 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-3/16a/c/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 3 / 16A / c / Solution by

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

When

Δ ≪ 1

, the small-argument expansion

sinh z = z + O (z^{3})

gives

f (y) = \frac{( 1 + i ) Δ y + O ( Δ ^{3} )}{( 1 + i ) Δ + O ( Δ ^{3} )} = y + O (Δ^{2}) .

(1)

Therefore

u (y, t) ≃ \frac{U _{0} y}{L _{0}} cos ω t .

(2)

The viscous diffusion time

L_{0}^{2} / ν

is then short compared with the oscillation period. Viscosity communicates the wall motion across the entire layer almost instantaneously, producing the linear profile of quasi-steady Couette flow.

 Read the full article

 New to topics? Read the docs here!