Euler Number Calculator
Enter pressure drop, density and velocity to compute the Euler number Eu = Δp/(ρ·v²), a dimensionless fluid-dynamics ratio.
Input Data
Results
At a glance:The Euler number Eu = Δp/(ρ·v²) is a dimensionless group in fluid dynamics representing the ratio of pressure forces to inertial forces (ρ·v² is the dynamic pressure scale). Large Eu means pressure effects dominate (strong pressure gradients, pumps, compressors); Eu ~1 indicates pressure and inertia are comparable. It is the pressure analogue of other dimensionless numbers and relates to the cavitation number and pressure coefficient. For dynamic similarity between a model and a full-scale flow, Eu (and other relevant numbers) should match.
Formula
Euler number: Eu = Δp/(ρ·v²)
$$\mathrm{Eu} = \dfrac{\Delta p}{\rho\,v^2}$$How to Use
- Enter the pressure drop Δp (Pa).
- Enter the density ρ (kg/m³) and velocity v (m/s).
- The calculator returns Eu.
Case Studies
Pressure loss in a duct
Δp = 500 Pa, ρ = 1.2 kg/m³, v = 10 m/s.
Eu = 500/(1.2×100) ≈ 4.17.
Pressure forces dominate over inertia here.
FAQ
What does the Euler number tell you?
It compares pressure forces to inertial forces. High Eu indicates strong pressure gradients relative to flow momentum — typical in pumps, nozzles and compressible flows.
Is it related to Reynolds number?
Both are dimensionless, but Euler number is about pressure vs inertia, while Reynolds number is inertia vs viscosity. They appear together in similarity analysis.
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References
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.