Euler number (physics)

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This article is about fluid flow calculations. For Euler's number, see e (mathematical constant).


The Euler number is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop e.g. over a restriction and the kinetic energy per volume, and is used to characterize losses in the flow.

It is defined as

\mathit{Eu}=\frac{p(\mathrm{upstream})-p(\mathrm{downstream})}{\frac{1}{2}\rho V^2}

where

  • ρ is the density of the fluid.
  • p(upstream) is the upstream pressure.
  • p(downstream) is the downstream pressure.
  • V is a characteristic velocity of the flow.

Somewhat the same structure, but with a different meaning is the Cavitation number:

The Cavitation number is a dimensionless number used in flow calculations. It expresses the relationship between the difference of a local absolute pressure from the vapor pressure and the kinetic energy per volume, and is used to characterize the potential of the flow to cavitate.

It is defined as

\mathit{Ca}=\frac{p-p_v}{\frac{1}{2}\rho V^2}

where

  • ρ is the density of the fluid.
  • p is the local pressure.
  • pv is the vapor pressure of the fluid.
  • V is a characteristic velocity of the flow.

[edit] See also

v • d • e
Dimensionless numbers in fluid dynamics
Archimedes • Atwood • Bagnold • Biot • Bond • Brinkman • Capillary • Cauchy • Damköhler • Dean • Deborah • Eckert • Ekman • Eötvös • Euler • Froude • Galilei • Grashof • ‎Görtler • Hagen • Knudsen • Laplace • Lewis • Mach • Magnetic Reynolds • Marangoni • Morton • Nusselt • Ohnesorge • Péclet • Prandtl • Rayleigh • Reynolds • Richardson • Roshko • Rossby • Ruark • Schmidt • Sherwood • Stanton • Stokes • Strouhal • Suratman • Taylor • Weber • Weissenberg • Womersley

[edit] References