Application of Probability and Entropy Concepts in Pipe‐Flow Study

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Abstract
A new velocity‐distribution equation based on the probability and entropy concepts is recommended as an alternative to the existing, power law and universal law equations for pipe‐flow studies. With only two parameters, the new equation can represent the velocity distribution in the entire flow field in a pipe, regardless of whether the flow is laminar or turbulent, and whether the pipe is smooth or rough. An application of this new velocity distribution equation has led to new equations relating the friction factor to entropy. A statistical method is also presented to analyze and quantify the uncertainty in the computed velocity distribution due to uncertainties in the related parameters or variables.

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