Editing Similitude (section)

== Typical applications ==
{{see also|List of dimensionless numbers}}

===Fluid mechanics===
Similitude has been well documented for a large number of engineering problems and is the basis of many textbook formulas and dimensionless quantities. These formulas and quantities are easy to use without having to repeat the laborious task of dimensional analysis and formula derivation. Simplification of the formulas (by neglecting some aspects of similitude) is common, and needs to be reviewed by the engineer for each application.

Similitude can be used to predict the performance of a new design based on data from an existing, similar design. In this case, the model is the existing design. Another use of similitude and models is in validation of [[computer simulation]]s with the ultimate goal of eliminating the need for physical models altogether.

Another application of similitude is to replace the operating fluid with a different test fluid. Wind tunnels, for example, have trouble with air liquefying in certain conditions so [[helium]] is sometimes used. Other applications may operate in dangerous or expensive fluids so the testing is carried out in a more convenient substitute.

Some common applications of similitude and associated dimensionless numbers;
{|!
|'''Incompressible flow''' (see example above)
| [[Reynolds number]], [[pressure coefficient]], ([[Froude number]] and [[Weber number]] for open channel hydraulics)
|-
|'''Compressible flows'''
| [[Reynolds number]], [[Mach number]], [[Prandtl number]], [[specific heat ratio]]
|-
|'''Flow-excited vibration'''
| [[Strouhal number]]
|-
|'''Centrifugal compressors'''
| [[Reynolds number]], [[Mach number]], [[pressure coefficient]], [[velocity ratio]]
|-
|'''Boundary layer thickness'''
| [[Reynolds number]], [[Womersley number]], [[Dynamic similarity (Reynolds and Womersley numbers)|dynamic similarity]]
|-
|
|}

===Solid mechanics: structural similitude===
[[File:Scaled composite laminated I-beams by structural similitude.jpg|thumb|Scaled composite laminated I-beams with different scales and lamination schemes designed based on structural similitude analysis.]]
[[File:Scaledbeams.jpg|thumb|Schematic of scaled composite laminated I-beams: prototype (top) and models with different scales and layups (bottom)]]
Similitude analysis is a powerful engineering tool to design the scaled-down structures. Although both dimensional analysis and direct use of the governing equations may be used to derive the scaling laws, the latter results in more specific scaling laws.<ref>{{cite journal |last1=Rezaeepazhand |first1=J. |first2=G.J. |last2=Simitses |first3=J.H. |last3=Starnes |title=Scale models for laminated cylindrical shells subjected to axial compression |journal=Composite Structures |volume=34 |issue=4 |pages=371–9 |date=1996 |doi=10.1016/0263-8223(95)00154-9 |url=}}</ref> The design of the scaled-down composite structures can be successfully carried out using the complete and partial similarities.<ref>{{cite conference |last1=Asl |first1=M.E. |last2=Niezrecki |first2=C. |last3=Sherwood |first3=J. |last4=Avitabile |first4=P.  |title=Similitude Analysis of Composite I-Beams with Application to Subcomponent Testing of Wind Turbine Blades |url=https://www.researchgate.net/publication/278409912 |doi=10.1007/978-3-319-22449-7_14 |book-title=Experimental and Applied Mechanics |publisher=Springer |date=2016 |isbn=978-3-319-22449-7 |pages=115–126  |volume=4 |series=Conference Proceedings of the Society for Experimental Mechanics Series}}</ref> In the design of the scaled structures under complete similarity condition, all the derived scaling laws must be satisfied between the model and prototype which yields the perfect similarity between the two scales. However, the design of a scaled-down structure which is perfectly similar to its prototype has the practical limitation, especially for laminated structures. Relaxing some of the scaling laws may eliminate the limitation of the design under complete similarity condition and yields the scaled models that are partially similar to their prototype. However, the design of the scaled structures under the partial similarity condition must follow a deliberate methodology to ensure the accuracy of the scaled structure in predicting the structural response of the prototype.<ref>{{cite journal |first1=M.E. |last1=Asl |first2=C. |last2=Niezrecki |first3=J. |last3=Sherwood |first4=P. |last4=Avitabile |title=Vibration prediction of thin-walled composite I-beams using scaled models |journal=Thin-Walled Structures |volume=113 |issue= |pages=151–161 |date=2017 |doi=10.1016/j.tws.2017.01.020 |url=https://www.researchgate.net/publication/278410038|doi-access=free }}</ref> Scaled models can be designed to replicate the dynamic characteristic (e.g. frequencies, mode shapes and damping ratios) of their full-scale counterparts. However, appropriate response scaling laws need to be derived to predict the dynamic response of the full-scale prototype from the experimental data of the scaled model.<ref>{{cite conference |last1=Eydani Asl |first1=M. |last2=Niezrecki |first2=C. |last3=Sherwood |first3=J. |last4=Avitabile |first4=P. |title=Predicting the Vibration Response in Subcomponent Testing of Wind Turbine Blades |url=https://www.researchgate.net/publication/312651479 |doi=10.1007/978-3-319-15048-2_11 |book-title=Special Topics in Structural Dynamics |volume=6 |series=Conference Proceedings of the Society for Experimental Mechanics Series  |publisher=Springer |date=2015 |isbn=978-3-319-15048-2 |pages=115–123 }}</ref>