Euler Number Calculator

Euler number definition:

Note: some textbooks use Eu = ΔP/(ρV²) without the ½. This calculator uses the ΔP/q form.

Three equivalent forms:

Typical Eu / K values for common devices:

Where Eu appears in fluid mechanics:

• Minor losses: ΔP = K × ½ρV² → K = Eu
• Pressure coefficient: C_p = (P − P_∞) / (½ρV_∞²) = Eu
• Cavitation number: σ = (P − P_v) / (½ρV²) = Eu when P_ref = P_v
• Orifice / nozzle: Eu = 1/C_d² − 1 (for incompressible orifice flow)
• Drag: C_D ≡ drag force / (q × A) — pressure drag term

Where:

• Eu = Euler number (dimensionless)
• ΔP = pressure difference [Pa]
• ρ = fluid density [kg/m³]
• V = characteristic velocity [m/s]
• q = dynamic pressure = ½ρV² [Pa]