In a sewage$-$treatment plant, a large stirred concrete tank initially contains $440000$ litres of a mixture of water and suspended solids. The amount of solids in the tank is known to be $10000kg$ fine suspended solids. To flush the solids out, water is pumped into the tank at a rate of $40000$ litres$/$h$.$ A mixture of liquid and solids leaves at the same rate of $40000$ litres$/$h$.$ Flushing with water is allowed to continue for a period of $5$ hours.

a$.$ Draw a completely labelled block flow diagram of the process. Use the symbols $m$ and $x$ for mass flow rate and mass fraction, respectively. Use subscript symbols $S$ and $W$ for suspended solids and water, respectively.

b$.$ Proceed to do all the necessary mass balance calculations, so that you can determine the concentration of suspended solids $($in $\frac{g}{L})$ in the tank after $5$ hours. Do the necessary simplifications and degrees of freedom analyses to determine where you should start, and where you should proceed after completing calculations for each subsystem if applicable. Explain what you do and show all calculations. Make sure that mass balance and other equations are clearly written down.