Consider a fluid of constant density ρ and viscousity μ. The flow is assumed to be governed by the Navier-Stokes equation:
ρ(∂v/∂t+(v·∇)v)=-∇p+μ∆v
and the continuity (incompressibility) condition:
∇·v=0
where v denotes the velocity and p is the pressure. Let S0 denotes the surface of the body which moves with constant velocity in one direction. In this case, show that the most commonly used force formula (on the body) is;
∬ pn dA + μ∬ n×ω dA
S0 S0
where ω is the vorticity vector and n denotes unit normal vector to the body surface.