effect would have become more pronounced as the surface area increased dramatically such as with Tube E. Regardless, the data effectively show the effects of tube diameter versus length on pumping speed. Be aware that Tube E never achieved 10~3 torr after three hours of trying to stabilize to the lower pressure.

Inspecting Table 7.1, the mean free path of a molecule ranged from an estimated 7 to 70 mm for the ranges of this experiment's pressures. Without even getting to molecular flow, the efficiency of Tube D and E compared to Tube A (in cross area) is similar to a 44 lane freeway with only one lane open during rush hour. Another thing to consider is that at 10"3 torr, with the mean free path at about 7 mm, by going from a 10-mm-i.d. tube to a 6-mm-i.d. tube, flow transport would be slowed considerably. This should serve to show that pressure and tubing i.d. is interrelated.

Whether turbulent, viscous, or molecular flow, the fastest transport through tubes is when the diameter is large and/or the length is small. Fortunately, at a certain point, larger diameters or shorter tubes make no significant difference in performance.

7.2.9 Throughput and Pumping Speed

There will always be a net transport of gas from one end of a system to another if there is a pressure difference between the two parts. The quantity of gas (at a specific temperature and pressure) that passes a given plane in a given amount of time is called the throughput or mass flow rate ( 0 . When throughput is equal to zero, you have a steady-state condition. Throughput is measured in pressure-volume per unit of time, such as torr-liters per sec or 1 Pa-M3/S = 1W (watt). Interestingly enough, because force is required to move the gas, throughput can also be considered as the amount of energy per unit time passing through a plane.

A different measurement of gas transport is the volumetric flow rate (S), which is also called the pumping speed. The units of volumetric flow rate are simply volume/time, such as liters per second. The difference between Q and S is that S is independent of the quality of the vacuum. Throughput and volumetric flow are related to each other by the pressure P and are expressed in Eq. (7.7). The relationship of mass flow, volumetric flow, and pressure is demonstrated in Fig. 7.9.

In a typical vacuum system, tubes are connected to tubes, which are connected to traps, which are connected to other tubes, and so forth. The transport of gas through a system of these tubes is called conductance (Q . Every tube within the system offers a different conductance depending on its length and diameter.

Conductance is the throughput (Q) divided by the difference between the pressure going into the tube (P,) and the pressure going out of the tube (P2) [see Eq. (7.8)]. Although conductance and volumetric flow rates have the same units, conductance is used to describe the ability, or efficiency, of a gas flowing through a

S = 85 I/sec

P = 1x107 torr

Fig. 7.9 A system in a steady-state condition showing the relationship between Q, S, and P.From The Fundamentals of Vacuum Technology,3rd Edition FIG. 13, by H.G. Tompkins, © 1997 by the American Vacuum Society, American Institute of Physics, New York, reproduced (abstracted) with permission

section (one or more) of tubing, while volumetric flow rate deals with the amount of gas that can go past a single plane of the system:

Vacuum systems are generally not made with one tube and one easy way to calculate conductance. Rather, vacuum systems are constructed with many tubes of different sizes. The total conductance of an entire system is calculated by adding all the reciprocals of the conductance of the various parts [see Fig. 7.10)] and is shown in Eq. (7.9):

(7.9)

ct C\ C2 C3 C4

What can be seen from Eq. (7.9) and Fig. 7.10 is that by placing a stopcock mid-length on a tube will minimally effect conductance, especially if the length of the stopcock section is as short as possible and the size of the stopcock is as large as possible. Common sense, economy, and experience are good guides for this.