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 ks values required by the Colebrook-White equation. Until now, converting C to ks required knowledge of both the Reynolds number and pipe diameter originally used to determine C. The current effort derives implicit equations relating C to ks 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.