The fictitious Coriolis, centrifugal and Euler forces, present in a rotating frame of reference, are stemming from the change to a non-inertial frame of reference, and are defined using the vector of angular velocity, , and the density, ρ. This amounts to adding to the momentum equation a volume force equal to

where rp = r − rbp, with rbp a position vector on the axis of rotation. The first term on the right-hand side is the centrifugal force, the second term the Coriolis force, and the third term the Euler force. With these forces, the momentum equation reads:

Introducing a constant reference density ρref, this equation is equivalently written:

where r is the position vector and rref is an arbitrary reference position vector. From this equation, it is convenient to define the reduced pressure which accounts for the hydrostatic pressure stemming from the centrifugal force as

When the relative pressure formulation is used, also the hydrostatic pressure, , stemming from the centrifugal force, is taken into account when compensating for the hydrostatic pressure at a pressure boundary conditions. When a reduced pressure formulation is used, is used to define the absolute pressure, see also the section on Gravity.

In a porous domain, the Coriolis force should be divided by the porosity εp, such that the volume force added to the momentum equation becomes