| The dispersion of soluble matter introduced into a slow stream of solvent in a capillary tube can be described by means of a virtual coefficient of diffusion (Taylor 1953a) which represents the combined action of variation of velocity over the cross-section of the tube and molecluar diffusion in a radial direction. The analogous problem of dispersion in turbulent flow can be solved in the same way. In that case the virtual coefficient of diffusion K is found to be 10\cdot 1av* or K = 7\cdot 14aU surd ¦Ã . Here a is the radius of the pipe, U is the mean flow velocity, ¦Ã is the resistance coefficient and v* 'friction velocity'. Experiments are described in which brine was injected into a straight 3/8 in. pipe and the conductivity recorded at a point downstream. The theoretical prediction was verified with both smooth and very rough pipes. A small amount of curvature was found to increase the dispersion greatly. When a fluid is forced into a pipe already full of another fluid with which it can mix, the interface spreads through a length S as it passes down the pipe. When the interface has moved through a distance X, theory leads to the formula S2 = 437aX(v*/U). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.
Taylor, G.I., 1953. Dispersion of soluble matter in solvent flowing slowly trough a tube, Proc. R. Soc. London, Ser. A, Vol. 219, pp. 186-203.
Lubach-2004-Heat and water vapour diffusivities.pdf
Heat and Water Vapour Diffusivities Near the Base of a Disturbed Stable Internal Boundary Layer
Journal Boundary-Layer Meteorology
Publisher Springer Netherlands
ISSN 0006-8314 (Print) 1573-1472 (Online)
Issue Volume 94, Number 1 / January, 2000
DOI 10.1023/A:1002402515319
Pages 23-63
Subject Collection Earth and Environmental Science
SpringerLink Date Saturday, October 30, 2004
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Heat and Water Vapour Diffusivities Near the Base of a Disturbed Stable Internal Boundary Layer
Johannes Laubach1, Keith G. McNaughton2 and John D. Wilson3
(1) Max-Planck-Institut f¨¹r Biogeochemie, Postfach 10 01 64, D-07701 Jena, Germany
(2) INRA-Bioclimatologie, B. P. 81, F-33883 Villenave d`Ornon Cedex, France
(3) University of Alberta, Edmonton, Alberta, T6G 2E3, Canada
Abstract We present results from an experiment that wasdesigned to investigate turbulent transportrelationships in a nearly homogeneous boundary layerdisturbed by unsteady wind swings, as found at thebase of an advective inversion with a convectiveboundary layer overhead. In such a situation wemeasured vertical gradients and eddy fluxes of temperature andhumidity at two heights. From these, the turbulentdiffusivities of heat and water vapour are obtained,and compared to the predictions of Monin-Obukhovsimilarity theory and those of a numericalsecond-order closure model. It is found that themeasured diffusivities exceed both predictions. Thisis interpreted as a consequence of the unsteadyconditions. It is also found that the diffusivity forheat is roughly 10% larger than that for watervapour. This is in agreement with a theoreticaltreatment of the unsteadiness effects that wedeveloped in an earlier publication. This result isnot reproduced by the numerical model because themodel has no provision for unsteady conditions. Ourresult disagrees with that from an earlier, verysimilar, field experiment, which may be due to asystematic underestimation of sensible heat flux in the older experiment. | 