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Aims. Collections of dust, grains, and planetesimals are often treated as apressureless fluid. We study the validity of neglecting the pressure of such afluid by computing it exactly for the case of particles settling in a disk.Methods. We solve a modified collisionless Boltzmann equation for the particlesand 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, ismore than 1/2, the particle fluid cannot be considered as pressureless. Whilewe 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 turbulentflows.

On the pressure of collisionless particle fluids. The case of solids settling in disks