= Solution
Assume steady fully developed laminar flow of a <Newtonian fluid> in a long circular tube, with no slip at a rigid wall. The <Hagen-Poiseuille equation> gives the volume flow rate
$$
Q=\frac{\pi R^4\Delta p}{8\eta\ell},
$$
where $R$ is the lumen radius, $\ell$ the tube length, $\eta$ the <dynamic viscosity> and $\Delta p$ the pressure drop. If $\Delta p$, $\ell$ and $\eta$ remain fixed, then
$$
\frac{Q_{\mathrm{new}}}{Q_{\mathrm{old}}}=\left(\frac{R_{\mathrm{new}}}{R_{\mathrm{old}}}\right)^4.
$$
Thus doubling the flow requires
$$
\boxed{R_{\mathrm{new}}=2^{1/4}R_{\mathrm{old}}\simeq1.189R_{\mathrm{old}},\qquad
\frac{\Delta R}{R_{\mathrm{old}}}\simeq18.9\%}.
$$
This estimate neglects pulsation, arterial compliance, entrance losses, the detailed shape of a stenosis and changes in the rest of the circulatory resistance. It treats <blood> as a homogeneous <Newtonian fluid> and assumes that enlarging the artery does not change its applied pressure drop. These assumptions supply the intended fourth-power scaling; an actual circulation need not keep that pressure drop fixed.
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