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Euler Number Equation and Calculator

Fluids Flow Design and Engineering
Hydraulic & Pneumatic Design Engineering

Euler Number Equation and Calculator

The Euler number (Eu) is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop caused by a restriction and the kinetic energy per volume of the flow, and is used to characterize energy losses in the flow, where a perfect frictionless flow corresponds to an Euler number of 0. The inverse of the Euler number is referred to as the Ruark Number with the symbol Ru.

Eq. 1
Eu = (P_u - P_d ) / ( ρ · v ² )

Eu = Pressure forces / inertial forces

An alternative definition of the Euler number is given by Shah and Sekulic
Eq. 2
Eu = (P_u - P_d ) / ( 0.5 · ρ · v ² )

Eu = Pressure drop / dynamic head

Where:

ρ = Density of Fluid (kg/m³)
P_u = Upstream Pressure (kg/ms²)
P_d = Downstream Pressure (kg/ms²)
V = Velocity of Flow (m/s)
Eu = Euler Number (dimensionless)

Source:

• Wikipedia

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