You measure the viscosity of a sludge in the lab and conclude that it can be described as a power law fluid with a flow index of 0.45 , a viscosity of 7 poise at a shear rate of $1 \mathrm{~s}^{-1}$, and a density of $1.2 \mathrm{~g} / \mathrm{cm}^{3}$.

(a) What horsepower would be required to pump the sludge through a 3 in. sch 40 pipeline, $1000 \mathrm{ft}$ long, at a rate of $100 \mathrm{gpm}$ ?

(b) The viscosity data show that the sludge could also be described by the Bingham plastic model, with a viscosity of 7 poise at a shear rate of $1 \mathrm{~s}^{-1}$ and a viscosity of 0.354 poise at a shear rate of $100 \mathrm{~s}^{-1}$. Using this model, what required horsepower would you predict for this pipeline?

(c) Which answer do you think would be the most reliable and why?