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The cumulants of the distribution of concentration of a solute dispersing in solvent flowing through a tube

Published online by Cambridge University Press:  29 March 2006

P. C. Chatwin
P. C. Chatwin
Affiliation:
Department of Applied Mathematics, The University of Liverpool
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Abstract

The mean distribution of concentration of a solute over the cross-section of a tube through which a solvent is flowing is given approximately by the solution of an equation of the heat-conduction type (Taylor 1953, 1954). One solution of this equation is a Gaussian curve but observed distributions are normally not Gaussian. On the basis of an equation derived by Chatwin (1970) it is shown here that the deviation of an observed distribution from the Gaussian curve with the same mean and variance is not determined by the heat-conduction equation, although the practical importance of this remark may be small if the initial distribution of solute is greatly elongated along the tube axis.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 51 , Issue 1 , 11 January 1972 , pp. 63 - 67
Copyright
© 1972 Cambridge University Press

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References

Aris, R. 1956 Proc. Roy. Soc. A 235, 67.
Chatwin, P. C. 1970 J. Fluid Mech. 43, 321.
Kendall, M. G. & Stuart, A. 1958 The Advanced Theory of Statistics, vol. 1. London: Griffin.
Sayre, W. W. 1968 J. Hyd. Div., Proc. A.S.C.E. 94, 1549.
Taylor, G. I. 1953 Proc. Roy. Soc. A 219, 186.
Taylor, G. I. 1954 Proc. Roy. Soc. A 223, 446.