﻿﻿ ﻿ ﻿﻿ Towards the derivation of hydrodynamics equations by the dimensional analysis method
 Articolul precedent Articolul urmator 96 2 Ultima descărcare din IBN: 2019-09-05 13:35 Căutarea după subiecte similare conform CZU 532.5:519.6:517.958 (1) Mişcarea lichidelor. Hidrodinamică (34) Matematică computațională. Analiză numerică. Programarea calculatoarelor (79) Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (118) SM ISO690:2012GROSU, 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. EXPORT metadate: Google Scholar Crossref CERIF BibTeXDataCiteDublin Core
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