The Performance of Explicit Formulas for Determining the Darcy-Weisbach Friction Factor

Abstract

The Darcy-Weisbach equation is the most recommended equation for determining the pressure loss in pressurized pipes because of its wide applicability. However, one of the largest obstacles to implementing this equation is the friction factor (f) calculation. This factor can be precisely determined using the Colebrook equation, which is implicit. Thus, the objective of this study was to compare six explicit equations for calculating the Darcy-Weisbach friction factor with the implicit Colebrook equation based on the relative error. Based on the results, the equations of Vatankhah and Offor & Alabi were the most highly recommended. These six explicit formulas showed a mean relative error of less than ± 1% compared to the Colebrook equation, except for the Swamee and Jain equation, for which the laminar regime generated a mean relative error of 1.83%.

Iterative calculation of local head loss coefficient of emitters in lateral lines

“…6), based on an absolute roughness (e) for PVC pipes of 0.00001 m (Carvalho & Oliveira, 2008). According to Rocha et al (2017) and Minhoni et al (2020), this equation can be applied to regimes laminar flow, hydraulically smooth turbulent flow, transitional flow, and rough turbulent flow. Furthermore, to quantify the Reynolds number (Eq.…”

Análisis de las pérdidas de carga en flujo turbulento en un laboratorio universitario de mecánica de fluidos

“…En la practica la dificultad de esta ecuación DW se centra en la determinación del factor de fricción (Cengel y Cimbala, 2018). Sin embargo, en la literatura es posible encontrar diferentes modelos matemáticos tanto de carácter implícitos como explícitos en función de dos números adimensionales: número de Reynolds (Re) y la rugosidad relativa de la tubería (k/D), para obtener el factor de fricción (Offor y Alabi, 2016;Zeghadnia et al, 2019;Minhoni et al, 2020). Una clasificación estándar del régimen de flujo de fluidos en tuberías circulares es (Cengel y Cimbala, 2018): Re<2300 (Régimen laminar); 2300<Re<4000 (Régimen de transición); y Re>4000 (Régimen turbulento).…”

Simplified Scobey formula for determining head loss in pressurized pipes

“…Among the head loss equations applied to pressurized pipes, the Darcy-Weisbach equation can be applied under any condition of velocity, temperature, roughness and Reynolds number (ALLEN, 1999;LI et al, 2017), being considered the most complete and, because of this, the most recommended equation (LAPERUTA NETO et al, 2011;GEISENHOFF, 2018;MELO et al, 2019;MINHONI et al, 2020). On the other hand, calculating continuous head loss with the Darcy-Weisbach equation is relatively difficult, since it involves separately the calculation of the friction factor, which is not considered to be simple (VON BERNUTH, 1990;JAMIL et al, 2020).…”