 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-1/16d/i/solution

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

The speeds are

U = q / A

upstream and

v = q / (2 a)

in either daughter vessel. Bernoulli therefore gives

p_{up} - p_{down} = \frac{ρ}{2} (v^{2} - U^{2}) = \frac{ρ q ^{2}}{2} (\frac{1}{4 a ^{2}} - \frac{1}{A ^{2}}) .

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