Schmidt Number Calculator

What is the Schmidt Number?

The Schmidt number (Sc) is a dimensionless quantity that compares momentum diffusivity (kinematic viscosity) to mass diffusivity. Named after German engineer Ernst Schmidt, it is the mass-transfer analogue of the Prandtl number for heat transfer. When Sc is close to 1, velocity and concentration boundary layers grow at similar rates. For dissolved species in liquids, Sc typically ranges from 100 to over 10,000, indicating that mass diffuses much more slowly than momentum. For related dimensionless parameters, explore our Sherwood Number Calculator and Lewis Number Calculator.

How to Use the Schmidt Number Calculator

Select the value you want to solve for from the dropdown, then enter the remaining two values. The calculator instantly computes the result using the Schmidt number formula. Use the regime indicator to understand whether mass or momentum diffusion dominates.

Schmidt Number Formula

The Schmidt number is defined as the ratio of kinematic viscosity to mass diffusivity:

Sc = ν / D

Where:

Sc = Schmidt number (dimensionless)
ν = Kinematic viscosity (m²/s)
D = Mass diffusivity (m²/s)

The calculator also solves for kinematic viscosity (ν = Sc × D) and mass diffusivity (D = ν / Sc), allowing you to work backward from known dimensionless numbers.

Applications of the Schmidt Number

Chemical Reactor Design: Used in Sherwood-number correlations to predict mass-transfer coefficients in packed columns, absorbers, and separation equipment.
Gas Absorption: Determines the rate of gas dissolution into liquid in scrubbers and distillation columns.
Environmental Modeling: Estimates pollutant dispersion rates in rivers, atmospheric boundary layers, and groundwater.
Electrochemistry: Characterizes mass-transfer boundary layers at electrode surfaces for current density predictions.
Bioprocess Engineering: Predicts oxygen transfer rates in fermentation broths and bioreactor design.

Typical Schmidt Number Values

Gases (atmospheric pressure): 0.5 to 2
Dissolved gases in water: 200 to 1,000
Ions in electrolyte solutions: 500 to 10,000
Liquid hydrocarbons: 100 to 500

Relationship to Other Dimensionless Numbers

The Schmidt number is related to the Prandtl number (Pr) and Lewis number (Le) through: Le = Sc / Pr. If you know any two of these dimensionless numbers, you can compute the third. This relationship is particularly useful in combustion modeling and coupled heat-and-mass transfer problems.

Frequently Asked Questions

What does the Schmidt number tell you?

The Schmidt number indicates the relative thickness of the velocity and concentration boundary layers. When Sc is much greater than 1 (typical for liquids), the concentration boundary layer is much thinner than the velocity boundary layer, meaning mass transfer resistance is concentrated in a very thin region near surfaces.

How is Schmidt number different from Prandtl number?

Both are dimensionless ratios of momentum diffusivity to another diffusivity. Sc uses mass diffusivity (Sc = ν/D), while Pr uses thermal diffusivity (Pr = ν/α). In gases, both Sc and Pr are near 1. In liquids, Sc is typically 100-1,000 while Pr is 1-10.

What is a typical Schmidt number for gases?

For gases at atmospheric pressure, Sc is usually between 0.5 and 2. For example, Sc is about 0.6 for hydrogen in air and about 1.0 for carbon monoxide in air. This means velocity and concentration boundary layers have similar thicknesses in gas-phase systems.

How is the Schmidt number used in industry?

Chemical engineers use the Schmidt number in Sherwood-number correlations (such as Sh = 2 + 0.6 Re^0.5 Sc^0.33) to predict mass-transfer coefficients for designing equipment like gas absorbers, distillation columns, and catalytic reactors without expensive pilot-plant testing.

Does temperature affect the Schmidt number?

Yes, significantly. Temperature affects both kinematic viscosity and mass diffusivity, often in opposite directions. In liquids, viscosity decreases with temperature while diffusivity increases, so Sc drops dramatically as temperature rises. In gases, both increase with temperature, so the net effect on Sc is smaller.

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