In the free molecular flow range, the pumping performance of a turbomo
lecular pump has been predicted for various values of the dimensionles
s blade velocity ratio C by employing the integral method and the test
particle Monte-Carlo (MC) method in the calculation of the transmissi
on probability. Also, new approximate method combining the double row
solutions, so called double-approximation (DA), is presented here. The
calculated values of transmission probability for the single row agre
e quantitatively with the previous known numerical results. For a six-
row pump, the MC method is employed to calculate the overall transmiss
ion probability for the entire set of blade rows. When the results of
the approximate method combining the single row solutions are compared
with those of the MC method at C=0.4, the previously known approximat
e method overestimates as much as 34% than does the MC method. But, th
e new DA method gives more accurate results within 10% of relative err
or with respect to the MC method.