The dimensions and measured quantities in the viscometer in Problem 34 are known to the following precision:

\[\begin{aligned}& \hline T: \pm 1 % \text { of full scale (full scale }=500,000 \text { dyn } \mathrm{cm} \text { ) } \\& \Omega: \quad \pm 1 % \text { of reading } \\& D_{\mathrm{o}}, D_{\mathrm{i}}, \text { and } L: \quad \pm 0.002 \mathrm{in} .\end{aligned}\]

Estimate the maximum percentage uncertainty in the measured viscosity of the sample for each of the three data points.

Problem 34

Your boss gives you a sample of "gunk" and asks you to measure its viscosity. You do this in a cup and bob viscometer that has an outer (cup) diameter of 2 in., an inner (bob) diameter of $1.75 \mathrm{in}$., and a bob length of $4 \mathrm{in}$. You run the viscometer at three speeds and record the following data:

Rotational Velocity, $\boldsymbol{\Omega}(\mathbf{r p m})$	Torque on Bob, $\boldsymbol{T}(\mathbf{d y n} \mathbf{~ c m})$
1	10,500
10	50,000
100	240,000

(a) How would you classify the viscous properties of this material?

(b) Calculate the viscosity of the sample in $\mathrm{cP}$.

(c) What viscosity model best represents these data, and what are the values of the viscous properties (i.e., the model parameters) for the model?