Proposal of a new formula for the calculation of the Hazen-Williams coefficient

Abstract

The calculation of the head losses in pipes is done by  several formulas, like, Darcy (1875), Manning-Strickler (1885), Scobey (1920), or Hazen-Williams (1906); these formulas have the same calculation principle.

They compute the hydraulic gradient as a function of the flow rate Q, the diameter D and the coefficients indicating the roughness of the pipes (, C_HW and Ks, which are generally from tables).

The choice of Hazen-Williams coefficient C_HW is very complex, but this is not the case for the roughness, which a simple use of a roughness tester can accurately know.

The objective of this paper is to propose a relationship giving the Hazen-Williams coefficient taking into consideration all the parameters governing the flow, which are: the absolute roughness of the pipe e, the diameter D, the flow rate Q, the Reynolds number R, the kinematic viscosity ), using two methods (analytical and graphic).