You have a sample of a sediment that is non-Newtonian. You measure its viscosity in a cup and bob viscometer having a cup radius of $3.0 \mathrm{~cm}$, a bob radius of $2.5 \mathrm{~cm}$, and a length of $5 \mathrm{~cm}$. At a rotational speed of $10 \mathrm{rpm}$, the torque transmitted to the bob is $700 \mathrm{dyn} \mathrm{cm}$, and at $100 \mathrm{rpm}$, the torque is 2500 dyn $\mathrm{cm}$.

(a) What is the viscosity of the sample?

(b) Determine the values of the model parameters that represent the sediment viscous properties if it is represented by (i) the power law model or (ii) the Bingham plastic model.

(c) What would the flow rate of the sediment be (in $\mathrm{cm}^{3} / \mathrm{s}$ ) in a $2 \mathrm{~cm}$ diameter tube, $50 \mathrm{~m}$ long, that is subjected to a differential pressure driving force of 25 psi assuming that (i) the power law model and (ii) the Bingham plastic model apply?

Which of these two answers do you think is best, and why?