The pressure gradient force results from the local fluid pressure gradient around the particle and is defined as:

(6–27)

This force is only important if large fluids pressure gradients exist and if the particle density is smaller than or similar to the fluid density. Neglecting diffusive and source terms in the steady-state momentum equation, the pressure gradient can be replaced by the velocity gradient. Assuming a constant fluids density, the pressure gradient force can be written as

(6–28)

leading to the following contribution to the right hand side of Equation 6–7:

(6–29)

with

(6–30)

necessary if the particles are solved in a rotating system. The term is shifted to the rotation term (see Equation 6–19), therefore, the implemented pressure gradient term reduces to

(6–31)

The particle momentum source due to the pressure gradient force is computed from:

(6–32)