Review and analytical comparison of equations estimating the values of the Darcy friction factor

Abstract

The article presents explicit formulas used to calculate the Darcy factor and examines their accuracy and applicability in various operating conditions, i.e., at different values of Reynolds number and roughness. The obtained results were compared with those obtained from the commonly recommended Colebrook-White equation. Subsequently, a comparative analysis was conducted using indicators such as mean error, relative error, and maximum relative error. The Colebrook-White equation cannot be transformed into explicit form, requiring an iterative solution. Convergence of the linear resistance coefficient at a level lower than 0.1% typically requires at least 6 approximations. Ultimately, it was found that many available approximations of the Colebrook-White equation are highly accurate.