Număr Reynolds

Numărul Reynolds (Re) este o mărime adimensională folosită în mecanica fluidelor pentru caracterizarea unei curgeri, în special a regimului: laminar, tranzitoriu sau turbulent.

Conceptul a fost introdus de George Gabriel Stokes în 1851,[1] dar a fost numit după Osborne Reynolds (1842–1912), care l-a popularizat în 1883.[2][3]

Definiție

Numărul Reynolds este raportul dintre forțele de inerție și forțele de frecare viscoasă. Expresia sa matematică este:[4]

unde:

  • este viteza fluidului, în [m/s],
  • este dimensiunea caracteristică, în [m],
  • este masa volumică a fluidului, în [kg/m³],
  • este viscozitatea dinamică a fluidului, în [Pa.s],
  • este viscozitatea cinematică a fluidului, în [m²/s] ().

Unitățile indicate (în SI) sunt informative, deoarece numărul Reynolds fiind adimensional, valoarea sa este aceeași în orice sistem de unități coerent.

Calitativ, numărul Reynolds poate caracteriza raportul dintre transportul momentului forței prin convecție și cel prin difuzie.

Numărul Reynolds și regimul de curgere

Curgerile la care numărul Reynolds este mare decurg turbulent, iar cele la care este mic decurg laminar. Pentru curgeri în țevi, un număr Reynolds peste 4000 indică o curgere turbulentă, iar unul sub 2100 o curgere laminară. Domeniul care corespunde curgerilor cu număr Reynolds între 2100 și 4000 este considerat de tranziție.[5]

Note

  1. ^ en Stokes, George (). „On the Effect of the Internal Friction of Fluids on the Motion of Pendulums”. Transactions of the Cambridge Philosophical Society. 9: 8–106. 
  2. ^ en Reynolds, Osborne (). „An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels”. Philosophical Transactions of the Royal Society. 174 (0): 935–982. doi:10.1098/rstl.1883.0029. JSTOR 109431. 
  3. ^ en Rott, N. (). „Note on the history of the Reynolds number”. Annual Review of Fluid Mechanics. 22 (1): 1–11. doi:10.1146/annurev.fl.22.010190.000245. 
  4. ^ Remus Răduleț și colab. Lexiconul Tehnic Român, București: Editura Tehnică, 1957-1966.
  5. ^ en Flow in pipes, sciencedirect.com, Fig.7.7, citând pe Yasuki Nakayama, Introduction to Fluid Mechanics, (Second Edition), 2018

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