4. a) A sphere with diameter d and density p, is released from rest and falls under the action of gravity through a flui

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4 A A Sphere With Diameter D And Density P Is Released From Rest And Falls Under The Action Of Gravity Through A Flui 1 (472.31 KiB) Viewed 9 times

4. a) A sphere with diameter d and density p, is released from rest and falls under the action of gravity through a fluid of density p, and viscosity μ. By considering a force balance upon the sphere, and assuming Stokes law for the drag force F: F = 3 raud where u is the velocity of the sphere, show that the velocity of the sphere at time is given by the equation: k₁ U= ·(1 - e-k₂²) where the parameters k, and k₂ are equal to: Ps-Prg 18μ k₁ and k₂= d²ps Ps [8] b) A PVC sphere, 0.1 mm in diameter, with density 1350 kg m³, falls from rest through oil with 800 kg m³ density and 2x 10³ Pa s viscosity. Calculate the terminal velocity of the sphere. Is the Stokes law applicable in this case? [8] c) For the problem described in part b), calculate the time the sphere needs to reach 99% of the terminal velocity. [4] =