Schmidt Number Calculator

Formula Used

The Schmidt number is a dimensionless ratio comparing momentum diffusivity to mass diffusivity: Sc = ν / D. If you only have dynamic viscosity and density, the calculator first computes ν = μ / ρ, then evaluates Sc = (μ / ρ) / D.

• ν is kinematic viscosity (m²/s).
• μ is dynamic viscosity (Pa·s).
• ρ is density (kg/m³).
• D is mass diffusivity (m²/s).

How to Use This Calculator

1. Select an input method: use ν and D or use μ, ρ, and D.
2. Enter values and select units for each quantity.
3. Click Calculate Schmidt Number to compute Sc.
4. Use Download CSV or Download PDF after a result is shown.
5. Compare against the example table to validate typical ranges.

Example Data Table

These numbers are illustrative. Use measured properties for design work.

Professional Guide

1) What the Schmidt number represents

The Schmidt number (Sc) compares momentum diffusivity to mass diffusivity. It is defined as Sc = ν / D, where ν is kinematic viscosity and D is species mass diffusivity. Because both terms have units of m²/s, Sc is dimensionless and ideal for scaling transport behavior between different fluids and conditions.

2) Typical ranges you can expect

In many gases, Sc often stays close to unity because viscosity and diffusivity are of comparable order. For example, air with common vapors can yield Sc around 0.7–1.0. In liquids, diffusivity is usually much smaller than viscosity, so Sc becomes large. Water with small solutes often sits near Sc ≈ 300–1000, while viscous oils with slow diffusion may exceed 10⁵.

3) Why Sc matters in mass transfer calculations

Engineering correlations frequently blend Sc with Reynolds number to predict Sherwood number and mass-transfer coefficients. When Sc is high, concentration boundary layers are thinner than velocity boundary layers, and surface renewal can be strongly limiting. When Sc approaches one, momentum and species diffusion act on similar length scales, simplifying scaling assumptions.

4) Choosing inputs: ν and D versus μ, ρ, and D

Many property tables provide kinematic viscosity directly, making ν and D the cleanest pathway. If you only have dynamic viscosity μ and density ρ, the calculator derives ν = μ/ρ. This is useful for laboratory reports and process datasheets where μ is reported in mPa·s (or cP) and ρ is reported in kg/m³ (or g/cm³).

5) Unit conversion and consistency checks

The calculator converts all inputs to SI before computing Sc. A quick reliability check is to compare the computed ν against known values: water near room temperature is roughly 1.0×10⁻⁶ m²/s, while air is around 1.5×10⁻⁵ m²/s. If your ν is orders of magnitude off, re-check units or decimal placement.

6) Interpreting the result for design decisions

Sc > 1 indicates momentum diffuses faster than species, which is common in liquids. This often implies higher sensitivity to mixing and near-wall gradients. Sc < 1 suggests species diffusion is relatively fast, which is more common in some gas mixtures. Knowing which regime you are in helps prioritize turbulence enhancement, interfacial area, or residence time.

7) Practical examples from common fluids

Using ν = 1.0×10⁻⁶ m²/s and D = 2.0×10⁻⁹ m²/s gives Sc = 500, matching a typical water–solute scenario. For air, ν = 1.5×10⁻⁵ m²/s and D = 2.0×10⁻⁵ m²/s yields Sc = 0.75. A light oil example with ν = 5.0×10⁻⁵ m²/s and D = 1.0×10⁻¹⁰ m²/s produces Sc = 5.0×10⁵, highlighting diffusion limitation.

8) Exporting results for reports and validation

After you compute Sc, use the CSV export for spreadsheets and quick comparison across cases. Use the PDF export for lab notebooks and design notes. Keeping ν, D, and derived values together makes it easier to audit assumptions and reproduce results during peer review or process safety checks.

FAQs

1) Is the Schmidt number always greater than one?

No. Many gases have Sc near one, and some mixtures can be below one. Liquids commonly have Sc well above one because diffusivity is much smaller than viscosity.

2) Which diffusivity should I use for mixtures?

Use the mass diffusivity of the specific species in the host fluid at your temperature and pressure. For multicomponent systems, choose the diffusivity relevant to the controlling transfer step.

3) Why does the calculator ask for μ and ρ?

Some datasets report dynamic viscosity and density rather than kinematic viscosity. The calculator converts them to ν using ν = μ/ρ, then computes Sc = ν/D.

4) What units are safest for entering data?

SI units are safest: ν in m²/s, D in m²/s, μ in Pa·s, and ρ in kg/m³. If you use other units, confirm the selected unit dropdown matches your data source.

5) What does a very high Sc imply physically?

Very high Sc means species diffusion is slow compared with momentum diffusion. Mass transfer tends to be limited by thin concentration layers, so mixing and near-wall transport become more important.

6) Can I use Sc directly to compute a mass-transfer coefficient?

Sc is usually combined with Reynolds number in Sherwood correlations to estimate mass-transfer coefficients. You still need flow geometry, velocity, and a suitable correlation for your regime.

7) Why don’t my results match a handbook exactly?

Property values vary with temperature, pressure, composition, and measurement method. Ensure all properties are at the same conditions and use consistent definitions for diffusivity and viscosity.