While being recorded. I've got something to give you. I'm on vacation next week and I want to get this form to you that you know. Good afternoon. This is Kimberly Hambrick. It is now 2 o'clock and I want to get our webinar started. I want to do a few housekeeping items in that we did try to mute all the participants' lines, but we had an issue with one of our presenters not being able to speak. So I would like to ask all the participants to please mute their phone lines. Either mute it by your button on your phone or do star 6 which works with the system. I thank you so much for understanding why we'd like to have all the phone lines muted and keep some of the distractions at a minute. So again, this is Kimberly Hambrick and I thank you again for muting your phone lines. I want to welcome you all to the simulated workplace changing CTE in West Virginia. I'm the associate director of the Appalachia Regional Comprehensive Center and we're putting this webinar on in partnership with my colleague from the National Association of State Directors of Career Technical Education. I'll introduce her better here in a second. I apologize. Something popped up on my screen. Before we get started, I do want to follow a few housekeeping items. As I said, we would like for you all to mute your phone lines so we can keep the distractions down. You have a up on your top, you'll see a note box which is how you can connect to Adobe if you have connection issues. You've heard that the webinar is being recorded so it will be archived and available later. And we do have a chat box that you see about Midway Down. Thank you, there's an attendee chat. That's where we'd like for you to ask your questions. We do have a time at the end for questions and answers. We may not get to all of them during our presentation, but we will be archiving the questions, having our presenters answer them, and we will follow up and share those afterwards. So again, please mute your phone lines. No, because I don't want to get that heat, yeah. Some of you will probably have a few questions about where you can find information from the PowerPoint and the webinar recording, and so we do have the websites here where you can get it afterwards. And if you're interested in learning more about simulated work place, also link that as well. And these will also be included in the follow-up material so you have them. Before we do get started, we wanted to take a quick poll to find out where our webinar participants are from. So if you wouldn't mind, if you would, please look at the poll that's on the screen, which of the following best describes you. And just quickly let us know it represents you. And again, please mute your phone lines. Okay, great. So just by quickly looking, we have 23% of the audience from the State Education Agency staff, and 17% are other, and we also have State Education Agency leaders. Thank you. That just helps us know a little bit more about who is in the audience. So as I said earlier, my name is Kimberly Hambrick, and I'm the ARC Associate Director. The ARC is the Appalaster Regional Center, and we are one of 16 regional centers. Our mission is to design initiatives in partnership with our four states, Kentucky, Tennessee, Virginia, and West Virginia. And those initiatives will improve educational outcomes for students, close the achievement gaps, and enhance instructional quality. One of the key areas that we focus on is implementing college and career-ready standards and aligned high-quality assessments for all students. And that really is the key area that we're focusing the webinar on today. Today marks the launch of our webinar series on CTE and partnership with National Association of State Directors of Career Technical Education Consortium. And at this time, I'd like to introduce my co-partner, Andrea Zimmerman, who is a State Policy Association Consortium. Thanks, Kimberly. And here at NAVS with CTECH, we are happy to be joining with ARC for this webinar series. It gives us an opportunity to really take a look at some high-quality examples of CTE in the state. So a little bit about NAVS with CTECH and who we are, but we represent the state-level leaders who oversee the CTE programs and policies impacting secondary, post-secondary education in the workforce. And that includes folks like Kathy Vantoni, the West Virginia State CTE Director, who will be presenting today. And it's really thanks to Kathy that we've been watching the simulated workplaces grow and evolve over the last few years. And in fact, in 2014, we awarded one of our inaugural Excellence in Action Awards to the Carpentry Program at Tulsa High School in Fort Gay, West Virginia, which is a simulated workplace site. And now these awards are designed to lift up high-quality, high-impact programs of study. And our panel of judges, when looking at the application, really saw how the simulated workplace at Tulsa exemplified exactly that. And in particular, through its integrated academic and technical courses and innovative work-based learning method. And so it's with that that I'd like to hand it off to Kathy to introduce the rest of today's presenters. Yes, good afternoon, Andrea. We're tickled to death to be here. The presenters with me today are Jan Hanlon, who is a secondary curriculum director in one of our county school systems. Doug Sands, who is a CTE instructor in the United Technical Center. Gary Clay, who is a business leader who is with the West Virginia Manufacturing Association and has played a huge role in the development of simulated workplace. And Austin Coffee, he is a student that has been in the simulated workplace for a year now, and we're tickled to death to have him so he can share his experiences. Simulated workplace was created because of the situation that was happening across West Virginia. Five to ten years, I have listened to business and industry at meetings, at conferences, and the message went from, you know, these are the skill sets we need for quality employees, and oh, by the way, you know, they need to show up for work. Well, that changed dramatically up until last year that employers were almost shouting at us that just send me somebody that's drug-free, can show up, do a full day's work, we'll train them. And that was the message, and I'm thinking, you know, what's going on? We have SkillsUSA winners. We have outstanding students, CTE students that are graduating. What's happening here? So one of the things that we figured out was the change is students understanding the business processes. We deliver great technical skill sets. But were we delivering the business processes that students can be successful when they take those skill sets into the workplace? So we decided to take some bold steps and move this forward. So we engaged business, and we also did higher ed folks, and we brought them in to talk about what if we changed the entire environment of our CTE classroom and had it actually working as a company would work. Now, it's not products that they make to sell outside the school building. This is actually operating and students understanding business processes and the fact that their attendance, the work that they do, and the tests that they take actually impact a business's bottom line because it impacts their company's bottom line. And so with the business folks, we identified 12 protocols that were absolutely mandatory in every one of the simulated workplace companies. We did that for a number of reasons. One, to make sure the structure was consistent across the state and everybody was on the same level as we started to implement these simulated workplace protocols. So our goals were that we didn't want to change everything. We're changing the whole culture of career tech and education. So we had to have time to get it implemented, and we knew that we couldn't just start statewide. So we set aside four years for our implementation process, and we began with pilots, and then we moved every year. We started out with 80 sites. We are now up to 501 sites. By 2016, that's the way we will do business in West Virginia. So when we first started, we had to get buy-in from our key stakeholders, and these were our business people. These were instructors. These were our students. These were everybody that was involved in the simulated workplace to make it happen, and we started with our pilots. So the whole purpose was to increase student leadership and engagement. CTE probably has more student engagement than any other classroom in education. However, it still wasn't to the level that we were looking for. We wanted our instructors to transition from actual teacher-type driven instruction to facilitators of learning and allow students to manage and take over these companies as the teacher facilitated that and monitored their progress. So it was a school-wide cultural change, and you will hear later from one of the instructors to see what the differences were. This is probably the most important slide, because people, when they hear a simulated workplace, our instructors, they get the room perspective of what they think this is. It's not a curriculum. It's an environment. It changes the way that we deliver career technical education. So it is not a curriculum. I can't stress that enough, because when we were starting with instructors, we kept getting this question, well, I really like this, but when am I going to have time to teach it? So the whole idea is that this is an environment of which they enter. It's an opportunity for students to be accountable for their own learning, because what they do in that classroom is directly impacts their company that they're in, their bottom line, or their value. And their companies are evaluated based on attendance, based on test scores, based on drug testing. The whole nine yards all go together to give this company a monetary value of which we'll get into later. It's an opportunity for teachers and instructors to be flexible and to be very engaging as they are in the actual workplace. They get an opportunity to facilitate learning that these students would see in an actual workplace. And it also requires high academics and high technical learning, because that's where the better students are, the more their company is valued. Okay, so we started engaging our stakeholders from the start. We had to establish a climate for change. People had to know what was going on. We started with the Manufacturing Association. That's why Gary Clay, who's on the line, was such an integral part of this. So we started with that group. Most of all, we wanted feedback from our pilots, from our instructors, and most of all, our students. We wanted to know, do they like this? Is it more engaging? Do they feel it's worth doing? And it's very interesting, because you will see later, our students are probably our biggest supporters of simulated workplace. So let's get to, like I said, this is in now in state policy in West Virginia. It's how we're going to be doing business. It will be mandatory in 2016. Kathy, this is Kimberly. I'm sorry, I advanced it too fast. We wanted to have Gary talk. I apologize for that. Okay. I apologize. Okay, so we're going to go over to Gary. Okay, Gary. All right, I've got a question. Okay. Yeah, I'll talk a little bit about the engagement process that Kathy was talking about. It was several years ago that the West Virginia Manufacturers Association, which I represent, engaged Dr. Dantoni to talk about what we needed from potential employees. And the easier part of that was sitting down talking about... We created a great manufacturing pathway program with all the technical skills we were looking for, put that all together. But we also asked her for some soft skills. These are things that the students were missing. And those included a passion for safety, good attendance records and showing up on time. If you don't show up for school, what makes me believe that you're going to show up for work? Being drug and alcohol-free, an attitude that this was not just a job but a career, a teamwork mentality. We find many students today who prefer to work by themselves, but that's not the real world in our environment. We were also looking for a knowledge of improvement methodologies, process improvement methodologies, and a desire to understand how their efforts made a difference in the company and helped to improve and ensure their future. And these skills were important to all career and technical students no matter where they're going to work. It wasn't just manufacturing, this applies to all the students in technical education. And the simulated workplaces addressing all these areas, and the students are truly engaged. So that's my part. Jan, do you want to talk about the CTE School Administrator engagement? Yes, I do, Kathy. Thank you. As a CTE Administrator, what I needed to do to make sure that this change happened is I needed to inform, like the CTE instructors, of what simulated workplace was about. And I needed them to have I in and want to participate in simulated workplace. The next thing that I needed to do was to inform our local school board members and our county superintendent of simulated workplace. And I needed them to embrace the idea of drug testing CTE students with imperatives. I also needed to reach out to our business leaders because I wanted them to be excited about the change that was about to happen. As Gary said, concentrating on those professional attitudes for children or for students. And I knew that if business and industry were to embrace this concept that our students would be successful. Okay. All right. So, like I said, this is in our policy now. This is how we're going to be doing business. And we established between business folks and ourselves, the 12 protocols that we would follow for simulated workplaces across the state of West Virginia. So I'm going to let our folks talk about these protocols a little bit. The reason that, first of all, the reason we need the protocols I said earlier is so that we can standardize and make sure everybody's on the same page. So, Jan, if you would like to talk about the first one, changing the traditional classroom into a company. Okay. Every simulated workplace instructor's classroom should look different. Each classroom should mimic that of each profession. The environment or the classroom should be courteous, self-safe, clean. It should be a place where expectations are clear and teamwork and leadership is definitely encouraged. Students are in charge of the learning and the instructor becomes the facilitator. Student-led projects are one of the main focuses of simulated workplace. We should provide a meeting or a conference area for students to meet and to set goals and to make certain that our students are on task. Also, in the protocols, it gives attention to attendance. Like Gary said, we wanted to have a method for students' attendance to be tracked. In our facility at Ralph R. Willis, we use a commcloth. And students, whenever they come to class, they punch their commcloth, or they lay their finger down to check in the class to track their attendance. And then the next protocol deals with drug testing. And, you know, we just basically wanted to provide a safe work environment, and we knew that if teens remain drug-free in those adolescent years, that data shows that they're more likely to remain drug-free during their professional career. And we wanted to deter students from drug use at all. We encourage students with a positive drug test to get counseling to overcome their substance abuse. Our local agency and county is responsible for developing the policy, how the drug test starts to be administered, and what services would be available if a student did have a positive drug test. In our county, if we do have a student with a positive drug test, we remove the student until a licensed therapist or counselor can do a risk assessment and determine whether they are a recreational user or if there is indeed a substance abuse problem. And then once that's determined, the student will then take another drug test to enter back into the simulated workplace environment. I do want to say at no time do we suspend the student for a positive drug test because we want that learning to continue. And then critical four on your slide deals with the application and the interview process. And I have to say that this is what really created that buy-in for our instructors for us to go school-wide with the simulated workplace environment. And our instructors, when they hire a workforce, they go to our free-flight school and they interview students based on that application. And then they, and it makes, it gives the students a way to make informed decisions about their future career goals. When a student is asked to fill out the application and to apply for a position in the company, it takes a commitment and a really, and thought to go through the process rather than just be inducted into a CTE program. We do not deny any student's entry into a public-funded CTE program unless that program is full and we take 20 students in each area. We use rubrics to interview the student and to judge or evaluate their application. On the application itself, at Ralph R. Willis, we added an attendance component and a behavior component. So after they're admitted into their company, therefore we rarely have any attendance issues or behavior problems, and I would like to say that our quality of our students has increased at our center. And this is Kimberly. We have a participant asking who pays for the drug testing. We do. The state does. And is that through special specific funds or a part of your, it was set up that way? It's set up. That's part of the state dollars that go out. We send out grants to the local counties. When I said this is the way we do business, we have revamped all of our vocational dollars to support the simulated workplace initiative. So we fill in where they have, where counties cannot afford. We help with special grants. Thank you. And thank you, Jan. Doug, if you'd like to talk about protocol 10. Sure. Thank you. One of the areas that we needed to deal with when we talked to business and Gary and different places like that was we had to really put a heavy emphasis and focus on safety and sustainability and repeatability were huge. And we were able to move into this 5S initiative, which has become an industry standard just about any shop or workspace that you walk into today. This is a language that they're using on a regular basis. So when our students go out, they're already speaking an industry language. They already understand what it is to make that work environment safe, but not only make it safe, but keep it safe and what it takes to sustain that. So this protocol was applied in every workspace, which has given us again that repeatability and sustainability. This is Gary. I'm going to talk about the protocols 11 and 12. And really, those are the business inspections and the portfolios. This is where the local businesses get involved in the program. And the business inspections were coming in and basically auditing the programs. And this activity is so important to go forward here. And I think on many levels, and it applies to everyone. For the instructors and the schools, this outside validation that they're teaching the right things, it's an opportunity for folks to come in and change or tweak things that aren't working or aren't correct for today's environment. And for the students, it's a chance to interact with maybe some future employers. A nice time to show their skills and promote themselves. And for the employers, probably most importantly, it's a chance you get in to go in and see how well these programs are working. You find out what great students there are. You actually go in and meet the students and see the passion that these kids have for their programs. It's also a chance to correct some of the things and make sure these programs are going to provide the skill sets and the soft skills that you're looking for. And now for the employer, you feel connected to the program, invested in a program because you've put your seal of approval on it. So a very important process, we believe. And the second thing, and we're really excited about the portfolio program that's going on here, many employers tell us they can't trust the high school diploma anymore. It doesn't mean that these students have 12th grade skills. Well, the portfolio shows what the student has accomplished. It includes their attendance records and whether they're on time for classes. It's a documented drug test. It's certifications of the skill accomplishments they've had, whether that be welding or any of those programs, those certificates are in there. And there's examples of the projects and things that they've worked on. It's much like an artist's portfolio. Here are the things I can do and here's examples of what I've accomplished. When I talk to hiring managers and tell them what these portfolios are and what things are in there, what manager wouldn't want to see an employee show up with a portfolio of all his skills and abilities in one place. They actually are extremely excited and this is a real positive thing from the program. So I'm going to pass it off to Austin now to talk about the student perspective. Hey, I'm Austin. I'm a student at Wyoming County Career and Tech Center. I go to Industrial Equipment Maintenance Program. I'll be a senior next year. What I would like to discuss is our program. We go by as a company because that's what you would see out in the real world. Our company name is Mountaineer Industrial Services and we organized our program into four groups. We have a safety team group, equipment tools and facility manager, inventory control and supply manager, and informational tech group. Each group has a specific task that they have to do. The safety team, which I'm a part of, I'm the leader of it. We have weekly safety meetings on different subjects every week. And each employee, which is the student, signs a paper to verify that they attended the meetings. They understand, you know, the accidents and stuff like that. And we keep records of the safety meetings and that's the safety. The thing we're trying, the safety team is developing is a hazard training form for visitors. It's a brief summary of hazards in our shop that we're familiar with, but they are not. Because we're more familiar with our shop than they are. One main safety that visitors have to do is wear safety glasses. That's mandatory in our shop. You do not step one foot in our shop unless you have safety glasses. Because if somebody is running any type of equipment, anything can fling in your eye or hurt you or whatever. But the safety team is going to come up with penalties, consequences. Like if you do not follow safety regulations, they're going to come up with different consequences. But in the beginning, when we first started the simulator workplace, I was a little bit sketchy of it. I didn't think it was going to go well and I thought it was going to be a waste of time actually. But once we started getting into it and started rolling with it, you know, it gets a little bit aggravating at times.   But once we started to get it rolling, it works really, really good. I mean, we've done it for a year now. It makes this more organized. It helps people stay safe, keeps different stuff clean, like the shop clean from anything like tripping hazards or anything like that. And also, I've learned being a part of the safety team that it could be a lifetime career. Like all the groups that we have, the four groups that we have, all the other companies in a real-life situation has similar groups. So each group that you're a part of, you can probably make a lifetime career out of it. Like each semester of the school year, we switch groups. We'll be in safety group one semester or one nine weeks, and then we'll switch to the informational technology manager. That I feel for each group. But once you get rolling with this thing, it smoothens out. It gets a little bit aggravated at times, but in a line out. The best thing about simulated workplace is the program gives you a little bit of a leeway. Like instead of them telling you, you got to do it like this, you can't change nothing, they're giving you a leeway to where you can make it to where it fits you. If you don't like something or like something don't feel right, you can make little tweaks to it. Like our company, we took it upon ourselves to change the names of our groups for it to fit our company and our business life. Austin, this is Kimberly. Thank you so much for giving the perspective of the students. Kathy, there is a question. You know, we have some questions coming in and I'm trying to keep some of them until the end, but there was one that's a little bit relevant here. And the participant is asking how often the classroom businesses are reincarnated so all students get the experience and bias. That's the way we do business. What are you asking? I mean, from now on, every CTE program someone enters, they're entering a business. They're not entering a CTE program. They're entering a company. Is that what you're asking? Yes, Kathy, I think that's exactly where they were getting at. Yes, we are no longer a welding program. We are no longer an industrial maintenance program. Students apply and are interviewed to come into a welding company at their school. And in some instances we have seniors setting on these seniors that are in the company setting on the interview process. What Austin was referring to, the students have a huge say in how their company operates. They develop policy and procedure manuals. They determine their name. They set forth the various organizational structure and they basically run their company and the structure becomes a facilitator. That is a huge cultural change. It is what we're seeing, and I'll get into that in a minute, is unbelievable. I'm getting ready to go into it, which is the data piece of it, I guess. What we're seeing so far is that we do student surveys. We do instructor surveys. We're only, you have to understand, we're only in our second year. We haven't even scratched the surface of our vision of what the simulated workplace will look like in another six years. But so far we have seen attendance rates go up, discipline referrals have gone down. We have a 96% approval rate from student surveys that we're getting. Our business inspection, so we're talking about these business people go into these companies and inspect, sort of like a health department inspects a restaurant. They have given me feedback. From this feedback we have changed some curriculum. We have added pieces of equipment. The companies have given us equipment when they wanted a certain piece for that particular program. We have had students been hired because of these inspections because business people saw what they were doing when they came in. So those business inspections, the business people absolutely endorse this program. So that's basically, we're very early on in our data. We're hoping to see we're going to start comparing our achievement rates, our test scores as we move forward. But at this point, most of our data is anecdotal. But that anecdotal data includes student focus groups. And I've asked the question to students across the West Virginia in at least five different settings. And I said, why do you like simulated workplaces? And without Biden and Eyelash, every single one of them in different situations looked at me and said, because we're respected. It absolutely floored me. These students have pushed the envelope of their companies and they're doing things in their companies that instructors have told me that they never even thought of that these kids have moved forward with. So what I'm seeing and what we're hearing and what's being activated in these classrooms, I would never go back to the traditional classrooms. So the lessons learned that we have done is, first of all, change doesn't happen really easily. It doesn't happen quickly. That's why we started with the pilots. We have tweaked this based on our pilot a little bit when we tried to put it in. You have to be careful. When you try to put simulated workplace in, my suggestion would be that you pick protocols, you sort of look at what do I want the first year to happen? What does it look like? They shouldn't have to look at the whole big picture because it will frustrate teachers and it will frustrate students. You have to support these teachers because they're going to be moving from a traditional instructional model to becoming a facilitator. That's not easy to do. Probably that's the biggest challenge of this whole piece. And you have to allow students to rise to the challenge. You know, the one thing I've learned about simulated workplace is evidently we put our finger on kids, our thumbs and kept them down. You let the finger up and let these kids believe I am amazed at what they are accomplishing in this last year that we saw. And then you have to have, of course, the partners with the employers because they will affect the change. This isn't for education. This is for business and industry. And it's a much deeper relationship of workplace than we ever had through just meeting or just doing business meetings. So where are we now in West Virginia? Next year will be our third year in. What our vision is, what I said was we just scratched the surface. Our big, big vision is that all of our career tech centers will become corporations. And every company within that will be part of the corporation. And the CEOs or the job formants or whatever the head student position is would meet with the CTE directors to talk about how do we improve our companies? What are the issues? If they come to a meeting and they look down, they see that the attendance issue in the welding company is far below the other companies. The students, along with the director of the center, will discuss strategies to improve attendance. They have a voice in their education. And the other is that this next year we're going to be sending out quarterly, I'm sorry, semi-annual reports to these companies to show students what their company has earned based on qualities of their attendance, their drug testing, their skill sets they've earned, their test scores, that their companies start getting a monetary value. But we have had so many wonderful ideas come out of this simulated workplace from students. Some students wanted paychecks. So I have some companies that give paychecks to their students. They have a payroll department in their company, and their paycheck is based on how many skill sets they've learned. Of course, it's virtual dollars. It's not true monetary dollars. But they can spend these dollars, you know, on other things that these schools have come up with. It's just been an unbelievable two years. And what we're seeing changing with students and the enthusiasm and also the instructors, even my instructors who have given me a push back on this situation are starting to turn.  So that's basically what simulated workplace is. And it's changing the culture, changing the environment so that students actually are experiencing learning about business processes in their career technical education classroom. Hey, thank you, Kathy. This is Kimberly. Before we get into the questions, our Q&A session, I just wanted to see if the other presenters on the line wanted to share a quick lesson learned from their perspective. Yes, Kimberly. This is Stan. I'd like to say something. Dr. D'Antoni says that this is, you know, it's not easy. But as a secondary education director, I want to say that this is the easiest initiative that I had to roll out, you know, and I rolled out in almost my 30 years. I rolled out Common Core, No Child Left Behind, and those were difficult. But this was relatively easy. And the reason why this was easy is I think we're doing right by kids through simulated workplace. We're empowering them for leadership roles. For instance, students rotate through a variety of jobs. Some are foremen, some are safety directors, some are quality assurance people. And so there's relevance for them to simulate a workplace. Another reason why it was so easy is because we went slow that first year to implement, to implement a simulated workplace. You know, when we provide the professional development for our instructors, we did not want to overwhelm the instructor. The instructors had the capability to customize each company and to make it effective. Our students at our center can tell what value they are to their company daily, weekly, quarterly, and by the end of the year. And all that becomes part of their portfolio process. So when students become empowered, it's really a win-win situation for students and industry officials. I know. Some days I go without. Great. Thank you, Jan. Gary Doug, do you have any questions learned? Sure. This is Doug. I'll just go real quick. Probably the biggest thing from an instructor's standpoint is making that transition from a traditional teacher to a facilitator. As an instructor, we have to learn to give up control and that's one of the most difficult things to do. You know, we have the book with the answers in it and to turn that over to the students and allow them to run with it is a difficult transition. So part of the work that we're doing now is going back in and offering professional development to begin to teach instructors how to become facilitators. To allow these students to go through and work their way through the processes themselves without having to have all the answers. So that's probably the biggest change for me as an instructor was changing that classroom to where I became the facilitator of it instead of talking together. Great. Thank you. Jan, those of you not speaking, please mute your phone. We're getting a little bit of background noise. Thank you. This is Gary and I'd like to talk from the business perspective. The big thing that we've learned here now too is how important this partnership between employers and schools is going to be going forward. The changes in business are changing. Things aren't changing every year. They're changing every three months. And for the simulated workplace to work, these changes are going to have to take place on a regular basis where students are going to have the right skill sets coming out here. The only thing that can happen is very close partnerships. You know, employers say that their most important asset are their employees. And if you were having problems with the raw materials, you'd button correct the position. That's what we're looking to happen here. And important is going to be the local programs. It's great for Dr. D'Antoni and I to be joined at the HIPP at the state level. And that's got these programs going. But the key success is going to come with those local partnerships with your local employers at your local school to find out what the requirements are. Because a lot of these kids are going to want to stay in their area for their jobs. Thanks. Great. Thank you, Gary. And Andrea, do you want to lead us through our questions and answer sessions? Absolutely. So we've got about 13 minutes to try and cover all of your great questions that we're getting. And actually, Gary and Kathy, this first question is to you and we're going to segue from your talk about getting businesses involved. And so if you could talk concretely about how did you get, you know, the businesses involved? You know, was there an MOU, et cetera? How did that function at work? Well, to begin with, I visited or contacted all the association, state associations, manufacturing business, coal mining association, oil and gas association. I made the Chamber of Commerce. So then I ended up after the first, first of all, we tried it that way. It was difficult. We had some business like Gary, for example, who was immediately willing to help. But we had a lot of small businesses in West Virginia that are one or two people and they had a difficult time giving up their time. So we, I finally contracted with a person outside of, and they went out and they worked with business and industry for a while. They still didn't have all the people we needed. So the next thing we did was we partnered with the workforce investment boards that are across the state of West Virginia. They helped us find employers that would go in and become business inspections. That was a huge help. This coming year, the National Guard that has all the expertise in these various areas and are also worked for folks have agreed to part with it. So that's basically how it all started. Gary, you want to add anything to that? Sure. I can talk specifically about the Manufacturers Association that Kathy knows. Like I said, we started first at the state level, sitting down talking with Kathy and talking about the programs. But now we've gone and it's really of the emphasis is on our association to get our members involved. Kathy and I have both promised if I have a school that's not working with our members, I'll call her. And if she has companies that aren't working with the school, she's going to call me and we're going to stress and get those folks in there. I think the big thing to do is there's a little bit of a sell that has to go on maybe with some of the smaller local employers, but it is critical for them. They're all telling us they can't find employees. If you can't find employees, you've got to be going to the school, to the source. These are the lifeblood in the future of your company or these employees and they need to be involved to be able to do these things. So it's not a matter of them doing you a favor, it's something that's important to their business for them to be there. So that's the approach we've taken. And Kathy and Gary, specifically for the extremely rural areas of West Virginia, did you have to do anything special there or were folks lining up ready to help out? No. Well, West Virginia is extremely rural. I think the whole space is extremely rural. But in our very, very rural areas, that's where we have engaged the national parks. That's where we're looking at the various workforce investment boards to help us in those particular areas. That's how we're trying to do it. Great. So now a question to you, Kathy. We did get a question about, did you look to other states for models or initiatives? And second to that, were there major infrastructure changes that you needed to do to implement this? No. We sort of did this based on conversations that we had with business and industry and just through all those conversations figured out or thought we figured out what the problem was, why employers couldn't find the employees. And what they were telling us, it was the soft skills. It wasn't a technical skill. So we changed the infrastructure. Not really. We reorganized the way we delivered. We changed the environment. But simulator work doesn't require a major dollars and it requires a change in attitude and a change in environment. And sometimes change in the culture and by working and acting and promoting as companies, it changes the dynamic and students really get into it. They have uniforms. That's part of it. They clock in and clock out. They have reports that are due. The instructor, they do it right. It's less work on the instructor because the students are responsible for all the workings of this company. It's amazing to watch. So this is where we're going to play away a little bit into some Perkins questions because we've got a lot of our state folks on the line. And so as you said, you reorganized some of your state funding to be able to better accommodate the simulated workplaces. Did you also do that with your Perkins money? Well, Perkins money, we have to send out per FTE. So I really don't have that much. We don't get that much Perkins compared to other states. West Virginia is a very small state. Those dollars pretty much go by what the rules are with Perkins. Where we tried to help is with our state funding, our vocational funding. We reorganized that. So the Perkins pretty much stays with its priorities the way it is. And so now, as you know with Perkins, there's different indicators about like technical skills assessments, et cetera. We've got a question here about do you use industry recognized certifications in the portfolio to demonstrate that TSA and how? We do industry recognized certifications. We are setting money aside of our state dollars next year to pay for industry recognized cert for students who cannot pay. All of our programs have a, if it is there, they are required to have an industry recognized certification with that program. And we pay for that student's ability to get that certification. So the answer to that technical assessments, we have portfolios and capstone. That's all part of the company's requirements. So a student to demonstrate their technical skill attainment, every completer has a portfolio that they present to business and industry, and a capstone that they have done to culminate what they have completed in their program. And that's all presented to business and industry. Okay. And this just to make sure that I don't know if you answered this part of the question, but there was a second question about does the state determine the certifications that are valued by business and industry? You know, what's that process? No, business and industry. We have asked, we have had focus groups. We reach out to the various employers to see which certifications that they think are important for us here. We also do NCCER, which is a certifications that go across state lines. So we look at certifications that industry, business and industry are telling us that they want. Okay. And this is Gary. I would also say that part of the audit process that takes place where the businesses come in, if things are changing and new certificates are coming out, we should start to hear some of those out of there. Or again, Kathy and I at the state level would be identifying some of those things that are changing. So again, business needs to be involved so those certificates evolve with the workplace. All right. One last question that we got here was about the role of post-secondary education in the simulated workplace, you know, dual concurrent enrollment, et cetera. We have what we call an EDGE program where students going through our programs have opportunities during free college credit with a program that's aligned with them at the post-secondary level. That is in our state law and students, that's also with their consortium. So yes, post-secondary is a piece of this through our career pathways. Right. Well, with that, I think we're kind of running out of time. So if there's any additional questions, please throw them into that chat box and we will certainly make sure to follow up and answer any other questions you do have. So with that, Kimberly, I'll hand it back to you. Great. Thank you. And again, I want to thank everyone for attending the webinar. Special thanks to our presenters and Kathy and the great team that she pulled together with the work happening in West Virginia. As we said in the beginning, and you know, we have it on the screen as well, and you will get a follow-up email that will show where the PowerPoint in the webinar and the recording are archived. There's two different sites. We'll also make sure to include information for where you can learn more about the simulated workplace. We also said early on that this was the first in a series of CTE webinars that we will be putting together. So we will definitely put you on the list for the other three as they come up in the near future. And we'd like to ask you to help us improve our work by completing the short evaluation survey that's going to up up on the screen in a minute. So please thank you for doing that. And again, as Andrea said, if you have any other questions, make sure you get them in the chat feature and we will answer those. So if nothing else, thank you again for your time. Thank you again to the presenters. And we look forward to having a conversation with you again soon.


This is the stuff that was the most common to be crossed with was the blue family, the white family, Breeder Steve's work, and a lot of Brothers Grimm. I loved the genius. I grew the, I had the Apollo and the genius in that era, I got them from friends that I met through there. They were both nice smoke, you know, I've always thought the Cinderella 99 was a little bullshit-ish. Yeah, I loved, I absolutely loved the Pineapple Fino C99. I was a sucker for it to pinnalling and pineapple together, make it taste like pineapple.  But Brothers Grimm was really famous in that era, and so a lot of their stuff was getting passed around, a lot of their straight clones that people found that got names and hybrids. Yeah. I would say. I did a lot of work with Apollo 13. That's the one I chose between the 11 and...


The last few classes we have seen the importance of the major nutrients like carbohydrates, proteins, fats and the energy that is supplied through the food in the body, the ways they are measured and how the recommended dietary allowance is given and what are the food sources etc. Now let us move on to the minor nutrients that is the vitamins and these vitamins are divided into two that is the fat soluble vitamins and water soluble vitamins. Initially we will start with the fat soluble vitamins which are vitamin A, D, E and K. So vitamins are essential organic substances which are required in very small amounts in the diet and but they are highly recommended for the normal function growth and maintenance of body tissues. And these vitamins cannot be synthesized in sufficient quantities in the body or sometimes they cannot be synthesized at all therefore we have to supply through the food and these are found in plant and animal sources and these should be supplied through diet. Now fat soluble vitamins they are not readily excreted and are stored in the cells. Now regarding the vitamin A it is a generic term for the class of compounds called retinoids. So there are different types of retinoids we have retinol, retinol and retinoic acid which have different functions in the body and carotenoids are the pigments that are present in fruits and vegetables in forming vitamin A and after this carotenoid goes into the body it gets converted into vitamin A. We have alpha and beta carotene which are examples of pro vitamins converted into vitamin A. Now the health benefits of vitamin A it helps to improve the immunity then strengthens the bones and teeth, helps to prevent cancer, reduces the risk of muscular degeneration and night blindness, then reduces stones, urinary stones, helps to protect skin against psoriasis and dryness acne, aids in maintaining healthy reproductive system, ensures proper muscle growth in children, beneficial in slowing down aging of the skin and protects against heart diseases and stroke. At the same time overdose of vitamin A may cause blurred vision and nausea. The functions of vitamin A we have seen and in brief it is used for vision, gene transcription, immune function, embryonic development and reproduction, hematopoiesis, bone metabolism, skin and cellular health and antioxidant activity. Regarding the visual function of vitamin A retinol that is present in retina of the eye it turns visual light into the nerve signals through the brain. So this retinoic acid it maintains the normal differentiation of the cells and makes up various structural components of the eye. So therefore because of this conversion the dark adaptation to light occurs in the human beings which is deficient when less amount of vitamin A in the food. The second function is gene transcription. So the retinoids that is RAR and RXR they are receptors which bind to the DNA and cause gene expression. And they are also used in the growth and differentiation of epithelial nervous and bone tissues. Regarding immune vitamin A increases the cell differentiation, produce cells involved in specific and non-specific immunological defenses. We all know that lymphocytes are used for the immune functions and mucosal surfaces also help in the non-specific immune defenses. It promotes normal growth and healthy nerve functions that means it is very important for functioning of the nerves. Now the dietary sources of vitamin A we have liver, liver is the best source of vitamin A those who are non-vegetarians but otherwise all the yellow and orange colored fruits and vegetables and dark green vegetables are rich in vitamin A. Now the recommended dietary allowances we can see for all the adults it is about 600 micrograms of retinol and in terms of you can convert retinol into beta carotene by multiplying into 8 therefore it is 4800 whereas the same amount is 9 to 7 to 17 years. And for pregnant women there is an increase by 200 micrograms and lactating women there is an increase by another 350 micrograms. And for an infant it is only 350 micrograms and 1 to 3 years 400 micrograms of retinol. Now we say vitamin A is very good for functioning of the body but at the same time when you consume excess of vitamin A it leads to some problems. So hypervitaminase is the term that is given for excess consumption of vitamin A when the dosage is 100 times more than the RDA it can be fatal. And the intake of vitamin A it can lead liver damage, hair loss, bone, muscle pain, loss of appetite, dry skin, mucous membrane, haemorrhages and coma whereas acute vitamin A hypervitaminosis that is when you take excess of vitamin A for a very short period. This leads to gastrointestinal upsets, nausea, headache, dizziness and muscle contraction. Now it cause vitamin A toxicity. So there is acute toxicity where the symptoms are headache, vomiting, stupor and death. And chronic toxicity there is weight loss, dryness of lips, bones and joint pains, hepatomegaly the liver gets enlarged and bone fractures. There are congenital malformations also because of toxicity of vitamin A. So it causes a change in the central nervous system, cardiac and craniofacial defects. Now the deficiency of vitamin A also is dangerous. So it causes conjunctival xerosis and corneal xerosis. Initial symptoms are the night blindness then followed by the biter sports then the cornea and the retina also are involved where xerosis of eye occurs and the person becomes blind. So biter sports are the keratin that is deposited in the conjunctiva of the eye. So this is associated with night blindness. It is a white patch that occurs in the outer corner of the conjunctiva in the eye. Follicular hyperkeratosis is the protein keratin is deposited around the hair follicle. So each hair follicle you have a keratin deposition and this leads to xerosis, immune suppression and anemia, impaired tissue growth. So all the hair follicles on the body have a protein deposition and the follicles are closed. This is how the xerophthalmia in the vitamin A deficiency looks. Pigmentation of the retina occurs and when the beta keratin is excess there is discoloration of skin. The skin becomes yellow in color or changes the color. So this is about the vitamin A, the functions, the sources, the deficiencies and recommendations and what happens when the vitamin A is in excess. Why we should take the balanced amount of vitamin A and to keep our body healthy though the vitamin A is required in very small amount it is a very important vitamin for various functions. Thank you.


Good morning and welcome you all to this session of the course. Now, last class we were discussing about the oblique shock wave and where we ended just we have to look that last class we are discussing again we just make a recapitulation that a oblique shock wave is like this where the inlet velocity or the incoming velocity v 1 is being deflected and this angle is the angle of deflection and this is beta and what we discussed last class is that this oblique shock wave can be treated as a normal shock provided the Mach number Mach 1 which is v 1 by a 1 is modified at m 1 sin beta and the Mach 2 actual Mach number is v 2 by a 2 the condition here took the section 2 section 1. So, it is m 2 that is the normal component sin beta minus delta that is this angle made by this velocity v 2 with the line parallel to the shock wave and similarly this is beta. So, this we discussed and finally, we under appreciated that a relationship between beta and delta and the Mach number initial m 1 sin beta or m 1 whatever you tell is very much important and then from a trigonometric relationship we arrived at this relation tan delta is 1 minus x where x was some quantity defined. So, finally, this is the expression this is the expression we derived where delta is this deflection angle beta is this shock wave angle well m 1 is the approach Mach number m 1. So, this is a very important relationship now two characteristic feature of this relationship is that you see when beta is pi by 2 this already we discussed earlier beta pi by 2 means that when the velocity of approach to the shock becomes 90 degree makes 90 degree angle to the shock that means this becomes a normal shock this is the normal shock condition normal shock then what happens what is the value of delta when beta cot beta will be 0 when beta is pi by 2 cos cot beta will be 0. So, therefore, delta is 0 now another case you see when m 1 sin beta is 1 then also delta is 0 this is because this becomes 0 and this m 1 sin beta 1 means sin beta is 1 by m 1 and this is the Mach angle that means beta becomes equal to the Mach angle because we know that for a Mach wave the angle which it makes with the flow stream direction is 1 by m 1 sin of that that means sin inverse 1 by m 1. That means this beta becomes the Mach angle that means the shock wave becomes a Mach wave. So, therefore, two extreme conditions where normal shock we already appreciated that the value of beta lies between two extreme values pi by 2 and sin inverse 1 by m 1 that means here you can write beta is equal to sin inverse 1 by m 1. So, within these two limits there is no deviation this is because for a normal shock the velocity before the shock and after the shock at the same direction similarly for a Mach wave the velocity before and after the shock the same and this again can be represented by this like this that a oblique shock is that oblique shock is between this two limit one is normal shock normal shock and another is the Mach this is the Mach wave Mach wave here also there is no deflection V 1 V 2 and the oblique shock remains somewhere here where there is a deflection of the velocity that is the delta sorry you cannot understand delta. So, therefore, the oblique shock wave lies between these two limit now you see that this particular formula this can be little bit we can do with this since beta is delta is 0 between pi by 2 and sin inverse 1 by m 1 which means that beta may have either maximum or minimum in between these two value because it is 0 0 to 0. So, that can be found out by making a derivative of this that if we can make this with respect to beta d delta d beta making 0 and checking for the second derivative whether it is less than 0 or greater than 0 we can find out the condition of maximum and minimum and if you perform this then this is your task I am not doing this the entire algebra in the class, but I tell you this thing if you do it then you get the delta has a maximum that d delta d beta is 0 when beta is given by this expression sin square beta. Now, this beta well in the book they sometimes write the max, but I will write the optimum value of beta where it is maximum delta that is gamma plus 1 by 4 gamma this is relatively complicated expression 1 by gamma m 1 square into 1 minus you can do it at your home this is a task for you 1 plus gamma minus 1 by 2 m 1 square plus gamma plus 1 divided by 16 m 1 4 really a little complicated one. So, this is the expression for the optimum value of beta where delta is maximum and if you put this value and you get the maximum value of delta that expression you can find out and more important thing is that how does it look now if you make that you will can find out the value of delta maximum and that all depends upon the mach number. So, therefore, the optimum value of beta where delta is maximum and the maximum value of delta which will be found out by replacing this in this equation for the value of beta one can get it is not very simple, but straight forward thing it will complicated. So, one can get a curve like this that I will explain now what is this curve we see it very carefully the curve is like this now we can find out we see that from here that now we what we are doing we are drawing the deflection angle with beta or beta with delta for different values of m 1. So, a family of curves for delta beta with different values of m 1 now for a given value of m 1 let us understand the curve as we have seen that beta is 0 here where sorry delta is 0 here where beta is sin inverse 1 by m or m 1. So, this is for a particular value of the m 1 this is for a given value of m 1 clear and it has a maximum that is the maximum delta that is the delta maximum clear now this as a value like that and this what is this this is the pi by 2 that means this is the normal shock limit this is the max. So, this is the shock wave angle for a given value of m 1 or all right and this clearly has a maximum value that is delta max here another one curve is drawn this one this is this is this is drawn because this gives the value of the beta optimum now what is this is the locus of m 2 now if you find out the locus of m 2 in the beta and delta plane just like that this is the locus of a given m 1 that how beta and delta changes for a given m 1 we know that the m 1 is related with m 2 this m 1 is related with m 2 this m 1 is related with m 2 because m 1 sin beta earlier we did that m 2 sin beta minus delta they work as the max number approach or inlet or at the upstream for a normal shock and that is after the normal shock the way the normal shock relates the downstream max number to the upstream max number with the same relation we have shown that is valid for this case. So, therefore, if we do that mathematics then we can plot in the figure the locus of the constant m 2 that means this is one and this is done for m 2 is equal to 1 I will explain it after what this is done for m 2 is equal to 1 m 2 is 1 means m 2 is the max number after the oblique shock. So, that locus is given. So, this is the picture now another interesting picture which is found from this figure is that for a given value of delta that is the deflection angle we get two values of beta that means there are two values of beta solution is obtained. So, now why abscissa is not coming given value sorry given value of delta there are two values now it is it is it is it is focused already it is ok. So, for a given values of delta we have two values of the shock angle now this delta is specified by the geometry of the flow this delta is the turning angle that we will understand solving problems that delta depends upon the geometry of the problem because delta is the turning. So, shock wave will take place depending upon the turning of the flow. So, the flow is turned by the geometry of the flow for example, the flow passes through a wedge. So, therefore, this deflection angle in fact is the input to the real problem. So, therefore, for a given delta depending upon the geometry of the problem we get two solutions from this as we see that two beta value. Now, if this two solutions if we see we will find out that you see this that is why a mach number one curve the locus of mach number one is given here m 2 1 mach number means m 2 1 and the values of m 2 below this curve in this plane is m 2 less than 1 and the value of the sorry m 2 less than 1 I am sorry it is m 2 greater than 1 it is already given m 2 greater than 1 and above this we can get the locus of all constant m which is m 2 less than 1. That means this solution of this shock wave angle gives a shock where after the oblique shock the velocity that is m 2 is greater than 1 the flow remains in the supersonic that already we discussed that after the oblique shock the flow may be supersonic may be sonic because the restriction is on the m 2 sin beta minus delta which has to be less than 1. So, m 2 may be greater than 1 whereas, this solution that this value of shock angle that the higher value gives rise to m 2 less than 1. That means if we read the m 2 value here that means this is a strong shock because it reduces the velocity to subsonic level and this is the weak shock. So, therefore, two solutions of beta out of which one the lower value corresponds to a weak shock solution and the higher value corresponds to a strong shock strong shock solution. So, usually it is very difficult it depends upon the circumstances which one will prevail, but it has been found experimentally that flow past external bodies or the external flows the solution or the shock wave the weak shock wave is found that means after the shock the flow becomes supersonic, but it may be subsonic depending upon the circumstances. So, if nothing is told for our purpose for solving problems specifically we usually take the solution of weak shock that we will do when we will solving the problem, but this is the total physical picture that the shock wave angle dependence with the turning angle for different values of m 1 and at the same time what will be the corresponding values of m 2 that is the mach number after the shock. Now, this thing can be shown here in a more compact form like this just you see this one is your this curve is your m 2 greater than 1. Now, you see this is a curve you can see probably this is deflection angle deflection angle delta this is deflection angle delta this is shock angle this is beta. Now, you see these are the families of curves for different m 1. So, this is one now one thing is that this is 1 by m 1 for given a for a given m 1 this is the for a given m 1 these are all corresponding mach wave limit, but the maximum limit is pi by 2 for all initial mach number. So, therefore, all this curve merges at 90 degree. So, m 1 values goes on this is m 1 values goes on increasing in this direction goes on increasing in this direction this is obvious, because if you see here the sin inverse 1 by m 1 is small when m 1 is high. So, therefore, m 1 increasing in this direction you see this is 1.4 1.6 234. Now, m 2 is equal to 1 this demarcates 2 series of 2 categories of mach numbers one category of mach number is here you can I will draw these are the mach numbers these are the mach numbers greater than 1 m 2 the less than 1 0.8 0.6 like that. Whereas, we get mach number here which are m 2 is greater than 1 that means, let for example 2. So, therefore, this curve this curve is m 2 1 m 2 1 demarcates the region of strong shock and the region of weak shock clear. And this one this this curve is the locus of the maximum deflection angle this is the locus of the this again coincides at the maximum value of the delta that I will come afterwards that delta max. Now, if what is this value why I stop here why the curve is like this is because if delta max is found out with m 1 then what is the value delta max by m 1 if you plot you will see that there is a limit. That means, if we now find just a minute I will show you that if we plot the delta max we calculate delta max and we plot delta max versus m then a interesting result will be there from 1 delta max. For example, delta max 0 10 this case I am just doing otherwise it will be easier 30 40 degree 50 then somewhere here for air it is calculated the values this value represents for air a for air a limiting value that 45.58 that means, with increasing m m 1 2 3 4 like that somewhere it is near 10 to the power 10 or something some value in ultimately asymptotic. That means, the maximum angle 45 that means, the turning angle cannot be more than 45.58 whatever may be the value of m whatever may be the value of m with m the turning angle changes that we have already seen the turning angle changes with m for a given shock wave angle you see we can have the turning angle changes with m with m changing the turning angle changes. But if we this is the curve if we now plot the delta max the maximum turning angle that means, this one this is the maximum turning angle for example, 1 m you choose this m m is equal to 2 this m curve what is the maximum turning angle this one this is the maximum turning angle if you choose this m this is the maximum turn that means, m is reduced if m increase this turning angle increases m is increasing in this direction I told you. So, as we increase the m the turning angle increase, but this becomes very close to each other and finally, this is totally become compact and finally, it reaches a value of 45.58 this is 45 45.58 for air this is a representative figure for air that means, if we increase the mach number very high also this will not reach go more than that then what is this that means, this physically implies one thing that if the angle is more than that just I am telling you two things coming to picture for example, the mach number is this one then I find out this is the maximum delta max mach number is this is the maximum turning angle for example, if mach number is 2 for example, I know this is the maximum turning angle if my turning angle is more than that what will happen do you know that if turning angle is more than the maximum that means, a flow through an wedge what is this turning angle turning angle is the flow is turned like this. So, if the wedge angle for example, this 2 alpha that means, the alpha is more than delta max for a given m 1 this wedge gives you the turning angle actually for flow then what happens for a given mach number the shock wave is not attached to this there becomes there occurs a detached shock this is known as detached shock detached shock the flow like this the detached shock is like this the flow takes place and this is a typical flow filled the detached shock this is m 2 is less than 1 this is m 1 and this becomes curved this is not this is not attached to the wedge this is detached shock this becomes curved and this type of shock is not amenable to the mathematical analysis we have done for a straight oblique shock. So, this is out of the scope of our discussion but you must know that this is there, but another interesting fact that if a body of this shape for example, of any shape which gives a turning angle given turning angle is accelerating with in the air that means, air flow is velocity is changing if it accelerates that it may so happen when the lower mach number is turning angle may be more than that, but higher mach number if we increase the mach number the turning angle increases when it accelerates and achieves a higher mach number then it may be such that the turning angle may be lower than delta max. So, therefore, when a body accelerates sometime it is observed that the shock is detached at lower mach number at again attached at higher mach number we will do we will solve some problems. So, that we can get some feel of this let us solve some problem then only you will let me see that I have some figure let me have a check that I have some figure which I will show like to show you this is the oblique shock is that shock curved shock detached shock. Let me solve a problem and then we will discuss the next part let us solve a problem first this is a first problem example one air flowing at m 2 mach number 2 with a pressure of the 80 kilo Pascal's and the temperature of 30 degree Celsius passes over a component of an aircraft that can be modeled as a wedge with an included angle of 8 degree that is aligned with the flow that is the flow is turn by both upper and lower surfaces of the wedge through an angle of 4 degree leading to the generation of a oblique shock wave find the pressure acting on the wedge circle just now I told that this is an example this type now what is this there is a wedge shape that means this is the wedge give a simple example the total angle included angle is 8 degree. That means this angle is 4 degree this side now this is the incoming air v 1 let the pressure p 1 temperature t 1 mach number is m 1 now what happens the flow will be turn through 4 degree both this sides that means one side we will just that means this is the flow which will be deflected because the streamline what will happen the streamline will be going like this so because of this wedge placed in the streamline is deflected and if the approach mach number is greater than one this deflection of streamline because of the presence of the wedge creates the oblique shock that is the concept that is the basic concept so this so this is the 4 degree this is the basic concept and this is the basic idea of the problem v 2 that is all so what we have to find out this is given that that is aligned with the flow that is the flow is turn by both upper and lower surfaces this is upper and lower surfaces of the wedge through an angle of 4 degree leading to the generation of oblique shock wave find the pressure acting on the wedge surface that means this surface p 2 so the same in both the sides I am just showing it here mach number will be m 2 temperature will be t 2 so how to solve the problem problem is very simple now m is 2 so first of all what we have to do with this m 2 the first job with this turning angle that means m 1 here is 2 turning angle here is 4 degree so with this m 1 with this turning angle we have to calculate the beta either from the equation you can tell sir I will calculate those who are very much interested in using the analytical equations that analytical expressions they can solve analytical expressions or you can see the chart because it will be easier that with m 1 2 and delta 4 if we see the chart m 1 2 we have to go for the different values this m 1 2 and delta at 4 degree one can find out what is the value of beta here beta also we will get 2 values one is for weak another is for strong and we take the strong solutions and from this figure we get the value of m 1 so from this what is the value of m 1 delta 4 m 1 sorry beta the value of beta is 33.4 degree that means we take the weak shock solution when nothing is told this is just a methodology weak if we can take strong shock solution also and find the result and which one will be correct that will be validated by the experiment so it is difficult to tell for the time being I am taking the weak shock solution so therefore the weak shock solution is the lower value of beta from the graph we are taking the beta 30 when beta is known things are done that means what is the procedure then we know m 1 sin beta we find out m 1 is 2 into sin 33.4 degree sorry and what is that value that is m n 1 that is m n that is that is told at m n 1 is m 1 sin beta and that become equal to 1.1 now we see the normal shock wave so from the normal shock wave with this as the m 1 plus plus I showed you that what the normal shock wave there will be an m 1 their column for in given m 1 we can find out the value of p 2 by p 1. So, for this m 1 this as the approach m to the shock or the inlet m 1 to the shock we can find out the value of p 2 by p 1 and that value is 1.245 that value is 1.245. So, this value if you just multiplied what is that 80 so p 2 is 1.245 into 80 kilo Pascal's so the value will be I am telling you the value I have done it it is 99.6 kilo Pascal's 99. Now, here this is the problem that pressure acting on the o h if it is told find out the velocity or the mach number here what is the mach number here I will find out the mach number after the flow how for this m 1 m n 1 from the shock table you find out m 2 that is not asked for, but I am adding this thing the book from where I have taken the problem this is not asked for now if I have to find out the m 2 here what you have to do you have to find out m 2 from shock table. That m 2 is what from shock table which you get from normal shock table is actually for the present case is m n 2 is actually m n 2 that is equal to m 2 that is m 2 from normal shock table is m n 2 and that is equal to m 2 sin beta. That means we know that for a oblique shock it is the sin component of the m act as the inlet and outlet m for a normal shock. So, when we solve the problem as equivalent to a normal shock always we have to read m 1 m 2 with respect to the normal shock wave which is nothing, but m n 1 that is m 1 sin beta and for m 2 it is sin beta minus. So, when we know both beta and delta we can from this we can find out the actual m 2 for this problem this is not given is not told here to find out. So, it is so this is one problem that we can discuss that for the shock then we will solve another problem then before that I think we have to discuss the reflection of shock wave reflection of shock wave we will discuss now the reflection of oblique shock what is that reflection of oblique shock wave oblique shock wave reflection of oblique shock wave what is meant by reflection of oblique shock wave. Now, it is very important that how the shock wave is reflected. Now, let us consider a case like this physically first of all that there is an wedge there is a wedge there is a wedge being.  Now, here if I show the velocity so it will go like this and this will be the v 2 turning this is the half angle here also what happens the flow will turn like this. Now, if there is a plate here flat plate for example. So, first I consider reflection by a flat plate simple case reflection by a flat plate then what will happen physically you see that this thing will ultimately become parallel to the plate after what the streamline will become parallel to the plate. This means that the shock comes here this is the shock wave shock wave strikes the plate and is being reflected such a way that this when comes to this reflected shock wave. So, this is the deflection for example, this value is delta. So, this is deflected this is again this is this direction deflected in the same value delta to make it parallel. That means initially this was the flow direction which was parallel to the plate for example, it is deflected by delta by the original shock wave this is original shock wave well and this is the reflected shock wave reflected shock reflected shock wave well. So, therefore, you see the original shock wave deviates this one by a angle delta that is the turning angle of this that is the angle imposed by this wedge shape body. So, then what I mean this side is a plate then again the flow stream will get reflected by the reflected shock wave same angle of deflection to make it parallel. This is a typical picture very simple case that how does a oblique shock wave gets reflected by the flat plate. Let us solve a problem based on that then only this things I think reflection of shock wave will be better clear from a problem. Let us see this problem example 2 well air flowing at m is equal to 2.5 mack 2.5 with a pressure of 60 kilo Pascal and a temperature of minus 20 degree Celsius passes over a wedge which turns the flow through an angle of the folding. Simple case that means there is a oblique shock takes place attached oblique shock to the wedge this is again told in the problem that leading to the generation of oblique shock waves this is true. One of the oblique shock waves as I have just described the same physics is being repeated in the problem with numerical data impinges on a flat wall which is parallel to the flow upstream of the wedge and is reflected from it find the pressure and velocity behind reflected shock wave that means this is the problem find the pressure and that means precisely this is the problem let this is 1 let this is 2 let this is 3. So, this we have to find out what is p 3 now what is given p 1 m 1 is 2.5 well p 1 is 60 kilo Pascal and t 1 is minus 20 degree Celsius these are the given data and delta is delta in both the cases is 4 degree it becomes again parallel to its original direction which is parallel to the wall this is the wall plane wall problem is very very simple first we find out the condition at 2 now m 1 is to first duty is to find out beta that means at delta is equal to 4 degree and m 1 is 2.5 I find beta the weak shock solution beta the lower value of beta and from the figure and this becomes equal to 26.6 degree that means I just search for this m 1 is 2.5 I go somewhere here that is the m 1 is 2 this is 3 and with the beta 4 degree we find out this find out this m 1 is 2.5 somewhere here it is 30. So, it may be 22.6 however I am not doing it here but this was found as this is the correct value. So, whenever I know beta so this side m 1 is m 1 sin beta m n 1 is m 1 sin beta whose value is 1.12 now I can read from normal shock table that this 1.12 what is the value of p 2 I can find out p 2 by p 1 p 2 by p 1 and that p 2 by p 1 that is found out is equal to 1.336. And t 2 by t 1 is found out this is all from normal shock table because now it is equivalent to a normal shock I am reading m 1 sin beta that 1.12 as m 1 in the normal shock table to find out p 2 by p 1 and t 2 by t 1. Therefore, I can find out p 2 and t 2 here because p 1 and t 1 is are given. Now, what will happen I have to find out the m 2 here how to find out m 2 here corresponding to this m n 1 I know an m n 2 from the table that is the m 2 from the shock table and that value is 0.897 that means this is the value of m 2 in the shock table that means the downstream Mach number corresponding to an upstream Mach number of 1.12. So, corresponding to an upstream Mach number of 1.12 I find the downstream Mach number m n 2 which downstream Mach number m 2 which is our m n 2 which is actually m 2 sin beta minus delta here beta I know 26.6 this is this value I know the 26.6 this is this is the 26.6 this is 26.6 this is 26.6 this is the beta we know. So, delta is 4 degree. So, we can find out m 2. So, what is m 2 m 2 we find out as 0.897 I write it sin of 26.6 minus 4 degree and that become equal to 2.33. Now, is another problem that second reflected shock wave that m 2 is 2 that is approaching with a m 2 2.334 which is being deflected this way by delta. So, therefore, now again with delta is equal to 4 degree and this m 2 as m 1 that means approach Mach. That means this m 2 that is here it will act as m 1 for this table we find out what is beta. That means for this table when we will use to find out this table this table this Mach number will be this one this 2.334. So, for this the shock wave angle will be 28.5 degree that means for the reflected shock this shock wave angle is different. So, shock wave angle is 28.5 degree this is now this is 28.5 degree now turned again by delta is 4 degree do with this 28.5 degree I decode again m n 2 this m n 2 is what this is with this approach m 2.334 which is our m 2 which I am using as if m 1 in this shock table 2.334 approach or to find out the value of beta with the delta m 1 that figure delta beta for different m 1 that figure. So, m n 2 is 2.334 into sin of this 0.5 I think you will understand this thing clearly. That means this becomes the sin component the normal component of the Mach number though Mach number is a though you should not use that what component Mach number is a scalar quantity it is the ratio of the velocity. But this is the way you can understand that the sin component of the Mach number which acts as the normal shock Mach number now with this m n 2 this becomes equals to I tell you sin this is sin 28.5 and this becomes equal to 1.111. Something like that you see 1.1 as I found find the solution now against this Mach number in the shock table. Now, this is the approach Mach number for the reflected shock I can find out the pressure ratio that means I can find out the p 3 by p 2 and this p 3 by p 2 I can find out 1.297 and I can find out t 3 by t 2 which will be read as t 2 by t 1 they are in the shock table. That means I will use this approach Mach number in the shock table as m 1 and find out p 3 by p t 3 by t 2. Earlier we found out p 2 t 2 because we knew that p 2 by p 1 and t 2 by t 1. So, therefore, we find out p 2 t 2 multiplying with p 1 and t 1 then p 3 by p 2 and t 3 by t 2 is known. So, we can find out p 3 t 3. So, final result is that p 3 is equal to 104.0 kilo Pascal and t 3 is 296 k. Now, velocity has to be found out. So, find the pressure and velocity behind the reflected shock how to find out velocity velocity is very simple you find out a 3 at root over gamma r t 3 well root over gamma r t 3 and when you get the velocity a 3 you get the v 3 as a 3 into m 3 what is m 3 m 3 is this one m n 2 you get here and you find out the corresponding value of m 3. That means you find out here a value of m n 3 from this with this value of the approach Mach number and that m n 3 value equals to I tell you 0.9108 0.9108 0.9108 then you find out m 3 decoded that is m n 3 is m 3 divided by that is m n 3 m 3 into sin beta minus delta. So, therefore, sin beta this beta is the beta for the reflected shock wave that means this beta 28.5 delta remains the same in both the cases. So, therefore, you get a value of m 3 is 2.17 fine. So, the m 3 if you put a 3 if you put you get a value of v 3 same as m n 3 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.9108 0.749 meter per second. So, therefore, we find out the pressure temperature and everything. So, you see that a Mach of 2.5 is ultimately reduced to Mach of 2.17 because we have chosen always the weak solutions always the weak solutions. I am also not sure which one will prevail, but we can have the strong solution is just only a change in the value and we will get the some we will follow the same procedure, but finally experiments we will tell which one is correct. So, this is the way we have to solve the problem. So, therefore, it is clear now again I am telling before closing the lecture on oblique shock that the oblique shock has to be treated always as a normal shock by considering the fact that the this the velocity component parallel to the oblique shock does not change. So, therefore, the normal component of the velocity acts as the same thing that is the that is the velocity of approach for a normal shock. So, we consider this Mach number M 1 sin beta if beta is the shock wave angle and M 2 sin beta minus delta if delta is the deflection angle as the Mach number before and after the shock and we can treat this as a normal shock that is the main thing and delta the turning angle is imposed by the problem geometry for which one has to find out beta depending upon the inlet Mach number M 1. This reduced Mach number is for using the normal shock table that means to convert the problem to a normal shock problem. So, this is the total thing for the oblique shock. So, therefore, today I will stop the oblique shock discussion and now I will start the another chapter I do not know whether the time is not or is there or not, but rather let me start at least the now the next question is that so far we have discussed about a discontinuity in the flow field where the pressure changes in a way that pressure is decreased and the supersonic flow is changed to either a supersonic flow or a subsonic flow in the form of deceleration either a supersonic flow or subsonic flow in a form of deceleration for a normal shock it is it has to be subsonic for an oblique shock it may be subsonic it may be supersonic, but it has to be decelerated where pressure temperature will increase. This type of wave is known as compression wave where the velocity is decreased and the pressure is increased and this type of wave may be stationary with respect to a static from a frame of reference or with respect to a coordinate frame of reference you can say and this can be moving also and in that case moving with a constant velocity we can attach the coordinate frame with the shock wave and we can analyze, but there are certain cases where this is not this compression wave does not occur. For example, I tell you just consider that so far we have considering a O H shape for example, a O H shape where the the direction is changed like that. Let us consider a we have considered a shape like this ok. So, this is the case where we have seen that there is a this we have not considered there will be a shock wave like this oblique shock wave where this will be there will be change like this the deflection ok. So, P 2 this is P 1 this is V 2 this is V 2 this is V 1 and it is true that V 2 is less than V 1 and obviously, P 2 is this has been proved P 2 is T 1 here also the oblique shock wave is there. So, that sorry that this difference and V 2 V 1 and V 2 is less than V 1 this is the wage and P 2 is greater than P 1, but what happens if a supersonic flow approaches a convex corner it may be smooth it may be sharp what happens. That means, this what happens what will happen that if this is the thing what will happen will there be a shock wave and this will be velocity will be turned like this and V 2 will be less than V 1 or V 2 will be greater than V 1 which one will prevail which one will prevail tell me. So, this is here we can show from the geometry that V 2 will be greater than V 1. Another example I am telling you that if there is a pipe this pressure is atmospheric pressure this pressure is P which is much greater than atmospheric pressure there is a valve or diaphragm whatever you take it is suddenly raptured it is made open made open the fluid will suddenly come out. Then what will happen this side the pressure will be released and velocity will suddenly slowly slowed in a compressible flow depending upon the extent of compressibility the velocity in the upstream will slowly be reduced and pressure in the upstream will slowly be reduced. So, what will happen so this means an expansion wave will move in this direction here also this will be a static expansion wave means this V 2 will increase whereas, the pressure will fall here also the fluid will start flowing that means there will be a that means what will happen in the upstream velocity will be generated because the flow has started suddenly open the discharge will take in an incompressible flow the same discharge will be instantaneously felt here, but in a compressible flow it is not felt here or the pressure felt here is P a then immediately the pressure will not be felt here as P a. So, therefore this will take time that means there will be a propagation of a wave which is an expansion wave why which makes the pressure low as it passes through and makes the velocity high because it was 0 similar thing happens this is a stationary wave where this V 2 will be higher than V 1 I will explain this in this case if it is a convex wedge or a convex corner rather sharp or smooth corner this type of oblique shock this is oblique shock will not occur this is oblique shock. So, this is oblique shock what happens this will be expansion here we will get expansion wave which I will discuss in the next class I think time is up. So, today we will finish it here ok thank you.


Namaste. My name is Kelly. I've been practicing yoga daily for 13 years now. And some of you may be wondering, how do you practice yoga? Isn't that something you eat with cereal or fruit? Well, yoga is not a dairy product. Yoga is actually an ancient form of exercise that combines breath work and meditation to help increase your balance, increase your strength, improve your flexibility, and it can also reduce stress, lower blood pressure. There are many benefits. Now, at first glance, you might think that yoga is easy because when you create a pose, then you hold that pose for a while without moving.  So let's do some yoga. Our first pose is called mountain pose. You want to stand with your feet about hip-width apart, toes pointing straight ahead. Press your feet down into the floor as though you were grounding deeply into the earth. And from there, imagine a string attached to your tailbone lengthening through the center of your body all the way through the crown of your head, helping to lift you up and create lightness.  Your palms may turn slightly outward. Once here, you want to inhale and exhale through your nose, breathing deeply and smoothly. You can hold this pose for 30 to 60 seconds, and this is also a good pose to do in between other poses. Our next pose is called downward dog pose. To do downward dog, you start on your hands and knees. Let your hands be forward of your shoulders, fingers pointing straight ahead, and they should be about shoulder distance apart. Your knees and your feet will be shoulder distance apart as well. Inhale and curl your toes under. Now exhale and straighten your legs. Push your hips upward so that you end up looking like an upside down letter V. Your weight should be evenly distributed between your hands and your feet. And try to keep your legs straight and remember to breathe. Hold this pose for at least 30 seconds. Exhale as you bring your knees back to the ground and repeat the downward dog pose several times. Our next pose is called triangle pose. Spread your feet well apart, at least 3 feet distance. Left toes angle inward, right leg will open all the way to the right. Reach your arms up shoulder height and as you inhale, lengthen your whole body up toward the sky. As you exhale, reach out to the right. Let your right hand slide all the way down as far down your leg as it will go. Your upper arm will point up to the sky and look up toward your fingertips. Hold this pose for 30 seconds or so. Breathing evenly. And to come up, reach up. Your hands can rest on your hips and we'll turn our feet. Your right toes will angle inward, your left leg will open all the way out to the side. Reach your arms up and extend them outward. Lengthen all the way up to the sky. Draw a breath in. And as you exhale, we want to bend to the left. Let your hand slide all the way down toward your ankle. Your upper arm reaches up to the sky once again and look up toward your fingertips. On this side as well, breathe smoothly and deeply. And to come out, reach up with that upper hand. Back to standing. Our next pose is actually two poses. Cat pose and cow pose. They work together. Start on your hands and knees. Draw a breath in with your spine and neutral. And as you exhale, round your spine up toward the sky. Imagine a cat when it wakes up from a nap, how it stretches way upward and your head will rest in between your upper arms. As you inhale, take your spine in the other direction.  Stretch gently. Now move back into cat pose as you exhale and as you inhale, move down into cow pose once again. You can move back and forth between these two with your breath. Do each several times and then bring your spine back to neutral. So there are five simple poses to get you started practicing yoga. Namaste. If you have more time, here are some optional poses that you can try. The first one is called frog pose. Squat down with your feet about hip width apart. Let your hands rest on the floor until you find your balance and try to keep your heels on the floor. When you feel centered, bring your hands to your heart in namaste position.  To come out of the pose, reach your hands forward and gently roll back until you're sitting on your hips once again. Our next pose is actually a family of poses called the snake poses.   Lower back to the starting position and repeat a few times. For mother snake pose, begin just like in baby snake. Lie flat with your forehead down and your hands by your chest.  Take a few breaths here and then gently lower back down to the starting position. You can repeat mother snake a few times as well. And the third of the family of snake poses is father snake. This is the most challenging snake pose of all. Begin as you would in baby snake. Lie flat, your forehead is down and your hands are at chest level. Press your palms down into the earth and lift your upper body as high as it will go. Bend your knees and lift your feet toward the sky. Gently bring your head back toward your feet and look up in the air. And then straighten your legs. Lower your upper body back to the ground. You can repeat this pose a few times also. Next is the mouse pose.  Make sure your feet are flat with your toenails pressed down toward the ground. Slowly bend forward and let your forehead rest on the floor. If this is uncomfortable, you can fold your arms and let your forehead rest on your forearms. Hold this resting pose for up to a minute. Now it is a resting pose, so enjoy your break. And those are the optional poses. Enjoy your yoga practice.


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