For an irrotational vortex, the circulation is zero along any closed contour that does not enclose the vortex axis; and has a fixed value,, for any contour that does enclose the axis once.
12.
In figure 2 the key col of peak A is at the meeting place of two closed contours, one encircling A ( and no higher peaks ) and the other containing at least one higher peak.
13.
(Note that, per Stokes's theorem, the closed line integral of H�dl around a contour is equal to the open surface integral of curl H�dA across the surface bounded by the closed contour.
14.
But a closed contour in the punctured plane might encircle one or more of the poles of ? ( " z " ), giving a contour integral that is not necessarily zero, by the residue theorem.
15.
The reason for this is that Burnt Mountain's elevation is estimated between and, based on 40-foot closed contours . } } The mountain is also considered to be the southern terminus of the Blue Ridge Mountains.
16.
However, it is impossible, in general, to synchronize clocks along a closed contour : starting out along the contour and returning to the starting point one would obtain a ? " x " 0 value different from zero.
17.
The imaginary axes on the two sheets point in opposite directions so that the counterclockwise sense of positive rotation is preserved as a closed contour moves from one sheet to the other ( remember, the second sheet is " upside down " ).
18.
Stated more simply this theorem says that if one observes a closed contour at one instant, and follows the contour over time ( by following the motion of all of its fluid elements ), the circulation over the two locations of this contour are equal.
19.
:At risk of spoiling some joke Basins tend to fill with water, so a small closed contour more often represents a peak; dry hollows are the exception, marked as described . talk ) 04 : 22, 26 May 2008 ( UTC)
20.
I can understand if he is put off by complex mathematical theories or well-established scientific explanations, because those require either a certain level of comprehension or a blind trust in " smarter " scientists who DO understand . ( I mean, I can write out some Maxwell equations and take a Cauchy integral and prove beyond any reasonable doubt that there is no way to have a " continuous never ending force-field " around a closed contour . . . but that requires knowledge of some higher math ! ) So my ( dis ) proof of the concepts in the machine might be worthless to the man.
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