Ohnesorge Number Calculator

Estimate viscous, inertial, and capillary balance for sprays. Review supporting Reynolds, Weber, and capillary values. Fast results, export tools, visuals, examples, and clear usage.

Calculator inputs

Enter fluid properties and a representative length such as droplet diameter, jet diameter, or nozzle width. Velocity is optional but useful for Re, We, and Ca.

Formula used

Ohnesorge number compares viscous effects with the combined inertia-surface-tension scale. It is especially useful for droplet formation, jets, ligaments, atomization, coating, and printing flows.

Oh = μ / √(ρ × σ × L)
Re = ρ × U × L / μ
We = ρ × U² × L / σ
Ca = μ × U / σ
La = ρ × σ × L / μ² = 1 / Oh²
Z = 1 / Oh

Variable meanings

μ = dynamic viscosity

ρ = density

σ = surface tension

L = characteristic length such as droplet diameter or nozzle width

Interpretation guide

Lower Oh values usually indicate easier breakup and stronger oscillation.

Moderate Oh values show balanced viscous damping and capillary response.

Higher Oh values indicate stronger damping and reduced atomization tendency.

How to use this calculator

1) Enter dynamic viscosity

Use the measured value for your liquid and choose the correct unit. cP and mPa·s are numerically identical.

2) Enter density and surface tension

These properties strongly affect droplet deformation and breakup, so use values that match temperature and composition.

3) Choose a characteristic length

Pick the size scale that represents the physics you are studying, such as a droplet diameter, ligament diameter, or nozzle width.

4) Add velocity if available

Velocity is not needed for Oh itself, but it lets the calculator return Reynolds, Weber, and capillary numbers for fuller interpretation.

5) Review the exported outputs

After calculation, use the CSV or PDF buttons to save the current scenario, document assumptions, and compare cases later.

Example data table

These sample cases show how the dimensionless balance changes with fluid properties and length scale.

Case μ (mPa·s) ρ (kg/m³) σ (mN/m) L (µm) Oh Typical behavior
Water microdroplet 1.0 998 72 100 0.0118 Weak damping and easy oscillation
Inkjet fluid 10.0 1030 32 30 0.3180 Transitional and often printable
Glycerol blend 120.0 1180 65 500 0.6128 Noticeably damped breakup
Liquid metal surrogate 4.5 6300 530 1000 0.0025 Inertia-surface tension dominated

FAQs

What is the Ohnesorge number?

It is a dimensionless number that compares viscous forces with the combined inertial and capillary scale. It helps predict droplet breakup, jet stability, and oscillation damping.

What characteristic length should I use?

Use the size that best represents the problem physics. Common choices are droplet diameter, jet diameter, filament diameter, or nozzle width.

How is Oh different from Reynolds and Weber numbers?

Reynolds compares inertia with viscosity. Weber compares inertia with surface tension. Ohnesorge combines viscosity against the inertia-capillary scale, so it stays independent of velocity.

What does a low Oh value indicate?

Low Oh usually means weaker viscous damping. Drops or jets can oscillate more strongly, deform more easily, and break up more readily under forcing.

What does a high Oh value indicate?

High Oh means viscosity strongly damps motion. Breakup can be delayed, oscillations fade faster, and atomization generally becomes harder.

Why is velocity optional here?

Velocity is not required for Oh because the formula uses viscosity, density, surface tension, and length only. It is optional for complementary Reynolds, Weber, and capillary numbers.

What is the inverse Ohnesorge number Z?

Z equals 1 divided by Oh. It is often used in inkjet work because a moderate range can indicate a practical balance between ejection and satellite formation.

Can I mix units in this calculator?

Yes. The tool converts all supported inputs into SI units internally, then calculates the reported dimensionless groups consistently.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.