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Differential pumping maintains different gas pressures in connected regions by restricting the connecting gas flow and pumping each region separately. A small aperture or narrow tube limits the vacuum conductance between stages.

In the molecular flow regime, a connection with conductance $C$ carries throughput $Q=C(p_1-p_2)$. A downstream stage pumped at effective speed $S$ has $S{p}_2=C(p_1-p_2)$ in steady state, giving $p_2/p_1=C/(S+C)$. This lets a source operate at a higher pressure while an adjacent particle beam travels in a better vacuum.^[ref]

In molecular flow, the gas mean free path is large compared with the channel or vessel dimensions, so molecules encounter walls more frequently than one another. The Knudsen number $\mathrm{Kn}=\lambda /L$ characterizes this regime.

For a small aperture of area $A$ between equilibrium gas reservoirs, the vacuum conductance is $C=A\overline{v}/4$, where $\overline{v}$ is the mean molecular speed. At fixed temperature this scales as the inverse square root of molecular mass. Continuum viscous-flow formulas need not apply.^[ref]

A laboratory vacuum is a region with substantially reduced gas pressure, rather than an experimentally perfect absence of matter. Lowering the number density increases the mean free path, allowing a molecular beam to travel with fewer collisions. In molecular flow, the mean free path exceeds the apparatus dimensions, so wall encounters dominate.

A vacuum pump competes with leaks and outgassing. For an isothermal vessel of volume $V$, constant gas load $Q$ in pressure-volume per unit time, and effective pumping speed $S$, gas balance givesThis ideal model predicts a pump-down time constant $V/S$ and a limiting pressure $Q/S$. A restricted connecting pipe reduces the effective pumping speed; a larger pump alone need not fix it. Measuring the pressure transient tests the model, while deviations can reveal changing outgassing or pumping speed.^[ref]