Improved algebraic, numerical, and graphical representations in fluid mechanics

The concept of equivalents is applied to fully developed flows through straight channels and two applications are introduced: the equivalents that produce equal rates of flow through channels of different cross‐sections, and the diminishment that occurs between the regimes of laminar and turbulent flow. This diminishment (i.e., the reduction of flow due to turbulence) is a counter‐intuitive finding, but it appears naturally when the flow equations in the two flow regimes are scaled appropriately for the same pressure gradient. The validity of the eddy diffusivity and the invalidity of the mixing‐length as measures of the shear stress due to turbulence have perhaps never before been demonstrated so clearly. The possible choices of primary variables and the consequences are also examined. The objective of these explorations is an improved understanding of the basic fluid mechanics by teachers, students, and industrial practitioners.