Schmidt Number Calculator

Understanding Schmidt Number Calculator

The Schmidt number is analogous to the Prandtl number but for mass transfer instead of heat transfer. For gases Sc ≈ 1, for liquids Sc ≈ 100-1000.

How to use this calculator

1. Enter the kinematic viscosity \(\nu\) of the fluid.
2. Enter the mass diffusivity \(D\) for the species in the same fluid.
3. Check that both values use consistent units, such as \(\text{m}^2/\text{s}\).
4. Read the Schmidt number \(Sc\), which is the ratio \(\nu / D\).

The formula explained

The calculator uses \(Sc = \frac{\nu}{D}\) to compute the Schmidt number. This tells you how much faster momentum diffuses compared with mass.

• Sc = Schmidt number, a dimensionless ratio
• \(\nu\) = kinematic viscosity of the fluid
• D = mass diffusivity of the species in the fluid

Step by step method

1. Write down the kinematic viscosity \(\nu\) and the mass diffusivity \(D\).
2. Divide \(\nu\) by \(D\) using \(Sc = \frac{\nu}{D}\).
3. Check that the units cancel, so the result is dimensionless.

Worked example

Problem. A liquid has kinematic viscosity \(\nu = 1.2 \times 10^{-6}\,\text{m}^2/\text{s}\) and mass diffusivity \(D = 3.0 \times 10^{-9}\,\text{m}^2/\text{s}\). Find the Schmidt number.

1. Use the formula \(Sc = \frac{\nu}{D}\).
2. Substitute the values, \(Sc = \frac{1.2 \times 10^{-6}}{3.0 \times 10^{-9}}\).
3. Compute the ratio, \(Sc = 400\).

Tips and common mistakes

• Make sure \(\nu\) and \(D\) are in matching units, otherwise the result will be wrong.
• A large \(Sc\) means momentum diffuses much faster than mass, while a small \(Sc\) means mass diffuses relatively quickly.

Frequently asked questions