[20 marks overall] You are to design a transfer system to feed a 70 wt. \% coal-water slurry to a boiler. However, you do not know the rheological properties of the slurry other than the fact that it is a Bingham plastic. Therefore, you decide to measure the properties using a Couette viscometer. The cup diameter is 100mm, the bob diameter is 98mm, and the length of the bob is 80mm. When the cup is rotated at 2rpm the torque is 2.4103Nm and at 20rpm the torque is 6.5103Nm. (a) [10 marks] What is the plastic viscosity and yield stress of this coal-water slurry? (b) [10 marks] The slurry is to be pumped from a large tank open to the atmosphere through a 3 -in sch. 40 steel pipe, 2000ft long, at a rate of 100gal(US)/min to a similar size holding tank also open to the atmosphere. The density of the coal and water are 2500kgm3 and 1000kgm3. Assuming the pipe is horizontal, and ignoring any losses related to flow out of or into the holding tanks, what horsepower would be required