7. Dimensional Analysis The purpose is to reduce the number of parameters or variables upon which a physical phenomenon depends. Variables like U , , , etc. will be rearranged as to eliminate the fundamental units. 7.1. Geometrical similarity In order for two fluid flows to be similar, the shape of the bodies involved must be geometrically similar; i.e. can be obtained from one another by scaling all dimensions by the same factor. 7.2. Dynamic similarity Flows which can be obtained from one another by scaling the dependent and independent variables, provided certain non-dimensional parameters are the same, are said to be dynamically similar. The magnitude of different forces, like pressure, viscosity, etc. acting at a given non-dimensional location and time are in the same ratio. This is more difficult to achieve * What are these non-dimensional parameters? * How can they be found? 68
7.3. Buckingham Pi Theorem Given the quantities that are related by a physical law, the number of dimensionless
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