Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 1 / 16C / a / i

Table of contents
- Solution i

Solution

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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