申論題

2.(50%) A solid sphere of radius R and density ps is immersed in the center of a deep tank of incompressible fluid of viscosity " and density ρ. At time zero, the sphere is suddenly released and falls in a straight line under the action of gravity. The sphere velocity u(t) increases from zero and reaches a steadily falling terminal velocity U. The quasi-steady drag F_D acting on the sphere may be calculated by reading C_D-Re plot shown in Figure 3 where C_D is the drag coefficient and Re-2RρU/μ is the particle Reynolds number.

(5) (5%) Now, we consider the motion of a spherical liquid droplet of identical radius R, density pu (ρ＜ρL-ρs)and viscosity iL that also falls at its terminal velocity U_Lin the low-Re regime. Do you expect a greater or a lower Co than that of the solid sphere if the liquid droplet falls at the same speed as the solid sphere? Why?