Vacuum Conductance & Effective Pumping Speed

Molecular-Flow Conductance

In the molecular-flow regime, gas molecules collide more often with the walls than with each other. Conductance then depends only on geometry, gas species, and temperature, and becomes independent of pressure. For a circular tube of diameter D and length L (in cm), a widely used approximation for air at room temperature is:

C_tube,air [L/s] ≈ 12.1 · D[cm]³ / L[cm]

For a thin orifice (hole) of area A (cm²), an often used approximation is:

C_hole,air [L/s] ≈ 11.6 · A[cm²]

These formulas come from Dushman and standard vacuum handbooks and are valid for molecular flow and sufficiently long tubes. For very short or wide tubes, end effects become important and more detailed models are needed.

Gas and Temperature Scaling

Molecular-flow conductance is proportional to the mean molecular speed ⟨v⟩, which scales as √(T/M), where T is gas temperature and M is molar mass. The tool scales conductance relative to air at 293 K:

C_gas,T = C_air · √(T / 293 K) · √(M_air / M_gas)

Heavier gases (larger M) have lower conductance, while higher temperature increases conductance slightly.

Series/Parallel Combination & Effective Pumping Speed

Conductances combine like electrical conductances: in parallel they add directly, while in series their reciprocals add:

Parallel: C_total = Σ C_i

Series: 1 / C_total = Σ (1 / C_i)

A pump with speed S connected through a total conductance C_total has an effective pumping speed at the chamber given by:

1 / S_eff = 1 / S + 1 / C_total

This explains why a high-speed pump connected via long, narrow lines can behave like a much smaller pump when viewed from the chamber.