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 spherevelocity u(t) increases from zero and reaches a steadily falling terminal velocity U. The quasi-steady drag FD acting on thesphere may be calculated by reading CD-Re plot shown in Figure 3 where CD is the drag coefficient and Re-2RρU/μ is theparticle Reynolds number.

【題組】(1) (10%) Formulate a general dynamic equation to describe the sphere transient unsteady motion u(t) from time zero with aproper initial condition. Explain the physical meaning of every term in your equation.