Calculator Inputs
This tool classifies the gas flow regime using the Knudsen number, Kn = λ / L. Use a representative length L such as tube diameter, channel height, or nozzle throat.
Formula Used
The classification is based on the Knudsen number:
For an ideal gas with an effective molecular diameter d, the mean free path is:
Regime thresholds used here are common engineering guidelines: Kn < 0.01 (continuum), 0.01–0.1 (slip), 0.1–10 (transition), > 10 (free-molecular).
How to Use This Calculator
- Enter temperature, pressure, and a representative characteristic length.
- Select a gas preset, or enable custom molecular diameter and molar mass.
- Click Calculate Regime to compute λ, Kn, and related diagnostics.
- Use the export buttons to save results for reports or lab notes.
Example Data Table
These example cases illustrate typical regimes by changing pressure and length scale (air, 300 K, d ≈ 0.365 nm). Values are approximate.
| Temperature (K) | Pressure | Length L | Mean free path λ (m) | Kn | Regime |
|---|---|---|---|---|---|
| 300 | 1 atm | 10 mm | ~6.7×10⁻⁸ | ~6.7×10⁻⁶ | Continuum |
| 300 | 10 kPa | 100 μm | ~6.7×10⁻⁷ | ~6.7×10⁻³ | Continuum (edge) |
| 300 | 100 Pa | 100 μm | ~6.7×10⁻⁵ | ~0.67 | Transition |
| 300 | 1 mTorr | 1 mm | ~5×10⁻² | ~50 | Free-molecular |
Gas Flow Regime Article
1. Why flow regime classification matters
Gas behavior shifts when the characteristic length becomes comparable to the molecular mean free path. Selecting the right regime helps you choose valid equations, estimate uncertainty, and avoid large errors in friction, mass flow, and heat transfer across microdevices and vacuum hardware.
2. Knudsen number as the key metric
The calculator uses the Knudsen number, Kn = λ/L, to quantify rarefaction. When Kn is very small, the gas behaves like a continuous fluid. As Kn rises, wall interactions dominate and kinetic effects appear, eventually requiring molecular or particle-based modeling.
3. Mean free path depends on pressure and diameter
For an ideal gas with an effective collision diameter d, the mean free path follows λ = kB·T /(√2·π·d²·P). Lower pressure increases λ linearly, while higher temperature increases λ proportionally. Larger molecular diameter reduces λ through the d² term.
4. Continuum flow and classical engineering tools
In continuum flow (Kn < 0.01), Navier–Stokes with no-slip walls is typically appropriate. Standard correlations for pipe friction, boundary layers, and convection are most reliable here. Typical examples include atmospheric ducts, large tubes, and many industrial process lines.
5. Slip flow and near-wall corrections
Slip flow (0.01–0.1) occurs when the bulk still resembles a continuum but the wall region needs modified boundary conditions. Velocity slip and temperature jump can change pressure drop and heat flux. This regime is common in small channels at reduced pressures.
6. Transition flow and hybrid modeling
Transition flow (0.1–10) is a mixed regime where neither continuum nor free-molecular assumptions hold fully. Results depend strongly on geometry and surface accommodation. Engineers often use transitional correlations, moment methods, or particle techniques such as DSMC for higher fidelity.
7. Free-molecular flow in high vacuum systems
In free-molecular flow (Kn > 10), collisions are rare compared with wall impacts, so transport becomes ballistic. Conductance scales differently than in viscous flow, and pumping speed calculations must use molecular-flow formulas. This regime dominates in high-vacuum manifolds and chambers.
8. Practical workflow for consistent reporting
Start by choosing a representative length L (tube diameter, channel height, or orifice size). Use realistic temperature and pressure, then confirm gas properties using presets or custom molecular data. Export CSV or PDF to document Kn, λ, and the identified regime alongside your test conditions. In air at 1 atm and 300 K, λ is about 6–7×10⁻⁸ m, so millimeter channels stay continuum while micron gaps can show slip.
FAQs
1) What is the characteristic length L?
L is the geometry scale that controls rarefaction, such as tube diameter, channel height, or nozzle throat. Use the dimension that best represents where collisions and wall effects influence transport.
2) Why does lower pressure increase Kn?
Mean free path is inversely proportional to pressure. When pressure drops, molecules travel farther between collisions, increasing λ and therefore increasing Kn for the same length scale.
3) Are the regime thresholds exact?
No. Kn ranges are widely used guidelines. Surface roughness, accommodation, temperature gradients, and complex geometries can shift practical limits, so treat boundaries as transition zones.
4) Which gas properties matter most here?
Effective molecular diameter strongly affects λ through d². Molar mass is used to estimate thermal speed and collision time. Pressure and temperature typically drive the largest changes in Kn.
5) Can I use this for microfluidic devices?
Yes. Microchannels often fall into slip or transition regimes, especially at reduced pressures. Choose L as channel height or hydraulic diameter to make the regime estimate meaningful.
6) What does collision time tell me?
Collision time τ approximates how frequently molecules collide. Short τ implies dense gas and continuum behavior. Long τ indicates rarefied conditions where wall interactions become more important.
7) When should I consider kinetic simulation?
When Kn is roughly 0.1 or higher, continuum assumptions weaken. For detailed predictions in complex geometries, consider DSMC or other kinetic approaches, particularly in the transition and free-molecular regimes.