Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 334 / 1 / c / ii

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- Solution ii

Solution

Each daughter has the planar Poiseuille relation

Q_{i} = \frac{2 h ^{3}}{3 μ} G_{i}, G_{i} = - \frac{d p _{i}}{d x} .

Hence

G_{i} = \frac{3 μ Q _{i}}{2 h ^{3}} = O (\frac{μ Q _{i}}{h ^{3}}) .

The higher-flow daughter therefore requires the larger pressure-gradient magnitude:

Q_{2} > Q_{1} ⟹ G_{2} > G_{1} .

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