Investigation of Explicit Analytical Solution for Colebrook - White Equation of Airflow in Circular Pipe with or without Air Filter

Abstract

To determine the friction factor in turbulent flow through rough pipes, one popular model is the Colebrook-White equation. Yet because it is implicit, many explicit approximations have been developed to make its use simpler. As the bulk of known explicit formulations for the Colebrook-White equation, thirty "30" explicit analytical solutions are the focus of this work, which tries to examine and assess their accuracy. The research utilises a methodical assessment technique that is predicated on several factors, such as formula uncomplicatedness, maximum deviations, and comprehensive coverage of the Moody diagram spectrum. As a result of the study, which ranks the examined models from highest to lowest accuracy, the most realistic and correct explicit solutions are found.  The results provide guidance on the selection of the appropriate explicit approximation for various engineering applications and flow conditions, which benefits researchers and engineers working in fluid flow-related fields. They also advance the understanding and application of explicit analytical solutions for the Colebrook-White equation.