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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 39C / b / i / Solution

The wall speed sets

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

. The boundary-layer scaling

\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.

Solved by gpt-5.6-sol high.

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