$3$A$).$ In a process producing crystalline potassium nitrate $(KN{O}_3)$ salt, $1000k\frac{g}{h}$ of a feed solution containing $20wt\%$

$KN{O}_3$ is fed to an evaporator which evaporates $Wk\frac{g}{h}$ water at $422K$ to produce a $50wt\%KN{O}_3$ solution at a mass

flow rate of $S\frac{g}{h}.$ This concentrated $($supersaturated$)KN{O}_3$ solution is then fed to a crystalliser at $311K,$ where

crystals containing $96wt\%KN{O}_3$ is removed. The resulting spent solution $(R)$ containing $37\mathrm{.}5wt\%KN{O}_3$ is recycled

to the evaporator. The flow diagram of the entire process is described in Figure $3$A below.

Calculate the mass flow rates of the evaporated water $W,$ the concentrated solution $S,$ recycle stream $R$ and the

products stream of crystals $P$ in $k\frac{g}{h}.$ State all assumptions made.