Euler number (physics)

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, where a perfect frictionless flow corresponds to an Euler number of 1.

It is defined as

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

where

• \(\rho\) 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.

The cavitation number has a similar structure, but a different meaning and use:

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

\[ \mathrm{Ca}=\frac{p-p_v}{\frac{1}{2}\rho V^2} \]

where

• \(\rho\) 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.

See also

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

References

bs:Eulerov broj (fizika)