Editing Dimensional analysis (section)

=== Fluid mechanics ===
In [[fluid mechanics]], dimensional analysis is performed to obtain dimensionless [[Buckingham π theorem|pi terms]] or groups. According to the principles of dimensional analysis, any prototype can be described by a series of these terms or groups that describe the behaviour of the system. Using suitable pi terms or groups, it is possible to develop a similar set of pi terms for a model that has the same dimensional relationships.<ref>{{Cite book |last1=Waite |first1=Lee |title=Applied Biofluid Mechanics |url=https://archive.org/details/appliedbiofluidm00wait |url-access=limited |last2=Fine |first2=Jerry |date=2007 |publisher=McGraw-Hill |isbn=978-0-07-147217-3 |location=New York |page=[https://archive.org/details/appliedbiofluidm00wait/page/n278 260]}}</ref> In other words, pi terms provide a shortcut to developing a model representing a certain prototype. Common dimensionless groups in fluid mechanics include:
* [[Reynolds number]] ({{math|Re}}), generally important in all types of fluid problems: <math display="block">\mathrm{Re} = \frac{\rho\,ud}{\mu}.</math>
* [[Froude number]] ({{math|Fr}}), modeling flow with a free surface: <math display="block">\mathrm{Fr} = \frac{u}{\sqrt{g\,L}}.</math>
* [[Euler number (physics)|Euler number]] ({{math|Eu}}), used in problems in which pressure is of interest: <math display="block">\mathrm{Eu} = \frac{\Delta p}{\rho u^2}.</math>
* [[Mach number]] ({{math|Ma}}), important in high speed flows where the velocity approaches or exceeds the local speed of sound: <math display="block">\mathrm{Ma} = \frac{u}{c},</math> where {{math|''c''}} is the local speed of sound.