Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 39D / v

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- Solution v

Solution

Integrating the traction over the sphere gives

F = \int_{r = a} σ \cdot n d S = - \frac{3 μ}{2 a} U (4 π a^{2}) .

Hence the force exerted by the fluid on the sphere is

F = - 6 π μ a U .

This is Stokes' drag law; the sign is opposite to the sphere's velocity.

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