A single effect evaporator is required to concentrate a solution from $10$ wt $\%$ solids to $30$ wt $\%$

solids at the rate of $250$ kg of feed per hour. The pressure in the evaporator is $77$ kPa absolute$,$

and the steam is available at $200$ kPa gauge pressure with the overall heat transfer coefficient

$1700$ J$/$m

$2$

s $\backslash$deg C$.$

Assume that the temperature of the feed is $18\backslash$deg C and that the boiling point of the solution under

the pressure of $77$ kPa absolute$.$ Assume, also, that the specific heat of the solution is the same

as for water, that is $4\mathrm{.}186$ x $103$

J$/$ kg $\backslash$deg C$,$ and the latent heat of vaporization of the solution is the

same as that for water under the same conditions.

$($i$)$ Draw a diagram to show the flow conditions, $[5$ marks$]$

$($ii$)$ Find the quantity of steam required and $[20$ marks$]$

$($iii$)$ The heat transfer area of the evaporator.