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The flow of rarefied gases through long tubes of circular cross‐section
Author(s) -
Datta Ravindra,
Rinker Robert G.
Publication year - 1981
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450590302
Subject(s) - knudsen number , laminar flow , kinetic theory , boltzmann equation , flow (mathematics) , simple (philosophy) , mechanics , physics , statistical physics , boltzmann constant , mean free path , cross section (physics) , free molecular flow , classical mechanics , thermodynamics , philosophy , epistemology , scattering , optics , quantum mechanics
A brief review is presented of various models of rarefied gas flow in long tubes. The complex treatments based on the Boltzmann equation provide only numerical solutions for the transition region unless some arbitrary assumptions are made, while those based on the traditional approach of simple kinetic theory have usually involved empiricism to a greater or lesser extent. An analytic expression is derived here based on a physically realistic model, making use of simple kinetic theory and containing no arbitrary assumptions. The model is completely predictive and adequately describes the flow in long tubes over the entire pressure range, from free‐molecule to continuum laminar flow, and also predicts the “Knudsen minimum” in the transition region. The concept of a “geometric mean free path” is introduced and appears to be useful in analyzing rarefied gas dynamics in a confined space. A relation is also obtained for the viscosity coefficient in the transition region.