Dimensionless numbers in fluid mechanics are a set of dimensionless quantities that have an important role in analyzing the behavior of fluids. Common examples include the Reynolds or the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, flow speed, etc.
Diffusive numbers in transport phenomena[edit]
| vs. | Inertial | Viscous | Thermal | Mass |
|---|---|---|---|---|
| Inertial | vd | Re | Pe | PeAB |
| Viscous | Re−1 | μ, ρν | Pr | Sc |
| Thermal | Pe−1 | Pr−1 | α | Le |
| Mass | PeAB−1 | Sc−1 | Le−1 | D |
As a general example of how dimensionless numbers arise in fluid mechanics, the classical numbers in transport phenomena of mass, momentum, and energy are principally analyzed by the ratio of effective diffusivities in each transport mechanism. The six dimensionless numbers give the relative strengths of the different phenomena of inertia, viscosity, conductive heat transport, and diffusive mass transport. (In the table, the diagonals give common symbols for the quantities, and the given dimensionless number is the ratio of the left column quantity over top row quantity; e.g. Re = inertial force/viscous force = vd/ν.) These same quantities may alternatively be expressed as ratios of characteristic time, length, or energy scales. Such forms are less commonly used in practice, but can provide insight into particular applications.
https://en.wikipedia.org/wiki/Dimensionless_numbers_in_fluid_mechanics
https://en.wikipedia.org/wiki/Euler_number_(physics)
https://en.wikipedia.org/wiki/Halbach_array
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