Entropy and Probability Concepts in Hydraulics
Publication: Journal of Hydraulic Engineering
Volume 113, Issue 5
Abstract
The concept of entropy based on probability has been applied in modeling the vertical distributions of the velocity, shear stress, and (suspended) sediment concentration in open‐channel flows. A velocity distribution equation derived by the entropy‐maximization principle has advantages over the Prandtl‐von Karman universal velocity distribution equation. The (maximized) entropy functions derived for the velocity distribution and sediment transport are effective in reflecting the effects of the size of suspended sediment, coarseness of bed material, and sediment concentration. They can, therefore, be used as variables for characterizing and comparing various open‐channel flows. Through their sensitivities to the various parameters needed to describe the flow and sediment transport characteristics, the entropy functions can also be used to obtain much‐needed, new equations for the estimation of parameters difficult to determine owing to insufficient numbers of equations available. The entropy concept provides an excellent vehicle for introducing probability into hydraulics, and such an introduction makes dealing with uncertainties inherent in hydraulic processes possible and help developing sampling schemes, in addition to the modeling and parameters estimation mentioned earlier.
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References
1.
Chiu, C.‐L., “Stochastic Model of Motion of Solid Particles,” Journal of the Hydraulic Division, ASCE, Vol. 93, No. 5, Sep., 1967, pp. 203–218.
2.
Christensen, R., “Entropy Minimax Multivariate Statistical Modeling—I: Theory,” International Journal of General Systems, Vol. 11, Gordon and Breach Science Publishers, Inc., and OPA Ltd., 1985, pp. 23–277.
3.
Einstein, H. A., and Chien, N., “Effects of Heavy Sediment Concentration near the Bed on Velocity and Sediment Distribution,” Report No. 8, M.R.D. Sediment Sever, U.S. Army Corps of Engineers, Omaha, Neb., Aug., 1955.
4.
Goldman, S., Information Theory, Prentice‐Hall, Inc., New York, N.Y., 1953.
5.
Jaynes, E. T., “Information Theory and Statistical Mechanics I,” Physics Review, Vol. 106, 1957, pp. 620–630.
6.
Leopold, L. B., and Langbein, W. B., “The Concept of Entropy in Landscape Evolution,” Geological Survey Professional Paper 500‐A, U.S. Government Printing Office, Washington, D.C., 1962.
7.
Shannon, C. E., “A Mathematical Theory of Communication,” The Bell System Technical Journal, Vol. 27, Oct., 1948, pp. 623–656.
8.
Shore, J. E., and Johnson, R. W., “Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross‐Entropy,” Transactions on Information Theory, IEEE, Vol. II‐26, No. 1, Jan., 1980.
9.
Tchen, C. M., “Mean Value and Correlation Problems Connected with the Motion of Small Particles Suspended in a Turbulent Fluid,” dissertation presented to the Technische Hogeschool, at Delft, Holland, in 1947, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
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Copyright © 1987 ASCE.
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Published online: May 1, 1987
Published in print: May 1987
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