Radius sensitivity of Poiseuille-flow uncertainty

For $Q\propto a^4\Delta P/(\eta L)$ and independent small errors, ${\sigma }_Q^2/Q^2=16{\sigma }_a^2/a^2+{\sigma }_{\Delta P}^2/\Delta P^2+{\sigma }_{\eta }^2/{\eta }^2+{\sigma }_L^2/L^2$. Independent pressure errors add in quadrature before dividing by the pressure difference. Bounded worst-case errors instead add absolute derivative contributions.