scholarly journals 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]

2017 ◽  
Author(s):  
Dejan Brkić ◽  
Brkic Dejan
Keyword(s):  
Gene Expression ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Relative Error ◽  
Energy Security ◽  
Gene Expression Programming ◽  
Security Systems ◽  
Flow Friction ◽  
Programming Analysis ◽  
Maximal Relative Error

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. ; JRC.F.3-Energy Security, Systems and Market

scholarly journals Very accurate explicit approximations for calculation of the Colebrook friction factor

2017 ◽  
Author(s):  
Žarko Ćojbašić ◽  
Dejan Brkić
Keyword(s):  
Genetic Algorithms ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Relative Error ◽  
Iterative Procedure ◽  
Iterative Solution ◽  
Flow Through ◽  
Maximal Relative Error ◽  
Looped Network

To date, the Colebrook equation is mostly accepted as an unofficial standard for calculation of the friction factor in turbulent flow through pipes. Unfortunately, the unknown friction factor in the Colebrook equation is given implicitly. Therefore, the implicit Colebrook equation has to be solved in an iterative procedure or using some of the appropriate explicit correlations proposed by many authors. Although the iterative solution is simple and very accurate, it can cause some problems during the calculation of looped network of pipes or similar systems of pipes. Therefore, explicit approximations are favorable in these cases. Up to date, the most accurate approximations have maximal relative error of no more than 0.14% compared to the very accurate iterative solution. Here two explicit approximations are presented, based on already existing models which are improved using genetic algorithms optimization. They are with the maximal relative error of no more than 0.0083% and 0.0026%.

scholarly journals Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

2017 ◽  
Author(s):  
Dejan Brkić ◽  
Žarko Ćojbašić
Keyword(s):  
Turbulent Flow ◽  
Friction Factor ◽  
Iterative Solution ◽  
Good Prediction ◽  
Pipe Surface ◽  
Flow Friction ◽  
Relative Roughness ◽  
Complex Models ◽  
Transient Zone ◽  
Maximal Relative Error

Today, Colebrook’s equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook’s equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook’s equation and its Moody’s plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

scholarly journals Prediction of Discharge Capacity of Labyrinth Weir with Gene Expression Programming

2020 ◽  
Author(s):  
Hossein Bonakdari ◽  
Isa Ebtehaj ◽  
Bahram Gharabaghi ◽  
Ali Sharifi ◽  
Amir Mosavi
Keyword(s):  
Gene Expression ◽  
Relative Error ◽  
Discharge Coefficient ◽  
Gene Expression Programming ◽  
Vertex Angle ◽  
Dimensionless Parameters ◽  
Labyrinth Weir ◽  
Predicted Values ◽  
Crest Length ◽  
Labyrinth Weirs

This paper proposes a model based on gene expression programming for predicting discharge coefficient of triangular labyrinth weirs. The parameters influencing discharge coefficient prediction were first examined and presented as crest height ratio to the head over the crest of the weir (p/y), crest length of water to channel width (L/W), crest length of water to the head over the crest of the weir (L/y), Froude number (F=V/√(gy)) and vertex angle () dimensionless parameters. Different models were then presented using sensitivity analysis in order to examine each of the dimensionless parameters presented in this study. In addition, an equation was presented through the use of nonlinear regression (NLR) for the purpose of comparison with GEP. The results of the studies conducted by using different statistical indexes indicated that GEP is more capable than NLR. This is to the extent that GEP predicts the discharge coefficient with an average relative error of approximately 2.5% in such a manner that the predicted values have less than 5% relative error in the worst model.

Estimation of the Darcy–Weisbach friction factor for ungauged streams using Gene Expression Programming and Extreme Learning Machines

2019 ◽  
Vol 568 ◽  
pp. 311-321 ◽  
Author(s):  
Heather Anne Milukow ◽  
Andrew D. Binns ◽  
Jan Adamowski ◽  
Hossein Bonakdari ◽  
Bahram Gharabaghi
Keyword(s):  
Gene Expression ◽  
Friction Factor ◽  
Gene Expression Programming ◽  
Extreme Learning Machines ◽  
Learning Machines
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