Kelvin's circulation theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 30/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Kelvin%27s_circulation_theorem


00:01:26 1 Mathematical proof
00:09:07 2 Bjerknes' circulation theorem
00:11:31 3 See also
00:11:49 4 Notes



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SUMMARY
=======
In fluid mechanics, Kelvin's circulation theorem (named after William Thomson, 1st Baron Kelvin who published it in 1869) states In a barotropic ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time. Stated mathematically:

  
    
      
        
          
            
              
                D
              
              Γ
            
            
              
                D
              
              t
            
          
        
        =
        0
      
    
    {\displaystyle {\frac {\mathrm {D} \Gamma }{\mathrm {D} t}}=0}
  where 
  
    
      
        Γ
      
    
    {\displaystyle \Gamma }
   is the circulation around a material contour 
  
    
      
        C
        (
        t
        )
      
    
    {\displaystyle C(t)}
  . 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.
This theorem does not hold in cases with viscous stresses, nonconservative body forces (for example a coriolis force) or non-barotropic pressure-density relations.