題組內容

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 FD acting on the sphere may be calculated by reading CD-Re plot shown in Figure 3 where CD is the drag coefficient and Re-2RρU/μ is the particle Reynolds number.
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(4) (8%) Perform dimension analysis to find all the relevant non-dimensional flow variables with one that involves the transient timescale T as a dimensionless time scale, T'.