Euler number (physics)

From Wikipedia, the free encyclopedia

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

It is defined as

<math>

\mathit{Eu}=\frac{p(upstream)-p(downstream)}{\frac{1}{2}\rho V^2} </math>

where

• <math>\rho</math> is the density of the fluid.
• <math>p(upstream)</math> is the upstream pressure.
• <math>p (downstream)</math> is the downstream pressure.
• <math>V</math> 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

<math>

\mathit{Ca}=\frac{p-p_v}{\frac{1}{2}\rho V^2} </math>

where

• <math>\rho</math> is the density of the fluid.
• <math>p</math> is the local pressure.
• <math>p_v</math> is the vapor pressure of the fluid.
• <math>V</math> is a characteristic velocity of the flow.

[edit] See also

• Reynolds number for use in flow analysis and similarity of flows

[edit] References

• Batchelor, G.K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press. ISBN 0-521-09817-3eu:Euler zenbakia