Entropy as a Probability Concept in Energy-Gradient Distribution

by Cao Shuyou, San Diego State Univ, United States,
Howard H. Chang, San Diego State Univ, United States,

Document Type: Proceeding Paper

Part of: Hydraulic Engineering


The concept of entropy based on probability theory instead of thermodynamic principle has been applied to study the distribution of energy gradient along alluvial rivers. The formulas of dimensionless energy gradient distribution and dimensionless longitudinal profiles are derived in this paper by the entropy-maximization principle and the calculus of variations. These formulas cover all of three kinds of river longitudinal profiles: uniform, concave, and convex. The differences among these profiles are attributed to the variations of flow, sediment, and boundary conditions of the river reach. Comparisons of analysis with field data for three kinds of longitudinal profiles appear to support the entropy maximization principle as applied to the distribution of energy gradient. The correlation coefficients for all cases investigated are greater than 0.992, the standard deviations are less than 0.17, based on the regression analysis of field data and analytical results.

Subject Headings: Field tests | Regression analysis | Entropy methods | Probability | Power transmission | Probability distribution | Hydraulic gradients | Rivers and streams

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