Talk:Circulation (fluid dynamics)
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what (expletive deleted) are the units/dimentions for circulation???
m^2 s^-1 ???!!!
Yes (velocity times length). Linuxlad 07:47, 12 May 2006 (UTC)
More needs to be said about this.
The formula for lift based on this "circulation" parameter is a hypothesis only, contrived out of dimensional analysis, which is a necessary but not a sufficient condition for acceptability. A proof would require derivation from a known law like F = ma or a formal attempt to make it a law itself. Such attempts are readily discouraged by finding cases where it does not hold. Typically, wing profile designs try to optimize the lift force using it and in going to great lengths to shape the profile in so doing, such as by creating a large hump on its upper surface, one quickly finds that the credibility of this theory is stretched beyond allowable limits.
Yet in lieu of anything else to take its place, this is what is the basis for all modern day practice. For wind energy, in particular, which is still in its formative years, some serious concern exists here. AnthonyChessick 21:01, 30 July 2006 (UTC)
Two Points - this is a page on circulation, which has a clear mathematical derivation, and whose dimensionality is sufficiently stated earlier. Turning to the (Kutta-Joukowski) lift formula, (a bolt-on here, but still), see say Batchelor's Fluid Dynamics, formula 6.4.26. The formula is for a 2-d wing, force per unit span. It follows by integrating (the vector form of) F=integral (P.dA) around the surface of the body (or alternatvely by considering momentum flows). HTH Bob aka --Linuxlad 14:14, 25 July 2006 (UTC)
Under 6.4.26 on page 406 of my edition of Batchelor he goes on to say, "The remarkable side-force or 'lift' on the body, which is the foundation of the theory of the lifting action of aeroplane wings, arises from the combined effect of the forward motion of the body and the circulation round it, and is independent of the size, shape, and orientation of the body."
In giving his expertise some credit, I don't think he means this literally but only that he places all his analysis on the flows and is blind to how the body causes them. Still, in making bold statements such as this, he seems given to going to unusual lengths to support Kutta and Joukowski. This is a dangerous fascination with detailed intricacies that are unproven and whose support by the basic laws of motion is in some question and the fact that they have survived so well is only a testament to how strongly the modern world adheres to what is complex and a challenge to fathom thoroughly. The words themselves give away the tenuousness of this analysis. Derivative material from this that appears in other textbooks never includes the all-important momentum considerations and their authors can not really be faulted on this account.
The "Lift" entry has a cautionary statement that it is under some controversy but I would think that this same controversy extends here as well regarding the appearance of the lift formula using circulation, not to belabor this. AnthonyChessick 21:01, 30 July 2006 (UTC)
More can be said about the concept of the Circulation Parameter as a vehicle by which the Lift Force may be calculated. In the Mechanics branch of Physics, a vector cross product strikingly similar to the one shown in this article as handed down from the literature occurs in describing the force moment supporting a rotating body like a gyroscope while it precesses but does not fall to the ground. Can it be that early aerodynamics work actually conceived of the Lift Force as something coming out of the Coriolis acceleration of air depicted as rotating as described with a Circulation Parameter around the airfoil profile? If this is so and I hope it is not in support of what is in the books, then it is simply a non explanation of the Lift Force, an attempt to make it sound like the gyroscopic effect. Everyone is familiar with a hand held bicycle wheel that can be made to spin and then supported with a finger on one end of its shaft while it precesses and seemingly levitates. If this is so, again, this is not a valid mathematical tool by which Lift may be explained and the popularity with which this continues to be held requires it be clearly and meaningfully overturned. AnthonyChessick 17:22, 1 August 2006 (UTC)
A suggestion here is, in other words, to lay the Circulation Parameter to rest with a comment to this effect in the subject entry. Batchelor, and through him, Prandtl and Kutta and Joukowski, make many suppositions and hypotheses concerning fluid flow, such as use of an arcane velocity potential, three dimensional vector differentials especially those in curvilinear co-ordinate systems, the Kutta Condition, reliance on the inviscid nature of (and thus the near "disappearance of drag" at) high Reynolds Numbers, and many ad hoc parameters in their mathematical descriptions that are not defined in a Glossary. The resultant treatments of Fluid Dynamics appear to most sincere users as a problem of deciphering hieroglyphics and as suitable fodder for only computers with the application there even in doubt. This need not be. In other words, I find the material highly "kinematic", that is, with little attention to providing a guide to engineering realities involving averaged mass flows and momentum rather than spending time on unusual behaviors of fluid flows and unusual ways of presenting descriptions of them. The Lift Force is a prime example of this, not to present an invitation to engage in polemics over this observation. Anthony Chessick 17:50, 7 August 2006 (UTC)
