In this paper, explicit friction factor formulae (Fff), which is a function of Reynolds number (Re) and relative roughness (Rr) were updated and evaluated. Fff were obtained from archive and conduct performance evaluation. Performance evaluation of the Fff were conducted using relative error; model of selection (MSC) and the Akaike Information Criterion (AIC) using Colebrook-White's friction factors as the reference Ff. The study revealed that there are 47 Fff in use. The growth of the Fff can be grouped into four subgroups based on the pattern and into three subgroups based on number of authors and into three subgroups, based on the accuracy. The growth rates were combinations of linear and exponential based on the pattern. The study revealed that Fff provided the lowest relative error of less than 1.00%, the highest MSC of greater than 6.64 and the lowest AIC of less than -34324.17. The study concluded that the recent and third generation Fff are the best and using Microsoft Excel Solver for calculating Ff in the pipe flow systems is a good tool for engineers.
TopIntroduction
Water and solutions are used in many technological and engineering processes (chemical, mechanical, water treatment and distribution, biomedical and pharmaceutical processes). Movement of these essential materials in the reservoir is channeled by the conservation of mass, momentum, and energy. Applications of these movements range from the low-temperature condition in gas liquefaction to high temperatures and pressures in rocket momentum systems. Actual design of all these processes requires an accurate knowledge and values of the fluid transport parameters in the pipeline and channel systems. In a specific situation, viscosity of the liquid, diameter of the pipes and tubes coupled with the friction factor are needed to calculate headloss and energy requirement in the channel and pipeline systems. A precise value of friction factor is necessary in the computation of headloss and the energy. In mechanical, chemical, water supply and biomedical processes, numerous factors are involved in the pipe network and liquefied transport systems. In medical sciences and biomedical engineering, conveyance of a physiological liquid takes place through the catheter tube into the body of a human being, which indicates that accurate computation of Ff in the catheter is an significant factor to discharge adequate liquid. Some of these significant design factors in the pipeline systems are the lengths, diameters and Ff of the pipes, water level in the reservoirs, head-discharge characteristics of the pump, water demands at different nodes and performance characteristics of different valves and minor elements in the pipe systems (Gupta and Bhave, 2007; Özger and Yıldırım, 2009a; 2009b).
Parts of these parameters in pipe network systems remain fixed at different periods of the pipe, while some parameters would fluctuate during the life span of the pipe systems. The fluctuating parameters can be considered to be imprecise parameters. Basic equation for computing the head loss in the pipe network and pipeline system is either Hazen-Williams or Darcy-Weisbach equation that requires calculation of Ff. Darcy – Weisbach equation is expressed as follows:
(1a).
(1b)Colebrook – White’s formula presented an implict expression for calculating Ff. The expressions are (Colebrook and White 1937; Colebrook, 1939; Mahendra, 2008; Mehran and Ayub, 2011; Oke et al., 2015a):
(2a)(2b)(2c)where; λ is the friction factor; k is effective roughness size of the pipe wall and Re is the Reynolds number.