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## MethodologiesIn the following some methodologies related to similarity and dimensional analysis will be introduced. We start with methodologies, like empirical identification of scales or identification of relevant parameters, the Parameter Approach. Basic models describing the phenomena under consideration are not required for this method. Instead a mathematically formal procedure can be applied to reduce the number of quantities to a minimum number of dimensionless quantities. The methods described in the following sections, the Law and Equation Approach, need some basic physical models or even a complete mathematical frameworks for the relevant phenomena. So, provided there is a good model - usually a set of differential equations - we can derive dimensionless parameters and even identify the relative importance of a single effect for a scenario. These methods do not require a broad understanding of the physics but simply assume that the problem is modelled correctly with these equations and that the analyst is able to identify the right representative quantities or scales. All methods yield dimensionless parameters or \Pi-numbers which have to be the same in the model and in the prototype to guarantee similarity: $$ {\Pi_i}^' = \Pi_i $$ From these conditions scale factors for basic quantities, like time, length, forces etc, can be derived, which can instruct the analyst in designing a model, model experiment respectively. |

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