In fluid mechanics, the force density is the negative gradient of pressure.

It has the physical dimensions of force per unit volume.

Force density is represented by the symbol f,[1] and given by the following equation, where p is the pressure: The net force on a differential volume element dV of the fluid is: Force density acts in different ways which is caused by the boundary conditions.

In a sphere placed in an arbitrary non-stationary flow field of viscous incompressible fluid for stick boundary conditions where the force density's calculations leads to show the generalisation of Faxen's theorem to force multipole moments of arbitrary order.

In a sphere moving in an incompressible fluid in a non-stationary flow with mixed stick-slip boundary condition where the force of density shows an expression of the Faxén type for the total force, but the total torque and the symmetric force-dipole moment.