How to Use Knudsen Number Calculator
The Knudsen Number Calculator characterises whether a gas flow can be treated as a continuum or requires kinetic-theory correction, by computing the ratio of molecular mean free path to a characteristic length.
- Select input mode — choose “direct λ and L” if you have tabulated values, or “compute from gas state” if you know temperature, pressure and molecule diameter.
- Enter mean free path λ directly, or provide T, P and molecule diameter d in advanced mode to estimate λ from kinetic theory.
- Enter characteristic length L — pipe or channel diameter, gap width, particle diameter or channel height depending on the application.
- Read Kn and the automatically assigned flow regime label.
- Use the regime guide to decide whether Navier–Stokes (Kn < 0.001), slip-corrected NS (0.001–0.1), DSMC (0.1–10), or free-molecular models (>10) are appropriate.
Formula & Theory — Knudsen Number Calculator
The Knudsen Number Calculator uses kinetic-gas-theory expressions to compute λ and derive Kn:
Kn = λ / L
λ = k_B · T / ( √2 · π · d² · P )| Symbol | Meaning | SI Unit |
|---|---|---|
| Kn | Knudsen number (dimensionless) | — |
| λ | Molecular mean free path | m |
| L | Characteristic length | m |
| k_B | Boltzmann constant (1.380649 × 10⁻²³) | J/K |
| T | Absolute temperature | K |
| d | Kinetic diameter of gas molecule | m |
| P | Gas pressure | Pa |
Regime summary: continuum Kn < 0.001 — Navier–Stokes valid; slip flow 0.001–0.1 — NS with velocity-slip and temperature-jump boundary conditions; transition 0.1–10 — DSMC or Boltzmann equation required; free molecular Kn > 10 — molecule–wall collisions dominate over molecule–molecule collisions. Kinetic diameters: N₂ ≈ 3.7 × 10⁻¹⁰ m, O₂ ≈ 3.5 × 10⁻¹⁰ m, He ≈ 2.6 × 10⁻¹⁰ m.
Use Cases for Knudsen Number Calculator
- MEMS device design — evaluate whether squeeze-film damping models in micro-gaps and comb-drive structures require rarefaction corrections for accurate dynamic simulation.
- Vacuum engineering — classify pump lines and vacuum chamber operating pressures to choose the correct flow conductance formula (viscous, intermediate or molecular).
- Atmospheric re-entry — map the Kn evolution from continuum hypersonic flow (low altitude) to free-molecular regime (upper atmosphere, >80 km) for heat-shield design.
- Aerosol and particulate physics — apply the Cunningham slip correction factor to particle drag forces when particle size approaches the mean free path.
- Micro and nano-channel flows — assess where slip-velocity corrections become significant in lab-on-chip microreactors and gas chromatography columns.
- Heat conduction in thin films — identify the regime where the Fourier law breaks down and phonon-boundary scattering (ballistic transport) must be modelled.