Use dimensional analysis to derive an empirical expression for the drag force, F_D for the most general assumptions as follows: assume that the submerged body illustrated in Figure 10.2 is moving at a low speed in a stationary, homogeneous, viscous, compressible fluid, with a possible wave action at the free surface. As a result, the fluid would exert a drag force, F_D on the body, while the effect of the lift force, FL would be negligible (low speed). The inertia force (F_I = Ma = ρv²L² ) and the drag force, FD will always be important. Using Table 11.7 as a guide, the additional dominant/significant physical forces and dominant physical quantities in the flow situation are the viscous force for laminar flow, F_V = τA = μvL; the elastic force, F_E = EvA = EvL² ; the gravitational force, F_G = Mg = ρL³ g; the absolute surface roughness, ɛ; and the geometry, L_i. Thus, the important physical quantities include: ρ, v, L, F_D, μ, Ev, g, ɛ, and L_i.

Figure 10.2