You must design a piping system to handle a sludge waste product. However, you don't know the properties of the sludge, so you test it in a cup and bob viscometer with a cup diameter of $10 \mathrm{~cm}$, a bob diameter of $9.8 \mathrm{~cm}$, and a bob length of $8 \mathrm{~cm}$. When the cup is rotated at $2 \mathrm{rpm}$, the torque on the bob is $2.4 \times 10^{4} \mathrm{dyn} \mathrm{cm}$, and at $20 \mathrm{rpm}$, it is $6.5 \times 10^{4} \mathrm{dyn} \mathrm{cm}$.

(a) If you use the power law model to describe the sludge, what are the values of the flow index and consistency?

(b) If you use the Bingham plastic model instead, what are the values of the yield stress and limiting viscosity?