### Euler number (physics)

The **Euler number** (**Eu**) 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. The inverse of the Euler number is referred to as the **Ruark Number** with the symbol **Ru**.

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_{\mathrm{upstream}} is the upstream pressure.
- p_{\mathrm{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** (**Ca**) 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_\mathrm{v}}{\frac{1}{2}\rho V^2}

where

- \rho is the density of the fluid.
- p is the local pressure.
- p_\mathrm{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