that is$,=fn().$

$7.$ A paint sample is tested in a Couette $($cup and bob$)$ viscometer that has an outer radius of $5cm,$ an inner radius of $4\mathrm{.}9cm,$ and a bob length of $10cm.$ When the outer cylinder is rotated at a speed of $4rpm,$ the torque on the bob is $0\mathrm{.}0151Nm,$ and at a speed of $20rpm,$ the torque is $0\mathrm{.}0226Nm.$

$($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$)$ tha could be used.

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