The same suspension as that in Problem 39 above was subsequently tested in a $28 \mathrm{~mm}$ internal diameter pipe, and the following data reported:

$\Gamma\left(\mathrm{s}^{-1}\right)$	127	200	289	406	557	744	951	1079	1409	1610
$\tau_{w}(\mathrm{~Pa})$	31	32.8	33.6	34.2	36.4	37.8	40.0	43.4	66.0	79.25

Obtain the true shear stress, shear rate, and viscosity for this material using this information. Is this consistent with the results obtained in Problem 39? If not, give possible reasons.

Problem 39

A kaolin-in-water suspension was tested in a $13 \mathrm{~mm}$ internal diameter horizontal tube, and the following data were reported:

$\Gamma\left(\mathrm{s}^{-1}\right)$	660	803	978	1208	1518	1790	2081	2300	2629	2988
$\tau_{w}(\mathrm{~Pa})$	37.7	38.4	40.1	41.7	43.3	44.8	46.7	48.2	62.7	73.6

Obtain the true shear stress, shear rate, and viscosity for this suspension. Does this suspension exhibit a yield stress? Fit a suitable viscosity model to approximate the rheology of this suspension.