Research on physical (scale) models is based on the theory of similarity between the model and prototype. This theory provides guidance on the preparation of experiments, computation of model parameters, processing of results, limits of their validity and likely scale effects. In technical disciplines, including hydraulics, the theory of similarity is generally based on one of three approaches (or their combination):
The first approach determines the criteria of similarity from a system of homogeneous (differential) equations, which express the investigated phenomenon mathematically (see e.g. Section 5.5).
If no equations are available, we have to resort to the second path – dimensional analysis – which, on its own or together with sound empirical equations, may form the basis for determining the conditions of similarity. The use of dimensional analysis requires a careful preliminary appraisal of the physical basis of each investigated phenomenon and of the parameters influencing it; these may have to be determined by separate experiments. A combination of physical and dimensional analyses may have to be used to achieve the required results. For further details, see Section 5.2.
The third route could be denoted as the method of synthesis – see Section 5.3.