Geometrical and dynamic similarity

This text has thrown up a need to describe the conditions that must be satisfied in order to compare the behaviour of two solid bodies interacting with a flowing fluid. First there is the question of shape. The two bodies must be the same shape[1] exactly except perhaps for the surface texture and they must also be set in the same attitude relative to the undisturbed fluid that flows over them. They are then said to be geometrically similar as a shorthand description just as we use one-dimensional flow as shorthand in pipe and channel flow. There is still the question of speeds and when the two operate at speeds that give the same flow patterns and, in turn, forces that can be related by simple mathematics the two are said to be dynamically similar. The two speeds are said to be corresponding speeds.

 

We can carry these descriptions on into aerodynamics.