Knudsen Number Calculator

Understanding Knudsen Number Calculator

The Knudsen number determines whether continuum mechanics or molecular dynamics should be used: Kn < 0.01 (continuum), 0.01-0.1 (slip), 0.1-10 (transition), > 10 (free molecular).

How to use this calculator

1. Enter the mean free path \(\lambda\) in your chosen length unit.
2. Enter the characteristic length \(L\) in the same unit.
3. Click calculate to get \(Kn\).
4. Use the result to judge the flow regime, since larger values mean molecular effects are more important.

The formula explained

The calculator uses \(Kn = \frac{\lambda}{L}\). This gives a dimensionless ratio that compares how far molecules travel between collisions to the size of the system.

• Kn = Knudsen number, a dimensionless flow parameter
• \(\lambda\) = mean free path of the gas molecules
• L = characteristic length of the system

Step by step method

1. Measure or estimate the mean free path \(\lambda\).
2. Measure the characteristic length \(L\) of the object or channel.
3. Divide \(\lambda\) by \(L\) to get \(Kn\).

Worked example

Problem. A gas has a mean free path of \(6.0 \times 10^{-8}\,\text{m}\) in a microchannel with characteristic length \(2.0 \times 10^{-6}\,\text{m}\). Find the Knudsen number.

1. Write the formula, \(Kn = \frac{\lambda}{L}\).
2. Substitute the values, \(Kn = \frac{6.0 \times 10^{-8}}{2.0 \times 10^{-6}}\).
3. Compute the ratio, \(Kn = 3.0 \times 10^{-2}\).

Tips and common mistakes

• Make sure \(\lambda\) and \(L\) use the same unit, otherwise the ratio will be wrong.
• A small \(Kn\) means continuum flow is a good approximation, while a larger \(Kn\) means rarefied or molecular flow effects become more important.

Frequently asked questions