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 s1 , and a density of...

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 s1 , and a density of 1.2 g/cm3 .

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

(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 s1 and a viscosity of 0.354 poise at a shear rate of 100 s1 . Using this model, what required horsepower would you predict for the above pipeline?

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