A triple effect forward feed evaporator concentrates a sugar solution $100k\frac{g}{s}$ of solution containing $28$ mass $\%CuS{O}_4$ is cooled slowly to $10C$ to form

crystals of $CuS{O}_4*5H_{2}O.$ The solubility of $CuS{O}_4$ at $10C$ is $9\mathrm{.}9k\frac{g}{100}kg$ water. It is

estimated that $4\%$ of the water entering the crystallizer is lost by evaporation.

$3\mathrm{.}1.$ Draw a diagram of the crystallizer showing all streams around it and use the

yield method to calculate mass of crystals produced in the crystallizer.

Additional information: $Cu=63\mathrm{.}5\frac{g}{m}ol,H=1\frac{g}{m}ol,S=32\frac{g}{m}ol,O=16\frac{g}{m}$olfrom $8$ mass $\%$

to $35\%.$ The feed enters at $30000k\frac{g}{h}$ at $27C$ and the pressure in the vapour space

of the third effect is $16$ kPa $.$ Fresh saturated steam is available at $205$ kPa $.$ The liquid

heat capacity is given by $C_p=4\mathrm{.}19-2\mathrm{.}55(k\frac{J}{k}g.K)$ where x is the mass fraction of

sugar. It can be assumed that the BPR$\text{'}$s can be neglected. The overall heat transfer

coefficients are: $U_1=3\mathrm{.}123$;$U_2=1\mathrm{.}987$ and $U_3=1\mathrm{.}136k\frac{W}{m^2}.K.$

Do only one iteration.

$1\mathrm{.}1.$ Draw a flowsheet for this process.

$1\mathrm{.}2.$ Determine the flow rates of the vapour and liquid streams for each evaporator.

$1\mathrm{.}3.$ Calculate the Cp$\text{'}$s in each effect. List all assumptions.

$1\mathrm{.}4.$ Determine the heat balance around each evaporator.