Knudsen Number Calculator

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Determine the flow regime of a fluid by comparing the mean free path to a characteristic length.

Dimensionless Parameters

Input Method

Characteristic Length (L)

Flow Regime Results

Enter length scales to determine flow regime

About this calculator

Quick Reference

λMean Free Path

LCharacteristic Length

kBBoltzmann Constant

dEffective Particle Diameter

Overview

The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. It helps determine whether statistical mechanics or the continuum mechanics of fluid dynamics should be used to model the situation.

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Pro Tips

Kn < 0.01: Continuum flow (Navier-Stokes equations apply).
0.01 < Kn < 0.1: Slip flow.
0.1 < Kn < 10: Transition flow.
Kn > 10: Free molecular flow (Individual molecules don't collide much).

Fun Facts

"The number is named after Danish physicist Martin Knudsen (1871–1949)."
"High Knudsen numbers are common in microfluidics and vacuum systems."
"The mean free path of air at sea level is about 68 nanometers."

Formula: Kn = λ / L