A human artery has a pressure drop $P_{\text{b}\text{a}\text{d}}=1\mathrm{.}5mmHg$ and a flow rate $Q=3m\frac{L}{m}in.$ A surgeon will dilate the artery, changing the radius $r_{\text{b}\text{a}\text{d}}{r}_{\text{g}\text{o}\text{o}\text{d}}.$

Model the artery as a pipe of fixed radius $r_{\text{b}\text{a}\text{d}}$~~$0\mathrm{.}25cm,$ and find the new radius $r_{\text{g}\text{o}\text{o}\text{d}}$ that is required to keep the same flow rate but with a smaller pressure drop of $P_{\text{g}\text{o}\text{o}\text{d}}=1mmHg.$