Performance evaluation for darcy friction factor formulae using colebrook-white as reference

Abstract

Estimation of Darcy friction factor and pipe network analysis are essential ingredients in the design and distribution of potable water. Common formulae for friction factors estimate include Colebrook-White, Moody, Swamee and Jain, Barr, Haaland, Tsal and Wood formulae. Accuracy of pipe network analysis depends on Darcy friction factor, but little is known on update of these formulae and their performance in developing countries. In this paper, as a follow up on our previous studies, Oke (2007); Babatola et al. (2008) an overview and performance evaluation of these formulae is presented using statistical methods (model of selection criterion and statistical errors). Darcy Friction factor formulae were obtained from archive. These formulae were used to estimate friction factors in pipes at various Reynolds number and relative roughness. Estimated friction factors were evaluated statistically using absolute error, total error, mean error and model of selection criterion using Colebrook-White friction factor as the reference friction factor. Colebrook-White was used as reference because it is widely recommended formulae and has a wide range of Reynolds number. The study revealed that friction factor in pipes varies with the formulae and varies from 0.0157 to 0.0727. In all cases Tsal formula has the smallest friction factors. Based on the mean error, accuracy were in order of Newton Raphson > Prandtl and Nikurdse > Zingrang and Sylvester > Serghide > Barr > Swamee and Jain > Eck > Haaland > Brkic > Wood > Moody > Chen (1979) > Buzzelli > Sonnad and Goudar > Vatankhah and Kouchakzadeh > Monzon et al > Churchill (1973)> Jain > Round > Manadilli > Evangleids et al > Avci Kargoz > Tsal > Churchill (1977) > Chen (1985). It is concluded that Newton Raphson ; Prandtl and Nikurdse; Zingrang and Sylvester ; Serghide ; Barr; Swamee and Jain; Eck ; Haaland ; Brkic ; Wood and Moody are first choice friction formulae based on the values of model of selection criterion.

 Keywords: Darcy Friction Factor, Pipe Flow, Statistical Methods, Darcy Friction Formulae.