Knudsen Number Calculator

Knudsen Number:

\\[ Kn = \frac{\lambda}{L} \\]

Mean Free Path:

\\[ \lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P} \\]

Flow Regime:

• Continuum: \\(Kn < 0.01\\)
• Slip: \\(0.01 \leq Kn < 0.1\\)
• Transitional: \\(0.1 \leq Kn < 10\\)
• Free Molecular: \\(Kn \geq 10\\)

Where:

• \\(Kn\\): Knudsen number (dimensionless)
• \\(\lambda\\): Mean free path (m)
• \\(L\\): Characteristic length (m)
• \\(k_B\\): Boltzmann constant (\\(1.380649 \times 10^{-23} \, \text{J/K}\\))
• \\(T\\): Temperature (K)
• \\(P\\): Pressure (Pa)
• \\(d\\): Molecular diameter (m)

\\[ \lambda = \frac{1.380649 \times 10^{-23} \times 300}{\sqrt{2} \pi (3.7 \times 10^{-10})^2 \times 101325} \approx 6.799 \times 10^{-8} \, \text{m} \\] \\[ Kn = \frac{6.799 \times 10^{-8}}{0.001} \approx 6.799 \times 10^{-5} \\]

Flow Regime: Continuum (\\(Kn < 0.01\\))