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 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 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.

Friction factor and heat transfer of nanofluid in the turbulent flow through a 90° bend

2021 ◽  
Vol 33 (6) ◽  
pp. 1105-1118
Author(s):  
Pei-jie Zhang ◽  
Jian-zhong Lin ◽  
Xiao-ke Ku
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Flow Through

Measurement of Semi-Local Friction Factor of Gas Flow in Micro-Tube

2013 ◽  
Author(s):  
D. Kawashima ◽  
Y. Asako
Keyword(s):  
Surface Roughness ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Gas Flow ◽  
Flow Region ◽  
Nitrogen Gas ◽  
Gaseous Flow ◽  
Flow Through ◽  
Local Pressures ◽  
Measured Pressure

This paper presents experimental results on friction factor of gaseous flow in a PEEK micro-tube with relative surface roughness of 0.04 %. The experiments were performed for nitrogen gas flow through the micro-tube with 514.4 μm in diameter and 50 mm in length. Three pressure taps holes with 5 mm interval were drilled and the local pressures were measured. Friction factor is obtained from the measured pressure differences. The experiments were conducted for turbulent flow region. The friction factor obtained by the present study are compared with those in available literature and also numerical results. The friction factor obtained is slightly higher than the value of Blasius formula.

scholarly journals solutions of the CW equation for flow friction

2017 ◽  
Author(s):  
Dejan Brkić
Keyword(s):  
Fluid Flow ◽  
Friction Factor ◽  
Explicit Form ◽  
Iterative Procedure ◽  
Lambert W Function ◽  
Explicit Formulas ◽  
Flow Friction ◽  
Transcendental Functions ◽  
Flow Through

The empirical Colebrook–White (CW) equation belongs to the group of transcendental functions. The CW function is used for the determination of hydraulic resistances associated with fluid flow through pipes, flow of rivers, etc. Since the CW equation is implicit in fluid flow friction factor, it has to be approximately solved using iterative procedure or using some of the approximate explicit formulas developed by many authors. Alternate mathematical equivalents to the original expression of the CW equation, but now in the explicit form developed using the Lambert W-function, are shown (with related solutions). The W-function is also transcendental, but it is used more general compared with the CW function. Hence, the solution to the W-function developed by mathematicians can be used effectively for the CW function which is of interest only for hydraulics.

Heat transfer and friction factor of turbulent flow through a horizontal semi-circular duct

2010 ◽  
Vol 47 (4) ◽  
pp. 377-384 ◽  
Author(s):  
N. S. Berbish ◽  
M. Moawed ◽  
M. Ammar ◽  
R. I. Afifi
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Circular Duct ◽  
Flow Through
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