Thermoelectric materials: Difference between revisions

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{{Other uses|Helmholtz theorem (disambiguation)}}
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In [[fluid mechanics]], '''Helmholtz's theorems''', named after [[Hermann von Helmholtz]], describe the three-dimensional motion of fluid in the vicinity of [[vortex]] filaments. These theorems apply to [[inviscid flow]]s and flows where the influence of [[viscosity|viscous forces]] are small and can be ignored.
 
Helmholtz’s three theorems are as follows:<ref>Kuethe and Schetzer, ''Foundations of Aerodynamics'', Section 2.14</ref><br />
'''Helmholtz’s first theorem:'''<br />
:''The strength of a vortex filament is constant along its length.''
'''Helmholtz’s second theorem:'''<br />
:''A vortex filament cannot end in a fluid; it must extend to the boundaries of the fluid or form a closed path.''
'''Helmholtz’s third theorem:'''<br />
:''In the absence of rotational external forces, a fluid that is initially irrotational remains irrotational.''
 
Helmholtz’s theorems apply to inviscid flows. In observations of vortices in real fluids the strength of the vortices always decays gradually due to the dissipative effect of [[Viscosity|viscous forces]].
 
Alternative expressions of the three theorems are as follows:<br />
1. The strength of a vortex tube does not vary with time.<ref>
The strength of a vortex tube ([[Circulation (fluid dynamics)|circulation]]), is defined as:
: <math>\Gamma = \int_{A} \vec{\omega} \cdot \vec{n} dA = \oint_{c} \vec{u} \cdot d\vec{s} </math>
where <math>\Gamma</math> is also the circulation, <math>\vec{\omega}</math> is the [[vorticity]] [[Vector (geometric)|vector]], <math>\vec{n}</math> is the normal vector to a surface '''A''', formed by taking a cross-section of the vortex-tube with elemental area '''dA''', <math>\vec{u}</math> is the [[velocity]] vector on the closed curve '''C''', which bounds the surface '''A'''. The convention for defining the sense of circulation and the normal to the surface '''A''' is given by the [[right-hand rule|right-hand screw rule]]. The third theorem states that this strength is the same for all cross-sections A of the tube and is independent of time. This is equivalent to saying
: <math>\frac{D \Gamma}{Dt} = 0</math></ref><br />
2. Fluid elements lying on a vortex line at some instant continue to lie on that vortex line. More simply, vortex lines move with the fluid.  Also vortex lines and tubes must appear as a closed loop, extend to infinity or start/end at solid boundaries.<br />
3. Fluid elements initially free of vorticity remain free of vorticity.
 
'''Helmholtz’s theorems''' have application in understanding:
:[[Lift (force)#Stages of lift production|Generation of lift]] on an [[airfoil]]
:[[Starting vortex]]
:[[Horseshoe vortex]]
:[[Wingtip vortices]].
 
'''Helmholtz’s theorems''' are now generally proven with reference to [[Kelvin's circulation theorem]]. However the Helmholtz's theorems were published in 1858, nine years before the 1867 publication of Kelvin's theorem. There was much communication between the two men on the subject of vortex lines, with many references to the application of their theorems to the study of [[smoke ring]]s.{{Citation needed|date=May 2008}}
 
== Notes ==
<references/>
 
==References==
* M. J. Lighthill,  ''An Informal Introduction to Theoretical Fluid Mechanics'', Oxford University Press, 1986, ISBN 0-19-853630-5
* [[Philip Saffman|P. G. Saffman]], ''Vortex Dynamics'', Cambridge University Press, 1995, ISBN 0-521-42058-X
* [[George Batchelor|G. K. Batchelor]], ''An Introduction to Fluid Dynamics'', Cambridge University Press (1967, reprinted in 2000).
* Kundu, P and Cohen, I, ''Fluid Mechanics'', 2nd edition, Academic Press 2002.
* George B. Arfken and Hans J. Weber, ''Mathematical Methods for Physicists'', 4th edition, Academic Press: San Diego (1995) pp.&nbsp;92–93
* A.M. Kuethe and J.D. Schetzer (1959), ''Foundations of Aerodynamics'', 2nd edition.  John Wiley & Sons, Inc. New York ISBN 0-471-50952-3
 
{{DEFAULTSORT:Helmholtz's Theorems}}
[[Category:Aerodynamics]]
[[Category:Fluid dynamics]]
[[Category:Theorems in mathematical physics]]

Latest revision as of 17:40, 3 January 2015

  • The surfaces of the teeth must be clean and without plaque. Not to mention you can be taught the importance of getting a good dietary diet and how that can go an extended way toward aiding you receive greatest final results from therapy strategies inside. Since it is a succulent, aloe vera has a high water content, but it also contains hundreds of active plant compounds known as phytochemicals, as well as a multitude of vitamins, enzymes, salacylic acid, amino acids, minerals, lignans, sugars and fatty acids. Based on the history and clinical findings of the patient, the etiology of the hyperpigmentation may include postinflammatory hyperpigmentation, drugs, photosensitizing agents, ultraviolet light, or systemic disease (eg, Addison disease, liver disease, pregnancy, pituitary tumors). When you file your nails, make sure you don't file in only one direction.

    The discoloration on your teeth may not be caused by actual staining but simply by plaque build-up, which is difficult to remove without the professional tools your dentist has. During the olden times, people made use of medicinal plants and other natural resources to treat their problems with aging skin. Wang and his colleagues have applied for patents in the United States, Japan and Taiwan. You can even give a photo a more artistic look by using plugins like Topaz Adjust and AKIVIS Art - Work. Papaya also contains antioxidants which can promote cell renewal plus could possibly also quit skin aging too.

    Research thoroughly all products associated with skin lightening by reading up on each product including what's in it, how it actually works to solve your skin problems, adverse effects as well as the maintaining aspects and other qualities of the products. CSC further disclosed that some of these products do not include formaldehyde as ingredients in their labels but were substituted with other ingredients that served as formaldehyde-releasing preservatives. Cigarettes can make your teeth turn yellow, but with the treatment, you can forget all about it and turn your smile into a brand new one. In order to improve the effect of whitening, people should deal with the accumulation of melanin. Stress is regarded as the biggest aspects within the spread of acne.

    Sugar with honey applied to our skin can exfoliate them just as well as the salons can. Doing this assures that the clay won't sink to the bottom of the soap. Hydrogen Peroxide acts as quite an effective whitener and you will find them in teeth whitening creams and hair color kits. Keep reading if you want to go darker or try red tints. You can make mint toothpaste by mixing half of a teaspoon of baking soda, half of a teaspoon of sea salt, a drop of clove oil and two drops of mint oil.

    Once you have identified the allergy you may have and start to treat it, you may find that your circles will begin to fade. Another hazard are the unknown effects of some of the synthetic ingredients the cosmetic industry is so prone to include in their products. The majority of those billions of dollars in revenue consist of products that women are using to make their skin fairer. In fact, people go to travel or even go outdoors in summer are easy to suffer the damage of sunshine. It is said that skin is the mirror of our inner body.

    If you loved this write-up and you would like to get additional info relating to how to lighten skin color [stylax.info] kindly check out the site.
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