$13\mathrm{.}11($USCS units$)$ An extruder has a barrel diameter $=5\mathrm{.}0$ in and length $=12ft.$ The extruder screw rotates at $50re\frac{v}{m}in$; it has channel depth $=0\mathrm{.}30$ in and flight angle $=17\mathrm{.}7.$ The plastic melt has a shear viscosity $=100({10}^{-4})lb-s\frac{ec}{i{n}^2}.$ Find $($a$)$ the extruder characteristic, $($b$)$ the values of $Q$ and $p$ at the operating point if the die characteristic is $Q_x=0\mathrm{.}00150p.$