Strömungsmechanik in der Gestalt von Eigenparametern

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