Explicit Determinations of the Colebrook Equation for the Flow Friction Factor by Statistical Analysis

• Published in: Chemical engineering & technology 2015-08, Vol.38 (8), p.1387-1396
• Main Authors: Heydari, Amir, Narimani, Elhameh, Pakniya, Fatemeh
• Format: Article
• Language: English
• Subjects: Approximation; Colebrook equation; Complexity; Complexity index; Fluid dynamics; Fluid flow; Friction factor; Mathematical analysis; Relative error; Response surface design; Turbulence; Turbulent flow
• ISSN: 0930-7516; 1521-4125
• DOI: 10.1002/ceat.201400590

The implicit Colebrook equation is considered as a fundamental equation for estimating the friction factor for turbulent flows in pipes. A large number of simple and accurate explicit approximations cover just a limited area of turbulent regime inside rough or smooth pipes. Here, three explicit approximations of the friction factor were determined. The friction factor data were fitted into polynomials using the response surface design of Minitab® software. To reduce the relative error of the first approximation compared with the implicit Colebrook equation, the domain was divided into two regions based on the Reynolds number (Re). To compare the accuracy and complexity of the approximations with existing relations, advanced comparison analysis based on the relative error was performed. The second set of approximations defined in two ranges of Re demonstrated high accuracy and a satisfying complexity index. In order to determine explicit equations of the friction factor, data of such factors resulting from an iterative solution of the Colebrook equation were fitted into three polynomials. Accuracy and complexity of the obtained approximations were compared with existing equations by advanced comparison analysis based on the relative error.