 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-3/38c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Let

U

be the streamwise speed and

δ

the layer width. Continuity gives

v \sim U δ / x

\frac{U ^{2}}{x} \sim \frac{νU}{δ ^{2}} .

The imposed stress gives

ρ νU / δ \sim S x^{- 1/2}

. Eliminating

U

yields

δ \sim (\frac{ρ ν ^{2}}{S})^{1/3} x^{1/2},

and

U \sim (\frac{S ^{2}}{ρ ^{2} ν})^{1/3},

which is independent of

x

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