The transmission and the number of reflections of successful neutron t
rajectories through a straight cylindrical tube with a coaxial apertur
e at its entrance have been calculated, assuming that a beam with a co
nical angular divergence is incident along the axis of the cylinder. T
he calculation models neutron transmission measurements through tubes
that have been defined by a cadmium aperture placed at the entrance of
the tube. The addition of an aperture not only lowers the acceptance,
but also reduces the average number of reflections relative to unrest
ricted transmission. The aperture prevents neutrons having trajectorie
s with tight spirals down the tube from entering near the periphery of
the tube. This model might also be useful for understanding the reduc
ed transmission through a tube with slightly crimped edges or through
imperfectly cut glass polycapillaries.