Calculator Inputs
Formula Used
Direct formula
Kn = λ / L
Kn is the Knudsen number, λ is mean free path, and L is characteristic length.
Estimated mean free path formula
λ = kBT / (√2 π d² P)
Here, kB is Boltzmann’s constant, T is temperature, d is molecular diameter, and P is pressure.
Flow regime guide
- Kn < 0.001: Continuum flow
- 0.001 ≤ Kn < 0.1: Slip flow
- 0.1 ≤ Kn < 10: Transition flow
- Kn ≥ 10: Free molecular flow
How to Use This Calculator
- Select the input mode.
- Use direct mode when mean free path is known.
- Use estimate mode when gas properties are available.
- Enter all values with suitable units.
- Click the calculate button.
- Read the Knudsen number and detected regime.
- Review the interpretation and suggested modeling approach.
- Download a CSV or PDF report if needed.
Example Data Table
| Case | Mean Free Path | Characteristic Length | Knudsen Number | Regime |
|---|---|---|---|---|
| Room-air channel | 68 nm | 5 mm | 1.36e-5 | Continuum Flow |
| Microchannel | 68 nm | 20 µm | 0.0034 | Slip Flow |
| MEMS gap | 68 nm | 0.5 µm | 0.1360 | Transition Flow |
| High-vacuum cavity | 1.5 mm | 100 µm | 15.0000 | Free Molecular Flow |
Frequently Asked Questions
1) What does the Knudsen number measure?
It compares molecular mean free path with a characteristic length. The ratio reveals whether flow behaves like a continuum or requires kinetic treatment.
2) What should I use for characteristic length?
Use the dimension that most strongly limits the flow. Common choices include channel diameter, pore width, gap spacing, or tube radius.
3) Why does pressure change the result?
Lower pressure increases mean free path because molecules collide less often. That makes the Knudsen number larger for the same geometry.
4) Why does small geometry matter so much?
As characteristic length shrinks, the ratio λ/L grows quickly. Microscale devices can enter slip or transition regimes even at ordinary conditions.
5) Which mode should I choose?
Choose direct mode when mean free path is already known. Choose estimate mode when you know temperature, pressure, molecular diameter, and length scale.
6) Can this calculator help with vacuum systems?
Yes. Vacuum systems often show larger mean free paths, making Kn especially useful for deciding whether continuum assumptions break down.
7) Why is the chart logarithmic?
Knudsen number can span many orders of magnitude. Logarithmic axes make regime boundaries and scale changes easier to compare visually.
8) Can I use this for liquids?
It is mainly intended for gases and rarefied flow analysis. Liquids usually require different physical assumptions and modeling choices.