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 v^{2})

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