Ohnesorge Number Calculator
Enter viscosity, density, surface tension and length to compute the Ohnesorge number Oh = μ/√(ρ·σ·L).
Input Data
Results
At a glance:The Ohnesorge number Oh = μ/√(ρ·σ·L) is a dimensionless group in fluid mechanics comparing viscous forces to surface-tension forces (the ratio of the viscous length scale μ/√(ρσ) to the geometric length L). It appears in free-surface and atomization problems — inkjet printing, sprays, coatings — where both viscosity and surface tension matter. It relates to the Reynolds and Weber numbers by Oh = We^(1/2)/Re = μ/(ρ·v·L)·√(ρ·L/σ). Low Oh (viscosity negligible) → easy droplet breakup; high Oh (viscous dominates) → ligaments persist. This tool computes Oh from μ, ρ, σ, L.
Formula
Oh = μ/√(ρ·σ·L)
Oh = √We / Re
$$\mathrm{Oh} = \dfrac{\mu}{\sqrt{\rho\,\sigma\,L}} = \dfrac{\sqrt{\mathrm{We}}}{\mathrm{Re}}$$How to Use
- Enter dynamic viscosity μ (Pa·s).
- Enter density ρ, surface tension σ and length L.
- The calculator returns Oh.
Case Studies
Inkjet droplet
μ = 0.01 Pa·s, ρ = 1000, σ = 0.03, L = 2e-5 m.
Oh = 0.01/√(1000×0.03×2e-5) ≈ 0.129.
Moderate Oh — printable, breaks into drops.
FAQ
Why is Oh useful for sprays?
It predicts whether a liquid jet breaks into drops: low Oh (thin, low-surface-tension liquids) atomize readily; high Oh (viscous syrups) form stable ligaments.
How is it linked to Re and We?
Oh = √We/Re, combining the viscous (Re) and capillary (We) effects into one parameter.
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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.