A dimensionless number used in fluid dynamics as a measure of the ratio of pressure forces to inertial forces, often written in terms of a pressure difference, Δp.

EU = p / (ρ v2)

p = pressure (or Δp = pressure difference), ρ = density, v = velocity


The Euler number was named for the famous Swiss mathematician Leonhard Euler. Some form of the Euler number is usually found in problems where pressure (or pressure differences) is important.

Two other variants of the Euler number (both dimensionless) are:

Pressure coefficent = Δp / (½ ρ v 2)

and the Cavitation number.


also see Dimensionless numbers and Buckingham Pi Theorem

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