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2015 | OriginalPaper | Buchkapitel

3. General Features of Fluid Mechanics

verfasst von : Roberto Mauri

Erschienen in: Transport Phenomena in Multiphase Flows

Verlag: Springer International Publishing

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Abstract

In this chapter we introduce some basic concepts of fluid mechanics. After observing in Sect. 3.1 that viscous effects are necessary to justify the existence of friction and drag forces, in Sect. 3.2 we define the Reynolds number, Re, as the ratio between convective and diffusive momentum fluxes, deriving a scaling of the drag force in the limits of small and large Re. Then, in Sect. 3.3, we observe that within these scaling laws there are some inconsistencies, which can be resolved only by introducing the concept of boundary layer. Finally, after a brief discussion on the boundary conditions, in Sect. 3.5 we present a brief qualitative overview of turbulence. A more complete description of this very complex subject can be found in Chap. 18.

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Vorheriges Kapitel Statics of Fluids

Nächstes Kapitel Macroscopic Balances

Note that the potential flow model, instead, can account for the existence of the so-called lift force, perpendicular to the flow direction, since by definition it does not do any work.

Jean-Baptiste le Rond d'Alembert (1717–1783) was a French mathematician, engineer, philosopher, and music theorist, who, in 1752, proved that potential flow theory results in the prediction of zero drag. It was a fortune that the brothers Orville and Wilbur Wright were not expert fluid dynamicists, so that they did not hesitate in starting their flight experiments well before Prandtl introduced the concept of boundary layer, thus explaining why airplanes can fly.

Named after the Irish fluid dynamicist Osborne Reynolds (1842–1912), although it was introduced first by George Gabriel Stokes in 1851. Starting from the consideration that the fluid motion in a pipe can only depend on the diameter of the tube, and the viscosity, density and mean velocity of the fluid, Reynolds understood that the number that bears his name is the only way these four quantities can be grouped together, forming a non-dimensional quantity (see Problem 3.1).

Named after the French physicist Jean Claude Eugène Péclet (1793–1857).

Ludwig Prandtl (1875–1953) was a German engineer. He is considered the founder of modern aeronautical engineering. In 1904 he published the seminar paper “fluid flow in very little friction,” where he described the boundary layer and its importance for drag and streamlining.

This analysis is valid only when the flow field is laminar (see Sect. 3.5).

In addition to the viscous drag, we should also take into account the pressure drag, which can also be traced to viscous effects.

Paul Richard Heinrich Blasius (1883–1970) was a German fluid dynamicist. He was one of the first students of L. Prandtl.

Actually, this analysis can be repeated also when Re ≪ 1. In this case, however, convective and diffusive effects balance each other very far from the wall, i.e. at a distance Δ ≫ L, such that Re _Δ = VΔ/ν = O(1). The technique of separating the outer region r > Δ, where convection prevails, from the inner region r < Δ, where diffusion is dominant, is called matched asymptotic expansion.

The smoother the pipe and the closer to the entrance, the more laminar the flow will be.

Named after Andrey Nikolaevich Kolmogorov (1903–1987), a Russian mathematician who worked on stochastic processes and turbulence.

Titel: General Features of Fluid Mechanics
verfasst von: Roberto Mauri
Verlag: Springer International Publishing
Buch: Transport Phenomena in Multiphase Flows
Print ISBN: 978-3-319-15792-4

Electronic ISBN: 978-3-319-15793-1

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-15793-1_3

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