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Example 8: A smooth sphere with density ρs = 1500 kg/m3 (sand) is falling in water. Recall that for a sphere volume is V = π 6 D3 and surface area is As = π D2 where D is diameter. (a) Find terminal velocity for D = 0.10 mm. (b) Find terminal velocity for D = 5.0 cm. € flow fields for parts (a) and (b) € for both a smooth and rough surface and (c) Sketch indicate how your answers to (a) and (b) change. Known: ρs = 1500 kg/m3, (a) D = 0.10 mm, (b) D = 5.0 cm Assumptions: Steady flow, water is a Newtonian fluid with constant properties at STP, quiescent water far from boundaries Find: Terminal velocity, U, for (a) and (b), (c) sketch flow fields for smooth and rough Solution: Properties: for water at STP ρ = 999 kg/m3 µ = 1.12 x 10-3 N•s/m2 Answers: (a) 2.4 mm/s, (b) 0.81 m/s Streamlines for cylinder in uniform cross flow for a range of Reynolds numbers: CD = 1 2 D ρ U 2 Ap € Drag coefficient, CD, versus Reynolds number, Re, where D is total drag, U is uniform velocity, D is diameter, Ap is projected frontal area, ρ is density, and µ is viscosity.