Editing Similitude (section)

== Overview ==
Engineering models are used to study complex fluid dynamics problems where calculations and computer simulations are not reliable. Models are usually smaller than the final design, but not always. [[Scale model]]s allow testing of a design prior to building, and in many cases are a critical step in the development process.

Construction of a scale model, however, must be accompanied by an analysis to determine what conditions it is tested under. 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. Similitude is achieved when testing conditions are created such that the test results are applicable to the real design.

[[File:Similitude (model).png|thumb|right|280px|The three conditions required for a model to have similitude with an application.]]

The following criteria are required to achieve similitude;
* [[Similarity (geometry)|Geometric similarity]] &ndash; the model is the same shape as the application, usually scaled.
* [[Kinematic similarity]] &ndash; fluid flow of both the model and real application must undergo similar time rates of change motions. (fluid streamlines are similar)
* [[Dynamic similarity (Reynolds and Womersley numbers)|Dynamic similarity]] &ndash; ratios of all forces acting on corresponding fluid particles and boundary surfaces in the two systems are constant.

To satisfy the above conditions the application is analyzed; 
# All parameters required to describe the system are identified using principles from [[continuum mechanics]].
# [[Dimensional analysis]] is used to express the system with as few independent variables and as many [[Dimensionless number|dimensionless parameters]] as possible.
# The values of the dimensionless parameters are held to be the same for both the scale model and application. This can be done because they are dimensionless and will ensure dynamic similitude between the model and the application. The resulting equations are used to derive scaling laws which dictate model testing conditions.

It is often impossible to achieve strict similitude during a model test. The greater the departure from the application's operating conditions, the more difficult achieving similitude is. In these cases some aspects of similitude may be neglected, focusing on only the most important parameters.

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. Under given loading conditions the fatigue damage in an un-notched specimen is comparable to that of a notched specimen. Similitude suggests that the component fatigue life of the two objects will also be similar.