Explicit pipe friction factor equations: evaluation, classification, and proposal

Abstract

The Colebrook equation has been used to estimate the friction factor (f) in turbulent fluids. In this regard, many equations have been proposed to eliminate the iterative process of the Colebrook equation. The goal of this article was to perform an evaluation, classification, and proposal of the friction factor for better development of hydraulic projects. In this study, Gene Expression Programming (GEP), Newton-Raphson, and Python algorithms were applied. The accuracy and model selection were performed with the Maximum Relative Error (∆f/f), Percentage Standard Deviation (PSD), Model Selection Criterion (MSC), and Akaike Information Criterion (AIC). Of the 30 equations evaluated, the Vatankhah equation was the most accurate and simplest to obtain the friction factor with a classification of very high, reaching a value of ∆f/f<0.5% and 1.5

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显式管道摩擦系数方程:评价、分类和建议

已使用Colebrook方程来估计湍流流体中的摩擦系数(f)。在这方面，已经提出了许多方程来消除Colebrook方程的迭代过程。本文的目的是对水力工程的摩擦系数进行评价、分类和建议，以便更好地开发水力工程。本研究采用基因表达编程(Gene Expression Programming, GEP)、Newton-Raphson和Python算法。采用最大相对误差(∆f/f)、百分比标准差(PSD)、模型选择标准(MSC)和赤池信息标准(AIC)进行准确性和模型选择。在评估的30个方程中，Vatankhah方程最准确，最容易获得摩擦系数，其分类为很高，达到∆f/f<0.5%和1.5<PSD<1.6。建立了新的方程，得到了显式f，收敛速度快，精度高。结果表明，GEP、误差理论和选择准则的结合提供了一个更可靠、更强的模型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。