text: In fluid mechanics, dimensional analysis is performed to obtain dimensionless 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. 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 (), generally important in all types of fluid problems: 
  * Froude number (), modeling flow with a free surface: 
  * Euler number (), used in problems in which pressure is of interest: 
  * Mach number (), important in high speed flows where the velocity approaches or exceeds the local speed of sound:  where  is the local speed of sound.