Hey everybody, how's it going? I'm Scott and I'm here to talk about support. It's great to be here in Prague. I haven't been to Europe in a long time, so it's nice to be back. I am sort of irritated because I spent about three months memorizing this session in Czech and I've been here for two days now and everyone's speaking English, so I think maybe next time we should make that a little bit more clear. Unless you want to hear the Czech version, it's about four hours long. OK. Dobre den. OK. Wait, that's not right. Sorry. OK. Cool, so let me just start off with the obligatory. My name is Scott Massey. I work for Pantheon. I'm the Director of Customer Success and that is basically support. It's onboarding. It's any of the stuff that we do to help people be successful on our platform, so that's training sometimes, that's doing a lot of screencasts and telling people how to develop on our platform and be successful. Before that, I worked at Promet, which was a Drupal shop in Chicago. I built their support team and before that I worked in IT managed services, which is basically supporting Cisco, Citrix, Microsoft stuff for a shop in for a IT company in Chicago. My, yeah, so there's my Twitter stuff and I wanted to share something that I've never told another human being. These are three things that I've left in my search browser when I was doing training sessions for people on Pantheon. So hopefully when you guys come up and ask questions you can share something that you've never told another human being. I don't remember why I was looking up Chinese dog doesn't want a bath but I think it was probably a YouTube video for my wife. So here's what we're going to talk about. We'll talk about why people think support is a drag. We'll talk about building sustainable support products. I have some case studies that I kind of want to run through to sort of give you some real world examples of how to structure support that I think is good, the tools, how to hire people for support and just a little bit of sort of philosophy and hand-waving. I've done this before for people at different Drupal cons and that kind of thing and so just before we start, how many of you work for a dev shop or something that offers Drupal support? How many are looking to maybe add support? How many are end users who are looking for support? There's three guys right in the front here. So that's about the usual demograph. So this is sort of geared towards people who have it, who struggle and I've definitely experienced a lot of the things and maybe we can sort of share our experiences and get a little bit better at it. So why offer support? I think there's a lot of reasons that people sort of fall into that role maybe because they built the site for someone or they've taken over a site for another dev shop or something like that. But the real reason that we do it is why we offer support, I think, has a lot to do with credibility and especially if it sites that we've built, it has a lot to do with putting our money where our mouth is in terms of the technical debt we incur when we build the site and being able to offer the end user the promise of long-term support. So it's definitely more of a marriage than a fling and I think you sort of have to think of it like that. I also think that the benefit of doing it is, well there's several benefits, but the one thing about the fact that it's like a fixed income, instead of just doing projects, in addition to that, it moves you up the ladder of trust so to speak and from a vendor to an advisor towards actually kind of a stakeholder in the client's process and decision-making process. Before I started working for Pantheon, not all of our clients were like this but there were a couple of clients that we would meet with them manually and help them figure out their budget for the next year for their IT expenditures and to me that's a good place to be because it indicates the trust that they have in you and it also kind of indicates that you're the de facto person they're going to go to when they make choice or the de facto shop they're going to go to when they make choices about who they're going to get to build their site or who they're going to go to. So I think it's important to not just offer it because if you offer support poorly or begrudgingly I think it causes pain on all levels and it doesn't really secure you or move you up that sort of ladder of trust. So I think the first key to doing support well is understanding that what you're doing is you're building these products and you're offering service products and so there's products and then there's not really good products and so an anti-product is kind of like the column on the left where hey, just call us when anything happens or if something goes wrong and we'll help you fix it or we built your site and then say, you know, you get a phone call and it's like hey, you know, you built us that feeds integration and originally it was for Twitter but now we're, you know, we're downloading Chinese newspapers and it's not working so that's a bug and you need to fix it, you know, or if you're accepting new projects from people and you get a call that hey, I'm a Drupal developer and I have this site that I'm building for the Czech government and it's overdue by a month and there's like five things that I don't know how to do so I need you to help me fix it ASAP. Like I think those are sort of recipes for failure and I think when you build kind of your product line of support services it's a good litmus test to kind of see what, if things fit into that product list those are your strengths and if they don't then they might not be good things to take, like you might not win with them. So what I want to talk about is kind of how to build these successful products, you know, for example support development. Like when it's a product that means you can attach parameters to it, you can, you know, you spell it out for sales, what the limitations are, what you cover, what you don't cover, you specify the billing rates and if a product is successful with just changing a minimal number of parameters you should be able to use it over and over, you know, so if you sell block hour agreements, you know, you should be able to just say 50 hours or 100 hours, you know, at 100 hours the hourly rate drops by, you know, a certain amount, but essentially it's the same kind of thing. You know, there's been examples when I worked at Promet in Chicago, we had a client that had already built a site on D7 and they wanted to continue working with the dev shop that they had, but the dev shop used SVN, SVN sort of in a half ass manner and they wanted to use Git, they knew they needed to move to Git, these guys weren't going to migrate to Git at that point in time. So they hired us to basically just be their release management and we set up a schedule where we pushed things, you know, where if we saw anything that had been committed to the repo, we would push it to dev, we worked out the QA workflow to where, you know, we would let them know we pushed things and they would check on it and then we would push it to live and so forth. If anything went wrong, we would revert it and that's kind of all we did and it was kind of cool because it sort of put us in that loop of trust, you know, where if they needed decisions they kind of knew who to come to for a second opinion and eventually we sort of became more of the de facto go-to. So I think like creating products that you can support and sustain is beneficial even if they're not just your typical kind of Drupal support. And additionally like another one is doing updates for people, like just doing updates by itself may not seem like of much value but it is for a lot of people who may just need something who are happy to manage their own site or, you know, just need to take care of the minimum basics. And so what I want to do is some case studies of these three fictional people and how they made support work for them. So the first one is this girl Aria and she's a site builder. She knows a little bit of PHP. She's mainly built, you know, a few sites for people, for friends, for family, that kind of thing. And so her issue is is that as a freelancer she has a lot of stuff on her plate. You know, she has to do her own marketing. She has to look for new clients. She actually has to build the site. But in addition to that, the existing clients say 10 of them a month are calling her to ask questions. And then maybe, you know, 10 customers are calling her for five hours a day or five hours a month and maybe she's doing three hours of billable work from that. And then all together, that's about a week's worth of work. Like 25% of her month is doing work that's not really well organized. It's not bringing her in new business. It's just sort of upkeep on existing sites. So a use case for her, she goes to meet with her, you know, support consultant and this person, they set a strategy and the target is like existing clients. The client she already has on our platform is to monetize the free and kind of piecemeal work that she's been doing for the people. So the change in messaging is like prior when we were talking about like, well, you built this and now it's a bug. The messaging that has to start like really high, you know, in the discovery period is like, you know, Drupal is this great way to build sites, but keep in mind, your site is a custom site. It uses custom code. Even if it's contrib modules, your end user is really well educated on what they're getting, the benefits of using Drupal, of which there are many, but the fact that bugs exist in life, they're suffering. We will figure out a way to address these things and it will get worked out because I know what I'm doing and this is how I do it with my support products. And I think it's also really, you know, rather than wait for the first month's invoice to go where you built for the time that you've spent talking about Drupal, it's good to say, you know, as we build these support products, what I'm going to do is I'm going to set up this ticketing system, so after we launch, there's going to be a ticketing system. If we talk on the phone about it, it's going to be billable. If you give me a really complete, concise ticket of what's going on, how to replicate the problem, that's not billable and that will save you money and it will save me time and we can be much further along on this problem rather than conversing about it, which is real hard to do plus it's billable for you end user. So you create these products where you say, okay, I'm going to give you a block of hours a month. I know over the last few months we've probably talked about five hours a month, so let's just start out with five block hours recurring each month and you use them or you lose them but we can kind of knock out these things rather than piecemeal. You tell me how you want that five hours spent or we can save it for emergencies or that kind of thing and then you set up a second one that's just monitoring. Okay, here's monitoring and on the back end I set up my Pingdom account, I set up my PagerDuty account and I find a good host. I know of a really good one by the way if you want to talk about it and you have something on the back end to kind of support this product that basically just says I'm not a sysadmin, we picked a host. They'll support the platform but I'll be the point of contact. So if something goes wrong it'll wake me up but I can get on the phone and manage it and make sure that it's done. And then the final product that I would offer you as an end user is like your managed updates because there's security, there's core updates and so what I'd like to do is the way that I do it is when security updates come out we do it in a week. We do it up with a QA workflow plan where either you have a couple days to go through it or you let me QA it, I create my Selenium tests for X amount of dollars or euros up front and that's how we handle updates and then so we do security updates that week can trip updates, we do quarterly let's set something like that you work that out at the beginning in the event that you push a contrib update and it breaks something hopefully you've built a great site that might not ever happen but suppose it does you can either revert it or you can use the block hours to fix it because that's the nature sometimes bugs happen I want to be successful I want to be around forever I want to support you forever I need to make money on this as I go listen to her support consultant which doesn't really exist as a role but she does that and she comes up with these numbers just 500 units of currency for five hours a month and then just a low price for the monitoring plan because it's just monitoring it's waking up possibly in the middle of the night but the host will hopefully be handling any issues and then the updates which would be $200 $50 a month to handle all the updates and so what we have is the $500 is a block hour agreement a monthly recurring block hour agreement the 50 is managed services from the managed service world it's flat $50 and then the updates are a flat $50 or a flat $200 and so what that does it sort of puts the risk on you and puts the onus on you as the developer to be able to make that profitable but if you amortize that over a year as long as you're doing less than 24 hours worth of work you're roughly making your margins so hopefully again I found that this works because core updates shouldn't break anything can trip updates might but you're doing it quarterly so you can give them the option to hold off or it's not going to add a new feature so we can wait on it but security and core gets done so this is an example for her and so we're looking at instead of roughly 400 based on what's billable the end result for you bundle it all these different agreements together into a managed service agreement and they pay $750 a month so the next example is like in America you have to attach a number to your dev shop in order to make it real so I made this one Hodor 9 which is a dev shop in America that's been around a while and they put out a lot of sites and they're pretty well established the problem is they've been offering support for a while and it's really disorganized project managers are managing support as well they hate it devs are getting pulled off of projects to work on support issues for really difficult problems everyone's getting burnt out the devs don't want to work on support and they can they have a list of up places they could be working and maybe they don't want to be doing support they want to work on fun projects not picking up the phone whenever there's a fire because trust me no one ever calls support because things are going swimmingly and they just want to say hi so so that's the problem so the strategy we've already sort of talked about existing customers now let's just focus on like new clients the new people that come in and they're looking for support and generally and so the goal is to make it sustainable and so like the risk is is you get the call and this is a support client that I've handled before where it's like hey so you do support right I googled support and Drupal and your name came up so that's great I have this D6 site it's actually our intranet and it's actually running on WAMP a Windows NT server and so if you want to do any work I'll give you a dongle so you can VPN to a dev site and do the work there and then we'll push the changes together and so that is enough to make like your developer just you know post his resume and say thanks but I'm not going to work on this and so the message that you want to convey now is like that's awesome but we work on supportable working sites and that may not be one now that's kind of an extreme example but you may get someone that just comes in a more typical example is like someone who comes in with a laundry list of like hey you do support that's great I need a dozen things done here they are and so it sounds simple but the issue that you run into is you know you say sure we'll do it and then you look at the site and you see like um panels there's always sweet context and like eight other things that kind of do the same thing and some are enabled and there's like one panel that's active across the whole site and you know there's you know you sort of like shit what have I done you know and so so the model for handling this that I have found to be successful is you say sure we're happy to look at the site and from there we go through onboarding and from there we you know once we get things into a supportable state then we start working on the issues and so some people will balk at that and I think it's important for the success of your developers and the long term success of your company to know when to say no you know there's like um the Groucho Marks line about you know I don't want to be part of any club that would have me as a member and so it's the same kind of thing like when someone's looking for support it's almost like an indicator in itself like maybe they were fired by their you know especially if someone comes up to you and say yeah our devs were really assholes at the last place you know so um you know we know that you're good so we know you'll fix it especially if you know the devs it's a small community so a lot of times it turns out that they might be a difficult client to handle or they had some sort of weird use case that that um is difficult to solve so you have this site audit that you've developed and so yesterday there was a pretty good session on site audits uh there's many different places where you should be able to piece one together pretty quickly if you don't have one who has a site audit that they do so um really with me I've tried a couple different times the one that we use now at Pantheon is actually pretty good uh and it's available like anyone can use it it's a bunch of Drush commands that we created and it's just a project called site underscore audit and it's a bunch of Drush commands it's sort of Pantheon centric for like our enterprise stuff so it tests to see if caching is working and it to me like a lot of the site audits like you can spend a lot of time digging into like hacked encoder and things like that which are all useful um all really useful uh I also think that there's a lot of things that are uh really closely correlated with a problematic site you know the number of modules that are enabled things like that and so like the thing that we built kind of checks for that but also uh the Drupalcon uh Portland uh session that we did two uh women one from chapter three and one from ProMed in Chicago all go into detail on their site audit and what they check for you know like uh PHP in fields and things like that to sort of give a feel for like how difficult it's gonna manage or you know if somehow you know they make a small change what it might affect across the whole site so design this site audit hopefully you can execute it within a few hours I don't know depending on the custom stuff like the guy yesterday was saying sometimes it can take up to 30 days but execute it quickly and bill for it you know say because what you're gonna give them like the one that we have um it uses like the Twitter bootstrap so it actually generates like that report there you can use it from the command line but it also gives some a nice deliverable that you can say hey you may not know much about your site but after this you'll know a little bit more and it's gonna be thirty two hundred dollars and that's what we charged and it covers your time and um the resources that you put into doing it so you develop this site audit and if it passes then you just you say that's great let's have an onboarding call let's have a kickoff call let's talk about what we need to fix um if it doesn't pass then you say okay so here's here's how we handle support now that we see that there's bigger problems that we need to fix to make your site supportable um we we think we can do it you know in an agile fashion it's gonna take fifty hours and so let's start out let's take these fifty hours let's get the site to where we know it's gonna last and we can start doing the work you want some will say no you know it's up to you to kinda make the call if you wanna bypass that I would say no like I think that there's I have found at least in my neighborhood there's a lot of people looking for support and if you build a roster of supportable sites it makes life so uh for an example to project the revenue here they do this one time site audit and they charge thirty two hundred clams for it and then there's a problem and they fix it over fifty hours you know so it ends up costing ends up costing more than they thought they wanted it to cost and then they say okay so now that we're done with that let's set up a monthly recurring plan similar to what we talked about with ARIA where we do updates we do monitoring only this time there's an SLA where we actually guarantee that someone's gonna get to you within two hours or four hours and you base that on the amount of time it's gonna take for one person to not get the call and then the next person hopefully to get it and then you add some padding and you come up with a number that you feel that you can live with and offer and you tack on an SLA to that and you build a little bit more for it and then you come up you know say that they don't want to do a monthly recurring user lose kind of hourly commitment then they just buy two hundred block hours you do it at a slightly higher rate because they're not doing monthly recurring like monthly recurring is the best for a dev shop if they're not gonna go for that that's fine it's just a little bit higher and then you know there's sort of an example of what your total annual revenue is for that client and then the last one which is just sort of like kind of a thought experiment is this guy Joffrey and he knows nothing about coding or site building what he does know is about how to speak English good and he also is a you know he graduated with an English degree which in America they say is like the most useless degree to have and so this guy he really the problem is that he can't pay his rent and the bills for you know the seven kingdoms that he also happens to be king of so his strategy is to target other dev shops other C level people who have blogs and he's gonna create a product that delivers content management because in my experience I had several clients who were not computer savvy and struggled with whizzy wig and really needed someone to do that and there are people out there that do this pretty successfully and it's something that a lot of dev shops don't think about offering it's like we don't want to offer content management we'd rather not even offer support but you know we definitely don't want to be editing content for people but there's also a way to do it where if you know you teach someone how to use whizzy wig you teach them how to you know create a Google analytics report that sort of shows what happened to content for the month you give them like a QA workflow and you say this is you know you send me the ideas I'll clean it up it's gonna come back to you I'm gonna download an image from Shutterstock that I think is kind of appropriate stick it in there we'll do five a month and we'll bill 500 bucks a month for it to make sure your content is updated we kind of ride you and PM you a little bit to make sure that content on your site is always updated and so this is you know maybe not depending on what your payroll expenses are this might be pretty close to the same margins you might be able to make based on you know how you know the rate that you can hire people at so you know it's just sort of a thought so we're doing my time here okay three more hours so project mind and support mind so the important thing to think of is the biggest thing that I've noticed working with other dev shops is the usual approach is trying to approach support as if it's a project and you get really good at agile or waterfall and then you get to support and it all goes crazy because it's all these various issues that come up and then go away and disappear and then ten issues completely unrelated to come up and then the third one is a really difficult problem that ends up taking forty days and then the you know the developer has to try and estimate on a site that he's never seen before or maybe hasn't touched in months and so that's where a lot of those things get go haywire and that's why having kind of these processes in place is really important so you build these processes you know because generally what comes up you have problems like my site is doing something weird you know you have incidences my site just went away you have requests like I'd like my site to do this and then you have change management like it's time to go from D6 to D7 or whatever and so like those categories are sort of a good framework for how you build your products and how you sort of respond to kind of emergency situations and so the way to think about support is not projects but what helps me is kind of a standard in case model so standards are repeatable processes like if my wife if I come home from work and my wife says let's go out to eat that means I say okay and I change my clothes and we go out to eat that doesn't mean like I debate it or I complain about it or I mention that I just went out to eat the night before because I know my life is much better if we just go out to eat that's like a standard I don't care if I went out the last seven nights we're going out to eat again tonight easy you know that's how you build like a standard but see I'd say that accounts for maybe 25% of Drupal support related issues most of them are cases so you treat them as case management and that's where you need to do some investigative skills you need to do some troubleshooting you can gradually build the standards of the tasks that need to be done and the goal is to make as much as possible standards rather than cases so then the difficult stuff at the very least if you have like a level one and level two support person level one can look at it and say I don't know the answer but I do know that I'm supposed to get log files I'm supposed to check this and this and then I'm supposed to summarize and give level two a replicatable way to reproduce the error so you have your level one person which maybe at a lower pay level or lower experience at least they know how to build build it up and summarize it and give them like a neat gift rep package for the level two person more of like the problems incidents all that cool stuff about like service delivery framework available via itil like which has existed for a while like support is actually pretty well defined maybe as much as project management is it's just that it tends to be like on the enterprise IT managed services world but you can it's very completely dry boring reading but it has a lot of cool stuff for building support projects and then so like my onboarding thing is really important because this is where we get into really what matters with support almost as much as technical chops is the soft skills and the ability to quickly kind of build a process where people are familiar with how you do it so you have this onboarding call you know say that like we talk about you know they've done the site audit and they're ready to go you have an onboarding call and this is what you go over you go over the processes they need to know immediately like how to create a ticket how to create an emergency ticket how to call me how like what a ticket needs to have in it for us to get right to work on it what hours were available for support how to reach us that kind of thing then you cover all the questions you take all the questions that people have asked you over the last 10 months and you compress them all into a 30 minute call where you answer all those questions that keep coming up so you you theoretically kind of answer the first two standard deviations of questions and then you do it like the most important thing the weirdest thing is people actually like to see my face when we do this call so doing it on the phone is nowhere near as effective in the long run as doing a go-to meeting or WebEx or something where you're connecting and you're seeing like this is a human being so before they start you know the sort of the email furious typing at a nameless face they know that we've talked and I'm you know I'm like a human being I have feelings I ache I cry and then you set expectations and like one of the biggest expectations in support is about estimation and it needs to be for me it really needs to be explained up front that estimation is by definition what wrong it's incorrect like it's me like estimation is trainable like you can get better at it and most PMs know after they've worked with any developer for any specific amount of time like how much they need to multiply their estimate to get kind of the real time you know it might be 1.5 it might be 3 it might be 0.5 sometimes but I think that's something that management needs to help train people and you can kind of go back and look at histories and see how things really ended up taking and kind of help with the process a little bit but it always needs to be explained that it's an imperfect science the more we get to know your site the better it'll be but it's kind of inexact so let's talk about hiring and retention it's hard to find someone who is really super at Drupal and wants to do support I said it it's also hard to find someone who has the soft skills to want to deal with an angry customer sometimes or to be able to explain things to someone who gets frustrated by technical jargon and so generally my advice is to find someone who's really good at one thing and really willing to learn the other I think you can to a certain extent you can kind of teach both you can at least help people get better but only really to make the effort and I think that to help them get better at the technical side of it I think that's a good thing for bench time I think that's a good thing for level one people to kind of see how level two what kind of information they need and slowly sort of build their chops that way and also I think that you know building tools like the site audit and things like that are great tools to help a level one person kind of get more familiar with with Drupal with doing support and that kind of thing the soft skills so one thing that I really recommend is verbal judo verbal judo is like has anyone ever heard of it yeah verbal judo originally is what they teach the police to teach people to be persuasive without being violent and you can hear there's a great example like we're doing good on time so I want to tell this story because it was really amazing so I'm in North Carolina and I'm sitting outside at a Starbucks and pretty typical American scenario right so so I'm sitting out at a Starbucks and I hear a policeman like a plain clothes policeman get on the phone and he says hey I'm looking for your son and then obviously the son's not there and he said okay well this is kind of serious because there was a child who there was an incident of child molestation that was reported to us the police and there was a name given and so we ran that name through our computers and two names came up and the child described the person as being about 250 pounds and so the first person was under it was way under that so I don't think that you know it's not him probably but we see here that the records for your son says that he's about 195 so that's very different so all I need to do is I need to go by there and just give him an eyeball give him a quick look just so I can check that box just so I can show that I've done my job and we can just move on and like you know what was really going on there right and I was like verbal judo that's what's going on like being able to say things in a way to get what you want and so you won't have to deal with situations that seriously like in Drupal development hopefully there is like the dark Drupal underworld which is another session at another con somewhere but you know there are times when you are asking the client to do something that they don't want to do you're asking the client to sometimes if they call and they're pissed then the correct you know the normal response from me as a human is to respond in kind you know or maybe even level up a notch you know I'm a human being if someone's insulting me or my company or threatening my financial security I'm going to you know want to fight back but it's amazing what happens not if you I'm so sorry if you say that is unbelievable that is unacceptable let me see what we can do right now to kind of resolve this problem and you let them know that you understand without just giving sort of a blanket apology for whatever and you immediately go to get to the bottom of so verbal judo you can see like this guy on youtube he's passed away but you can also download the books on kindle or whatever and it's a good read it's a quick read and it gives it sort of helps to explain what soft skills are and how to use them effectively the next thing that we developed at pantheon is cakes and so you won't find this in google because I made it up and so cakes stands for um for uh uh what does it stand for um let's go um it stands for uh completion accuracy execution and empathy and this is how we do ticket reviews just like you do code reviews we do ticket reviews because we tried like sending level 2 tickets back to level 1 so they can see how it was fixed um and that didn't work so much um but we do find that if level 1 has a problem with a ticket they can tag it with for review and then twice a week my team gets together and they go over tickets that were solved or in progress and they review what happened and they talk about you know was I complete was I accurate um did I execute the ticket workflow like did I escalate it right that sort of thing and was I empathetic like was I a jerk was I too short did I not look at the problem enough or was I responding fine you know and so it's amazing how well these things actually work because everyone you know it's a blameless sort of area you know way to get better at something and then also using metrics like you look at metrics like to me one of the most um wall building metrics is utilization you know if at the end of the week you say hey um you are only like 30% billable what's going on you know and it might be because he was solving a problem that was so hard that you had to write off hours or something like that there's a lot of metrics you can use like one of the metrics that we use that's really valuable is what percent of tickets did first level resolve like we want that to get better we want them to resolve you know most of the tickets you know it would be great if they could resolve all of them but we know that's not going to happen but the more they can resolve on their own it's sort of empowering and they want to get better at it too you know or we look at first response resolution like how ease how much were they able to like be like Batman and just wrap their wings around the problem and think of what it might be do a bunch of quick debugging with like here's the issue here's how you resolve it you know that kind of thing like using metrics as sort of an empowering tool is a good thing to do um and then like for managers I think one important consideration this is like something you can probably Google it's called the leader detractor scale and so the leader is someone who does what's expected does something extra and help someone you know like a real sort of overachiever kind of person a contributor at the level below that someone who does what's expected and something extra and like those are the two groups that you really want to look for and nurture and hire because everything below that you know even someone who does only what's expected sometimes in support isn't enough like if you say hey check this out it might be a cron issue then you'll get a ticket back saying wasn't a cron issue you know the customer is still suffering um they've done exactly what you asked them or what they thought you wanted so it's kind of a you know a back and forth kind of thing but you really want to look for people who can sort of you know really empathize with the issue so um that's that was a really bad animated gif um I think that's kind of all I wanted to talk about um I hope you liked it and if you have any questions let's uh let's talk so thank you Nick um so email bravery was uh email bravery is when when you send an email it's also you can see it in various parts of the internet where people are willing to say something that they would not say to someone's face via email and to me the best way to combat email bravery and I am I have done it so I'm not saying sometimes customers get mad they type emotionally and that's not good for a support department to be on the receiving end of that so here's how you fight it my favorite image is like someone typing it and sending it and like take that and then they look at their phone and their phone rings like that's how you combat email bravery like as soon as you receive that email pick up the phone and call and directly say hey it sounds like you're upset you know or hey we screwed up and you know it's amazing how quickly you can turn it around sir yeah um okay so ticketing system that's a real that's a great question and um so in the IT managed services world there's a couple really good products like the cream of the crop is like a Siebel system that handles all that and it also handles like agreements and block hours and all that SLAs that sort of thing the next step down that I used at my managed services company is don't write this down because I'm going to tell you why you're not going to buy it in a minute um is a company called connect wise and connect wise also handles block hour agreements all that stuff if it handles it as a customer portal it does all that stuff you're not going to buy it because one there's like a $12,000 initial fee to just get it set up the number two reason you may not buy it is it because it requires a dot net application to be installed on your computer um which you know ruled it out for when I pitched it to the Drupal shop um so we we at Pantheon use desk which is a sales force come sales force product um it's not perfect but it works um I think the main the the thing the thing that you need to consider is you really want to get something that does billing and we ended up using a product called this is this doesn't have a very happy ending by the way um I found a product called blue folder which became packet trap as they went down the poor naming ladder that became packet trap and I was actually going to bring it up here but I went to the site and they were bought by Dell which everyone was excited about which quickly killed the product all together so um now my recommendation would be desk works okay it doesn't handle like billing and which can suck up a lot of time um consider something like desk or Zen desk or fresh desk plus maybe something like harvest um that can handle the time entry and billing and that sort of stuff another consideration is any of those most likely have a way to write something um you know you could set up another database like an agreement kind of thing that um takes billable time and we'll dev it down the hours so I wish that maybe there is a better product out there I couldn't find one or else I would have talked about it here uh so we have people using pantheon in Europe we do not have a uh Euro data center I should have started with that that seems to be a common question we didn't we didn't know you liked us no we have people using it in Europe we have a lot of people using it in Europe Australia especially in conjunction with the CDN but um but yeah we will eventually we want to we like it here sorry sir I wasn't paying attention what does the X stand for in cakes execution I sort of had to you know thank you you're welcome so um 546 so an agile approach to support doesn't always work sometimes it does it works when for me it works best when it's that initial you've onboarded someone and there's a bunch of problems you know or when there's a laundry list you know if you have a client that has like I need these 10 things that need to get done like after you've gone through that that lends itself to like an agile kind of thing again that's really hard to estimate because usually it's your first look at a site when you're handling that so it's really important to stress that estimation is going to be way off base so there's no more questions thanks a lot and it's awesome being here we'll be around oh Wonderkraut is doing a similar support related thing tomorrow at 1045 and then there's going to be a buff right after that at around 12ish so if you want to talk more about support um there are a cool bunch of dudes and we'll all hang out together and talk about support


The Fed's Jackson Hole Symposium, which brings together central bankers from around the world, will be held virtually. Climate activists believe the Fed should be much more aggressive in stopping banks from financing fossil fuels. We're here in Denver, Colorado, outside of the Federal Reserve Building to send a message to the Federal Reserve Board. I'm so sick of people in power saying there's nothing else that they can do. It is time for the Federal Reserve to play the role that they can play and be a whistleblower and call the stops on financing fossil fuel infrastructure and development. We're here at the Federal Reserve because we know that the banking industry is part of the problem. We are here in a city right now where we've had such high ozone levels that people for 30 days straight have not had clean air and we know it's worse in the communities that I come from. I am from a frontline community with multiple kinds of pollution. We know the banks continue to fund it. U.S. banks are driving the planet off a cliff. The largest funders of fossil fuels are Chase Bank, Bank of America and Citibank. And it's the Federal Reserve's job to step in and blow the whistle. The Fed has control over the banking and the financial system in the United States which contributes almost a trillion dollars a year to the fossil fuel industry. Without that support, they couldn't do what they're doing. Follow the money and that's where the money is. Ahead of COP26, we are calling on the Federal Reserve to phase out all fossil fuel financing by 2030. We have to remember the timeline here so again the Fed Chairman's terms is set to expire in February of next year which means that the Biden administration will have to make some sort of announcement of probably soon. It's time for President Joe Biden to appoint a climate champion to lead the Federal Reserve who will stop funding the climate destroyers. We need to get somebody in the Fed will actually do something to control the banks make them acknowledge the risk and the damage they're doing. I know what I want those candidates to do and that is to funnel the money into renewable energy and to revamping a sustainable economy in the United States. It's imperative that they stand up for our communities. Stand up, Biden! Tell Biden to nominate a climate leader in bedshare. Sign this petition and share this video.


Some good tea because it's cold all right today marks 15 years 15 years that I've been at ILM NNS Yes, I'm a nerd so many Star Wars goodies and things here. I'm just such nerd, but yes today 15 years and with 15 years Comes this Now it's a bit of a cheat you get this as a Disney employee But I haven't been with Disney over 15 years. It's been I don't know six or seven years whenever Disney bought Lucasfilm. Let's see what that is Ooh That's the back. That's the front. Let's see who first of all Comes with a little pin 15 years What a cheat then in here. Let's take this out. I'm gonna break it. Yeah Pretty sturdy look at that present it to a Jean-Lenis house. It's spelled correctly. I love it because you never know Recognizing 15 magical years with the Walt Disney Company. That's a lie It's not technically good little Mickey high five That is pretty crazy I have to say I put it down without breaking it It's been very cool got to see Skywalker Ranch work on Star Wars and all my childhood movies It's been absolutely bananas lots of movies on my resume some good some bad But all of them fun to work on that was one of the main things that was fascinating where you get to work on Awesome movies and then as years go by it's just the people that you get to know there just a great company It's really really great people there 15 years it's been pretty cool


Hi guys, welcome back to my channel. Today's video is going to be a fun review of this Lululemon yoga mat and this yoga mat I recently purchased because I used to use this blue yoga mat that I just found in my garage that my mom used for a while and it was one of those foamy ones It was just kind of like a puff foam mat Before we get into this video, who is your favorite fitness blogger? If you guys come from my workout videos, then I already know some of your guys's favorites But if you are new to my channel, I would love to know who your favorite fitness bloggers are. This specific mat is called the Reversible Mat 5mm. I think that stands for millimeter for the thickness here. If you guys are interested in getting it I will have it linked down below. They have so many different color patterns and this one I got in just a Light pink. I would unroll it here. Let me see if I can unroll this so I Guess you could use this side But I typically use the pink side for the front like the part that I work out on But it's basically just a big sheet of rubber We have the Lululemon logo here and then we also have the Lululemon logo on the pink side So before we get into my opinion, I'm just going to read you guys some facts about this mat It is designed for yoga. I don't do yoga. I just do like normal exercises But the top layer absorbs moisture to help get a grip during sweaty practices And that's basically the key reason why I got this I wanted something that my hands wouldn't like slip on or my feet for that matter It's a natural rubber that gives you cushioning and a textured grip for low sweat practices The anti-microbial additive helps prevent mold and mildew on the mat contains latex The dimensions are 26 inches by 71 inches and the thickness is 5 millimeters The weight is 5 pounds 24 ounces and I must say this thing's super heavy when I first got it I was like, oh my gosh, this mat is like a weight in itself It does smell a little bit and they do warn you before you purchase it So that's a little overview of the mat. They are a little bit pricey and they do cost $78 but if you compare that to the leggings that cost 100 I mean, you're kind of getting a deal Lululemon. I don't know why it's so expensive I really don't understand if you can tell me leave it in the comments Now I'm gonna answer the question right off the bat. Is this thing worth it? Should you invest in one? There are a lot of reviews about this that probably aren't the most positive But I think it's totally worth it. I was looking for a good mat that I could sweat on and not slip I was having a really hard time with the blue mat because my feet would slip and it was just not good One time my hand slipped out from under me. It was just not a good experience I didn't want to invest so much money into a mat before I didn't even know if I was going to stick to working out But I proved to myself after the few weeks that I've been working out I'm like, yes, I'm going to continue this lifestyle So I definitely wanted to invest in a better mat So for my workouts and for what I do, this is the perfect mat I also love the colors the smell for me doesn't bother me. I actually I know it sounds weird But I actually kind of like the smell of rubber. It doesn't affect my workouts or anything like that Honestly, it's a really good mat. I don't see any problems with it I saw online that they did say that there was peeling But I mean I've been using this for two weeks now and I mean I roll it up every day and I don't see any Crazy peeling issues now. I'm gonna get into the negatives of this mat So depending on what colors you get, this is a really light pink It shows your sweat hardcore man When you have a drip of sweat on this thing, it will show it does absorb it like it it doesn't I don't know There's some weird thing in this mat that Absorbs it super fast. So it's wet, but like your hand doesn't slip But I don't recommend this pink color if you do sweat a lot and if you're working out at a gym I could kind of see how that could be embarrassing because your sweat would be all over this mat because mine certainly is Definitely something to consider if you do sweat a lot maybe buy the black mat I personally like this color and it matches a lot of my workout stuff So I chose and I was looking specifically for a pink mat and this one came up. This could be a positive or negative It's very heavy. Like I said, it's weighs five pounds because it's pretty heavy It won't move on you a whole lot is what I found I don't have a problem with this one moving a lot of you guys loved my Satisfying blue mat moving when I was working out this one doesn't move as much Another thing that some people might not like is the smell it smells of rubber But like I said, that doesn't really bother me and obviously if you're allergic to latex Don't buy this product But I guess the biggest negative is that you can see your sweat stains the rest of it I don't really see having a big problem. Sometimes it gets folds in it They're not visible like when the thing is stretched out. See like when it's folding there. It'll have like a little fold Mark you can't really see it. It's not like it's ripping or breaking. So overall, I really like this product I definitely would consider getting a really good quality mat That will hold up for quite a while rather than it just buying one on Amazon So if you guys want to check out this mat, I will have it linked down below like I said But they have other different types of mats that you could choose from and I don't know I would just I would check it out so you guys can see for yourself, but overall a plus I love this Lululemon mat. I don't regret buying it. What's so ever overall This is a really positive review that is not sponsored by Lululemon. If you enjoyed this video Make sure you give it a thumbs up Don't forget to subscribe to my channel and answer the question of the day and I'll see you guys in my next video Bye


So people I am back with another Outriders video and today I showcased you this great farm for legendos, epics, titanium, high level loot xp, world tier xp, the works. How's it going guys? My name's DPJ and if you enjoyed the video leaving a like really helps out and if you like what you see I want to see more Outriders on a daily basis be sure to subscribe. Okay so this was showcased to me by my pal Silent Wraith aka Jacob aka Tolster aka scummy scumbag but what it is it's basically a mission a lot of you will have probably progressed past by now but if you haven't anyway keep it in mind for when you eventually get here but it's a mission where you go and hunt a monster, it's a guaranteed couple of epics from this actual boss you can get legendos drop you can get all sorts but at least guaranteed to epics a ton of titanium xp and much more.


It is a good time to summarize what we have learnt in residence time distribution so far. So we have looked at what is a non-ideal reactor and what is the residence time distribution function, what are its definitions and we had looked at what are the ways to measure it experimentally that is looking at the pulse and the step input and we have also came we also looked at what are the RTD or the residence time distribution functions E curve and the cumulative distribution function F curve in the last lecture. So today let us start with this lecture, let us start with looking at the properties of different functions and also proceed further. So suppose if I look at the an important property of the residence time distribution is the mean residence time. So the mean residence time is actually given by the first moment. So if I Tm is the symbol that I will use for mean residence time it is actually given by the first moment of the of E of t that is the RTD function. So E of t is actually a distribution and that distribution can actually be used to decipher some of the properties of the distribution itself and some of the properties of the reactor system. For example mean residence time is an important property that is actually used to control various things in the system. When there is no dispersion across boundaries that is between the point of injection and the entrance of the reactor. Here in these situations the space time that is tau which is equal to V by the volumetric flow rate with which the fluid is actually flowing through the reactor that is equal to the mean residence time itself. Now this is independent of any RTD function that is actually representing the non-ideal behavior of the reactor under no dispersion conditions irrespective of the RTD function the mean residence time that we obtained would be exactly equal to the space time of the reactor itself. So this is true for all RTDs this is true for all RTD all residence time distributions irrespective of what type of reactor as long as the dispersion is actually absent. So now let us look at how to calculate the mean residence time from the residence time distribution function E of t. So tm which is the mean residence time is actually given by the first moment as we observed as I mentioned in the previous note a few moments ago that is 0 to infinity t into E of t dt divided by integral 0 to infinity E of t dt. So that is the residence time distribution and because the integral of the E curve which is the RTD function between 0 to infinity that is equal to 1 this expression can further be simplified as integral between 0 to infinity t into E of t dt. So that is the expression for the mean residence time if the RTD function E of t is known. So if the residence time distribution function is known one can simply plug it in in this expression and find out what is the mean residence time. Now suppose let us look at suppose let us consider a reactor and let us assume that it is filled with species A and let us say that at time t equal to 0 a tracer molecule tracer species B is injected into the reactor let us say it is a dye and then in some time dt. So let us say that the amount of tracer which is actually leaving the reactor in this time delta t whose age is actually lies between that time is actually given by V times dt where V is the volumetric flow rate with which the fluid actually leaves the reactor and that is equal to the volume of the tracer which is actually leaving the that is actually the volume of the effluent stream which is actually leaving the reactor not the tracer. So now suppose if we want to know that the species has been there for a long time suppose see so species A has been in the reactor for a long time. So remember V dt is the volume of the effluent which is actually leaving the reactor in this time dt and if you want to know what is the volume of species A which is actually leaving in that time delta t so then that will be given by dV which is equal to the total volume of the fluid that is actually leaving the reactor multiplied by 1 minus f of t. So f of t is basically the fraction that has been in the reactor for time which is greater than t. This is the fraction which is actually so that is the fraction in the reactor residing for time larger than t. So 1 minus f t multiplied by the volume of the effluent stream will actually tell us what is the amount of species A which is actually leaving the reactor in that small time dt. So now if we sum this over all the molecules of A then that will tell us what is the net volume of the species which is actually leaving the reactor. So if we sum over all A molecules see the total volume that is leaving is given by 0 to infinity V dt into 1 minus f of t. So from here if we assume that the volumetric flow rate with which the fluid stream leaves the reactor if that remains constant and this is generally not true for gas stream but it is normally true for liquid streams that is actually leaving the reactor. If it is a gas stream suppose if it is operated under constant pressure and under isothermal conditions that is constant temperature and if the number of molecules or number of moles does not change because of the reaction then one may also assume that the volumetric flow rate with which the fluid leaves the reactor the effluent stream volumetric flow rate is probably perhaps remains constant. So by using this we can say that V equal to V0 into integral 1 minus f t dt. So now we can integrate this by parts. So if we integrate we will find that V by V0 that is equal to t into 1 minus f of t limits 0 to infinity plus integral 0 to 1 tdf. So that is the integral this is basically when we do an integration by parts we can see that we can split the integral into two sections this t into 1 minus f t evaluated between 0 and infinity and 0 to 1 t times df. Now if I look at the f curve the f curve typically looks like this. So this is with respect to time and this is 1. So at time t equal to 0 f of t is 0 and when t goes to infinity 1 minus f of t is 0. So that can actually be easily seen from the f t curve or the f curve. So now substituting these expressions we will find that V by V0 that is equal to tau which is the space time of the reactor and that is 0 to 1 t times df. So what is df? df is nothing but the residence time distribution itself dt into dt gives the first differential of the f curve and therefore V by V0 that is equal to tau and that is equal to integral 0 to 1 t times E of t dt and that is nothing but the mean residence time itself. So this shows that for any RTD if there is no dispersion between the point of injection and the entrance of the reactor one can show that the mean residence time is actually equal to the space time of the reactor itself irrespective of what is the RTD function E of t. So clearly for V equal to V0 for constant volumetric flow rate then tau equal to tm if no dispersion. And remember that this V equal to V0 is true for gases only if the reactor is operated under constant pressure drop and the temperature is maintained constant that is isothermal conditions and if the number of moles does not change because of the reaction only under those conditions the effluent stream volumetric flow rate may be assumed as a constant. So therefore the exact volume of the reactor, exact volume of the reactor if there is no dispersion is actually given by V0 multiplied by the average residence time. So if the average residence time is known then we can actually calculate what is the exact volume of the reactor in which the fluid is actually flowing. So are there other properties so we looked at mean residence time and we also showed that the mean residence time should be equal to the space time irrespective of the RTD function as long as the dispersion is negligible or 0 and also if the volumetric flow rate with which the fluid stream leaves remains nearly constant. So are there other properties and the answer is yes there are other properties so the other properties is we can also estimate what is the variance of the distribution and that can be obtained using the second moment obtained using the second moment. So the sigma square which is the variance is given by 0 to infinity t minus tm square into E of t dt and so now if we expand this square this product here so we can expand this as 0 to infinity t square plus tm square minus 2 into t t into tm into E of t dt. So that is the integral and this is nothing but 0 to infinity t square E of t dt minus tm square. So this essentially variance essentially quantifies the spread in the distribution of the RTD function. So that is another property that is actually very commonly used in the real systems and the third property which is not very commonly used is the skewness property it is called the skewness and that is obtained using the third moment of the distribution and that is given by if s q s is the skewness parameter there will be 1 by sigma to the power of 3 by 2 where sigma is the standard deviation that is square root of the variance 0 to infinity t minus tm the whole cube into E of t dt. So that is the skewness and this is basically reflects the extent to which the distribution residence time distribution function is skewn. So remember that it may be skewed in either directions so for example if the residence time distribution looks like this then it is sort of skewed to the right hand side of the mean. So the s cube essentially says how skewed is the distribution with respect to the mean of the distribution itself. So now once we know these properties next the question is from real reactor data suppose if there is a tracer that goes inside and from the real data is it possible to estimate some of these parameters and what are the steps that is involved. So let us look at how to calculate the mean residence time and sigma square from the actual data. So normally the actual data that one would get is basically the measurement of concentration as a function of time. So let us say that there are several concentrations that has been measured let us say from time 1 to 10 and there has been concentration CT that has been measured. So then one needs to create a table where as a first step one calculates E of t. So we know the formula for E of t which is essentially given by CT divided by the integral of C over the whole time domain and then the next thing one needs to estimate is t into E of t. So this column provides an estimate of the first moment which is the mean residence time can be used to find the mean residence time and the next step is to estimate t minus tm the whole square and then find out t minus tm the whole square into E of t and then from here one can actually find out what is tm square into E of t. So one can make such a table moment the experimental data of time versus concentration is available of the tracer is available then one can actually fill up this table and from this express from this column one can estimate the mean residence time and from this column one can actually estimate what is the sigma square. So and one needs to use an appropriate numerical integration scheme remember that the concentration is actually discrete values at different time points and so one has to use appropriate numerical integration appropriate numerical integration in order to complete this table. Once this table is complete we will actually be able to estimate what is the mean residence time and the variance for the distribution that represents the RTD function for the reactor. Now the suppose if we change the suppose if there is a reactor and we know the RTD function suppose we know the RTD function suppose we know the E curve for a given volumetric flow rate V1. Now if we want to find out what is the E curve or the RTD function for a different volumetric flow rate. So now let us consider the situation where we are actually feeding the reactor with a fluid of volumetric flow rate which is less than V1. So then the amount of time that the fluid stream spends inside the reactor is going to be larger because the volumetric flow rate is actually lesser than V1 and as a result the E curve would actually look like this the slope of the E curve will correspondingly change. So now because of this problem so this corresponds to volumetric flow rate V2 and because of this issue it is very difficult to now compare the E curves at different conditions because the E curve is now going to be dependent on the volume of the reactor and also on the volumetric flow rate with which the fluid is actually being fed into the reactor. Even for a fixed volume the E curve is now going to be a function of the volumetric flow rate because the volumetric flow rate decides the residence time of the fluid stream inside the reactor. So therefore the tau 1 which is the space time when the volumetric flow rate is V1 is given by V by V1 and tau 2 is given by V by V2. So clearly the amount of time that is spent by the second in the second case that is when when the fluid is being fed at a volumetric flow rate of V2 that is going to clearly be larger than that of the time that is actually spent by the fluid elements inside the reactor when the volumetric flow rate is V1 because V2 is actually smaller than V1. So because ET depends on properties such as volumetric flow rate it is difficult to compare. So as a result it is useful to actually define a normalized RTD function in order to facilitate the ability to compare different RTD curves. So let us look at what is the normalized RTD function. So suppose if we define theta as the ratio of T divided by tau where tau is the space time of the reactor. If we define theta as the ratio of time versus the space time of the reactor then we can now rewrite the RTD function E theta as basically tau multiplied by ET. So that is tau is the space time multiplied by the corresponding RTD function gives the normalized RTD function E of theta and so now theta here which is the ratio of time to tau essentially represents the number of reactor volumes of fluid based on the entrance condition that have actually flowed through the reactor in that particular time t. So now this normalized RTD function E theta provides a facilitates a way by which the performance of the reactor or the RTD function itself can be compared when the sizes are different. So therefore if we look at the RTD curve of the normalized RTD function then the curve looks like this where so irrespective of whatever is the volumetric flow rate for a given reactor volume the RTD function essentially looks like this. So now there is another definition that one needs to know is the internal age distribution and the symbol that is commonly used is I of alpha where I of alpha d alpha that essentially represents the fraction of the material that is present inside the reactor in a time span of alpha in a time span for a period between that is between alpha and alpha plus d alpha.  So E alpha essentially represents the age of the fluid that actually is leaving the reactor and I alpha represents the age of the fluid that is actually present inside the reactor. So these two have its own utility and particularly the internal the age of the fluid elements that is actually present inside the reactor has a significant importance when one looks at when one wants to study the unsteady state behavior unsteady state behavior of a particular reactor. In particular a good example of that would be that suppose if there is a catalytic reaction and the catalyst is actually decaying with time then it is important to know what is the internal age distribution and it is important to actually consider the age distribution in modeling the performance of such kind of a reactor. So I alpha the internal age distribution is essentially given by 1 by tau into 1 minus f of alpha and E of alpha as we know is actually given by minus d by d alpha tau into alpha because of the connection between the E curve and the f curve. So the relationship between the E curve and the I curve is nothing but E of alpha is minus d by d alpha into tau into I alpha. Now for a CSTR for an ideal CSTR I alpha is essentially given by 1 by tau into exponential of minus alpha by tau. So that is the internal age distribution for a CSTR. After all these definitions that we have seen that is the E curve, f curve and the I curve and the mean residence time variance and skewness let us look at the residence time distribution in ideal reactors. So particularly we will consider two cases one is plug flow and ideal batch reactor and second one is we will look at the single CSTR case. So these two we will look at and we will attempt to find out how to get the RTD for RTD curves for these two types of ideal reactors. So let us first consider the plug flow reactor. Let us consider the plug flow reactor. So what is the property of the plug flow reactor? All atoms or all molecules of the material which is actually entering the reactor will spend exactly the same amount of time before they leave the reactor which means that all elements or all molecules of the material will have exactly the same residence time. So same residence time for all fluid elements that is actually entering and leaving the reactor. So therefore the RTD function must have the following properties. So first thing is it must have a spike of infinite height because all of them will have same residence time therefore they will all leave like a plug. So therefore the E curve must have a spike of infinite height and also it must have 0 width and not just that the area under the curve should be equal to 1. The spike will be exactly at the mean residence time and that is very important because that is the property which actually captures the nature of the plug flow reactor. So therefore the spike will be exactly at t equal to v by v0 that is equal to tau which is the space time of the reactor and because there is no dispersion the space time of the reactor will also be equal to the mean residence time of the reactor or in the non-dimensional terms theta equal to t by tau that is equal to 1. So therefore the corresponding E curve because of these properties of the RTD function for the plug flow reactor the E curve should simply be represented by the direct delta function centered at the space time of the reactor. So this is the direct delta function that is the direct delta function and it is defined as follows. So direct delta function delta x that is equal to 0 if x is not equal to 0 and it is equal to infinity when x is exactly equal to 0 and the property of this E curve is actually given by minus infinity to plus infinity delta x dx should be equal to 1 that is the property of the direct delta function in addition to that the another important property is by that the satisfies the convolution integral that is equal to g of tau. So integral of gx if gx is some function of x multiplied by the delta function to dx that is equal to g evaluated at that value of tau itself where x minus tau is actually equal to 0 that is where the spike is actually present. So now let us calculate the mean residence time for this RTD curve. So the mean residence time tm is actually given by integral 0 to infinity t into E of t dt that is the that is the definition for the mean residence time in terms of the RTD function. So that is equal to plugging in the E curve for plug flow reactor we will find that 0 to infinity t into delta of t minus tau into dt and that is nothing but tau itself. So therefore the mean residence time is exactly equal to the space time and this actually one would easily guess because we said that the an important property of the plug flow reactor is that all material that is actually entering the reactor and leaving the reactor will actually have exactly the same residence time and that the E curve is actually going to be centered at the space time. So therefore the mean residence time must be exactly equal to the space time of the plug flow reactor itself which is which one would actually guess and it is also clearly shown by the RTD function also. So now let us look at the second moment that is the variance of the of the distribution. So that is given by 0 to infinity t minus tm the whole square into E of t into dt. So that is equal to tm square into delta function into dt and so now we open up this the t minus tm whole square and then if one integrates we will find that this essentially reduces to t square into delta of t minus tau into dt 0 to infinity plus integral 0 to infinity tm square delta of x minus tau dt minus 2 integral t into t m into delta of x minus tau dt and that is essentially so the first term here because of the property of the delta function is it will simply be equal to tau square and the second property will simply be equal to plus tm square. So that will be the second one and the third one will simply be 2 into t into tm t into delta function integral tm is constant so that will come out of the integral and t into the delta function will essentially be equal to the mean residence time. So that will be equal to 2 tm square and that is equal to 0 because the mean residence time and the space time are exactly equal. So therefore the variance is actually equal to 0 and that reflects the property of the RTD function that actually we intuitively guessed that is the there has to be a spike at exactly t equal to tau with an area under the curve is equal to 1 and the height of the spike is equal to infinity which means that the variance should be equal to 0 for the distribution. So let us look at the f curve for the plug flow reactor. So for a plug flow reactor the f curve f of t is essentially given by 0 to t e of t by dt that is by definition and so that is equal to integral 0 to t delta of t minus tau dt that is equal to 1 by we know that this integral is equal to 1 and therefore the f of t curve is nothing but 1 and so as a result the properties or the RTD function for the plug flow reactor is essentially given by e of t to summarize is equal to delta function of t minus tau. So that is the summary for plug flow reactor where the residence time distribution function is essentially given by delta t minus tau and the mean residence time is equal to the space time of the reactor which is the volume divided by the volumetric flow rate and the sigma square is essentially 0 the variance is actually 0 and the f t is essentially equal to 1. So therefore if we actually attempt to sketch the e curve and the f curve we will find that so that is time and suppose if this is tau here at t equal to 0 if there is a spike tracer that is actually put into the plug flow reactor so that is the spike then exactly after a delay of tau time which is the space time of the plug flow reactor the tracer will actually come out and the same amount same quantity of tracer will actually come out of the reactor so that is the out stream and the height will be infinity. Now suppose if I look at the f curve so this is the e curve and suppose if I look at the f curve of the reactor suppose if I look at the f curve of the reactor then exactly at tau equal to exactly at t equal to tau that is the space time or the mean residence time of the plug flow reactor the f of f value will be exactly equal to 1. So that is the e curve and the f curve for a plug flow reactor. Now let us look at the CSTR case what is the RTD function for a single CSTR. Now suppose if here is a CSTR and this is the inlet stream and this is the outlet stream of the CSTR and the CSTR is well mixed and it is assumed that it is a ideal CSTR and therefore it is a completely well mixed system and let us now because it is completely well mixed system the concentration of the species which inside the reactor should be equal to the concentration of the species and the effluent stream as well. So which means that the outlet concentration is equal to the concentration of the species in the reactor and let us now write a material balance on an inert tracer suppose there is an inert tracer which is actually fed into the reactor. So let us say that an inert tracer is fed into the reactor and if the concentration of the inert tracer is actually C0 at t equal to 0. So time t equal to 0 some C0 quantity of tracer is actually fed into the reactor and now we can write a material balance in order to find out what is the RTD function. So for any time greater than 0 whatever fluid is actually whatever tracer is entering the reactor that should minus whatever is actually leaving that should be equal to the accumulation of the tracer inside the reactor. Now if we assume that it is a pulse tracer if it is actually a pulse tracer which means that the time at which the tracer is actually fed into the CSTR is exactly t equal to 0 and nothing before and nothing after t equal to 0. So therefore at any time greater than 0 no tracer is actually entering the reactor. So therefore the inlet is 0 minus what leaves is the volumetric flow rate V of the effluent stream multiplied by the concentration of the tracer C and that should be equal to V into dC by dt which is the accumulation of the tracer in the CSTR. Now because the concentration of the species inside the reactor is equal to the concentration at which the species is actually leaving the reactor the C here essentially represents the outlet concentration of the species from the reactor that reflects the concentration of the species with which it actually leaves the reactor in the effluent stream. So now one can actually integrate this expression to find out that C of t is equal to C naught into exponential of minus t by tau where T C naught is the initial tracer concentration initial pulse tracer concentration concentration of the initial tracer that is actually fed as a pulse tracer and from this we can find out that E of t is given by C t divided by integral 0 to infinity C of t dt. So now we know the expression for C t the dependence of C on time and other properties so we can plug that in here we will see that is exponential of minus t by tau divided by integral 0 to infinity minus t by tau. So performing the integration we will find that because C naught is constant one can actually cancel out C naught from the numerator and denominator and so we will find that this will be equal to 1 by tau into exponential of minus t by tau. So that will be the residence time distribution function for a single CSTR. Now in terms of the dimensionless in terms of the normalized RTD function E of theta is essentially given by exponential of minus theta where theta is actually t by tau and E of theta is nothing but tau into E of t. So that is the normalized residence time distribution function and now we can actually find out what is the f curve so f of theta is nothing but integral 0 to theta E theta into d theta that is actually 1 minus exponential of minus theta.  So let us attempt to sketch the E curve and the f curve. So the normalized RTD function so the E curve essentially looks like this it is an exponential dk and then the corresponding f curve is actually looks like this. So this is 1 and this is theta. So it actually essentially looks like this and so the mean can actually be estimated as tm that is equal to integral 0 to infinity. These are different properties of the distribution t into E of t dt that should be equal to integral 0 to infinity t by tau into exponential of minus t by tau and that should be equal to tau. So that is exactly what we observed before if there is no dispersion then irrespective of whatever is the RTD then the mean distribution time should be equal to the space time of the reactor itself and now the next the variance sigma square is given by 0 to infinity t minus tm square into E of t dt and that should be equal to tau square integral 0 to infinity x minus 1 the whole square into exponential of minus x dx. So where the change of variable is done by by setting x equal to t by alpha and so integrating this is a standard expression so while integrating this expression one can find that is equal to tau square which means that the standard deviation of the distribution is actually equal to the space time of the reactor itself. So for a single CSTR for a single CSTR the mean residence time is equal to the space time of the reactor and the standard deviation of the residence time function is also equal to the mean residence time of the reactor itself. So now if we compare the various compare the RTD function and the various properties of CSTR we can find that so suppose if you make a comparison we can summarize the function and the properties that we have found so far for a plug flow reactor and a CSTR. So the residence time distribution function E of t is essentially the delta function for a plug flow reactor which means that there is just a delay and whatever is fed into the reactor is going to come out of the reactor exactly after a certain delay and the delay is given by the space time of the reactor and here delta x is actually defined as 0 for x not equal to 0 and infinity for x equal to 0 and the corresponding RTD function for CSTR is 1 by tau exponential of minus t by tau where tau is given by the v by v tau is the space time which is given by volume of the reactor divided by the corresponding volumetric flow rate and then the mean residence time for a plug flow reactor is given by tau and it is the same for the CSTR because there is no dispersion and so the mean residence time should be equal to the space time of the reactor itself and the variance for a plug flow reactor is 0 while for a CSTR it is actually equal to the space time of the reactor itself and then the f curve actually is 1 for a plug flow reactor and it is 1 minus exponential of minus t by tau for a CSTR. So that summarizes the various properties of the RTD that summarizes the RTD function and the various properties of the function for the plug flow reactor and a CSTR. So next let us look at the another reactor laminar flow reactor. Let us try to estimate the RTD function for the laminar flow reactor LFR will be referred to as LFR hereafter. So suppose if there is a tank and there is a fluid stream which is actually entering at 0 and leaving at L so that is the length of the reactor that is L and the fluid is actually entering under laminar conditions and it is expected that there will be a parabolic velocity profile, there will be a parabolic velocity profile with maximum at the centre and 0 near the walls, maximum at the centre and 0 near the walls. So suppose if the centre of the reactor is so that is the centre of the reactor and that is r equal to 0. So if I label this coordinates as r and at r equal to 0 it will be maximum velocity and at r equal to r which is the periphery the velocity will be 0. So that is a parabolic velocity profile that is the parabolic velocity with which the velocity profile with which the fluid is actually flowing through the reactor. Now clearly this suggests that the fluid particles which are actually fluid elements which are actually at the centre they will actually have the shortest residence time because they have the maximum velocity and so they will leave the reactor much faster than the they will leave the reactor faster than the other fluid elements which are actually present in other radial locations other than 0. So now so therefore the velocity profile u is actually given by u max which is the maximum velocity at the centre multiplied by 1 minus r by r the whole square. Now often this maximum velocity may not be known so instead what may be known is the average velocity that is the velocity of the fluid stream averaged across the whole cross section and that can actually be estimated from the velocity profile from the local velocity expression. So u average which is the average velocity at a given cross section is given by volumetric flow rate divided by the area of the reactor at that cross section and that is given by 1 by pi r square into integral 0 to r u max into 1 minus r by r the whole square into 2 pi r dr. So here I have assumed that if this is the cross section of the reactor if that is the cross section of the reactor then let us assume that there is a small element which is present here from the centre and that is located at a distance r and the thickness of this is actually dr. So therefore the volumetric flow rate of the fluid and at any cross section is given by the local velocity multiplied by 2 pi r dr into integrated over the whole integrated between 0 and r. So that gives the volumetric flow rate at that cross section and pi r square is the corresponding area at that cross section. So from this integrating this expression we will find that will be equal to u max by pi r square multiplied by 2 pi r square by 2 minus 2 pi by r square into r power 4 by 4 into and the limits are 0 to r and that is equal to u max by 2. So the maximum velocity is simply twice the average velocity that is the average over the cross section of a of the reactor and in fact the average velocity is also called as the cup mixing average and so u max is equal to 2 times u average. So substituting this in the expression for the velocity we can actually rewrite the velocity expression as u equal to 2 times u average multiplied by 1 minus r by r the whole square and that is equal to 2 v naught by pi r square v naught is the volumetric flow rate with which the fluid is actually flowing at that cross section into 1 minus r by r the whole square. So that is the expression for the volumetric velocity with which the fluid is actually flowing as a function of the radial position. Now we can now estimate what is the time that is actually spent by the fluid particles at a that is entering at a given location r. So that is actually given by the length of the reactor L divided by the velocity with which the fluid is actually flowing in that radial location r which is actually u r and that is given by pi r square by v naught into L into 1 by 2 times 1 minus r by r the whole square. So that is the time that is taken by different fluid elements that is actually entering the reactor at any r location. So that is actually equal to tau divided by 2 into 1 minus r by r the whole square where tau is given tau is the space time of the reactor which is given by v divided by v naught. So now we need to relate the we need to now relate what is the we need to find out what is the RTD function ET. So in order to find that we need to know what is the fraction of this fluid that is leaving and what is the age of that particular fluid. So now the volume of the fluid the volumetric flow rate between r and r plus dr. So that is the volumetric flow rate of the fluid which is actually flowing between r and r plus dr and that is given by dv that is equal to u r into 2 pi r dr. So that is the volumetric flow rate of the fluid which is actually flowing in this element dr that is between r and r plus dr. So now the fraction of the total that is actually flowing through this small element dr is actually given by dv divided by v naught where v naught is the total volumetric flow rate dv by v naught gives the fraction of the fluid that is actually flowing through this element dr. So that is given by u r divided by v naught into 2 pi r dr. So that is the fraction of the fluid that is actually flowing through this element dr and in fact that is nothing but the E of t into dt because the fraction of the fluid that is actually flowing through this small element dr and also the fluid which is actually between v and dv which is spending the time t and t plus delta t is what is given by this RTD function E of t dt and that should be equal to dv by v naught which is actually the fluid which is flowing between v and v plus dv whose residence time is actually between t and t plus delta t. So what we have seen so far in this lecture is essentially different properties of the residence time distribution which is the mean we have looked at the variance and we looked at this queerness and then we went on moved on to the residence time distribution of the ideal reactors particularly we considered the plug flow reactor and then we found out what is the residence time distribution for this particular reactor and what are the properties of the residence time distribution and specifically we found out what is the E curve and the F curve as related to the time as a function of time and next we looked at the residence time distribution function for a single CSTR we found the E curve and the F curve and the corresponding properties and then initiated discussion on the laminar flow reactor. Thank you.


Let's get started if you take a look at the hair right here. It's super weak, right? If she had thicker hair might not be as weak I'm gonna bring this up and make it nice and strong also want it to be just below or just at the shoulder for this haircut That's where we're gonna aim. Now.  I'm gonna draw a straight down Center back vertical line and again, we're gonna move the occipital bone The slightly diagonal forward parting Arrest the hair over nice and tight and then I slide my clip the ys part clip slide it up underneath and clip it together That holds this entire section nice and tight to the head It keeps everything out of the way keeps me nice and organized now I'm gonna do the same thing on the opposite side keeping my eyes Square with the section so as I look at this I'm keeping my eyes Parallel to what I'm sectioning so that that way I can see exactly what line.  That's totally okay. Just be aware of it That'll give me a little extra length in the back If you didn't want are in the front if you didn't want that extra length Then all you have to do is just round this section across So then once you get that line cut you can check your balance back And now I've got a nice full feeling in the back of the head if she had super thick hair You could always layer into this a little bit to create a little bit lighter shape But for me personally, I like cutting this one length and I'll layer into this part of the haircut I'm gonna go in and do some condensed cutting on the head shape here. I'm gonna take my clip out now This is where everybody comes in and they say well, how do you find your guy? I'm gonna comb the hair up like this and to try to keep my finger basically parallel to this parting And then I'm gonna cut across Let me see if I can do this getting in your guys's way That I'm gonna do the same thing on the opposite side This will all come up and bring some of the other side up as well You're combing it up over top of the parting and parallel Now what I'll do once I comb that hair down. I'm gonna check Your pieces make sure that they kind of match up cutting off some of this disconnect that happened at the bottom Our initial guide at the bottom That's why we cut that guy cut it nice and full. So cutting this hair here is just gonna make that line even more blunt It's so much better than tying in the layers to the bottom just layering it up because it keeps that fullness on the bottom Check that out. You can see look at these layers and how they play out in the haircut as I come through here I would just a center parting here Section this off and this doesn't have to be perfect this sectioning because we're really just gonna debulk a little bit You know, you want you don't want to be crazy, but it doesn't have to be perfect Then I grab my texturizing scissor. This is where the OG's in the room can give me a little help But all of these tools that I'm showing you guys these scissors. This is my scissor created by Mizetani scissors This is a Mizetani acro leaf wide. It's a dry cutting Texturizing scissor you can also use it on slightly damp wet hair So what I'm gonna do is I'm gonna go in at an angle like this and then I'm gonna go in an angle like this As I go in to cut in this basically what I'm gonna do slide through Just like that That removes some of that bulk and then I'm gonna do the same thing on the opposite side at the same angle so pop through You can see just glides right through the hair. Then I'll take a look See that thickness that I want if I want to just take a little bit more no problem And then I flip the scissor around and I go the opposite direction So just debulks it so if you have fine hair go the first route if you have thick hair through the second one and just take Take out some of that bulk and we're gonna move into the side of the haircut I'm gonna start on the thicker side the heavier side, which is our right-hand side here. I'm gonna let that out And I'm just gonna start working the hair in the direction. I'm gonna take the parting Kim shout out to Detroit, Michigan now take a horizontal parting across this I'm gonna clip it away So now I want to connect these two points, so I've got my longer point from the balanced line that we cut in the back We're gonna connect these two things together I'm actually wondering if that person is even talking to me.  I've got the weak side.  I want to talk about this for a second. It's super proud of this tool This is our tool that we created the our patent pending with our design patent This is a three-in-one razor cutting tool So there's removable blades so you can change them out make sure that they're nice and sharp So I'm gonna go here show you guys kind of pop this open you can see blades inside Obviously, I haven't changed these razors three different razors inside you have then you just pop This back on and then put the top on to the razor and you're good to go You got a hundred percent cutting of the hair So if you want to cut lines in the hair right there, then you've got your fifty percent Texturizing sides will take out fifty percent of hair and then you have a twenty five percent texture side You know this tool is super popular We're selling it all over the world if you want to pick it up go to shop FSE I'm gonna show you guys how easy it is to detail the entire front of this haircut to create a really cool Look first things first you can draw right in to underneath the chins instead of pulling this out with a scissor Cutting it and then hoping it falls in the right place I can literally just comb the hair down like this and then take my hundred percent cut cutting side and come right in here and Just softly cut into the face frame which will create little pieces right underneath the chin Which is all I really need now. I'm gonna take this entire triangle section This is one thing I love about the tri-raiser. You don't have to you don't have to break up your sections too much It cuts through like a hot knife through butter So basically pull this section over to me the tri-raiser blades are really firm So they're not flimsy at all. So when you go in to cut there's no give So it just cuts right through the hair unlike some other razors that have like a softer blade so they last longer and Get cut more hair at once so I'm gonna go through here and I just want to kind of glide Through this bang so I bring everything over to me and I just come right through here And then I cut a soft line the more I move back and forth the softer this bang will be Do I want a hard line or do I want a soft line? I'm gonna go kind of medium in here cut through it now as it comes down You can see the angle that we create so then as this is combed over It's gonna be a nice soft side bang and then we've just got this little bit left on the bottom So then I come over to this part of the haircut here and I'm gonna softly again underneath the chin Just carve some of those pieces create that pieciness right there and then in the sides again Go in with that 25 texture side angle the tri-raiser back So I just come in here and I slide in and just remove 25% Thank you guys so much for watching this video if you made it this far in the video Make sure you write made it in the chat or the comments I'd love to see that also know this that if you you use the code made it at checkout on our online store shop FSE You will get 10% off order of a hundred dollars or more So hundred dollars or more type made it one word in the Checkout box and you'll get 10% off your order also make sure you hit the like button Hit the notification bell which is up there as well and make sure you subscribe to the channel Whether you're watching this on YouTube or Facebook got videos coming out all the time. All right Thank you guys so much for watching


The results of this study suggest that breast milk contains high levels of tryptophan, TRP, which is important for infant neurodevelopment. However, the levels of free TRP are lower in pre-term breast milk than in-term breast milk. Additionally, the levels of TRP metabolites such as chineurinine, KYN, and chineurinic acid, Keener, increase over time in term breast milk, while they remain unchanged in pre-term breast milk. Furthermore, the study found that the levels of pro-inflammatory cytokines such as tumor necrosis factor alpha, TNF, interleukin-6, Illinois-6, and interleukin-8, Illinois-8, are higher in both term and pre-term breast milk at day 7 postpartum when compared to day 14 postpartum. These findings suggest that the presence of TRP and its metabolites in breast milk may be associated with the neurological development of exclusively breastfed pre-term infants. This article was authored by Louisa Rourke, Gerard Clark, Eva Nolan, and others.