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Circulation is the amount of force that pushes along a closed boundary or path. It's the total "push" you get when going along a path, such as a circle. A vector field is usually the source of the circulation. If you had a paper boat in a whirlpool, the circulation would be the amount of force that pushed it along as it went in a circle. The more circulation, the more pushing force you have.
Curl is simply the circulation per unit area, circulation density, or rate of rotation amount of twisting at a single point. Imagine shrinking your whirlpool down smaller and smaller while keeping the force the same: you'll have a lot of power in a small area, so will have a large curl. If you widen the whirlpool while keeping the force the same as before, then you'll have a smaller curl.
And of course, zero circulation means zero curl. Circulation is the amount of "pushing" force along a path. Curl is the amount of pushing, twisting, or turning force when you shrink the path down to a single point. Let's use water as an example.
Suppose we have a flow of water and we want to determine if it has curl or not: is there any twisting or pushing force? To test this, we put a paddle wheel into the water and notice if it turns the paddle is verticalsticking out of the water like a revolving door -- not like a paddlewheel boat :. If the paddle does turn, it means this field has curl at that point. If it doesn't turn, then there's no curl.
What does it really mean if the paddle turns? Well, it means the water is pushing harder on one side than the other, making it twist.
The larger the difference, the more forceful the twist and the bigger the curl. Also, a turning paddle wheel indicates that the field is "uneven" and not symmetric; if the field were even, then it would push on all sides equally and the paddle wouldn't turn at all. The fact that there is a "twist" means the field is not conservative this has nothing to do with its political views. A conservative field is "fair" in the sense that work needed to move from point A to point B, along any path, is the same.
For example, consider a river: its field is conservative. Sure, you can get a free ride downstream, but then you have to do work to get back to your starting point. Or, you can do work to move upstream, and get a free ride back. Either way, the amount of work you "put in" is the same as what you get back.Vorticity, Stream function, Bernoulli's equation
However, in a field with curl like a whirlpoolyou can get a free ride by moving in the direction of the twist. In a whirlpool, you can get a free trip by moving with the current in a circle. If you fight the current and go the wrong way, you have to use energy with no free ride at all. Conservative fields have zero curl: there are no free twists to push you along.
Alternatively, if a field has curl, it is not conservative. Gravity is another example of a conservative field. Technically, if you lift a rock and then let it fall, the energy you get from falling is the same as what you put in to lift the rock. Theoretically speaking, no energy was gained or lost in this transaction. To be technical, curl is a vectorwhich means it has a both a magnitude and a direction.In fluid dynamicscirculation is the line integral of the velocity fieldaround a closed curve.
In potential flow with a region of vorticityall closed curves that enclose the vorticity have the same numerical value for circulation. The circulation around a region of vorticity is the same for all closed curves that enclose the vorticity.
This is known as the Kutta—Joukowski theorem. This equation applies around airfoils, where the circulation is generated by airfoil action; and around spinning objects experiencing the Magnus effect where the circulation is induced mechanically. In airfoil action, the magnitude of the circulation is determined by the Kutta condition. The circulation on every closed curve around the airfoil has the same value, and is related to the lift generated by each unit length of span. Provided the closed curve encloses the airfoil, the choice of curve is arbitrary.
Circulation is often used in computational fluid dynamics as an intermediate variable to calculate forces on an airfoil or other body. Thus vorticity is the circulation per unit area, taken around a local infinitesimal loop. Correspondingly, the flux of vorticity vectors through a surface S is equal to the circulation around its perimeter. From Wikipedia, the free encyclopedia. Line integral of the fluid velocity around a closed curve. Solid mechanics. Fluid mechanics.
Surface tension Capillary action. Main article: Kutta—Joukowski theorem. Fox; Alan T. McDonald; Philip J. Pritchard Introduction to Fluid Mechanics 6 ed. Kuethe; J.
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In fluid kinematics I can't understand the meaning of these terms : vorticity and circulation. Can somebody give me a description of these terms so that a lay person can understand them easily? There are fundamental types of motion or deformation for a fluid element: translation, rotation, linear strain and shear strain.
Usually all these types of motion occur concurrently which makes the analysis of fluid dynamics somehow difficult. When it comes to expressing the rate of rotation of a fluid element it becomes quite challenging, Why?
Flow from A to B is rotational has voriticity while flow from A to C is irrotational has no vorticity. You can find many examples for rotational flows such as in wake regions behind blunt bodies and flow through turbomachines. According to this lecture :. Sign up to join this community.
The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. What is the meaning of vorticity and circulation? Ask Question. Asked 5 years, 3 months ago. Active 1 month ago. Viewed 13k times. Algo 1, 1 1 gold badge 12 12 silver badges 29 29 bronze badges.
Tarun M. Tarun 1 1 gold badge 3 3 silver badges 12 12 bronze badges. Active Oldest Votes. What does it mean?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. Is there any significance to that? Is there any heuristic way to think about circulation which helps understand the dimensions? The best way to gain intuition about circulation is to think of it as a measure of the number of vortex lines through a surface.
Vorticity is analogous to the electric current density, and velocity is analogous to the magnetic field. Circulation is a useful concept in fluid dynamics primarily because it obeys a conservation law in the absence of viscosity Kelvin's circulation thoerem. So instead of understanding the units via action as you had suggested, think about angular momentum instead.
And the conservation law for circulation that I mentioned above Kelvin's can be interpreted as conservation of angular momentum for the fluid. Don't confuse circulation with the vortex that produces it. Circulation is irrotational flow, vortices are rotational and are found in the boundary layer. The flux of the vorticity is circulation. In aerodynamic applications, I find it helps to understand its physical meaning by dividing the circulation by the distance it acts over i.
This velocity multiplied by the airstream velocity and by air density gives you the pressure difference that lifts the wing. The question is "What is the unit of circulation? Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. What do the dimensions of circulation mean, and how is circulation related to action?
Ask Question. Asked 8 years, 7 months ago.In Thomas Young introduced his Croonian lecture to the Royal Society on the function of the heart and arteries with the words: The mechanical motions, which take place in an animal body, are regulated by the same general laws as the motions of inanimate bodies For Young this was a natural approach to physiology; like many other scientists in the nineteenth century, he paid scant attention to the distinction between biological and physical science.
Indeed, during his lifetime he was both a practising physician and a professor of physics; and, although he is remembered today mainly for his work on the wave theory of light and because the elastic modulus of materials is named after him, he also wrote authoritatively about optic mechanisms, colour vision, and the blood circulation, including wave propagation in arteries. This polymath tradition seems to have been particularly strong among the early students of the circulation, as names like Borelli, Hales, Bernoulli, Euler, Poiseuille, Helmholtz, Fick, and Frank testify; but, as science developed, so did specialization and the study of the cardiovascular system became separated from physical science.
This process was not, of course, complete because collaborative work between scientists from different disciplines has always gone on. However, its scale was quite limited, and many medical and physiological workers found it difficult to comprehend because of their inadequate background in mathematics and mechanics, just as physical scientists found the complexity and empiricism of physiological studies, as well as the terminology, forbidding.
The separation caused by specialization has now assumed new importance. Over about the last twenty years physical scientists and engineers have made considerable contributions to the understanding of the mechanics of the circulation. These have strongly stimulated collaborative research, but at the same time have made the field increasingly difficult for those with a limited training in physics and mathematics.
Several recent reviews and monographs bear witness to the importance of this interdisciplinary work, but do little to help the medical reader, since they invariably assume an understanding of mechanics and are often quite mathematical in format. This book is an attempt to alleviate the problem. It is intended as an introductory text on the mechanics of the circulation which, so far as is practicable, avoids mathematical formulations and presents mechanics in readily comprehensible terms.
Our experience in teaching students of physiology and medicine, and cardiological physicians and surgeons, suggests that this approach is helpful, and it is to such a readership that the book is primarily directed.
In addition, we think that the book will prove useful to physical scientists, mathematicians, and engineers interested in the field, since it provides the relevant anatomical and physiological background to the mechanics, and gives definitions of terms and numerical data wherever possible.
The book is divided into two parts. The first part, 'Background mechanics', provides a non-mathematical outline of the physical processes and mechanisms which have general importance in the circulation. Thus it forms a physical introduction to the later material, though since it is self-contained and deals in a general rather than a specific way with solid and fluid mechanics and mass transport, it may also prove useful as a background to the study of systems other than the circulation.
The second part, 'The mechanics of the circulation', examines in some detail the physiological events that occur in the circulation and the physical mechanisms that underlie them.
Circulation (fluid dynamics)
It deals first with the relevant properties of blood and then considers the circulation systematically, starting with the heart and moving forward chapter by chapter through the circulation. No attempt is made to deal in detail with active physiological mechanisms such as reflexes, but the resulting changes in the physical properties of the system are studied. In each chapter the relevant anatomical and physiological background is presented first, followed by a discussion of the mechanics.
There is extensive cross-referencing to physical processes already examined earlier in the book; more specialized physical processes, relevant to the mechanics of a part of the circulation, are introduced as they arise. We have attempted to cover all the mechanical features of the circulation which are currently considered important.
However, the book is not intended as a research review, and we have therefore largely avoided citing original research references in the text.
Instead, we have provided a reading list for each chapter in the second part of the book, chosen to guide readers unfamiliar with the literature to suitable reviews and sources. In addition, we have, wherever possible, taken our illustrations from important sources, in many cases the original research literature, so that the references given in the Figure captions supplement the reading list. A temptation in writing an interdisciplinary book of this kind is to oversimplify, usually at the expense of one of the disciplines; we have tried hard to avoid doing this.
We have also tried, wherever possible, to supply numerical data; for convenience the more important measured and derived values, which'are referred to repeatedly throughout the book, are collected together in a table reproduced on the end-pages. The units used are those of the Systeme Internationale, though with quantities such as pressure, where confusion might arise, we have added the traditional units.
Since physical scale is important to so much of mechanics, and the dog is the only species for which anything like a comprehensive range of reliable measurements is available, we have given values from this animal throughout the book. Even so, we have had to turn to other species in describing the microcirculation, though this is a region where inter-species differences in scale appear to be relatively slight.The Project Team is formed by experienced, professional, tipsters whose target is to provide sport predictions which minimize the risk of loss of money.
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How Does It Works. Place single or multiple bets at your bookmaker. Introductory Offer: Join Us For Only 5 Euros. Each year, we ask some of the smartest people in journalism and digital media what they think is coming in the next 12 months. To promote and elevate the standards of journalismThe Nieman Journalism Lab is a collaborative attempt to figure out how quality journalism can survive and thrive in the Internet age. But next year is a good time to start.
But some of them will. Because there is an audience for it, and a market for it. We, the people who use media mostly as consumers and sharers, have to upgrade ourselves, too. Well, okay, maybe 20 or so. Every hire a journalism program makes must be able to teach courses in the digital realm. Do both deserve the same amount of attention. But with our journalistic institutions under threat economically, politically, and culturally, that bedrock is cracking.
So instead, we will acknowledge our strengths: Proximity.Latest Facebook live updates the weekend. Follow me live on Twitter or slightly delayed on this blog post. Here is where I will be blogging tonight, but I will also try to post everything on Twitter. And, here is my Facebook Live from today. Basically, Clinton has a small, but meaningful lead heading into debate. Clinton is still likely to win and other insights in my bi-weekly Facebook chat.
We discuss PA, ground game, Brexit, and nature of probability. Facebook Live talk about election updates (Clinton winning, but tighter), do not unskew polls yourself it is dangerous, and states are highly correlated. I comment on the weekend and 50-state polls. In short, deplorables comment is not very impactful.
Join me live at 1 PM ET on Thursday for next Facebook Live. Talked about the state of the election, debates, and took questions. Tune in live next time at 12 PM ET on Monday: Facebook. Next Facebook Live at 12 PM ET on Tuesday, September 6. Have a great Labor Day Weekend. Most recent Facebook Live on both the stability of PredictWise and what would happen if the election were held today.
I have started to do a Facebook Live question and answer every Monday and Thursday. Here is today (August 25, 2016) link. I just added two new posts (and, hoping for a third later tonight. But, I do not believe their topline numbers, because they should not be using 2012 vote as proxy for party identification.
Some thoughts on aggregating state-by-state predictions into topline election forecasts. No evidence of a Bradley Effect in polling.