Chris Dean’s Personal Website

Aim:

The aim of this experiment was to observe the different factors that influence the effective pumping speed of a rotary pump.

Background:

The very first pumps were used for raising water and mining, as they still are today, but nowadays pumps have many more applications, other than just moving fluids around (although that’s still essentially all they do).

In this experiment the pump is used to create a vacuum in a chamber, and is based upon one of the first useful designs for such a piece of apparatus. Vacuum pumps have a great deal of practical applications in today’s world and not only for physics experiments. They are used for example, to create the vacuums in light bulbs or televisions tubes, for producing an atmosphere devoid of any gasses that may react (either chemically or physically) with sensitive apparatus as in the making of complex electrical circuits, and sometimes in other industrial processes where a vacuum is necessary, such as freeze-drying or the melting of reactive metals such as titanium. In general though, pumps are classified into one of three groups depending on the way in which energy is imparted to the fluid in order to move it from one place to another:

1. Volumetric displacement
2. Addition of kinetic energy
3. Use of electromagnetic force.

Volumetric displacement is where the fluid is transported either mechanically (by the sweeping action of a rotating vane – as in this experiment) or by the use of another fluid (using air to pump water from a coal mine, for example). A pump that mechanically displaces the fluid is generally known as a positive displacement pump
and generally moves relatively low volumes of fluid at high pressure.

The addition of kinetic energy to a fluid can be achieved by either using an impeller rotating at high speed (cf the rotating vane – above) or by providing an impulse in the direction of flow (in a bicycle pump for example). And generally kinetic pumps
impel high volumes at low pressure.

And lastly if we were to use an electromagnetic force to provide the pumping action, the fluid has to be a good electrical conductor in order to be moved at all.

The pump that is being considered in this experiment is the oil sealed rotary vane pump, and can be considered as both a volumetric displacement and a kinetic pump, all rolled into one. It is very useful as a ‘roughing’ pump and can be used to evacuate the majority of gas (at around atmospheric pressure) from a closed vessel before a more specialised pump, such as diffusion pump, is used to increase the vacuum further for use in applications such as electrical micro-circuit production.

Gaede first developed the rotary vane pump in 1905, and it has three main parts, these are: The stator (pump housing), the rotor and vanes, and lastly the oil seal.

The stator is really a large sealed tube that houses the rotor and vanes, and has both an inlet and exhaust hole. The rotor is a bar that runs along the length of the stator and has the (spring loaded) vanes (solid plates, similar to the blades of a propeller) attached to it. The vanes are kept in contact with the stator wall via an oil coating, which is used as a seal between each ‘compartment’ formed by any two neighbouring vanes and the stator wall. The whole pump set up is finally surrounded by a jacket of oil to minimise gas leaking to and from the atmosphere.

The pump basically works according to the following method:

1. The inlet valve between the pump and the system to be evacuated is opened to increase the system’s volume. Gas expands to fill the volume and therefore enters the pump. The valve is then closed.
   

1. The rotor (and vanes) inside the stator rotate, and effectively move the gas from one greater volume ’side’ of the pump to the other smaller volume side. This process causes the gas to be compressed in the smaller volume and also therefore leaves a vacuum in the ‘compartment’ where the gas once was.
   

1. Finally, when the gas is compressed so much that its pressure is greater than that of the atmosphere (which holds a valve to the outside shut), it pushes open the exhaust valve and is expelled into the atmosphere.
   

The pumping speed (the quantity of gas moved per second) is greatest from atmospheric pressure to about one torr, then as the ultimate pressure (the pressure to which the pump is capable of pumping) is reached the speed decreases to zero. The ultimate pressure for this pump is about 10^-1 torr or 10^-3 torr if two such pumps are connected in series. For this pump the ultimate pressure is reached when the mean free path of the gas molecules is greater than the dimensions of the vessel being evacuated, and therefore very few molecules actually pass into the mouth of the pump. If the mouth of the pump (the size of the inlet valve) was variable them we may have been able to achieve slightly lower pressures by increasing its size. However at this stage a second pump (such as a diffusion pump) really needs to be employed to significantly lower the pressure any more. This is why the rotary vane pump is a good roughing pump for other more specialised devices such as the diffusion pump.

Lastly the ultimate pressures possible are limited by leakage between the high and low-pressure ’sides’ of the pump. This
is
mainly due to non-exhausted gas being carried back to the low-pressure side, or vapours that were once dissolved in the sealing oil evaporating off when exposed again, to the low-pressure side. The decomposition of the oil when exposed to ‘hot spots’ caused by friction can also affect the ultimate pressure as can bad pitting on the stator or vane (caused by pumping a corrosive gas, for example) which leads to the oil seal being partially or even completely broken down.

Using some sort of cooling apparatus along side the pump may reduce the decomposition of oil and the vapours in the sealing oil can be removed by using either a vapour trap or by gas ballasting.

Gas ballasting is the deliberate input of air (via a one way gas ballast valve) into the high-pressure side of the pump, so that any vapours being pumped do not condense under the high pressure there and pollute the oil. In other words the total pressure on the high-pressure side is increased (so that the outlet valve is opened ‘early’) without increasing the partial pressure of the vapour, so that any vapours can be released before they have the chance to liquefy.

The vapour trap is a more costly and more difficult arrangement to set up as it involves passing the gas being pumped through a chemical that will absorb any vapours before pumping. This would be fairly useful if the only contaminant was, say water vapour, but as any number of different contaminant vapours could be present, gas ballasting is an all-round better way of doing things.

The overall efficiency of the pump mainly depends upon how well the pump is sealed and the quality of the surface finishes throughout the pump.

Lastly, in this experiment we will be using a Pirani Thermal conductivity gauge to measure the low-pressure situations around 10^-1 torr. It determines the pressure based upon the rate at which heat is dissipated from a hot filament. It is basically a Wheatstone
bridge, with one arm being the heated filament in the vacuum system.
The filament’s resistance depends upon its temperature, which, in turn, depends on the rate of dissipation of thermal energy through the gas. As the wire is struck by passing gas molecules, it gives up some if its heat to them, thus causing the temperature of the wire and therefore the resistance to drop slightly. The bridge is powered from a constant voltage source, and any unbalanced current (due to the temperature changes) is converted directly to torr.

A diagram of the pump taken from the lab script is shown on the next page

Assumptions:

1. When working out the volume of the chamber and its pipes and connectors that were to be pumped out we assumed that the valves had the same volume as the pipes they were connecting, the chamber could be considered as a composite of straight sections and domes only, and lastly that all pipe work was connected at sharp right angles and not ‘curved around’.

1. That the Pirani gauges held no volume of gas to be pumped what so ever.

1. The time taken to open the valves was instantaneous and had no effect on the pumping speed

1. For the first experiment we could have closed V1 and opened V2 to let the air from the chamber fill the pipes as much as possible before entering the pump, and therefore give us a better idea of the effective pumping speed. This would be difficult in the second experiment however, as the gas would have taken some time to fill the pipe work through the aperture, and then subsequent pumping would not have give an accurate representation of the effect of the restrictive aperture. And as we later wanted to compare both values for the effective pumping speed, we decided that we could make a better comparison if this was not done in either experiment. The result being that we assume that the pump is evacuating the chamber directly and not the associated pipe work past V2.

1. That the dimensions of the space to be evacuated are as stated in the results analysis.

1. The temperature of the room is constant

1. The quantity of gas entering the pump is the same as that expelled from the atmosphere, i.e. that the pump is working perfectly

Method:

1. The apparatus was carefully assembled as in the following diagram (from the lab script) except the blank off, which was already permanently sealed by glass, and not a bung or other kind of removable seal:

1. AA1 (the Air Admittance Valve) was closed off and the rotary vane pump was started (from now on I will refer to the rotary vane pump just as ‘the pump’ as it is the only pump being used in this experiment) with the gas ballast off. As the glugging of the pump stopped after a few moments, we knew that we didn’t have any large leaks.

1. Next with the ¼ swing valve closed we attached P1 to the control box and switched it on. We then slowly opened V1 and V3 and saw the gauge reading fall down to just below 10^-1 torr so we knew that there were no leaks in our system of pipes.

1. We then mounted the glass chamber (after checking it for cracks and other obvious imperfections) on top of its ‘connector’ and mounted the blanking tube on top of the chamber. We then put the metal safety cage around the chamber and connected P2.

1. Then we closed both AA2 and V3 and slowly opened V2 to pump the chamber out as a test run. The chamber pressure reached just below 10^-1 torr, so we knew we were all right to start the experiment for real.

1. We closed V1 to cut the pump off from the chamber and then very slowly opened the air inlet so that the chamber was returned to atmospheric pressure. Once the chamber was returned to normal pressure the air inlet was closed again, V2 was closed and we opened V1 to evacuate the tubing up to V2. We then opened the gas ballast valve for 10 minutes to attempt to remove any unwanted vapours dissolved in the oil, and achieve the best results from the pump.

1. Next we took the measurements we required to determine the effective pumping speed of the pump. We both drew a copy of table 1 (see results), and using a stopwatch timed how long the pump took to evacuate the chamber down to the specified pressures in the table. To give some idea of our reaction time errors we repeated the experiment once each.

1. After taking this data we restored the chamber pressure (as before) and isolated the pump by closing V1.

1. For our second experiment we fitted a small disk with a 1mm hole in the centre between the pipe work and the chamber base so that we could measure the effect of such a restrictive aperture on the pumping speed. We then evacuated the pipe work up to V2 as before and opened the gas ballast valve for 10 minutes.

1. Once the aperture was in place the experiment was completed as the previous one was, but only one of us took readings due to time restrictions (see table 2).

Results:

Table 1:    

Graph 1:

Table 2:    

Graph 2 (a):

Sources of Errors:

A big error in our results is obviously due to our own personal reaction times, we have attempted to minimise this by taking two lots of results and averaging them, although this is still not perfect. Ideally we would have used an electronic data logger to record our results, or we would have had to repeat the experiment many times to obtain a representative distribution of results.

Another error comes from the accuracy of our meters and measurements as are shown in the tables.

The other errors could be due to not opening valves quick enough and small undetected leaks in the apparatus.

In the results analysis below the major errors come from the slopes of the graphs (via choosing the best fit) and even more so, the assumptions involved in approximating the volume to be pumped.

Results Analysis:

Experiment 1:

We want measure the effective pumping speed of the pump by using it to evacuate the chamber and measuring how long it takes to get from one pressure p_a (760 torr, atmospheric pressure) to a lower pressure p_b.

If a volume dV of air from the chamber enters the pump in a time dt its speed is given by:

From Boyle’s Law we know that pV is constant at constant T, so:

This can be re-written as:

It follows that:

And:

And when we plot a graph of p against t on semi-log axes we can observe 2 linear regions on the graph. And the corresponding plot of ln p against t has a gradient of

The first slope has a gradient of

The second slope has a gradient of

The volume to be evacuated is the same in both scenarios, and this is calculated (approximately, with reference to diagram) as follows:

Note: All measurements are ± 0.5 mm

Measurements:

Section A:     Dimensions:    Length = 115 mm;    Internal Diameter = 25 mm

Section B:     Dimensions:    Length = 101 mm;    Internal Diameter = 24 mm

Section C (i):     Dimensions:    Length = 53 mm;    Internal Diameter = 27 mm

Section C (ii):     Dimensions:    Length = 155 mm;    Internal Diameter = 15 mm

Section D (i):     Dimensions:    Length = 43 mm;    Internal Diameter = 82 mm

Section D (ii):     Dimensions:    Length = 18 mm;    Internal Diameter = 59 mm

Section E:     Dimensions:    Length = 140 mm;    Internal Diameter = 26 mm

Section F:     Dimensions:    Length = 20 mm;    Internal Diameter = 7 mm

Section G:     Dimensions:    Length = 70 mm;    Internal Diameter = 15 mm

Section H:     Dimensions:    Length = 150 mm;    Internal Diameter = 140 mm

Note: I am assuming further that the shaded parts of the diagram on the next page do not contribute to the overall volume being pumped

Volumes:

Section A:    

Cylinder = p(0.5 X 0.025)²
X 0.115 + Dome = 0.5(⁴/₃p (0.5 X 0.025)³) = 6.05 X 10^-5m³ (± 0.02 X 10^-5 m³)

Section B:     

Cylinder = p(0.5 X 0.024)²
X 0.101 = 4.57 X 10^-5 m³ (± 0.02 X 10^-5 m³)

Section C:     

Cylinder = p(0.5 X 0.027)²X0.053 + Cylinder = p(0.5 X 0.015)²X0.155 = 5.07X10^-5 m³ (± 0.02 X 10^-5 m³)

Section D:     

Cylinder = p(0.5X0.082)²
X 0.043 + Cylinder = p(0.5X0.059)²
X 0.018 = 2.76X10^-4 m³ (± 0.02 X 10^-5 m³)

Section E:     

-Cylinder = p(0.5X0.026)²
X 0.140 + Dome = 0.5(⁴/₃p (0.5X0.026)³) = -7.89 X 10^-5 m³ (± 0.02 X 10^-5 m³)

Section F:     

Cylinder = p(0.5 X 0.007)²
X 0.020 = 7.70 X 10^-7 m³ (± 0.02 X 10^-5 m³)

Section G:     

Cylinder = p(0.5 X 0.015)²
X 0.070 = 1.24 X 10^-5 m³ (± 0.02 X 10^-5 m³)

Section H:     

Cylinder = p(0.5 X 0.140)²
X 150 + Dome = 0.5(⁴/₃p (0.5 X 0.140)³) = 3.03 X 10^-3 m³ (± 0.02 X 10^-5 m³)

Total Volume Evacuated » 3.40 X 10^-3 m³ (± 0.02 X 10^-5 m³) = 3.4 litres (± 0.2 X 10^-3 litres)

Gradient 1 = – 0.34 s^-1 = Þ S = 0.34V = 0.34 s^-1
X 3.40 X 10^-3 m³ = 1.156 X 10^-3 m³ s^-1

= 69.36 l min^-1

Gradient 2 = – 0.01 s^-1 = Þ S = 0.01V = 0.01 s^-1
X 3.40 X 10^-3 m³ = 3.4 X 10^-5 m³ s^-1

= 2.04 l min^-1

Deducing C:

    Þ
l min^-1

C = 3.77 X 10^-3 m³ s^-1 (± 5 X 10^-3 m³ s^-1)

Table of Effective Pumping Speeds for Experiment 1:

Experiment 2:

Plotting the graph on semi-log axes allows us to again see 2 linear regions on the graph and therefore the plot of ln p against t has a gradient of

The first slope has a gradient of

The second slope has a gradient of

Gradient 1 = -0.04 s^-1 = Þ S = 0.04V = 0.04 s^-1
X 3.40 X 10^-3 m³ = 1.36 X 10^-4 m³ s^-1

= 8.16 l min^-1

Gradient 2 = -7.76 X 10^-3 s^-1 = Þ S = 7.76 X 10^-3V = 7.76 X 10^-3 s^-1
X 3.40 X 10^-3 m³ = 2.64 X 10^-5 m³ s^-1

= 1.58 l min^-1

Deducing C:

    Þ
l min^-1

C = 0.15 m³ s^-1 (± 5 X 10^-3 m³ s^-1)

Deducing C (for the aperture):

    NB: C₁ is the value of C from experiment 1

Þl min^-1

C = 0.15 m³ s^-1 (± 5 X 10^-3 m³ s^-1)

Table of Effective Pumping Speeds for Experiment 2:

On graph 1 we can see that there are effectively two linear regions (roughly) shown by the two dotted lines, with a curved ‘cross-over’ section in between them. These correspond to the change over from macroscopic to microscopic gas laws. For the ‘first’ linear region (that with the steepest gradient) the assumptions that we make in modelling a macroscopic gas hold true, as there is a great deal of gas in the system. Therefore the pump works normally and achieves its maximum pumping speed. As more and more gas is removed however, these assumptions break down causing the effective pump speed to decrease rapidly, until it virtually stops altogether (when the mean free path of the gas molecules becomes comparable to the dimensions of the chamber).

The same kind of effect is shown in the second experiment but is much less pronounced due to the aperture restricting the gas flow from the start.

The conductance of the pipes was 3.77 X 10^-3 m³ s^-1 (± 5 X 10^-3 m³ s^-1). With the aperture the total conductance was 0.15 m³ s^-1 (± 5 X 10^-3 m³ s^-1) and the conductance of the aperture alone was also

0.15 m³ s^-1 (± 5 X 10^-3 m³ s^-1). This shows the large effect an aperture has on the conductance of the pipes, and when in place it’s conductance is effectively the conductance of the pipes. So if we wanted to regulate the conductance of some pipe work for use in pumping apparatus, we could do so in the limit of the diameter of the pipe, by using an aperture of known conductance in the same way as we did here.

On the first graph of pumping speed against pressure you can see more dramatically how the pumping speed decreases with respect to the pressure. But the second graph appears to show us that pumping speed actually increases with the decrease in pressure. However if we examine the data we find that both at high pressure and at low pressures the pumping speed increases with pressure as expected, but there appears to be two different curves showing this effect. I don’t know the reason for this, it may that our data is wrong, but if not there must, at some point be a cross over between one curve and the other. This change over may be an effect of changing over from, again, the macroscopic to the microscopic gas regimes, but I can’t be sure.

Conclusion:

All in all the experiment was a success.

The conductance of the pipes was 3.77 X 10^-3 m³ s^-1 (± 5 X 10^-3 m³ s^-1)

The conductance of the aperture was 0.15 m³ s^-1 (± 5 X 10^-3 m³ s^-1).

The effective pumping speeds (without obstruction) were: 69.36 l min^-1 for high pressure

2.04 l min^-1 for low pressure

The effective pumping speeds (with obstruction) were: 8.16 l min^-1 for high pressure

1.58 l min^-1
for low pressure

To improve the experiment an exact volume reading of the chamber could have been taken, the results could have been taken using a data logger. The length of the pipe work could have been decreases and the valves replace with others of a more suitable design (that open quicker). Also the best-fit lines could have been calculated rather than ‘guessed’.

Bibliography:

Encyclopaedia Britannica 1999, CDROM Version

Grolier Year 2000 CDROM Encyclopaedia

Physics For A Level, 2^nd Edition, F. Azzopardi.

Longmans general physics, 1962, 6^th Edition.

 

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