There are many forces that act on solids, but there are only four main forces present in fluids:
Gravity – this is always present, but is sometimes negligible in comparison to other forces
Pressure – this is also always present, and is always modelled as compressive and normal to the surface
Viscous – this is always present as well, and similar to gravity, can sometimes be ignored
Surface Tension – this is only present where a liquid meets another medium, like in bubbles and sprays
Since fluids are constantly moving, the forces surrounding them are constantly changing. We split these forces into two types: body forces and surface forces.
Body forces are forces that act everywhere throughout the body. They occur when a body is subjected to an external field, and the magnitude of such forces depends on the volume of the body.
Gravity is a body force
The gravitational force per unit volume is given by:
Therefore, the magnitude of the force acting on an element of volume δV (from the continuum assumption) is given by:
Since acceleration due to gravity is constant, the gravitational force depends only on density and volume.
As the name suggests, a surface force is distributed across a surface, and (just like body forces) we use it in terms of intensity: the force per unit area. You may recognise this as pressure or stress – it is the same.
If the force is evenly distributed across the surface, the stress on the surface, τ, is given by:
However, when the force is not evenly distributed, we apply the continuum assumption to a small section of the surface, δA: