Discussion of “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation” by Saeed Samadianfard [ J. Pet. Sci. Eng. 92–93 (2012) 48–55

Dejan Brkić

doi:10.1016/j.petrol.2014.06.007

Abstract

Maximal relative error of the explicit approximation to the Colebrook equation for flow friction presented in the discussed paper by Saeed Samadianfard [J. Pet. Sci. Eng. 92–93 (2012) 48–55; doi. 10.1016/j.petrol.2012.06.005] is investigated. Samadianfard claims that his approximation is very accurate with the maximal relative error of no more than 0.08152%. Here is shown that this error is about 7%. Related comments about the paper are also enclosed.

Highlights

Samadianfard (2012) presents an approximate explicit formula as a replacement for the implicitly given Colebrook equation for fluid flow pipe friction
Error analysis Samadianfard (2012) claims that his approximation (2) [Eq (29) of the discussed paper] produces maximal relative error, ɷmax of no more than 0.08152% compared with the very accurate iterative solution of the implicit Colebrook equation, ʄ0
Samadianfard (2012), results are shown in Table 1 and compared with the results from Table 2 of the original paper by Samadianfard (2012)

Summary

Introduction

Samadianfard (2012) presents an approximate explicit formula as a replacement for the implicitly given Colebrook equation for fluid flow pipe friction. The empirical Colebrook equation (1) [Eq 1a of the discussed paper] relates the unknown flow friction factor (ʄ0) with the known Reynolds number (Re) and the known relative roughness of inner pipe surface (ɸ/D). 2. Error analysis Samadianfard (2012) claims that his approximation (2) [Eq (29) of the discussed paper] produces maximal relative error, ɷmax of no more than 0.08152% compared with the very accurate iterative solution of the implicit Colebrook equation, ʄ0. Samadianfard (2012), results are shown in Table 1 and compared with the results from Table 2 of the original paper by Samadianfard (2012) According to this second check, the maximal relative error ɷmax is about 6.9107% and mean (average) relative error in the range of applicability of equation is about 1.2595%. Samadianfard (2012) uses nonͲinteger power such as Reɸ/D which in computer environment usually means exp[(ɸ/D)ͼln(Re)] where ‘ln’ is natural (Napierian) logarithm (Clamond 2009)

Reference notes

Findings

Conclusion