Physics 405

Homework assignment #5 - Vacuum Systems

1) Calculate the conductance (in liters/second) of air at room temperature in the molecular flow regime through:

(a) a round tube of length 30 cm and diameter 5.0 cm;

(b) a round tube of length 30 cm and diameter 1.0 cm;

(c) 25 tubes of length 30 cm and diameter 1.0 cm connected in parallel;

(d) 25 tubes of length 30 cm and diameter 1.0 cm connected in series (i.e. one tube of total length 7.5 × 10² cm).

2) You wish to pump out a cubical stainless steel chamber of dimensions 10 cm × 10 cm × 10 cm.  You have a pump with a pumping speed of 10 l/s.  For each tubing arrangement (a)-(d) above, give the ultimate pressure obtained in the stainless steel chamber in steady state.  Assume that stainless steel outgasses at 1.0 × 10^-8 Torr-l/cm²s, and that the whole system is in the molecular flow regime.  Ignore outgassing from the tubes.

Hint: Treat the pump as a pipe with conductance of 10 l/s connected to a perfect reservoir at zero pressure.