$(25$points$)$Powdered milk is an $$important worldwide commodity. It is $$desired to build a hopper for storage of $$non$-$fat powdered milk. The powdered milk has a flow function of fc$=0\mathrm{.}18$$1+142[$all in Pa$].$The effective angle of $$internal friction, $,$ is $50.$The angle of $$wall friction of $$the bulk solids against stainless steel is $28.$Use the attached chart to $$assist in $$your calculations. Because powdered milk can degrade with time, it is $$desired to $$use a mass flow hopper. The hopper geometry is $$conical$.$ The bulk density is $$given by $$the equation $=320(1+$$41910)0\mathrm{.}197$where is in kgm$3$and is in Pa $.$ a$3$safety factor diameter $=12$ft$=3\mathrm{.}65$m$.$