A paint sample is tested in a Couette (cup and bob) viscometer that has an outer radius of $5 \mathrm{~cm}$, an inner radius of $4.9 \mathrm{~cm}$, and a bob length of $10 \mathrm{~cm}$. When the outer cylinder is rotated at a speed of $4 \mathrm{rpm}$, the torque on the bob is $0.0151 \mathrm{~N} \mathrm{~m}$, and at a speed of $20 \mathrm{rpm}$, the torque is $0.0226 \mathrm{~N} \mathrm{~m}$.

(a) What are the corresponding values of shear stress and shear rate for these two data points (in cgs units)?

(b) What can you conclude about the viscous properties of the paint sample?

(c) Which of the following models could be used to describe the paint:

(i) Newtonian

(ii) Bingham plastic

(iii) Power law?

Explain why.

(d) Determine the values of the fluid properties (i.e., parameters) of the models in (c) that could be used.

(e) What would the viscosity of the paint be at a shear rate of $500 \mathrm{~s}^{-1}$ (in poise)?