Relationship between Hazen–William and Colebrook–White Roughness Values

Despite advances in computing technology and derivation of explicit approximation formulas, the experimentally verified and widely applicable Colebrook–White friction factor formula is often rejected in favor of the limited and less accurate Hazen–Williams equation. The general reluctance of practicing engineers to embrace the Colebrook–White formula may be due to the relatively large available database for Hazen–Williams $C$ coefficient values versus a relatively small database of the equivalent sand roughness $k_s$ values required by the Colebrook–White equation. Until now, converting $C$ to $k_s$ required knowledge of both the Reynolds number and pipe diameter originally used to determine $C$ . The current effort derives implicit equations relating $C$ to $k_s$ that do not require additional information and compare well with published data. The exact solution is approximated with a single explicit equation, accurate to within 4% error.