Greetings laddingtons, today I want to respond to a somewhat commonly asked question And that is why I sometimes refer to myself as an elf and before I begin to elaborate I would like to aim a Massive heartfelt thank you to Styx hexenhammer 666 Who gave me a shout out in a recent video? So thank you for that Styx and Also this speaks very highly of you because that is a clear sign of confidence when you can give Attention and shout outs to other people. So tips pickle hub at Styx hexenhammer 666 Thank you much appreciated So on to the elven question at hand. There is actually quite a few different perspectives or Points I would like to bring up here. So it's not only that I think Lord of the Rings and Warhammer is great Obviously, I'm a big fan of both and I'm a big fan of fantasy But the elven question goes a bit deeper than that So we can take the first the aesthetic point. I kind of look like an elf Just how it is same thing with the physique. I Do have a somewhat elven physique a bit jacked elf, but still, you know with a smaller waist and a bit tall And everything like that. So an elven appearance obviously with a hair as well secondly elven doom and referring to myself as an elf is a Response to boomer masculinity and what boomer masculinity is is the kind of guys who says oh Real men eat meat or real men do not care about how they look or real men do this and that now if we look upon Lord of the Rings who has the highest kill count in the entire fellowship Yeah, it is legolas and then you still have guys who say oh he's so gay and everything like that because of Whatever reasons because he doesn't have a beard or because This and that so that is a response obviously high capacity for violence in accord with the primordial truth is a good Sign as a man So if someone says a real man eats meat, then I say no that's absolutely not the case a real man It's determined by his actions and his capacity for violence strength enlightenment. How reliable he is all of these things are Legolas yeah, he checks off all of these points. So Elves are very masculine in that regard. They don't look masculine because they look perhaps with feminine But it's the capacity that matters.  It's not about fantasy necessarily It's also about the elven archetype among humans So what would you prefer some guy who goes around thinking that's that he is so hence all the time Thinking he's the coolest ever or would you rather have a calm disciplined guy who doesn't go around being all You know brash like that, but he keeps his composure and you know that when it's when it's go time you know that he can You know show up step up when it when it matters. So that is also something of you With the elven archetype that it's not about going around being all Hensh all the time, but it's about when it time comes then you have the capacity for Violence so a bit like a martial artist like a true martial artist I suppose so that is the response to the boomer masculinity point that men are Determined by what to eat or what they look like a man is supposed to be determined upon his qualities So the next question viewing elves as an human archetype in behavior You don't you can't really imagine legolas or any other elf going down the street being obnoxious or Being disrespectful towards others an elf is an ubermensch It's an overman who is disciplined and orderly and is as far from a subhuman as is possible So a subhuman is someone who is very impulsive who can't control his primal instincts who you know act upon Emotions where he has the opposite of a subhuman and ubermensch an overman is someone who keeps Himself under control even if he has an impulse he overrides that his mind is in complete control of his body so to complete the different things so you can view an orc on one side an elf on the other side the elf has superb discipline he does never act out of order He never lets his emotions get the best of him even though he can be emotional. He never lets emotions Get him into bad situations where he as an orc may be Impulsive never thinks about the consequences, etc. So an elf in the archetype of a human is someone who is Disciplined in that regard Then next point if you look upon an elven society it's obviously close to nature disciplined orderly they value beauty and Structure hierarchy all of these things and an elven individual values usually Basically all literature as well. They value Enlightenment they value marshal prowess they value art and the finer things so if you look upon European Culture for example are you an archetype elf who appreciates the Higher culture of Europe or are you an orc who appreciates perhaps drama shows on the TV The elven archetype obviously appreciates the more beautiful and cultured things So yeah, those were just some points in regards to why I when I talk about elves, etc I primarily mean it as an human archetype of something higher So if you're talking about an elven society, it's a goal that we can strive to watch something That is a bit more in tune with nature who values Order hierarchy enlightenment beauty and everything like that So I hope this was somewhat informative at least and gave you some new perspectives Looking quite juicy as well today X-XO boom


Hey everybody, Dr. O here. In this video, I'm going to cover the science behind the number one reason poor sleep makes us gain weight.  So here you see my before and after picture. I weighed 414 pounds in the picture on the left. I was able to lose 49 pounds in 10 weeks, 101.2 pounds in 6 months and 165 pounds in one year.  It completely changed who I was. Let's go ahead and look at how this lack of sleep led me to overeat and is probably leading you to overeat as well. So how does your body make you eat more or at least want to eat more when you haven't been sleeping well? It's because poor sleep scrambles your hunger hormones. So let's look at the two key ones here. And they are leptin and ghrelin. Don't worry, there won't be a test, but leptin and ghrelin are the two key hormones that control how hungry you are. So leptin tells you that you're full.   It also should make you move more. It's pretty cool how it does that as well. But here's the problem. A single night of short sleep decreases leptin levels by almost 20%, about 18%. And it also decreases leptin sensitivity by 30%. So that means that if you didn't sleep well last night, your leptin levels are almost 20% lower and the leptin you do have is 30% less effective. So instead of getting the message that you're full, your body's getting the message that you are hungry. So low leptin levels are a key reason that you're hungry if you haven't slept well. Number two is grayling. So grayling is a hunger hormone. Grayling is a hormone released by your stomach, especially when it's empty that tells your brain that you should be eating, that you should be filling your stomach. So again, a single night of short sleep increases grayling by almost 30%. So your leptin levels are 20% lower and 30% less sensitive or less effective. Your grayling levels are almost 30% higher. Both of these hormonal messages are telling your body that you need to eat. Your body is literally screaming for food. So let's look at the data though. Let's look at how big of a deal this is. So what does the science say? Effects of sleep restriction on metabolism-related parameters in healthy adults, a comprehensive review and meta-analysis of randomized controlled trials. So this study found that if people weren't sleeping well, they were consuming 252.8 more calories per day. That would be 92,272 calories per year. That's more than 26 pounds of fat. But this next study is even worse. The effects of partial sleep deprivation on energy balance, a systematic review and meta-analysis. This study found that if you're sleep deprived, your energy intake increased by 385 calories per day. That's 140,525 calories per year, the equivalent of 40 pounds of body fat. This same study though also looked at sleep extension. So if someone's supposed to be sleeping seven to nine hours and they're sleeping five hours, they're eating 385 more calories than they should. But what if you take someone that is sleeping, let's say seven hours and you get them sleeping eight hours? So sleep extension reduced calorie intake by 156 calories per day. So if you take 385 calories from eating more of your poorly sleeping and you add 156 calories that you're now eating less because you've extended your sleep and you're sleeping better. That's a 541 calorie difference. That's 197,465 calories per year and that's the equivalent of over 56 pounds of fat. So what's the key takeaway here? A lack of sleep could be the main reason that you're eating too many calories. Look at these numbers. They're undeniable. So what's our action steps? We haven't talked about solutions yet, but if a lack of sleep is your problem, sleep is going to be the solution and I'll be teaching you over a hundred tips that can help you get better sleep along the way in this course. So take this seriously and I hope this helps. Have a wonderful day. Be blessed.


Good morning y'all. Happy Monday. Let's see Whoo morning y'all. Happy Monday I just spent the last two days in bed because I saw the last vlog or follow me on Instagram I scratched my eye with a mascara wand really bad in the middle of filming something and I ended up like having a corneal abrasion. It was so bad. There was like two cuts It was the most painful thing ever good news is it is one of the most painful things ever bad news is You know, that's the bad. No bad news is it's one of the most painful things ever good news is that it heals pretty quickly So I woke up this morning feeling pretty normal like my body feels kind of run down from like all this stuff I was doing but um My eye feels better.  I need to get back into the swing of things I literally have been in my dark room for the past 48 hours So I need to like get back in the swing of things today. It's Monday I leave for Fort Worth in New York on Friday a week from today is my live show. Just crazy actually. Oh my god I'm so excited. I'm kind of starting to get nervous a little update, but Yeah, I'm really excited. I do a little podcast hot girl walk to get into like this swing of things this week And then a Pilates later of like a lunch thing later And I'm just getting work done doing laundry So they like a little productive Monday getting back into the swing of things after I've been in a dark room for two days Love that. Don't ever do what I did. That was the worst experience of my life and it happened at my seven shop Anyways and giving you a little update on the skincare that I've been using this video is sponsored by rotor So this is a customized prescription skincare Which I am such a big fan of because it's made like personalized to you dermatologist design There's a free 10-minute online visit which I love because getting me to go to another appointment like I don't want to I can do it for my home.  Oh my god Like how did that even happen? I've literally been like about this summer saying mr. handsome fitzy man We've been having really great quality time together the past two days He has never been nicer to me. I think he felt bad Coco. You were nice kind of too. I think All right, I'm finally sharing my little goodie bag They gave me from my pop-up this weekend I don't know how to pronounce this and I don't sound stupid, but I'm really excited because I've seen this all over Dallas So these are the cool and glow towelettes And then this is okay like come on collagen I mass I actually just ran out of I mass and I needed more so I'm very excited We have these like toned and sculpts little resistance bands Which I actually am really excited for because I want to start putting resistance bands on when I walk the trail and Then little hair ties like so cute. I got a bunch of GH pieces this really pretty necklace This bracelet, okay, like this is very similar to the one that I wear every day But I can stack them all like that's so cute I'm actually really into braces these days some more hoops some cute earrings a really cute necklace I'm gonna put this up in my little case, but like so cute. So this is from gratefully Helena I mean like literally the cutest thing ever. I love. Oh and then I have another thing. Sorry. Oh, I also so this is from Caffeinated beauty bar, which is a really cute little shop and then gave me this big tea Which is actually probably what I should be wearing over my workout stuff right now But this is actually like really light Super cute love that. So thank you guys everyone love this go support Dallas based businesses But like these are just the cutest thing ever. I love them. Okay, this actually feels a lot better Just having something like oversized, but I also wanted to show you got these allies in her wing pants I might be wearing these to the live show. I haven't decided yet. I have to try all this on on like Wednesday I have probably four or five different orders for a four-day trip to New York Different outfits, but I haven't been able to write this on yet. They're super cute all length of them I got them on revolve the little Alexander wing patch Which I love we're actually adding patches for the oak kind stuff Actually, they should get here today. Hopefully so anyways have these and then I have a bunch of merch That we're giving the girls all my best friends from Dallas. We're coming on the trip to New York for the live show so I'm very exciting. I need to put all this away soon get my life back in order Really get to work here. All right. I've changed into more weather Fitting a tire. I actually think I'm gonna buy a new Mac book I've been thinking about it for a while look at this on my Mac book this line as you can see it's not great I Don't want to wait until I like have to get a new computer So I kind of just want to get one now, but I want to get like the most storage It is a fire truck just don't buy it was so loud Like what laptop should I be getting I'm probably gonna buy it before I post this video so like maybe I shouldn't But I do need it so I want a 14 inch. I think I want a 14 inch 16 inches are like really big Okay, I think I'm gonna get the Mac book pro 14 inch So anyway, I'm gonna get a new computer that's gonna come in a month But honestly, I'll be grateful that I did it now. I Just figure it out because I need One like I've had this laptop since college Which is not that long ago But I edit on it. I feel like I wear down laptops pretty quickly, but I've had it for a few years Like I've had it. I want to say my junior year of college So I was like four years ago almost three years ago. How am I this just might be the most exciting week The podcast has had since it launched three weeks ago. Not three weeks. He hoped three years ago All right. It is now 230. I have showered. I feel so clean and good I went to haplodis and then I got lunch with Jenna who's the founder of finish. It's just so nice Being surrounded by women who are older than me who like know a lot more than me that are entrepreneurs and like go-getters I think that's like the biggest pro one of the biggest pros of Dallas for me is that Well, like maybe there's not a ton of people my age who are doing what I'm doing There's a lot of people who are like ten years older than me that have a lot more wisdom that I should be going to for more things and like that is so Like willing to give if that makes sense I mean obviously like a lot of things are mutually beneficial But it's just nice being around people who are older than me and inspire me and I just like cool Anyways, I'm back from watching Pilates showered on my robe. I have my oil like sinking into my skin I'm actually gonna like give you guys a little house tour because it needs to be fixed like my bedding My bed is just tragic right now. I need to get new pillows for my bed those I got rid of months ago because So I've had a bloody nose on them when she slept over so I need to get new pillow replacements I love these ones from Target and then I'll take you guys downstairs because I have questions Okay, the closet is obviously pretty much done actually I'll take you in there really quickly here is the closet space I have this up here to do my makeup on which has made it really easy I want to get a fun little rug in here to make it cozy like maybe like pink and white checkered Something fun. I don't know. Let me know what you guys think I need to replace that light and then this room is like completely done These are just like outfits that I want to wear some, you know, whatever. There's there's a method to this, but it doesn't matter So down here, I do want to replace this art with something I just have a bunch of bags here that I need to take upstairs, but I just have random little trinkets on here and I do want to replace the art I just had it forever, but I I'm not as like urgent to do that because it's not really bothering me Then you come over here. This coffee table is going to be gone this week My couch is CB2 the drapes which I could change into like a beige. The only thing is like this That piece of art in there actually brings in the cool tones. It just looks weird on camera I need to get a rug and I did order a new rug So we'll see how I like that and I need to get new stuff for the coffee table I kind of want to get a really thin table for underneath the TV We'll see. I got this chair from Target. I feel like once the rug comes everything will come together I really really want to I mean, I'm not gonna replace the table Honestly, just because it's so heavy and I don't mind the table as much. I would like a wooden table at this point But like I'll just get over it However, I need all new chairs.  They're so like 2018 I need to be done with them, but I just can't decide what chairs I want and I need to order them like sooner rather than later Just because obviously everything's taking so long. So that's the main thing. What chair should I get? What should I do with the coffee table?  I need y'all's input. Please let me know They're a little bit anxious. So I'm gonna have the array compils. I haven't tried these in a long time This is a new bottle of them. I think since like 2020 everyone breathes about array bloat pills specifically, but Anyways, I'm just gonna take two pills and I'll let you guys know how I feel. Here we go guys really easy That reminds me. I really need to get my vitamins organized. So for the next probably 40 minutes I'm gonna have to sort of prep just got a ton of work done now It is time for me to actually get ready. What do y'all play in your house all the time I always have Chris table to non. Okay, I'm gonna make a little bit of coffee because I'm actually exhausted I have my cute little chamberlain coffee cup Doing heated workouts in Texas heat in the summer it just like Takes you out like I'm just so tired So in my closet I have my coffee I'm gonna change into what I think I'm wearing I'm going to the Rangers games night with my dad. By the way, I think I said that the Rangers invited us in Very excited. Um, I grew up going to games with my dad So I feel cool now that I can take him, you know, anyways, I'm gonna do a little haul first thing. I got these jeans She's like low-waisted into her baggy and I think they're like perfect Are they like oh wait through the lioness ones. Okay. I actually love this cut in a medium No, I love it a small. I don't know why I got a medium. Maybe it'll work There is really baggy pants And I think this would be super cute with like this and just a tank top and sneakers for bass or a baseball game What am I saying? So I'm gonna try these on and then we'll do the rest of it because I got the cutest Literally the cutest dress thing I've ever purchased. I'm telling you in the summer. I live by purchase probably by the way Obviously, I bothers me. I'm money not sponsored obviously, but anyways, I'm gonna give you all a little haul I'll be right back. Alright, so the first thing I have are these jeans They're lioness pants and I have them in different colors I will say I think the other colors are like more flattering But they're still like really cool baggy pants and they look good with heels I'm wearing the most sneakers today. This is just what I'm wearing to the Rangers game, but It's still really casual and just like cozy and it feels like cool girl going to baseball game You know what I mean? Next thing I have is this dress, which I think is the prettiest dress I've ever owned in my life Princess Wally so cute. I got it in a size six Um, let me make sure yeah size six. I mean just like the cutest dress I Live in their dresses in the summer because it is so hot like I can't wear anything else And I just like cannot recommend enough Incredible can't wait to wear that. I also got this just like simple white dress Which again, I will be wearing a ton this summer. I got it in a size six. This looks a little bit like bigger Though I think I should have gotten size down, but just like a simple go-to White dress. I love this. I also got this pink top this like little corset thing Which I feel like these are so in I say I got is just this black like baby at all tank top and these are just so Classic, I feel like you can really never go wrong with them. Oh, there we go Okay, I'm like out of hangers now. Okay. I got this matching green set I'm going to New York this week and obviously so I just needed options. I'll try this on and see how I like it I if my new Shoes were in that my new sneakers were and I would love it, but I Don't know when they're coming in. It's taken literally weeks. I also bought just this black like banjo Top, I don't love strapless things. I feel like they fall a lot But I feel like this might be fine and then also I got This set which like I'm still really if you're on I almost was like going to me to return it But I feel like I'm gonna end up really liking it. It's a skirt with a slit It's super light which is what I always need and the top is just like super lightweight again matching set like can't go Wrong, so she would have a tan it'll look a lot better So that is my haul for today. I'm gonna go do a little bit of makeup I'm gonna show you guys my fave products that I've been using I'm a little bit scarred and terrified to make one now that I gave myself a corneal abrasion, so okay. I'm just gonna show you the Products that I've been loving because the lighting was really rough to show you I did my makeup this blush from Dior I only started using this weekend and I think it's like my number one holy grail product I know this has been all over tech talk. I finally got it. It's the Dior Backstage rosy glow in pink it like lifts your cheeks I don't know how else to describe it other than it is incredible like literally incredible Then I've been going back to an og at the Nars Laguna bronzer. I've been loving it I mean we all use this in what 2012 and Now I just I don't know I revisited it and I don't know why I ever left loved this bronzer This concealer. I actually really like I'm really picky with concealers And I think I've never found the perfect under eye concealer, but I do really like this one It's really easy and it definitely like makes me look a little more awake I obviously love all things rare beauty the rare beauty liquid blush. I'm obsessed with this isn't happy This is another holy grail product of mine actually put it on underneath the other blush I showed you but I just love your beauty I used the rare beauties into moisturizer or the foundation and this and then the highlight like all the time Incredible and then I have this milk makeup setting powder, which I like again I've never found a setting powder that I'm like this is my holy grail best thing I ever use But I do really like this one and I have been using it a ton lately some anyways That's a little update on what I've been loving makeup wise this blush like look this is how Like pigmented the Dior backstage blushes. I've only used it for a few days and like look at that It's already all over there. So anyway, it's been loving that also random. I've been loving the capari Hydrating body milk. I love anything capari like your lip products and body products or body like their shower gels They're lotion to everything. It's so incredible. So I've been loving this as well So and last but not least I just got a new one of these. It's the daily hydration body oil That's the body oil I've been using whether I'm doing like lymphatic drainage or just like putting oil on my skin That's what I use for my body. It takes a while to kind of like seep in there, but it's really really moisturizing Okay, I finished my makeup. You can't really see I think I'm gonna go through with my Dyson era for like five minutes and Try to do something with my hair.  Goodbye was a billionaire I would have someone do my hair every single day. All right guys. I truly feel like a different person now That I did my hair. It's crazy What ten minutes styling your hair will do for your confidence Here's the outfit. I really do want to wear this Louis bag. This has been really convenient lately, but I don't know what Their policy is my bias care for a bag I brought recently. I went to a game have about an hour left of work They need to do my dad's gonna pick you up at six So I need to get stuff done. I'm definitely getting a hot dog tonight.  This is what I do when I'm feeling down a little bit off anxious Which I've been feeling all day today. I play the Taylor Swift's reputation stadium tour I'm not getting it cures all my anxiety puts me in a great mood inspires me. I mean like it saves my life I'm not getting I've done this for years I


in the last class arrived at the simplified forms of the governing equations. So let us continue with the governing equations which are written here. First let us consider the r momentum equation. So in the r momentum equation first of all let us see that what is this Br. Br is the body force component in the radial direction. There is a body force component in the radial direction that is true but until and unless this extent of the pipe is very large it is like a very high radius pipe then that effect of that body force is not going to be important along the r direction. So this therefore may be neglected. So you come up with pressure gradient along r equal to 0 or approximately equal to 0 that means p is not a function of r only not a function of r that means p is a function of z only. So you can write when you come to the z momentum equation this as dp dz. You can combine that term with the body force term to have ddz of p plus rho gz sin theta is equal to mu into 1 by r d dr of r d vz dr because vz is a function of r only that we showed in the last class therefore it boils down to an ordinary derivative. So this p plus rho gz sin theta is like p plus rho gh so this is like p star the piezometric pressure. We again are having an equation where you have dp star dz is equal to mu into 1 by r d dr of r d vz dr where the left hand side is a function of g only the right hand side is a function of r only. So this is function of g only this is function of r only and again this may be valid if each is a constant. So each equal to constant say equal to c. So the first thing that we may do is to find out the velocity profile from this so we consider the right hand side and integrate it so you have d of r d vz dr is equal to c by mu r dr. So this you may integrate so once you integrate you have r d vz dr is equal to c r square by 2 mu plus c 1 which means d vz dr is equal to c r by 2 mu plus c 1 by r. So you may integrate it once more so if you integrate it once more you will get vz as a function of r. So let us do that so you have vz equal to c r square by 2 mu plus c 1 ln r plus c 2 sorry 4 mu yes 4 mu plus c 1 ln r plus c 2. Now c 1 and c 2 are the constants of integration that we have to find out from the boundary conditions. So what are the boundary conditions here boundary conditions so one of the boundary conditions that is at the wall is straight forward at small r equal to capital R you have vz equal to 0 no slip boundary condition. What happens at small r equal to 0 that is a point of singularity so to say and but physical problem is that vz has to be defined at small r equal to 0 I mean you cannot have a situation where there is vz undefined at small r equal to 0 because it is a physical problem the pipe is entirely filled up with a fluid with some velocity at r equal to 0 there it should be a well defined velocity and that is possible so vz is at r equal to 0 vz must be finite it cannot be infinite or it cannot be undefined in other words therefore from the second condition you must have c 1 equal to 0 this is from the boundary condition number 2 and from the boundary condition number 1 so this is boundary condition number 1 and this is boundary condition number 2. So from boundary condition number 1 you have 0 equal to c r square by 4 mu plus c 2 that means c 2 is minus c r square by 4 mu so the velocity profile becomes vz equal to c by 4 mu into or if we write minus c by 4 mu into capital R square minus small r square and as usual you see that the c which is like dp star dz that has to be negative to drive the flow along the positive z direction which means that vz has to be positive if c is negative. Now you may express c in terms of the average velocity what we did for the plane Poiseuille flow for the Heggen Poiseuille flow also the same thing is valid. So what is the average velocity v average it is integral of vz over the area of cross section divided by the area of cross section. So vz what is the area of cross what is the elemental area that you can choose say at a distance r you take a strip of width dr. So if you if you just draw its other view so you have taken at a radius r some strip so you are talking about such a strip of width dr and this strip is 2 pi r dr so vz into 2 pi r dr from 0 to capital R divided by pi capital R square is the area. So let us do this integration quickly so 2 into integral of 0 to r you have the minus c by 4 mu so what is v average in terms of c so minus c by 2 mu then you integrate it r square so r 4 by 2 minus r 4 by 4 by pi r square sorry pi is not there pi has got cancelled. So this is equal to minus c r square by 8 mu so this is one important result which will use subsequently but at least let us write the expression for the velocity profile by writing c in terms of this. So vz becomes in place of c you write minus 8 mu v average by r square that into 1 by 4 mu again there is a minus sign into r square minus small r square that means vz by v average is 2 into 1 minus small r square by capital R square this is the velocity profile in terms of the average velocity. Recall the flow between 2 parallel plates it was like 3 by 2 into 1 minus y square by 8 square so it is quite similar the coefficient is different just because of the different geometry and it is also a parabolic type of velocity profile because it is square with the local radius. Now you can find out what is the wall shear stress so let us find out what is the wall shear stress so it will be like mu we will adjust the sign positive or negative later on mu into the rate of deformation this is like tau rz proper subscript with the index now one of the important things is see positive tau with like mu du dy so this is like just like mu du dy first of all vr is 0 so this term is not there so it is just like mu du dy but the thing is see the r direction is towards the solid boundary it is not away from the solid boundary so that has to be compensated with the minus sign here. So if you have a solid boundary like this if you have this as y then you have like mu du dy so y is away from the solid boundary towards the fluid the reason is you want to write it as a positive shear stress so you want u to be increasing in the y direction so y equal to 0 is like the no slip and then u increases but here the r direction is opposite to that so you have to make it up with the minus sign so the wall shear stress therefore if you just differentiate it with respect to r so dvz dr is like 2v average so this entire thing evaluated at small r equal to capital R that is at the wall wall is located at small r equal to capital R so 2v average into minus 2 so minus 4v average by r is the dvz dr right therefore the wall shear stress is 4 mu v average by r what is the coefficient of friction or the Fanning's friction coefficient that is tau wall by half rho into v average square this we introduced in one of our previous classes this friction coefficient it is a non dimensional way of writing the shear stress so it is 4 mu v average by r basically it becomes 8 mu v average by r rho v average square so it is 8 divided by rho v average r by mu the denominator is the Reynolds number based on radius r but usually for this type of geometry the length scale that is taken is 2r or the diameter of the pipe so if you just consider that then the cf becomes 8 into 2 divided by rho v average into the diameter by mu where diameter is 2 into r so this is 16 by the Reynolds number based on the diameter of the pipe as engineers what we want to do with this friction friction coefficient so what importance or implication it has to us so if it is large it is small we will understand that if it is large maybe the frictional effect is large but how do we take care of that in a design and that may be visualized more effectively if you consider now the dp star dz term which is equal to c so to do that let us come back to this equation v average written in terms of c so what is c? c is equal to dp star dz so let us write dp star dz in terms of the other parameters so it becomes minus 8 mu v average by r square so minus 8 mu v average by r square and what is this dp star dz this is if you have pressure at the inlet as say p in if you have pressure at the outlet as say p out and the distance over which this pressure difference is there is l then first of all we could derive that dp star dz is a constant that means p star versus z is a linear profile so this is as good as p star out minus p star in by l so this we just write as p star out minus p star in by l so in other words it is minus of p star in minus p star out by l I mean why we are writing it in this way is see the p star in minus p star out is the driving delta p star for the flow the driving difference in piezometric pressure that should drive the flow see why this driving pressure difference is necessary it is necessary because you have viscous resistance in the flow so this is a manifestation of the consequence of the effect of viscous resistance that is being exerted in the flow so you have to have a driving pressure gradient which is a favorable pressure gradient that is dp star dz negative to make this flow occur so when you have this one this delta p star so what it in effect does in effect it overcomes the viscous resistance so the viscous resistance also may be expressed in form of a pressure unit so the viscous resistance therefore you may say that delta p star is nothing but the delta p star because of the viscous resistance and we may write it in terms of a head some unit of length so we remember that the pressure is nothing but some length unit into rho into g and the length unit is the equivalent unit of pressure expressed in terms of length with which we call as head so that is what we discussed also earlier so if we write it in terms of a head length unit as head with a subscript h f for friction f for friction so we can write it h f rho g where this h f as engineers we understand that this is a loss of head due to fluid friction therefore it is possible to write this expression dp star dz if we come back here in terms of this delta p star as h f rho g so you have h f rho g by l is equal to 8 mu v average by r square of course it is possible to write it in terms of in terms of the diameter so it is so 8 becomes 32 here okay so it is also possible to write the average velocity in terms of the flow rate that is sometimes important because if the flow rate is q it is just q by pi d square by 4 because in the experiment you usually measure the flow rate so it is we are trying to write the equation in terms of experimentally measurable parameters so from this what you get is h f is equal to 128 mu q l by rho g pi d to the power 4 okay and this is what we are trying to and this equation is known as Hagen Poiseuille's equation so what it gives? It gives a direct indication of the loss of head due to viscous effects in the flow if the flow had viscosity 0 there would have been no loss of head and we can see that the loss of head is directly proportional to the flow rate it is proportional to the length over which the fluid is flowing which is understandable and inversely proportional to the fourth power of the diameter so if you make the diameter very very small the loss of head will be very large that means to drive flow through a very small tube say a tube of micron size you require a huge pumping power because there is a huge head loss because of the frictional effects that is one of the challenges in having a flow in a micro or a nano channel in a very small channel so the whole understanding is that like those are advanced topics but you see that the basic of fluid mechanics gives us a clue that what are the challenges as you make the sides smaller and smaller what are the engineering challenges in terms of having the flow now it is also possible to express it in terms of a non-dimensional form by writing this in this way by writing this as some factor f into l by d into v average square by 2g so this is just a non-dimensional way of writing it see l by d is a sort of aspect ratio of the pipe it is a non-dimensional parameter so and v square by 2g is the kinetic energy head so the head loss expressed as fraction of the kinetic energy head this f is that sort of fraction so what is that so if you just equate these two so you have hf as rho g rho sorry f l by d v square by 2g and that is equal to whatever expression of hf what we had so 32 mu v bar by d square so from here what we can conclude what is f 64 divided by rho v bar into okay by just by equating these two so that means this f becomes 64 by the Reynolds number so this sort of non-dimensionalization was first introduced by an engineer known as Darcy. So this friction factor is also known as Darcy's friction factor so it is just a different way of writing the friction or frictional coefficient you can see clearly that f and cf are related by f is equal to 4 into cf so just is the same thing expressed in terms of in different ways so one looks into it in the view point of a pressure drop another looks into it in the form of a wall shear stress and here they are related because you have to overcome the wall shear stress and therefore you have a pressure drop so that is how they are related and this 4 coefficient is just because the difference in which they are defined but physically they imply the same so if it is Manning's friction factor that is cf and if it is Darcy's friction factor it is f so now so we have a clear idea that if you have flow through a pipe there is a head loss the head loss is because of the viscous effects in the flow and you require a driving pressure gradient the driving pressure gradient is to overcome an energy loss the energy loss may be expressed in terms of a head and that head is given by this expression so that is what we learn and as engineer it is important because say you are given a length of the pipe see I mean let us think about how this helps in design say you are given a length of a pipe say 10 centimeter length of a pipe you are given a flow rate that you expect out of it say some meter cube per second you know what is the viscosity of the fluid and density of the fluid like that so your problem is that what should be the power of that pump that is necessary to drive the flow this is one of the very basic elementary problem so to know that you have to know that what is the pressure drop that is taking place and first of all if you find out what is the hf what is the head loss over that length then that into rho into g is the pressure drop and the pump should have enough power to overcome that so the pump should have a power that is developed that is given by rho g into q into the head loss it has to overcome that loss so this is like a unit of power so if you know that what is the flow rate if you know what is the head that the pump has to supply then you know that what is the power of the pump that is necessary and so it comes into so a very basic elemental mathematical work also is necessary even for a very crude design work which is there in the day to day life of fluid mechanics like flow through pipes okay now we come to another example example 5 and that will be like the final example before we will be moving to the next chapter so the final example is about flow between 2 rotating cylinders long rotating cylinders this is the problem that we are going to revisit because this problem we introduced when we were discussing about viscosity and its measurement so you have 2 cylinders concentric cylinders of radii r1 and r2 let us say that the inner cylinder is rotating with an angular velocity omega 1 and the outer cylinder is rotating with an angular velocity omega 2 and these angular velocities are like these are not functions of anything these are constant angular velocities and we are considering a steady flow of a Newtonian fluid of constant properties which is which are kept the fluid is kept in the gap between the 2 cylinders this type of problem is important because we have discussed that it gives a principle of the measurement of viscosity of an unknown fluid so principle of a device known as viscometer so we have earlier qualitatively used the one dimensional form of the Newton's law of viscosity to like get an estimation of what happens here but now what we will do we will try to do it in a more careful way by using the proper equations of motion so first of all we have to understand that what are the important variables which are involved here so again by the nature of the problem the geometry of the problem the cylindrical polar coordinate system seems to be a proper choice so the r theta g coordinate system now the corresponding velocity components are there vr v theta vz the first assumption that we will make is that the length of the cylinder which is perpendicular to the plane of the figure is very large what is the consequence of making the length large large means large in comparison to the radius so if l is large then what is the consequence in terms of your analysis it effectively boils down to a 2 dimensional problem in the r theta plane so the z gradient is not important so when you come to the r theta component you have vr and v theta these things are there next is what about the partial derivative with respect to theta see when you are solving a problem it is not that the assumptions are given to you it is important to come up with the assumptions based on the physical description of the problem see the inner cylinder rotates with an angular velocity which does not does not have any preference over theta right it is not that at different theta it is different the outer cylinder also rotates with an angular velocity that does not have any preference over any theta and therefore in between we expect that it whatever is the behavior should not have any preference over theta so that means the derivative with respect to theta for whatever the flow parameters that should be 0 that should automatically follow from the physical description of the problem next what we will do we will now go to the basic equations again we will go to the cylindrical coordinate system equations navier stokes equation but first we will go to the continuity equation so if we go to the continuity equation you see we are talking about the continuity equation in the cylindrical polar coordinate system first term because we are considering the steady flow the density gradient derivative that is 0 with respect to time the second term the second term is like if you want you should keep it the third term and the fourth term see because there is no derivative with respect to theta the second term is 0 no gradient with respect to z so that term is 0 so only one term is r into vr the derivative of that that means d dr of r vr that is equal to 0 just like what we had for a Heggen Poiseuille flow and what will be the obvious conclusion that vr is not a r into vr or vr is not a function of r so we know that at 2 different radii vr is 0 r equal to r1 and r equal to r2 and that is good enough for us to say that vr is equal to 0 for all r because vr is not a function of r so the problem has boiled down to only one velocity component that is v theta okay so with this understanding let us now go back to the momentum equations let us look into the momentum equations first the r momentum equation that is the first equation written in the slide so you have vr equal to 0 so all the terms in the left hand side are 0 except the term involving v theta so in the left hand side you have minus rho v theta square by r okay and it is the centripetal effect so we may understand physically what it is so when it is a rotating thing it is a centripetal acceleration because of the tangential component of the velocity right hand side you have first term minus dp dr that term is there the remaining terms first term has vr so that is 0 second term has again vr that is 0 third term again has vr and fourth term has the derivative with respect to theta so that is 0 there is no body force along r okay so you have the r momentum equation what it gives dp dr is rho v theta square by r no that is what I said that is always a special case so you also have to satisfy the boundary conditions and consider it for all r or for all possible cases vr proportional to 1 by r is only a special case but you have to consider that it should be true for all possible velocity fields it is not just for one particular velocity field not only that you have to satisfy vr say 0 at r equal to r1 and r equal to r2 so if you have say r into vr as some constant c so that is vr equal to c by r then at r equal to r1 how do you ensure that vr will be 0 you have to ensure that the boundaries you have normal component of velocity 0 that you have to keep in mind so the r momentum equation you have dp dr as rho v theta square by r let us look into the other momentum equation see the z momentum equation is useless here because it involves all the terms which have vz and there is the nobody force along z and only it gives that dp dz equal to 0 that is the z momentum equation only term that remains important is dp dz equal to 0 the most important momentum equation will be that theta momentum equation so theta momentum equation if you see that is the second equation written in the slide first you go to the left hand side you have first the flow is steady so the first term is 0 next you have vr is there so vr into that is 0 third term derivative with respect to theta so that term is 0 fourth term because vr is 0 that is equal to 0 fifth term vz is 0 so or even if you do not consider that that gradient with respect to z is 0 because z is large so in either way the left hand side totally becomes 0 right hand side first term dp d theta is 0 because there is no theta variation second term is very much there because you have v theta as a function of r which is which is what we are going to solve next term it is a gradient with respect to theta so that is 0 the term after that you have derivative with respect to z that is 0 the next term you have vr that is 0 and you have no body force no body force along theta therefore it boils down to mu sorry theta momentum let us write the terms 1 by r mu into 1 by r sorry ddr of so ddr of 1 by r ddr of rv theta that is equal to 0 so see now v theta could be function of what v theta could be function of r theta and z it is not a function of z because there is no gradient with respect to z the length is large v theta is not a function of theta because there is a there is no variation with respect to theta for anything so v theta is a function of r only and therefore we may write it as an ordinary differential equation so we may just write it equivalently as ddr of 1 by r ddr rv theta is equal to 0 so if you integrate it you will get d of 1 by r ddr of rv theta that means 1 by r ddr of rv theta is equal to say some c1 so rv theta is equal to c1 or d of rv theta is c1 rdr right so if you integrate it you will get d of 1 by r so if you integrate it rv theta is equal to c1 r square by 2 plus c2 and v theta therefore becomes c1 r by 2 plus c2 by r so it is like of the form ar plus b by r right so if you look into this equation can you recall that the corresponding components of this velocities are related to the vortex flows that we have studied earlier so what is the first component that is like a forced vortex and this is free vortex or irrotational vortex so it is like a combination of free and forced vortex that is going to be the resultant velocity field now and if you want to get the pressure distribution you have to go back to the r momentum equation to get the radial pressure distribution so you know now v theta as a function of r you may substitute and integrate it with respect to r to get the pressure as a function of r we are not going into that but what we will do is we will find out what is the expression for the wall shear stress so we are interested in tau r theta or just shear stress at different locations so if you want to write so there is an expression for tau r theta and I am just writing it down here and I will tell you that what is the origin or rationale behind this expression so this is for a Newtonian fluid just written just express in terms of the r theta coordinate system so it is just like just think of 2 coordinates like if it was tau xy that was what mu so basically you are having a cross gradient x component of velocity with y gradient and y component of velocity with x gradient so similarly you have a theta component of velocity with r gradient and r component of velocity with theta gradient and this 1 by r these adjustments are there because of the use of the cylindrical polar coordinate system so these adjustments are also quite obvious that if you have say this term so you have vr with respect to theta see you want a gradient that means it should be the velocity divided by a length so this is d theta so r d theta is like an elemental length in a cylindrical polar coordinate system so that is why 1 by r term has to come outside so in this way you may relate this term with the general understanding of the curvilinear systems so again it is not very important to go into the derivation of this term but we will just utilize this to calculate the stress so if you now write this is mu r d dr of v theta by r so v theta by r is we have not yet completed the expression for v theta because a and b are 2 constants of integrations to be evaluated but that we can straight forward do from the boundary condition but at least let us look into the form first so v theta by r is a plus b by r square so v theta by r is a plus b by r square and therefore d dr of v theta by r is minus b by r cube sorry minus 2 b by r cube so you have this as minus 2 b by r cube theta derivative is not there so minus 2 mu b by r square what is the so one important thing is independent of theta but dependent on r the next thing is that what is the elemental shear force because of this so if you consider an element at a radius r you have a line element like this because it is independent of theta otherwise you could have taken a small line element with r d theta but because it is independent of theta we are taking a total peripheral line element so what is the elemental shear force on that so the shear force is f at a distance r is tau r theta into 2 pi r into l so 2 pi r is the perimeter of this times the length is the outer surface over which this tau r theta is tangentially acting so that becomes minus 2 mu b by r square so into 2 pi r l and what is the moment of this force with respect to the axis of the cylinders at a radius r that is f r into r and you can clearly see that is equal to minus 2 pi mu b l which is independent of r so if you remember that while dealing with the understanding of the principle of viscometer we said that same moment or torque is transmitted at all radius and this is what it shows that at any arbitrary radius the torque which is there is the shear torque the torque due to the shear force is independent of the local radius this is one of the very important understandings now to find out the constants a and b you have to use the boundary conditions so what are the boundary conditions let us just write the boundary conditions and try to find out a and b so the boundary conditions are at r equal to r1 p theta is omega 1 into r1 no slip boundary condition so velocity of the fluid same as velocity of the solid and at r is equal to r2 v theta is omega 2 into r2 so you substitute that so omega 1 r1 is equal to a r1 plus b by r1 and omega 2 r2 is equal to a r2 plus b by r2 so it is possible to find out a and b from these two right these are like capital as per our notations so this is the boundary conditions so a r1 plus b by r1 a r2 plus b by r2 now let us say that we want to solve a problem which is a bit of a modified version of this one what is that modified problem so the modified problem is you have one single cylinder solid cylinder rotating with an angular velocity omega in a fluid of large extent so one cylinder of radius r and of large length rotating with omega so there is no inner or outer concept so how can you solve this problem by considering the solution of this one so omega 1 so r1 is equal to capital R omega 1 equal to omega r2 tends to infinity and omega 2 equal to 0 so if you do that let us see that what forms the constants of integration state for that particular case so you have r2 tends to infinity and omega 2 equal to 0 so when r2 tends to infinity this term is 0 omega 2 is 0 that means a equal to 0 so this will straight away give you a equal to 0 that means b is equal to omega into r square so tau r theta in that case becomes minus 2 mu omega into r square by r square and what is the v theta there v theta is just b by r because a is 0 so omega r square by r so it has become like a free vortex we have seen earlier that a free vortex flow is an irrotational flow right so that much we know that means the vorticity vector if you calculate that will be a null vector that we showed by calculating the circulation and the vorticity now let us try to find out what is the shear force on the fluid and that is something which is very very interesting so we have calculated the shear force locally at a radius and may be they are taught due to that but over the volume what is the total shear force that is acting to do that what we will do is we will write the momentum equation just in a vector form so the momentum equation is rho okay so this is the vector form we have derived this vector form and the advantage with the vector form is whatever vector operation that we will be doing on it so long as it is in a vector operation form we do not explicitly mention which coordinate system it is so it remains valid for all types of coordinate systems so the problem or the situation that we were looking for in that particular situation the left hand side was 0 always by the consideration of fully developed flow and steady flow so this term was 0 and this term was 0 because of the sort of either fully developed or may be 0 gradients in certain direction say theta or z direction for whatever reason the left hand side always came to be 0 for the example that we were talking about so in the vector form also it is like that so you have the gradient of p is equal to mu into this now let us try to use this particular term and see this is what this is basically a force per unit volume right so if we want to find out that what is the force per unit volume because of viscous effects this is the term that is coming into the picture okay so this you can say that is the f per unit volume mu into this now what we will do is let us say we want to take the curl of both sides or just by looking into another way let us try to find out this term I mean we may take a curl of this side this and do but let us just look into this so we want to take the curl of the curl of the velocity vector so that is given by the vector identity so in this vector identity let us now try to use this vector identity so what we will do is we will consider an incompressible flow so incompressible flow when you are considering an incompressible flow what is the consequence of that you have the divergence of the velocity vector equal to 0 so when you have divergence of the velocity vector 0 then you have that del square v is equal to minus of curl of curl of v right and curl of v is the vorticity vector right therefore you can write that del square v is equal to minus curl of the vorticity vector but the zeta is the vorticity this force that is mu del square v therefore we can write this as mu minus mu into curl of the vorticity vector so this is what this is the viscous force per unit volume right so this is shear force per unit volume it does not matter whether it is the equation is simplified to this form or not even if the left hand side all the terms are there still this happens to be the viscous force per unit volume so this particular term so only these terms were simplified to this extent for the problems that we discussed but for all problems it will not be like that but for all problems for a Newtonian fluid with a constant viscosity this is going to be the viscous force per unit volume now you look into this special case so this for this free vortex we know that it is an irrotational flow so that means curl of the velocity vector is 0 that means the vorticity vector is a null vector so that means this term is 0 okay so you see an example if you recall one of our very introductory lectures in fluid mechanics we mentioned one thing that fluid mechanics is a beautiful subject because it gives something which is non-intuitive and this is one example you have shear stress not equal to 0 but shear force equal to 0 if you recall we mentioned this as a non-intuitive example that you have shear stress not equal to 0 right this is b is not equal to 0 it is varying with the radius but you now find that because of the irrotationality the shear force is 0 with this example one of the very non-intuitive things we learn out of fluid mechanics that there may be cases where the shear stress is not 0 but the shear force is 0 and that we can get from very elementary mathematical consideration of this type of flow. So to summarize we have looked into examples of exact solutions of the Navier-Stokes equations mostly for steady flows we have not done it for unsteady flows that is not there in the purview of this elementary course but at least for steady flows and fully developed types of flows we have worked out the solutions and we have come to conclusion that simple closed form solutions of Navier-Stokes equations are possible for such types of flows and these give rise to certain important insights from engineering and scientific principles. So we will conclude this chapter here and from the next lecture we will start with another important facet of the equations of motion for viscous flows and that is the turbulent flows. So we will start with the introduction of turbulence from the next lecture. Thank you.


All right, everybody. Good morning. Thank you all for being here For this very very special announcement. We have four speakers for you today. We'll begin with the Aurora police chief chief Nick Mets They will have dinner police chief Paul Payson followed by US Attorney for the district of Colorado mr. Jason Dunn and The acting assistant special agent in charge mr. Jeff Russell, so if you could please hold your questions until all of the Presenters have presented so at this point. I'd like to invite up Thank you Good morning, and again first of all, thank you for taking the time to be here this morning This is a very important topic to us Two nights ago for people in Aurora were shot Fortunately all survived. It's another sad reminder of the number of high-profile youth related Shootings that we are seeing throughout our metro region And I was watching the news last night and one of the reporters that actually comment commented that Something to the effect of our society seems to be getting Numb to the news of this kind of violence going on in our region particularly as it pertains to youth and I want to Take the opportunity today to tell you that that may be the case, but law enforcement in our metro region is not numb to this Human toll human lives have been shattered human families have been shattered And so the the impact that this is having on our region is staggering And so we want to make sure as law enforcement partners throughout this region that we are taking extra steps To do that to take care of this. We're very fortunate in the metro region that our law enforcement partners work Very well together our local and federal partners Strategize together and work well and communicate well together, and you don't see that in all parts of the country We have a number of task forces here in our area. We have task forces that work on bank robberies human trafficking Internet crimes against children those kinds of things and now we have a task force that is going to be dedicated to combatting violence particularly gun violence in our communities For years, we've had the MGTF otherwise known as the metro gang task force That that task force was primarily Dedicated towards eradicating gang violence We want to take this one step further and so we've basically put MGTF aside and we've created a new a new Initiative in which we are calling Raven and Raven stands for regional anti-violence enforcement network It's not only going to work on gang violence But but primarily it's going to be it's going to focus on gun violence in our region The difference primarily well, let me back up here Primarily, we're going to continue to do the things like the boots on the ground the investigations all the things that that MGTF Used to do but with one added component and that added component is going to be the use of science and the use of our crime labs Whether it's a Denver crime lab or the new unified Metro Metro crime lab Located in Centennial through our ATF partners in the crime gun intelligence Center So Raven will be taken a multi agency approach and in partnership with the US Attorney's Office and partnership with ATF HSI and many other local and other federal partners We are coming together to to do our best to combat and and read significantly reduce gun violence in our communities You remember when I started off. I said we had four people shot in Aurora two nights ago That again was a very staggering event for us and one that we put all our resources toward When we got the call about this shooting one of the things that we did immediately it was we contacted Raven and we told Raven We needed them to take part in this investigation And so Raven made a played a significant role in cooperation with our major crimes unit our SWAT our fast teams And we were able to arrest a suspect this morning who was involved in that in that shooting There was some great work done and again This is just one example of many and then you'll hear about some later the great work that Raven has done Right now, I'd like to introduce Chief Paul Payson of the Denver Police Department And he's going to explain in a little bit more detail what Raven is Chief Thank you. So good morning all. Thank you very much for being here. We're very excited about this This is the first of its kind anywhere in the country. It's bringing together innovation and collaboration so we can more effectively address gun violence Gun violence doesn't stay in Denver or Aurora. It impacts the entire Metro region and for us to maximize our effectiveness We have to work together in order to address this and as you heard innovation technology CGIC the metro region has been a national leader with the CGIC model And we're now taking that next step enhancing What has already been a great program and making that better? What it means by better is getting that technology side of things linking those guns together But more importantly finding out that human intelligence side who the shooters are our goal with this is to get Shooters people that are creating harm to our metro area off the street in Hours and days not weeks and months and by working together collaboratively Holding people accountable whether that's through the Denver district attorney's office a Rapa ho Adams Douglas or the U.S. Attorney's office. That's how we are going to make the metro area much safer by working together I now have the great pleasure of introducing our U.S. Attorney Jason Dunn Good morning I've been the U.S. Attorney for about eight months now and when I came in one of the things I realized immediately was that We're really fortunate in Colorado and in somewhat unique across the country because we have truly great partnerships and collaboration among state and federal agencies and local agencies here in the district of Colorado And so that makes my job a lot easier and it makes it easier for I think All of us to make Colorado a safer place And so when I came in I talked to my staff and I said look we're going to prioritize Whatever we can do to have the biggest impact we can on public safety And so when we were asked to be part of this effort, I full-heartedly said absolutely we're going to do that We're going to dedicate resources to it because we think this is a great effort This is smart enforcement and it's a way to have a significant impact on public safety as the chief said Primarily these cases will likely be bought brought At the local level by the district attorney's office, but we're here to be a partner in that and offer Federal law where it is most appropriate work and have the biggest impact a couple ways we can do that We have at the federal level we have felon in possession charges So if you have someone who has committed a fire a prior felony And then is in possession with a firearm we have mandatory minimum sentences at the federal level We can use as a as a tool to get those particularly dangerous people off the street We also have statutory charges we can bring when someone uses a gun In an act of violence or in connection with Drug trafficking where we can get mandatory minimum sentences We have RICO charges and vicar which is Acts of violence in in relation to organized crime And then also at the federal level we have what are statutory presumptions about detention So when someone is arrested is in this pending federal proceedings Whereas at the state level they might be more easily able to bond out particularly in rural parts of the state But also here in the metro area We can there's a there's a federal presumption of detention And so we can get dangerous people off the street pending Federal proceedings, so we're appropriate. We're going to work closely with our our local partners and help implement Raven and I think you'll see a significant impact on public safety. So we're happy to be part of it. Thank you I'll turn it over to now The special agent in charge Dave booth with alcohol tobacco and fires Thank you I'm just going to give you a brief overview of a type of case that raven works and has worked That is depicted over here on the timeline as well as the the chart the map Back in april 2017 through march of 2018. There are a series of 13 seemingly not connected shootings These shootings involved aggravated robberies aggravated burglaries armed burglaries and multiple homicides But these these cases were all tied together by raven by the use of forensic technology Nyebin and other advanced investigative techniques Ultimately all these shootings were tied to to one criminal street gang The investigation led to the arrest of 19 defendants Currently 15 of those defendants have pled guilty To their charges for a total of 115 years combined They're not only were they charged individually. They were charged with the colorado organized crime control act which enhanced their sentences This case is again, it's a great example of the collaboration and the regional Connection that we have here with raven At this point, I'd like to ask if anyone has any questions for any of the speakers Correct so you heard cjic mentioned before it stands for crime gun intelligence center This exists has been existing for several years here in the metro area Raven is just has expanded upon that and we've taken in more partners and we're just we're trying to put the message out It's it's not just denver. It's not just aurora or lakewood. It's everyone in the surrounding counties


Folks, I think most people are connected before class ends. I want to go through what's actually going to happen. So I'm recording this right now. I'll post it online so you can review it before Friday. And so you can make sure that everybody knows what's going on. OK, so you have 100% full access. You have root access to the server. In the email, every team is on a network 10.41.teamnumber.2. The team number is also in the name of your VM. It should be very clear what your team numbers are. It's 1 through 23, or 1 through 24 of the team numbers. OK, so there's actually some information behind the firewall here. So this is why I sent information to the group leaders about proxies. So this dash D8080 is saying, set up a SOX proxy. So SSH is going to listen on my local port 8080. And any traffic that it gets, it's going to send it out over that network. So I can do this. Now all of my traffic is going to be coming from that machine. Well, first you have to configure Firefox. I actually, since I've never used Firefox, I just keep Firefox always in proxy mode so that I can use it like that. Where are the settings for this? Firefox, forever, since there we go. Like, always change these things. Advanced, network, settings, settings. And you set the SOX proxy to be local host. I'm going to report you put there in the dash D command. So for me, it's 8080. This is because this is what I SSH, and I put dash D in 8080s. This is saying, open a SOX proxy, listen on port 8080. This way, I'm telling Firefox connect to the SOX proxy at local host on port 8080. So now once I do this, when I go to, let's say, we type in our team name or our team number here, I'm <IP_ADDRESS>, and I'm accessing my team name, my team from here. So this is, what port is this accessing on my server? 80, port 80 on my server. So it has a list of all the services. Like you see, there's a test service, www, that is running on port 9,000. The machine I'm currently on is number 23. But I can change this. The whole point is, on my server, there are two services running. A web server, a web calendar web service on port 9,000, and a binary service listening on port 8,000.  So by changing the IP, I can access deep ones test service, deep twos test service, and so on, all the way up to 23. So this is how you can access all the other teams. You can't SSH if you have a machine, but you can access them through the services. So the question is, where do these services live on the actual machine, right? So this is my server, now I'm on.  I didn't send you guys the passwords. That's right. Yes, for the scoreboard. OK, yes, I'll do that after this. So there is a scoreboard. There'll be a username and password, and I need to send that to you. I'm sorry, I forgot. Because otherwise, if this is how you submit flags, so if another team has your password, they'll submit a flag as you, or, I guess, would be good for you, whatever, we don't want to allow that. So there's a scoreboard that shows you the services, it shows you how a routine is doing, everything like that. But where does everything live, right? That's the important thing. So first off, the first thing you should check out is what users are present on our system, right? Or what users have home directories on our system. To check out the users, we checked out an EDC password, right? So we have several users here. We have the WWW user, which is the default at 480 page that we saw, so that's actually not interesting. Or maybe it is, maybe I put it back over there, but I have it intentionally. The Ubuntu is the user I use to administer the servers, so don't mess with this. CTF is your account, right? This is how you're playing with these things. Scorebot is also incredibly important. So there are, so we'll talk about the scorebot in a second, do not mess with the scorebot directory. These other two, test service binary and test service WWW, right, these are the very important ones. So if we look in home test service binary, we'll see we actually have to be pseudo-wide because the permissions here are that it's, we are in the other group right here and we have zero permissions, right? Three cents because we have multiple binaries running, so you wouldn't want binaries to be messing with each other. So if we look in here, we see that there is a test service, there's testservice.c. So I can look at this, I can see, please enter a command, read in the 100 magnetic characters in a command, enter an argument, and then some things happen. But I said that these are running on some of these on our, on Fort what? What does that mean? 8,000, yeah, or like, yeah, 8,000, right? So I can use netcap, 8,000, and now I'm interacting with this service, so I can enter a command, and it'll give me output, right? So you can all do this, and when I'm accessing local hosts, I'm really accessing <IP_ADDRESS>, and I can access anybody else's binary service by changing my IP address, right? So we're accessing these things over the network. But is this actually a network service? Any networking commands in here? It fits in one page. No, it's just printing stuff out, right? It's printing things out, it's using print app and scan app. So we're using the magic of a functionality program called XINETD, it's a daemon that listens on certain ports that we tell it to, and then invokes programs whenever it gets input from there. So it's actually a super cool, easy way to turn a binary application into a network application. So if we look at, all of you should look at your XINETD directory, there is a test service binary thing in there. And so if we look at that, we can see that this is what's actually configuring our service. So it's saying that it's running, it's expecting TCP connections on port 8,000. It will accept connections from any host, and it is using the user test service binary. And when it gets executed, it executes this test service program. And every time a connection comes in, it spawns a new test service process. And then that test, the cool thing is this test service process thinks that it's using standard in and standard out, but it's really happening over a network. So it makes writing it from my perspective a lot easier and understanding what's going on through your perspective also easier. Questions on that? Yes. So to patch that, all you have to do is just recompile the code and then everything goes to magic. Yes. So if you recompile whatever the executable is in, let's see, where's the config? Right, wherever you, whatever executable you put in here is test service, it will treat any incoming connection to 48,000. We'll do that. So if you want to patch test service, you change it from file to code and then put it here. Make sense? So during the competition, so one of the things is how do I find out what services are running? Well, A, you look at on port 80 of your machine will be the list of all the services and all the ports. All right, you will also be able to see inside the xinatd.d directory, there will be all the service descriptions there. So you'll know exactly what files are being executed based on what ports. Now the question is where does the web stuff live? What is the test service, duh, duh, duh? So if you look inside here, it's got something in here, it's got a flag, it's got a public html directory, so if you look at the public html directory, it's got a CGI bin, and it's got an index.thp page. So this is the content of whatever's running on port 9,000 here, and there's kind of other stuff in here, so you don't have to play around with it. So the configuration for this, if you want to know what maps, specifically what port to what user, I believe, was ETC, Apache, sites enabled. Yes, so inside sites enabled, there's a test service www.configuration, so looking at that tells you that on port 9,000, it gets mapped to test service www.publichtmlcgi bin. And the important thing is to not mess with the public htmlcgi because it's set up, Apache is set up specially such that the incoming request executes as this user not as any other user. So that way it's not executing as root permissions or www, it's executing specifically as this user when it gets executed. Questions on how to map ports to services? So what's the goal? So inside the home directories, inside test service www, we have a flag, and the flag is owned by root, but readable by the test service www group. And the same thing in test service binary, there's also a flag, that's readable and writable by root, but readable by, oh, that's wrong. Should be legible by test service binary. And so the idea is, so this one's broken, but if we go here, so what did the code look like for the index.php page? What is this doing? If there is a test parameter that we can get ready, and based on that either, if it is not set, then return this aloha per page, or else it actually includes the code. So test can be a php file. Right? Yeah, could be. So here's my page, right? So what case is this? It's equal to yes, so this has a test get parameter, and that's equal to no. Yeah, so here there's no parameter here in the URL. So it outputs this page, and I'm going to go to the aloha per, I try a test, I go here, and it outputs yes. So why does it output yes? So there's a php file that's having the same name as the test parameter, that's including that file to it. Is it a php file? Yes. So how do you explain this to get the flag? Like creating our own file, and creating our own file. Yeah, that would be creating the flag. How are you going to create your own file though, with this service? I can do it on my server, I can't do it on your server, right? Yeah, but we would change the link of the yes file, of the yes file. How do you change the link? I don't have access to your machine, I only have access to mine. Directory traversal, because we are here at CGI did, we go up one directory, up one directory. So we're trying to access test service www flag. So we see that flag there, that flag here, we submit this on the submission system, and we get some flag points. We get some points. Questions on kind of basic operations, I have to fix the scoreboard and stuff so I can show you how you would submit things. The gamebot is broken at the moment, it's not actually distributing flags, it's a fake flag, go ahead and play. Can you create a video on it? I'm creating it right now. All this is being recorded. Other questions? Yes, where are the other services gonna be? What side are they? This is one service and one flag. Yes. So we're gonna have many services work, are they gonna be? They will be depending on what they are and what I'm gonna call them. They will have a user and they'll either be web pages or they will be binary services. So it should be clear the mapping including ports and services and what they are. So are all the flags supposed to be just like in random place or anywhere? Hey guys, just a minute, let me answer these questions so we're not all talking over the recording. So there are multiple, so there's gonna be, there'll be flags set every 10 minutes, let's say. So new flags will be set. Each service has its own flag. So you should not be able to break into one service and access the other services flags. So every service has its own flag, it will be named flag and everything will start with the letters FLG so it will be super, super, super clear. We'll have different services with different applications, right? Yes, there'll be different services. They will each be different. You will, that's why you have teams so you can kind of all work on different things. Yeah, please. Are the services gonna be there from the beginning? Yes, services, all services will be there from the beginning. They'll access to source probably, yeah, source. They'll access to source code and everything so that should be good. Are we allowed to use any tools? Okay, so let's talk about this. So we need to establish some ground rules. Okay, so A, so part of what we're doing is we're actually checking that your services are available, right? Like I said, the scoreboard will tell you which ones of your services are up. So you can't just, for instance, for this, for the one we just saw, right, the index.php page, did we just completely remove this functionality? Have we gotten rid of the vulnerability? Yes, have we removed significant functionality from the application? Also yes, right? So the test scripts are testing to make sure that you don't remove the functionality. It also means that you can't walk traffic into your machine from the other machines. So you can't just firewall off access to these IPs, so your ports need to be accessible from every other team. So that's out of bounds. You can't just firewall off your ports to the other teams, that's super lame. Okay, some other rules. You can pretty much do, I think, almost anything you want. The other big thing that I have to ask, because I've been trying to figure out something aside, and I don't think there's a really good technical way we can do this, but the binaries, like we've been seeing, right, we've been playing with binaries that have ASLR disabled and that have all these security features disabled, right? So just compiling those with the correct flags is super lame. I mean, we haven't really gone over how to do more advanced exploits that get around ASLR and all of those things, right? So, you know, enabling ASLR in your system or doing something like that is super lame, so let's all agree we're not going to do that, right? It's much cooler to actually fix the vulnerability than to just recompile it and hope that things go away, right? So I will change, I'll set it up so that when you do GCC, it automatically does all the flags for you, so you don't have to worry about that when you're compiling everything.  It's only an hour and 15 minutes, right? So the challenges have to be quite small enough that you're not going to spend an eight or 10 or 12 hours that took you to break one level on the homework assignments. I may be one crazy level, we'll see, but, you know, so it's just like, because it has to be simple enough that you can exploit it without all these defensive techniques. So I think that'll be fun for everyone. Everyone agree with those? Okay, third option, it is super easy. Sometimes you can mess up things. If you change something, you've changed something, maybe a set you ID root or something. So if you do get root on somebody else's system, I don't know, let me know, send me an email, send me a screenshot of something, but don't, you know, it's only an hour and 15 minutes, it's like hard to recover from that. So don't, you know, don't do anything malicious and ruin the fun for everyone else, right?  Come with me. No, that's super lame. We change our values or environmental variables that the program holds. In one way, so you can't change any of the input-output because that's part of the specification of the program. I think that's probably all I'll say. But remember, right, remember, so patching, fixing yourself is important, but you're gonna get way more points by exploiting. Like every time you submit a flag, it's gonna be 50 or 100 points, right? So like, developing a new exploit and being able to exploit all the other teams that submit their flags, right? You get significantly more points than if you just spend your time doing defense. Well, now you've just limited what other people can get, but you have really increased your score. So it's only gonna come out if you're like neck and neck with another team, you'll geek out the way. How do we submit the flags? The flags will be submitted through the scoreboard. So I don't have that working right now, and I want to get through all of this. So what I'll do is I'll leave this test environment open until Sunday, let's say, and then I'll kill it on Sunday. I'll send out emails and everything, so that way. And I'll send out emails when the flag system is running and putting new flags in because I have to update some configuration options because I messed up on the level. So I have to make sure that's all working. So when everything's working, you can practice submitting flags, all that stuff, which should be pretty cool. All right, any other questions before we go? Yes? The flag is going to help you. Obviously, you're just not having anybody help you, right? No, no, it's definitely available. Yeah, yeah. So other teams get credit for that, too. And one of the things you should not be able to do the system is supposed to be designed so that when you do exploit a level, you can't change the flag or anything else. Also, you should be able to remove your own flags, right? That's also super lame. The flags are just going to prove that you've won, that you've solved the challenge, right? You just change it to flag one, don't just gonna find that, but that's fine. All right, good. Sweet. All right, see y'all on Friday, Monday. We'll be in touch.