 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-1/16c/a/i/solution

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

Across the two vertical faces of a control rectangle, the mass fluxes are

ρ u (y, t) δy

with opposite signs, since

u

is independent of

x

. There is no flux across the horizontal faces because the

y

-velocity is zero. The net mass flux is therefore zero, equivalently

\nabla \cdot u = \frac{\partial u}{\partial x} = 0.

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