  The hierarchy of moment equations derived from the nonlinear Boltzmann
equation is solved for a gas of Maxwell molecules undergoing a stationary
Poiseuille flow induced by an external force in a pipe. The solution is
obtained as a perturbation expansion in powers of the force (through third
order). A critical comparison is done between the Navier-Stokes theory and the
predictions obtained from the Boltzmann equation for the profiles of the
hydrodynamic quantities and their fluxes. The Navier-Stokes description fails
to first order and, especially, to second order in the force. Thus, the
hydrostatic pressure is not uniform, the temperature profile exhibits a
non-monotonic behavior, a longitudinal component of the flux exists in the
absence of longitudinal thermal gradient, and normal stress differences are
present. On the other hand, comparison with the Bhatnagar-Gross-Krook model
kinetic equation shows that the latter is able to capture the correct
functional dependence of the fields, although the numerical values of the
coefficients are in general between 0.38 and 1.38 times the Boltzmann values. A
short comparison with the results corresponding to the planar Poiseuille flow
is also carried out.
