Approximations of the Darcy–Weisbach friction factor in a vertical pipe with full flow regime

Abstract

Abstract The discharge in a full flow regime represents the discharge capacity of a vertical pipe, and the Darcy–Weisbach friction factor () is an important variable to calculate discharge. Since all existing equations for contain the Reynolds number (Re), it is problematic if the velocity is unknown. In this study, the performance of existing equations collected from studies on vertical pipes is assessed, and an approximation for the of vertical pipes in the full flow regime, without Re, is proposed. The performance of the Brkić and Praks equation is the best, with a maximum relative error (MRE) of 0.003% (extremely accurate). The MRE of the new approximation is 0.43%, and its assessment level is very accurate. This work is expected to provide a reference for the design and investigation of the drainage of vertical pipes.