Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 2 / 37A / b / iii

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- Solution iii

Solution

The rate at which the upper and lower boundaries do work on the fluid, per unit area, is

W = τ U_{-} - τ U_{+} = τ (U_{-} - U_{+}) .

The definition of

τ

gives

W = τ^{2} (\frac{d _{+}}{μ _{+}} + \frac{d _{-}}{μ _{-}}) = D,

which is the required mechanical-energy balance.

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