A straight vertical tube, $100 \mathrm{~cm}$ long and $2 \mathrm{~mm}$ ID, is attached to the bottom of a large vessel. The vessel is open to the atmosphere and contains a liquid with a density of $1 \mathrm{~g} / \mathrm{cm}^{3}$ to a depth of $20 \mathrm{~cm}$ above the bottom of the vessel.

(a) If the liquid drains through the tube at a rate of $3 \mathrm{~cm}^{3} / \mathrm{s}$, what is its viscosity?

(b) What is the largest tube diameter that can be used in this system to measure the viscosity of liquids that are at least as viscous as water, for the same liquid level in the vessel? Assume that the density is the same as water.

(c) A non-Newtonian fluid, represented by the power law model, is introduced into the vessel with the $2 \mathrm{~mm}$ diameter tube attached. If the fluid has a flow index of 0.65 , an apparent viscosity of $5 \mathrm{cP}$ at a shear rate of $10 \mathrm{~s}^{-1}$, and a density of $1.2 \mathrm{~g} / \mathrm{cm}^{3}$, how fast will it drain through the tube, if the level is $20 \mathrm{~cm}$ above the bottom of the vessel?