$\backslash$gamma $=0$ for $\backslash$sigma $=$ Y

$.$

$(12\mathrm{.}4)$Problem $12\mathrm{.}1$

A CaCO$3-$filled PP melt is found to obey the relationship given by Eq$.(12\mathrm{.}4),$ in

whichY is $2\mathrm{.}5\backslash$times $104$ Pa$,$ K is $4\mathrm{.}5\backslash$times $104$ Pa $$s$0\mathrm{.}5,$ and n $=0\mathrm{.}5$ at $200$C$.($a$)$ Sketch the

viscosity versus shear rate curve. $($b$)$ Sketch velocity and shear stress distributions

in a long cylindrical tube through which this material is extruded. $($c$)$ What will the

pressure drop be when this material is extruded in a long flat film die $(60$ cm wide,

$0\mathrm{.}2$ cm thick, and $10$ cm long$)$ at a volumetric flow rate of $100$ cm$3/$s at $200$C$?$