Euler Number

A dimensionless value used for analyzing fluid flow dynamics problems where the pressure difference between two points is important. The Euler Number measures the ratio of pressure forces to inertial forces.

Euler Number Calculator

The Euler Number is a dimensionless value used for analyzing fluid flow dynamics problems where the pressure difference between two points is important.

Formula

Eu = dp / (ρ v²)

Where:

Eu = Euler number (dimensionless)
dp = differential pressure (Pa)
ρ = density (kg/m³)
v = fluid flow velocity (m/s)

Note

A perfect frictionless flow corresponds to an Euler number equal to 1.

Pressure Coefficient

Pressure Coefficient = dp / (½ ρ v²)

Calculator

Inputs

Differential Pressure (Pa)

Fluid Density (kg/m³)

Fluid Flow Velocity (m/s)

Results

Euler Number-- -

Pressure Coefficient-- -

Dynamic Pressure-- Pa

Parameter	Value	Unit	Description
Differential Pressure (dp)	inputs.dp	Pa	Pressure difference between two points
Fluid Density (ρ)	inputs.rho	kg/m³	Density of the fluid
Fluid Velocity (v)	inputs.v	m/s	Velocity of fluid flow
Euler Number	inputs.dp / (inputs.rho * inputs.v * inputs.v)	-	Ratio of pressure forces to inertial forces
Dynamic Pressure	0.5 * inputs.rho * inputs.v * inputs.v	Pa	Kinetic energy per unit volume