Euler number (physics)

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

:$mathit\{Eu\}=frac\{p(mathrm\{upstream\})-p(mathrm\{downstream\})\}\{\; ho\; V^2\}$

where
*$ho$ 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

:$mathit\{Ca\}=frac\{p-p\_v\}\{frac\{1\}\{2\}\; ho\; V^2\}$

where
*$ho$ is the density of the fluid.
*$p$ is the local pressure.
*$p\_v$ is the vapor pressure of the fluid.
*$V$ is a characteristic velocity of the flow.

ee also

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

References

* Batchelor, G.K. (1967). "An Introduction to Fluid Dynamics". Cambridge University Press. ISBN 0-521-09817-3