The drag force exerted by a fluid with viscosity ponto a sphere with diameter d is Fo = 3rtvdu, where v is the velocity of the fluid in m/sec. The viscosity of water is 0.001 Pa. sec. The weight of a sphere when placed underwater is the sphere's buoyant weight: Fe = ned (p - Pw)/6, where p = mass density of the material that sphere is composed of, and pw = mass density of water = 1000 kg/m?. a. Consider a very small spherical soil grain, with d = 0.01mm. The grain material density is 2650 kg/ml. Determine the minimum fluid velocity (in m/sec) required for the fluid to transport such a grain via drag. Hint: equate the buoyant weight to the drag force and solve for v. Note: d must be in meters
b. Consider now a medium-sized spherical soil grain, with d = 1 mm. Determine the minimum fluid velocity (in m/sec) required for the fluid to transport such a grain via drag.
c. Consider now a large-sized spherical soil grain, with d = 10 mm. Determine the minimum fluid velocity (in m/sec) required for the fluid to transport such a grain via drag.