Lecture 39: Geomteric and dynamic similarities, examples
Similitude: To scale–up or down a model to the prototype, two types of similarities are required from the perspective of fluid dynamics: (1) geometrical similarity (2) dynamic similarity
Geometric similarity: The model and the prototype must be similar in shape.
(Fig. 39a)
This is essential because one can use a constant scale factor to relate the dimensions of model and prototype.
Dynamic similarity: The flow conditions in two cases are such that all forces (pressure viscous, surface tension, etc) must be parallel and may also be scaled by a constant scaled factor at all corresponding points. Such requirement is restrictive and may be difficult to implement under certain experiential conditions. Dimensional analysis can be used to identify the dimensional groups to achieve dynamic similarity between geometrically similar flows.
For example, in the flow past a sphere, drag on a model can be related to the prototype by a scale–factor if Reynolds numbers are matched. In other words,
Therefore, the types of fluid in two cases may be different: . Yet the drags on the two objects may be scaled as long as .
. Yet the drags on the two objects may be scaled as long as 
.
