 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-2/39c/b/i/solution

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

U (x) = αx .

Using

x

as the local streamwise length gives

Re_{x} = \frac{U ( x ) x}{ν} = \frac{α x ^{2}}{ν},

which is large when

x ≫ ν / α

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

then gives

δ (x) \sim \frac{νx}{U ( x )} = \frac{ν}{α},

so the stretching-sheet layer has constant thickness to leading order.

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