Question $6-$ Scaled$-$Up Process $(15\%)$

For a polymeric product, if the molten polymer may be described by the power law model with a flow index $($n$)$ of $0\mathrm{.}5.$ 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.

In the production, the molten polymer flows in a pipe with the length of $L=12$ meter at an average velocity of $V=26\mathrm{.}6c\frac{m}{m}in.$

q$.$ 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? $)$