Difference between drag force and viscous force

Hi Rachel,

Maybe it's too late, but I will still give an answer for posterity.

The drag force and the viscous force are two different forces that compose, together with other forces, the fluid-particle interaction force that you find both in the equation of motion of the particle and in the Navier-Stokes equations of the fluid. The viscous force is the force applied to the particle due to the presence of the deviatoric (viscous) part of the fluid stress tensor, which is the cause of the friction between fluid layers. So it exists because the fluid has a certain viscosity. The other component of the fluid stress tensor is the hydrostatic one, so the static pressure, which is expressed by the pressure gradient, and by the way, this force is included in the fluid-particle interaction force as well.

On the other hand, the pressure and the viscous forces are the cause of the drag force. So the drag force is a consequence of these forces and can indeed be divided into pressure and friction drag. However, while viscous and pressure forces are ALWAYS present even if the object is still, the drag force acts on the particle ONLY if there is a relative movement between the particle and the fluid. Furthermore, the drag force strongly depends on the shape and the size of the particle. At an intermediate and high Reynolds number, we don't have an exact analytical solution of the drag force and we need to model it through correlations like the Di Felice one.

So coming to your question, you cannot incorporate the viscous force into the drag force, even though one is a consequence of the other one, because they are two different forces, both acting on a particle moving through a fluid.

Hope it helps,

Cheers,
Dario