Question $7-$ Process Scale$-$Up $(15$ points$)$

In spinning, a molten polymer is transported through a pipe @ $128k\frac{g}{h}r$ to the spinning machine. The pipe's diameter is $10$ centimeters and length is $12$ meters. The molten polymer may be described by the power law model with a flow index of $0\mathrm{.}5.$ Its density is $1\mathrm{.}04\frac{g}{c}{m}^3.$ At temperatures above the melting point, the polymer will degrade. If more than $1\%$ polymer stay in the pipe for at least $100$min, the polymer quality will not be acceptable due to degradation.

Use the chart below,

a$.$ Estimate the fraction of the polymer that stays in the pipe for more than $100$ minutes and the average residence time of this fraction in the pipe $(10\%)$

b$.$ Does the polymer survive the flow conditions? $(5\%)$