Past exam of the soft condensed matter course of the University of Cambridge / 2015 / Paper 1 / 1 / c / Solution

The independent fluid-mechanical relation iswhere $\rho$ is fluid mass density, $\eta$ dynamic viscosity and $\nu$ kinematic viscosity. For a generic rigid sphere, the convention must specify whether $L$ is its diameter or radius; their Reynolds numbers differ by a factor of two. The ratio compares advective inertia $\rho U^2/L$ with viscous stress gradients $\eta U/L^2$. Small Reynolds number supports a creeping-flow approximation when unsteady fluid inertia is also negligible. No organism-specific size, speed or propulsion calculation is made here.