  Aims. Collections of dust, grains, and planetesimals are often treated as a
pressureless fluid. We study the validity of neglecting the pressure of such a
fluid by computing it exactly for the case of particles settling in a disk.
Methods. We solve a modified collisionless Boltzmann equation for the particles
and compute the corresponding moments of the phase space distribution: density,
momentum, and pressure. Results. We find that whenever the Stokes number,
defined as the ratio of the gas drag timescale to the orbital timescale, is
more than 1/2, the particle fluid cannot be considered as pressureless. While
we show it only in the simple case of particles settling in a laminar disk,
this property is likely to remain true for most flows, including turbulent
flows.
