$(10$ pts$)$ An extruder has a length to diameter ratio of $26.$ The flight angle, $A,$ on the screw is $15$ degrees while the pitch of the screw is $4\mathrm{.}2$ in $,$ and the channel depth, dc$,$ is $0\mathrm{.}15$ in $.$ The barrel heats the polypropylene melt to $500F,$ which provides a melt viscosity of $0\mathrm{.}0025$ lb $\frac{s}{i}{n}^2.$ In operation the screw rotates at $50re\frac{v}{m}in$ and a volume flow rate of $3\mathrm{.}5i\frac{n^3}{sec}$ at the end of the barrel is generated. What is the head pressure generated by the die end?