An MSMPR-type crystallizer is to be designed to produce 2,000 lb/h of crystals of the heptahydrate of magnesium sulfate with a predominant crystal size of 35 mesh. The magma will be 15 vol% crystals. The temperature in the crystallizer will be 50°C and the residence time 2 h. The densities of the crystals and mother liquor are 1.68 and 1.32 g/cm³, respectively. Determine: 

(a) The exiting flow rates in ft³/h of crystals, mother liquor, and magma; 

(b) The crystallizer volume in gallons, if the vapor space equals the magma space; 

(c) The approximate dimensions in feet of the crystallizer, if the body is cylindrical with a height equal to twice the diameter; 

(d) The required crystal growth rate in ft/h;
(e) The necessary nucleation rate in nuclei/h-ft³ of mother liquor in the crystallizer; 

(f) The number of crystals produced per hour; 

(g) A screen analysis table covering a U.S. mesh range of 3-1/2 to 200, giving the predicted % cumulative and % differential screen analyses of the product crystals; 

(h) Plots of the screen analyses predicted in part (g).