Question $5(20$ pts$).$ An evaporator and a crystallizer are used to crystallize $10000k\frac{g}{h}r20$ wt$.\%KN{O}_3$ solution $($F$).$ The evaporator works at $300F$ and the amount of pure water it evaporates every hour is shown with $W.$ The $KN{O}_3$ solution which exits evaporator contains $50$ wt$.\%KN{O}_3$ and its flowrate is shown with $M.$ This solution enters the crystallizer unit and the flowrate of produced $KN{O}_3$ crystals in this unit which also contain water is shown with $C$ and they contain $4$ wt$.\%$ water and balance $KN{O}_3.$ The recycle stream $($R$)$ from crystallizer unit to evaporator, is a saturated solution at $100F$ with a ratio of $0\mathrm{.}6kgKN\frac{O_3}{k}g$ water.

a$)$ Draw and label the flowchart of the process and perform degrees of freedom analyses.

b$)$ Calculate the quantity of recycle stream in $k\frac{g}{h}r.$