 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ib/paper-1/17d/d/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Q = \int_{0}^{h} u (y) d y = \frac{ρ g h ^{3}}{12 μ} \frac{4 + kh / μ}{1 + kh / μ} .

Therefore

Q ⟶ \frac{ρ g h ^{3}}{3 μ} (k \to 0), Q ⟶ \frac{ρ g h ^{3}}{12 μ} (k \to \infty) .

The first is the stress-free film; the second has an effectively immobilized free surface.

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