Calculate the Knudsen number to determine gas flow regime — continuum, slip, transition, or free molecular — from mean free path and characteristic length.
The Knudsen number (Kn) is a dimensionless number that determines which physical model best describes gas flow in a given situation. Defined as the ratio of the molecular mean free path to the characteristic length of the system, it tells you whether molecules interact primarily with each other (continuum flow) or with the walls of the system (free molecular flow).
At everyday scales and pressures, Kn is tiny and the familiar Navier-Stokes equations work perfectly. But in microfluidics, vacuum systems, high-altitude flight, and space environments, Kn can become large enough to require specialized methods like DSMC (Direct Simulation Monte Carlo) or molecular dynamics.
This Knudsen Number Calculator computes Kn from the mean free path and characteristic length, identifies the flow regime, and provides a visual regime indicator. You can either enter the mean free path directly or compute it from temperature, pressure, and molecular diameter. Preset buttons cover applications from Standard atmosphere to vacuum chambers and re-entry vehicles. A regime comparison table summarizes the modeling approaches for each range.
Use this tool to decide whether a gas-flow problem can be treated as continuum flow or whether you need slip corrections, transition models, or rarefied-gas methods. It gives a quick regime check before you choose a CFD, slip-flow, or molecular model. That makes it easier to match the flow regime to the solver before you start the analysis.
Kn = λ / L Mean Free Path: λ = kT / (√2 × π × d² × P) k = 1.381 × 10⁻²³ J/K (Boltzmann constant) d = molecular diameter Regimes: Kn < 0.01 continuum; 0.01–0.1 slip; 0.1–10 transition; > 10 free molecular
Result: Kn = 6.8 × 10⁻⁸, Continuum Flow
Air at standard conditions has a mean free path of ~68 nm. In a 1 m pipe, Kn is vanishingly small — solidly in the continuum regime.
The Knudsen number compares mean free path with system size. When the mean free path is tiny relative to the geometry, collisions between molecules dominate and continuum fluid mechanics works well. As Kn grows, wall interactions and non-equilibrium effects become too important to ignore.
Continuum flow generally supports Navier-Stokes with no-slip walls. Slip flow still uses continuum equations, but the wall boundary condition changes. Transition flow is harder because neither continuum nor free-molecular descriptions are fully satisfactory on their own. Free molecular flow is the regime where molecules interact with boundaries far more often than with each other.
The exact regime boundaries are practical rules of thumb, not universal physical discontinuities. Surface accommodation, geometry, gas species, and the output you care about can all shift which model is acceptable.
The average distance a molecule travels between collisions with other molecules. It depends on temperature, pressure, and molecular size, so it can change a lot with operating conditions.
It matters whenever molecular spacing is no longer negligible compared with device size, such as in vacuum systems, MEMS devices, upper-atmosphere flight, and spacecraft environments. In those cases, continuum assumptions can stop matching the actual flow.
Direct Simulation Monte Carlo is a particle-based method used for rarefied-gas flow when continuum equations with standard boundary conditions are no longer reliable. It tracks molecular collisions statistically rather than solving a continuum field everywhere.
In the slip flow regime (0.01 < Kn < 0.1), the gas velocity at walls is not zero. Navier-Stokes can be used with modified boundary conditions.
At higher altitudes, pressure drops and mean free path increases dramatically. Above ~100 km, spacecraft experience transition and free molecular flow.
Technically yes, but the concept is mainly useful for gases. Liquid molecules are already closely packed, making the mean free path concept less meaningful.