Performance of explicit approximations of the coefficient of head loss for pressurized conduits

Bruna D Pimenta,Luis H B Ben,Jardel H Kirchner,Wellington Mezzomo,Adroaldo D Robaina,Marcia X Peiter

doi:10.1590/1807-1929/agriambi.v22n5p301-307

Bruna D Pimenta, Luis H B Ben + Show 4 more

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https://doi.org/10.1590/1807-1929/agriambi.v22n5p301-307

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Abstract

ABSTRACT One of the parameters involved in the design of pressurized hydraulic systems is the pressure drop in the pipes. The verification of the pressure drop can be performed through the Darcy-Weisbach formulation, which considers a coefficient of head loss (f) that can be estimated by the implicit Colebrook-White equation. However, for this determination, it is necessary to use numerical methods or the Moody diagram. Because of this, numerous explicit approaches have been proposed to overcome such limitation. In this sense, the objective of this study was to analyze the explicit approximations of the f for pressurized conduits in comparison to the Colebrook-White formulation, determining the most precise ones so that they can be used as an alternative solution that is valid for the turbulent flow regime. Twenty nine explicit equations found in the literature were analysed, determining the f through the Reynolds number in the range of 4 × 103 ≤ Re ≤ 108 and a relative roughness (Ɛ/D) of 10-6 ≤ Ɛ/D ≤ 5 × 10-2, and obtaining 160 points for each equation. The performance index and relative error of the formulations were analyzed in relation to the Colebrook-White equation. Considering the equations analyzed, we found seven that presented excellent performance and high precision, highlighting the formulation of Offor & Alabi, which can be used as an alternative to the Colebrook-White standard equation.

Highlights

The estimation of head loss in pressurized conduits is a significant problem in optimization studies, hydraulic analysis of ducts, and water distribution systems (Bardestani et al, 2017).The Colebrook-White (1937) (CW) equation has been considered as the most accurate approximation for the determination of the head loss coefficient (f) and has been used as a reference standard; it uses the Reynolds number (Re) and the relative roughness of the pipe (Ɛ/D) (Heydari et al, 2015; Brkić & Ćojbašić, 2016) and is valid for a wide range of applicability: 2 × 103 < Re < 108 and 0 ≤ Ɛ/D ≥ 0.05
The objective of this research was to analyze some explicit approximations of the pressure loss coefficient for pressurized conduits, determining the most accurate ones so that they can be used as an alternative to the CW formulation
We can conclude that all explicit equations obtained a satisfactory performance for the estimation of the f when compared with the implicit CW formulation

Summary

Introduction

The estimation of head loss in pressurized conduits is a significant problem in optimization studies, hydraulic analysis of ducts, and water distribution systems (Bardestani et al, 2017).The Colebrook-White (1937) (CW) equation has been considered as the most accurate approximation for the determination of the head loss coefficient (f) and has been used as a reference standard; it uses the Reynolds number (Re) and the relative roughness of the pipe (Ɛ/D) (Heydari et al, 2015; Brkić & Ćojbašić, 2016) and is valid for a wide range of applicability: 2 × 103 < Re < 108 and 0 ≤ Ɛ/D ≥ 0.05. According to Brkić & Ćojbašić (2017), explicit approximations give a relatively good prediction of the f and can accurately reproduce the CW equation and the Moody (1944) diagram. In some of these explicit equations, their relative error is so small that they can be used directly instead of the CW equation (Çoban, 2012)

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