with α α and β β depending on the diameter and the type of pipe wall. Weisbach's work was published in the United States of America in 1848 and soon became well known there. In contrast, it did not initially gain much traction in France, where Prony equation, which had a polynomial form in terms of velocity (often approximated by the square of the velocity), continued to be used. Beyond the historical developments, Weisbach's formula had the objective merit of adhering to dimensional analysis, resulting in a dimensionless friction factor f. The complexity of f, dependent on the mechanics of the boundary layer and the flow regime (laminar, transitional, or turbulent), tended to obscure its dependence on the quantities in Weisbach's formula, leading many researchers to derive irrational and dimensionally inconsistent empirical formulas. It was understood not long after Weisbach's work that the friction factor f depended on the flow regime and was independent of the Reynolds number (and thus the velocity) only in the case of rough pipes in a turbulent flow regime (Prandtl-von Kármán equation).