 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/ii/paper-1/37a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

The steady rectilinear equation is

u^{''} (y) = - G

, with no-slip conditions

u (0) = 0

and

u (a) = U

. Two integrations give the Couette-Poiseuille flow

u (y) = [\frac{U y}{a} + \frac{G}{2} y (a - y)] x, v = w = 0.

The first term is driven by the moving wall and the second by the specified pressure gradient.

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