1.3 Intermittent flow is experienced from a cylindrical silo with a hopper that is more than ten years old. You have been employed as a new graduate and are asked to investigate the problem and make recommendations for improvement. You checked the design criteria by remeasuring the powder properties and the powder-wall friction. The powder properties are found to be unchanged, but you discover that the hopper wall has become heavily scored as reflected by the change in the angle of wall friction. Based on your analysis, you recommend some modifications to the hopper which will result in significant improvements. Use the information and data you collected as summarised below, and perform all the necessary calculations to answer the following questions: a) What caused the problem with the hopper that you found in your investigation? b) Was the original design of the hopper when new correct? c) What are your recommended modifications regarding the hopper angle and/or outlet diameter? d) What are the rates of discharge (i) when new, (ii) before, and (iii) after the modifications? Data: Current design: Hopper half angle (0) = 30; Outlet diameter =0.55 m Powder characteristics: Bulk density = 1800 kg/m; Mean particle diameter = 5 mm Angle of internal friction (8) = 50 Powder Flow Function data from shear cell tests: Oy = 0.44 0c +1.44 Where both the yield stress (Oy) and consolidating stress (Oc) are in units of kPa. Kinematic angle of wall friction test data: when new: Wall normal stress 2.00 4.00 8.00 (Ow, kPa) (tw, kPa) Wall shear stress 0.35 0.71 1.41 current condition: 2.00 4.00 8.00 Wall normal stress Wall shear stress (Ow, kPa) (tw, kPa) 0.81 1.61 3.23