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# Conductance Calculations

Please see the information on VacTran, the computer modeling program that calculates conductances and creates virtual vacuum systems.

Using a formula he derived, Dushman calculated the conductances for cylindrical tubes based on their measured dimensions, producing the table below. The equation may err by as much as 12% for systems in free molecular flow (see J. Vac. Sci. Tech., Vol. 4, No.3, page 338). However, given the uncertainties and errors in measuring effective pumping speeds, base pressure, gas load, etc., this level of error is mostly insignificant.

Using Dushman's Table • Measure the overall length of the tube in any convenient units.
• Measure the tube 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 Dushman's table.
• Convert the radius to centimeters. This gives the 'a(cm)' used in Dushman's table.
• Enter the numeral at the appropriate 'a' row.
• Go right until under the value of the calculated 'L/a' ratio. If the exact number is not available, use the next larger 'L/a' or interpolate. This gives the conductance value of a straight cylindrical tube in liters/second.
 a(cm) Conductance of tube of air at 25°C (liters per second) L/a = 0 1 2 4 8 12 16 30 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 1,320.000 887.200 677.900 473.900 305.700 226.900 180.500 105.200 7.0 1,797.000 1,208.000 922.800 644.900 416.100 308.800 245.700 143.200 8.0 2,347.000 1,577.000 1,205.000 842.400 543.600 403.300 320.800 187.100 9.0 2,970.000 1,996.000 1,525.000 1,066.000 687.900 510.500 406.100 236.800 10.0 3,666.000 2,464.000 1,883.000 1,316.000 849.200 630.200 501.300 292.200

Reprinted from page 99 of Scientific Foundations of Vacuum Technique by Saul Dushman 2nd edition (J.J. Laffery - editor) with permission from John Wiley & Sons. Copyright © 1962 by John Wiley & Sons.

Adopting some general rules, Dushman's results can be applied to tubes of other cross-sections. The results will not be totally accurate, but, since the calculated conductances are likely underestimated, it is often worthwhile to use them. • For tubes with right-angle bends, measure 'L' as the shortest distance shown (see drawing on the right). Calculate the conductance from the table as if the tube were straight, then divide the conductance by 2 for every right-angle bend.
• For tubes with rectangular or square cross-section (or even the annulus between two tubes), calculate the open area and find the radius of a cylindrical tube with an equal open area. Calculate the conductance of this 'equivalent tube' using Dushman's table.
• If the diameter changes along the length of the tube, use the smallest diameter to calculate 'a'.

### Conductance Conclusions

When designing a vacuum system or changing components in an existing one, always attempt to maximize conductance. In any high-vacuum situation, keep these points in mind:

• It is all too easy to lower conductance accidentally.
• Make all tubes and components as short as possible and as open (with large diameters) as possible.
• The part with the smallest conductance determines the maximum conductance.
• In high-vacuum or UHV applications, the concept of the conductance being too high has no meaning. The converse, however -- a conductance 'too low' -- happens all too frequently.