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Pfeiffer <strong>Vacuum</strong><br />
Page 150<br />
<strong>Vacuum</strong> <strong>Technology</strong><br />
The process gas is admitted to the chamber (1) via a gas flow regulator (5). The butterfly<br />
valve (4) that is controlled by pressure p throttles the pumping speed of the turbopump (2).<br />
a<br />
After the conclusion of the process step, the gas supply is shut off and the control valve<br />
opens completely to cleanly evacuate the chamber again. As this is happening, a new work<br />
piece is loaded into the process chamber. Further information relating to pumping high<br />
gas loads as well as corrosive and abrasive substances is provided in Section 2.7.3.<br />
7.3 Piping conductivities<br />
In calculating the pump-down times of vessels, we have left piping resistance out of consideration<br />
for both Roots pumping stations as well as for turbopumping stations. <strong>How</strong>ever<br />
the piping between a vessel and a pump will also reduce the volume flow rate.<br />
7.3.1 Laminar conductivity<br />
Let us consider the pumping station for the drying system in Section 7.2.2 (Figure 7.2) and<br />
calculate the drop in pressure between condenser and backing pump. In this case, a gas<br />
throughput of Q = 4,285 . 2.9722 10 - 2 = 127 Pa . m³ / s is specified as a result of the pressure<br />
of 4,285 Pa and the volume flow rate S of the backing pump of 107 m³ / h = 2.9722 v . - 2 10<br />
m³ / s. The DN 63 piping has an inside diameter of 0.07 m and a length of 2 m. Two 90° pipe<br />
bends having an equivalent length of 0.2 m each are also taken into consideration.<br />
From p = 4,285 mbar and l 2 – . p2 = 6.65 . - 3 10 Pa . m as well as the pipe diameter d = 0.07 m<br />
we use the Knudsen number (Formula 1-9) to determine the flow range and obtain<br />
Kn = 2.22 . 10 - 5 –<br />
Kn =<br />
l<br />
d<br />
. Since Kn is less than 0.01, this results in viscous flow. This can be either<br />
laminar or turbulent, although we prefer laminar flow as the conductivities here are significantly<br />
higher than for turbulent flow, which means that significantly lower volume flow losses<br />
will occur. The Reynolds number Re must be less than 2,300 for laminar flow.<br />
To calculate the Reynolds number, we first determine the flow velocity v in the piping:<br />
4 . S m<br />
v<br />
v = = 8.66<br />
d 2 . p s<br />
and the density � of the air at 42.85 mbar from the air density � 0 = 1.293 kg / m³ at<br />
atmospheric pressure.<br />
1.293 . 42.85 kg<br />
� = = 0.0547<br />
1013 m 3<br />
�<br />
Re = . v . d<br />
�<br />
= 1.822, i.e. laminar flow.<br />
We use Formula 1-21 to calculate pressure p 1 :<br />
p . d 4 p . d 4<br />
L Rl = . ( p 1 + p 2 ) = . p –<br />
256 . � . l 128 . � . l<br />
and in accordance with Formula 1-10:<br />
and multiply by �p = p 1 - p 2 to obtain the gas throughput:<br />
p . d 4<br />
Q = L . �p = . 2 ( p1<br />
Ri - p 2)<br />
. 2<br />
256 . � . l<br />
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