Use dimensional analysis to derive an empirical expression for the drag force, FD 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, FD on the body, while the effect of the lift force, FL would be negligible (low speed). The inertia force (F= Ma = ρv2L) 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, FV = τA = μvL; the elastic force, FE = EvA = EvL2 ; the gravitational force, FG = Mg = ρL3 g; the absolute surface roughness, ɛ; and the geometry, Li. Thus, the important physical quantities include: ρ, v, L, FD, μ, Ev, g, ɛ, and Li.

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Figure 10.2

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