Kinematic Similarity
Kinematic similarity refers to similarity of motion.
Since motions are described by distance and time, it implies similarity of lengths (i.e., geometrical similarity) and, in addition, similarity of time intervals.
If the corresponding lengths in the two systems are in a fixed ratio, the velocities of corresponding particles must be in a fixed ratio of magnitude of corresponding time intervals.
If the ratio of corresponding lengths, known as the scale factor, is lr and the ratio of corresponding time intervals is tr, then the magnitudes of correspondingvelocities are in the ratio lr/tr and the magnitudes of corresponding accelerations are in the ratio lr/t2 r.
A well-known example of kinematic similarity is found in a planetarium. Here the galaxies of stars and planets in space are reproduced in accordance with a certain length scale and in simulating the motions of the planets, a fixed ratio of time intervals (and hence velocities and accelerations) is used.
When fluid motions are kinematically similar, the patterns formed by streamlines are geometrically similar at corresponding times.
Since the impermeable boundaries also represent streamlines, kinematically similar flows are possible only past geometrically similar boundaries.
Therefore, geometric similarity is a necessary condition for the kinematic similarity to be achieved, but not the sufficient one.
For example, geometrically similar boundaries may ensure geometrically similar streamlines in the near vicinity of the boundary but not at a distance from the boundary.
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