Computer-based analysis of explicit approximations to the implicit Colebrook-White equation in turbulent flow friction factor calculation
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Tarih
2009
Yazarlar
Dergi Başlığı
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Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The implicit Colebrook-White equation has been widely used to estimate the friction factor for turbulent fluid-flow in rough-pipes. In this paper, the state-of-the-art review for the most currently available explicit alternatives to the Colebrook-White equation, is presented. An extensive comparison test was established on the 20 x 500 grid, for a wide range of relative roughness (epsilon/D) and Reynolds number (R) values (1 x 10(-6) <= epsilon/D <= 5 x 10(-2); 4 x 10(3) <= R <= 10(8)), covering a large portion of turbulent flow zone in Moody's diagram. Based on the comprehensive error analysis, the magnitude points in which the maximum absolute and the maximum relative error are occurred at the pair of epsilon/D and R values, are observed. A limiting case of the most of these approximations provided friction factor estimates that are characterized by a mean absolute error of 5 x 10(-4), a maximum absolute error of 4 x 10(-3) whereas, a mean relative error of 1.3% and a maximum relative error of 5.8%, over the entire range of epsilon/D and R values, respectively. For practical purposes, the complete results for the maximum and the mean relative errors versus the 20 sets of epsilon/D value, are also indicated in two comparative figures. The examination results for error properties of these approximations gives one an opportunity to practically evaluate the most accurate formula among of all the previous explicit models; and showing in this way its great flexibility for estimating turbulent flow friction factor. Comparative analysis for the mean relative error profile revealed, the classification for the best-fitted six equations examined was in a good agreement with those of the best model selection criterion claimed in the recent literature, for all performed simulations.
Açıklama
Anahtar Kelimeler
Fluid Mechanics, Turbulent Flow, C-W Friction Factor, Moody's Diagram, Closed Form Solution, Explicit Scheme, Analysis, Excel Spreadsheet, Techdig 2.0 Software
Kaynak
Advances in Engineering Software
WoS Q Değeri
N/A
Scopus Q Değeri
Q1
Cilt
40
Sayı
11
