An introduction is given to the theory of models and similitude as applicable in structural mechanics and hydrodynamics serving as a theoretical basis for some of the results of the subsequent papers of this course. Dynamical similarity exists between model and prototype, when the ratios of the different forces are the same in both situations. In structural mechanics the following forces are acting: elastic force divided in bending forces and shear forces, gravity force, inertial force, and external force. Herewith 4 dimensionless Numbers can be formed, which govern dynamical similarity. Especially in constructions acting upon by hydrodynamic forces the Cauchi number represents the ratio of the bending force to the external hydrodynamic force. In fluid mechanics the following forces can be present: steady as well as unsteady inertial forces, viscous force, pressure force, gravity force and capillary force. Complete dynamical similarity requires equableness of the dimensionless numbers of Strouhal, Reynolds, Euler, Froude and Weber. The relationships of these numbers with other numbers are discussed, such as Lagrange, Bond, Mach, Rossbey, Taylor, Cauchy, Thoma, Several examples are given for the use of these numbers to represent forces and moments on bodies in a fluid, viscous flow through a thin channel and rotating pumps.
Abstract