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As two adjacent streamlines form the boundaries of the streamtubes, the mass flow rate through each streamtube must be conserved, i. To conserve the mass flow rate in the upper streamline as it becomes narrower, the fluid must flow faster. Similarly, to conserve the mass flow rate in the lower streamtube as it widens, the fluid must slow down. However, this does not explain how asymmetric airfoils with pronounced positive camber at zero angle of attack, as shown in the figure below, create lift. In fact, such profiles were successfully used on early aircraft due to their resemblance to bird wings.

Again, this theory does not explain all the physical phenomena we would like it to explain, and is therefore not the rigorous theory we are looking for. Asymmetric airfoil with pronounced camber [1]. Indeed, we can imagine a flow around a 2D cylinder shown in the figure below. The flow is symmetric from left-to-right and top-to-bottom and experiences no lift. If we now start the cylinder spinning at the rate in the clockwise direction shown, the velocity of air increases on the upper surface reduced pressure and reduces on the lower surface higher pressure.

This asymmetric flow top-to-bottom therefore creates lift. Note that the rotation of the cylinder has moved the stagnation point towards the rear end of the cylinder where the bottom and top flows converge downwards and therefore broken the symmetry of the flow. Hence, in this example, lift is created by a combination of a free-stream velocity and flow circulation, i.

Flow around a rotating cylinder that induces lift. In the example above, lift was induced by creating an asymmetry in the curvature of the streamlines. In the stationary cylinder we had streamlines curving in one direction on the top surface, and by the same amount in the opposite direction on the bottom surface. Rotating the cylinder created an asymmetry in streamline curvature between the top and bottom surfaces more curvature upwards then curvature downwards. We can create a similar asymmetry in the flow with a stationary cylinder by placing a small sharp-edged flap at the rear edge and positioned slightly downwards.

Real viscous flow might not necessarily flow as smoothly around the little flap as shown in the diagram below, but this mental model is a neat tool to imagine how we can morphologically transition from a rotating cylinder that produces lift to an airfoil. This is shown via the series of diagrams below. A similar streamline profile could also be created with a symmetric airfoil that introduces asymmetry into the flow by being positioned at a positive angle of attack.

If we consider purely stead-state flow and neglect the effects of gravity, surface tension and friction we can derive some very basic, yet insightful, equations that explain the induced pressure difference. Quite intuitively this argument shows that a force acting parallel to a streamline causes the flow to accelerate or decelerate along its tangential path, whereas a force acting perpendicular to the flow direction causes the streamline to curve. However, this approach is valid only along a single streamline. Flow along a straight streamline [2]. Flow along a curved streamline [2].

One positive characteristic of this theory is that it explains other phenomena outside our interest in airfoils. Vortices, such as tornados, consist of concentric circles of streamlines, which suggests that the pressure decreases as we move from the outside to the core of the vortex. This observation agrees with our intuitive understanding of tornados sucking objects into the sky. With this understanding we can now return to the study of airfoils. Consider the simple flow path along a curved plate shown in the figure below.

At point A the flow field is unperturbed by the presence of the airflow and the local pressure is equal to the atmospheric pressure. As we move down along the dashed curve we see that the flow starts to curve around the curved plate. Hence, the pressure is decreasing as we move closer to the airfoil surface and. On the bottom half the situation is reversed. Point C is again undisturbed by the airflow but the flow is increasingly curved as me closer to D. However, when moving from C to D, the pressure is increasing because pressure increases moving away from the centre of curvature, which on the bottom of the airfoil is towards point C.

Flow around a curved airfoil [2]. A couple of interesting observations follow from the above discussion. Nature typically uses thin wings with high camber, whereas man-made flying machines typically have thicker airfoils due to their improved structural performance, i. In the figure below, the deep camber thinner wing shows highly curved flow in the same direction on both the top and bottom surfaces. Deep camber thin wing with high lift [2]. Shallow camber thick wing with less lift [2].

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The more shallow camber thicker wing has flow curved in two different directions on the bottom surface and will therefore result in less pressure difference between the top and bottom surfaces. Thus, for maximum lift, the thin, deeply cambered airfoils used by birds are the optimum configuration. In conclusion, we have investigated a number of different theories explaining how lift is created around airfoils. Each theory was investigated in terms of the simplicity and validity of its underlying assumptions, and the diversity of phenomena it can describe. The centripetal forces that arise in the curved flow lead to a drop in pressure across the streamlines towards the centre of curvature.

This means that if a body leads to asymmetric curved streamlines across it, then the induced pressure differential arising from the asymmetry induces a net lift force. A previous version of this article referenced a misleading and incorrect example of a highly cambered airfoil as a counterexample to the theory of airfoils deflecting airflow downwards and the theoretical explanation using control volumes. Dr Thomas Albrecht of Monash University pointed this error out to me see the discussion in the comments and his contribution in improving the article is gratefully acknowledged.

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Physics Education 38 6 pp. Hi I enjoy your newsletters. They relate information in terms which can be understood by those other than engineers. Please check out my blog to see why I am interested in aerospace. Keep up the good work. Please correct this, it adds to the confusion as to how lift is generated, and discredits you as an aerospace engineer. Also, angle of attack is defined as the angle between free-stream velocity and the chord line. Free-stream velocity is the one very far away from the wing. In your figure, AoA is clearly non-zero ie, the camber line is not horizontal.

Hi Thomas, thank for your thoughtful comment. With the highly cambered wing I was trying to address the claim that an airfoil works simply by pushing air downwards, and as a reaction, the airfoil therefore experiences lift. So we draw a control volume around the airfoil, observe a net change in momentum in the vertical plane between the beginning and end of the control volume, and hence the airfoil encounters lift.

I have now included a new example of a rotating cylinder and a clearer explanation of what I meant. Thanks for pointing out the flaws in my thinking on this topic and let me know if you see anything wrong with the new example. Thanks, Rainer. Some more comments: OK, we seem to agree that explanation of pushing air downwards is correct. The flow must be extremely viscous to not separate and follow the curvature of the upper half of the cylinder. Such creeping flow is far from any practical application; also, if the flow is that viscous, it would probably creep around the sharp flap, as well.

For practical Reynolds numbers OTOH, the boundary layer would just separate once the pressure increases after the widest part of the cylinder, leaving the flap in the dead water zone basically ineffective. View all 11 comments. This story was soooo good!!! I loved it and i can not wait for the rest of the books!!! The truth is that i had no idea about this book until i stepped upon it on instagram and i thought so Why not??? It sounds like something that i would read and thank God that i got impulsive and dove in it!!!! Even though unrealistic in some parts!!!

But still If you have read Boys of Brayshaw High , then you're gonna enjoyed this book too!!! And from that moment, a shit storm is coming on her way in the form of a bitch mother, a powerful organization and four cocky, rich, gorgeous assholes that didn't leave her in peace!!! And the worst of them all is their leader, Sebastian Beckett!!! I really couldn't give a fuck what a bunch of rich kids thought about me.

What did I have to lose now? The boys are having their eyes upon her all the time and they are determined to break her But Riley is a tough kid and she is giving hell back and after a while, she is becoming a part of them, even if she didn't want to had anything to do with them Or did she??? All that pretty skin. Those bright blue eyes. When we're done with you, there won't be a piece of you untouched. It's not a reverse harem story this one!!! Yep, Riley will get attached to all of them Dylan, Evan, Jasper But her heart is being claimed by the worst of them all Riley is drown to him since day one He is getting under her skin all the time, but the things that are standing between them are too many Money and power are the worst of them all and an Elite that had planned their fate for far too long ago To learn to protect myself, because if there was one thing I knew about the heirs of Delta, they now had the power to really hurt me.

I couldn't let that happen. I had such little left in my life, if I lost one more thing I wasn't sure I'd survive. Will Riley fit in with the rest of the crew??? And for how long before shits will hit the fan??? Will Beck make her a priority or Delta will be always his priority??? And what the hell is really happening in there??? Too many secrets, lies and betrayals are lying in the air and i need some freakin' answers ASAP!!!!

What will happen after that awfully ending in here?? And we all have to play the game. She was a girl with personality and a badass attitude!!! She loved racing It was a part of her and she was actually a butterfly Free in her spirit And she couldn't be caged!!! I know that she is destined to greatness and i know that she will find her way after all And her love and caring for the guys was so beautiful!!!

Of course, her relationship with Sebastian was different and very intense!!! But there is actually a hope for these two??? I wouldn't touch you with a ten foot pole. No pretty exterior is worth the rotten interior.

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Call me crazy but I have standards. You want to tell me you don't feel this magnetic pull between us? That sexual tension that just keeps fucking building every time we're near? That's all in my head, is it? He was tempered, cocky, wild, gorgeous and soooo skilled I think that Sebastian has a very heavy load upon his shoulders and that's the reason that he can't be as open as he wants with Riley I also believe that he has real feelings for her, but Delta will always standing in their way Unless, they will do something for that!!! You're just everywhere.

In my fucking head. I can't I need to stop. This is not a world that works with That you'd stay away, because being near me is a death sentence But you're a part of this, whether we like it or not. So, maybe instead of pushing you away, I should hold you tighter. God, i loved them all!!! Dylan was always sooo serious and deadly But he had a heart of gold Jasper was sooo funny and silly He was the most approachable of them all.. As for Evan??? I disliked him for the "spare" comment, but he had proven himself The truth is that i would love to read their stories too!!!

I'm sure that they could be really interesting And some are harder to recover from. But this This is the only important thing we have. I think that Dante is a little bit shaddy, but still I liked him very much and i'm waited to find more about his role in all of that, because i"m sure that there are more to him!!! Of course, i hated Riley's biological mother and i don't trust her a bit!!!

Also the guys's fathers sucked!!!! I also need some fuckin' answers about Oscar's death!!! I'm positive that Riley's appearance in Delta wasn't sooo accidentally after all!!!! I need the next book as you can realize Especially aftert that damn cliffy!!! I'd given my trust to the heirs, and they had betrayed me. I'd given my heart to Beck, and he had smashed it into a million fucking pieces View all 26 comments.

Mar 18, Lindsey Marie rated it it was amazing. It had all the NA feels to it, but it was somewhat darker. If you enjoyed the Amo Jones Elite Series. Jun 30, Kim rated it it was ok Shelves: read-in , romance , kindle-unlimited , contemporary , new-adult.

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Mar 25, Kira rated it it was ok Shelves: abandoned-series , eyeroll-inducing , asshole-alpha , insta-love , over-the-top-drama , dark-romance , tstl-heroine , young-adult. So many things about this were ridiculous such as the rules at the school and way the Delta company worked. The boys were so amazing that they lived, according to them, through more than one plane crash because they were trained in survival.

Yeah right. These kids ranged in age from 17 to 20, but they were all in high school.

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It's beyond me as to why a 20 year old who is set to take control of a portion of a 2. It's beyond me as to why a 20 year old who is set to take control of a portion of a large business in a few months was still in high school. His family was insanely rich. They would have bought his way out of high school if he had been too dumb to graduate, which he wasn't. Despite all of them being young, the boys had extreme survival skills and their medical capabilities rivaled those of doctors.

They were also businessmen and highly trained killers. You know, just the usual things rich teens are. The situation with Riley didn't make a lot of sense either. Why would she have been given away especially when heirs were important? She went from being hated by the guys to loved overnight and vice versa. At first she hated her situation. As she learned more about the shitty situation she was being thrown into, she didn't care about the danger because the guys were her friends.

They were virtually strangers! She may not have had the various skills the guys did, but at 17, she was a legendary underground car racer. Once again, super realistic. It ended on a huge cliffhanger. I hadn't known exactly what would happen but view spoiler [the betrayal was expected. It proved that she was a pathetic kid in way over her head. Considering she was betrayed by everyone in her new life, I don't want to read the next book.

I don't want their poor behavior to be either explained away or forgiven. As far as the end goes, I'm guessing she didn't actually shoot anyone. If she did, I've lost all respect for her because she's their puppet. Broken wings was amazing! A bully romance with four hot Elite guys and a kick ass heroine Lies, deceit, broken trust, passion and a shit tonne of secrets.

The writing was amazing and I loved how action packed and fast paced the book was. Sebastian Roman motherfucking Beckett was just everything. Cold calculating, ruthless, sweet and gentle all rolled in to one. He is the king and I want to be his queen. A kick ass, take no shit, middle finger to anyone who questions her girl. Her inner dialogue was hysterical and had me LOL constantly. That ending I am not ok and I kind of need book 2 NOW!!

Enter the dark world of the Heirs of Delta and their queen View 2 comments. Mar 19, Rebecca ellis rated it it was amazing. This book probably has the most infuriating cliffhanger in cliffhanger history. So, just be prepared for that. Riley is such an amazing character. I absolutely love her and want to be her when I grow up. Dante is just I dont even know what to say about them.

Dylan can do no wrong. Yeah, I get that that's kind of a double standard but idfc. Fight me. I'm still kind of on the fence with Evan I'm still kind of on the fence with Evan and Jasper right now. We'll see. I just Tate and Jaymin pretty much nailed this. The two of them writing together is pretty much a wet dream for a reader like me.

So, yeah. Read this book. It's awesome and all that jazz. View 1 comment. May 08, Jina Bazzar rated it liked it. Will I sound a little crazy if I say this book would have been more believable if the main characters were some sort of supernaturals? Alpha werewolves, or shifters, or even fae or something ruthless? In any case, I read the whole story and overall it was a good read. Railey Jameson recently lost her parents where suddenly after a few days her biological mother appears who is one of the rich " fucking hell! Railey Jameson recently lost her parents where suddenly after a few days her biological mother appears who is one of the richest in the world as her family is a Deboise.

Her biological Family is rich and famous as they are a group of 5 who rules the world and now Railey had just become one of their pawns. Sebastian Beckett is the leader of the heir group as his parents are as well among one of the 5 families. He and his 4 friends rule are the schools and now it's their turn to rule over Railey as well, but little do they know who Railey Jameson actually is. It was still Illogical, but it was what it was.

A new young adult, dark book by Jaymin Eve where there are 4 boys and one girl trying to find themselves but bound because of their parents who rule over them. The story takes intresting twists and turns, it's funny, serious, mysterious, suspenseful and predominantly romantic as the relationship between Beck and Railey escalates over time.

Because hell yes he is! He is dominant, the leader of the group, cold, but sometimes sweet, possessive Like DAMN! The other guys in the group The four elite guys are nothing like the guys I have previously encountered with. They are all cold and knows how to put on a mask but deep inside they still want to live a normal life. The four hates their parents but bound to do what they say and that's why the four stick together because they have no one except themselves and now there is Railey as their fifth member. The book was great and I couldn't keep it down for a minute, it ends with a cliffhanger which made me scream and crave to read the next part!

Dark, crazy, illegal crimes, steamy sex, terror, suspense, hilarious, friendship bonding, family problems and many more things to look forward to in this book as I highly recommend it to read!!! May 26, Jessica rated it did not like it Shelves: ku-trash-read. Mar 22, BLuvsBooks rated it it was amazing. Just finished a reread! Fantastic characters, great writing, secrets, action, mystery, elite groups, rivalry and loyalties.

I loved the Heroine Riley and the four guys. Riley has lost her parents and gets sent to live with her birth parents during her senior year of high school.

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She is thrust in world with wealth and full of secrets and mystery. She meets her neighbors at the academy and soon find out they are heirs to the delta company. Car racing, fighting, surviving, friendship, love, and los Just finished a reread! Car racing, fighting, surviving, friendship, love, and loss ensue. Loyalty and Trust is tested. Who should she trust? Why is she there? So many questions! Mar 22, Christy Bailey rated it it was amazing. Such and amazing tailspin of a story. I can't even comprehend what I just read I just know it was amazing!

Such an emotional ride that I didn't want to put down once I started on it! I'm seriously hungover right now and can't wait for book two to come out. I need it asap! This was such a beautiful book with amazing characters! I loved it! Apr 04, Christina rated it really liked it Shelves: alpha , new-adult , highschool , bazillionaire. Besides the fact that this book is completely ridiculous, I liked it. May 23, Laci added it. Not a bad story or badly written to that point, I just couldn't get past the high school thing.

I know stories are fiction but I just couldn't move past thinking the actions of these characters didn't match the with the setting and age of the characters. So just a little to far fetched for this old lady. Mar 29, Ella Heart rated it it was amazing Shelves: awsome-books , must-read , popcorn , billionaires , misunderstanding-to-a-new-level , problem-children , rich-kids-with-problem , cliffhanger , guilty-pleasure. This like the worst kind of guilty pleasure there is.

Rich kid with problem and power. Broken Strong young college going boys - who had the first female member included. Sure the girl had faced many problem, and this book had many sexist things going on, but seriously i couldn't bring myself to care about that - at all. An 5 This book is a Damn Craving Stars I can't remember the last time when i giggled like a school girl and anticipated for the next thing to happen in a novel with an exited clap. And i know that's wrong, but no one can help themselves to stop eating chocolates when its right in front of you, no matter the kind of company it came from as long as it is tasty!

This book was exotic, funny, Sarcastic but most of all it was about family, friends and trust. It was so lovable and nice that it made me read the rest of the author books. And damn, if they weren't good. I hope you all enjoy reading this, because i certainly did. I would definitely recommend this book. It's a must buy. You won't regret it! Here are some lines that i enjoyed in this book:- Fucking hell, why are the hot ones always psychopaths.

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Apr 10, Emma James rated it it was amazing. Absolutely loved this book. The book I actually wanted to read is still processing on Amazon and isn't live yet, so I settled for another dark rich high school sort of story. It wasn't awful but it wasn't good either. The main idea about this book compared to other "rich academy with hot boys" novels is that the focus is less on the school part and more on the families and the like dark underworld of corporations and wealth.

Riley is the discarded daughter of a rich, powerful family we learn the mom abandoned her out of spi The book I actually wanted to read is still processing on Amazon and isn't live yet, so I settled for another dark rich high school sort of story. Riley is the discarded daughter of a rich, powerful family we learn the mom abandoned her out of spite I guess? Each of the families has an heir as a requirement to have a say within Delta and have a say and Riley is now the replacement for her older brother, Oscar, who has died.

It's necessary for Riley to be brought in as the replacement since her biological mom lost her uterus birthing Riley and is incapable of having more kids and to retain power there must be a blood heir. The heirs are tasked with fighting against competing corporations and what not with survivalist training and weapons and violence and Riley is brought into that fold and forms a like brotherhood bond with these four other heirs. The idea isn't bad honestly. But the issue is that we never scratch below the surface and things happen as rapid fire pacing within very little time.

Riley has like made an enemy of them on one page and a handful later she's like under their protection and having sex with Sebastian on the reg. I don't feel like the stakes or expectations or much of anything was established very well; for a book that wants to dive into politics of wealthy families and corporations it sure doesn't spend much time establishing things. You're just supposed to kind of rely on prior knowledge of secret rich people corruption to plug in the holes I guess and everything else is just supposed to realistically unfold in very little time.

I didn't really care for any of the characters or their relationships or anything. This book is pretty crass and crude.