Similitude
Similitude's main application is in hydraulic and aerospace engineering to test fluid flow conditions with scaled models.
Engineering models are used to study complex fluid dynamics problems where calculations and computer simulations aren't reliable.
Scale models allow testing of a design prior to building, and in many cases are a critical step in the development process.
While the geometry may be simply scaled, other parameters, such as pressure, temperature or the velocity and type of fluid may need to be altered.
The greater the departure from the application's operating conditions, the more difficult achieving similitude is.
The design of marine vessels remains more of an art than a science in large part because dynamic similitude is especially difficult to attain for a vessel that is partially submerged: a ship is affected by wind forces in the air above it, by hydrodynamic forces within the water under it, and especially by wave motions at the interface between the water and the air.
The scaling requirements for each of these phenomena differ, so models cannot replicate what happens to a full sized vessel nearly so well as can be done for an aircraft or submarine—each of which operates entirely within one medium.
Similitude is a term used widely in fracture mechanics relating to the strain life approach.
A free body diagram is constructed and the relevant relationships of force and velocity are formulated using techniques from continuum mechanics.
[1] Invoking the Buckingham π theorem shows that the system can be described with two dimensionless numbers and one independent variable.
in watts required by the submarine is then: Note that even though the model is scaled smaller, the water velocity needs to be increased for testing.
Similitude has been well documented for a large number of engineering problems and is the basis of many textbook formulas and dimensionless quantities.
Simplification of the formulas (by neglecting some aspects of similitude) is common, and needs to be reviewed by the engineer for each application.
Other applications may operate in dangerous or expensive fluids so the testing is carried out in a more convenient substitute.
[3] The design of the scaled-down composite structures can be successfully carried out using the complete and partial similarities.
[5] Scaled models can be designed to replicate the dynamic characteristic (e.g. frequencies, mode shapes and damping ratios) of their full-scale counterparts.
