Darrigol O. Worlds of flow. A history of hydrodynamics from the Bernoullis to Prandtl (794382), страница 75
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Perhaps for the same reason, some of his output was brilliantly original. 7875 Hagen [1 854] p. 8 1 . Hagen believed that the maximum trans1atory velocity of the fluid, being superior to itsaverage velocity, could exceed the value for which the pressure becomes negative according to Bernoulli's law. Onhis establishing of the Poiseuille law, see Chapter 3, pp. 140-1 .76Hagen [1 854] pp. 80-1 .77Cf. Lamb [1913] pp. xv-xxi, Gibson [1946], Allen [1970].78Reyno1ds's duplicate discoveries include the deflection of sound in a velocity gradient (known to Stokes), thelaw of discharge of gases under pressure (known to Saint-Venant), and the internal cohesion of liquids (known toLap1ace); cf. Allen [1970] pp.
26-7, and J. J. Thomson, quoted ibid. p. 25: 'When he took up a problem, he did notbegin by making a bibliography and reading the literature about the subject, but thought it out for himself from246WORLDS OF FLOWReynolds did his famous work on the transition between laminar and turbulent flow inthe 1 880s. Two themes of his earlier research conditioned his approach. The first was theimportance of eddying motion in fluids, and the second was the dimensional properties ofmatter related to its molecular structure. A paper of 1874 on steam boilers brought the twothemes together. Reynolds puzzled over the rapidity of the transfer of heat through thesurface of the boiler.
His interest in this problem was not solely practical: 79The rapidity with which heat will pass from one fluid to another, through anintervening plate of metal, is a matter of such practical importance that I need notapologize for introducing it here. Besides its practical value, it also forms a subject ofvery great philosophical interest, being intimately connected with, if it does not formpart of, molecular philosophy.As an admirer of James Joule and James Clerk Maxwell, Reynolds had a deep·interest inthe kinetic molecular theory of heat and the resulting insights into transfer phenomena. Inthe boiler case, he concluded that ordinary diffusion bound to invisible molecular agitation did not suffice to explain the observed heat transfer. Adding to this process 'the eddiescaused by visible motion which mixes the fluid up and continually brings fresh particlesinto contact with the surface', he deduced the form A + Bv of the total heat transfer rate,where v denotes the velocity of the water along the walls of the boiler.
He also noted theanalogy with the Prony form av + m? of fluid resistance in pipes. 806.5.3 Revealing vorticesIn the same year, Reynolds encountered eddying fluid motion while investigating theracing of the engines of steamers. As British seamen had learned at their expense, whenthe rotational velocity of the propeller becomes too large, its propelling action as well as itscounteracting torque on the engine's axis suddenly diminish.
A damaging racing of theengine follows. Reynolds explained this behavior by a clever analogy with efflux from avase. The velocity of the water expelled by the propeller in its rotation, he reasoned, cannotexceed the velocity of efflux through an opening of the same breadth as its own. For avelocity higher than this critical velocity, a vacuum should be created around the propeller,or air should be sucked in if the propeller breaks the water surface.
81According to this theory, a deeper immersion of the propeller should retard the racing(for the efflux velocity depends on the head of water) and the injection of air next to itshould lower the critical velocity (for the efflux velocity into air is smaller than that into avacuum). While verifying the second prediction, Reynolds found out that air did not rise inbubbles from the screw, but followed it in a long horizontal tail. Suspecting some peculiarity of the motion of the water behind the screw, he injected dye instead of air and observedthe beginning before reading what had been written about it.
There is, I think, a good deal to be said for thismethod. Many people's minds are more alert when they are thinking than when they are reading, and less liable toaccept a plausible hypothesis which will not bear criticism.'79Reynolds [1874c] p. 81. Cf. Silver [1970].80Reynolds [1 874c] p. 82. Reynold's argnment is strikingly similar to that found in Saint-Venant [1838] on theadditional retardation caused by eddy formation in the pipes of steam engines (see earlier on p. 230).81Reynolds [1 874a]. Reynolds later elaborated on cavitation in fluids. Cavitation in turbines was alreadyknown to Euler, cf.
Ackeret [1957] p. L.TURBULENCE247a complex vortex pattern in the trail. Similar experiments with a vane moving obliquelythrough water displayed vortex bands issuing from the angles of the vane.From these observations, Reynolds inferred that hidden vortex motion played 'asystematic part in almost every form of fluid motion'.
These considerations came we11after Helmholtz's famous paper of 1 858 on the theory of vortex motion, and afterThomsen's, Tait's, and Maxwell's involvement in a vortex theory of matter. Reynoldsconvinced himself, in conversations with William Froude and William Thomson, that hisforerunners had only seen the tip of the iceberg. The foJlowing year he brought invisiblevortex formation to bear on a phenomenon well known to sailors, namely, the power thatrain has to calm the sea.
Letting a drop of water falJ on calm water covered by a thin layerof dye, he observed the formation of a vortex ring at the surface folJowed by a downwardvertical motion. When the drops of rain falJ on agitated water, he reasoned, part of themomentum of this agitation is carried away by the induced vortices, so that the agitationgradualJy diminishes. 82Reynolds made vortex motion the subject of a popuJar conference at the Royal Institution in 1 877.
He began by promising a revelation:In this room, you are accustomed to have set before you the latest triumphs of mindover matter, the secrets last wrested from nature from the gigantic efforts of reason,imagination, and the most skillful manipulation. To-night, however, after you haveseen what I shall endeavour to show you, I think you will readily admit that for oncethe case is reversed, and that the triumph rests with nature, in having for so longconcealed what has been eagerly sought, and what is at last found to have been sothinly covered.He went on with the failure of hydrodynamics to account for the actual motion of fluidsand propounded that this failure was due to the lack of empirical knowledge of theirinternal motions.
83Reynolds then recalled casual observations of vortex rings above chimneys, from themouth of a smoker, or from Tait's smoke box. These rings had only been studied 'for theirown sake, and for such light as they might throw on the constitution of matter.' ToReynolds's knowledge, no one had understood their essential role in fluid motion. This hecould reveal 'by the simple process ofcolouring water', which he had first applied to elucidatethe motion of water behind a prope1ler or oblique vane. By the same means, he studied thevortex rings formed behind a disc moved flatly through water.
The resistance to the disc'smotion appeared to be caused by the continual production and release of such rings. 84Reynolds emphasized that 'imagination or reason had failed to show' such forms offluid motion. Everyone knew the impotence ofrational hydrodynamics, but 'it wouJd seemthat a certain pride in mathematics has prevented those engaged in these investigationsfrom availing themselves of methods which might reflect on the infallibility of reason.'Only with hints from colored water could mathematicians proceed further:85Now that we can see what we are about, mathematics can be most usefully applied;and it is expected that when these facts come to be considered by those best able to do83Reyno1ds [1877a] p. 1 84.'2Reyno1ds [1 877a] p.
188, [1 875].84/bid. pp. 187, 191.85Jbid. pp. 185, 191.WORLDS OF FLOW248so, the theory of fluid motion will be placed on the same footing as the other branchesof applied mechanics.6.5.4 The dimensional properties ofmatterMeanwhile, Reynolds became interested in what he called 'the dimensional properties ofmatter'. The context was an attempt to explain the working of William Crookes's radiometer by evaporation from the black side of its vanes. According to the kinetic theory ofgases, Reynolds reasoned, the ejection of a molecule from the surface of a vane implies arecoil of this vane with a momentum opposite to that of the molecule.
Through specificexperiments, he verified that the evaporation of a liquid caused a pressure on its surface. Inan appendix to the ensuing paper, he noted that Crookes's effect could also be explainedby surface heating: the adsorbed molecules of the residual gas leave the dark side of a vaneat a higher velocity than those of the silvery side.
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