![]() Unfortunately, it is not always possible to match all relevant similarity parameters at a smaller scale, and only partial similarity may be possible. In that case, engineers can usually study the physical characteristics of the full or larger-scale system (e.g., one still in the design process) at a smaller scale and under the controlled environment of the laboratory or in the wind tunnel. Suppose all of the relevant similarity parameters for a given problem can be matched. Therefore, understanding the principles associated with dynamic similarity and applying them is very important in engineering analyses. Similarity parameters of various types are used in all fields of engineering. However, in general, many other relevant similarity parameters arise in aerodynamics and engineering problem-solving, such as the Froude number, Weber number, Strouhal number, Stokes number, Prandtl number, Womesley number, etc. As previously discussed, the critical aerodynamic similarity parameters are the Reynolds and Mach numbers. If the values of the similarity parameters are the same, then the physics of both situations will be correctly scaled, so both will have the correct physical similarity. Therefore, any claim that “dynamic similarity” has been achieved also implies that geometric and kinematic similarity conditions have been met.ĭynamic similarity can be achieved by matching the values of the similarity parameters between two different circumstances, e.g., in two or more separate experiments or at model scale and full scale, which may be challenging to achieve in practice. A prerequisite for dynamic similarity is geometric similarity and kinematic similarity. In general, geometric similarity focuses on the scaling of dimensions, kinematic similarity on the scaling of displacements and velocities, and dynamic similarity on the scaling of integrated values such as forces. A sub-scale model application is said to have similitude with the actual (real) application if the two applications share the same geometric, kinematic, and dynamic similarities. ![]() The need for similarity or similitude is a concept that always arises when testing sub-scale engineering models in the laboratory or the wind tunnel. The principle of dynamic similarity is closely connected to the concepts used in dimensional analysis.
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