For a particle of velocity v (SI unit: m/s) in a fluid of velocity
u (SI unit: m/s), the pressure gradient force term
Fp (SI unit: N) is (
Ref. 19)
where, as in the Virtual Mass Force in the previous section,
mf (SI unit: kg) is the mass of the fluid displaced by the particle volume,
dp (SI unit: m) is the particle diameter, and
ρ (SI unit: kg/m
3) is the density of the fluid at the particle’s position.
Unlike the virtual mass force, however, the material derivative D (not
d) follows the fluid velocity direction rather than the particle velocity direction. That is,