A sample of coal slurry is tested in a Couette (cup and bob) viscometer. The bob has a diameter of \($10.0\) \mathrm{~cm}$ and a length of \($8.0\) \mathrm{~cm}\($,\) and the cup has a diameter of \($10.2\) \mathrm{~cm}\($.\) When the cup is rotated at a rate of \($2\) \mathrm{rpm}\($,\) the torque on the bob is \($6.75\) \times 10^{4} \mathrm{dyn} \mathrm{cm}\($,\) and at a rate of \($50\) \mathrm{rpm}\($,\) it is \($2.44\) \times 10^{6}$ dyn \($\mathrm{cm}$.\) If the slurry follows the power law model, what are the values of the flow index and consistency coefficient? If the slurry follows the Bingham plastic model, what are the values of the yield stress and the limiting viscosity? What would the viscosity of this slurry be at a shear rate of \($500\) \mathrm{~s}^{-1}$ as predicted by each of these models? Which number would you be more likely to believe, and why?