Knudsen Number Calculator
Determine flow regimes in gas dynamics and rarefied gas flows
Calculate Knudsen Number
Select a vacuum level to auto-fill typical mean free path values
Average distance between molecular collisions
Typical dimension of the system (pipe diameter, channel width, etc.)
Knudsen Number Results
Formula: Kn = λ/L
Input values: λ = 0.000e+0 m, L = 0.000e+0 m
Analysis
Example: Air Flow Through a Pipe
Problem
System: Air flow through a 10 cm diameter pipe
Conditions: Room temperature (300 K), atmospheric pressure
Mean free path: λ = 68 nm (typical for air at 1 atm)
Characteristic length: L = 10 cm (pipe diameter)
Solution
Kn = λ/L = (68 × 10⁻⁹ m) / (0.1 m)
Kn = 6.8 × 10⁻⁷
Result: Kn ≪ 0.001 → Continuum flow
Continuum mechanics equations (Navier-Stokes) are fully applicable.
Vacuum Levels
Applications
Aerospace
High-altitude flight, spacecraft design
Vacuum Technology
Vacuum pumps, chambers, systems
MEMS
Microelectromechanical systems
Physics Tips
Kn < 0.01: Use continuum mechanics
Kn > 0.1: Use kinetic theory
Dimensionless number - units cancel out
Critical for rarefied gas dynamics
Understanding the Knudsen Number
What is the Knudsen Number?
The Knudsen number (Kn) is a dimensionless parameter that characterizes the degree of rarefaction in a gas flow. It represents the ratio of the molecular mean free path to the characteristic length scale of the system. This ratio determines which flow regime governs the gas behavior and which mathematical models should be applied.
Physical Significance
- •Low Kn: Frequent intermolecular collisions, continuum behavior
- •High Kn: Rare intermolecular collisions, molecular behavior
- •Determines validity of continuum approximation
- •Critical for accurate flow modeling
Knudsen Number Formula
Kn = λ/L
- Kn: Knudsen number (dimensionless)
- λ: Mean free path of gas molecules
- L: Characteristic length of the system
Applications
- • High-altitude aerodynamics
- • Vacuum system design
- • Microfluidics and MEMS
- • Space vehicle design
- • Gas sensor development
- • Molecular beam experiments
Note: The characteristic length L is typically the smallest relevant dimension of the system, such as pipe diameter, channel height, or obstacle size.