Euler number (physics)

Additional recommended knowledge

Recognize and detect the effects of electrostatic charges on your balance

Safe Weighing Range Ensures Accurate Results

How to ensure accurate weighing results every day?

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