New explicit correlation to compute the friction factor under turbulent flow in pipes¹

Nova correlação explícita para calcular o fator de atrito sob fluxo turbulento em tubos

HIGHLIGHTS

The correlation facilitates the calculation of head losses in hydraulic systems.

The correlation was design for regimes of high and low turbulence.

The best performance of the correlation is obtained for a range of roughness that goes from 10^-2 to 5 × 10^-3.

Key words:
Colebrook’s equation; pressure drop in pipes; maximum relative error

ABSTRACT

Colebrook’s implicit equation has been widely used to estimate the friction factor in pipes under turbulent flow. This friction factor is used to calculate pressure drops to solve different problems and applications of Engineering such as the design of water distribution systems. Many researchers have proposed explicit approximations to estimate the friction factor without carrying out iterative calculations. In this study, a new explicit correlation is given to determine the friction factor in cylindrical pipes under turbulent flow. This study allows evaluating the characteristics of the new explicit approximation of the friction factor and compare them with the value obtained using Colebrook’s equation and with other explicit approximations developed by several authors. This has allowed finding a new equation of simple structure and of few mathematical operations that approximates the value of the friction factor with a maximum relative error of 1.60% with respect to the value solved for Colebrook’s equation.

Key words:
Colebrook’s equation; pressure drop in pipes; maximum relative error