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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]

The pumping speed at a specified inlet is the gas throughput divided by the inlet pressure: $S=Q/p$. Its units are volume per time, commonly litres per second. A pump's speed depends on gas species and operating conditions.

Connecting a pump of speed $S_p$ through a line of vacuum conductance $C$ gives $1/S_{\mathrm{eff}}=1/S_p+1/C$ in the linear flow regime. Thus a large pump cannot compensate for an arbitrarily restrictive connection.^[ref]

Vacuum conductance relates gas throughput to a pressure difference across a connection: $Q=C(p_1-p_2)$. For throughput in $\mathrm{Pa}{\mathrm{m}}^3{\mathrm{s}}^{-1}$, conductance $C$ has units ${\mathrm{m}}^3{\mathrm{s}}^{-1}$, the same units as pumping speed.

For a pump of speed $S$ connected through a line of conductance $C$, a simple steady balance gives $1/S_{\mathrm{eff}}=1/S+1/C$. Thus a $100\mathrm{L}{\mathrm{s}}^{-1}$ pump behind a $10\mathrm{L}{\mathrm{s}}^{-1}$ connection supplies only about $9.1\mathrm{L}{\mathrm{s}}^{-1}$ at the chamber. Conductance depends on geometry, gas and flow regime; the pressure-independent molecular-flow value should not be used indiscriminately in viscous flow.^[ref]

A vacuum pump lowers gas pressure by removing gas from a vessel or trapping it so that it no longer contributes to the free gas population. Mechanical displacement, momentum transfer and capture are distinct operating mechanisms.

Its relevant performance includes pumping speed, attainable pressure and gas dependence. The pressure achieved in an apparatus also depends on connecting vacuum conductance, leaks and outgassing; the pump's advertised limit is therefore not a complete system specification.^[ref]

Vacuum technology creates, measures and maintains gas pressures below the surroundings for experiments and manufacturing. Pumps remove gas while leaks, permeation and outgassing replenish it. Clean surfaces and appropriate materials can therefore matter as much as nominal pump capacity.

In a simple steady model, a gas throughput $Q$ balanced by effective pumping speed $S_{\mathrm{eff}}$ gives $p=Q/S_{\mathrm{eff}}$. Connecting pipes reduce that speed through their vacuum conductance. The model assumes a specified gas, flow regime and suitable pressure-gauge interpretation; a pressure reading is not automatically a composition-independent measurement of every residual species.^[ref]