 Solution

ID: past-exam-of-the-advanced-fluid-dynamics-course-of-the-university-of-oxford/2023/2/c/solution

\frac{4 π a ^{3}}{3} (ρ - ρ) g - 6 π μ a U = 0.

Hence

U = \frac{2 a ^{2} ( ρ - ρ )}{9 μ} g, ∣ U ∣ = \frac{2 a ^{2} ∣ ρ - ρ ∣}{9 μ} ∣ g ∣.

A denser sphere falls in the direction of

g

; a lighter one rises. Equal densities give no sedimentation. The calculation assumes negligible fluid Reynolds number, an unbounded fluid, and negligible transient body acceleration after terminal settling. The fluid mass density enters through buoyancy and through the small-Reynolds number condition.

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