Euler number (physics)

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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

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

where

• ρ 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

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