**Last month we discussed Gas Molecules and Gas Flow and at the end of the article mentioned the term Conductance.**

Fig. 1. Throughput in a Vacuum Furnace. |

This time we will talk a bit more about conductance in vacuum system piping and why it has to be taken into consideration in the design of a typical vacuum furnace or similar vacuum system. Firstly though, we will discuss Throughput.

**Throughput**

Have you ever wondered why vacuum pipes and connections are of several different sizes on any vacuum system? I would suggest that most users don’t really give it any thought. It is what it is. So let’s look at the sections of a vacuum system and again try to visualize those gas molecules, which are so tiny we can’t see them, and understand the conditions at different places in the system.

Pumping speed of large mechanical vacuum pumps is usually indicated in cubic feet per minute. That can be denoted in several ways; cfm, cu ft /min or ft^{3} min^{-1}. This is also shown in metric terms as cubic meters/hour, liters/min and l/min also shown as m^{3} hr^{-1} and l min^{-1}.

Although the last terms are the most modern, in training I tend to use “cfm” and “l/min” as easy terms to write, and not to use negative powers of ten. In this case the “-1” denotes that time is the divisor, under the line, in the written equation or formula, i.e. per unit time, but some students who are new to vacuum technology or engineering terms think of negative powers of ten as a vacuum or a reading of pressure lower than atmospheric pressure.

So pumping speed units indicate the volume of gas being pumped in a certain time, but they do not relate that pumping speed to any pressure term. If the pressure term is added then we can determine the mass of gas that is flowing at that point in the system.

Throughput is a constant at any point in the vacuum system, during normal operation. (Fig. 1) In this example I have assigned a pumping speed “S” for the diffusion pump of 8000 l/sec. That makes the diffusion pump inlet diameter about 20 inches (about 500 mm). The vacuum chamber pressure “P” is shown as 1 x 10^{-6} Torr which is a typical pressure for many vacuum applications. (Remember that 1 x 10^{-6} represents a 1 millionth part of 1 Torr)

^{-1}Torr l/min.

^{-2}Torr, because we know that Q is constant at 4.8 x 10

^{-1}Torr l/min we can calculate P which is 9.6 x 10

^{0}l/min.

^{-1}Torr l/min, P is calculated to be 6.3 x 10

^{-4}l/min.

The gas, in the vacuum chamber at 1 x 10^{-6} Torr, (position 1) is in molecular flow, where the gas molecules move in a random direction and collide more frequently with surfaces inside the chamber than they do with other molecules. The pumping speed is entirely dependent on the inlet size of the diffusion pump; the larger the pump inlet, the more gas molecules will enter the pump.

As the gas molecules pass through the vapor jets of the diffusion pump they are compressed to a smaller volume and higher pressure, as shown in the backing line (position 2). At a pressure of about 5 x 10^{-2} Torr the gas molecules are now in transition from molecular flow to viscous or continuum flow. (This backing line may have a 3 to 6 inch diameter depending on the combination of diffusion and mechanical pumps used.)

The gas molecules in transitional flow now move down the pipeline to the lower pressure generated at the inlet of the mechanical backing pump where they are compressed again, up to atmospheric pressure, and exhausted from the system (position 3).

From this example we learn a bit more about gas molecules moving through the vacuum furnace system. At a low pressure in the vacuum chamber a huge volume of gas is first compressed in the diffusion pump by a factor of about 10,000 times, from 1 x 10^{-6} up to 1 x 10^{-2} Torr. That gas is then compressed about another 15,000 times in the mechanical pump allowing it to be exhausted into the air at 760 Torr. Neither vacuum pump can compress the gas from the vacuum chamber pressure up to atmospheric pressure on its own, but working as two pumps in series it can be done successfully.

The example shown starts at an already low pressure in the vacuum chamber. If we look at another set of numbers with the vacuum chamber pressure at around 1 x 10^{-3} Torr, throughput Q would be 1000 times larger at 4.8 x 10^{2} which is 480 Torr l/min. Because P will remain in the same range at position 2 and the same at position 3, calculations show the pumping speed S also about 1000 times higher at those places in the pumping system.

Fig. 2. Conductance in pipes. |

**Conductance**

The conductance between two points in a vacuum system is expressed as the quantity flow rate of gas flowing through a device divided by the resulting pressure drop.

C per meter = Q / P_{1}– P_{2} and is expressed in liters per second (l/sec)

Conductance values are used to determine the “effective” pump speed at the vacuum chamber, which can be quite different from the “rated” pump speed of the vacuum pump at its inlet connection. This knowledge is used to select the correct size of mechanical vacuum pump to rough out the vacuum chamber in the required time.

The roughing line shown in Fig. 1 runs horizontally from the side of the vacuum chamber and then an elbow turns it downwards to run to the mechanical vacuum pump inlet. There is always a roughing valve in this pipeline to allow the roughing line to be opened and closed as needed. The valve has its own conductance rating and some manufacturers will show that in their valve literature. For this simple example we will ignore the valve conductance and only consider the pipeline which may have a total length of 2 meters or 3 meters depending on the system design. We will look at both options to see the difference.

If the mechanical roughing and backing pump is similar to a Stokes 212, having a rated pumping speed (Sp) of 150 cfm, it will have an inlet size of 3 inches. That is close to the 70 mm pipe size shown on Fig. 2 so we will use the values of conductance for the 70 mm pipe size on that graph. To complete the calculation we have to express the pump speed (Sp) in l/sec. We multiply 150 cfm by the factor shown in Fig.3 which is 0.472 to give a pump speed of 70.8 l/sec.

The conductance varies with pressure so we need to compare different pressures to try to visualize the “big picture” – of gas molecules that we can’t see. The pressure used is the “average pressure” in the pipeline being studied.

Fig. 3. Pump speed conversions. |

The first pressure to consider is 1 Torr as it is close to the highest pressure on the Fig. 2 chart. (At pressures above 1 Torr the higher values of conductance allow lots of gas flow and the pump speed loss is much lower.)

If we do the same calculations for the roughing line at an average pressure of 1 x 10^{-2} Torr, a 100 times lower pressure, let’s see the results.

Fig. 4. The effect of roughing line conductance. |

^{-2}Torr is 60 l/sec [Fig. 2 purple arrows] the calculation then shows: Se = 68.9 cfm

These numbers are tabulated in Fig. 4 to make them easier to read.

In another article we can look at how conductance may affect pumping speed above the oil diffusion pump and in the backing line.

**Conclusions**

For throughput: the pressures at different points in the system show the very high compression ratios developed by the oil diffusion pump and mechanical pump. Compare them to the compression ratio of a typical car engine which is about 8 to 1.

For conductance: as the roughing line pressure drops below about 1 Torr the effective rough pumping speed at the chamber is reduced considerably as the roughing line becomes longer, due to conductance losses in the piping.

Roughing pipelines should be as short as possible, and as large a bore as practical.

Note: If the roughing line has an oversized bore to increase the conductance, it also adds extra volume to the system that has to be evacuated. At some point the time needed to evacuate the added volume cancels out the increased effective pump speed at the chamber and no improvement is seen.

**References:**

The equations used are from “Modern Vacuum Practice”, written and published in the UK by Nigel Harris.

**Howard Tring / Tel: (610) 792-3505 / E-mail: [email protected]** **/** **Web: www.vacuumandlowpressure.com**

Howard Tring is the owner of Vacuum and Low Pressure Consulting, a company that supplies vacuum pump accessories such as reconditioned inlet traps and exhaust filters and new replacement elements for exhaust filters. Howard also offers on-site vacuum technology and oil sealed vacuum pump repair training and consulting services, customized to the needs of the client. Howard is a member of ASM International and the Heat Treat Society, the AVS, the SME, the SVC and the American Society for Training and Development.

**Copyright October 2013, Tring Enterprises LLC** – Comments on this article are welcome. I do not profess to know everything about any specific vacuum related subject. However, I have worked in the vacuum pump industry a long time and have seen good, bad and ugly. Please contact me with any comment or question. All messages related to the content of the article will be answered.