  The Euler and Navier-Stokes equations both belong to a closed system of three
transport equations, describing the particle number density N, the macroscopic
velocity v and the temperature T. These sytems are complete, leaving no room
for any additional equation. Nonetheless, it is common practice in parts of the
literature to replace the thermal equation by the incompressibility condition
div v = 0, motivated by the wish to obtain simpler equations. It is shown that
this procedure is physically inconsistent in several ways, with the consequence
that incompressibility is not a property that can be enforced by an external
condition. Incompressible behaviour, if existing, will have to follow
self-consistently from the full set of transport equations.
