Since conductance in molecular flow is independent of pressure and since most high vacuum applications are in molecular flow, the calculations discussed here are appropriate only for that flow regime. Two books edited by J.M. Lafferty are invaluable when making conductance calculations. The first is Scientific Foundations of Vacuum Technique (by Saul Dushman, 2nd ed., J.M. Lafferty, editor), from which we have reprinted a table from p.99 with permission from John Wiley & Sons ©1962. The second is Scientific Foundations of Vacuum Science and Technology (J.M. Lafferty, editor, John Wiley & Sons ©1998) which has a chapter by R. Gordon Livesey with a wealth of information and equations for calculating conductances in molecular, transitional, and continuum flow regimes.
Examples of conductance calculations for straight cylindrical components using Dushman's table are given in the sidebar. To calculate conductances of non-cylindrical components, find the appropriate equation in Lafferty's second book or, for less accurate estimates, use Dushman's table and some rules of thumb:
- Right-Angle Bends: Measure the tube length “L” as the shorter distance (along the inside of the bend). Calculate the conductance from the table as if the tube were straight and then divide by 2 for every right-angle bend.
- Non-Cylindrical Cross-Section: Calculate the “open” area of the tube or annulus and find the radius of a cylindrical tube with an equal area. Calculate the conductance of this “equivalent tube”.
- Diameter Changes: If a tube changes diameter along its length, the safest way to calculate conductance is to use the smaller diameter to calculate “a” (the radius). But if the smaller diameter portion is short compared to the total tube length, the underestimation may be extreme. In such cases, calculate the conductance of the small diameter and large diameter section as separate tubes and combine then in series (see Combining Conductances).
a (cm) |
F_{o} | F_{t} - Conductance of tube (liters sec^{-1}) for air at 25°C | ||||||
---|---|---|---|---|---|---|---|---|
L/a = 1 | 2 | 4 | 8 | 12 | 16 | 30 | ||
K = 0.672 | 0.514 | 0.359 | 0.232 | 0.172 | 0.137 | 0.080 | ||
0.1 | 0.367 | 0.246 | 0.188 | 0.132 | 0.085 | 0.063 | 0.050 | 0.029 |
0.2 | 1.466 | 0.986 | 0.753 | 0.527 | 0.340 | 0.252 | 0.200 | 0.117 |
0.3 | 3.300 | 2.217 | 1.664 | 1.184 | 0.764 | 0.567 | 0.451 | 0.263 |
0.4 | 5.866 | 3.943 | 3.013 | 2.106 | 1.358 | 1.008 | 0.802 | 0.468 |
0.5 | 9.166 | 6.160 | 4.708 | 3.291 | 2.122 | 1.575 | 1.253 | 0.731 |
0.6 | 13.200 | 8.872 | 6.779 | 4.739 | 3.057 | 2.269 | 1.805 | 1.052 |
0.7 | 17.970 | 12.080 | 9.228 | 6.449 | 4.161 | 3.088 | 2.457 | 1.432 |
0.8 | 23.470 | 15.770 | 12.050 | 8.424 | 5.436 | 4.033 | 3.208 | 1.871 |
0.9 | 29.700 | 19.960 | 15.250 | 10.660 | 6.879 | 5.105 | 4.061 | 2.368 |
1.0 | 36.660 | 24.640 | 18.830 | 13.160 | 8.492 | 6.302 | 5.013 | 2.922 |
2.0 | 146.600 | 98.560 | 75.340 | 52.650 | 33.970 | 25.210 | 20.050 | 11.690 |
3.0 | 330.000 | 221.700 | 166.400 | 118.400 | 76.420 | 56.710 | 45.110 | 26.300 |
4.0 | 586.600 | 394.300 | 301.300 | 210.600 | 135.800 | 100.800 | 80.210 | 46.770 |
5.0 | 916.600 | 616.000 | 470.800 | 329.100 | 212.200 | 157.500 | 125.300 | 73.100 |
6.0 | 1320.000 | 887.200 | 677.900 | 473.900 | 305.700 | 226.900 | 180.500 | 105.200 |
7.0 | 1797.000 | 1208.000 | 922.800 | 644.900 | 416.100 | 308.800 | 245.700 | 143.200 |
8.0 | 2347.000 | 1577.000 | 1205.000 | 842.400 | 543.600 | 403.300 | 320.800 | 187.100 |
9.0 | 2970.000 | 1996.000 | 1525.000 | 1066.000 | 687.900 | 510.500 | 406.100 | 236.800 |
10.0 | 3666.000 | 2464.000 | 1883.000 | 1316.000 | 849.200 | 630.200 | 501.300 | 292.200 |
Calculating Conductance
The conductance of an orifice — a hole in an infinitely thin plate — is determined as follows:
- Measure the orifice's radius in centimeters.
- Enter the table at the appropriate “a” (radius) row. Go right to the F_{0} column and read the conductance in L/s.
The conductance of a straight cylindrical tube is calculated as follows:
- Measure the (overall) length of the tube in any convenient units.
- Measure the tube's ID in the same units.
- Divide the ID by 2 to give the radius.
- Divide the length by the radius (this gives the “L/a” ratio used in the table).
- Convert the radius to centimeters (this gives “a” (cm) to use in the table).
- Enter the table at the appropriate “a” row
Go right until under the value of the calculated “L/a” ratio. If the exact match is not available, use the next larger “L/a” value or interpolate.