Abstract
A formula is derived for the transmission probability (and hence, gas flow conductance) of a long tube, having a uniform elliptical cross-section, valid in the molecular flow regime (long mean free paths). Comparison with long tubes of circular and rectangular section having the same area showed relatively close agreement in transmission probabilities between elliptical and rectangular section tubes for the same ratio of axes or length of sides respectively. Variations from a circular, square (or triangular) section remained within 10% down to axes or side ratios of 0.3. Existing formulae in the literature, applicable to elliptical sections, show deviations increasing with the ellipticity. It is shown that the frequently used relation involving the ratio of cross-sectional area to perimeter for tubes of various shapes (other than circular) may lead to large errors.
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