 For a circular pipe with a fluid of density "ρ" and viscosity "μ", the hydraulic slope "S" can be expressed
In laminar flow (that is, with Re 
where we have introduced the Darcy friction factor "f""D" (but see "Confusion with the Fanning friction factor");
Note that the value of this dimensionless factor depends on the pipe diameter "D" and the roughness of the pipe surface ε.Furthermore, it varies as well with the flow velocity "V" and on the physical properties of the fluid (usually cast together into the Reynolds number Re).Thus, the friction loss is not precisely proportional to the flow velocity squared, nor to the inverse of the pipe diameter