 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-1/16c/b/solution

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

L

fluid cylinder is

F_{p} = π R^{2} [p (z_{0}) - p (z_{0} + L)] = - π R^{2} L \frac{\partial p}{\partial z} .

From part (a),

μ w^{'} (R) = \frac{R}{2} \frac{\partial p}{\partial z} .

Multiplying this wall shear stress by the lateral area

2 π R L

gives

F_{wall} = 2 π R L μ w^{'} (R) = π R^{2} L \frac{\partial p}{\partial z} .

Consequently

F_{p} + F_{wall} = 0,

which is the required steady force balance.

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