase 2 safety and accessibility the parking lot the Super Service Center is where we're updating that for the Sendul's zone you have the list here and the list varies from outdoor multi-use pavilion thank you for the drywall repair building the middle school is the MPRHPAC unit so we're definitely going to be moving forward for summer 19 for the South Zone you have the Scott, the Quiti, the Loni perimeter safety fencing ADA accessibility for Vince Scott Loni front entrance improvements and it's going to look pretty nice and the site safety Bahado Middle School perimeter fencing and safety improvements for the site as well and that's in the South Zone district wide one of the items we heard loud and clear in my site visits is we see throughout the district the need for whether it's carpet, tile or vinyl or pouring and so these are the sites throughout the district that we will have some pouring repairs and installations throughout and then for a clock bell paging we have some aging systems throughout the district Renaissance and Bradley and then Bradley we're currently in discussion right now to the comment about Mr. Beecher mentioned installing action and so for Bradley I mentioned we've been meeting with the principal and we are actually looking at two and we're looking at it right now whether installing a track a walking track for the kids and or painting the school this summer and so one of those items will be completed this summer we're still finalizing the cost estimates with the architects et cetera these are non bond projects so these are other projects that we take on the facilities department and other funding sources so migrant head start the facility needs specific per site in our head start program prop 39 energy efficiency projects this is not prop 39 charter but this is the HAC upgrades and lighting upgrades for our dependent charter schools and then you have the prop 39 at EA Hall or navigator charter and that's the portable restroom which enables navigator charter to have limited access to EA Hall campus and so it separates both entities and then in child development the Watsonville Children's Center a forum placement new carpet and tiles PBI football field the demolition of the portables and you can see we are working on the grading and leveling the field out and so ribbon cutting and thank you and our superintendent for her leadership to making that happen and I'd like to thank our facilities team and our facilities lawyers and our consultants to helping us hit that deadline so we're very excited we're moving forward the demolition has been completed we're working on the clearing of the grub and the grade and et cetera and now we're working on the removal modification irrigation system to be reinstalled in a great position but overall I'm pleased to announce construction is on the timeline and we're on schedule and so we're really excited about that the auditorium this one is an estimated timeline I mentioned estimated because this is with the city planning department and so these are verbal agreements that would come to and we are going to it's a partnership where I would say it's going a lot smoother than the football field permitting process and so they shorten down for example their six month review legal review window they've shrunk that down to approximately six weeks and so we have the milestones there Jen Ford the staff reports to the planning commission and all the attendants there and on the 15th we are meeting with the architect our leadership team facilities and reviewing value engineering and the scope timeline and the budget of the auditorium just making sure and nice surprise for the champion of Swellows award that I got this evening but the other piece is the design of the auditorium to making sure that it's eco friendly and it's easy to maintain from the exterior so lessons learned that we learned from the other buildings that we have on that campus and then it goes to the council and we'll come back around but we'll provide an update to the board as we proceed but this is moving forward we expect in 2019 for the project to start it's still to be determined on the start date because we have a process of going out to bid etc so that we just want to make sure this is a ten minute timeline that I want to provide just to show how we're making progress moving forward with our citizen board oversight committee and Mr. Beecher's leadership I'd like to thank him for his leadership he's agreed and really supported in having quarterly meetings and as he mentioned we were having only two meetings a year and now we change that to quarterly so that we can get in the front and to some of the questions that we answered to have full transparency prior to summer, during summer, after summer and just a pulse check on the funding the other piece is making sure that we have for our new principals a new principal orientation and a training because as we have new leadership at the site not only do they inherit the student achievement plan and the academic component of it they also inherit the business operation side of that and so we want to make sure they're successful the other piece is to invite in partnership with the board is a 2019 summer success bus tour after we complete our projects we're going to have a bus tour of all the projects completed in partnership with the CBOC and the members of the community and our elected officials one of the biggest challenges and I think Mr. Beecher touched on it is we need to define our developing project master schedule with budgets and that is something that we're working on right now in the latest terms what are the projects in 2019 what's the dollar amount over and over on the budget 2020, 21, 22 so it's a multi-year master schedule of projects and how they are funded and so it's really like a roadmap for a facilities plan and that's something we did not have but we're developing now and the other component that we're working on right now so we can link up with our financial system to making sure that we can track every dollar spent in how we are funding our projects throughout and the other component is building our internal team which we are working on right now in staffing and recruitment of our department for planning specialists senior construction manager and positions that are needed okay public speaker is Stacy Anderson still here? yes she's still here hi once again I have a lot of concerns about what's going on with our facilities at our schools our school should be a community where you should feel safe and invited just walking out right now it's completely pitch dark you can't go out there without your flashlight on your phone or whatever stuff like that easy maintenance should be maintained preventative maintenance it's safety, it's a safety issue anybody could get rid of my next thing is I've been at five schools in this district north, south, center and they all had major major issues and a lot of it could have been prevented by preventative maintenance clearing our ringing gutters you know taking care of our facilities painting them when they need it and it's not happening I don't know if we're understaffed or if it's for management on the upper end I really don't know what the answer is but it needs to be addressed it's really staffing our schools the grants have breasts our kids could get tetanus there's rats in the portables you're looking at infectious diseases and now I'm going to move over to him Sir, you said Bradley, he's already spent four out of six million they have more than half of this alright cause I was gonna say I'd like to see his breath because I haven't seen Bradley spend hardly anything other than their new belt system I'm around a lot of schools and I see a lot of things and I feel really bad for these kids these kids should have a great place to come to or it's inviting it's nice I'm not saying we have to have state of the art anything but you know mull on our windows or broken things up there kids can get hurt if that falls it's not let's keep maintaining our buildings better and do better by our kids a reminder that when we did the facilities on back in 2010 we identified that we really needed to spend $300 million the first for the basis we started well the tribe 210 then I think it was 180 and eventually ended up with 150 half of what we identified prior to that in 2008 we cut 28% of our classified staff which included a huge number of facility people and so the ability to maintain our facilities went down big time I'm not trying to make excuses for Joe's guys it's just if you don't have people you do the best you can with what you got and I know I personally and other people have we had high school students complaining about the restrooms can't we maintain the restrooms for me on the COC I'm sitting there going we're putting in all these new facilities and we really don't have enough people to maintain them they're going to just go downhill that problem still exists from my perspective we haven't been able to hire back that 28% of the people we cut and so the staff we've got 28% so yeah it sounds like making excuses but that's reality that's what we're facing we've got dryrod out there and we need money to go fix that and that will cover the measure also Joe do you want to add to that? I'll just be short and brief we have the work order system we're reviewing it and we're providing the board support to establish a deferred maintenance budget which is the 3% so we have that established so we met with the department and we're reviewing all the work orders and making sure that when you complete the work orders so that's currently under review and so I'll provide an update at a bigger point in time thank you okay any other questions from the question? two questions mini white and e-all I know I've been under the student parent committees for a long time and I know recently they asked for any remaining money to be put to portables two we still have a pile of dirt here at e-all which has been there a long time and I would just like to follow up and see what's going on with that alright so definitely a shift I think I know we touched on this how do we move forward so one of the items that for e-all and mini white we have an allocation in the bond program it's not enough to complete the big picture project so for e-all we don't have enough to do a football field and track etc and for mini white we do not have enough to demolish all the portables that are in place with all brand new but the direction and the board approved I believe last month to architectural firm not the same one to do a review and assessment of each canvas and the directive is what can we get done with the money that we have rather than holding on and saying we don't have enough is what can we complete with the money we have and move it forward and so I say that like for example mini white there's 15 portables and we don't have enough money to do 15 10 or 20 and so that's the direction now and so that's a big shift from what was before and then the field the mountain or the dirt we're looking at that right now it is clean dirt and there is dirty dirt but that has been tested and it is clean dirt so we're also looking at that for pvi would be either used as backfill for the leveling of the field and we're maintaining it for e-all field but one way or another we're going to make sure that and I know it's an eyesore so we're going to form a union on that to the principles that we do in e-all now currently right now the architects were just recently approved by the board so they're fairly they did complete site visits and they're doing very preliminary reviews right now there will be a meeting with the principals to kind of give them the big picture and then but also I believe both architectural firms did get input from the principles of kind of the need of the campus and how they use the campus so that's been done but then we're going to come back around with kind of the preliminary drawings I know for sure that the parents in the school sector really might want all remaining money to be put to principals I mean to portables and I just want to relay that message thank you I just want to be able to go back to these parent councils and import back in the most minute, thank you I just have one quick question because I get the same constant complaints that Danny does Joe with regards to the dirt because of how it has been there it's not just you know we talked earlier about equity it's not just that it's an eyesore you have to it brings on another perspective it makes it look like it's a good dumping ground let's just dump it there it's been there for a long time so could you tell us a time frame I heard what you said could be done with it I understand construction I know that it was between clean dirt and clean dirt we have heard from administration it will be gone by X, Y, and Z we're sorry it's there but it will be gone at least what could you tell us what we could say six months a year I would say within six months we'll know within I would say a month the timeline and then know when that dirt will be either used at PBI or we need to relocate or use it somewhere else in a cost analysis because believe it or not clean dirt is expensive but if we just relocate it and get rid of it what is the cost to do that and then we'll need that within the month we'll know the timeline for PBI and then also what that credit looks like because that's also a resource to that project so we should get something in return because I think the community is wise and good dirt and so why the heck we just donated it to get rid of it so I mean you've given us at least some response to tell our constituents who are complaining so it would be nice to know hopefully within six months it could stop being here and if it's still there then I guess any of you are going to ask you why within six months and I do understand and with the superintendent's support we are shifting on responses within our law program because we understand the importance of coming through a map and then showing our voters for a future fund that these projects have been completed and so we are working here I get to talk so like many districts in the state of California we face devastating budget cuts for year after year after year and I think in my tenure we cut about $56 million in those years we are right now up to I think and I don't know what the governors may revise maybe up to the 2008 standard in terms of allocated budget for this district so well I mean that's not good obviously because of the crazy amounts of costs that we've incurred so between health benefits and salary increases that takes up a giant piece of our budget and we're still at 2008 levels so like Mr. Beatrice said we did cut a ginormous amount of staff I remember Bobby Salazar telling me at one time I also had like 17 custodians at the deepest part of our budget cuts I think he was the only one there was him and there was a night staff to cover all that for your campus or whatever it is and clean everything I mean it just we cut as much as we could until we couldn't cut anymore so that explains and at the same time the state cut our deferred maintenance money so we weren't getting any of that so essentially we were left completely devastated so little by little that's one of the reasons our campaign is so hard for this bond is because it was the only way at that time to make any improvements in our facilities so all of us up here are very well aware of the crumbling infrastructure that we have here in this district because this is a very old district and in addition all over the state we are very well aware I think the governor's award that he's trying to remediate that now I think the improvements that we made are important when we sold this bond program to every single school site we wanted them to have buy-in because they're stakeholders and we allowed them to sort of prioritize decisions and in some cases those decisions make the best for the school and we had to reprioritize them like Mr. Beecher said and do roofs which are not sexy you know but they absolutely need it because we have to protect our buildings so a lot of money was reallocated to the roofs which you know people don't see that because it's up anyway we needed 300 to just do the bare minimums we only got 150 going on so thank you for all the work and I know you're running a skeleton crew in your office I saw that Howard retired congratulations to Howard but I worry that that whole crew that knows what to do in facilities and maintenance we just don't have the depth of experience there so I'm looking forward to seeing the new crew and I did have a question I did also so we are moving forward and we're building an internal capacity and we have Ryan he's one of our planning specialists that is taking the leave and then we're also maximizing other facility funding so what we get from the state in your corrective work cuts and that flexibility given to districts but there's other, there's local funding that we're also trying to maximize and then we went up to the eligibility so we're maximizing and the other thing is when we got, when we went out for that run we were sure that there would be all this sort of matching dollars from the federal government that never came so we thought we could maximize the 150 into something that was close to 300 and much of that never ever came to fruition it just wasn't available though so that was another issue my question about EA Hall EA Hall was really a hero's big thing like he wanted the fields completed correct so you're telling me would I just hear you say we don't have enough money to complete the fields here correct there's not enough to complete the football field the track, etc but what we're doing now is like the direction to the architect is what can we get done with the money we have and then my role was to find other funding to fill in the gap so Orph to Orph has been a very generous partner with us and so really want us to reach out to them because if you want me to do it I will but they have money that they could provide for the track I appreciate that and Orph to Orph did and I should have put that on their phone they did reach out for PV High and they also mentioned EA Hall field so they already approached over the other thing you know I heard you talk about Bradley putting in maybe a track well I wrote a grant for Valencia 10 years ago and got $10,000 to put in our little track at Valencia that came from the work tool so they'll do elementary schools too so I encourage you to reach out to them and I'll help if you need it thank you okay we're actually going to be able to finish the agenda I mean Levin is a consent agenda okay the speakers are there any deferred items okay can I have a motion and actually 11.6 so we vote on what we have so I'm going to so I'm going to have a second we're going to vote and they go to the deferred so okay so you have a first and a second you have a first and a second yeah she amended it she amended it I'll second so all those in favor do 11.5 11.3 11.3 so this is just a question about the final location if Dr. Rodriguez could speak to this I didn't really think the other school districts seemed to get like so much more money and we have got a very small amount of money so our original intention was to apply for two separate grants these grants require matching funds so we were also applying with the consortium with the city of Watsonville Hartnell College Cabrillo College and PBPSA the second grant did not materialize and so therefore we were left with just the small grant which had a very small action why did the other school districts get such large allocations like SLB for example because they did not do they only did one petition and so they were able to support the matching if we would have received both grants we would only have been able to afford this grant because we were going for a large amount in the other grant and there's a matching component they gave us 200,000 we had to commit 200,000 of district funding so we just didn't get the grant they did not choose us there was an error in submission and so it was not submitted correctly okay thank you I might have a little quick oh sorry we're voting on 11.3 of motion we just mentioned the grant on the first half what? okay all those in favor all those in favor all those post okay you're doing 11.5 okay 11.5 so this is a consent for transportation plan to ensure school stability for students in foster care so this was a confusing backup for me to understand who's paying for what so I was wondering if somebody could speak to that because I get the idea and the intent I looked at John welfare so I totally get it but it's just they've talked a lot here about LEA and so who is actually going to be paying for the transportation? they answer that as an intent right now basically the overview is generated on student best interest so it really is up to the LEAs to work together depending on the placement of the actual child so if the child is going to be added in our county perspective it really is up to the entire TM team and those pieces that go into placement for students as well as to whether the student will be able to still come back to the original district of origin or maybe just their placement so it is kind of a team decision as to what that looks like in terms of what it means financially for us this has been going on all the way in our region in terms of best interest for students and working out with each other and really figuring out where does that student necessarily belong what are the transportation needs and occurrences but there's been no cost to impact to insider so we have just as many kids from the majority of our kids stay within our district at least those that do go out we've made arrangements to be able to take care of that and by Tversa so we receive students from others as well they're LEAs are we considered an LEA we are a local education agency that was like the secret district I mean the COE so it's us it's us too okay I don't know if it doesn't pay for any of this transportation it's on the education system I have the latest when that has happened so sometimes depending on the agency and what it looks like so this is county generated as well so as a county team basically the rest of the districts have gotten together and said that to this point this has been very renewable for us to be able to have a conversation back and forth as to really where the student gets to be able to stay within our own region because we're larger okay everybody satisfied okay do you have a motion all those in favor any other deferred yes so 11 points 11.1 no that's not it sorry 11.16 that's what I meant 11.16 16 navigator I'll speak to this so when we talk about the navigator to our school about first year 5 to 2 million dollars out of our budget is this an addition these bathrooms that we need to build out and all the other things to build out is that an additional cost on top of level 5 to 2 million so they're the cost to us will be approximately 2 million this year it will be a loss of about 2 million dollars plus all the construction no including okay great this is what Joe spoke to this in his presentation this is the same thing right that was the connection I made Joe talked about it coming out of measure L funds no okay because it was in the measure L that's why it got confused it was in the summer school it was in the summer project so it was on the last slide that includes other funding sources okay I'll make a motion to approve 11.16 motion no 1 closed session item 2.2 I move to approve the certificate of personal report as presented by district administration on May 22nd 2019 with 137 and 12 additional action items motion no 2 closed session item 2.3 I move to approve the classified personal report as presented by district administration on May 22nd, 2019 with 53 and 5 additional action items and that's been number one the power of alienified school district is pleased to announce the selection of Carlos Baran as the new principal at MST Elementary Carlos comes to us with moderate minutes in the school district where he served as assistant principal in the school district Carlos has served as the power of he served as the principal Carlos was a student of the power of alienified school district and expressed his desire to impact his community and the district that served him the power of alienified school district is excited to bring back one of its own to support our teachers and students and that's been number 2 the power of alienified school district is pleased to announce the selection of Carlos Baran as the new coordinator for migrant seasonal hit start disabilities mental health program Mr. Rocha possesses a number of outstanding qualifications including a master's in early childhood education and a bachelor's degree in human development for Pacific Hills College and a socialist degree in early childhood education for Korea he is a certified designed result developer pro-cold trainer pre-K class observer and a pro-class opening doors parenting correctly facilitated Mr. Rocha is currently a quality enrichment coach for encompass community services where he also served as a supervisor and new teacher and has been a teacher since 2005 Mr. Rocha also served as coach for first 5 senators county with his very experience as a coach working with principal students we believe that Mr. Rocha will be a great asset for migrant seasonal hit start this is going to be for our next actually 2.7 final settlement agreement and we'll use for one special education student the vote will be 7-2 here you go thank you very much so our next meeting is going to be June 12 Wednesday at the district office board with this time


We have been looking at predicting the conversion in an non-ideal reactor provided the RTD function as function is known. So there are two types of models that we are going to discuss, one is the segregation model, the other one is the maximum mixedness model and these are two extremes which actually provide a bound for the conversion depending upon which is the, what is the order of reaction and the kinetics of the reaction which is conducted in the reactor. So these two extremes are the early mixing, early mixing model, a regime, early mixing that is one extreme and the model that represents early mixing is the complete segregation model while the late mixing which is the other extreme that represents the maximum mixedness model. So these two extremes essentially represent the two levels of mixing where the, two levels of mixing of the macro fluid globules that we actually defined in the last lecture. So let us look at the first one, the segregation model of a reactor. Now suppose let us consider a CSTR, so let us consider a CSTR or tank reactor, it could actually be any reactor and the, let us assume that the fluid elements of different ages they do not mix that is the, that is the segregation model and which also which means that they remain segregated all through, they remain segregated all through and the flow is essentially like a series of globules where one globule enters the reactor at a certain time and that gain that spends some time, another globule which enters at a different time the age of that particular globule is going to be different and which means that the globules of different ages they do not mix with each other. So, so flow is essentially a series of, series of globules and we may assume each globule as a batch reactor because it does not mix, so whatever reactant which is present in this globule it continues to undergo reaction as long as all the species which is present in that globule is gradually going to complete conversion. So therefore, each globule is considered as a, we may consider that as a batch reactor. So now how do we model this? So we can actually depict this, depict the segregation, depict this particular aspect in a CSTR as basically a tank which contains several globules and each of these globules are now going to have different ages, so that is going to have a different age, this is going to have a different age and this is going to have different age and each of these globules can actually in principle be of different sizes as well. Properties that are of these globules will be that they will be of different sizes and then more importantly because they do not mix each of these globules as actually going to retain their identity, they are going to retain their identity and there is no exchange or exchange between globules. So there is no exchange of molecules or matter between different globules and each of these globules will continue to have maintained its own identity. Now one may also depict the same picture, similar model in a plug flow reactor. Suppose we have a continuous flow plug flow reactor, so suppose if we model a continuous flow system of which is a continuous flow system of the non-ideal reactor as a plug flow reactor, suppose if we model this as a plug flow reactor then if you want to incorporate a segregated model for this non-ideal reactor this may be depicted as follows. Suppose if there is a tube and if there is a fluid which is flowing at a certain volumetric flow rate V0 into this tube and if the volume of the tube is V, now instead of the fluid leaving from the other end of the reactor directly the fluid can actually be taken out from the side of this tube at different locations along the side of the reactor and they can all be joined together and together they actually leave the reactor. So now each of these streams if because they are withdrawn at different locations each of the globules will actually have different residence time. So the location where the fluid is actually withdrawn from the reactor can actually be decided based on the residence time distribution of the actual non-ideal reactor. So suppose if this is the residence time distribution, if that is the residence time distribution and that is the E curve which is the RTD function which is actually measured experimentally of a real reactor then based on this RTD function such kind of a withdrawing of the fluid from the reactor can actually be designed. So the fluid which is actually withdrawn from the reactor right at the entry location is going to have the shortest residence time and the one which is actually withdrawn at the other end of the reactor is going to have the longest residence time. So that is going to have a long residence time. So therefore what we have done is we have removed batches of fluids from different locations inside the reactor and the location from where it is withdrawn is actually specified by the residence time distribution function E of t which may be measured experimentally for a non-ideal reactor. And because we are withdrawing from the side there is no interchange of molecules between each of these globules when they are actually present inside the reactor where the reaction actually occurs and each of these can actually be considered as actually a batch reactor. So what it suggests is that the mixing for this kind of system as actually the fluid appears as a well mixed system when it enters the reactor but when it leaves the globules are actually completely segregated. So therefore the reaction time in batch in each of the batch reactors that is each of the globules which may be which is basically withdrawn from different locations along the side of the reactor that time the reaction time of batch reactor of each of the batch reactor is equal to the time spent in the reactor. So this is the reaction time spent by each of the batch reactors. Remember that every location from where the fluid is actually withdrawn from the side of the reactor that globule can actually be considered as a batch reactor and the time that is spent by the reaction time of each of these globules that is each of these batch reactor is equal to the time that it actually spends in the reactor itself. So therefore the mean conversion if x bar is the mean conversion that is equal to the average conversion over all globules. So what is of interest is essentially this mean conversion. So we want to predict the conversion of the reactor and what we essentially require to need to predict is this mean conversion from the reactor. So how do we find this mean conversion? So the mean conversion of globules with residence time of a certain time interval dt. So let us say that the mean conversion of globules with residence time between t and t plus dt in that small interval of time if that globule has a residence time in this small time interval then that is essentially given by the conversion achieved by a globule after spending t amount of time in the reactor and that multiplied by the fraction of globules with residence time between t and t plus delta t. So that is the abstraction of how to get a mean conversion of globules with a certain residence time between t and t plus delta t which is essentially the conversion achieved by the globule after spending that time t amount of time inside the reactor multiplied by the fraction of the globules with that residence time between t and t plus delta t. So now if you put the corresponding expressions corresponding to each of these terms in the mean conversion we will find that dx bar which is the mean conversion of the globules whose residence time is between t and t plus delta t. So that should be equal to the conversion achieved by a globule after spending that time in the reactor multiplied by the fraction that has a age between t and t plus delta t. So therefore from here we can write the dx bar by dt which is the mean conversion that is equal to xt into e of t and therefore x is equal to integral 0 to infinity x of t e of t dt. So remember that the x of t which is actually present inside the integrand that is essentially the conversion in batch reactor because we consider each of these globules as actually a batch reactor. So that is the conversion as though it were a batch reactor and that multiplied by the corresponding residence time distribution integrated over all residence times will give the mean conversion. So let us consider a first order reaction where A goes to products with the rate which is the specific reaction rate k and for a batch reactor the performance equation is d minus dna by dt that is equal to minus rA into v where v is the volume of the reactor and let us assume that it is a constant volume system and so now we can use the relationship between the number of moles with the corresponding conversion and we can rewrite this equation as na0 into dx by dt that is equal to minus rA into v which is equal to k CA0 into 1 minus x into v and so from here we can easily decipher that the conversion is equal to exponential of minus k into t and remember that the CA0 into v is essentially equal to that is equal to na0. So therefore the conversion as though a conversion in each of these globules is given by 1 minus exponential of minus kt and so from here we can now find out what is the mean conversion we know the mean conversion is equal to integral 0 to infinity that is over all residence time of the product of the conversion in the batch reactor multiplied by the corresponding residence time. So therefore x bar is equal to 0 to infinity x of t E of t dt and so that is equal to integral 0 to infinity 1 minus exponential minus kt E of t dt. Now suppose if it were suppose if the reactor is actually a plug flow reactor so suppose if it is a plug flow reactor then the residence time distribution E of t is simply given by the delta function of t minus tau where tau is the space time of the reactor which is the ratio of the volume to the volumetric flow rate of the reactor. So now from for a plug flow reactor it will simply be 1 minus integral 0 to infinity exponential of minus kt into delta function t minus tau dt and that is nothing but 1 minus exponential of minus k into tau and k into tau is essentially the dimensionless quantity called the Damkohler number this is the Damkohler number which is the ratio of the space time to the reaction time and so we can write this as exponential of minus da. So that is the mean conversion that would be achieved if it were to be an ideal plug flow reactor and what is interesting is that the model that we actually obtain from the segregated model is actually same as that of the mole balance of the plug flow reactor. We know that from the mole balance of the plug flow reactor the performance is actually performance equation suggests that the conversion is actually equal to 1 minus exponential of minus da and let us see how that is the case. So the mole balance of a plug flow reactor on species A is nothing but dx by d tau that is equal to k into 1 minus x and therefore x is equal to 1 minus exponential of minus k into tau which is equal to 1 minus exponential of minus da. So therefore the conversion that is up that is actually achieved by using a completely segregated model is actually exactly equal to the conversion that is achieved by an ideal plug flow reactor if it were to be a first order reaction. In fact we observed this in one of the lectures before that we mentioned that if it is a first order reaction then it does not only RTD function is sufficient to estimate the conversion and the level of mixing actually does not play any role. So we will see in a short while as to why that is the case. Now before we look at that let us consider if it were to be a CSTR. So the residence time distribution function for a CSTR is given by 1 by tau into exponential of minus t by tau. So therefore x bar the mean conversion plugging this into the integral and integrating the expression shows that x bar is equal to tau into k divided by 1 plus tau into k which is equal to the Damkohler number divided by 1 plus Damkohler number. So now if we write the mole balance for a CSTR so the performance equation for the CSTR is the mole balance on A is FA naught which is the molar flow rate of the species at inlet that multiplied by x is equal to minus rA multiplied by V that is equal to k into CA naught into 1 minus x into V. And minus rA is the rate of generation minus rA is the rate at which the species is actually being consumed. So from here we can see that x is equal to tau into k by 1 plus tau where tau is the space time of the reactor 1 plus DA. So clearly you can see that the conversion achieved through a segregated model is actually exactly same as the conversion that is achieved from the performance equation of the ideal CSTR. So this suggests that the for a first order reaction the information of RTD function is actually sufficient and the degree of mixing is not going to add any additional information and the RTD function itself can be used to predict the conversion mean conversion of the reactor. Now the question is why is that the case? So the reason is the complete mixing or segregation actually makes no difference for first order reaction. This is because the rate of change of conversion actually does not depend upon the concentration of the reacting molecule. So the rate of change of conversion independent of concentration of the reaction reacting molecule. So this is the reason why for a first order reaction the RTD function alone is sufficient to predict the conversion that is achieved by the non-ideal reactor. So the rate of change of conversion is independent of the concentration of the reacting species that explains why for a first order reaction RTD function is sufficient to estimate the conversion of the reactor. So now let us extend this to a laminar flow reactor LFR stands for the laminar flow reactor and the residence time distribution is given by 0 for t less than tau by 2 and tau square by 2 t cube for t greater than or equal to tau by 2. So that is the residence time distribution for a laminar flow reactor which we have actually derived in the previous lecture. In the normalized form E of theta is equal to 0 1 by 2 theta cube and this is theta less than 0.5 and theta greater than or equal to 0.5. So now we can plug this distribution into the conversion equation and we can find that will be equal to 1 minus 0 to infinity exponential of minus k into t into E of t dt and that is equal to 1 minus integral 0 to infinity exponential of minus k tau theta into E of theta into d theta. So on performing the integration by substituting the corresponding distribution one can find that the mean conversion in a laminar flow reactor is essentially given by 1 minus 1 minus 0.5 into the space time multiplied by the specific reaction rate into exponential of minus 0.5 k tau minus 0.5 k tau the whole square integral 0.5 to infinity exponential of minus tau k theta divided by theta into d theta. So that is the expression and if one solves this integral one will be able to find out what is the conversion in a laminar flow reactor. So let us now compare the mean conversion that is achieved using these three different types of reactors. So if we plot as a function of the Damkohler number which is the ratio of the space time to the reaction time x bar. So the CSTR would actually be like this and the plug flow reactor would actually predict a much higher conversion for a first order reaction remember this is for a first order and the laminar flow reactor would be somewhere in between. So the plug flow and the CSTR they sort of provide a bound for the predict conversion of the first order reaction in a non-ideal reactor and such kind of graphs actually can be generated for such kind of plots can be generated for reactions of other orders and other types of kinetics. So what it suggests is that for a first order reaction the extent of mixing not required while for other reactions other kinetics extent of mixing plays an important role. So extent of mixing actually plays an important role and it is required in order to predict the conversion of the non-ideal reactor. So now let us move to the next model which is the maximum mixedness model. Let us look at the maximum mixedness model. So the segregated fluid is one where the mixing between the fluid globules actually does not occur. So there is no exchange of material between the globules which are present inside the reactor. So the flow is essentially like a series of globules which are actually flowing through the reactor. On the other hand that is called the minimum segregation, minimum mixedness model where the globules do not actually interact with each other and each of the globules behave like a batch reactor. On the other extreme is a maximum mixedness model where the globules, the matter which is present in different globules they are allowed to actually mix and interact with each other and therefore the molecules which are of different ages they all mix with each other and that is that kind of representation or that kind of a situation is called the maximum mixedness model. So let us look at how to estimate the conversion for that kind of a situation. So maximum mixedness is achieved when there is complete mixing as fluid enters. So as soon as they get into the reactor all the globules can actually exchange matter with each of them and so therefore there is complete mixing. So the maximum mixedness is the complete mixing of the fluid right at the entry point of the reactor. So how do we depict such kind of a situation is we can consider a plug flow reactor with side feed. So where the feed is actually fed through the sides of the plug flow reactor at different locations and that can be used to depict the situation of maximum mixedness in a non-ideal reactor. So suppose if we know the residence time distribution function so if we know the E of t of a real reactor then we can actually mimic the reactor by using a plug flow reactor and instead of providing a feed at the entry to the plug flow reactor whose volume is V we can actually split the we can actually feed them through the sides. We can feed them through the sides and the feed through the side can actually be according to the we can split the feed and feed them through the side and this feed could be according to a certain distribution function which is the residence time function of the real reactor. So the residence time distribution function could be something like this where the side entrance is actually according to this distribution function. So which suggests that the mixing actually occurs as early as possible and then they actually go into the reactor. So mixing earliest possible which corresponds to the maximum mixedness situation in the reactor. So now suppose we define lambda as the time to move from a particular point to end of the reactor. So that is the time taken by a fluid element to move from a particular location inside the reactor to the end of the reactor. So remember that we have now represent the non-ideal reactor using a plug flow with the side stream in different locations in the side of the plug flow reactor. So now this also reflects the life expectancy at that point that is the amount of time that actually the fluid particles are going to spend inside the reactor which is actually fed into the reactor at that point in the side. So now we can now draw schematic of this reactor. So suppose if this is the plug flow reactor with a volume V and then we now make a feed, we feed the fluid, we feed the reactor with fluid along the sides and according to a certain residence time distribution function. Now if we assume that this is lambda equal to 0 because the time that is actually spent by the fluid that is pumped into the reactor near the exit of the reactor is almost equal to 0. So therefore lambda equal to 0 is the life expectancy of the fluid that enters the reactor in this location is going to be 0. So lambda equal to 0 starts from here and then lambda equal to infinity which is the maximum time that is taken inside the reactor is at the entry of the reactor and if the volumetric flow rate of the fluid is V and V equal to 0 is this location and V equal to V0 that is the full volume of the reactor. Now if we now identify a small element and if the volume of that element is delta V and the flux with which the fluid actually enters that element is given by V into CA that is the volumetric flow rate at that location and if this point is lambda in the life expectancy dimension and this is lambda plus delta lambda. So that is the difference in the life expectancy from this point to this point. So this will be V into CA at lambda plus delta lambda and whatever is leaving from here will be VCA at lambda. Now what is the amount of fluid that actually enters through the side? So that amount of the volumetric flow rate with which the fluid is actually going to enter is let us say is given by V at that location and we will be calculating that in a short while. So what is the flow rate with which the fluid actually enters a small element delta V? So the flow rate in at delta V so that is equal to the volumetric flow rate V0 that is the overall volumetric flow rate of the reactor. So we are essentially trying to calculate what is the volumetric flow rate with which the fluid is actually entering in this small element delta V. So flow rate in at delta V should be equal to V0 which is the volumetric flow rate with which the fluid is being pumped into multiplied by the fraction of fluid with life expectancy. So let us call this life expectancy, life expectancy between lambda and lambda plus d lambda. So that is equal to V0 multiplied by the corresponding E lambda times d lambda where E lambda is the essentially the RTD function which says what is the residence time distribution of the fluid element inside the reactor. So now once we know this we can now write a flow rate balance, we can now formulate a flow rate balance and the flow rate balance is volumetric flow rate at lambda should be equal to the volumetric flow rate of the fluid at lambda plus d lambda plus whatever is actually added through the side. So that will be equal to V0 into E lambda d lambda. So this is the flow rate in through the side. So that is the flow in through the side of the plug flow reactor and so now we know, so now we can actually take the limits of delta lambda going to 0. So limit delta lambda going to 0, this essentially becomes d V lambda by d lambda that is equal to minus V0 into E lambda. So that is the differential equation which captures what is the flow rate at a certain life expectancy lambda. So now V0 is the flow rate with which the fluid is actually flowing at the entrance of the reactor. So which means at entrance that is when conversion is actually equal to 0. So before V0 is the overall volumetric flow rate of the fluid that is actually flowing through the reactor. So now we can actually integrate this expression as V lambda equal to 0 at as lambda tends to infinity. So the flow rate of the fluid that is actually at the entrance is V0 and the conversion at that location is equal to 0 and so therefore the amount of fluid that is actually right at the entry point of the reactor, remember that it is a feed that is coming at different locations in the side. So at the volumetric flow rate of the fluid whose age is almost equal to infinity is equal to 0 and V lambda is equal to V lambda at some lambda equal to lambda that is at certain age let us assume that V lambda is the corresponding volumetric flow rate and so using these two as limits we can now integrate to find that V lambda equal to V0 into integral 0 to integral lambda to infinity E lambda d lambda which is equal to V0 into 1 minus f of lambda. So that is the volumetric flow rate with which the fluid is actually flowing at any location lambda. So now the objective is to find the overall conversion need to find x. So that is the objective. So how do we find x? We need to write a mole balance of the species in order to find the conversion of the species in the reactor. So before we write a mole balance we need to know certain aspects of the reactor certain aspects before we write the mole balance. For example, what is the amount of species? What is the rate at which enters the small element delta V? So this can actually be found by using what is the volume of the fluid whose life expectancy is actually between the between lambda and lambda plus d lambda. So the volume of the fluid with life expectancy between between lambda and lambda plus d lambda. So if we know this volume this volume multiplied by the concentration will tell us what is the number of moles that is actually entering that particular element delta V. So that is equal to so delta V will be equal to V0 into 1 minus f of lambda. So that is the volumetric flow rate multiplied by the corresponding age delta lambda will tell us what is the volume of the fluid with that certain life expectancy that is equal to that somewhere between lambda and lambda plus d lambda. So now what is the rate of generation of the species? What is the rate of generation of species that is actually given by the rate at which the species is being consumed multiplied by the corresponding volume delta V. So that is equal to Ra into V0 into 1 minus f lambda into delta lambda. So we now have all information that we need to write the mole balance. So let us now write the mole balance for this particular species. So the mole balance for the species is so mole balance on a between with life expectancy of lambda and lambda plus d lambda. So let us write the mole balance for this. So what is the rate at which things are coming inside at lambda plus d lambda? Remember that the age of the fluid is actually decreasing from the exit of the reactor increasing from the exit of the reactor while the positive direction is actually increase of volume from the entry of the reactor to the exit of the reactor. So in that lambda plus d lambda plus the introduction through the side what is the rate at which things are actually introduced into the reactor through the sides minus what leaves the reactor, what leaves that element at lambda plus whatever is generated by reaction. So that should be equal to 0. So that is the mole balance on a for age between lambda and lambda plus d lambda. So we know all these quantities. So V0 into 1 minus f lambda. So that is the volumetric flow rate at lambda, lambda plus d lambda into CA at evaluated at lambda plus d lambda will tell us what is the rate at which the species is actually getting into that element plus the whatever is introduced through the sides that is given by V0 into E lambda d lambda multiplied by CA0 where CA0 is the concentration of the species in the feed stream minus V0 into 1 minus f lambda into CA evaluated at lambda plus r a into V0 which is the volumetric flow rate of the feed into 1 minus f lambda multiplied by d lambda equal to 0. So that is the mole balance on a between the age lambda and lambda plus d lambda. So now we can actually divide this expression by V0 into delta lambda. We can divide this expression by V0 and d lambda and take limit as d lambda goes to 0. So that will be CA0 into E lambda plus d by d lambda into 1 minus f of lambda into CA lambda plus r a into 1 minus f of lambda equal to 0. So that is the expression for that is the mole balance. And so now we can open up this differential here and we can rewrite this expression as CA0 into E lambda E of lambda plus d CA lambda by d lambda into 1 minus f lambda minus CA lambda into d f lambda by d lambda plus r a into 1 minus f lambda equal to 0. Now if we stare at this expression, this d f by d lambda is nothing but the RTD function E lambda where f is the f curve or the cumulative distribution function. So using this property we can actually write the mole balance. So the final mole balance essentially is d CA of lambda by d lambda that is equal to minus r a plus CA minus CA0 into E lambda by 1 minus f lambda. So that is the mole balance for the species for a maximum mixedness model. And so in terms of conversion we can actually write this expression as minus CA0 dx by d lambda that is equal to minus r a minus CA0 into E lambda by 1 minus f of lambda. And so that can actually be written as dx by d lambda equal to r a which is the rate of generation of the species divided by CA0 which is the concentration of the species in the fluid inlet stream into E lambda by 1 minus f lambda into the conversion x. So while solving this equation we will be able to find out what is the conversion if we know the residence time distribution function. So what are the boundary conditions for this equation? The boundary conditions are very simple. So lambda goes to infinity when CA equal to CA0 that is at the entry point into the reactor the age of the fluid is actually approximately infinity. So how do we integrate this? We have to integrate this equation from backwards starting from very large lambda. So we have to integrate this equation by starting from large lambda and move backwards till lambda equal to 0. So that is the method to integrate this equation and once we integrate the equation we will be able to find out what is the conversion under the situation of maximum mixedness. So now if RTD is known then the conversion for the maximum mixedness situation can actually be, model can be estimated. So this conversion provides a bound for the conversion of the species in the non-ideal reactor and so for n greater than 1 it is been observed that for n greater than 1 the maximum mixedness model, maximum mixedness model gives the lower bound on the conversion. So the maximum mixedness model actually gives the lower bound on the conversion and the complete segregation model gives the upper bound on the conversion. So now we have looked at the single reaction case. Now it is possible to extend it to multiple reactions. In reality many reactions can actually occur simultaneously in parallel. So there can be sequence reactions, there can be sequential parallel reactions etc. So several reactions can actually happen simultaneously in a reactor. So is it possible to predict conversion when there are multiple reactions happening inside the reactor and the answer is yes it is possible. So it is very simple to extend the segregation and the maximum mixedness model for multiple reactions. So if there are multiple reactions which are actually happening and let us say A and B are the reactants and P is let us say the products which is formed. Let us say the products which is formed and if it is a segregation model, if it is a complete segregation model then if we assume that each globule has different concentrations of A and B and if we assume that each of them behave like a batch reactor which is one of the assumptions of the segregation model each of these globules then C A bar which is the concentration of the species, the average concentration of the species. Remember that if you are looking at multiple reactions and multiple species it is actually better to work with concentrations rather than conversion. So the average concentration of species A will simply be integral 0 to infinity C A of t E of t dt where E of t dt is the residence time function distribution function of that reactor and similarly C B is given by integral 0 to infinity C B t into residence time of the reactor and the C A t and C B t are essentially the concentrations can be achieved from a batch reactor because this is the concentration of the species in each of the globule and we assume that each of these globules actually behave like a batch reactor. So now if we write the batch reactor performance equation for each of these species, so if there are Q reactions occurring simultaneously, so the reactor volume is V and Q reactions are occurring and there are Q reactions which are occurring simultaneously then for batch reactor we can write the performance equation as d C A by dt that is equal to the rate of generation of R A so that is equal to sigma 1 to Q that is sum over all the reactions and the reaction rate of the individual reactions which is leading to the formation of species A and similarly we can write for the species B d C B by dt equal to R B which is equal to sum 1 to Q R I B. Now this actually has to in order to find the concentration of the species A and B in this model in this reactor for following this aggregation model. So these two batch reactor rate expressions has to be solved simultaneously with the other two reactions which represent the overall concentration of the species in the reactor. So d C A bar by dt that is equal to C A T into E of T so that defines how the concentration of the species overall concentration of the species in the reactor that changes with time and the corresponding equation for species B that is equal to of T into E of T. So by solving these four equations simultaneously this one equation 1 equation 2 equation 3 and 4 so these four equations have to be solved simultaneously and we need to find C A of T and C B of T so that gives us the concentration of the species as a function of time which actually follows the segregation model. So next let us look at the multiple reactions for the maximum mixedness model. So for a maximum mixedness case so if it is the maximum mixedness model once again if we assume that there are Q reactions which are actually happening simultaneously then the model equation is d C A by d lambda is just an extension of the single reaction case. So d C A by d lambda is minus summation of reaction rate over all reactions which is actually happening simultaneously plus C A minus C A naught where C A naught is the concentration of the species in the feed stream of the reactor multiplied by E lambda which is the distribution function for that particular reactor divided by 1 minus F lambda and similarly for d C B by d lambda that is equal to minus sum I equal to 1 to Q R I B plus C B minus C B naught into E lambda by 1 minus F lambda. So where E is the RTD function for that particular reactor and F is the cumulative distribution function. So now once we know the rate law for all of the reactions so if we know the rate law so we can simply have to plug in this rate law and then solve for the concentration. So solve for C A and C B from large value of lambda to lambda equal to 0. So once we solve this equation we will be able to find out what is the concentration of C A and C B as a function of different age. So this is the set of equations and this can actually be extended for many other species even if n species are participating one can actually write the maximum mixedness model for all n species and similarly for the segregation model. So let us summarize what we have actually discussed in the last several lectures in the residence time distribution problems. So first we looked at the ideal versus non-ideal reactors we looked at ideal versus non-ideal reactors and then we looked at the RTD functions we looked at the RTD functions what is RTD function why do we need RTD function etc and then we looked at measurement of RTD functions measurement of the RTD distribution function in real reactors where we looked at the pulse tracer input and we looked at the step tracer input and we looked at how to perform these experiments and how to actually estimate the RTD function what to measure etc etc and then we looked at RTD properties of distribution properties of RTD function so particularly we looked at the mean we looked at the variance and then we looked at the skewness of the distribution which actually tells us how skewed is the function around the mean of the distribution and then we looked at RTD that is the residence time distribution in ideal reactors we looked at plug flow reactor we looked at single CSTR and then we looked at the laminar flow reactor these are the three cases that we looked at for RTD in ideal reactors and then we observed that the RTD function can actually be used for diagnostics purposes in order to estimate whether the reactor is operating under perfect conditions usually it never is perfect but how close is it to a perfect operation whether there is bypassing of the fluids that is actually entering the reactor or and if there is a dead volume which may be present inside the reactor and then we looked at the combination of reactors we looked at combination of reactors particularly we looked at the PFR-CSTR combination and we looked at how to estimate the residence time distribution and we also observed that if the residence time distribution for PFR followed by CSTR and CSTR followed by PFR is actually same however the sequence actually dictates as to what is going to be the performance of the combination of reactor so which is suggested that the RTD function alone is insufficient to actually predict the complete conversion or it is not the complete picture of the performance of the reactor additional piece of information is required and from there we marched on to the next topic of looking at the predicting the conversion so in this case we looked at the segregation model we looked at the segregation model and we looked at the maximum mixedness model we looked at maximum mixedness model and then we extended we we looked at these models for first order reaction and we also extended this to multiple reactions thank you.