When there is fluid flow through the vacuum pipeline, the easness of fluid flow is called the conductance. Let the pressure at the two ends of the vacuum pipeline be p1, p2, respectively, C represents the flow conductance (Fig.1), and then the flow can be expressed as

**Q=CΔp**

**Fig. 1 Flow diagram of vacuum piping**

In a vacuum system, gas flow can be roughly classified into viscous flow and molecular flow. When the mean free path of gas molecules is sufficiently smaller than the inner diameter of the tube, intermolecular collisions are the main phenomenon, and the viscous flow plays a dominate role. The conductance of viscous flow can be showed as below (take circular tube as an example):

**C= (πa4p/8η)/L**

Where p—the average pressure of the conduit (= (p1+p2)/2)

η———viscosity

When the mean free path of gas molecules is larger than the inner diameter of the tube, the collision of gas molecules with the inner wall of the tube is the main phenomenon, ie, the molecular flow plays a dominate role. The flow of molecular flow can be expressed as

**C=(2πa3v/3)/L**

Where v —the average velocity of the gas molecules.

Two tubes whose conductance is respectively C1 and C2 are in parallel with each other (Figure 2), the gas flow in the vacuum pipeline is Q1 and Q2 respectively, according to the flow definition:

**Q1=C1(p1-p2)**

** **

**Q2=C2(p1-p2)**

**Fig.2 Flow diagram of parallel pipes**

Full flow is

**Q=Q1+Q2= (C1+C2)(p1-p2)**

Therefore, the synthetic conductance is

**C=C1+C2**

Synthetic conductance of general parallel vacuum pipelines is

**C=C1 +C2 +C3 +... = ∑Ci**

When two vacuum conduits whose conductance is respectively C1 and C2 are connected in series (Fig.3), the gas flow rates in the different vacuum conduits are equal. According to the definition:

**Q=C1(p1-px), Q=C2(px-p2)**

px is the pressure at the vacuum piping connection.

**Fig. 3 Flow diagram of a series vacuum pipeline**

Eliminating px

**Q=(1/C1+1/C2)-1(p1-p2)**

Therefore, the synthetic conductance is

**C=(1/C1+1/C2)-1**

For the cascade, the general formula of the conductance can be expressed as

**1/C=1/C1+1/C2+1/C3+... = ∑1/Ci**