Towards the derivation of hydrodynamics equations by the dimensional analysis method
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Mişcarea lichidelor. Hidrodinamică (33)
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Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (84)
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GROSU, Fiodor; BOLOGA, Mircea. Towards the derivation of hydrodynamics equations by the dimensional analysis method. In: Materials Science and Condensed Matter Physics. Ediția a 9-a, 25-28 septembrie 2018, Chișinău. Chișinău, Republica Moldova: Institutul de Fizică Aplicată, 2018, p. 249.
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Materials Science and Condensed Matter Physics
Ediția a 9-a, 2018
Conferința "International Conference on Materials Science and Condensed Matter Physics"
Chișinău, Moldova, 25-28 septembrie 2018

Towards the derivation of hydrodynamics equations by the dimensional analysis method


CZU: 532.5:519.6:517.958
Pag. 249-249

Grosu Fiodor, Bologa Mircea
 
Institute of Applied Physics
 
Disponibil în IBN: 11 februarie 2019


Rezumat

The notion of convective transfer when the value of F varies both at a given point (locally) and due to the motion of the liquid is widely used in the hydrodynamics:  , (1) where v is the velocity field. If the right-hand side of the equation (1) were known, then we would have an equation (law) for the evolution of the quantity F. Therefore, the essence of the derivation of the equations of hydrodynamics is the determination of the right-hand side. We propose to seek a solution in the following form ( is the correction factor, p is the pressure): (v , v , v ) x y zwhere k,l,m,n are exponents found from (2) by the dimensional analysis method. Example:  1. The equation for mass conservation (equation of continuity). Letting and adding the ―trial function‖ ( ) with a multiplier to the right-hand side of (1), we get the solution: F  2. The equation of convective heat conductivity. Starting from the dimensional equation  (4) 3. The equation of convective diffusion. Similar to the previous case  (5) 4. Equations of motion for an ideal fluid (Euler's equation).   (6) [ ( ) ] p t 6. Equations of motion for a viscous fluid (Navier-Stokes equation). The force of viscous friction:  (,) ( , , , ) m n k p p m=2; n=1;k=0. 2 2 M L T, (7) 2 () () rot(rot) 7. Navier-Stokes equation in the modern form  2 [ ( ) ] ( / 3) ( ) p t