dynamic similarity

dynamic similarity [dī¦nam·ik ‚sim·ə′lar·əd·ē]

(mechanical engineering)

A relation between two mechanical systems (often referred to as model and prototype) such that by proportional alterations of the units of length, mass, and time, measured quantities in the one system go identically (or with a constant multiple for each) into those in the other; in particular, this implies constant ratios of forces in the two systems.

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Dynamic similarity

A relationship existing between two fluid flows when they have identical types of forces that are parallel at all corresponding points, with magnitudes related by a constant scale factor. Dynamic similarity makes it possible to scale results from model tests to predict corresponding results for the full-scale prototype.

Dynamic similarity requires faithful reproduction of detail on the model (geometric similarity); the same flow pattern, including boundary shapes (kinematic similarity); and test conditions that match relevant dimensionless ratios between model and prototype. Dynamically similar flows are said to be homologous. It may not be possible in a practical test to match all dimensionless parameters. It is most important to match parameters that represent the dominant physical effects. Thus, correct simulation of viscous effects requires that Reynolds number be matched; Mach number may be ignored if compressibility effects are not important. In ship model tests, Froude number must be matched to duplicate wave patterns; the effect of Reynolds number on viscous drag may be predicted analytically. See Dimensional analysis, Dimensionless groups, Fluid mechanics, Froude number, Mach number, Reynolds number