Problem $11$

Sugar is to be produced at a rate of $1,000k\frac{g}{h}$ from sugar cane that can be viewed as

made of $16\%$ sugar, $25\%$ water, and $59\%$ pulp. The process is as follows: Sugar cane

in being supplied to a mill. There are two streams exiting the mill; a waste stream

$($known as bagasse$)$ which contains $80\%$ pulp, and a product stream containing $13\%$

sugar and $14\%$ pulp. The product stream is passed through a screen. Two streams are

coming out of the screen; a solids stream containing $95\%$ pulp $($this is another waste

stream$)$ and a liquid stream containing $15\%$ sugar. The liquid stream is being supplied

to an evaporator to reduce its water content. The liquid stream coming out of the

evaporator contains sugar at $40\%$ and is being supplied to a crystallizer. Out of the

crystallizer, we get the real product stream $($sugar$)$ in pure form, and a waste stream

made of pure water. All compositions given above are in terms of weight$\%.$

Draw a flow sheet for the process described above.

Calculate the mass flow rates and compositions of all stream involved in this process.

Calculate the sugar recovery obtained with this process $($i$.$e$.,$ calculate the sugar

produced as final product per unit amount of sugar in the cane $($supplied to the system$).$