The Hazen-Williams equation is still widely used nowadays, despite its applicability limits that many research workers have highlighted. The equation contains a constant coefficient C which depends only on the material of the pipe. However, many studies have asserted that C should depend on both the relative roughness of the pipe and the Reynolds number. This dependence of C on the relative roughness and the Reynolds number was highlighted by Liou, in particular, through a relationship that interests the present study. A readjustment of Liou's relationship led to an implicit dimensionless equation that was translated into a C dimensionless diagram. Furthermore, the derived dimensionless relationship from the transformation of the Hazen-Williams equation, along with the dimensionless diagram, speeds up the slope of the energy grade line calculation. The dimensionless C relationship reaches a maximum for a given value of the relative roughness. A deep analysis of this relationship led to the successful establishment of the explicit dependence of C maximum on the relative roughness.


Hazen-Williams coefficient, Darcy-Weisbach, Galileo number, Dimensionless diagram.

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