Solve the following Process Engineering problems using the Given, Find, Assumptions, Analysis and Conclusions sections described in the $"$GE $163$ Process Engineering Problem Solution Requirements Winter $2024"$ document found on Canvas.

Question $1($Type B$)$

A settling tank and related streams are shown in Figure $1,$ below. Dimensions in meters are given in the figure $($neglect the volume of rounded tank corners and equipment inside$).$ The width of the tank $($into the page$)$ is $2m.$ The height of the solid and liquid within the tank is $5m.$ A slurry flows into the settling tank at a rate of $0\mathrm{.}1\frac{m^3}{m}in$ with $30\%$ solids $($by volume$).$ Due to the placement of the "Clarified Water Out" stream, the overall volume of solids and liquids within the settling tank will remain constant. However, $0\mathrm{.}05\%$ percentage of input solids are remaining$/$accumulating on the bottom of the settling tank. Therefore, the tank requires periodic cleanings to remove accumulated solids. Assume that the "Clarified Water Out" and "Solids Out" are both pure streams. The tank must be cleaned of solids when the height of solids accumulated within the tank reaches a height of $1m.$ Calculate the total volume of water that can be clarified in between solids cleanings using the General Balance Equation. Give your answer to $6$ significant figures.

Slurry In

Figure $1.$ Slurry settling tank