The perfect transfusion. Always transfusion. Owens transfusion mix is made in the USA with real juice to create instantly delicious cocktails with perfect combinations All summer long available online at Owens site or at the barstool store Or check it out at a store near you. So man, make sure you go check out these Owen mixers They make the best cocktails. We got you know, we got them at the crib to always drinking cocktails Using new Amsterdam vodka as well.  It's very easy Okay. Let's get in the M-M-M-M-M-M-M-M-M million dollars worth a game, right? Yeah Let me talk to the youngins for a second. Right? I want to tell the youngins about being great out here I want to I want to tell all the youngins out here. Right? Just do me a favor And even, even, even not, not, not even if you're younger, not, but just do me a favor. Look at Walo, right?  Be Walo last three. Be the latter half of Walo. Walo was young, immature, didn't know who he was, wasn't really a follower, was a leader. I was. He was a leader. You wasn't my leader, but you was a leader, but you listened to me. You followed me, but you was a leader to other niggas. So I didn't regret it, but douchebag.  So you got to understand your mistakes out here is at a minimum. But then he came home the last three years and he took the same exact energy. He the same exact nigga. He took the same exact energy and he channeled it in a positive way. And look at the man's glow.   It might have to pay for it for the rest of your life.  You might got to pay for it for three to six or five to 10. And it's some youngins out here that's hopefully listening to this to say, you know what, it's time for me to be great. Now I ain't got time to waste. I feel with OG saying, man, you know what? My life is more than going to prison. My life is more than going to the graveyard. My life is more than losing all the niggas that surround me. So be the latter half a while or use him as an example because he the same nigga. Nothing ain't changed with him. The only thing that's changed is he channeled his energy in a positive way and God blessed him for it. So to all the youngins out there, man, don't wait to us too late to be great. I want to say something to go on top of that. I had the sister walk up to me. She said, Dan, while it seemed like you only highlight and it's like you only talking to the to the kids is doing wrong with the young boys is doing wrong. The young boys are shooting and this and the third. First of all, I'm talking a by salute. All the young brothers out there is doing right. I'm always talking a by because just because you're doing right, don't mean you had thoughts of doing something wrong where you might be impressionable by the thing. So I'm talking a by sister is just that I got to talk even more to the young boys that's getting crazy because a lot of them they're looking for attention that they never had. That's why they do some of the things that they do and a lot of them never had nobody to really talk to them or just say, man, I love you or give them a hug or just give them some game. You know what I mean? That and I ain't trying to give you no package. I ain't trying to do nothing. I ain't trying to have you on no dummy mission. I'm just trying to give it to you. So you don't have to take the route I took. You know what I mean? And I just try to be the old head that I wish I had when I was coming up.   There's somebody out there right now, right? You're a young boy, man. I'm talking to you.       And I ain't saying anybody built, but you got some people that convinced they self that they built for it until they wake up dead. Or they wake up in prison, are they? So you saying they wake up like this? Yeah, you know what I mean? They say that in the hood, wake up dead. I guess you wake up. You don't wake up. You wake up somewhere else. You wake up not here.  Is that you got? Yes, it is. Come on in. How I get here? You got caught slipping. They popped you in your biscuit.  You come on in, though. You want to be a killer? I want to go back. It's too late. Yeah, man, that lifestyle. Man, I was just doing a training Sunday morning, right? I sent out a text message to everybody signed up. I get a response back from a family member that said that a young man got murdered and some gang related activity in a drive by, right?   Right. So it can just be so quick and to think like somebody that's in the community that's trying to, like, you know, get that game kind of happened just overnight. Like I found while, though, like a year and a half ago and I remember when I was I was just coming out of jail myself and that and that positivity, right?  Talking to the people, man.  But but that we need more of that, like, because it's necessary because a lot of people think whatever they're going through in that moment is going to be what has to be their final destination. You're not what you're not. But basically, Tony, say, number one, you're not what you're going through. And before we go to another, I just want to say this to the mom, the young boy that I was just talking to.  Ain't nothing wrong with saying, you know what? Well, selling some dope or running around with this gun on me.    Like, and it's cool to say, listen, you know what, I ain't built for this. Tell them that again. It's cool to say, I ain't built for this because or even though, you know, man, I'm going to tell that mean this ain't for you, man. Like a lot of you dudes don't it is pressure that you want to say, you don't want to say, man, I ain't built for this. But it's cool to say, I ain't built for this and walk away and go and square up. Ain't nothing wrong with being the L seven, man, the square, man. And I'm going to keep it all the way. You called me from jail and you told me that straight up, man. I said, cuz man, get out the streets, man.  Now you wasn't in the street.  I did say that I said it.   You heard from old head of the block. He told you, you tried to run it on me, but I remember you saying that.   And that's what all the chicks like. That's what everybody like. And that's the only people that get attention. But that dude, they got that nine to five. That dude, that's a separate driver. That dude, that's the security guard. Right at that dude. Listen, man, I salute all you do is just work in a day.   And I'm going to do some mansion.  A lot of people talk about man enough, but they can't do it. And if you go and if you're going to do it, just go, just go cold turkey, man, you can't play both sides of the fence.  You can't do like that. You can't catch up like that. But for those again, like I'm going to say, it's cool to say this ain't for me. Let me get into a sponsor as we before we go forward, man. This next sponsors for a lot of you cast. Some of your young boys might even need this. I know dudes like you like need the Roman swipes. One thing about these Roman swipes is they straight to the point. I'm talking about they are clinically proven, clinically proven, right? I'm talking about you will last longer in bed, right? Effective, easy to use, easy to use, fast acting and don't require a prescription. These are joints in a fit of your wallet. They were the script. These are joints. Gilly be having like when you ready to be like swipe. Because listen, all you got to do is swipe it real quick. She'd be like, oh, yeah, I'm excuse me, baby. Could you grab that pull it out, swipe it. Some people that are white girl, she told me she asked me to make sure I get a case of these joints for her people. But that's another story. She put it on me to put your business out there, white girl. You said he just can't last long. He ain't strong. You can't last long. You understand that you do. You think about not holding on. But that's another story. One thing about these Roman swipes, man, listen, man, all you got to do is swipe, let it dry and you're good to go. You're good to go like a pro.  You're going to be on the beat.   He was a tackler like Tony. He tackled me, you see what I'm saying? Because you swipe, swipe, swipe, swipe, swipe, swipe, let it dry, get busy. I'm telling you, go all the way in, swipe, let it dry and get busy, man. One thing about this I need you to do. Go to get Roman dot com slash backs was it. That's not the back slash millions. And you could get your first month of swipes for just five hours when you choose a month plan. That's get Roman dot coms back slash million get strong last long. So she can hold on. Get Roman dot com back slash millions. Hey, let me ask you a question slash, I guess. Backslash is the other way. I'm in slash slash millions. Okay. Slash Roman dot com slash millions. Yeah, I'll be getting mixed up. Top five fat rappers of all time. First of all, Biggie number one. Biggie number one. Big punch. Heavy D big pun fat, Joe. Damn, eight ball, eight ball, eight ball, uh, Rick Ross Ross, boss. Uh, could you say Gucci Gucci was fat? He was fat. Gucci was fat at one time. Oh, Gucci. Yeah. What was big boy fat? I don't want to disrespect no one. Oh, C. Lo C. Lo. Yeah. Uh, C. Lo was chubby. What's ice cube fat?  You sure ice cube. I got Biggie number one. Biggie is definitely number one. We're big planet. The new guy that's out that sings a song. Biggie big pun. Listen, Biggie big pun. Rick Ross Ross. What about a heavy D? Heavy a legend.  That's four. So who we agreeing on first versus Biggie? First is definitely number one and then pun. Then big pun. Bun? Oh, no. Big pun before Ross. No, I got Ross number two. I don't know because I feel like I like skinny Ross too. I'm giving pun right at the beginning. Ross still considered fat.  No, I like.  You can't do that. Damn, you right. I'm trying to think.  You can't do that. It's big pun. Fat boys was the first rappers, but we can't. They ain't out of the top five.  OK, we going, we going. Biggie Smalls, big pun.  I don't remember. He's dead.  He's dead. Yeah, come on. But is we going to put heavy D in front of eight ball? MJJ. No, I mean, eight ball. We can't put it. Yo, some of these brothers is going. So we just like able. We got to salute heavy. Heavy is a legend. Heavy was fly. You know, money early in Mount Vernon. He was fly. He was. He was out there. He had real confidence. Right. Like Biggie probably got his confidence from heavy. Right. And Biggie, I'm going to keep it all the way real.  She took them niggas to a different level. Because they was glad to see that.   However, I stake her down to the socks. Mixing rocks, filtered rocks. Am I Jim Knox in your Mr. Bishi girl? See me when he never holds. Crete me in the teepee as I lay down laws like Alan. Copy, stop it. If you think you're going to make a profit, don't see my ones. Don't see my guns. Get it. Now tell your friends. Papa, hit it. Then split it in two as I roll with the junior mafia.  I'm clocking your facade. She's watching you once again. I'm in game. Then we talk about how we dress in this and diamond necklaces, stretch lexuses, the sex is just. Oh, what about sauce money back? I get deeper and deeper. Help your read. Yeah, Biggie. Come on, let's get your mic in me. No, sauce money is not in there. Sauce money. I gave Biggie some cool. Chief, he was still. So it's even heavy D. She gets Charlie Baltimore. It's even heavy D. It's even heavy D. It's even heavy. You ain't got to do all that. Yeah, she is. He like to do all that. Damn, Tony, like she could be my Charlie now. Come on. Shout to Charlie. What's what's what's beautiful? I don't see the resemblance though.  Well, it's cool.  You look like your name, Harley. Harley, Charlie Merlin. You Harley Baltimore.  I'm just Harley Merlin. At least she cute. You look like him. No, he look like me. As you talking about that's what I used to get at nigga baths. Fuckers, you talking about.  First person took advantage of your innocence. Pussy put a spell over the don't call them people. But I did change your play. I got a lot of I didn't go. A lot of I did. I did get me. Can I get one time? It held his little legs. And you know, you hold the move legs.    That's what I told you.  You ain't telling me that stuff. Had your whole legs in the air.     I was telling the truth. No, Gil was it. Gil was it. Listen, you know a lot of these dudes out here. I just want to say something. And you know a lot of these dudes like Gil's a child snitch. When they was scared. Mom, he done this. He was that type of. He was a child snitch.  I put it out there. He was a child snitch. Pussy, I ain't no child snitch.   I only told you one time, Pussy.  Who drunk all the Kool-Aid? I only told Daddy on you one time. I don't drunk all the Kool-Aid.  I only told Daddy on you one time.  Hey, let me listen, right? Let's talk about, look, like, you come home from prison, right? I see you all the time. You bump into motherfuckers that. Look. Every time. How we spend time here? Nanny. Nanny. Yeah. I'm recording right now, Nanny. I'm going to call you when I get there. That's the boss. Nanny going there.  And let me say, um. Damn, how you speak that? And let me say, rest in peace to me too, old man. And rest in peace to Uncle, man. Yeah, he by. Yeah, I'm saying. We can go. Yeah, we can go. You're wrong. One of our uncles passed away, so rest in peace to Uncle. But, um, like, I see we be out.  I was in jail with him. I was in jail with him. Yeah, I was in jail with him. I was in jail.  I didn't say that a lot.  That's really doing something out here, trying to make a way, trying to change their life. You feel what I'm saying?  The nigga was locked up. You feel what I'm saying? But it actually be.    Yeah, man, I'm out here doing construction. Man, I be doing, you know, 28 an hour, man.  Yeah, everybody we run into. And it's like society wants you to believe it. Like a lot of times you don't get a second chance when you go to jail. And the reason I'm saying you don't get a second chance because sometimes when you got that felony or whatever on your jacket, people judge you for that even after you did your physical time, even if you did your probation or parole.  But I will say this, Gil, Gil said that to me one time. I never forget. He's like, yo, I see him like, hey, why you see that? You was in jail, were they doing good?   And you know, a lot of people say people go back or whatever, even when I was in jail, I ain't see a lot, a lot of people came back versus who was going home. You got a lot of great individuals that just committed crimes.  It's all levels of crime. But if you say you believe in a justice system and you believe in a whole American structure, you also got to believe in rehabilitation that motherfuckin' can change.  How you this down the third? It's like, fuck, I did my time. You making me do my time again? Right.  I never did my time for the crime I done. You know, in some crimes it's heinious and I understand people who's never gonna let it go. But it's like, when somebody do their time, it's like, damn, give them a shot. You know? And because I done ran into a lot of dudes that put some plans down in prison and they came right out here in materializing. Like they didn't even had a felony on their jacket.         Right. I mean, live through the moment, get through it and bounce back and do your thing. Everything is possible. If you can see it, you can be it. You know, that's real. I love that man. You just spoke my whole story. You know? Shit, two and a half years ago in jail, now I'm a millionaire. So it's crazy, you know? You can change your life. No, no, no.  Yeah. Real millionaire. Yeah. Like Lamborghini paid for, huh? Cash. That's like me. Like last year, I ain't had nothing. Now I'm here. You know, it's a different game. And I caught the bus here.  And I caught the bus.  He go half on my Uber's.  Hey, let me tell you something. At least I'm gonna half with you.     I bought you crab cakes. I bought crab cakes up there. I'm crab cakes legendary. I'm taking some home. I'm in the fridge right now.  Shout out to the motherfucking eats by Drake, too. It's by Drake, fed us. You know what I mean? Real talk is he, he came, he came, you know, and he had the whole story. The crab cake burgers, the baby crab cake burgers. Man, them bitches was popping too. They was popping. They was pop locking up. Tony ate four of them bitches. Tony went in, dipped them in the sauce. That gangster sauce. Smothered them in the, that gangster, that gangster sauce.   Shoot your tongue up, what? Not on duty, huh?  I'm sorry.  So you saying the percentages of the people that you've seen come back to the people that you've seen on the streets that's doing good with you? It's hard for me to think, but you with me all the time and you see every time we're running somebody like, they be like, damn, baby, what's going on, man? Listen, man, I work in the union. Oh, damn, man, I'm the supervisor here. Oh, damn, man, yeah, I got this property. I'm doing real estate. I got my own construction. We ain't running to, we might've ran into out of a hundred people. We might've run into one or two that was clocking. That was sitting on the corner pumping. Like it was 88. Like a couple. And then when they do seem, they'll be like, wow, man, I'm gonna get it together, baby. I'm just, man, straight up. He always be like, we coming out of the store.  You gonna get it when everybody along clock come on different times. So you'll get it, man, but just be safe. You know what I mean?  They be like, all right. Absolutely. So you wanna speak on any of that? Yeah, I wanna say that. I want this nigga to pay the whole over and I have. What's that?  He lost. Let me ask y'all a question. What's the top 10 athletes of all time? No sport in, you know, no sport at all included. Jordan. You know, I think Jordan's the number one athlete of all time. Top 10 athletes of all time. Hold on for one second. She's so pretty. A2, I'm recording. Babe, can I call you right back? Oh yeah, I'm recording. Babe, can I call you right back? You too. All right. Deion Sanders. Deion Sanders. I think prime time. I think Deion Sanders is one of the, first of all, he had the whole thing, he backed his playover, he had a mouthpiece and he backed it up with the play on the field, baseball field, football field. Only thing I gotta say is that when I was coming up playing sports, me and him played the same position in the country, like everybody was at this. He had a Jerry Kerr, I had a Jerry Kerr.   Couple of miles. You know, it was deep though. It was deep.  It was. He was at Florida. I was going to pistol. All right. Don't forget your boy Shaq, the diesel. Can't forget Shaq. Shit. Can't forget Shaq in the top 10.  You gotta put Shaq. Shaq was the most dominant player. No, Muhammad Ali. Muhammad Ali.  Tiger Woods. Hold on, we got Mike. We definitely got Tiger Woods. Tiger Woods. We got Mayweather. Muhammad Ali. That's three. Gotta throw Mayweather in there. Gotta throw Mayweather in there. Because the reason why you gotta throw Mayweather in there because Mayweather changed the whole the business side. Dynamic of the business side. Not because he fought the best opposition at the best time because he absolutely did not.  Old Pacquiao. Old Pacquiao, oh yeah. But he won though. He won though. No, no, no, no. We're not taking nothing away from him winning. You should have seen when I was. You feel what I'm saying? All I'm saying is, he didn't fight those guys in the front like Muhammad Ali for Joe Frazier, but he definitely is one of the greatest. He is the greatest defensive fighter of all time. I ain't never by a sport, but nobody's ever done it like that. Without a doubt. Me and Benar was a sport. Real calculated. Very boring, but very calculated. Very boring though. But you gotta put him in there because he changed first of all, he won undefeated and he changed the whole state of the boxing business. Like this dude has made $200 million. Crazy. 36 minutes. What is that? It's 100s easy. You feel what I'm saying? So we got, so come on, man. We got Jordan. We got, we got Dionne Sanders. We got Tiger Woods. LeBron. We got Muhammad Ali. We got Mayweather. LeBron. We got LeBron.  They had the foul, they had to foul Shaq. Right. They had to go hack a Shaq just to change again. He literally stopped him, bro. I think ten is hard because I want to ask about two people, Kobe. Yeah. Then I'm going to ask about, I ain't going to fight. I'm going to ask about- Kobe is in the top 10 athletes of all time. What about, what about, what about, hold, let me ask you something. Hold, we gon, we gon, hold, hold. He's gonna be pissed at that.  I'm gonna say this.  I'm gonna just say that. But I'm gonna say this though. I'm gonna say this. Is what's the name going on there? You made it. I'm just asking, because of all these rings. Tom Brady? Tom Brady. Is he going in there?  Brady's a goat. That's eight. We got two more. Kobe Bryant is in that list. Whoa. Kobe Bryant has to be in there. I'm out of it, Kobe Bryant. You know, I'll- Who else, how many more? We got one more. We got one more. We ain't put no track athletes in there. Usain Bolt? Yeah, Bolt. Usain Bolt. Oh, you up, it gotta be him. Fastest nigga live. No, no, no, no, no, hold on, wait. What about- Wait, wait, wait. Michael Phelps.  Woman boxer. Top 10 athletes all top. Hold on, let's get this right. Hold on, one more top. One more top, right? Michael Jordan. Mm-hmm. Right? Mm-hmm. Wow. Deion Sanders, right? Shaq. I don't know my Shaq on this. I don't know. I don't think Shaq's been one of them. What? Shaq was the most dominant.  Shaquille O'Neal, right? Let's go. Michael Phelps. I'm tripping. How many gold medals Michael got? I lied. I lied. Clarissa Shields. Hell yeah. Yeah. We gotta throw her in there. I'm tripping.  She beat the fucking...   Oh, we set it up.   She beat both of them. Call her up here. We got it. My money's on us. Let me just say this. She a big gill. I know she a big gill.   Oh, so she can't...  So you've a beater? I won't fight her.  Can she beat the Baltimore bomber? No, she a whooped. She a whooped. She a whooped. She a whooped. She a whooped. I even wallow at the jump in it. Street fighting is different.  No, there ain't no way. She gonna run. My money's on us. Let me tell you something.  How time you say that, you sleep.  I'm talking about giving...  She hit me with a little body shot. I ain't know what happened to me.     Bop, bop. You gonna fall. I'm out of here.   We was up, remember we was up. She came back with it.   She gave me, she gave me this, man.  Remember, we was up, we was up. Sweat show, she gave me a little body, a little fender work. Gave me invitation to the bathroom. I was in there, up there. What?  Real talk, she got, and she won two gold medals, and she got all the belts. She a legend.  Shout out to Clarissa Shields, man. Shout out to you, Clarissa. Put Kobe in there.  I wasn't a Kobe fan, just because Kobe passed, I'm not gonna fight. Use AI fan. You'll throw AI in there.  You'll throw AI in there before Jordan. I love that. Shout out to AI, man, my brother.  Bubba Chuck! We ain't had too many footballs in there. VA! You know what I mean, we never get lists as done, because it's always a... Look, because y'all motherfuckers can't agree on nothing, man. It's you. You feel what I'm saying? Like, that'd be the motherfucking problem. Y'all can't agree on that. It's you. Let's get to my next spot, so, man. Amsterdam. New Amsterdam, Valka, right. New Amsterdam, Valka is pretty much the best Valka on the market right now. It's the official Valka for Barstool Sports. It was born from an uncompromising passion for great Valka. This commitment to excellence enabled New Amsterdam to produce Valka of superb taste and unparalleled smoothness. New Amsterdam is a premium 80-proof Valka made from some of the finest quality grains from America's heartland. It's five times distilled for unparalleled smoothness. It's filtered three times for that clean, crisp, smooth, enjoyable taste. You know, you could drink New Amsterdam with anything straight up on the rocks, juice, soda, or you can make the famous New Amsterdam mule. It's up to you. Tutti uses it for cocktails and she uses the Owen Mixer as well. Tutti Vsauce stuff. I remember we said Chicago. Tutti Vsauce. Her neighbor, they was filling it. They was filling it. I'ma keep it all. We're real. If y'all wasn't in that Uber with us, that motherfucker, that cook, that truck. We said the same thing. If y'all was in it. It would have been a scene. Yeah, it would have been a murder scene. He said the same thing. I would have told that driver, listen, homie.  It was cold as a hooker's heart out there, motherfucker. You hear me? It was nigga. I'm gonna go to Chicago. Yeah, we gonna take you. You just gotta act right. Let me ask you a question, right? Yeah. I ain't even gonna ask you. No, ask it. I can't do that. I don't wanna put your business out of school. Put it out, put it out. Leave your truths, man. No, I ain't gonna do that. It's me, I was working for a game. Don't be scared. Leave your truths. I'll leave my truths. Anything you wanna know about me, cause I'm a open book. You know what I mean? I ain't gonna ask you. Ask me. Why you scared? I ain't scared. You gonna punch on you? No, I'm not. I used to.     So you never won one fight? I'm telling this dude, right? No, I ain't even gonna talk about it. It was about time when he got a massage down land and I ain't, it was a long story. It was just a little spice involved. I wasn't gonna tell you what it was. Massage from a man, Ellen? It was a little in between, but listen, no, no, no. It's a deep story, but I- No judgment here, Gil. I wanna ask you, Gil, I'm telling Gil. Gil whole thing is about black, black people being racist, right? Yeah. And why do you say that? First of all, you gotta have a structure. It's deep. It gets deep for you to be able to put that, that infrastructure together in order to be, but you want some- I asked him.   Yeah. Cause every nigga I know, as soon as they got some money, they said I'm getting away from these niggas. I think that's more for, that ain't about racist, that's about safety purposes. Right. Because when you start, people was thinking more on the safety procedure.  Racist on what time? What did you talk about? Right, I don't, yeah. Okay, prime example. So you saying it's a safety thing? Because if once you get a certain amount of money, you're not safe to get it. So, okay, so you saying, me living around niggas, I'm not safe. No, I'm not saying that. Okay, let me just say something. If an Asian person said that, I can't live around niggas, I'm not safe.    So you saying that about- That's basically what you're saying. That's how black people say it. It's a safety thing, you can't live around niggas when you get money. No, no, what I'm saying is, people think about, that's people first thought. I wanna live in a safer environment, I wanna live in a better environment for my children. Because right now, this environment could be great. Okay, I wanna live in a safer environment that's not around black people. That's not somewhat racist. Yeah. I'm asking y'all, I'm getting this money, I'm moving around motherfucking, multicolored motherfuckers, I ain't livin', that's not somewhat- It's one thing if you move out the ghetto and then you never revisit.  So if you lived in a ghetto, you supposed to revisit the ghetto? I love that he visit.  When I make it big, I'ma still come back and sit on the steps with y'all. Why? What you mean?  They got Mona, she out there all day long. They didn't smoke the Mona. I die right on the steps. They know it's true. Like a black amount. Sit on the steps. Like a black amount. When I come back in a hood, you feel me? When I'm chillin', I'm givin' back to the community. So you don't slide through other than that?  Oh, I smoke weed. I'ma go smoke weed in the hood. No, nigga, come holla at me. I'm here. We out the way.  Not, oh, I get money to go back in the hood and fake stunt on some niggas. How many people you think feel like that? I've had the debate a thousand times. People always say, like, if I, you know, when I do, let's manifest it, yeah, speaking of this, this is when I do make it to the next level, I feel like I am going to still come to pop out. I'ma pop out. And guess what? I'm at the block party.   You know what?  You never had a million dollars.  So you think I wouldn't? Then you get that million dollars. Guess what you do? You buy that fancy car. Is it really not safe to sit on the steps in your neighbor? Is it really not safe to do that? First of all, if you make it big, you make it rich, it's not safe to go sit on the steps. Will you get that million dollars? Come on. It turned into 700,000. Now the taxes hit you. True. Niggas, first of all, I don't even dig it. And so many motherfuckers who say that, if I ever had a million dollars, I'd never go broke again. Them niggas would be brokers of motherfucking. Because they're first ones.  Why you gotta look at me when we talk about broke? So is. I'm only broke one on this couch. I'm asking y'all, why everybody still don't wanna speak up?   Mona, the politician. I'm asking. Listen, it's coming. Mona. You said, yeah, why you say that? I say, yeah, because it is, man, you know what it is, man. What did you do? It's for, man.   You know what I mean? You got a whole whole. This nigga done told me, he said, dawg.   I know you did. Yes, he did.   Oh my God. Yeah, so you know how it is. Like the local niggas, you know, was always coming on campus, you know, busting in niggas' crib.  I want the ones to stay on stage. Okay. So as far as the atmosphere, as far as college, dope, HBCU experienced me.    Like the whole idea is to get your kids in the position to be in a better position than you were, right?  That's where the patience part comes in. Yeah, like we really, Speak on your sport. We really, we really be, we really be, you know, we race to a certain extent. We know we'd be like, yo, let's get away from the niggas. Like it's so many people that say that. Like I gotta move away. I gotta go move in the white neighborhood. It's said off, it's frequently, right? But, but people don't want to really be honest about it. When I bought my first house, I've aimed for a house, a neighborhood that was mixed. I don't feel comfortable being the only black person. I don't trust those motherfuckers. I said it. I'd rather live in a mixed community. I understand not want to live in urban areas because the school district sucks, it's violent, blah, blah, blah. But I'm not aiming to get away from black people. No, no, no, not me. No, I didn't say the aim was to get away from black people. I said, mother fuckers, everybody I know soon as they got some money, he said, I'm getting away from these niggas. And you're right, you're right. Oh, okay.  You didn't say it too. Who? You. When I said it. You said I'm aiming for a mixed community. I'm getting away.   You're trying to. You're right. She's trying to.  Listen, I could have went all white. I just went and felt comfortable like that. But rather be mixed, a mixed, you know, area. One neighbor was Jamaica, one neighbor was Agent across street, they were white.    Like, you know, it was a white boy walking down the street, where you lock your door or move to the other side.  Come on, let's be for real. Yo, that's the reality of what happened. You just be for real. It's done been plenty motherfuckin' times.   He's been robbed, he's done been, excuse me.    Yeah, I'm sayin'.   And if it was a group of white guys that were like, excuse me, buddy. Well, yeah, absolutely. What's up, Jim? How you doin', Bob? Two, two, two. Excuse me, this is my whip. The niggas over there ain't sayin' nothin', just chillin' like this. Niggas ain't even talkin'.  Why they chillin' right there? Like, oh no, you think I'ma walk into the uh. That's hammy. You think I'ma slip on motherfuckin' uh? No, I'm not. Uh-uh. Yo, I'm over here. Dude, I see you niggas.  Let's keep it real. So if it was a white motherfuckin' standin' by your car, what you doin'? Excuse me, Jim. You guys must be inebriated. This is my vehicle. Excuse me.  She's a fuckin'- She's an inebriated.   Hey, have you ever peered out a pass for white? Say what? Where were the white girls? How would the white girl talk? I don't know. I'm not a white girl. No, you just did it. I can't speak Caucasian now. Please. You heard it. You heard it. Speak Caucasian. They still know I'm black. If you seen us standin' in your car, us three black guys, what you gon' say in the Caucasian? If I seen you three niggas in my car? See, whoa, look it, here it is. Sorry, guys, you must be lost. This is my car. That's it. That was a bootleg white voice. I can't really do it. I can't do a whole white girl. That was w-w-w-w-wack. That was it. W-w-w-w-white. That's why the names don't call me white girl. I'm not a white girl. I can't speak properly. I hate that we do that. We call that speakin' white. No, we're not sayin' speakin' white.  No, it ain't sayin' speakin' white.  Tried to deliver it. Yeah, the delivery. Like he was a Caucasian. Buddies. And you're not. Hey, listen. Let me get y'all me and I was worth a game, right? Tall you motherfuckers out there.  Where you wake up every day to see your partner breathin'.   Just leave, man. Stop puttin' that fuckin' stress on your heart, man. Y'all don't even like each other no more, man. Motherfuckers stay in relationships cause they feel like they just be scared to start over, man. Somebody out there that's compatible for you, man. You feel what I'm sayin'?   I heard him say it.  But a couple hours went by and he was like, all right, dawg, I'm about to go to the crib. I was there.  All these women be goin' home on Tuesdays to hate, too. A lot of these going in with this nigga. Well, I did it. Right. Girl, I'm talkin' to you later. I gotta go in with this nigga.   That motherfucker got me wrong.  I'm gonna tell you one thing.  Girl, why don't you just leave him? No, that nigga payin' all the bills. I ain't leavin' that motherfucker. That's not why. That's not why. Women have a lot of hope. Women have a lot of hope. There's not a lot of these bitches out here that have lost all the hope. They ain't even got the mother's thing. I think people don't know when to draw the line. Like, when is enough is enough because you don't wanna be a quitter. And then it's like, is it that to leave? A quitter.  And then the biggest thing is the fear. Like you see it. People really think there's nobody out there when really it's plenty of dick in the sea girl leave. Get on Instagram, child. Thirst trap. They will DM you, girl. You always promote in a... Thirst trap.  People be like, I know women this day. So you take niggas off of Instagram on a thirst trap? No, no. Like, why it always gotta be me? But you advertise this, dude. Because I'm giving them a vibe. All the little girls out there. I go live all the time and I connect people together and then they start talkin' all the time. People meet each other on social media. I seen your filthy DM. Dude's bein' a hot DM. There's a lot of niggas out here. There's a lot of women out there.  Give you the real red bottom. Yep. Don't stay in a relationship thinking there's nobody out here. There's niggas out here. Like, they out here.  Leave them. You single? Not today. See, just man, you see every week, A of the day, I'm single on Tuesday. I get dumped every Monday. What's today, Wednesday? We good.  That's the weekend. I usually get dumped on Monday. Weekends be rough. Weekends be rough. Why you get dumped? Listen, it's not an interview.  No, but why you get dumped? I get dumped but through a reason. What type of dude is you looking for? Explain to your guy he's out there, Mr. Wonderfor is out there. Who is Mr. Wonderfor? I like, I'm very understated.  So you see, that's the problem.  I need you. That's your fuckin' problem.  There you go. Listen, I...  I'm gonna put you through something.   You just ruined the niggas.  Shit, I rode one and I said, I ain't never getting on one again. I almost pissed myself.  So you... I'm worth it. I'm a good person. Why you get dumped that Monday?  It's not my fault we get it together by Tuesday. Let's move on. Cooking ain't making big beans that hot dogs would do. I don't make no big beans and hot dogs. I sell cabbage and rice and beans. Oh, you're here? You got a lot of boys that's trying to eat a plate of them. I cook. I cook. First of all, I'm submissive, you know? Okay, so you play the roles? I mean, I'm submissive.  What the... You don't have to be submissive these days of time. You don't have to be submissive. I think men need that.  Like, you know, the light went out. Baby, the light went out then. The light went out then. All I had to do is change the light both then, baby. I couldn't even figure that out.  Girl, you know how I fix the light.  What else you like? Look at him now. It's clicking.   She said thank you. It ain't number one button. And he went full.  No, no, no, no, no, no, no.  Here he goes. No, no, no. Shit. Here he comes. Here he comes. I can't never get one. You know what I do in the house? Nothing.  That's it.  You think I got kids and I'm changing the garbage? Do you fix it? Fix it. He paid people to fix it. I didn't know this.  You had to prep the piece?  It was. He don't hate clothes. Ooh.  You ain't buy me no clothes. Tell him this, please.  Remember, she bought you K-wide jelly.      You did take the pump. Why did you lie, Wallo?  Wallo, you got right to that door and said, don't forget my pump.   You got right to that door and said, Gil, grab the pump. You never grabbed the pump, bro. Gil, grab the pump for you. I never did a nigga.  We're playing hours for a game. We honest on this show.    Oh, that's spicy. That is spicy. It's kinky in here. Niggas is kinky. I got to get new company, man. You do. Y'all niggas shan condoms, man.  But he definitely took the pump. He asked Gil, pass me that pump. On the way out, we all heard him. Everybody heard it, Lowe. Gil, pass me that pump. It went just like, yo, you know you talk fast. Pump the pump, the pump, pass me the pump. That's how I did it. The pump, the pump. Absolutely. And then Pop used it. Then he used it and gave it to Pop. Pop didn't use that. Pop don't need it. How do you know? Here he go. I can't be confident in my guy. That's my dog. But I can't be confident in my guy. She twinkie watcher. This is that size usually got big meat. I know the way it go. You pack his watcher. But Pop said he's before that. Pack his watcher. That's my dog. I hope all my niggas got big dicks. Damn, she be watching Pop. The rule for all y'all. Damn. It's like, no matter what they say about y'all. Pop and pump. He had that pump. He ain't Brian Pumper. It's Bobby Pumper. Fist pump. This is Bobby Pumper. Bobby Pumper, Brian's cousin. Hey. But y'all both use the same joint. That's crazy.  Bobby Pumper, Brian Pumper's cousin. Introducing.  Introducing. Please, is she here bragging about it?   That's my dog.  Small guys usually be on me. Unless you have small, tiny hands. Oh, she poised the hands. Wait a minute. First of all, do me a favor. Fuck, you talk about. Listen, listen. First of all, listen. Whoa, look how tiny my hands are over here. But how big are your hands? Let's say, wow, Gil. Yeah, first of all, I could pop a basketball. I bet you neither one of these niggas could pop a basketball. I could get all of them. Get the basketball!  Look at it.  Look at it.  You can pop on the ball. All right. Tony, do you realize if I got it? Do you realize if I was to slap Joe Buttons, it would be his whole face? Oh, my God. Like, do you realize? Rob, you better not slap that thing. Hey, I think we're sweating, though, bro. No, no, I'm just, no, I'm just playing. Nine violent, nine violent. Yeah, none of that.  The basketball right there, though, we can see if you could pop a basketball, Tony.  Get the ball, get the ball.  Look at Lil' Thumbs. How you going to pop a basketball with Lil' Thumbs? You want to put a wager on it? Hold on, sit down, Tony. My turn. Sit down, Tony. What you talking about, bro? How tall are you? Yeah, who you talking about right now? Let me try. How tall are you? Why are you trying? Yeah, why are you jumping back, man? Yeah, yeah, yeah, yeah. Here, low. What you talking about? They never let the girls play. No, this is your own slip. Yeah. My head. My head. Hold on, this is your slip. You 6'1", too. Yeah, I told you, Tony. The pack. 6'1". 6'1". Yeah. Let me see. No, this is your own slip. My hand's a little wet.   Let me try.  He said if you were to pop that joint, she a nigga. I did it. Look at her hands. Look at her hands. Look at her hands. Look at her hands. I did it. She's talking about it. I did it. She's talking about it. She talking about it. He's talking about it. Baby. No, no. No. Captain, Captain. Captain.   Why are you falling, bro? Hold it out. Hold it out. Hold it out. Hold it out. Hold it out. No, no. Go here, Walo. My hands stay. Look at him. That's how you should grip this cell. The ball ain't regulation, Walo. We're bad singers over there, man.  That's how you should grip this cell. That's how you should grip this cell.  Hey, but hold up.  You lying on me.  No, no, no, no, no, no. Straight out, bro. That's not pomming. Put it on. Put it out there. Put it back.  So you see I did it. Game on. Fuck, bro. I'm with you. You see how I'm doing it. Barely. Barely. Barely. I'm wrong with you, man. From the Smud Association of the Prison. When I first got into the joint, I shot on some pages, right? You did what? I was squeezing off, and I got a little outside of myself. He hit the page. And I hit the page. That's like a major violation.  Yeah, listen. Listen, my homie O'Hare had let him see the book. He was like, oh, man. He said, you can check the joint.  I'm like, I'm gonna get the cell. I'm like, yo, O.G., I got you. I'm gonna respect your joint. But this Smud book was so crazy, right? It was called The Black Video Illustrated. It was so crazy. I'm shaking the dice. I'm from here.  You talk to me like that. Where you been at? Oh, you get interactive like that. Oh, I don't play no games. We have a conversation. Do you say her name like Monant? No. I give her a name that I want to name her. Oh, OK. So it depends on how I'm feeling. One day I might be feeling good for Rashida. The next day I might be Kiki. It's a different type of vibe. So I'm shaking the dice. I'm from here. Six. Six. Seven. So next year, you know, I split. I'm like, damn, I was trying to pull back, but I couldn't because I was an amateur in the Smud porn book game. So I didn't know.  So I had to take the tissue and try to pull it off. I'm pulling the babies off the joint, right?   This nigga, listen. This nigga wore T-shirt wave caps, nigga. This nigga wasn't no joke. He wore two shirts, T-shirt wave caps, and he walked around the jail with a weight belt all the time. Oh, my God.  I'm like, damn.  I'm like, I'm gonna lay this joint near the window so it can blow and try to be cool, right? And I'm like, damn. So it bubbled the page. It was never right. So I tried to pass you over. And this joint was cool. I mean, this is that third. Old head, man.  Listen, listen, listen. And ever since then, he used to grin on me. And I used to be like, damn.  You know what I'm talking about?  That shirt was, that shirt was like brown. It was regularly a white shirt. So that means this dude had some timing. He wasn't playing no games.      He was like, yeah, I might got something for you.  Five heart beat waves. But hold on, you niggas shake the dice, pick the book up, seam it all on your hands.  Then they dab each other. Y'all niggas passing chlamydia all around the jail.    No, no, no, I don't know nothing about that. That's the whole thing.  Hot twist.  He know. They said they heard some screaming coming out yourself. They said it wasn't big teddy. They said it wasn't big teddy. That's all I'm saying. They said it wasn't big teddy. I'm just telling you what they said. Check out the new take, get that smut off my name. Listen, don't put that smut on my name. Check out the t-shirt, man. You see it right here. Pop up on the screen. Take it out. Hit it in the link below. You know how to go. All right. Don't put that smut on my name. Get that where? Make sure y'all pick that t-shirt up. Hey, listen, man. Each and every Sunday, make sure y'all go check out that Rona Proof at 3 o'clock. Rony. If you went to Rona, get to it with Rony. Tony the Rony. Every Sunday, 3 o'clock. 10 step strategy. RonaProof.com. Break down what you do. We're going into a wholesale real estate. He's attacking you into the real estate game.  He liked to be sweaty. Oh, I'm sweaty. I'm a football player. I like to rass the men when I'm sweaty. Oh, wow. That's rassable. That's rassable. I'm a football player with a helmet on. And a jock strap. I want to tackle you down while I'm sweating. Tony the Jack.  No, I wasn't doing that. I ain't playing sports in jail. He was in with a helmet on. You use a linebacker in jail, bro?  At the jail, bro. No, they got linebackers. We got a helmet on a jail. Nigga tomorrow, won't you? I was in jail to back the child line. That means you put the food on the child line when they run out. She knew what the linebackers were. You used to play football in jail. I never worked in the kitchen. I did. I was a kitchen warden. He was on the bench until you were starting. I hate it. It was very depressing working in the kitchen. It was you on the bench until you started, bro. Okay. And hot. And stinky and sweaty. Hey, yo, yo, yo. I want to prove, man. I'm going to teach you a 10-step strategy, how you can get started in real estate without having money, capital, credit, none of that. You can get started making real money. So a lot of people have been asking me how they can get paid. A lot of people have been definitely like from the podcast. Man, I haven't had over, I think we're about a thousand plus people now into my actual course. Getting crazy results. Over a hundred grand made already from people, you know, learning how to get started in real estate. So you don't need to be a realtor. You can do it from anywhere in the country. You don't have to leave the house. So it's super dope. I teach the strategy live on every Sunday at 3 p.m. Eastern Standard Time. And it's a free, the Sunday webinar is free. And then I have a paid course as well. So just so people don't get the confusion with that. But every Sunday I do a 10 step free call for people. Maronaproof.com. Maronaproof.com. Hey, listen, man, we appreciate y'all for tapping in each and every week, making us the number one music podcast in the country. Crazy. Number one. Number one. I'll go by the name of Gilly the King. I'm Wallo 267.  But we call her white girl. Tony the Tackle. Well, he liked that name. He finally came out. He finally came out. He liked Triple T. And he had the dreads. Tony the Tackler. And he had the dreads back then. And for some reason, he looked like he was crawlsaw back then. He took his niggas like this. He was like you crawlsaw the whole time. Yeah. You would believe it, too.  I don't even like it. Hey, yo, everybody, I'm the Madden God. No, he ain't.     Yeah, yeah.  He was a couple. He don't like that.  It's just like that. Right.


Good morning. So, in the last class, we discussed the flow through a conical nozzle. We have shown that what are the losses, how they come in because of the 3-D effect. And then we said that if we kind of reduce the half cone angle, we can reduce those losses. The ultimate reduction is if you can get the flow to be parallel to the axis. And then we discussed that why a shaped nozzle whose goal is to get a parallel flow at the exit will be more advantageous over a conical nozzle. So, today now we are going to discuss about design of the shaped nozzles. There are two ways of doing it. One is, so we are talking about shaped nozzle. First is, if is given a specified nozzle geometry, this actually is a roundabout way. First we choose a nozzle geometry and then we can set up a numerical solution of equations of motion for the whole nozzle. We can use a finite difference scheme, a finite volume scheme, a finite element scheme whatever. So, this the primary thing is that the shape must be specified. With the specified shape, then we solve the full Navier stokes. We can give proper boundary conditions to the wall. Even thermal boundary conditions, we can have a fluid structure interaction code also. So, we can solve for at present, we can solve for the full flow field. But the problem is that this is very time consuming and expensive. It will give us the full velocity field, full pressure field etcetera. First of all the solution itself is going to be very time consuming and expensive, because the Reynolds number is quite high. The flow is going to be turbulent and it is quite high temperature. It has to be compressible. So, it is a compressible turbulent flow modeling with the wall conditions, which are neither isothermal nor adiabatic. There is heat transfer through the wall. So, all this needs to be modeled. So, therefore, it is quite time consuming and expensive. And it will give only one solution for one geometry. Our goal is to design the shape. So, then what we have to do is, we have to try different shapes and then optimize. So, therefore, then try different shapes and optimize. So, essentially the entire program in coming up with the design of a curve nozzle or a shape nozzle, which will give us the parallel flow at the exit and required pressure, required velocity is going to be quite expensive, if you do it this way. The easier method then is something that gives us the shape as the solution. We specify the exit conditions or the required conditions. Something that gives the shape as the solution will be an easier method, much more cheaper. And that is where method of characteristics comes in. The point here is the method of characteristics is applicable only to supersonic flows. It is not applicable to subsonic flows. So, therefore, the method of characteristics of course, for supersonic flows is widely used, because first of all it is simple and secondly supersonic portion is of importance. We have discussed that in the previous class, that the subsonic portion, the converging portion or subsonic portion is not that important, because since we have favorable pressure gradient, we can take any simple shape and that will give us a proper flow. Supersonic portion is the important part, where we need to have the design. So, method of characteristics then will gives us the initial shape. At present the practice is the initial shape we get from method of characteristics. Then we go to this, do the full analysis and check the validity of the initial design. That is a much cheaper approach and gives us much better solution. So, now we will focus on this method of characteristics. Method of characteristics depend on the fact that in supersonic flow, the influence of a small pressure difference is limited in a specific region. So, if you have a small pressure perturbation, it does not influence the entire flow field. It is limited to a particular region and the method of characteristics is build upon that. So, let us understand what I mean. Let us consider that I have a small source of pressure disturbance sitting here and we have a flow coming. This is a supersonic flow at a velocity u. This is source of pressure disturbance. It can be a loudspeaker, it can be a small pulse generator or something. Now, the flow is coming at supersonic speed. What happens is that we know that the disturbances propagate sound, particularly the compression waves or particularly the pressure waves, propagates through the air or the medium through sound waves. So, initially if the flow is subsonic, then let me put it this way. First let us look at a subsonic. First let us look at there is no flow. We have a source here. When this source propagates, it will propagate uniformly all around the disturbance.   This is unbiased stationary flow, the stationary condition.  This will change this pattern. So, now what happens is that more will be propagating on this side, less will be propagating on this side. So, there is a change in pattern. It may not look like this. There is a change in pattern. That is called biasing. As we keep on increasing this speed, still the flow is subsonic, some information will always propagate. There will be some effect of bias, but it will always propagate upstream also. If you keep on increasing the flow speed, when it becomes sonic, then now this information will just rarely be able to because what happens is that it is trying to go this side and the flow is coming on this side with the same speed. It will stop the information from propagating. When it becomes supersonic, then it will not propagate upstream at all. It will only go in the downstream region. So, then if I draw the schematic of propagation of this information, it will look like this, like a cone and this is how the information is going to propagate. We call point B. This is point A. So, at point A, we have a source of disturbance. This disturbance propagates with a like a spherical wave at a particular speed, which is the speed of sound. Now, the center of the spherical wave is moving downstream with a velocity u. This is the center of the spherical wave. This is moving downstream with a velocity u. So, at time t, it has moved from this location to this location and the distance between these two will be equal to u t because the flow is moving this source away. Now, at any time, if I look from time t equal to 0, it was here. Time t equal to t plus 0 plus delta t, it was here. Slowly, it is moving away and at every time, then depending on the time t, it is moving at certain location and it is going also. So, the influence of this, that is if I put a microphone here, it will not hear it. Only if the microphone is put here, it will hear this. So, the domain of influence is only limited to this cone and then, this cone is given by this angle alpha. So, to alpha, this is the limit of influence. So, the zone of influence is limited to a cone of half angle alpha here. Now, first of all, how do we get this half angle? At time t, the disturbance emitting from here is propagating with the speed of sound a. At time t, this source has reached this point. This distance is u t. The disturbance that emitted from here will reach this point. The distance will be a times t, where a is speed of sound. So, this is a t. So, the radius of this sphere is a t. So, at every location, that is how we get this radius. So, therefore, now this angle alpha, I am not drawn it properly, it will be something like this. So, angle alpha will be sine inverse a t by u t. This is my angle alpha, this is a t by u t. Actually, this will be h, p by h. So, I can cancel this thing and what is u by a? This mark number. So, therefore, this is equal to sine inverse 1 by m. So, or alpha will reach this point alpha equal to tan inverse a t upon square root of u t square minus a t square. This can also be written as tan inverse 1 upon m square minus 1. So, alpha is equal to tan inverse m square minus 1. Remember that I said at the beginning that is applicable only to supersonic flow and that is why it is coming from here. If mark number is less than 1, this becomes imaginary. We cannot define alpha. So, therefore, alpha is defined only if mark number is greater than 1. Even at mark number equal to 1, this is 0. So, it is infinite. So, that is something that is the limiting case. So, alpha is now the domain of influence rather the mark angle. Alpha is called the mark angle and this is the domain of influence for this sound source. So, this is how now the method of characteristics I will come to first. I have defined the mark angle alpha. Now, we will come to the method of characteristics. Let us consider now and this lines by the way are called mark lines. So, the limit of influence is essentially bounded by the mark lines. So, what do we see here? For this point here, what will be the angle of the mark lines given by alpha depends on the incoming flow mark number. So, essentially how much the mark lines will turn depends on the incoming flow mark number. So, that is what the mark line is. So, if I look at these two mark lines, this is the upstream of this mark line. If the flow upstream of a mark line is uniform like in this case, then what we can see here that the mark line is going to be straight line. That is what in this case is, but if this flow is not uniform, then at different locations we have different mark numbers, the mark line will curve. So, another point here is that on this domain of influence everywhere, the flow properties are uniform. So, within the limit of influence, the flow properties are uniform. Here, the flow is uniform coming in. Therefore, the mark line is straight. So, if you have a straight mark line, the flow properties are uniform downstream of the mark line. So, these are the few things that we actually use when we employ a method of characteristics that if we have uniform flow, the mark lines are straight lines and within the limit of influence, the flow properties are uniform. These are the things that we are going to use. Now, let us look at a nozzle and see that how we use this information in the case of a nozzle. So, let me now go to a proper nozzle, proper shaped nozzle. Let me consider a shaped nozzle like this. We are not still going to the full nozzle. I am just showing a part of it. This is our central line. We have a let us say supersonic flow coming here into this nozzle. Now, we have a point here a. From this point, here we have uniform flow. So, from this point, a mark line will emerge. Go like this. Since we are talking about a symmetric nozzle, just opposite side, there is another mark line, another point a dash from where another mark line will emerge and go like this. So, if nothing happens in between here and here, this mark lines will be straight and travel like this. But now, if this was a straight section, this is what is going to happen. But here it is curved. As it is curved, if I look at a supersonic flow over a curvature, what happens? The flow comes here. Because of the curvature, there is an expansion fan about it, it turns and then goes like this. So, it accelerates. So, the mark number here is greater than the mark number here because of this curvature. So, if I look at this small portion here, there is a curvature. Because of this, the flow is accelerated. So, now, if I come to this point, at this point the mark number is more than at this point. So, now, another mark line will emit from here and for that mark number, this is higher. This mark number is higher. So, what happens to alpha? So, this is reducing. So, alpha is increasing because sin alpha is 0, sin 0 is 0, sin 90 is 1. So, alpha is, mark number is increasing, alpha is reducing because sin inverse alpha is reducing. So, alpha is reducing. So, alpha decreases which means something that was at this angle now may be at this angle, slightly this angle. So, if I drop another mark line from here, it will go like this, right, slight decrease in mark angle. Now, if I look at these two, this mark line was straight with certain property, uniform property. This has straight with some other property, but these two mark numbers are different. So, when they intersect, they will bring in a change, right, which will be dependent on the mark number here and the mark number here. So, now, this mark lines will start to curve, right. It is no longer straight line because there are non-uniform properties merging. So, the mark lines will start to change. Let me draw it on the one side only. Similarly, from this side. So, we get a pattern like this. We get a pattern like this, like this. We get a pattern now. As you can see, this looks like a grid pattern. Where the mark lines are now intersecting at different points. So, we got a point D here, a point E here, like that. At different points, this mark lines are intersecting. Now, in between these two mark lines, the flow is still uniform. But now, since this and this mark line are different, these are two different mark lines. So, the uniform flow will neither be this nor be this. It will be a different condition, although it is uniform, but it will be a different condition. And that is how the flow will propagate. That when it goes along, there is going to be change in the mark number. So, now, this mark number change will depend on this curvature and the incoming flow mark number. So, the initial curvature that is provided that will dictate what kind of flow will be emerging. So, let me just summarize. Suppose, we have a uniform flow which enters the diverging portion of the nozzle here. The wall curvature initially, like we have shown here, will establish pressure gradients that are going to turn the stream lines. So, the stream lines are going to be turned. So, because the fluid will be flowing along the wall, like we have shown here, the stream lines are turned like this. Since, we are neglecting friction in this case, the fluid can be assumed to be sliding freely. So, the flow is like in this case in the expansion plan, it is sliding smoothly over the surface. So, at this point, we have a small variation in angle d theta.  And now, this disturbance will propagate along this line. From here to here. And at what angle it will move, depends on the incoming flow mark number. So, it creates a mark line there. Similar disturbance will be propagating from this point. So, this small curvature here, now is our source of disturbance. The flow was coming smoothly here. There is a small curvature that creates the disturbance. So, that is the initial point which creates the initial mark lines. So, these are the two mark lines that are created. Now, we have a continuous curvature at this point, beyond this. So, because of this curvature from every point, there will be mark line that will be coming up. And by the way, if I look at the mark lines here, the mark lines which are emitting from here are moving in this direction. The mark lines which are emitting from here are moving in this direction. The mark lines emitting from the lower duct wall are called left running mark lines. So, these are called left running mark lines. And emitting from the upper wall are called right running mark lines. So, this is the nomenclature that is used. So, we have left running mark lines and right running mark lines. And they are crossing each other in this exact manner as we have drawn here. Now, this designation of left running and right running refer to the direction in which the lines approximate to propagate approximately propagates or rather appears to propagate downstream to an observer looking downstream. So, if I look, let us say if you have a observer sitting here, observer is standing let us say at this point and looking downstream. And there that observer looks at this line. So, this line with respect to that observer is left. This line with respect to that observer is right. That is why these are called left running and these are called right running. So, observer is sitting here and looking downstream. That is why this nomenclature is used. Now, if I look at this region a b c or this region a prime b prime c prime let us say. If I look at this region or that region where if I look at this region there is only one type of mark line here. Of course, it is bounded by the other type. Similarly, on this region there is only one type of mark line bounded by other type here. So, it is only same type of mark line present in both of this. Whereas, we have already discussed that if we have a single type of mark line then the fluid properties are going to be constant just upstream or downstream of each line. So, if I look at this region the fluid properties are going to be constant. Similarly, in this region the fluid properties are constant. Of course, it is going to change from here to here because there are two mark lines that are present, but within a particular region the fluid properties are going to be constant the same type of mark number. So, specifying the properties along any streamline within this. Now, the stream lines are moving like this. Let us say choose this streamline. We specify the property along any streamline will specify that in that entire region. So, specifying the properties along any streamline will be sufficient to describe everything in that region. Now, what is our limiting streamline? The wall. So, if we can specify the property along the wall this is our limiting streamline then the properties all along these are specified within this zone. Of course, within this zone and this zone. So, specifying the wall properties will specify the properties in between everywhere. Now, let us see that what is happening in this region more closely. This region let us say that this point there is a curvature of d theta the flow is turning by amount d theta which is given here. Let us see that how do we get the property variations now when the flow is turning by this amount d theta. So, for that I will draw this diagram a bigger diagram to represent the flow. Let us consider this that we have a velocity coming in this direction u and the flow is turning by a small angle d theta because of that there is a mark line that is emitting. So, upstream mark number here is m this is the upstream mark number m the disturbance propagate at an angle alpha. So, this is my angle alpha this is the mark angle that we have already discussed and we can estimate alpha as tan inverse 1 upon m square minus 1. So, this now any fluid crossing this mark line will have a change in its direction. So, the stream line any stream line crossing the mark line must have a direction change. So, that it continues to be parallel to this wall. So, there is going to be a change in the direction. So, let me consider this this is the stream line it is coming here and this direction gets changed. So, now it moves in a manner parallel to this right. So, this is what is the change direction stream line is going to move and now just to draw an analogy this is like a Prandtl Mayer flow expansion path. So, we know that when the flow supersonic flow changes direction because of the increase in angle it accelerates. So, this velocity is going to increase. So, let us say the velocity now is u plus d u whereas, this flow velocity was u this is the same flow I am just drawing it on this side velocity is u. Then for this I can have a there is a change in direction now of the flow and this angle is alpha this is better.  So, if I draw this a triangle just for the increase d u d v this is the overall increase this is the vector diagram only for the change part.  So, the total velocity increases d capital d u. So, there is a if you look at this there is no change in momentum component parallel to the mark line parallel to the mark line it does not change. So, the change in velocity is particularly let me just this diagram is. So, the change in velocity is primarily in the v direction not in the u direction from this diagram we can get d v is u d theta this is my u this is u d theta d v is u d theta and d u from here is equal to this is the change in the x component. Let me write a different notation capital u for the actual velocity otherwise because I am representing the change also with the small u. So, I can write a different notation here. So, d v is equal to capital u d theta and d u is equal to d u which is the change in velocity.  So, this is equal to d u by u d theta right and tan alpha I know is equal to d u by u d theta this value. So, tan alpha is equal to 1 upon square root of m square minus 1 right. So, this is equal to 1 upon square root of m square minus 1. So, I can get now an expression for d theta that is the change in angle which is equal to square root of rather let me write this therefore, d u by u equal to d theta upon square root of m square minus 1. So, this is the change in velocity because of this change in angle and as we can see the change in velocity is function of the change in angle as well as the incoming flow mark number. So, based on that we get this expression. Now, from the definition of mark number u square is equal to m square gamma r t right and from isentropic flow assumption this actually is applicable to any adiabatic flow did not be isentropic. We get the isentropic relationship t naught by t given like this I can get t coming here.  So, the velocity now can be written as a function of t naught which is the stagnation temperature mark number that is more important is it can be written in terms of mark number. So, we have represented velocity in terms of the mark number now what we can do is we can differentiate this.  Let me call this equation 1 what actually what we are trying to do is to change get an expression for change in mark number when there is a curvature what we got is a change in velocity we want to represent it as change in mark number.  So, let me again see what we have done we have derived this expression here which is relating the velocity change to the angle change and of course, is function of the mark number. The velocity we have expressed in terms of the mark number then we differentiated that and got an expression for d u by u in terms of mark number and here we have a expression for d u by u in terms of theta and mark number when we combine this two we get this expression. So, what is this equation representing the change in mark number as a function of incoming flow mark number and change in angle theta d theta right. So, this is what we wanted to get because we have the curvature we want to know when there is a curvature how much change in mark number we can expect or we can estimate from that from this equation. So, the change in mark number here relate to a change in direction of streamline for isentropic flow because d theta is the change in direction of streamline and we are considering isentropic flow completely here this is something that you have to keep in mind that all this derivation isentropic flow is inherent. So, what we are doing now is completely for isentropic flow it is applicable only to isentropic flow. So, therefore, because this was isentropic this description this is isentropic. So, we are doing it for isentropic flow. So, this is the variation in mark number because of change in streamline which is brought about by change in this wall angle. So, now, once we have this mark number change we can estimate the change in other properties also d t by t will be equal to by just differentiating the isentropic relationships we can get this let me call this equation 3 this is a change in temperature. So, once again differentiating that isentropic relationship we get this and since we are talking about an isentropic flow without any work done there is no work done here an isentropic flow therefore, stagnation temperature remains constant. So, t naught is constant in this case therefore, when we differentiate this t naught goes away goes away similarly stagnation pressure is constant. So, we can take the isentropic relationship for pressure differentiate it we can get the relationship for change in pressure. So, that will be given by change in pressure relationship will be given as d p by p is equal to minus gamma by 2 t m square 1 plus gamma minus 1 by 2 m square let me call this equation 4. Similarly, we can get the change in density d rho by rho is minus d m square upon 2 1 plus gamma minus 1 by 2 m square let me call this equation 5. So, we have 5 equations listed here 1 2 3 4 5 all this equation actually represent the change in flow properties when the angle theta or the wall curvature is changed for a supersonic flow with the mach number m right. We are now getting a change in velocity change in mach number change in temperature pressure and density and this is what we wanted to estimate how the properties change when we have the variation in angle. So, now the wall curvature then is giving us all the required changes that we are looking for. So, the wall curvature now can be replaced here we have in this case what we have done is we have considered a small curvature right. So, using this small curvature which make the calculate this changes right. So, then what we can do is this is our finite curvature we can break it into many small curvatures right. So, for this we know how much is d theta we just get all this then come to this when we come to this point now this mach number has come from that solution and then we have another change in theta. So, another change will occur we can get the conditions here. So, we move downstream we keep on changing the wall curvature and we keep on changing getting the new flow properties because of change in wall curvature till we come to this point at the end. So, the wall curvature can be replaced by finite number of straight line segments right. So, this is a curved wall what we have done is we have removed replaced it by many many straight line segments. And thus, there is a change in the wall the flow properties in the flow field corresponding to each infinite symbol small turn can be calculated now right. So, if you break this curvature into many many small straight line curvatures we can calculate the entire property variation here during this third portion. Now, so what we have done so far once again go back to our original drawing we are now focusing on this portion only we are focusing on this is the straight line C A C B A dash B dash remember what I said is that in this portion either in this region or in this region there is only one type of mach line on this side we have all right learning mach lines here we have all left learning mach lines. So, therefore, the property variation essentially if I get the variation in the wall that is good enough. So, from here to here then knowing the wall curvature here I can get all the property variations and that is what we are doing. So, what we are doing is the from here to here we are breaking this wall into many small segments and calculating the variation here. And since for each of them we have the same property nothing changes. So, we can get the full property variation within this zone. So, this is the first part of our problem our problem actually has multiple parts. First part is when we have only single type of mach lines that we have now explained how to get the property variation one thing for this portion we need to know theta variation right. So, this curvature for this portion must be specified. So, for this portion it is not designed it is initial curvature is specified. So, we get all this from there. So, this theta variation is specified on this wall we get all this. Now, coming back to this now when we come to this zone. So, here do it just like this. So, as I as we have seen here this portion and this portion we have only single type of mach lines. When we come to this portion now we see that the mach lines are crossing left running and right running are crossing right. And not only that if I look at this domain it has come from here and here, but if I look at this one it has come from some other location right. So, therefore, this mach line up to this is ok when it crosses this it has also cross this mach line. So, the properties have changed here. So, at this point there is a different property when it comes here again is a different property whereas, this has seen only one change right. So, there is a continuous change in the properties. So, now we have mach lines crossing each other or the flow crossing each other with different properties and now that makes it little more complex. So, what now we have is intersection of two mach lines first of all it can be a intersection of one left running essentially always a left running and right running mach line will intersect. But the point is that these two mach lines may not have emitted from the same disturbance. So, therefore, the mach number and the flow properties corresponding to these two mach lines may not be same they can be same also. For example, if I look at this point this mach line and this mach line are same. So, when we come to this domain it has the same property, but this and this are there going going across they may not be coming from the same mach line or same emitted from the same property. In that case one mach line has emitted from a flow with mach M 1 other has emitted from a flow with mach M 2 and then the mach angles are going to be different for these two. So, that needs to be accounted for then we the next thing what we are going to see is that when the two mach line intersect how do the properties change and this is one part finally, what is our goal is to make the flow straight or design is not complete. So, next thing what we will do is we will look at how the mach lines intersect what will be the property variation and then so far here the wall itself was enough to give us the conditions. Now, we will design the wall curvature that what kind of the theta should be given here the theta was specified. Now, we will change the theta in such a way that we get finally, a uniform flow at the exit. Let us say this is our nozzle we will get a flow which is uniform like this. This is what we want to do for that first we have to understand how the properties will change when the mach lines intersect and the next is to complete the design. So, I think we have spent almost used up the time today. So, what I will do is I will stop here today in the next class we is first talk about the intersection of mach lines then continue with the design process using method of characteristics and finish this discussion. After that we talk little bit about plug nozzles which are other other type of shape nozzles and then the effect of friction we will talk about the effect of heated heat transfer we will talk about little bit there will be just small descriptions. The main focus in the next class will be completing this method of characteristics particularly when the mach lines cross each other what happens. So, I will stop here now in the next class we will continue from here.