Problem 3 A cylindrical tower being filled with catalyst pellets via a conveyor belt at the rate of 150 Ib/min. The tower is 75 ft tall with diameter 22 A. Because of the porous nature of the packed pellets, the effective (bulk) density of the pile of pellets at any given point of the bed depends on the amount of the pellets above it. The bulk density at height h above the bottom of the tower is p(h) = a + b(Hy-h). 4 = 0.62 lb/. b =0,0030 lb/ft where Hy is the the total height of pellets in the tower. a) Calculate the mass of pellets in the tower in lb when the tower is full. b) Calculate how long it will take to fill the tower c) Make a plot of the height of pellets in the tower in ft as a function of time in hr. HINT: When the tower is filled up to height Hr. the mass of pellets in a thin slice of thickness dh at height he above the bottom of the tower is dm = Atph)dh = Ar (a + b(Hy - A)) dh where Ay is the cross sectional arca of the tower. "To find the total mass in the tower integrate from h = 0 to h = Hr. 1 HN d22