Relationship between Hazen-William coefficient and Colebrook-White friction factor: Application in water network analysis

Although Darcy-Weisbach (D-W) equation has been accepted as a standard resistance equation in pressurized flow, some researchers and engineers still prefer to utilize Hazen-Williams (H-W) equation for analyzing water distribution networks (WDNs) in practice. The main difference between roughness coefficients of these two resistance equations is that D-W friction factor varies with Reynolds number of flow field while H-W coefficient is usually considered as a fixed value for a specific material. In this paper, discrepancies between solving three pipe networks using these two resistance equations are investigated. These networks were solved using two hydraulic solver named gradient algorithm and finite element method assuming different values for roughness values. In order to compare the results, equivalent friction factors based on these two resistance equations were required to be used. In this regard, several methods for computing equivalent roughness values were selected from the literature. The first category uses Reynolds number and pipe diameter data for converting D-W friction factor to H-W coefficients and vice versa. On the other hand, the second one is exclusively a function of pipe diameter. The obtained results demonstrate that errors of solving networks with H-W coefficients are not significant in comparison with the results obtained by the D-W equation. More importantly, the method, which only exploits pipe diameter for roughness conversion, is appeared to be not reliable for some cases considered in this paper.