a) A sphere with diameter d and density ps is released from rest and falls under the action of gravity through a fluid o

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A A Sphere With Diameter D And Density Ps Is Released From Rest And Falls Under The Action Of Gravity Through A Fluid O 1 (135.19 KiB) Viewed 12 times

a) A sphere with diameter d and density ps is released from rest and falls under the action of gravity through a fluid of density pf and viscosity u. By considering a force balance upon the sphere and assuming Stokes law for the drag force F (F = 3Tuud, where u is the velocity of the sphere) show that the velocity of the sphere at time t is given by the equation ki U = k2 (1 (1 – e-kat) where 18μ ki = Ps - Pf g, and k2 Ps = d²ps [18] b) A PVC sphere, 0.1 mm in diameter, with density 1350 kg m-?, falls from rest though oil with 850 kg m’ density and 5x10- Pa s viscosity. Calculate the terminal velocity of the sphere. Is the Stokes law applicable in this case? [12] c) Calculate the time the sphere needs to reach 99% of the terminal velocity. [5]