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Manual Calculation

 

Since conductance in molecular flow is independent of pressure and since most high vacuum applications are in molecular flow, the calculations discussed here and in the sidebar 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 2nd 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, 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)
Fo Ft - 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 appropriae "a" (radius) row. Go right to the F0 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.

 

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