Molecular vs viscous flow in vacuum piping
How to identify flow regimes from pressure and geometry, and why conductance formulas change between molecular and viscous conditions.
By Semiconductor Tools Editorial Team · Last updated: 2026-06-14
Gas flow regime determines which conductance model applies. Using molecular-flow formulas at roughing pressures—or viscous formulas at UHV—produces errors of 10× or more. The Knudsen number Kn = λ/D provides a first-order classification.
Regime summary
- Molecular (Kn > 1): C ∝ D³/L for tubes; pressure-independent to first order. Use Conductance Calculator.
- Viscous (Kn < 0.01): Hagen–Poiseuille; C increases with pressure.
- Transition (0.01 < Kn < 1): Neither limit accurate; bracket with both models.
Worked example — Gate valve orifice in two regimes
Foreline tube ID 8 cm, length 200 cm. Evaluate at 100 mTorr and 1×10⁻⁵ Torr with N₂ at 300 K.
- Mean Free Path at 100 mTorr: λ ≈ 0.66 mm. Kn = λ/D ≈ 0.00008 → viscous during roughing.
- At 1×10⁻⁵ Torr: λ ≈ 6.6 cm. Kn ≈ 0.83 → transition for 8 cm pipe.
- At 1×10⁻⁷ Torr: λ ≈ 6.6 m. Kn ≫ 1 → molecular; Conductance Calculator tube formula applies for Seff estimates.
- Practical takeaway: during roughing, valve opening affects viscous conductance; near base, molecular orifice formula dominates—PM that slightly closes a valve hurts molecular Seff far more than roughing speed.