Developments in unsteady pipe flow friction modelling

A review of the explicit friction factor equations developed to replace the Colebrook equation is presented. Explicit friction factor equations are developed which yield a very high degree of precision compared to the Colebrook equation. A new explicit equation, which offers a reasonable compromise between complexity and accuracy, is presented and recommended for the calculation of all turbulent pipe flow friction factors for all roughness ratios and Reynold’s numbers.

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Excel VBA-Based User Defined Functions for Highly Precise Colebrook’s Pipe Flow Friction Approximations: A Comparative Overview

10.20944/preprints202104.0177.v1 ◽

2021 ◽

Author(s):

Dejan Brkić ◽

Zoran Stajić

Keyword(s):

Pipe Flow ◽

Review Paper ◽

Iterative Scheme ◽

Accurate Solution ◽

Lambert W Function ◽

General Application ◽

Flow Friction ◽

Visual Basic For Applications ◽

Principal Branch ◽

Manual Tasks

This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User Defined Functions – UDFs written in Visual Basic for Applications – VBA, a common programming language for MS Excel spreadsheet solver. Accuracy of the friction factor computed using nine to date the most accurate explicit approximations is compared with the sufficiently accurate solution obtained through an iterative scheme which gives satisfying results after sufficient number of iterations. The codes are given for the presented approximations, for the used iterative scheme and for the Colebrook equation expressed through the Lambert W-function (including its cognate Wright ω-function). The developed code for the principal branch of the Lambert W-function has additional and more general application for solving different problems from variety branches of engineering and physics. The approach from this review paper automates computational processes and speeds up manual tasks.

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Compressibility effects on flow friction in a fully developed pipe flow

10.2514/6.1988-3586 ◽

1988 ◽

Cited By ~ 1

Author(s):

SREEDHARA MURTHY ◽

KEN GEE ◽

FRANK STEINLE

Keyword(s):

Pipe Flow ◽

Flow Friction ◽

Compressibility Effects

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Uncertainty of pipe flow friction factor equations

Mechanics Research Communications ◽

10.1016/j.mechrescom.2021.103764 ◽

2021 ◽

pp. 103764

Author(s):

Luiz Eduardo Muzzo ◽

Gláucio Kenji Matoba ◽

Luís Frölén Ribeiro

Keyword(s):

Friction Factor ◽

Pipe Flow ◽

Flow Friction

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Determination of the Darcy Pipe Flow Friction Factor as a Routine in Visual Basic for MS Excel

ANES/ASME 2006 Joint XXX ◽

10.1115/anes/asme2006-0016 ◽

2006 ◽

Author(s):

Ignacio R. Martín-Domínguez ◽

Ma. Teresa Alarcón-Herrera ◽

Jorge A. Escobedo-Bretado

Keyword(s):

Friction Factor ◽

Pipe Flow ◽

Visual Basic ◽

Flow Friction

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EXCEL VBA-BASED USER DEFINED FUNCTIONS FOR HIGHLY PRECISE COLEBROOK’S PIPE FLOW FRICTION APPROXIMATIONS: A COMPARATIVE OVERVIEW

Facta Universitatis Series Mechanical Engineering ◽

10.22190/fume210111044b ◽

2021 ◽

Vol 19 (2) ◽

pp. 253

Author(s):

Dejan Brkić ◽

Zoran Stajić

Keyword(s):

Pipe Flow ◽

Review Paper ◽

Iterative Scheme ◽

Accurate Solution ◽

Lambert W Function ◽

General Application ◽

Flow Friction ◽

Visual Basic For Applications ◽

Principal Branch ◽

Manual Tasks

This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User Defined Functions – UDFs written in Visual Basic for Applications – VBA, a common programming language for MS Excel spreadsheet solver. Accuracy of the friction factor computed using nine to date the most accurate explicit approximations is compared with the sufficiently accurate solution obtained through an iterative scheme which gives satisfying results after sufficient number of iterations. The codes are given for the presented approximations, for the used iterative scheme and for the Colebrook equation expressed through the Lambert W-function (including its cognate Wright ω-function). The developed code for the principal branch of the Lambert W-function has additional and more general application for solving different problems from variety branches of engineering and physics. The approach from this review paper automates computational processes and speeds up manual tasks.

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Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

Applied Sciences ◽

10.3390/app8112036 ◽

2018 ◽

Vol 8 (11) ◽

pp. 2036 ◽

Cited By ~ 18

Author(s):

Dejan Brkić ◽

Pavel Praks

Keyword(s):

Laminar Flow ◽

Turbulent Flow ◽

Pipe Flow ◽

Flow Regimes ◽

Hydraulic Model ◽

Friction Model ◽

Newtonian Fluids ◽

Turbulent Regime ◽

Flow Friction ◽

Switching Functions

This paper provides a new unified formula for Newtonian fluids valid for all pipe flow regimes from laminar to fully rough turbulent flow. This includes laminar flow; the unstable sharp jump from laminar to turbulent flow; and all types of turbulent regimes, including the smooth turbulent regime, the partial non-fully developed turbulent regime, and the fully developed rough turbulent regime. The new unified formula follows the inflectional form of curves suggested in Nikuradse’s experiment rather than the monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula uses switching functions and interchangeable formulas for the laminar, smooth turbulent, and fully rough turbulent flow regimes. Thus, the formulation presented below represents a coherent hydraulic model suitable for engineering use. This new flow friction model is more flexible than existing literature models and provides smooth and computationally cheap transitions between hydraulic regimes.

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New explicit correlations for turbulent flow friction factor

10.31219/osf.io/mazk2 ◽

2017 ◽

Author(s):

Dejan Brkić

Keyword(s):

Turbulent Flow ◽

Friction Factor ◽

Pipe Flow ◽

Single Phase ◽

Turbulent Pipe Flow ◽

Pipe Surface ◽

Flow Friction ◽

Total Absence ◽

Friction Factors ◽

Transient Zone

Two new correlations of single-phase friction factor for turbulent pipe flow are shown in this paper. These two formulas are actually explicit approximations of iterative Colebrook's relation for calculation of flow friction factor. Calculated friction factors are valid for whole turbulent flow including hydraulically smooth and rough pipes with special attention on transient zone of turbulence between them. Hydraulically smooth regime of turbulence does not occur only in total absence of roughness of inner pipe surface, but also, four new relations for this theoretical regime are presented. Some recent formulas for turbulent flow friction calculation are also commented.

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Suitability for coding of the Colebrook’s flow friction relation expressed by symbolic regression approximations of the Wright-ω function

Reports in Mechanical Engineering ◽

10.31181/rme200101174p ◽

2020 ◽

Vol 1 (1) ◽

pp. 174-179

Author(s):

Pavel Praks ◽

◽

Dejan Brkić ◽

Keyword(s):

Artificial Intelligence ◽

Asymptotic Expansion ◽

Pipe Flow ◽

Numerical Experiments ◽

Special Functions ◽

Symbolic Regression ◽

Lambert W Function ◽

Flow Friction ◽

Classical Formulation ◽

Speed And Accuracy

This article analyses a form of the empirical Colebrook’s pipe flow friction equation given originally by the Lambert W-function and recently also by the Wright ω-function. These special functions are used to explicitly express the unknown flow friction factor of the Colebrook equation, which is in its classical formulation given implicitly. Explicit approximations of the Colebrook equation based on approximations of the Wright ω-function given by an asymptotic expansion and symbolic regression were analyzed in respect of speed and accuracy. Numerical experiments on 8 million Sobol’s quasi-Monte points clearly show that also both approaches lead to approximately the same complexity in terms of speed of execution in computers. However, the relative error of the developed symbolic regression-based approximations is reduced significantly, in comparison with the classical basic asymptotic expansion. These numerical results indicate promising results of artificial intelligence (symbolic regression) for developing fast and accurate explicit approximations.

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