Abstract
Three different types of flow are investigated, namely viscous flow, “no length” problems, i.e. flow along straight walls, and “single length” problems in the cases of the flow around geometrically similar objects, respectively, fully developed laminar or turbulent flow in straight tubes. With these types of flow a maximum number of four eigenparameters is identified, namely the two material properties: fluid density ρ F and viscosity μ, and two system parameters: characteristic length D and characteristic velocity u. With the help of these eigenparameters the respective dimensionless and invariant forms of the Navier–Stokes equation are derived. The invariant forms result in dimensionless coordinates and velocities in the form of ratios, respectively, Reynolds numbers. Aerodynamic resistance manifests in the form of single scaling factors with the dimensions of pressure gradients. In Part II of the paper exemplary applications, in particular with respect to the influence of fluid dynamics on the heat transfer, are discussed.
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