Everybody forced here rip in 2022 tops archive six series retired player edition baseball 20 box case number 14 Random hit style will type in the hits as we go along We'll do the random at the end to see who's getting what makes her joining everybody. Good luck. Let's see some big cards here Calling of that out of this case. We're right Bradley So the baseball sold out tonight guys check out the schedule for our basketball and football breaks that still have spots available We've got NT basketball cases tiered random styles and just a few teams left for the PYT's Start off with a dusty Baker the player dust 12 to 24, right player dusting. Yeah, nice card there Dusty is in this a lot Next up is Darryl strawberry 8 of 88 Yeah, I pulled the move on move on auto out of pristine. I gotta get at least one nice move on card from my collection I think One decent move on one out of one Scott Rowland nice out of Bowman heritage Scott Rowland one of one oh Six Bowman heritage. Yeah, those 90s Graves rotations were like the best of that decade for sure Sean Green 3 of 14 Good start to this case too That rolling a sweet looking Wow, look at this 204 a dual auto Eddie Murray Cal Ripken Jr. I Have never seen a dual out of sig series Good luck on that one everybody to a for Murray and Cal. I did not I did not I do I've never seen that 88 tops dude. That's awesome Geez man. Let's guys are pretty good Red Lynn 13 of 22 angels Fred Lynn here Fred Lynn 13 of 22 George Foster 28 of 31 so many George Foster's no bananas Foster real shame real shame Mookie Wilson 24 of 59 Mookie 24 of 59 Next up.  That's pretty dope That's one of one Don Trell Willis Shannon Stewart for 40 of 48 Shannon not Dave Shannon Stewart 40 of 48 Chavez One of one you can barely see it one of one Eric Chavez now from a tops finest. Oh nine. I Like that car design. I don't know what it is man It's very mid-2000s. Oh, I love one of one Eric Chavez Lee Smith six of 47 Lee Smith my signature to All-star welcome Steve Finley had this card last break Steve Finley 9 of 28. I guess technically six But you know what I mean when I say mid-2000s. What would you what would you call those years then? Jim Cotts 96 of 99, what would you call like 2000-2009? the Early 2000s we're set technically in the early 2000s then if you want to look at it by mid-2000s is like 2050 Berge Jenkins 27 of 38. I don't know six Mid Single digit 2000s. I don't know man not qualified to say Tony Perez three of 54 a lot of reds legends in this Tony Perez three of 54 Wars a gaming promo to got promos on promos now She oh, that's a big mag Kent Herbeck like broke the box 17 of 53 mag is huge. Is the card bigger? I think it is Does anyone know if these cards are bigger first for whatever reason? 88 tops the mag is much is much wider Kent Herbeck 17 of 53 Kent Herbeck is absolutely a twins legend Okay, so they were bigger. Okay. Okay. I was like I'm losing it here Dude Carlos Delgado one of one from tops total Delgado was a beast at the plate dude. Oh Three tops Carlos Delgado one of one. Why would they make cards that were too big and then just not do it again? Eric Davis 29 of 99. I guess the 80s were a time for you know mistakes for cards Eric Davis 29 of 99. I thought we're pulling all the big red machine reds and that's dope. No more one of one Classic renditions from archives. Oh one or heritage. Oh one. Sorry. We're opening archives right now. I don't Heritage oh one. No more Garcia power one of one. Heck. Yeah, man. Really good case I can't believe he pulled that Cal and that uh That ripkin together. Good luck guys on the random And thank you again for joining. We will randomize. Geez, dude. That's a one and a two three times just three times Got the good old punters bounce one Two three Brett G down to Allen B and three times on the hits best of luck everybody one two three Fred Lynn then a Sean Green There you go Brett G Fred Lynn Chris B Jim cut James E Lee Smith Paul O Kent Herbeck Andrew S Mookie Wilson John H with the Eddie Murray and Cal Ripken junior Two of for a dual auto. That's pretty sick Allen B Steve Finley Chris B They're rolling one of one. That was a cool card John A with the Nomar one of one and Eric Davis James E Tony Perez Chris S Dusty Baker Vaughn with the Eric Chavez one of one Allen B Daryl Strawberry Chris B George Foster Steven G Delgado one of one Allen B Shannon Stewart Jason S Don Trowell Willis one of one Vaughn with Fergie Jankin Jenkins and Allen B with Sean Green We'll get the results posted. Thanks again everybody on the definitive now


This is stock number 10375. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used heavy-duty truck headquarters. Today we are checking out this super clean 2014 Ford F350 Crew cab short box single rear wheel. This truck has the 6.7 liter power stroke diesel and has been fully Safety Dan inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off and This truck has been gone through mechanically 100% per our state of Wisconsin Inspection process and is 100% ready to go. Kodiak Brown Metallic over pale adobe is the color scheme. We shoot all of our videos in 1080p 60 frames per second So if you have HD capabilities on your computer tablet or smartphone device turn them on right now because it is like you're right here Looking at the vehicle with me and definitely your best way to check out the vehicle before seeing it in person So you can get a really good idea of the overall quality and condition of the vehicle Before making the trip to come see it in person 20-inch factory alloy rims with the chrome covers open-country Toyo extreme 35 by 12 and a half R20 LT tires with right around half the tread left maybe a little bit more Kind of like 60 70% on there has the FX4 Rancho shocks frame and under bodies in really nice condition Headlight lenses are nice and clear Front bumper and lower valance are in excellent shape. No dents or dings on that Has the chrome trimmed grille that's in really nice shape. I didn't see any peeling or anything And the hood itself is in really nice shape Didn't see any dents or dings in that Passengers side fenders in nice shape And the passenger side rim Very nice and clean. No scuffs or scrapes on there And as you go down this side of the truck you can see just how clear that body is How clean that body is how reflective and mirror like that paint is And that's really why we take these HD videos So if you are far away or even if you're close by and just cannot make the trip down You can still see the truck hear the truck and have confidence In the vehicle that you're looking at before you even get here So that when you do get here, there's absolutely no surprises In fact, we offer a summit auto fast pass option on our website where you can apply for financing Get pre-approved even see a payment quote and appraise the trade if you have one All right on our website lower rockers are absolutely perfect factory chrome step bars frame and underbody Is very clean. It does have all the remaining factory exhaust So it hasn't been messed with anyway like that Box rails I always point this out on the trucks. You always want to make sure that these are corrosion free And these are in excellent shape this truck must have come from a place that did not have salt But a frame and underbody is really nice and the back tires have just as much tread As the front tires actually a little bit more and these are pro comp Extreme tires on the back still the 20 inch rims it does have the chrome tipped exhaust back here And as we come around to the back Rear bumper is in excellent shape Does have the back of parking sensors 4 pin and 7 pin wiring and the full Toing package with the receiver hitch. So we do have a painted on mural on this tailgate It's got a really nice wood scene on it And you got a big wolf on there Comes with a retracts Roll up tonneau cover Really some nice artwork on the back of this tailgate Was nicely done Bed's in pretty nice shape just a little bit of light duty usage With nothing too major and it does come with The 7 pin wiring if you wanted to put a fifth wheel or a goose neck in this truck Which this one has not had one in it, but you could definitely put one in it has the tailgate step assist as well And that tailgate shuts nice and solidly As we go down the rest of the side of the truck just as clean as that passenger side Has the nice fx4 stickers Driver side box no denser dings than that and the back tire has just as much tread As the rest That rim is in excellent shape too down the rest of this side of the truck no denser dings than the doors Does have the driver side door code entry, which we do have the code for comes with the power scope mirrors They power fold in and power extend out In fact, I always like to show that in the video.  There are no rips. There are no tears on the seats They're in nice shape has the factory floor mats auto headlamps power pedals And inside you can see that this truck has 44,544 miles comes with the leather wrap steering wheel that is in excellent condition audio controls on the right And bluetooth controls and cruise controls and information center controls on the left comes with the six speed automatic transmission with the optional tap shift the factory navigation and the my forward touch radio Your heated seats and climate controls right here as well as your cooled seats This is also where your backup camera shows up am fm and serious xm radio capabilities on here and bluetooth connectivity capabilities as well Turned out four-wheel drive downhill assist control stability control as well And you do have your factory brake controller for auxiliary switches And you get 110 volt 150 watt plug-in dual climate control there and all your other climate controls Passengers side seat and floor mat are in excellent shape. No rips or tears on there Headliner is in nice shape and it does come with a power sunroof Home link buttons.  No rips or tears back here You do get that power sliding rear window with the built-in rear defrost Once again, those seats are in excellent shape Factory floor mats back here as well 110 volt 150 watt plug-in back here as well And underneath the seats is a storage area And that locks with the ignition key And you do get a receiver hitch reducer on there Behind the seats, you're going to notice that there is a factory subwoofer And you have your latch tether anchors back there as well Last but not least there is a child safety lock for the back door On both sides And we'll take a quick look under the hood. I would personally like to thank you for checking out the video today And hopefully from this hd video you will have been able to tell just how clean this truck is All the way around inside and out under the hood. We have the 6.7 liter Power stroke diesel engine base very clean Runs very smooth has motocraft batteries. That's always a usually a really good sign that it was serviced at a Ford shop Factory Ford shop most of its life This truck has been fully safetyed and inspected by our service shop has a fresh oil and filter change All the fluids have been checked and topped off And this truck is 100 ready to go To see more pictures of this truck or one of our other 450 new and used cars trucks scvs mini vans wranglers Half tons three quarter tons one tons you name what we got to go to our website www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summit auto.com If you'd like to check out more hd videos, you can go to youtube.com Summit auto remember to like Subscribe and share on this video and all the videos that you see there In fact any second you will see a link to subscribe to our youtube channel on your lefty linked more Heavy duty truck videos like this one on your right If you have not been to our website on the bottom link to this vehicle on our website click those check us out And we're super excited to help you out with this super clean 2014 Ford f350 crew cab short box single rear wheel lariat ultimate fx4 package. Thanks again


Hey guys, it's Nate, AKA The Foot Accountant. Welcome back to the channel. Today, we're looking at my insane end of the year club tour. It is the end of the year, boys. The year is about over. And I want to take you guys through the cards and the players that I have in my club. We're ending the year with this Panini collection of cards in my FIFA Ultimate team. Pretty dope, pretty insane. I've had a lot of red list pack look this year. And I want to quickly go through the team, go through the club, share that with you guys and just kind of, almost as like a show off, kind of like a slight flex, I guess, as to what grinding, what trading at an elite level and even putting just a lot of effort in so you can upgrade packs, can open upgrade packs and maybe get lucky half the time could get you, right? This could be you guys next year, if you are following the channel, following the trading tips, getting involved in the discourse, stuff like that. You can have a chance to pack and have a club like this through trading without spending any coins. They make it easier and easier every year with the amount of special cards that come out with the availability of cards this year. This was one of the years where cards were the cheapest they've ever been in terms of price for team of the year cards, for just regular golds, icons, all that kind of stuff. Most icons, not the icon moments, but especially with all the upgrade packs at the end of the year with the best of stuff and packs. It was a crazy, it was a very easy year to have a crazy, crazy team. But a lot of the cards that we packed were not at the end of the year, like right now with the summer heat, with the pre-season promo, with the best of players and packs. We got a lot of this stuff during team of the season, which made it that much sweeter. So we're gonna take a quick look through my club and just talk about where some of these players come from, what they mean, and also some cards that maybe I missed out on throughout the year. Some cards I wish I would have done in terms of at that time it was great value for money and I kind of missed out on that SBC or doing that objective. So without further ado, let's jump into the club. As you guys know, we got the big three from the league on during league one team of the season. We were able to pack Mbappe, Neymar, and Benyeter all here in the first page on one day. I packed those three cards on one day, one pack opening during league one team of the season. It was nuts, best day of packs I've ever had in my entire life. To be quite honest with you, I've never packed Neymar, never packed Mbappe, at least in the past two years when they've been super meta. And then of course with Benyeter topping that off as well, dude, getting all three of those untradable during league one team in the season was insane. Like again, a lot of these cards came earlier in the year. I haven't had that great of pulls during like the 90 plus packs, the 92 plus guaranteed. The only one that I'm gonna show you is like 97 team O'Vehner. He came after team in the season ended. So again, these three guys right here like that day sticks out to me the most as the most red list pack luck and the luckiest I've been like ever on FIFA to get all those pulls in one day in the club, first donor untradable. And all the stuff you're seeing in the club today except for two cards are all untradable. So this is all stuff that I've been able to pack this year or do an SBC for or complete an objective for or it's come from like a guaranteed Tots pack or a guaranteed something or other pack. So all this is untradable. I literally have nothing tradable in my club except two players and I'll talk about those in a second. Team of the years, right? We had a great segment of the year with team of the seasons but team of the year this year, I packed my first ever team of the year. I packed Allison first and then I packed Conte not once but twice I ended up packing team of the year Conte twice untradable. I had to submit him to an SBC during team of the year which was very hard. But this is the best all around card I've ever used this year in FIFA 20. This dude was unbelievable, is unbelievable. And even though I don't play a lot of games we played 500 games with this Conte card alone. So GGs, if you have this card you know how insane that he is but I'd say those, this page right here with the Ben Yetter the Neymar, the Mbappe and the Conte those polls right there to me mean the most in terms of in my club, in terms of what they were worth when I packed pulled them. You know Neymar was six million coins when I packed him this that week of league on team of the season. Ben Yetter I think was like five million or something Mbappe was like three. So I mean that is a crazy amount of coins untradable value-wise at the time that I was able to get into my club, right? We packed Veran as well from La Liga team of the season from those upgrades. My best two red picks from the year, gold three Luis Alberto and silver one, Lewandowski headliner, Allison team of the season. A lot of people have packed him.  This happened last week, 7.8 million coins worth of card right here for Zinedine Zidane and I've only played one game with him bro. One game. I've only played with this card, unreal. I need to step up my game in September, right? I'm gonna have to play a few with him though to get a big sense of how this card plays. Some people say he's clunky, but dude icon moments 97 Zidane you gotta try him out, right? So again, this is the card that came from like a 92 plus tots. That's my best one from all these upgrade packs in the past couple of weeks. Aguero I packed during Prem team the season and rocked this guy for a couple of weeks and week in league. He was pretty solid. Ramos was during La Liga Tots, 243 games. IMO, best center back in the game for me. Griezmann got a lot of caps for the team as well. He was playing right mid for me a lot. Or left center mid in the 4-1-2-1-2. He was really good. Cruz Fakir were both guys that I didn't really play with that much. But they were nice pulls during La Liga Tots. A mobile with a high rated fodder card. Hummels with a high rated fodder. Basically, Oblak is a red. Guaranteed Sancho from the Sancho packs. I think I packed him by himself during Bundesliga Tots. But then I got another one and I just rinsed the first one in. Di Maria played a couple of games with I think. Maybe not. Papa Gomez I just packed recently. This one meant a lot to me man. Packing Yunmin Sun during Premier League team of the season as a Spurs fan. This one felt incredible. That was huge for the club, for my account. It just felt incredible. That was a big, big pull. Played a decent amount of games with him. Of course, Red Ter Stegen was a big pull during La Liga team of the season. Royce, I feel really proud about this one man. And not a lot of people have this card in tradeable. He was very hard to pack. Most times when you saw German center attack in mid, Dortmund, it was Brent. And I actually was able to get Royce. So that was a W. Moeller, Lukaku's SBC. Couple of other cards in the club. Holland is a pretty dope card. And then of course you have all the summer heats, right? I couldn't turn any of these in then. These cards are just so beastly. So good. Zlatan was a beast for me in the weekend league that I used to him. Of course, Vinicius, I'm famously known for calling this guy Vinicus in FIFA 19. Pogba's one of his best cards ever. Sanchez, dope card, Promas, dope card, all pack pulled. Barty actually packed today from the 92 plus guaranteed. And here we have the first tradeable card in my team. That is 94 in form. Harry Kane, I bought him for the spur squad. That's a GG. This card's actually really good. I've got another version of Kane. I'll talk about in a minute. Insane card, by the way. Anyway, I was able to pack Messi in tradeable this year. Part of the red list pack look. Packed him from a player pick during foot birthday, I think. Just a random Messi popped out from nowhere. That was dope. Played him on the right wing for a long time until team of the season. Rashford, Tots in there. Carvajal gets some games for me. Van De Beek, of course, GGMU. Got him red, DiBala. You know, people didn't like him at first. He's a pretty solid card. I haven't used it. I wore much, just a couple of games. Two games, legit. Of course, I got my man, Erickson. My lookalike, 45 games played with him. Bruno Fernandez, Ribbery, of course, all the SBCs from the Summer Heat promo. Hulk, we packed pulled. Talazos, packed pulled a couple of weeks ago. I had this card tradeable for a while that I used. Kaka came from a Prime Icon moments pack. Again, that's 1.3 million right there in the club. Ray Charleston was a striker that I used. After Premier League team in the season, I used Ray Charleston and Aguera up top for multiple weeks. Cause those guys were fantastic for me. This guy's a really, really good card. Loved using him in the latter part of this year. Insignia in there as well, used him some. Nine Golan, never really got playing time for me, unfortunately. This card is really dope. 88 games played, most is a super sub. Really, this is like Ben Yetter quality rat IMO in like in game, really, really good card. Lala, of course, solid right back. 114 caps for me, wow. Interesting. Then of course you got the whole 93 French squad here. Dembele, Bendy, Mendy, Kempembe, Andobale, and Langley with Figo as a Prime Icon moments that I packed earlier too. Balak was just packed like two days ago. And then of course my 92 Harry Kane. Now this is a very prized possession of my club. People always ask me, why have you not sold this card? And this is what I tell them, right? I bought him first owner in November.  I'm gonna buy this card, play with my favorite player, Harry Kane in game. Look at the stats, bro. 222 games played, 195 goals, 94 assists. And I think I was using a 4-4-2 or maybe a 4-1-2-1-2. So he was not a soul striker up top banging in goals. This guy was really, really good for me. Loved using Harry Kane and I just can't sell him, right? I love that dynamic image, love the card. That's gonna stay in the panini for the rest of the game. GGs, we love Harry Kane, that's right. Now, some of the other big pack pulls that I've had this year. Paul Pugba, untradable first owner during foot birthday from a player pick. And I also got another card from foot birthday as well. But this is where like the red list really, really began to start before team of the season. It was like, I had red list of luck, of course, before tots. And this was one of those examples. But during team of the season, it got even crazier, right? I mean, you guys have seen my tots counter right here. Yeah, 120 tots packed, insane amount of team of the season we got during that timeframe, we were just spamming packs. I found so Davey's pretty good left-back card, haven't used him enough. Calvin Phillips dope card as well. Got him during like the summer heat promo, I think. Bernardo Silva, right? As we get towards the back of the club here, there's a couple more club legends that I just don't have the guts to get rid of into an SBC. Bernardo Silva, you know, I actually turned in my duplicate team of the year content for this SBC, but 221 games played. He was a mainstay during team of the year in my club. This card means a lot to me, man, because I rocked him after team of the year because I packed him untradable right when Icon Moments came out. That was a crazy Icon Moments pull from Division Rivals Rewards, man. Division Rivals Rewards on the companion app literally in my car stopped on the way to work. I ripped this pack and boom, out pops McAlely that was dope. Crazy day, that one. This was from mid Icon SBC. Carlos Boateng, Alan Sando, some SBCs, Hakimi, and then Rashford as well was packed during foot birthday untradable. That was a dope pull, because this card actually was really, really good and gained for me, again, 150 caps for the club. And then of course, my team in the season came around. He kind of got demoted, but that was a really good card for my club as well. And then as we get towards the back, some of the Americans and other Spurs cards that we have back here from the storyline objectives that I've kept in just because I'm an American, you know, for the Panini. And then of course, Mr. Ryan Kent, this is a super sub of dreams. You gotta keep this guy in your club to remember just what FIFA 20 was as a game. This guy was so OP. Of course, when he was OP when he was in 84, then he got the boost to 87 with the preseason promo and he's just wild. So that's basically the end of my club because after this it goes to like 78 ratings, which is kind of like a lot of people's clubs right now at this stage of the year. But couple other cards that should be a part of my club that I actually ended up turning into SBCs at some point, which I probably shouldn't have. That was Louise's flashback card. I crafted this during team of the year. He was a lovely card for my squad, using him until team of the season. He was dope for me, really, really good in game. I didn't play a ton of games again, but this guy was fantastic. And then Roberto Carlos' baby from icon swap set one.  He was great. I think a lot of people use this card early on in foot because of the icon swaps and because you could get him so easily. Now, to end this thing off, we have two players that I wish I would have done the SBCs for earlier in this game of FIFA. And here's one of them, ScreamPK. I didn't do the ScreamPK SBC. Now I know a lot of you guys don't have this dude in the club anymore, but at the time, this was one of the best value SBCs of the year. Last year when they released this, it was insane. Caused some crazy market movements that day with link investments to this. Center backs across the game just died because of the pace boost on PK. I mean, plus 16 pace from his normal card. And then of course, a massive boost to the defense, the dribbling made this card really usable with I think medium, medium, high work rates at that stage of the game. You know, in November, this is a really good card, right? So a lot of people were using this guy and I do regret not doing this SBC. This is the other one for the Spurs Panini. I didn't do Daventon Sanchez, bro. I've got the 85, I didn't do the 88 though. I regret not doing that SBC just for the Spurs Panini, right? Again boys, this is the club man. This is the club with insane, you know, I guess I could chalk this up to insane pack luck I guess, but you know, I feel like I would have gotten a lot of these polls honestly just from spamming packs during the team of the season, during the summer heat timeframe. It was a GG of the year. The only thing I did not complete was packing a 99 rated player. I guess I'm gonna have to say that for next year unless I can somehow do it in this last week of the pre-season promo. So that's my end game club tour. Again, I'll give you one last look at my end game squad with a, you know, the set up of players that I think are the best in this game that I have in my club. This is like the best possible squad that I could have. Of course I could have possibly Langley instead of Millie Tao. Huge fan of Millie Tao though. Really, really, really fun card. This team is awesome, man. Love the team. They're so good, so fun to play with. And of course with good gameplay, but that's what we were able to grind towards this year. I think the Panini is looking great. It's looking awesome. And the fact that this is all first owner untradable makes it even better. All right boys, if you enjoyed this video smash the thumbs up on it. Comment down below if you have any questions of course. Subscribe to the channel if you are new. It's been Nate, The Foot Accountant. Catch you guys later. Peace out.


Hello at the end of the last class we made a list of a few applications of sprays and what we are going to do today is sort of zoom out a little bit and look at spray as a entity spray is a collection of about a million billion may be even a trillion drops okay and we want to see what sort of measures can I bring to a spray to gain a quantitative understanding of a spray. So we will start to make a list of a few different spray characteristics. Now before we turn to the audience and try to ask this question of them I want to suggest that there are basically two kinds of spray characteristics one that are macroscopic in nature and a second that is microscopic okay so we will make a list of a few different macroscopic qualities first and then move on to the microscopic qualities we will just take a steady spray so as opposed to a little perfume spray perfume spray is where you push the plunger down a whiff of perfume comes out there is a start and an end to it okay so we are going to talk about a spray that has no start and an end but it is just like a continuous perfume spray it is just easier to understand these qualitative aspects in that context then we will talk about an intermittent spray also and talk of some qualities of an intermittent spray as well okay so let us start listing a few different macroscopic qualities. So we will just say spread or span of the spray spray angle very nice okay I will also distinguish this between this and cone angle okay we will talk about that also penetration length droplet size okay we are going to list this in the I will distinguish this because this is going to occur in both the microscopic and the microscopic list okay so we will talk about talk of this in just a moment microscopic measure okay any others that we want to include velocity so we will just say velocity as a again a microscopic measure so we have already made a list of a few different things here the so and I want to add one to it which is one that is relevant to many different processes actual mass flow rate of the liquid we can add a few more but this is a good enough list okay so if I just take a typical spray let us say I have a spray nozzle from which I have the spray emanating now first of all I have these all these drops in the spray we have seen this many times the actual flow rate coming out in a steady sense is the liquid mass of the liquid flowing out per second this is relevant to surely many applications okay now talk of velocity there are two kinds of velocities okay the reason I wrote down microscopic measure is because I want to know sort of in a bulk so if I take a whole bulk of this spray what is like a velocity vector of that bulk okay but really speaking it is not of use to know what this whole bulk is doing I want to know what a what different points in the spray are doing okay so therefore there is a need to understand sprays using microscopic measures back to the mic microscopic I just want to complete the list here spread or span like for example that width at a target surface say for example if you are spray painting a wall I have the paint can about let us say 10 inches away from the wall when I push the plunger and this is a continuous spray because I can just walk along the wall and paint the wall when I am walking along the wall there is a certain width that the paint impact will cover that is important because I want to know how many passes I have to make of this can so if I look at a measure like that that gives me a width and clearly that is also tied to the cone angle or the spray angle so there are two kinds of angles and we will talk about them maybe about a week from now but essentially if I call that angle to theta to theta is what we will call the spray angle the cone angle is slightly different we will look at that in some detail in the sense that the angle very close to the nozzle here would be slightly different for different fluid mechanic reasons and that is often referred to as the cone angle so you have a cone angle that is usually larger than your spray angle penetration length now again some of these measures are all tied to each other because if I take a spray of a certain mass flow rate and somehow increase the width which also means increase the spray angle I am naturally going to decrease the penetration length because the drops on sort of the mass of drops are going to slow down so the penetration length is a measure of that all right so let us put this intuition to work we will look at a little video we made in this in our lab here this is a simple perfume spray that is going to go from start to end okay so let us play this video and see what we learn from it I want to pause it there to point to a few different things you look at you look at that angle there that is what that is the spray angle now as you go further downstream you can see that the spray angle is becomes less and less defined so as I go further and further downstream the spray angle becomes less and less defined because there is no spray edge the idea of a spray edge is an illusion it is not like the edge of this pen it is where the edge of a pen is well defined edge of a spray has to be defined by us and our definition of the spray edge is going to also influence our definition of the spray angle so if I say I want to go as far as I find no drop at all that is going to give me an almost 180 degree cone angle in many different sprays it is going to be a very large number in comparison to where I said I am going to go to a point where the mass flow rate drops below some critical value so mass flux okay that is the rate of mass flow per unit area drops below a certain value so I will say okay when there is very very few drops almost a mist I am not going to count that in my spray that is a simple definition of a spray edge we can find more quantitative definitions as well but our idea of a spray angle is clearly tied to that okay all right so here let us go on and continue to play this video I want you to understand two or three different aspects here you can see that there are some big white flashes right where my mouse is pointing okay those are in a sense big drops so I can go back to the start and show you where they started you see that that drop there that started is going to continue forward I want you to notice two differences here one of course this is not a steady spray but this idea also applies to a steady spray so the concept of having big drops alongside tiny tiny drops is not something that is out of the ordinary every spray of any commercial interest will have a range of drops that the spray has so typically the range is you is on the order of at least two or it is at least two orders of magnitude in span more often it is three orders of magnitude in span so the idea that you have drops that are ranging from nearly let us say a fraction of a micron of micrometer in diameter to hundreds of micrometers in diameter is not at all out of the ordinary in fact you can see this in this image okay now as you keep going you can see that the perfume has practically stagnated around and there is not much movement of the drops past that point so you spray and the spray goes into air and sort of the drops reach due to the drag from the surrounding air they sort of equilibrate they may continue to move forward by momentum conservation but it is diffused quite a bit so your spray width starts to increase as you go far downstream okay so now when I look when I go back and look at that like I said there are many different microscopic properties that are actually more important and relevant to a spray like for example at every point we said you are going to have a drop size distribution so I said point but we will qualify that in just a moment the idea that a spray is composed of several sizes of drops this is sort of obvious to us by now not just that that there is also a velocity distribution again I will qualify this to clearly distinguish it from the air around okay we are looking at droplet velocity distribution so you have drop size distribution and droplet velocity distribution that are all microscopic properties so these are now like I am looking at the individual droplet level I am almost looking at somehow understanding the spray from within as opposed to from without from outside okay what other microscopic properties can I list here I can look at in a typical spray like a perfume spray we looked at this yesterday as well in the last class we are interested in like a rate of evaporation or temperature dependence which is clearly temperature dependent okay so from there I can say somehow I am also there is also this idea that there is a droplet temperature distribution okay so these are all in some sense individual variables like a drop a single drop has a size it has a velocity and it has a temperature these are all at the droplet level they are properties that you can assign to a single drop now at the spray level what do I how do I convert this droplet level information into a spray level information okay there are two ways of doing it one I do this I do just this so I sit here play this video or I have a spray like this going I pause okay I pause the picture and then look at all the drops in this frame now this particular video is not particularly good to zoom in and zoom out although you could to some extent it is not quantitative but clearly that is just a question of camera resolution so if I have a sufficiently high resolution camera and these are not out of the ordinary also I can pretty much image every drop in this frame right now okay and from the image of every drop I can reconstruct the size of every drop so let us say we did this calculation last time there are approximately a million drops in this picture right now probably slightly less than a million I can image every drop get a size and get million numbers okay from that I can construct a histogram of what to do with this so once I go to the million drops in the picture so sample so let us first pose a question and then we will answer what is drop size distribution so I want to understand what is what do I really quantitatively mean by drop size distribution and how do I measure it that is what I want to get to we will spend quite a bit of time on this how do I measure it thing but I want to first start with what is drop size distribution and then that will naturally lead us into how do I measure it if I so I can take a freeze frame count every drop in the frame and measure its size okay this will give us essentially like a million numbers or slightly less than a million numbers and from there I can construct a histogram we are all familiar with the concept of a histogram okay I want to spend some time on that because it is there is some very important mathematical tools that we need to acquire to completely understand what the real histogram and what we can do with a histogram okay so let us say I do this histogram and it gives me something like this so this is diameter and this is count I can get the count versus diameter of every drop in this frame and that will give me a distribution clearly this is a drop size distribution in the spray this kind of an information is what we will call spatial drop size distribution because my independent coordinate of acquiring this information was x and y space another way of thinking at it is thinking about this is for every drop that I that I capture or count in the freeze frame I can also get its x and y coordinates okay so that all that automatically means I am in the process of acquiring the spatial drop size distribution because those x and y coordinates would be different for different drops okay another way of getting the same drop size distribution is to sit at a point in the spray so look at where my cursor is I will sit at that point in the spray and I have a way of just you know sitting in a launcher and counting every drop that is going by me okay so I am not moving in spatial coordinate I am just sitting at that one point and acquiring information of the droplet size droplet velocity droplet temperature if I want to really get specific about the spray of every every single drop going by me okay so let us let us look at that another way of doing the same thing so I can look at every drop in the spray that is going by me and get its drop size velocity in this case it could be a vector it could be both the x and y coordinate and temperature if I really want to get fancy of every drop now the independent coordinate that distinguishes different drops here is the time of arrival there are succession of drops coming through so every drop is going to have a different time stamp of when it arrived at my location okay as opposed to the previous way of sampling drop size distributions where I had a the distinguishing feature it was as x and y coordinate of the drop okay so I can now take the same let us say I sit there for 10 seconds and in 10 seconds like you know typical perfume with is like let us say 2 seconds and in 2 seconds I was able to sample let us say again a fraction of a million drops and I have now statistics of size velocity of every drop coming through there so I will just for now ignore the other quantities and look at only the size to sort of illustrate the point so I can now do the same histogram okay I will again the independent coordinate of this histogram is the same draw I am counting the number of drops in a certain bin okay now this distribution is what we will call the temporal drop size distribution okay so we started to talk of microscopic measures of which drop size distribution is one measure and when we when we listed this here it was actually a fairly simple thing to list you know there is different size drops we want to understand some information about the size drops we quickly found out that there is not one but there is two different drop size distributions now we are left in a limbo okay are they the same or under what conditions can we expect them to be the same under what conditions will they be totally different because they contain different pieces of information okay so before we completely understand under what conditions are they the same and under what conditions are they different okay I want to sort of make the equivalence between these two ways of sampling the same problem sampling the same physical system you are essentially measuring something about a physical system there are two ways of understanding any physical system okay one is what is called a random field approach especially a statistical system like a spray that is like some sort of an uncertainty some sort of a you are you have to resort to probabilistic measures at some point and under those situations there are two ways of doing it either a random field approach or what is called a point process approach okay we will talk about this in some detail but I want to sort of draw the equivalence between a field approach that is where I am looking at a spatial distribution of some quantity and a temporal distribution of the of another quantity as being two completely different ways of looking at the same system so in general we do not expect them to be the same they are completely different okay under what they will present one simple situation under which they will exactly be the same so if I say for example when are the the same is a very restrictive criteria okay I want to start with that because it is the easiest to understand they are exactly the same when you do two things one if I take a spray and in this case I cannot do a spray like a usual spray I take drops in a box so this is a box that has all these drops in it let me not let me not clutter the box with it okay there are different size drops if every drop in this box was moving to my right with exactly the same velocity okay so all the drops are moving to my right with exactly the same velocity then if I had a way of staying at this location I will call this XX sample drops so I am not sampling drops at a point but I am sampling drops passing through a certain cross sectional area and this is also possible measurable and quite routinely done so if I am able to sample drops passing through a certain cross section and I and I construct a drop size distribution from the sampling at a certain cross section this is like my temporal drop size distribution and if all the drops were moving with exactly the same velocity okay then essentially in the time let us say the width of this box was some delta divided by you is the time is the time taken for all the drops to pass through my cross section so whether I take a snapshot at some time t equal to 0 of this box or and then construct a spatial drop size distribution from all the drops in that box or whether I sit at location XX and sample all the drops come through that cross section and then construct the same distribution I will get exactly the same answers okay so really speaking there are two assumptions I made not one one assumption is that all the drops are moving with the same velocity okay I want to I showed you where I am going to show you where I cheated you into another assumption okay so one assumption the second assumption is this let us say this box is my frame correct this is the frame that I used to construct my image frame that I used to construct my spatial drop size distribution and then I am sampling for a certain time t capital T that is going to tell me the time over which I can sample to get the temporal drop size distribution okay so if delta is the width of this frame and capital T is the time of sampling it is only when capital T is exactly equal to delta divided by U that I get this if I choose capital T to be some other number other than delta divided by U let us take the simplest situation where capital T is less than delta divided by U okay what happens if capital T is less than delta divided by U I would have only sampled a part of this frame I would not have sampled the other half of the frame or other part of the frame which means now is there a guarantee that the drop size distribution I construct from half the frame is the same as the drop size distribution in the full frame there is no guarantee I could have had a completely different mix of drops in the back half of the frame I do not know that right so this criteria that capital T has to exactly be equal to delta divided by U so in other words if you made a freeze frame of a spray and you reconstructed a drop size distribution even if all the drops were moving with the same velocity I am constrained to sample at this capital T only to get the exact same distribution which is again very restrictive so T has to be exactly equal to delta divided by U this is not so obvious okay now clearly the first assumption and the second assumption are different in the basic philosophy one assumption number one I have no control over what actually happens in the spray all drops have to move at the same velocity I do not get to control that but the second is second looks more like a measurement thing okay the second looks more like so even if all drops are moving with approximately the same velocity can I make this equivalence the only way to make that equivalence is if somehow even if you make spatial drop size distribution measurements with some delta I make with another T okay I do not know what delta you used but I make it with some other T what sort of delta and T will give me approximately the same information okay or at least on what sort of delta and T relationship will give me information will allow the two kinds of distributions to tend towards each other the answer to that is as I keep making my delta larger and larger so your initial spatial size distribution is composed of a very large frame and you had enough resolution to actually size every drop in the spring and then I can take a time sampling that is also very large so I can sit there forever and ever and ever and then sample all the drops so if you if delta became infinitely large and T was also infinitely large all I need to know is then they are going to be approximately the same given that the drops are all moving with the same velocity okay so essentially the second criteria is an artifact of the idea that we are constrained with finite domain sampling and finite time sampling okay the fact that I cannot sit there and measure forever and ever I have to do my sampling in a finite time likewise my camera cannot zoom out to the entire region of the spray I am only constrained to a small part of the spray so these are the sort of the assumptions that underlie the equivalence between the spatial and the temporal drop size distributions now what about velocity let us talk a little bit about velocity as well and then we will move on to the third part so we will look at what velocity distribution is again if I go back to my image I can pause the image I can this is a paused image I can take another freeze frame just like this a short time thereafter and use some fairly simple algorithms simple or sophisticated to find the displacement of a drop so it is like we are going to get into this in some detail towards the end when we talk of measurement techniques but essentially I can image a drop image a set of drops now and a short time later and from those two images I can reconstruct a velocity field okay so one way is take images a small time apart another way of doing the same thing see how this is equivalent to the spatial information what distinguishes every particle here is its original x and y coordinate in the image so if the original x and y coordinates are of every particle in this in the original frame are different like we started to do with let me discuss with the drop size distribution the second way of doing it is exactly like the previous temporal size distribution which is I sit at one point and measure the velocity of every point coming through every drop coming by me okay so I can sample the second way so these are two different ways again like we discussed with drop size distribution it is not obvious that they have to be the same in fact in the case of velocity there is no reason to even believe that they will be the same because drops at different points are different in other words I cannot even start to ask the question under what conditions will these two be the same because they are two completely different pieces of information temperature and other like we discussed towards the end of the class last time we talked of concentration as being a parameter that qualifies each drop so if I have a fuel that I am spraying that has multiple components concentration of a certain component in a given single drop is a measure is a scalar measure that is associated with that drop it is like a scalar property not a measure scalar property associated with that drop so I can have this temperature is also another scalar property associated with the drop vector is a velocity is a vector property associated with the drop size is a scalar property I can get into lists of vector and scalar properties associated with these drops but the point is all of those properties can be measured in a spatial sense or in a temporal sense okay. Now the basic requirement for equivalence between these two is that we will only focus on the first one that all drops have to be moving with approximately the same velocity if not exactly the same velocity that principle is very often violated in a real spray and therefore these two measures are completely different and that violation is quantified in terms of what is called a size velocity correlation correlation the word has a meaning that there is somehow there is a if not a causality meaning somehow there is there is a sense that a certain size drops can be expected to move with a certain velocity that is known a priori okay that is the idea of a correlation. So I can now take this spray for example and when I played you can see in here that the larger drops for example right in the middle here are moving with a slightly higher velocity compared to the smaller drop at exactly the same spatial location or very nearly the same spatial location. So at least as far as this spray is concerned larger drops are moving with a higher velocity in comparison to the smaller drops and that is basically information that I can take to if I measure that in this perfume spray I can transport that information to another perfume spray that is somewhat similar in construction and I can apply this information to other processes as well where even if the nozzle design was not the same fluid mechanically if they were similar then larger drops in that other spray can also be expected to move with a higher velocity in comparison to the smaller drops and in general in many many different sprays spanning many different nozzle designs at any given point the large drops will tend to be moving slightly faster than the smaller drops on average okay. So this is the idea that this is a very important word because I cannot draw any conclusion on any two given pairs of drops if I give you two drops at a particular point and ask you the question is the larger drop moving faster can you for sure predict if the larger drop is going to move faster you cannot make that prediction all you can say is on average in a fairly large sample of similar drops similar large drops similar small drops the similar set of large drops is expected to move slightly faster than the similar set of small drops that is the only prediction you can make and that is the only idea that you can take away from a size velocity correlation all of the measures that we talked about all of the spray characteristics both macroscopic and microscopic that we listed thus far are only sort of steady spray characteristics. So these are we have discussed them thus far in the context of a spray that has no beginning and end in time and that is relatively unchanged in time okay. So let us sort of make sure we completely understand what we mean by steady because it is a very important you know we say we are making the steady flow assumption all the time let us understand what we mean exactly by that word steady spray in the next few minutes let us take the spatial distribution as our as our means of understanding steadiness. So I take a picture and I have reconstructed this drop size distribution I take a second image and a short time later let us say one second later and these two images are exactly alike now clearly they would not be exactly alike all I have to say is they are alike. So without going into the microscopic detail of which drop is at which x and y location in the image if I can take two frames okay that I took some time later and I am unable to tell which one was taken first so the timestamp the timestamp is indistinguishable the timestamp is not encoded into the picture itself that is the case of a steady spray okay. So if I go back to my old high speed video if I took this picture and then this picture the first image had the spray only about that far the second image has a spray almost further downstream that is the nature of our perfume spray works this is the clear a clear case of violation of my steady definition but if I drag this further down into my high speed video and now play it I took this image or I will go back okay I took this image and then another image a short time later now this is still a transient spray as far as my eye is concerned when there is a start and end but there was a time in the middle say about one second when I could not tell two images that came a hundred milliseconds apart okay so these in that time span there was a time span in the case of a perfume spray when I can treat the spray to be relatively steady okay so basic definition of steady okay for the case of this class okay is that I if I take two pictures of a spray and I cannot from all macroscopic measurements okay I am starting off with a less constrictive criteria first and then we will talk of the microscopic case I cannot tell which one came first okay then I am beginning to make the case that they are steady then if I make microscopic measurements of the drop size distribution so I am now recovering the statistics of the spray be it temporal or spatial if I can still claim that I cannot tell the difference as to which one came first or which one came next from the microscopic measurements of distributions I am still okay I can still call it a steady spray when I can begin to tell the difference like the first example we saw with a startup I can from a macroscopic measurement of a penetration length tell you that they are not the same I can tell which one came first so that is not the that is a clearly unsteady spray so if you take a clear case like a diesel engine where you have your injector operating a few hundred times a second can I treat can I use any information from all this literature concerning steady sprays for diesel sprays the answer is yes the answer is pick up that time window where you cannot tell the difference and there is a time window as long as you restrict the application of these models to describing the spray in that time window you are doing quite okay so just as a quick recap we talked of different measures or different characteristics of spray and then we talked of spatial versus temporal measurements and the equivalence thereof okay and then finally we made the case for a steady what do we mean by steady spray okay we will continue this discussion in the next class.