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1. Pressure and Throughput Distribution in Vacuum Systems
By Howard Tring
Last time the discussion was about throughput and conductance in vacuum systems. This time we will look at
the pressure profile throughout the vacuum system in a slightly different way than it was shown last time. The
first thought might be that once the vacuum system is under vacuum carrying out the process, the lowest
pressure will be in the vacuum chamber and that the highest pressure will be at the primary pump exhaust
which will be atmospheric pressure. As we see from Fig. 1, this is not quite correct.
Fig. 1 shows how the pressure changes through the
system and actual values of P pressure and S speed
are given in the table, Fig. 2. The pressures shown
assume that the chamber has been evacuated
(pumped down) to the process pressure needed and
conditions are stable.
The graph shows values of throughput Q, pressure P
and pumping speed S at four points in the system.
The dotted lines indicate the point where the values
occur in this example. As was stated last time,
throughput Q is constant at any point in the system.
That means that as pressure P changes in one
direction pumping speed S must change in the other
direction as Q is constant.
Although the graph shows P1 at the chamber outlet
to the vacuum pumps, let’s start at P2 the inlet to the
diffusion pump. In North America the American Vacuum Society (AVS) measures diffusion pump pumping
speeds at the inlet flange in liters per second (l/sec or l sec-1) , in Europe these speeds are measured one radius
above the pump inlet and as a result are slightly lower. For a vacuum system manufacturer it means that they
should be cautious when comparing the rated speed of a USA made diffusion pump against one made in
Europe.
At Q2 = S2 P2, the inlet to the diffusion pump, the pumping speed is shown as 600 l/sec and the pressure is
indicated as 2.0 x 10-6 Torr. As we discussed last time, conductance through piping and accessories reduces the
effective pumping speed so the effective pumping speed in the vacuum chamber will be lower than at the
pump inlet.
When we lookat the table for values atQ1 = S1 P1 atthe outletof the chamber we see thatthe effective pumping
speed has dropped to 200 l/sec due to conductance losses through the piping and the high vacuum valve, and
the pressure is higher at 6 x 10-6 Torr.
This shows why the vacuum piping should be as short as possible, to minimize conductance losses. In an
efficient design the high vacuum valve and diffusion pump would be mounted as close as possible to the
chamber outlet flange. In the case of chambers where the diffusion pump can’t be mounted underneath, the
rightangle high vacuumvalve is mounted directlyto the chamber outletflange, and the diffusionpump directly
Fig. 1. Pressure & Throughput in a vacuum
system.

2. below the valve. In some case a cold trap is mounted between the high vacuum valve and the diffusion pump.
(Cold traps will be discussed in a month or two.)
Returning to position 2, the inlet to the diffusion pump, and following the pressure line into the diffusion pump
we see the following. There is a slight pressure drop towards the top jet of the jet assembly, which is the lowest
pressure shown in this representation. Then, as the gas stream passes the top jet, it is compressed to a higher
pressure between the two jets. At the second jet there is another small pressure drop as the gas molecules
become entrained in the oil vapor jet and then the vapor jet compresses the gas stream to the pressure at
which it is exhausted towards the primary pump. At this point the graph shows Q3 = S3 P3. From the table the
value of S3 is shown 0.06 l/sec (or 3.6 l/min) and the pressure is now up to 2.0 x 10-2 Torr. Pressure P3 is about
what would be expected in the foreline of the primary vacuum pump.
The next section of the pressure line
indicates a gradual pressure drop in the
foreline until the gas stream reaches the
inlet of the primary pump, position 4. In
most heat treating furnaces the primary
pump will be either an oil sealed rotary
piston or rotary vane pump. Depending on
the size of the furnace these pumps may
also have a Roots design vacuum booster mounted on the inlet. The vacuum booster pump develops a very
high pumping speed in the pressure range from about 30 Torr to 10-2 Torr. This is the pressure range where
most of the water vapor is released from the chamber, hot zone and product surfaces.
At position 4, where Q4 = S4 P4, the pumping speed S4 is shown in the table as 1.2 l/sec (72 l/min) and pressure
P4 is shown as 1.0 x 10-3 Torr. This would indicate that the pump used in this example is a two stage rotary vane
pump rather than a single stage rotary piston pump that has an ultimate vacuum of about 1 x 10-2 Torr (10
microns).
The final part of the pressure line then shows an initial pressure drop on the inlet side of the rotary vane pump
as the gas expands into the void between the rotor and stator, and then a pressure rise as the gas is isolated,
compressed up to atmospheric pressure and expelled from the pump on the outlet side of the mechanism.
Following through these steps shows that there are a number of pressure changes through the system as the
gas molecules are pumped from the vacuum chamber to atmospheric pressure at the primary pump exhaust.
References:
The two figures used in this discussion are taken from the textbook “Modern Vacuum Practice” (3rd edition,
page 70) written and published in the UK by Nigel Harris. Both have been slightly modified to show Torr units.
Howard Tring / Tel: (610) 792-3505 / E-
mail: HowardT@VacuumAndLowPressure.com / 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
Fig. 2. Pressure and Pumping Speed table.

3. 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 December 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.
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Conductance and Throughput in Vacuum Pipelines
By Howard Tring
Last month we discussed Gas Molecules and Gas Flow and at the end of the article mentioned the term
Conductance.
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 ft3 min-1. This is also shown in metric terms as cubic meters/hour,
liters/min and l/min also shown as m3 hr-1and 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 thinkofnegative powers oftenas a vacuumor a reading ofpressure lowerthanatmospheric
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.
The formula for throughput is Q = P V / t = PS
Where Q = throughput, P = pressure, V = volume, S = pumping speed and t = time
Fig. 1. Throughput in a Vacuum Furnace.

4. 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 manyvacuumapplications. (Remember that1 x 10-6 represents a 1 millionthpartof1 Torr)
At position 1, the high vacuum pump inlet, the product of P and S show a throughput Q of 4.8 x 10-1 Torr l/min.
At position 2, in the backing line at the exhaust of the diffusion pump, the pump has compressed the gas to 5 x
10-2 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 100 l/min.
At position 3, the gas from the backing line has been compressed through the mechanical vacuum pump to
atmospheric pressure 760 Torr, and as Q is 4.8 x 10-1 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 ofgas 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 mechanicalpump allowing itto be exhausted into the air at760 Torr. Neither vacuumpump cancompress
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 102 which is 480 Torr l/min. Because P will remain in the same range at position 2 and the same at
position3, calculations showthe pumping speed S also about1000 times higher atthose places inthe pumping
system.
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 / P1- P2 and is expressed in liters per second (l/sec)
Therefore, ifthe pipe being considered hasa lengthof2 meters, the conductance fromthe chartinFig.2 is divided
by 2 to give the total conductance.
There are differentformulae forcalculating valuesofconductance inviscous andmolecularflow. Inthis discussion
we are looking at the roughing line conductance which for the most part will be in transitional flow conditions.

5. Although the conductance can be calculated, it is
easier to read the conductance (per meter) off the
graph in Fig. 2 for the example we are looking at.
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.
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.)
At an average pressure of 1Torr the 70 mm diameter
pipe shows a conductance of 3,000 l/sec (per meter).
[Fig.2 black arrows]
The formula for calculating the effective pump speed (Se) is:
Se = Sp x C / Sp + C so it is quite simple now to fill in the relevant numbers and obtain the answer. Make sure
that the units used all match, you can’t mix cfm and l/sec.
So, at 1 Torr, for a 1 meter pipe, the formula becomes: Se = 70.8 x 3000 / 70.8 + 3000
That becomes: Se = 212,400 / 3070.8
Fig. 2. Conductance in pipes.
Fig. 3. Pump speed conversions.

6. And the effective speed at the chamber is: Se = 69.18 l/sec or 146 cfm.
So, if the roughing line is 70 mm bore and 1 m long, the effective pump speed Se at the chamber has only
dropped 4 cfm from the rated pumps speed Sp.
Now, looking at roughing lines of 2 m and 3 m length, we will see quite a difference.
For a roughing line of 2 m length, Se is 146 / 2 = 73 cfm
If the roughing line is 3 m long, Se is 146 / 3 = 49 cfm.
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.
The conductance for a 1 m length pipe at 1 x 10-2 Torr
is 60 l/sec [Fig. 2 purple arrows] the calculation then
shows: Se = 68.9 cfm
For a roughing line of 2 m length, Se is about 35 cfm
If the roughing line is 3 m long, Se is about 23 cfm.
Either way, the results show a considerable loss of
pumping speed at the chamber inlet from the pump
inlet.
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 atdifferentpoints inthe systemshowthe veryhighcompressionratios developed
bythe oil diffusionpump and mechanicalpump. Compare themto the compressionratio ofa typicalcar 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.
Fig. 4. The effect of roughing line
conductance.