Improved method of determining friction factor in pipes

Abstract

Purpose -The purpose of this paper is to present an improved computational method for determining the friction factor for turbulent flow in pipes. Design/methodology/approach -Given that the absolute pipe roughness is generally constant in most systems, and that there are few changes to the pipe diameter, the proposed method uses a simplified equation for systems with a specific relative pipe roughness. The accuracy of the estimation of the friction factor using the proposed method is compared to the values obtained using the implicit Colebrook-White equation while the computational efficiency is determined by comparing the time taken to perform 300 million calculations. Findings -The proposed method offers a significant improvement in computational efficiency for its accuracy and is compared 28 of the explicit equations currently in use. Practical implications -This method enables a simplified equation to offer a significant improvement in computational efficiency for its accuracy and is easier to code, enabling engineers to more efficiently calculate frictional pressure loss for flow in pipes. Originality/value -Due to the complexities in flow regime and pipe roughness, there is a limit to the scope for further computational efficiency through simplification of the explicit equation. This paper presents a new method and simplified equation which combined are able to deliver results with similar accuracy to less computationally efficient explicit equations.

One-Log Call Iterative Solution of the Colebrook Equation for Flow Friction Based on Padé Polynomials

“…In this way the same accuracy is reached through the proposed less demanding procedure, after the same number of iterations as in the standard algorithm which uses -call in each iterative step. This is a good (Clamond 2009, Giustolisi et al 2011, Danish et al 2011, Winning and Coole 2013, Vatankhah 2018, Sonnad and Goudar 2004, Brkić 2012a, Winning and Coole 2015. The here presented iterative approach only introduces a computationally cheaper alternative to the standard iterative procedure.…”

“…Evaluated with various compilers and executed on various platforms, integer addition, subtraction, or multiplication requires less than 1 floating-point operation, float addition, subtraction, or multiplication about 1, float division 2-6, integer division 4-10, square root 5-20, while functions , , , as well and functions 10-40 floating-point operations. Winning and Coole (2015) (2, 3) is with polynomial of order 2 in numerator and of order 3 in denominator; Equation (6). Of course, low order formulas are simpler, but they have larger errors than high order formulas and vice versa.…”

Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on Wright-Omega Function

“…Further about accuracy of explicit approximations to the Colebrook equation can be found in Zigrang and Sylvester [37], Gregory and Fogarasi [38], Brkić [39,40], Winning and Coole [11,41], Brkić and Ćojbašić [42].…”

“…In computer environment, a logarithmic function and non-integer powers require more floating-point operations to be executed in the CPU compared with the simple arithmetic operations such as adding, subtracting, multiplication or division [10][11][12]. With the relative error of up to 0.0096%, the here proposed explicit approximation of the On the other hand, Biberg [4] adds division in the group of more expensive functions.…”

Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation – Numerical Validation

“…The exact solution to this equation does not exist with the exception of those through the Lambert -function [6][7][8], but anyway further the Lambert -function can be evaluated only approximately [9][10][11]. Many different explicit approximations of the Colebrook equation exist in the form , and they are with different degree of accuracy and complexity [12][13][14]. Many of approximations are based on internal iterative cycles [15][16][17] and therefore it is better to use more accurate iterative procedures if they require only few iterative steps.…”