The viscosity of a fluid sample is measured in a cup and bob viscometer. The bob is

Question:

The viscosity of a fluid sample is measured in a cup and bob viscometer. The bob is $15 \mathrm{~cm}$ long with a diameter of $9.8 \mathrm{~cm}$, and the cup has a diameter of $10 \mathrm{~cm}$. The cup rotates, and the torque is measured on the bob. The following data were obtained:

$\Omega(\mathrm{rpm})$	2	4	10	20	40
$T($ dyn cm)	$3.6 \times 10^{5}$	$3.8 \times 10^{5}$	$4.4 \times 10^{5}$	$5.4 \times 10^{5}$	$7.4 \times 10^{5}$

(a) Determine the viscosity of the sample.

(b) What viscosity model equation would be the most appropriate for describing the viscosity of this sample? Convert the data to corresponding values of viscosity versus shear rate, and plot them on appropriate axes consistent with the data and your equation. Use linear regression analysis in a form that is consistent with the plot to determine the values of each of the parameters in your equation.