  Macroscopic traffic models have recently been severely criticized to base on
lax analogies only and to have a number of deficiencies. Therefore, this paper
shows how to construct a logically consistent fluid-dynamic traffic model from
basic laws for the acceleration and interaction of vehicles. These
considerations lead to the gas-kinetic traffic equation of Paveri-Fontana. Its
stationary and spatially homogeneous solution implies equilibrium relations for
the `fundamental diagram', the variance-density relation, and other quantities
which are partly difficult to determine empirically.
  Paveri-Fontana's traffic equation allows the derivation of macroscopic moment
equations which build a system of non-closed equations. This system can be
closed by the well proved method of Chapman and Enskog which leads to
Euler-like traffic equations in zeroth-order approximation and to
Navier-Stokes-like traffic equations in first-order approximation. The latter
are finally corrected for the finite space requirements of vehicles. It is
shown that the resulting model is able to withstand the above mentioned
criticism.
